diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/AXg5j9SsgvI.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/AXg5j9SsgvI.srt
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@@ -0,0 +1,571 @@
+1
+00:00:00,000 --> 00:00:03,860
+السلام عليكم ورحمة الله وبركاته إن شاء الله رب
+
+2
+00:00:03,860 --> 00:00:07,520
+العالمين اليوم هنتكلم عن الـ life span development
+
+3
+00:00:07,520 --> 00:00:13,840
+خلال دراستنا للـ life span development هنتعرف على
+
+4
+00:00:13,840 --> 00:00:18,040
+الـ field of the study that examine the pattern of
+
+5
+00:00:18,040 --> 00:00:22,700
+growth, change and stability in behavior that occur
+
+6
+00:00:22,700 --> 00:00:27,320
+throughout the entire human life span هندرس
+
+7
+00:00:27,320 --> 00:00:32,220
+التغيرات اللي بتصير على عملية النمو والثبات اللي
+
+8
+00:00:32,220 --> 00:00:37,060
+بيكون في عملية النمو خلال فترة الحياة كلها entire
+
+9
+00:00:37,060 --> 00:00:42,780
+human life span Life span development theory
+
+10
+00:00:42,780 --> 00:00:47,200
+provides a framework for understanding human aging
+
+11
+00:00:47,200 --> 00:00:51,220
+هنتعرف على عملية الـ human aging والـ development
+
+12
+00:00:51,220 --> 00:00:57,540
+for human aging من خلال نظرية الـ life span
+
+13
+00:00:57,540 --> 00:01:05,480
+development الهدف الرئيسي للتهيئة في دراسة الهجوم 
+
+14
+00:01:05,480 --> 00:01:10,980
+هو أن يقدموا مجلد لتفسير وشرح التغيير المستمر
+
+15
+00:01:10,980 --> 00:01:18,720
+اللذي يحدث مع الوقت، الإنسان الممثل يعيش تحت حالة
+
+16
+00:01:18,720 --> 00:01:25,740
+ممثلة خلال دراستنا نتعرف على الهدف الرئيسي الهدف
+
+17
+00:01:25,740 --> 00:01:31,140
+الرئيسي للتغيير في دراسة الهجوم في دراسة الهجوم
+
+18
+00:01:31,140 --> 00:01:35,220
+وبنعرف أنها تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+19
+00:01:35,220 --> 00:01:37,780
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+20
+00:01:37,780 --> 00:01:39,580
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+21
+00:01:39,580 --> 00:01:40,900
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+22
+00:01:40,900 --> 00:01:40,920
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+23
+00:01:40,920 --> 00:01:44,270
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقد importance
+
+24
+00:01:44,270 --> 00:01:48,530
+of studying lifespan development بدنا نعرف شو
+
+25
+00:01:48,530 --> 00:01:50,970
+أهمية دراسة الـ life span development
+
+26
+00:01:50,970 --> 00:01:56,810
+responsibility for children is or will be a part
+
+27
+00:01:56,810 --> 00:02:04,150
+of our everyday lives احنا بنعرف أن عملية المسئولية
+
+28
+00:02:04,150 --> 00:02:08,570
+والرعاية على الأطفال هي مسئوليتنا احنا وجزء من
+
+29
+00:02:08,570 --> 00:02:13,570
+مهامنا اليومية كبشر وكعائلات و كـ physiotherapist
+
+30
+00:02:13,570 --> 00:02:19,110
+كمان ممكن أن نتعامل مع الأطفال the more we were
+
+31
+00:02:19,110 --> 00:02:23,950
+learn about children the more we can better deal
+
+32
+00:02:23,950 --> 00:02:27,670
+with them and assist them in becoming competent
+
+33
+00:02:27,670 --> 00:02:33,970
+human being كل ما عرفنا أكثر عن الأطفال وعن مراحل
+
+34
+00:02:33,970 --> 00:02:39,590
+نموهم كل ما كان تعاملنا معهم بشكل أفضل وكل ما كان
+
+35
+00:02:39,590 --> 00:02:45,290
+المساعد اللي احنا بنقدمها إليهم بشكل أفضل بكثير
+
+36
+00:02:47,130 --> 00:02:51,150
+Lifespan development give us insight about our
+
+37
+00:02:51,150 --> 00:02:57,770
+development as adult as well كمان دراسة الـ life
+
+38
+00:02:57,770 --> 00:03:03,630
+span development بتعطينا نظرة عن الـ development و
+
+39
+00:03:03,630 --> 00:03:07,090
+طبيعة الـ development اللي بتصير معانا as a human
+
+40
+00:03:07,090 --> 00:03:10,870
+being و adult human being، not the gene، شو اللي
+
+41
+00:03:10,870 --> 00:03:15,940
+بتصير معانا في عملية أنّه مو التطور to examine the
+
+42
+00:03:15,940 --> 00:03:21,240
+point in the time when life begin until time when
+
+43
+00:03:21,240 --> 00:03:26,680
+it ends at least life as we know it كمان بيعطينا
+
+44
+00:03:26,680 --> 00:03:34,180
+القدرة على أن احنا نتعرف على نقطة بداية الحياة و
+
+45
+00:03:34,180 --> 00:03:38,560
+نقطة نهاية الحياة على الأقل كما هو ظاهر من يوم
+
+46
+00:03:38,560 --> 00:03:43,200
+الولادة لحد الوفاة in thinking about the importance
+
+47
+00:03:43,200 --> 00:03:48,820
+of studying lifespan development consider the
+
+48
+00:03:48,820 --> 00:03:53,120
+following research findings خلال دراستنا للـ life
+
+49
+00:03:53,120 --> 00:03:59,400
+span development هنتعرف على بعض الدراسات ونتائج
+
+50
+00:03:59,400 --> 00:04:06,680
+بعض الدراسات إحدى الدراسات اللي صارت في 2001 بتقول
+
+51
+00:04:06,680 --> 00:04:10,840
+أن عملية الـ massage therapy Facilitate the growth
+
+52
+00:04:10,840 --> 00:04:15,300
+and improve the immune system functioning of
+
+53
+00:04:15,300 --> 00:04:21,680
+preterm infants يعني لو احنا على سبيل المثال بدأنا
+
+54
+00:04:21,680 --> 00:04:31,230
+نشتغل مساج لطفل مولود جديد ومولود جاب الموعد ممكن
+
+55
+00:04:31,230 --> 00:04:36,710
+شهور سبع شهور يكون ثمان شهور عملية المساج على هذول
+
+56
+00:04:36,710 --> 00:04:42,830
+الأطفال بتحسن من عملية أو من وظيفة الجهاز المناعي
+
+57
+00:04:42,830 --> 00:04:49,630
+وبتسرع في عملية نمو الجسدي أو الحركة عند هذول
+
+58
+00:04:49,630 --> 00:04:56,040
+الأطفال Secure attachment to parents in adolescence
+
+59
+00:04:56,040 --> 00:04:59,620
+is linked with a host of positive outcome for
+
+60
+00:04:59,620 --> 00:05:03,500
+adolescents such as positive peer relation and
+
+61
+00:05:03,500 --> 00:05:08,250
+emotional well-being كمان من خلال دراستنا النمو و
+
+62
+00:05:08,250 --> 00:05:12,690
+التطور كثير من الدراسات بتقول أنّه إذا كانت العلاقة
+
+63
+00:05:12,690 --> 00:05:17,070
+ما بين الأبوين في مرحلة والمراهقة أو الطفل في
+
+64
+00:05:17,070 --> 00:05:21,990
+مرحلة المراهقة هيكون إليها جانب إيجابي على عملية
+
+65
+00:05:21,990 --> 00:05:28,090
+النمو وعملية الـ emotional والـ being عند هذا
+
+66
+00:05:28,090 --> 00:05:28,690
+الإنسان
+
+67
+00:05:42,460 --> 00:05:47,400
+بالطبع هذه الدراسة كمان بتقول أن احنا كل ما كان
+
+68
+00:05:47,400 --> 00:05:52,080
+عندنا القدرة على زيادة الحياة أو زيادة عمر الخلية
+
+69
+00:05:52,080 --> 00:05:56,880
+في خلايا الاختبار هيكون عندنا في المستقبل أو ممكن
+
+70
+00:05:56,880 --> 00:06:02,810
+يصير في المستقبل شغلات اتحسنت من مستوى الحياة، اتزود
+
+71
+00:06:02,810 --> 00:06:06,570
+من فترة حياة الإنسان The historical perspective,
+
+72
+00:06:06,730 --> 00:06:10,990
+traditional and lifespan approach it التجارب
+
+73
+00:06:10,990 --> 00:06:13,050
+التقليدية التجريبية التجريبية التجريبية التجريبية
+
+74
+00:06:13,050 --> 00:06:13,370
+التجريبية التجريبية التجريبية التجريبية التجريبية
+
+75
+00:06:13,370 --> 00:06:15,890
+التجريبية التجريبية التجريبية التجريبية التجريبية
+
+76
+00:06:15,890 --> 00:06:19,550
+التجريبية التجريبية التجريبية التجريبية التجريبية
+
+77
+00:06:19,550 --> 00:06:25,530
+التجريبية التجريبية التجريبية التجريبية التجريبية
+
+78
+00:06:25,530 --> 00:06:28,330
+التجريبية التجريبية التجريبية التجريبية التجريبية
+
+79
+00:06:28,330 --> 00:06:29,150
+التجريبية التجريبية التجريبية التجريبية التجريبية
+
+80
+00:06:29,150 --> 00:06:34,930
+التجريبية التجريبية التجريبية التجارب التعريف
+
+81
+00:06:34,930 --> 00:06:41,390
+التقليدي والقديم كان بيركز على مرحلة الـ
+
+82
+00:06:41,390 --> 00:06:46,390
+development عند الأطفال من الولادة لحد ما يصلوا
+
+83
+00:06:46,390 --> 00:06:51,130
+مرحلة الـ blue وأحيانا بيعطي شيء من الانتباه
+
+84
+00:06:51,130 --> 00:06:56,270
+لمرحلة الـ adult hood الـ blue أو ما بيعطيهاش أي
+
+85
+00:06:56,270 --> 00:07:01,590
+اهتمام وبيقل اهتمام في هذه الدراسة كل ما زاد عمر
+
+86
+00:07:01,590 --> 00:07:05,720
+الإنسان يعني بالمختصر أن هذه الـ traditional
+
+87
+00:07:05,720 --> 00:07:10,140
+approach بتركز على دراسة التغيرات اللي بتصير عند
+
+88
+00:07:10,140 --> 00:07:14,660
+الأطفال من ساعة الولادة لحد ما يصير عمره أو ما
+
+89
+00:07:14,660 --> 00:07:19,880
+يصل مرحلة المراهقة وبعد هيك بتقل فترة الاهتمام
+
+90
+00:07:19,880 --> 00:07:23,460
+بالتغيرات اللي بتصير عند الإنسان سواء كان في مرحلة
+
+91
+00:07:23,460 --> 00:07:28,840
+البلوغ أو في مرحلة الشيخوخة الطفولة خصوصًا تعتبر
+
+92
+00:07:28,840 --> 00:07:34,760
+مرحلة تغيير كبير في التجارب التقليدية مرحلة
+
+93
+00:07:34,760 --> 00:07:40,140
+الطفولة لها الاهتمام الأكبر خلال دراستنا لعملية
+
+94
+00:07:40,140 --> 00:07:44,860
+النمو وتطور من خلال التجارب التقليدية in contrast,
+
+95
+00:07:45,220 --> 00:07:49,220
+the lifespan approach emphasizes developmental
+
+96
+00:07:49,220 --> 00:07:53,220
+changes during adulthood as well as its childhood
+
+97
+00:07:54,300 --> 00:07:59,300
+في المقابل هتلاقي أن الـ life span approach بركز
+
+98
+00:07:59,300 --> 00:08:04,200
+على عمليات التغير والـ stability والثبات اللي بتكون
+
+99
+00:08:04,200 --> 00:08:09,280
+during developmental change أو during development
+
+100
+00:08:09,280 --> 00:08:16,920
+from adulthood as well as childhood هيركز على
+
+101
+00:08:16,920 --> 00:08:23,490
+التغيرات اللي بتصير أثناء عملية النمو والتغير عند
+
+102
+00:08:23,490 --> 00:08:29,630
+الأطفال مثل ما هو عند الكبار Characteristics of
+
+103
+00:08:29,630 --> 00:08:34,350
+Lifespan Perspective Baldist View هندرس من خلاله
+
+104
+00:08:34,350 --> 00:08:39,950
+إن شاء الله رب العالمين خصائص النمو والتطور من
+
+105
+00:08:39,950 --> 00:08:45,690
+خلال دراستنا أو من منظور نظرية الـ life span
+
+106
+00:08:45,690 --> 00:08:50,060
+development وحنجلها لشخص بيسموه الـ بالتس if you
+
+107
+00:08:50,060 --> 00:08:56,140
+من منظور بالتس the lifespan perspective involves that
+
+108
+00:08:56,140 --> 00:09:00,600
+أو involve these basic contents development is
+
+109
+00:09:00,600 --> 00:09:05,880
+lifelong multidimensional multidirectional plastic
+
+110
+00:09:05,880 --> 00:09:11,020
+contextual multidisciplinary and involve a growth
+
+111
+00:09:11,020 --> 00:09:17,400
+maintenance and regulation إذا خلال دراستنا لـ
+
+112
+00:09:17,400 --> 00:09:22,320
+characteristics of lifespan development من منظور
+
+113
+00:09:22,320 --> 00:09:27,360
+بالتس هلاجي أن احنا هندرس الـ development على مدى
+
+114
+00:09:27,360 --> 00:09:31,680
+الحياة هلاجي أن احنا في عملية الدراسة نبدأ فيها
+
+115
+00:09:31,680 --> 00:09:36,380
+lifelong طول الحياة multidimensional و
+
+116
+00:09:36,380 --> 00:09:42,350
+multidirectional متعددة الأبعاد ومتعددة الجهات حاب
+
+117
+00:09:42,350 --> 00:09:48,030
+نعرف أن عملية الـ development متغيرة، plastic،
+
+118
+00:09:48,030 --> 00:09:51,470
+change، شو اللي بيصير فيها، contextual، المحتوى
+
+119
+00:09:51,470 --> 00:09:56,410
+تبعها، multidisciplinary، متعددة التخصصات، و
+
+120
+00:09:56,410 --> 00:10:01,190
+involves growth, maintenance and regulation، تشمل
+
+121
+00:10:01,190 --> 00:10:06,450
+الزيادة، الـ maintenance، الثبات أو البقاء، وعملية
+
+122
+00:10:06,450 --> 00:10:12,530
+التنظيم Some contemporary concerns
+
+123
+00:10:12,530 --> 00:10:17,470
+development and wellbeing of children and adults
+
+124
+00:10:27,970 --> 00:10:33,710
+اليوم، التطور والحياة للأطفال والشباب يمكّنهم من
+
+125
+00:10:33,710 --> 00:10:41,290
+الحصول على أهداف المجتمع والمعرفة والأساسيين اليوم
+
+126
+00:10:41,290 --> 00:10:47,290
+هنلاقي أن عملية التطور و الاهتمام بال development و
+
+127
+00:10:47,290 --> 00:10:53,210
+الـ well-being للأطفال و للكبار صارت محطة اهتمام 
+
+128
+00:10:53,210 --> 00:10:59,330
+العامة، عامة الناس بشكل عام، الـ scientists العلماء و
+
+129
+00:10:59,330 --> 00:11:05,370
+كمان صانعي السياسات أو الحكومات اللي بتكون موجودة
+
+130
+00:11:05,370 --> 00:11:10,720
+في هذا البلد، among the important contemporary
+
+131
+00:11:10,720 --> 00:11:16,560
+concerns are
+
+132
+00:11:16,560 --> 00:11:22,360
+family issues, parenting, education, socio-cultural
+
+133
+00:11:22,360 --> 00:11:30,280
+context and social policy خلال الدراسة لعملية ال
+
+134
+00:11:30,280 --> 00:11:37,130
+life span development هنلاقي إنه فيه تركيز على ال
+
+135
+00:11:37,130 --> 00:11:43,450
+family issues، شغلات أو الأمور اللي بتتعلق بالعائلة
+
+136
+00:11:43,450 --> 00:11:48,190
+إزاي الـ parenting الأبوة و دورها في عملية ال
+
+137
+00:11:48,190 --> 00:11:52,510
+development، الـ education التعليم و دوره في عملية ال
+
+138
+00:11:52,510 --> 00:11:56,510
+development، الـ social cultural context المحتوى 
+
+139
+00:11:56,510 --> 00:12:02,210
+الاجتماعي و الثقافي and social policy والسياسات
+
+140
+00:12:02,210 --> 00:12:06,350
+الاجتماعية اللي موجودة، three important socio
+
+141
+00:12:06,350 --> 00:12:11,210
+-cultural contexts are culture, ethnicity and
+
+142
+00:12:11,210 --> 00:12:17,290
+gender، تلت شغلات مهمة جدا لدراستنا و لدراسة عملية
+
+143
+00:12:17,290 --> 00:12:18,830
+النمو و التطور 
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/AXg5j9SsgvI_raw.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/AXg5j9SsgvI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..113de46722c2772509c5f5fcf9e50e04ba957b10
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/AXg5j9SsgvI_raw.srt
@@ -0,0 +1,576 @@
+1
+00:00:00,000 --> 00:00:03,860
+السلام عليكم ورحمة الله وبركاته ان شاء الله رب
+
+2
+00:00:03,860 --> 00:00:07,520
+العالمين اليوم هنتكلم عن ال life span development
+
+3
+00:00:07,520 --> 00:00:13,840
+خلال دراستنا لل life span development هنتعرف على
+
+4
+00:00:13,840 --> 00:00:18,040
+ال field of the study that examine the pattern of
+
+5
+00:00:18,040 --> 00:00:22,700
+growth, change and stabilityin behavior that occur
+
+6
+00:00:22,700 --> 00:00:27,320
+throughout the entire human life span هندرس
+
+7
+00:00:27,320 --> 00:00:32,220
+التغيرات اللي بتصير على عملية النمو و الثبات اللي
+
+8
+00:00:32,220 --> 00:00:37,060
+بيكون في عملية النمو خلال فترة الحياة كلها entire
+
+9
+00:00:37,060 --> 00:00:42,780
+human life spanLife span development theory
+
+10
+00:00:42,780 --> 00:00:47,200
+provides a framework for understanding human aging
+
+11
+00:00:47,200 --> 00:00:51,220
+هنتعرف على عملية ال human aging و ال development
+
+12
+00:00:51,220 --> 00:00:57,540
+for human aging من خلال نظرية ال life span
+
+13
+00:00:57,540 --> 00:01:05,480
+developmentالهدف الرئيسي للتهيأة في دراسة الهجوم
+
+14
+00:01:05,480 --> 00:01:10,980
+هو أن يقدموا مجلد لتفسير و تشرح التغيير المستمر
+
+15
+00:01:10,980 --> 00:01:18,720
+اللذي يحدث مع الوقت، الانسان الممثل يعيش تحت حالة
+
+16
+00:01:18,720 --> 00:01:25,740
+ممثلةخلال دراستنا نتعرف على الهدف الرئيسي الهدف
+
+17
+00:01:25,740 --> 00:01:31,140
+الرئيسي للتغيير في دراسة الهجوم في دراسة الهجوم
+
+18
+00:01:31,140 --> 00:01:35,220
+وبنعرف أنها تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+19
+00:01:35,220 --> 00:01:37,780
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+20
+00:01:37,780 --> 00:01:39,580
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+21
+00:01:39,580 --> 00:01:40,900
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+22
+00:01:40,900 --> 00:01:40,920
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+23
+00:01:40,920 --> 00:01:44,270
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدimportance
+
+24
+00:01:44,270 --> 00:01:48,530
+of studying lifespan development بدنا نعرف شو
+
+25
+00:01:48,530 --> 00:01:50,970
+أهمية دراسة ال life span development
+
+26
+00:01:50,970 --> 00:01:56,810
+responsibility for children is or will be a part
+
+27
+00:01:56,810 --> 00:02:04,150
+of our everyday livesاحنا بنعرف ان عملية المسئولية
+
+28
+00:02:04,150 --> 00:02:08,570
+و الرعاية على الأطفال هي مسئوليتنا احنا و جزء من
+
+29
+00:02:08,570 --> 00:02:13,570
+مهامنا اليومية كبشر و كعائلات و كphysiotherapist
+
+30
+00:02:13,570 --> 00:02:19,110
+كمان ممكن انه نتعامل مع الأطفالthe more we were
+
+31
+00:02:19,110 --> 00:02:23,950
+learn about children the more we can better deal
+
+32
+00:02:23,950 --> 00:02:27,670
+with them and assist them in becoming competent
+
+33
+00:02:27,670 --> 00:02:33,970
+human being كل ما عرفنا أكتر عن الأطفال و عن مراحل
+
+34
+00:02:33,970 --> 00:02:39,590
+نموهم كل ما كان تعاملنا معهم بشكل أفضل و كل ما كان
+
+35
+00:02:39,590 --> 00:02:45,290
+المساعد اللي احنا بنقدمها إليهم بشكل أفضل بكتير
+
+36
+00:02:47,130 --> 00:02:51,150
+Lifespan development give us insight about our
+
+37
+00:02:51,150 --> 00:02:57,770
+development as adult as well كمان دراسة ال life
+
+38
+00:02:57,770 --> 00:03:03,630
+span development بتعطينا نظرة عن ال development و
+
+39
+00:03:03,630 --> 00:03:07,090
+طبيعة ال development اللي بتصير معانا as a human
+
+40
+00:03:07,090 --> 00:03:10,870
+being و adult human being، not the gene، شو اللي
+
+41
+00:03:10,870 --> 00:03:15,940
+بتصير معانا في عملية إنه مو التطورto examine the
+
+42
+00:03:15,940 --> 00:03:21,240
+point in the time when life begin until time when
+
+43
+00:03:21,240 --> 00:03:26,680
+it ends at least life as we know it كمان بيعطينا
+
+44
+00:03:26,680 --> 00:03:34,180
+القدرة على انه احنا نتعرف على نقطة بداية الحياة و
+
+45
+00:03:34,180 --> 00:03:38,560
+نقطة نهاية الحياة على الأقل كما هو ظاهر من يوم
+
+46
+00:03:38,560 --> 00:03:43,200
+الولادة لحد الوفاةin thinking about the importance
+
+47
+00:03:43,200 --> 00:03:48,820
+of studying lifespan development consider the
+
+48
+00:03:48,820 --> 00:03:53,120
+following research findings خلال دراستنا لل life
+
+49
+00:03:53,120 --> 00:03:59,400
+span development هنتعرف على بعض الدراسات ونتائج
+
+50
+00:03:59,400 --> 00:04:06,680
+بعض الدراسات احد الدراسات اللي صارت في 2001 بتقول
+
+51
+00:04:06,680 --> 00:04:10,840
+ان عملية ال massage therapyFacilitate the growth
+
+52
+00:04:10,840 --> 00:04:15,300
+and improve the immune system functioning of
+
+53
+00:04:15,300 --> 00:04:21,680
+preterm infants يعني لو احنا على سبيل المثال بدأنا
+
+54
+00:04:21,680 --> 00:04:31,230
+نشتغل مساج لطفل مولود جديد ومولود جاب الموعدممكن
+
+55
+00:04:31,230 --> 00:04:36,710
+شهور سبع شهور يكون تمان شهور عملية المساج على هذول
+
+56
+00:04:36,710 --> 00:04:42,830
+الأطفال بتحسن من عملية او من وظيفة الجهاز المناعي
+
+57
+00:04:42,830 --> 00:04:49,630
+وبتسرق في عملية انمو الجسدي او الحركة عند هذول
+
+58
+00:04:49,630 --> 00:04:56,040
+الأطفالSecure attachment to parents in adolescence
+
+59
+00:04:56,040 --> 00:04:59,620
+is linked with a host of positive outcome for
+
+60
+00:04:59,620 --> 00:05:03,500
+adolescents such as positive peer relation and
+
+61
+00:05:03,500 --> 00:05:08,250
+emotional well-being كمان من خلال دراستنالنمو و
+
+62
+00:05:08,250 --> 00:05:12,690
+التطور كثير من الدراسات بتقول أنه إذا كانت العلاقة
+
+63
+00:05:12,690 --> 00:05:17,070
+ما بين الأبوين في مرحلة و المراهطة أو الطفل في
+
+64
+00:05:17,070 --> 00:05:21,990
+مرحلة المراهطة هيكون إليها جانب إيجابي على عملية
+
+65
+00:05:21,990 --> 00:05:28,090
+النمو و عملية ال emotional و ال being عند هذا
+
+66
+00:05:28,090 --> 00:05:28,690
+الإنسان
+
+67
+00:05:42,460 --> 00:05:47,400
+بالطبع هذه الدراسة كمان بتقول انه احنا كل ما كان
+
+68
+00:05:47,400 --> 00:05:52,080
+عندنا القدرة على زيادة الحياة او زيادة عمر الخلية
+
+69
+00:05:52,080 --> 00:05:56,880
+في خلايا الاختبار هيكون عندنا في المستقبل او ممكن
+
+70
+00:05:56,880 --> 00:06:02,810
+يصير في المستقبلشغلات اتحسن من مستوى الحياة، اتزود
+
+71
+00:06:02,810 --> 00:06:06,570
+من فترة حياة الإنسان The historical perspective,
+
+72
+00:06:06,730 --> 00:06:10,990
+traditional and lifespan approach itالتجارب
+
+73
+00:06:10,990 --> 00:06:13,050
+التقليدية التجاربية التجاربية التجاربية التجاربية
+
+74
+00:06:13,050 --> 00:06:13,370
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+75
+00:06:13,370 --> 00:06:15,890
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+76
+00:06:15,890 --> 00:06:19,550
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+77
+00:06:19,550 --> 00:06:25,530
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+78
+00:06:25,530 --> 00:06:28,330
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+79
+00:06:28,330 --> 00:06:28,330
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+80
+00:06:28,330 --> 00:06:29,150
+التجاربية التجاربية التجاربية التجاربية التجاربية
+
+81
+00:06:29,150 --> 00:06:34,930
+التجاربية التجاربية التجاربية التجاربالتعريف
+
+82
+00:06:34,930 --> 00:06:41,390
+التقليدي و القديم كان بيركز على مرحلة ال
+
+83
+00:06:41,390 --> 00:06:46,390
+development عند الأطفال من الولادة لحد ما يصلوا
+
+84
+00:06:46,390 --> 00:06:51,130
+مرحلة ال blue و أحيانا بيعطي شيء من الانتباه
+
+85
+00:06:51,130 --> 00:06:56,270
+لمرحلة ال adult hood ال blue أو مابيعطيهاش اي
+
+86
+00:06:56,270 --> 00:07:01,590
+اهتمام و بقل اهتمام في هذه الدراسة كل ما زاد عمر
+
+87
+00:07:01,590 --> 00:07:05,720
+الإنسانيعني بالمختصر أن هذه الـ traditional
+
+88
+00:07:05,720 --> 00:07:10,140
+approach بتركز على دراسة التغيرات اللي بتصير عند
+
+89
+00:07:10,140 --> 00:07:14,660
+الأطفال من ساعة الولادة لحد ما يصير عمره أو ما
+
+90
+00:07:14,660 --> 00:07:19,880
+يوصل مرحلة المراهقة وبعد هيك بتقل فترة الاهتمام
+
+91
+00:07:19,880 --> 00:07:23,460
+بالتغيرات اللي بتصير عند الإنسان سواء كان في مرحلة
+
+92
+00:07:23,460 --> 00:07:28,840
+البلوغ أو في مرحلة الشيخوخةالطفولة خصوصًا تعتبر
+
+93
+00:07:28,840 --> 00:07:34,760
+مرحلة تغيير كبير في التجارب التقليدية مرحلة
+
+94
+00:07:34,760 --> 00:07:40,140
+الطفولة لها الاهتمام الأكبر خلال دراستنا لعملية
+
+95
+00:07:40,140 --> 00:07:44,860
+النمو وتطور من خلال التجارب التقليدية in contrast,
+
+96
+00:07:45,220 --> 00:07:49,220
+the lifespan approach emphasizes developmental
+
+97
+00:07:49,220 --> 00:07:53,220
+changes during adulthood as well as its childhood
+
+98
+00:07:54,300 --> 00:07:59,300
+في المقابل هتلاقي ان ال life span approach بركز
+
+99
+00:07:59,300 --> 00:08:04,200
+على عمليات التغير وال stability والثبات اللي بتكون
+
+100
+00:08:04,200 --> 00:08:09,280
+during developmental change او during development
+
+101
+00:08:09,280 --> 00:08:16,920
+from adulthood as well as childhood هيركز على
+
+102
+00:08:16,920 --> 00:08:23,490
+التغيرات اللي بتصيرأثناء عملية النمو والتغير عند
+
+103
+00:08:23,490 --> 00:08:29,630
+الأطفال مثل ما هو عند الكبار Characteristics of
+
+104
+00:08:29,630 --> 00:08:34,350
+Lifespan Perspective Baldist View هندرس من خلاله
+
+105
+00:08:34,350 --> 00:08:39,950
+ان شاء الله رب العالمين خصائص النمو والتطور من
+
+106
+00:08:39,950 --> 00:08:45,690
+خلال دراستنا أو من منظور نظرية ال life span
+
+107
+00:08:45,690 --> 00:08:50,060
+developmentوحنجلها شخص بيسموه ال بالتس if you
+
+108
+00:08:50,060 --> 00:08:56,140
+منظور بالتس the lifespan perspective involves that
+
+109
+00:08:56,140 --> 00:09:00,600
+او involve these basic contents development is
+
+110
+00:09:00,600 --> 00:09:05,880
+lifelong multidimensional multidirectional plastic
+
+111
+00:09:05,880 --> 00:09:11,020
+contextual multidisciplinary and involve a growth
+
+112
+00:09:11,020 --> 00:09:17,400
+maintenance and regulationإذا خلال دراستنا لـ
+
+113
+00:09:17,400 --> 00:09:22,320
+characteristics of lifespan development من منظور
+
+114
+00:09:22,320 --> 00:09:27,360
+بالتس هلاجي انه احنا هندرس ال development على مدى
+
+115
+00:09:27,360 --> 00:09:31,680
+الحياة هلاجي انه احنا في عملية الدراسة نبدأ فيها
+
+116
+00:09:31,680 --> 00:09:36,380
+lifelong طول الحياة multidimensional و
+
+117
+00:09:36,380 --> 00:09:42,350
+multidirectional متعددة الأبعاد و متعددة الجهاتحاب
+
+118
+00:09:42,350 --> 00:09:48,030
+نعرف إن عملية الـ development متغيرة، plastic،
+
+119
+00:09:48,030 --> 00:09:51,470
+change، شو اللي بيصير فيها، contextual، المحتوى
+
+120
+00:09:51,470 --> 00:09:56,410
+تبعها، multidisciplinary، متعددة التخصصات، و
+
+121
+00:09:56,410 --> 00:10:01,190
+involves growth, maintenance and regulation، تشمل
+
+122
+00:10:01,190 --> 00:10:06,450
+الزيادة، ال maintenance، الثبات أو البقاء، وعملية
+
+123
+00:10:06,450 --> 00:10:12,530
+التنظيمSome contemporary concerns
+
+124
+00:10:12,530 --> 00:10:17,470
+development and wellbeing of children and adults
+
+125
+00:10:27,970 --> 00:10:33,710
+اليوم، التطور والحياة للأطفال والشباب يمكّنهم من
+
+126
+00:10:33,710 --> 00:10:41,290
+الحصول على أهداف المجتمع والمعرفة والأساسيين اليوم
+
+127
+00:10:41,290 --> 00:10:47,290
+هنلاقي أن عملية التطورو الاهتمام بال development و
+
+128
+00:10:47,290 --> 00:10:53,210
+ال will being للأطفال و للكبار صارت محطة اهتمام
+
+129
+00:10:53,210 --> 00:10:59,330
+العامة عامة الناس بشكل عام ال scientist العلماء و
+
+130
+00:10:59,330 --> 00:11:05,370
+كمان صانعين السياسات او الحكومات اللي بتكون موجودة
+
+131
+00:11:05,370 --> 00:11:10,720
+في هذا البلدamong the important contemporary
+
+132
+00:11:10,720 --> 00:11:16,560
+concerns are
+
+133
+00:11:16,560 --> 00:11:22,360
+family issues parenting education socio cultural
+
+134
+00:11:22,360 --> 00:11:30,280
+context and social policy خلال الدراسة لعملية ال
+
+135
+00:11:30,280 --> 00:11:37,130
+life span developmentهنلاقي إنه فيه تركيز على ال
+
+136
+00:11:37,130 --> 00:11:43,450
+family issues شغلات أو الأمور اللي بتتعلق بالعائلة
+
+137
+00:11:43,450 --> 00:11:48,190
+إزاي ال parenting الأبوه و دورها في عملية ال
+
+138
+00:11:48,190 --> 00:11:52,510
+development ال education تعليم و دوره في عملية ال
+
+139
+00:11:52,510 --> 00:11:56,510
+development ال social cultural context المحتوى
+
+140
+00:11:56,510 --> 00:12:02,210
+الاجتماعي و الثقافيand social policy والسياسات
+
+141
+00:12:02,210 --> 00:12:06,350
+الاجتماعية اللي موجودة three important socio
+
+142
+00:12:06,350 --> 00:12:11,210
+-cultural contexts are culture, ethnicity and
+
+143
+00:12:11,210 --> 00:12:17,290
+gender تلت شغلات مهمة جدا لدراستنا ولدراسة عملية
+
+144
+00:12:17,290 --> 00:12:18,830
+النمو والتطور
+
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/VqGaLfbVVZ8.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/VqGaLfbVVZ8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7585444c5610b22c273994b7b60bef564ac54ce0
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/VqGaLfbVVZ8.srt
@@ -0,0 +1,1603 @@
+1
+00:00:00,000 --> 00:00:04,100
+السلام عليكم ورحمة الله وبركاته اليوم إن شاء
+
+2
+00:00:04,100 --> 00:00:08,500
+الله رب العالمين هنتكلم أو هنكمل في موضوع الـ fetal
+
+3
+00:00:08,500 --> 00:00:13,820
+development فهنتكلم عن الـ placenta ونتكلم عن الـ
+
+4
+00:00:13,820 --> 00:00:18,420
+fetal circulation بداية بدنا نعرف أن الـ placenta
+
+5
+00:00:18,420 --> 00:00:24,010
+كحجم تقريبا 15 cm الـ diameter تبعها، الـ thickness
+
+6
+00:00:24,010 --> 00:00:28,450
+تبعها من أربع إلى خمس centimeter، الـ weight تبعها
+
+7
+00:00:28,450 --> 00:00:33,450
+حوالي خمسمية gram تقريبا نصف كيلو، the placenta is
+
+8
+00:00:33,450 --> 00:00:41,150
+essentially a vascular organ، تعتبر الـ placenta عضو 
+
+9
+00:00:41,150 --> 00:00:46,390
+غني بالـ blood supply زي ما احنا ملاحظين حرف الـ A
+
+10
+00:00:46,390 --> 00:00:51,970
+منفصل عن كلمة vascular ودلالة للمفرد، وكلمة
+
+11
+00:00:51,970 --> 00:00:56,870
+vascular معناها rich of blood supply، لكن لو كانت
+
+12
+00:00:56,870 --> 00:01:03,030
+حرف الـ A ملتصق تماما بكلمة vascular فمعناه أن هذا
+
+13
+00:01:03,030 --> 00:01:07,790
+العضو غير دموي أو غير غني بالأوعية الدموية، a
+
+14
+00:01:07,790 --> 00:01:13,070
+vascular organ. It's connected to the fetus by the
+
+15
+00:01:13,070 --> 00:01:16,110
+umbilical cord which transmit to umbilical
+
+16
+00:01:16,110 --> 00:01:20,870
+arteries from fetus to placenta and one umbilical
+
+17
+00:01:20,870 --> 00:01:25,650
+vein from placenta to fetus، حلاجة إنه المشيمة
+
+18
+00:01:25,650 --> 00:01:30,950
+مرتبطة بالجنين عن طريق الـ umbilical cord، الـ
+
+19
+00:01:30,950 --> 00:01:35,270
+umbilical cord بيحتوي على one umbilical vein
+
+20
+00:01:35,650 --> 00:01:39,850
+وبيحتوي على two umbilical arteries، بيحتوي على two
+
+21
+00:01:39,850 --> 00:01:44,290
+umbilical arteries و one umbilical vein، الـ
+
+22
+00:01:44,290 --> 00:01:47,490
+function تبع الـ umbilical arteries و الـ umbilical
+
+23
+00:01:47,490 --> 00:01:52,130
+vein مختلفة عن الـ normal function of arteries and
+
+24
+00:01:52,130 --> 00:01:55,610
+veins اللي احنا بنعرفها، احنا بنعرف أن الـ vein
+
+25
+00:01:55,610 --> 00:02:00,670
+بينقل الدم الغير مؤكسج الى القلب عشان يتم عملية
+
+26
+00:02:00,670 --> 00:02:08,670
+أكسجته، وبينقل أو الأوردة الشرايين أو الـ arteries
+
+27
+00:02:08,670 --> 00:02:13,690
+بتنقل الدم المؤكسج من القلب لباقي أجزاء و أجهزة
+
+28
+00:02:13,690 --> 00:02:20,170
+الجسم، الآن عند الجنين الأمر مختلف تماما، بداية
+
+29
+00:02:20,170 --> 00:02:27,860
+لبلاسنتا هي عبارة عن الجهاز الهضمي، عبارة عن الجهاز
+
+30
+00:02:27,860 --> 00:02:34,120
+التنفسي بالنسبة للجنين، it is work as a lung and
+
+31
+00:02:34,120 --> 00:02:40,300
+as a digestive system for the fetus، الـ placenta زي ما
+
+32
+00:02:40,300 --> 00:02:47,260
+قولنا مرتبطة ومرتبطة بجدار الرحم، في داخل الـ placenta
+
+33
+00:02:47,260 --> 00:02:52,350
+يوجد عندي chronic villi، الـ chronic villi هذه هي
+
+34
+00:02:52,350 --> 00:03:00,130
+اللي بتتم من خلالها عملية تبادل الغازات والأغذية
+
+35
+00:03:00,130 --> 00:03:07,210
+مع الأم، بحيث أنَّها تعطي للدورة الدموية تبع الأم الـ
+
+36
+00:03:07,210 --> 00:03:11,410
+waste products و الـ non-oxygenated blood أو خلاني
+
+37
+00:03:11,410 --> 00:03:15,800
+نقول ثاني أكسيد الكربون اللي موجود في الدم، وبتاخد
+
+38
+00:03:15,800 --> 00:03:19,440
+منها الـ oxygen وبتاخد منها الـ nutrients اللي لازمة
+
+39
+00:03:19,440 --> 00:03:25,000
+للجنين، زي ما احنا شايفين هذه طبعا هي عبارة عن
+
+40
+00:03:25,000 --> 00:03:26,520
+chronic villi.
+
+41
+00:03:30,060 --> 00:03:35,580
+وهذا طبعا بتساعد بشكل كبير جدا في عملية تبادل
+
+42
+00:03:35,580 --> 00:03:39,580
+الغازات، عملية التعاريج اللي موجود هنا عشان تزيد
+
+43
+00:03:39,580 --> 00:03:47,400
+مساحة التقاءها مع الدورة الدموية الخاصة بالأم، الآن
+
+44
+00:03:47,400 --> 00:03:55,160
+لو جينا نتعرف على الدورة الدموية تبع الجنين في داخل
+
+45
+00:03:55,160 --> 00:04:00,280
+الرحم، هلاجي في عندي أنا موجود عندي الـ placenta في
+
+46
+00:04:00,280 --> 00:04:04,360
+عندي الـ umbilical cord، وهذا طبعا اللي بيحتوي على
+
+47
+00:04:04,360 --> 00:04:08,240
+two umbilical arteries و one umbilical vein، في
+
+48
+00:04:08,240 --> 00:04:13,700
+عندي طبعا الـ ductus venosus اللي موجود عندي في
+
+49
+00:04:13,700 --> 00:04:20,810
+بداية دخول الدم الى الكبد الـ liver، وبعد هيك بينتقل
+
+50
+00:04:20,810 --> 00:04:25,150
+لـ الـ inferior vena cava، بعد هيك في عندي الـ heart
+
+51
+00:04:25,150 --> 00:04:32,360
+في عندي الـ aorta، في عندي الدورة الدورة الرئوية أو
+
+52
+00:04:32,360 --> 00:04:37,180
+دورة الدم الرئوية اللي بتوصل الدم على الرئتين
+
+53
+00:04:37,180 --> 00:04:43,260
+وفي عندي الأورطة اللي بيوصل الدم لباقي أجهزة الجسم
+
+54
+00:04:43,260 --> 00:04:46,980
+زي ما احنا شايفين الألوان اللي موجودة، اللون الأحمر
+
+55
+00:04:46,980 --> 00:04:51,860
+على الأخر عبارة عن rich blood supply، اللون الأزرق
+
+56
+00:04:51,860 --> 00:04:57,700
+اللي موجود طبعا low oxygen supply، اللون الأحمر high
+
+57
+00:04:57,700 --> 00:05:02,460
+أو rich oxygen supply، اللون الأزرق low oxygen
+
+58
+00:05:02,460 --> 00:05:06,920
+supply، وفي اللون البنفسجي طبعا هو mixed blood
+
+59
+00:05:06,920 --> 00:05:13,820
+محلاج هو الجزء الغالب، الآن خلينا نيجي نتفرج ونشوف
+
+60
+00:05:13,820 --> 00:05:19,820
+كيف ممكن أنَّها تصير الدورة الدموية عند الأطفال أو
+
+61
+00:05:19,820 --> 00:05:24,210
+في داخل الرحم، الآن احنا هنحكي عن موضوع الـ fetal
+
+62
+00:05:24,210 --> 00:05:29,450
+circulation زي ما احنا شايفين بتتكون طبعا عندي من
+
+63
+00:05:29,450 --> 00:05:37,950
+الـ placenta، الـ umbilical vein، الـ ductus venosus
+
+64
+00:05:37,950 --> 00:05:45,310
+وين الدم بيطلع من الكبد وبده يخش على الـ inferior
+
+65
+00:05:45,310 --> 00:05:46,650
+vena cava.
+
+66
+00:05:51,020 --> 00:05:55,240
+طبعا في عندي الـ ductus arteriosus زي ما احنا
+
+67
+00:05:55,240 --> 00:06:01,400
+شايفينها دي اللي بتربط ما بين الـ pulmonary artery و
+
+68
+00:06:01,400 --> 00:06:06,940
+ما بين الأورطة، في عندي الـ foramen ovale اللي موجود
+
+69
+00:06:06,940 --> 00:06:10,900
+في الـ septum الـ wall في جدار القلب، وهدي اللي طبعا
+
+70
+00:06:10,900 --> 00:06:16,040
+هنشوف عندها هتنقل الدم من الـ right side of the
+
+71
+00:06:16,040 --> 00:06:20,420
+heart to the left side of the heart، وفي عندي الـ
+
+72
+00:06:20,420 --> 00:06:32,080
+umbilical arteries، الآن
+
+73
+00:06:32,080 --> 00:06:39,700
+زي ما احنا شايفين الدم المؤكسج بينتقل من الـ placenta
+
+74
+00:06:45,270 --> 00:06:51,990
+بينتقل من الـ placenta وبيمر إلى الكبد من خلال الـ
+
+75
+00:06:51,990 --> 00:06:58,170
+ductus venosus، من خلال الـ ductus venosus بعد هيك
+
+76
+00:06:58,170 --> 00:07:09,410
+بينتقل للـ heart، الآن لما يعدي في الـ heart من
+
+77
+00:07:09,410 --> 00:07:14,030
+خلال الـ inferior vena cava، الـ inferior vena cava
+
+78
+00:07:14,030 --> 00:07:14,690
+اللي موجود
+
+79
+00:07:17,280 --> 00:07:21,600
+الـ right atrium بيصير لها filling، الـ right
+
+80
+00:07:21,600 --> 00:07:27,860
+ventricle بيصير لها filling، تمتلك بالدم المؤكسج
+
+81
+00:07:27,860 --> 00:07:32,080
+جزء من الدم، زي ما حكي أنا بينزل على الـ right
+
+82
+00:07:32,080 --> 00:07:38,120
+ventricle، وجزء آخر من الدم من خلال الـ foramen
+
+83
+00:07:38,120 --> 00:07:44,100
+ovale الفتحة اللي في جدار القلب تنتقل لـ left
+
+84
+00:07:44,100 --> 00:07:50,220
+atrium، بعد هيك لـ الـ left ventricle، الـ left
+
+85
+00:07:50,220 --> 00:07:59,660
+ventricle بيبدأ يضخ الدم المؤكسج من
+
+86
+00:07:59,660 --> 00:08:05,860
+خلال الأورطة، بعد هيك بيروح وبيتوزع على باقي أجزاء
+
+87
+00:08:05,860 --> 00:08:12,160
+الجسم، في حين أن بعض الدم اللي موجود في الـ right
+
+88
+00:08:12,160 --> 00:08:17,480
+ventricle، الـ right ventricle بيضخ الدم من خلال الـ
+
+89
+00:08:17,480 --> 00:08:26,300
+pulmonary artery، من خلال الشريان الرئوي طبعا هذه
+
+90
+00:08:26,300 --> 00:08:32,340
+الجزء هيروح على الـ lungs، لكن الـ lungs زي ما حكينا
+
+91
+00:08:32,340 --> 00:08:40,660
+هي عبارة عن unfunctional lungs، مابتشتغلش مش شغالة
+
+92
+00:08:40,660 --> 00:08:48,540
+فبيضطر في جزء من الدم طبعا بيروح على وين بيغذي
+
+93
+00:08:48,540 --> 00:08:53,580
+أنسجة القلب، بيغذي أنسجة الرئتين أنا اسف بيغذي
+
+94
+00:08:53,580 --> 00:09:00,880
+أنسجة الرئتين، إذا
+
+95
+00:09:00,880 --> 00:09:10,120
+الدم اللي بتتم ضخه من خلال الـ pulmonary artery زي
+
+96
+00:09:10,120 --> 00:09:13,780
+ما احنا شايفين هذه تقريبا نسبة 8%
+
+97
+00:09:13,780 --> 00:09:29,680
+بتغذي الدم، الـ left ventricle من خلال الأورطة زي
+
+98
+00:09:29,680 --> 00:09:34,500
+ما حكينا أنَّ الـ alveolus أو الـ alveoli حواصلات
+
+99
+00:09:34,500 --> 00:09:39,440
+الهوائية لسه مش شغالة not activated in the lungs
+
+100
+00:09:39,440 --> 00:09:47,400
+فبالتالي بيرجع الدم فقط بيعمل تغذية لأنسجة الرئتين
+
+101
+00:09:47,400 --> 00:09:54,400
+وبيرجع ثاني من خلال فتحة هنا بيسموها الـ ductus
+
+102
+00:09:54,400 --> 00:10:01,120
+arteriosus، الـ ductus arteriosus بتنقل الدم من الـ
+
+103
+00:10:01,120 --> 00:10:05,880
+pulmonary artery للأورطة، من الـ pulmonary artery
+
+104
+00:10:05,880 --> 00:10:11,220
+للأورطة، وفي الأورطة بيروح بدخ الدم لكل أجزاء الجسم
+
+105
+00:10:26,150 --> 00:10:32,330
+8% من الدم اللي بيروح من خلال الـ pulmonary artery
+
+106
+00:10:32,330 --> 00:10:37,370
+هو بيروح لتغذية الأنسجة تبع الـ lungs
+
+107
+00:10:40,570 --> 00:10:45,890
+الدم المتبقي بيمر من خلاله للأورطة، وبعد هيك بيروح
+
+108
+00:10:45,890 --> 00:10:52,950
+لباقي أجزاء الجسم، والدم غير مؤكسج بيروح من خلال
+
+109
+00:10:52,950 --> 00:10:58,770
+الـ pulmonary arteries وبيروح على الـ placenta عشان يتم
+
+110
+00:10:58,770 --> 00:11:04,030
+عملية التبادل، عند الولادة بتتم جس الـ umbilical
+
+111
+00:11:04,030 --> 00:11:10,870
+cord، بعد هيك تبدأ تشتغل الدورة الدموية كاملة عند
+
+112
+00:11:10,870 --> 00:11:16,710
+الطفل، الـ ductus arteriosus اللي هنا هتسكر هتصير
+
+113
+00:11:16,710 --> 00:11:22,850
+الدورة الدموية تصل للـ alveoli وتبدأ عملية تبادل
+
+114
+00:11:22,850 --> 00:11:29,510
+الغذائي، الـ ductus venosus هيتم توقفها كمان الـ
+
+115
+00:11:29,510 --> 00:11:36,170
+ductus venosus هتتوقف وهتسكر مباشرة، هيظل عند الـ
+
+116
+00:11:36,170 --> 00:11:40,990
+inferior vena cava بياخد الـ non-oxygenated blood
+
+117
+00:11:40,990 --> 00:11:45,770
+من الدورة الدموية الخاصة بالجنين أو الخاصة بالطفل
+
+118
+00:11:45,770 --> 00:11:51,130
+بعد ولادته، دم غير مؤكسج من الجزء السفلي من الجسم و
+
+119
+00:11:51,130 --> 00:11:54,730
+الـ superior vena cava بياخد من الجزء العلوي من
+
+120
+00:11:54,730 --> 00:11:59,430
+الجسم، وبتم الدورة الدموية اللي احنا بنعرفها الـ
+
+121
+00:11:59,430 --> 00:12:04,520
+right ventricle بدخ الدم لرئتين عشان تم عملية الـ
+
+122
+00:12:04,520 --> 00:12:10,000
+oxygen وتبادل الغازات، الـ left ventricle بدخ الدم
+
+123
+00:12:10,000 --> 00:12:16,440
+من خلال الأورطة وبيدخ لباقي أجزاء الجسم، هيك احنا
+
+124
+00:12:16,440 --> 00:12:21,940
+شفنا الدورة الدموية الخاصة بالـ fetus في أثناء وجوده
+
+125
+00:12:21,940 --> 00:12:30,440
+في داخل الرحم، الآن نيجي لمراحل النمو في داخل الرحم
+
+126
+00:12:30,440 --> 00:12:35,600
+وقلنا أنه from nine weeks after conception to
+
+127
+00:12:35,600 --> 00:12:42,000
+birth وسميناها الفترة هذه period of fetus
+
+128
+00:12:42,000 --> 00:12:52,540
+conception to birth من فترة الإخصاب لحد الولادة
+
+129
+00:12:52,540 --> 00:12:57,420
+increase in size and systems begin to function
+
+130
+00:12:58,710 --> 00:13:04,710
+بتبدأ تزيد حجم الجنين وبتبدأ أجهزة الجسم عنده
+
+131
+00:13:04,710 --> 00:13:13,570
+تشتغل age of viability 22 ل 28 أسبوع العمر اللي 
+
+132
+00:13:13,570 --> 00:13:19,350
+بيكون أو تبات فيه الروح بيكون فيه الأنسجة أو هذا
+
+133
+00:13:19,350 --> 00:13:24,130
+الجنين حي كائن حي على عمر 22 إلى 30
+
+134
+00:13:27,520 --> 00:13:33,680
+على عمر 22 إلى 28 أسبوع في
+
+135
+00:13:33,680 --> 00:13:38,000
+الشهر الأول زي ما احنا شايفين by the end of the
+
+136
+00:13:38,000 --> 00:13:43,380
+first month the embryo is about one واحدة على
+
+137
+00:13:43,380 --> 00:13:48,960
+عشرة of an inch عشر انش زي ما احنا شايفين كيف في
+
+138
+00:13:48,960 --> 00:13:54,520
+داخل الرحم مش مبين لكن لو جينا نفصل أكتر هلاجي أنه
+
+139
+00:13:54,520 --> 00:13:59,660
+في بعض الشغلات اللي موجودة the heart which is no
+
+140
+00:13:59,660 --> 00:14:06,120
+larger than an obesity يعني القلب ما بيجيش يعني جد
+
+141
+00:14:06,120 --> 00:14:16,420
+لب من لب البذر أو ال Clementina أو البرتقال وفي
+
+142
+00:14:16,420 --> 00:14:19,820
+هذه الفترة بيبدأ القلب ينبض
+
+143
+00:14:23,880 --> 00:14:29,440
+زي ما احنا شايفين كيف صورة حقيقية للجنين في خلال
+
+144
+00:14:29,440 --> 00:14:35,700
+الشهر الأول، لاحظوا كيف؟ وهذه مكبرة آلاف المرات،
+
+145
+00:14:35,700 --> 00:14:42,320
+مكبرة آلاف المرات في الشهر الثاني، the embryo is
+
+146
+00:14:42,320 --> 00:14:48,720
+about one inch length طوله تقريبا واحد إنش has a
+
+147
+00:14:48,720 --> 00:14:54,520
+distinct slightly webbed fingers تبدأ شكل الأصابع
+
+148
+00:14:54,520 --> 00:14:59,500
+الأيدين تبدأ تظهر شوية شوية veins are clearly
+
+149
+00:14:59,500 --> 00:15:07,420
+visible الأوردة واضحة ومرئية the heart has divided
+
+150
+00:15:07,420 --> 00:15:12,840
+into right and left chambers القلب في هذه العمر
+
+151
+00:15:12,840 --> 00:15:17,860
+منقسم إلى جزئين الجزء الأيمن والجزء الأيسر
+
+152
+00:15:20,120 --> 00:15:28,600
+هي صورة حقيقية للجنين عنده عمر شهرين طبعا احنا
+
+153
+00:15:28,600 --> 00:15:34,000
+بنحكي عن طوله يعني لا يتجاوز الواحد انش
+
+154
+00:15:37,540 --> 00:15:43,500
+عند عمر three months تلت شهور by now the fetus is
+
+155
+00:15:43,500 --> 00:15:47,760
+two and a half to three inches length طوله من
+
+156
+00:15:47,760 --> 00:15:52,360
+اتنين الى تلاتة انش أو اتنين و نص لتلاتة انش في
+
+157
+00:15:52,360 --> 00:15:59,080
+هذه المرحلة يعني احنا بنحكي تقريبا على سبعة سم و
+
+158
+00:15:59,080 --> 00:16:05,770
+نص من خمسة الى سبعة سم و نص حجمه أو طوله and is
+
+159
+00:16:05,770 --> 00:16:11,470
+fully formed كل أجهزة الجسم تقريبا اتكونت وال
+
+160
+00:16:11,470 --> 00:16:16,010
+upper و lower extremities اتكونت لكن مش مكتملة
+
+161
+00:16:16,010 --> 00:16:19,830
+النمو يعني بداية الأصابع، بداية ال upper limbs،
+
+162
+00:16:19,830 --> 00:16:20,930
+بداية ال lower limbs
+
+163
+00:16:24,150 --> 00:16:28,410
+he has begun swallowing and kicking مبدأ عملية
+
+164
+00:16:28,410 --> 00:16:34,410
+البلع طبعا البلع للسائل الأمينى اللي موجود و عملية
+
+165
+00:16:34,410 --> 00:16:40,090
+الرفس أو بداية الحركة بيبدأ يرفس أو بيبدأ يتحرك
+
+166
+00:16:40,090 --> 00:16:46,050
+لكن في هذا العمر الحركة بتكون ضعيفة جدا و غير
+
+167
+00:16:46,050 --> 00:16:51,830
+محسوسة عشان هيك الأم الحامل مابتقدرش تحس بالحركة
+
+168
+00:16:51,830 --> 00:16:57,190
+تبع الجنين All organs and muscles have formed and
+
+169
+00:16:57,190 --> 00:17:03,690
+are beginning to function كل مكونات الجسم كل أجهزة
+
+170
+00:17:03,690 --> 00:17:10,210
+الجسم تكون اتكونت و بتبدأ تشتغل تقريبا ما عدا زي
+
+171
+00:17:10,210 --> 00:17:13,770
+ما حكينا ال digestive system و ال respiratory
+
+172
+00:17:13,770 --> 00:17:18,910
+system عند
+
+173
+00:17:18,910 --> 00:17:20,990
+الشهر الرابع ال fourth month
+
+174
+00:17:28,990 --> 00:17:35,070
+الطفل أو الجنين في هذه المرحلة بيغطى بطبقة كثيفة
+
+175
+00:17:35,070 --> 00:17:40,530
+من الشعر اللي بيسموها شعر البطن أو شعر الحمل
+
+176
+00:17:44,650 --> 00:17:49,890
+Clearly نبضات القلب صارت أكثر وضوحا The mother may
+
+177
+00:17:49,890 --> 00:17:55,050
+feel baby's first kick الأم الحامل ممكن تقدر تحس
+
+178
+00:17:55,050 --> 00:18:00,590
+بحركة الجنين في خلال هذا العمر عند بداية الشهر
+
+179
+00:18:00,590 --> 00:18:02,290
+الرابع أو عند الشهر الرابع
+
+180
+00:18:05,500 --> 00:18:11,680
+لاحظوا كيف الحجم تبعه صار وكيف زي ما حكينا كل
+
+181
+00:18:11,680 --> 00:18:23,020
+أجهزة الجسم متكونة لكن تزداد نموها في الحجم five
+
+182
+00:18:23,020 --> 00:18:28,000
+months عند خمس شهور a protective coating called
+
+183
+00:18:28,000 --> 00:18:28,720
+vernix
+
+184
+00:18:31,080 --> 00:18:35,700
+الفرنيكس  تبدأ في التطبيق عند الشهر
+
+185
+00:18:35,700 --> 00:18:40,600
+الخامس بتبدأ طبقة بيسموها الفرنيكس تتكون
+
+186
+00:18:40,600 --> 00:18:48,020
+على جلد الطفل by the end of this month the baby
+
+187
+00:18:48,020 --> 00:18:53,520
+will be nearly eight inch long and weight almost a
+
+188
+00:18:53,520 --> 00:18:59,140
+pound بنهاية الشهر الخامس بيكون طوله تقريبا ثمانية
+
+189
+00:18:59,140 --> 00:19:09,860
+انش ووزنه حوالي one pound طبقة
+
+190
+00:19:09,860 --> 00:19:15,800
+ال vernix الفرنيكس هي طبقة الحماية اللي موجودة على
+
+191
+00:19:15,800 --> 00:19:23,800
+جسم الجنين وبيخلوها طبعا بعد الولادة الطبقة
+
+192
+00:19:23,800 --> 00:19:30,060
+البيضاء هذه لفترة لأنها بتعمل نوع من الحماية وبتزود
+
+193
+00:19:30,060 --> 00:19:37,060
+من مناعة الجنين at six months عند ست شهور
+
+194
+00:19:44,190 --> 00:19:50,750
+الرموش والحواجب أصبحت مرئية و أكثر وضوحا الرموش
+
+195
+00:19:50,750 --> 00:19:51,310
+أصبحت مرئية و أكثر وضوحا الرموش والحواجب أصبحت
+
+196
+00:19:51,310 --> 00:19:55,950
+مرئية و أكثر وضوحا الرموش والحواجب أصبحت مرئية و
+
+197
+00:19:55,950 --> 00:19:56,370
+أكثر وضوحا الرموش والحواجب أصبحت مرئية و أكثر
+
+198
+00:19:56,370 --> 00:20:01,230
+وضوحا الرموش والحواجب أصبحت مرئية و أكثر وضوحا
+
+199
+00:20:01,230 --> 00:20:08,450
+الرموش والحواجب أصبحت مرئية و أكثر وضوحا ما فيش ال
+
+200
+00:20:08,450 --> 00:20:13,030
+function of breathing ما في وظيفة التنفس هي حركة
+
+201
+00:20:13,030 --> 00:20:21,550
+كنوع من ال exercises وتمارين لعضلات التنفس the
+
+202
+00:20:21,550 --> 00:20:27,270
+fetus start to hear sounds عن ست شهور كمان بيبدأ
+
+203
+00:20:27,270 --> 00:20:32,030
+الجنين يسمع بعض الأصوات وخصوصا بيسمع نبضات قلب
+
+204
+00:20:32,030 --> 00:20:36,150
+الأم بيسمع الشغلات القريبة من الأم واللي متعود
+
+205
+00:20:36,150 --> 00:20:41,440
+عليها عشان هيك بنلاقي أن بعض الأطفال الأصوات اللي
+
+206
+00:20:41,440 --> 00:20:46,740
+اتعودوا عليها وهم في فترة الحمل ممكن أن لو
+
+207
+00:20:46,740 --> 00:20:52,020
+سمعوها بعد الولادة ولو كان في طفل بيبكي ممكن يسكت
+
+208
+00:20:52,020 --> 00:20:56,120
+ويهدأ لو سمع هذه الأصوات اللي متعود عليها يعني
+
+209
+00:20:56,120 --> 00:21:01,760
+كمثال لو كان في أم تعود أن تسمع قرآن في فترة
+
+210
+00:21:01,760 --> 00:21:06,300
+الحمل هذه وعندما الطفل يبدأ .. بعد الولادة عندما
+
+211
+00:21:06,300 --> 00:21:12,480
+الطفل يبدأ يبكي ممكن لو حطت القرآن بيبدأ يسكت
+
+212
+00:21:12,480 --> 00:21:17,820
+الطفل وينتبه أن هذا الصوت متعود عليه وأن أمه قريبة
+
+213
+00:21:17,820 --> 00:21:22,480
+منه طبقة
+
+214
+00:21:22,480 --> 00:21:28,720
+ال vernix الفرنيكس اللي هي موجودة على ال skin هي
+
+215
+00:21:28,720 --> 00:21:36,990
+طبقة تقريبا بيضاء على صفراء اللون اللي هو الشعر اللي
+
+216
+00:21:36,990 --> 00:21:43,850
+بيكون موجود على الجنين seven months by the end of
+
+217
+00:21:43,850 --> 00:21:47,750
+the seven month the baby weight about three and a
+
+218
+00:21:47,750 --> 00:21:52,670
+half pounds تقريبا تلاتة و نص pound and it is
+
+219
+00:21:52,670 --> 00:21:59,270
+about twelve inch long وطوله تقريبا إثنى عشر انش his
+
+220
+00:21:59,270 --> 00:22:04,890
+body is well formed كل أجزاء الجسم اتكونت وكل
+
+221
+00:22:04,890 --> 00:22:10,690
+أجهزة الجسم اتكونت fingernails cover his
+
+222
+00:22:10,690 --> 00:22:16,650
+fingertips كمان الأظافر بتكون اتكونت وبدت تغطي
+
+223
+00:22:16,650 --> 00:22:24,950
+الأصابع و رؤوس الأصابع زي ما احنا شايفين الآن الصورة
+
+224
+00:22:24,950 --> 00:22:31,900
+اللي بتوضح كيف الجنين في مرحلة الشهر السابع بيكون
+
+225
+00:22:31,900 --> 00:22:38,740
+مكتمل تقريبا النمو لكن الحجم تبعه أقل من الحجم تبع
+
+226
+00:22:38,740 --> 00:22:42,960
+الطفل الطبيعي عشان هيك بيلاقي أن في آخر شهرين
+
+227
+00:22:42,960 --> 00:22:49,340
+بيزداد حجم الطفل بشكل متسارع وبشكل كبير جدا eight
+
+228
+00:22:49,340 --> 00:22:53,380
+months عند الشهر الثامن the baby is gaining about
+
+229
+00:22:53,380 --> 00:22:59,380
+half a pound per week يعني نص باوند بيزيد في الأسبوع
+
+230
+00:22:59,380 --> 00:23:05,180
+في الشهر الأخير بيزيد تقريبا اتنين pound and
+
+231
+00:23:05,180 --> 00:23:09,040
+layers of fat are building تبدأ تكون طبقات من
+
+232
+00:23:09,040 --> 00:23:14,000
+الدهون تحت الجلد he has probably turned head down
+
+233
+00:23:14,000 --> 00:23:20,330
+in preparation for birth و بيبدأ يلف حاله و يدير
+
+234
+00:23:20,330 --> 00:23:26,610
+رأسه باتجاه طريق الخروج و تحضير لمرحلة الولادة he
+
+235
+00:23:26,610 --> 00:23:30,250
+weights between four to six pounds ووزنه ما بين
+
+236
+00:23:30,250 --> 00:23:36,900
+أربعة إلى ستة pound تقريبا عند الشهر التاسع the
+
+237
+00:23:36,900 --> 00:23:43,200
+baby is hefty six to seven pounds يعني وزنه ما بين
+
+238
+00:23:43,200 --> 00:23:46,900
+ستة إلى سبعة pound measures between تسعة و إثنى عشر
+
+239
+00:23:46,900 --> 00:23:54,740
+إلى إثنين و عشرين انش as he becomes more crowded the
+
+240
+00:23:54,740 --> 00:24:00,520
+mother feel him move around less وهذه طبعا ما يميز
+
+241
+00:24:00,520 --> 00:24:05,480
+الفترة أو الشهر الأخير أن أصبح الرحم ضيق على
+
+242
+00:24:05,480 --> 00:24:10,160
+الجنين وبالتالي حركته بتقل عشان هيك ممكن نلاقي بعض
+
+243
+00:24:10,160 --> 00:24:14,720
+الأمهات تقول أن حركة الجنين في الشهر الأخير قلت
+
+244
+00:24:14,720 --> 00:24:18,300
+وبتبدأ الأمهات اللي ما عندهم مش خبرة في الحمل كتير
+
+245
+00:24:18,300 --> 00:24:23,530
+تبدأ تقولتخاف لأ هذه طبعا قلة الحركة في الشهر
+
+246
+00:24:23,530 --> 00:24:29,310
+التاسع هي طبيعية لأن الرحم صار ضيق على الطفل
+
+247
+00:24:29,310 --> 00:24:35,390
+وبالتالي بيحد من حركة الطفل في داخل الرحم الآن
+
+248
+00:24:35,390 --> 00:24:41,330
+بدنا نعرف بعض العوامل اللي ممكن تسبب خطورة على ..
+
+249
+00:24:41,330 --> 00:24:46,560
+بعض العوامل اللي ممكن تسبب خطورة على مرحلة الحمل في
+
+250
+00:24:46,560 --> 00:24:49,960
+عندنا general risk factors اللي بتتعلق لـ 
+
+251
+00:24:49,960 --> 00:24:53,840
+nutrition و لازم يكون في عندنا adequate amount of
+
+252
+00:24:53,840 --> 00:24:58,540
+food كمية أكل مناسبة بتحتوي على البروتين ال
+
+253
+00:24:58,540 --> 00:25:05,130
+vitamins و minerals المعادن و stress الضغط النفسي
+
+254
+00:25:05,130 --> 00:25:08,410
+كمان decrease oxygen to the fetus and weakness
+
+255
+00:25:08,410 --> 00:25:15,610
+mother's immune system قلة ال oxygen بتقلل من
+
+256
+00:25:15,610 --> 00:25:21,110
+مناعة الأم  the mother's
+
+257
+00:25:21,110 --> 00:25:28,010
+age عمر الأم neither too young nor too old ما تكونش
+
+258
+00:25:28,010 --> 00:25:32,450
+صغير كتير وما تكونش كبير كتير لأنه على كل الحالتين
+
+259
+00:25:32,450 --> 00:25:37,510
+هيكون في خطورة على الحمل في هذه الفترة إذا كانت
+
+260
+00:25:37,510 --> 00:25:45,150
+الأم صغيرة جدا وإذا كانت كبيرة جدا Teratogens طبعا
+
+261
+00:25:45,150 --> 00:25:51,350
+في عندنا بعض العوامل البيئية والخارجية اللي ممكن
+
+262
+00:25:51,350 --> 00:25:55,950
+أنها تؤثر على الحمل زى في عندنا حاجة بسميها
+
+263
+00:25:55,950 --> 00:25:59,970
+التراتوجينز اللى عبارة عن environmental influences
+
+264
+00:25:59,970 --> 00:26:04,390
+or agents that can damage the developing organism
+
+265
+00:26:04,390 --> 00:26:11,910
+يعني عبارة عن عوامل بيئية خارجية ممكن تأثر و تضر
+
+266
+00:26:11,910 --> 00:26:16,070
+الجنين زى مثلا الأشعة عشان هيك بنقول أن الأم
+
+267
+00:26:16,070 --> 00:26:22,290
+ممنوعة تتعرض للأشعة في فترة الحمل ممنوع تاخد بعض
+
+268
+00:26:22,290 --> 00:26:27,110
+الأدوية و chemicals و دراجات كل هذه الشغلات ممكن
+
+269
+00:26:27,110 --> 00:26:34,430
+تعتبر teratogens وتسبب ضرر للحمل many diseases
+
+270
+00:26:34,430 --> 00:26:38,890
+pass through the placenta directly and attack the
+
+271
+00:26:38,890 --> 00:26:43,090
+fetus كتير من الأمراض ممكن أنها تنتقل من الأم
+
+272
+00:26:43,090 --> 00:26:49,130
+للجنين potentially dangerous drugs not limited to
+
+273
+00:26:49,130 --> 00:26:54,070
+cocaine include alcohol and caffeine طبعا هذا
+
+274
+00:26:54,070 --> 00:27:00,350
+بنقوله انه الأمهات المدخنات المدمنات اللي بتناول
+
+275
+00:27:00,350 --> 00:27:07,630
+الكحول هذه كلها عناصر تؤثر بشكل سلبي و عوامل قاتلة
+
+276
+00:27:07,630 --> 00:27:14,790
+لل developing organism أو ال developing fetus الـ
+
+277
+00:27:14,790 --> 00:27:19,470
+Environmental hazards are treacherous because we
+
+278
+00:27:19,470 --> 00:27:25,410
+are often unaware of their presence بعض المخاطر
+
+279
+00:27:25,410 --> 00:27:29,890
+الموجودة مثل المخاطر البيئية مثل التلوث البيئي مثل
+
+280
+00:27:29,890 --> 00:27:35,210
+الاسبستوز و الاسبست مادة الاسبست هذه بشكل عام هي
+
+281
+00:27:35,210 --> 00:27:42,150
+عوامل خطيرة و ما بننتبهش إليها فممكن تكون سبب في دمار
+
+282
+00:27:42,150 --> 00:27:51,270
+الجنين أو في ضرر الجنين طبعا
+
+283
+00:27:51,270 --> 00:27:58,490
+الجدول اللي موجود أمامنا بيوضح كم درجة الخطورة
+
+284
+00:27:58,490 --> 00:28:02,910
+اللي ممكن تصير على الجنين إذا اتعرضت الأم لل
+
+285
+00:28:02,910 --> 00:28:06,930
+Teratogen هذه في كل فترة من الحمل
+
+286
+00:28:10,080 --> 00:28:14,540
+إذا كان عمر الـ embryo من واحد إلى اثنين أسبوع طبعا
+
+287
+00:28:14,540 --> 00:28:21,160
+نحكي على الأسابيع و اتعرضت الأم في أول أيام
+
+288
+00:28:21,160 --> 00:28:26,420
+Lateral genes عوامل ممكن تلوث ممكن مواد كيميائية
+
+289
+00:28:26,420 --> 00:28:31,960
+أي إن كان وهي مرحلة انقسام الـ zygote مرحلة
+
+290
+00:28:31,960 --> 00:28:35,340
+الـ zygote في الغالب هيكون عملية الإجهاض و الـ
+
+291
+00:28:35,340 --> 00:28:40,960
+prenatal death ال death لهذا ال fetus هو القرار أو
+
+292
+00:28:40,960 --> 00:28:53,000
+المصير الأكيد إذا كان عمر الجنين 3,4,5,6,7,8,9
+
+293
+00:28:53,000 --> 00:29:03,520
+أسابيع هلاجي أنه الفترة الثانية من الحمل بتأثر بشكل
+
+294
+00:29:03,520 --> 00:29:08,060
+كبير جدا أو فترة ال first trimester الأول تلت شهور
+
+295
+00:29:08,060 --> 00:29:15,200
+هي أكثر مرحلة خاطرة على تكون الجنين وعلى نمو الجنين
+
+296
+00:29:15,200 --> 00:29:19,420
+في الشهر .. في الأسبوع الثالث مشاكل في الجهاز
+
+297
+00:29:19,420 --> 00:29:24,620
+القلبي و العصبي و مشاكل في القلب لو اتعرضت لمخاطر في
+
+298
+00:29:24,620 --> 00:29:29,800
+أسبوع الرابع هيكون في مشاكل في النظر مشاكل في
+
+299
+00:29:29,800 --> 00:29:36,110
+القلب في الأسبوع الخامس و في الأطراف مشاكل في السمع
+
+300
+00:29:36,110 --> 00:29:39,630
+مشاكل في الأسنان في نمو الأسنان ممكن يصير في
+
+301
+00:29:39,630 --> 00:29:44,710
+الأسبوع السادس تشوهات
+
+302
+00:29:44,710 --> 00:29:50,350
+كتير ممكن تكون موجودة ممكن نشوفها عند الجنين إذا
+
+303
+00:29:50,350 --> 00:29:55,110
+تعرضت الأم ما بين الأسبوع الثالث من الحمل لأسبوع
+
+304
+00:29:55,110 --> 00:30:01,010
+الثامن ممكن نشوف تشوهات في الجنين
+
+305
+00:30:03,580 --> 00:30:08,600
+لكن عند تسع شهور أو تسع أسابيع أو ستة عشر أسبوع طبعا
+
+306
+00:30:08,600 --> 00:30:13,340
+تبدأ تقل شوية شوية لكن عند تسع أسابيع هنلاقي ان ال
+
+307
+00:30:13,340 --> 00:30:17,460
+brain ممكن يصير فيه damage بشكل كبير جدا و خصوصا
+
+308
+00:30:17,460 --> 00:30:22,240
+الوظائف تبعته وهذا لا يعني ان بس فقط هذه المراحل
+
+309
+00:30:22,240 --> 00:30:26,620
+هي الأكثر خطورة لأ طول فترة الحمل الأم بتظلها
+
+310
+00:30:26,620 --> 00:30:34,110
+معرضة لإنه يصير في عندها مشاكل في النمو تبع الجنين
+
+311
+00:30:34,110 --> 00:30:38,730
+و ممكن تنتج عنه إعاقات إذا تعرضت لبعض الـ
+
+312
+00:30:38,730 --> 00:30:44,510
+teratogens العوامل البيئية اللي ممكن تأثر على
+
+313
+00:30:44,510 --> 00:30:49,870
+عملية النمو للجنين الآن
+
+314
+00:30:49,870 --> 00:30:59,310
+تمت نمو الجنين وبدأ ينولد أو جاهز لعملية الولادة
+
+315
+00:31:02,310 --> 00:31:07,650
+عملية الولادة طبعا هنلاقي ان عضلات الرحم هي العامل
+
+316
+00:31:07,650 --> 00:31:14,810
+الأساسي في عملية الولادة عشان هيك بنلاقي ان عضلات
+
+317
+00:31:14,810 --> 00:31:21,550
+جدار الرحم تبدأ تنقبض لما تبدأ تنقبض عضلات جدار
+
+318
+00:31:21,550 --> 00:31:27,550
+الرحم طبعا هي اللي بتكون بداية اللي احنا بسميها
+
+319
+00:31:27,550 --> 00:31:35,730
+الطلق عند السيدة الحامل تبدأ طبعا كل ما يزيد
+
+320
+00:31:35,730 --> 00:31:44,130
+الإنقباضات في عضلات الرحم بيزيد التوسع في عنق الرحم
+
+321
+00:31:44,130 --> 00:31:48,730
+the cervix is taken into the body of the uterus so
+
+322
+00:31:48,730 --> 00:31:55,290
+that the birth canal is wide وبالتالي تبدأ تتسع وتتوسع
+
+323
+00:31:55,290 --> 00:32:02,320
+قناة الولادة cervical dilatation begins and
+
+324
+00:32:02,320 --> 00:32:06,360
+especially after the fetal head enters the birth
+
+325
+00:32:06,360 --> 00:32:14,140
+canal مجرد ما يبدأ رأس الطفل يفوت على منطقة ال
+
+326
+00:32:14,140 --> 00:32:21,190
+cervix على منطقة عنق الرحم بتبدأ طبعا عنق الرحم
+
+327
+00:32:21,190 --> 00:32:26,410
+يتوسع بشكل كبير جدا the receptors اللي موجودة في
+
+328
+00:32:26,410 --> 00:32:31,530
+جدار الرحم و في عنق الرحم are stimulated و بيصيرلهم
+
+329
+00:32:31,530 --> 00:32:37,510
+تنبيه which reflexively causes secretion of
+
+330
+00:32:37,510 --> 00:32:43,690
+oxytocin مجرد ما يصير عملية ال stretch في عنق
+
+331
+00:32:43,690 --> 00:32:50,000
+الرحم تبدأ يفرز هرمون ال oxytocin من الـ posterior
+
+332
+00:32:50,000 --> 00:32:55,880
+pituitary gland الـ oxytocin وظيفته انه بيزود
+
+333
+00:32:55,880 --> 00:33:00,160
+انقباضات ال muscles اللي موجودة في جدار الرحم
+
+334
+00:33:00,160 --> 00:33:06,880
+و بيعمل توسع لعنق الرحم اذا بيوسع قناة الولادة
+
+335
+00:33:06,880 --> 00:33:14,560
+و بيزود انقباضات الرحم في عملية الولادة بيمر أو
+
+336
+00:33:14,560 --> 00:33:19,780
+بتمر في ثلاث مراحل المرحلة الأولى stage one اللي
+
+337
+00:33:19,780 --> 00:33:26,200
+بتشمل dilatation of the cervix مجرد ما ييجي الرأس
+
+338
+00:33:26,200 --> 00:33:33,800
+تجاه الرحم بيبدأ عملية ال stretching للرحم وبتبدأ
+
+339
+00:33:33,800 --> 00:33:38,670
+تتوسع قناة الولادة Contractions are greatest and
+
+340
+00:33:38,670 --> 00:33:43,270
+the cervix opens completely بيزيد عملية الإنقباضات
+
+341
+00:33:43,270 --> 00:33:53,170
+لعضلات الرحم تتوسع قناة الرحم و بتفتح كاملا حيث
+
+342
+00:33:53,170 --> 00:34:00,310
+أنها تسمح بمرور الرأس المرحلة الثانية بيبدأ يظهر
+
+343
+00:34:00,310 --> 00:34:07,120
+رأس الجنين أو رأس الطفل خلال عملية الولادة بعد هيك
+
+344
+00:34:07,120 --> 00:34:15,100
+بيكتمل عملية خروج الطفل من الرحم المرحلة الثالثة
+
+345
+00:34:15,100 --> 00:34:22,320
+هي مرحلة طرد أو تخلص من الـ placenta أو المشيمة
+
+346
+00:34:22,320 --> 00:34:29,280
+و بتتم فيها عملية يعني الـ Contractions بشكل أكبر وهذا
+
+347
+00:34:29,280 --> 00:34:35,560
+طبعا بيسحبها عملية النزيف لأنها ملتسقة بالأوعية
+
+348
+00:34:35,560 --> 00:34:42,060
+الدموية الخاصة بالـ  OM وبالتالي عند نزعها تعمل
+
+349
+00:34:42,060 --> 00:34:46,640
+ربشر بشكل كبير جدا للأوعية الدموية الموجودة في
+
+350
+00:34:46,640 --> 00:34:51,360
+منطقة الرحم وبالتالي تصبح عملية النزيف
+
+351
+00:34:55,030 --> 00:35:01,590
+هذه مراحل الولادة اللي احنا ممكن نشوفها طبعا زي ما
+
+352
+00:35:01,590 --> 00:35:07,760
+حكينا المرحلة الأولى هي مرحلة الضغط على قناة الرحم
+
+353
+00:35:07,760 --> 00:35:12,940
+و التوسع بالإضافة لمرحلة الانقباض البسيط اللي بيكون
+
+354
+00:35:12,940 --> 00:35:20,560
+في الرحم بيزيد الانقباض بيزيد توسع قناة الرحم بعد
+
+355
+00:35:20,560 --> 00:35:25,940
+هيك بيبدأ يطلع الرأس مرحلة خروج الرأس من الرحم بعد
+
+356
+00:35:25,940 --> 00:35:30,080
+هيك بيطلع باقي الجسم و المرحلة الثالثة خروج ال
+
+357
+00:35:30,080 --> 00:35:33,960
+placenta أو التخلص من ال placenta بعد اكتمال عملية
+
+358
+00:35:33,960 --> 00:35:40,390
+الولادة هذه مراحل الولادة اللي احنا بنعرفها و
+
+359
+00:35:40,390 --> 00:35:46,470
+بنشوفها طبعا هذا هو عبارة عن شرح للكلام اللي حكينا
+
+360
+00:35:46,470 --> 00:35:54,450
+عن موضوع الولادة الآن بعد ما ينولد الطفل بدنا
+
+361
+00:35:54,450 --> 00:36:00,450
+نتأكد نشوف ان الطفل هذا سليم ولا في عنده بعض
+
+362
+00:36:00,450 --> 00:36:07,060
+المشاكل طبعا عشان يعملوا هذا ال test فيه immediate
+
+363
+00:36:07,060 --> 00:36:12,840
+assessment فحص مباشر بعد عملية الولادة بيعملوا
+
+364
+00:36:12,840 --> 00:36:17,600
+evaluation لل respiratory and cardiac function فحص
+
+365
+00:36:17,600 --> 00:36:23,380
+التنفس و فحص الدورة الدموية من خلال test بيسموه
+
+366
+00:36:23,380 --> 00:36:30,180
+Apgar test الـ Apgar test هذا طبعا مدته اللي مسموح
+
+367
+00:36:30,180 --> 00:36:36,770
+انه نعملها من one minute  بعد الولادة لحد خمس دقائق إذا
+
+368
+00:36:36,770 --> 00:36:43,930
+زادت عن خمس دقائق بيفقد الهدف اللي هو ان عمل عشانه
+
+369
+00:36:43,930 --> 00:36:52,810
+و بيفقد وظيفته كفحص ممكن يفيدنا بيفحص طبعا ال heart
+
+370
+00:36:52,810 --> 00:36:58,220
+rate إذا كان في أول طبعا قولنا أول من دقيقة لخمس
+
+371
+00:36:58,220 --> 00:37:03,760
+دقائق absent ممكن تكون بنعطيله zero less than one
+
+372
+00:37:03,760 --> 00:37:07,780
+hundred بنعطيله واحد over one hundred بنعطيله
+
+373
+00:37:07,780 --> 00:37:12,840
+اثنين respiratory effort اذا كان ما تنفسش الطفل
+
+374
+00:37:12,840 --> 00:37:18,080
+يعطوله absent يعني بيعطوله zero slow and irregular
+
+375
+00:37:18,080 --> 00:37:24,200
+بطيء و غير منتظم بيعطوله واحد crying بيعطوله اثنين
+
+376
+00:37:24,200 --> 00:37:32,570
+إذا انولد الطفل بيبصرخ أو بيبكي، muscle tone إذا كانت
+
+377
+00:37:32,570 --> 00:37:38,610
+flaccid بيعطيه zero، some affliction of extremity
+
+378
+00:37:38,610 --> 00:37:43,090
+بيعطيه واحد، active movement بيحرك الحركات
+
+379
+00:37:43,090 --> 00:37:49,010
+العشوائية، بيعطيه اثنين، reflex irritability إذا كان
+
+380
+00:37:49,010 --> 00:37:54,870
+مافي أي استجابة لردات الفعل أو reflexes اللي بتنفحص 
+
+381
+00:37:54,870 --> 00:38:01,950
+طبعا هنا بيعطيه zero، إذا كان weak cry بيبكي لكن
+
+382
+00:38:01,950 --> 00:38:07,950
+بشكل ضعيف بيعطيه واحد، vigorous cry بيعطيه 
+
+383
+00:38:07,950 --> 00:38:16,570
+اثنين، يعني إذا كان ردة الفعل cry بالبكاء بيعطيه 
+
+384
+00:38:16,570 --> 00:38:21,770
+واحد، vigorous cry بيعطيه اثنين، the color اللون
+
+385
+00:38:21,770 --> 00:38:28,120
+تبع ال skin إذا كان blue or pale، absent يعني بياخد
+
+386
+00:38:28,120 --> 00:38:33,480
+zero، اللون الأزرق أو الشاحب، إذا كان pink body
+
+387
+00:38:33,480 --> 00:38:38,940
+بياخد واحد، entire body is pink إذا كان كل الجسم
+
+388
+00:38:38,940 --> 00:38:46,040
+لونه وردي بياخد درجة اثنين، الآن 
+
+389
+00:38:46,040 --> 00:38:51,820
+من خلال النتائج اللي اتجمعت من خلال الفحص، إذا كان
+
+390
+00:38:51,820 --> 00:38:56,820
+ال score تبع الطفل من سبعة إلى عشرة معناه أن الطفل
+
+391
+00:38:56,820 --> 00:39:02,240
+طبيعي، إذا كان ال score من أربعة إلى ستة معناه إنه
+
+392
+00:39:02,240 --> 00:39:07,140
+في عنده بيحتاج some assistant و special assistant
+
+393
+00:39:07,140 --> 00:39:12,540
+ممكن يفوت الحضانة، ممكن يحتاج فترة من الحضانة، إذا
+
+394
+00:39:12,540 --> 00:39:18,900
+كان ال score أقل من أربعة بيحتاج رعاية مكثفة
+
+395
+00:39:18,900 --> 00:39:24,000
+وبيحتاج عناية كبيرة، هيك
+
+396
+00:39:24,000 --> 00:39:28,340
+احنا بتبقى خلصنا مرحلة the development of the fetus
+
+397
+00:39:28,340 --> 00:39:34,420
+وشوفنا كيف عملية الدورة الدموية الخاصة بالجنين
+
+398
+00:39:34,420 --> 00:39:39,040
+وبعد هيك شوفنا كيف ممكن انه .. وشوفنا عملية
+
+399
+00:39:39,040 --> 00:39:44,060
+الولادة، وكيف نطمن على الجنين بعد عملية الولادة
+
+400
+00:39:44,500 --> 00:39:46,880
+المرة اللي جاي إن شاء الله رب العالمين هنحكي عن
+
+401
+00:39:46,880 --> 00:39:49,820
+the Reflexes of the child
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/VqGaLfbVVZ8_raw.json b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/VqGaLfbVVZ8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ffb1744751a4da85f07f9885a8f91d69914a3204
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/VqGaLfbVVZ8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2284, "start": 0.0, "end": 22.84, "text": "السلام عليكم و رحمة الله و بركاته اليوم ان شاء الله رب العالمين هنتكلم او هنكمل في موضوع ال fetal development فهنتكلم عن البلسينتا و نتكلم عن ال fetal circulation بداية بدنا نعرف ان البلسينتا كحجم تقريبا 15 cm ال diameter تبعها", "tokens": [6027, 3794, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984, 4032, 4724, 31747, 9307, 3224, 45595, 20498, 16472, 13412, 16606, 21984, 12602, 3555, 18863, 45340, 9957, 8032, 29399, 4117, 19528, 1975, 2407, 8032, 1863, 24793, 1211, 8978, 3714, 2407, 11242, 45367, 2423, 15136, 304, 3250, 6156, 3224, 29399, 4117, 19528, 18871, 29739, 1211, 3794, 9957, 2655, 995, 4032, 8717, 2655, 4117, 19528, 18871, 2423, 15136, 304, 23168, 4724, 28259, 10632, 47525, 8315, 8717, 3615, 28480, 16472, 29739, 1211, 3794, 9957, 2655, 995, 9122, 5016, 7435, 2304, 6055, 4587, 16572, 3555, 995, 2119, 14668, 2423, 14196, 6055, 3555, 3615, 11296], "avg_logprob": -0.18406249657273294, 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4.3, "end": 4.7, "word": " العالمين", "probability": 0.9943033854166666}, {"start": 4.7, "end": 5.54, "word": " هنتكلم", "probability": 0.93603515625}, {"start": 5.54, "end": 5.84, "word": " او", "probability": 0.752685546875}, {"start": 5.84, "end": 6.78, "word": " هنكمل", "probability": 0.96044921875}, {"start": 6.78, "end": 7.16, "word": " في", "probability": 0.86083984375}, {"start": 7.16, "end": 7.68, "word": " موضوع", "probability": 0.98095703125}, {"start": 7.68, "end": 8.12, "word": " ال", "probability": 0.9111328125}, {"start": 8.12, "end": 8.5, "word": " fetal", "probability": 0.607666015625}, {"start": 8.5, "end": 9.06, "word": " development", "probability": 0.947265625}, {"start": 9.06, "end": 10.4, "word": " فهنتكلم", "probability": 0.8548828125}, {"start": 10.4, "end": 10.84, "word": " عن", "probability": 0.99169921875}, {"start": 10.84, "end": 11.88, "word": " البلسينتا", "probability": 0.6142171223958334}, {"start": 11.88, "end": 12.52, "word": " و", "probability": 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"end": 20.4, "word": " 15", "probability": 0.8916015625}, {"start": 20.4, "end": 21.36, "word": " cm", "probability": 0.435302734375}, {"start": 21.36, "end": 21.9, "word": " ال", "probability": 0.18408203125}, {"start": 21.9, "end": 22.18, "word": " diameter", "probability": 0.9169921875}, {"start": 22.18, "end": 22.84, "word": " تبعها", "probability": 0.909912109375}], "temperature": 1.0}, {"id": 2, "seek": 3865, "start": 23.39, "end": 38.65, "text": "الـ thickness تبعها من أربع إلى خمس centimeter ال weight تبعها حوالي خمسمية gram تقريبا نصف كيلو the placenta is essentially a vascular organ تعتبر ال placenta", "tokens": [6027, 39184, 14855, 6055, 3555, 3615, 11296, 9154, 5551, 25513, 3615, 30731, 16490, 2304, 3794, 31914, 2423, 3364, 6055, 3555, 3615, 11296, 11331, 2407, 6027, 1829, 16490, 2304, 38251, 10632, 21353, 6055, 4587, 16572, 3555, 995, 8717, 9381, 5172, 9122, 26895, 2407, 264, 20831, 8938, 307, 4476, 257, 371, 22084, 1798, 6055, 34268, 26890, 2423, 20831, 8938], 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احنا شايفين", "tokens": [3555, 13546, 2407, 5016, 15844, 4032, 9957, 4724, 1829, 17082, 8848, 1829, 14739, 3794, 7435, 3660, 25062, 46152, 4724, 1829, 17082, 8848, 1829, 14739, 3794, 7435, 3660, 34892, 19986, 2655, 9957, 1975, 8315, 24525, 5172, 4724, 1829, 17082, 8848, 1829, 14739, 3794, 7435, 3660, 34892, 19986, 2655, 9957, 1975, 15730, 32748, 2304, 13672, 1829, 39894, 39237, 48812, 9778, 3224, 9154, 16490, 1211, 6027, 2423, 39184, 8331, 46386, 38520, 30767, 1829, 19446, 1975, 5016, 8315, 13412, 995, 33911, 9957], "avg_logprob": -0.19115901747836342, "compression_ratio": 1.7297297297297298, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 525.98, "end": 526.64, "word": "بيروح", "probability": 0.78607177734375}, {"start": 526.64, "end": 526.98, "word": " على", "probability": 0.6162109375}, {"start": 526.98, "end": 527.42, "word": " وين", "probability": 0.818359375}, {"start": 527.42, "end": 528.54, "word": " بيغذي", "probability": 0.758154296875}, {"start": 528.54, "end": 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"text": "هذه تقريبا نسبة تمانية في المية بتغذي الدم left ventricle من خلال الأورطة زي ما حكينا أن ال alveolus أو ال alveoli حواصلات الهوائية لسه مش شغالة not activated in the lungs فبالتالي", "tokens": [3224, 24192, 6055, 4587, 16572, 3555, 995, 8717, 35457, 3660, 46811, 7649, 10632, 8978, 9673, 10632, 39894, 17082, 8848, 1829, 32748, 2304, 1411, 6931, 1341, 306, 9154, 16490, 1211, 6027, 16247, 13063, 9566, 3660, 30767, 1829, 19446, 11331, 4117, 1829, 8315, 14739, 2423, 419, 303, 401, 301, 34051, 2423, 419, 303, 9384, 11331, 2407, 33546, 1211, 9307, 2423, 3224, 2407, 16373, 10632, 5296, 3794, 3224, 37893, 13412, 17082, 6027, 3660, 406, 18157, 294, 264, 19467, 6156, 3555, 6027, 2655, 6027, 1829], "avg_logprob": -0.24504572916321637, "compression_ratio": 1.4631578947368422, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 551.24, "end": 551.64, "word": "هذه", "probability": 0.541015625}, {"start": 551.64, "end": 552.2, "word": " تقريبا", "probability": 0.9171875}, {"start": 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{"start": 736.24, "end": 736.44, "word": " احنا", "probability": 0.8619791666666666}, {"start": 736.44, "end": 736.88, "word": " شفنا", "probability": 0.8701171875}, {"start": 736.88, "end": 737.7, "word": " الدورة", "probability": 0.9724934895833334}, {"start": 737.7, "end": 738.4, "word": " الدموية", "probability": 0.969482421875}, {"start": 738.4, "end": 739.62, "word": " الخاصة", "probability": 0.97802734375}, {"start": 739.62, "end": 740.78, "word": " بالفيتس", "probability": 0.7305908203125}, {"start": 740.78, "end": 741.02, "word": " في", "probability": 0.93701171875}, {"start": 741.02, "end": 741.44, "word": " أثناء", "probability": 0.9234619140625}, {"start": 741.44, "end": 741.94, "word": " وجوده", "probability": 0.9947916666666666}, {"start": 741.94, "end": 742.12, "word": " في", "probability": 0.83642578125}, {"start": 742.12, "end": 742.66, "word": " داخل", "probability": 0.9563802083333334}, {"start": 742.66, "end": 743.32, "word": " الرحل", "probability": 0.814453125}, {"start": 743.32, "end": 743.76, "word": " الان", "probability": 0.6197509765625}, {"start": 743.76, "end": 744.3, "word": " نيجي", "probability": 0.9090576171875}, {"start": 744.3, "end": 747.14, "word": " لمراحل", "probability": 0.8602294921875}, {"start": 747.14, "end": 748.4, "word": " النمو", "probability": 0.9637044270833334}], "temperature": 1.0}, {"id": 31, "seek": 77742, "start": 748.94, "end": 777.42, "text": "في داخل الرحم وقلنا انه from nine weeks after conception to birth وسمناها الفترة هذه period of fetus conception to birth من فترة الإخصاب لحد الولادة increase in size and systems begin to function", "tokens": [41185, 11778, 47283, 1211, 34892, 35571, 4032, 4587, 1211, 8315, 16472, 3224, 490, 4949, 3259, 934, 30698, 281, 3965, 4032, 38251, 8315, 11296, 27188, 2655, 25720, 29538, 2896, 295, 15136, 301, 30698, 281, 3965, 9154, 6156, 2655, 25720, 33688, 9778, 9381, 16758, 5296, 24401, 2423, 12610, 18513, 3660, 3488, 294, 2744, 293, 3652, 1841, 281, 2445], "avg_logprob": 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{"start": 755.6, "end": 755.96, "word": " birth", "probability": 0.97216796875}, {"start": 755.96, "end": 758.84, "word": " وسمناها", "probability": 0.807861328125}, {"start": 758.84, "end": 759.26, "word": " الفترة", "probability": 0.9728190104166666}, {"start": 759.26, "end": 759.66, "word": " هذه", "probability": 0.91943359375}, {"start": 759.66, "end": 760.52, "word": " period", "probability": 0.953125}, {"start": 760.52, "end": 761.2, "word": " of", "probability": 0.98388671875}, {"start": 761.2, "end": 762.0, "word": " fetus", "probability": 0.889404296875}, {"start": 762.0, "end": 764.96, "word": " conception", "probability": 0.89111328125}, {"start": 764.96, "end": 765.66, "word": " to", "probability": 0.970703125}, {"start": 765.66, "end": 766.08, "word": " birth", "probability": 0.97216796875}, {"start": 766.08, "end": 768.02, "word": " من", "probability": 0.98193359375}, {"start": 768.02, "end": 768.62, "word": " فترة", "probability": 0.9192708333333334}, {"start": 768.62, 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أجهزة الجسم عنده تشتغل age of viability 22 ل 28 أسبوع العمر اللي بيكون أو تبات فيه الروح بيكون فيه الانسجة أو هذا الجنين حي كائن حي على عمر 22 إلى 30", "tokens": [3555, 2655, 44510, 10721, 6055, 11622, 25708, 11331, 7435, 2304, 25724, 1863, 9957, 46599, 2655, 44510, 10721, 5551, 7435, 3224, 11622, 3660, 25724, 38251, 43242, 3224, 6055, 8592, 2655, 17082, 1211, 3205, 295, 1932, 2310, 5853, 5296, 7562, 5551, 35457, 45367, 18863, 29973, 13672, 1829, 4724, 1829, 30544, 34051, 6055, 3555, 9307, 8978, 3224, 2423, 32887, 5016, 4724, 1829, 30544, 8978, 3224, 2423, 7649, 3794, 7435, 3660, 34051, 23758, 25724, 1863, 9957, 11331, 1829, 9122, 16373, 1863, 11331, 1829, 15844, 6225, 29973, 5853, 30731, 2217], "avg_logprob": -0.231104644751826, "compression_ratio": 1.6021505376344085, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 778.71, "end": 779.19, "word": "بتبدأ", "probability": 0.741546630859375}, {"start": 779.19, "end": 779.75, "word": " تزيد", "probability": 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احنا شايفين by the end of the first month the imperial is about one واحدة على عشرة of an inch عشر انش زي ما احنا شايفين كيف في داخل الرحم مش مبين لكن لو جينا نفصل أكتر هلاجي انه في بعض", "tokens": [3615, 23942, 6225, 29973, 5853, 30731, 7562, 5551, 35457, 45367, 8978, 25124, 3224, 2288, 16247, 12610, 30767, 1829, 19446, 1975, 5016, 8315, 13412, 995, 33911, 9957, 538, 264, 917, 295, 264, 700, 1618, 264, 21143, 307, 466, 472, 36764, 24401, 3660, 15844, 6225, 8592, 25720, 295, 364, 7227, 6225, 46309, 16472, 8592, 30767, 1829, 19446, 1975, 5016, 8315, 13412, 995, 33911, 9957, 9122, 33911, 8978, 11778, 47283, 1211, 34892, 35571, 37893, 3714, 3555, 9957, 44381, 45164, 10874, 1829, 8315, 8717, 5172, 36520, 5551, 4117, 2655, 2288, 8032, 15040, 7435, 1829, 16472, 3224, 8978, 45030, 11242], "avg_logprob": -0.17236328140522042, "compression_ratio": 1.588235294117647, "no_speech_prob": 4.470348358154297e-06, "words": [{"start": 807.52, "end": 807.8, "word": "على", "probability": 0.877685546875}, {"start": 807.8, "end": 808.02, "word": " عمر", "probability": 0.91748046875}, {"start": 808.02, "end": 808.64, "word": " 22", "probability": 0.71630859375}, {"start": 808.64, "end": 808.82, "word": " إلى", "probability": 0.323486328125}, {"start": 808.82, "end": 809.34, "word": " 28", "probability": 0.97998046875}, {"start": 809.34, "end": 810.3, "word": " أسبوع", "probability": 0.9007161458333334}, {"start": 810.3, "end": 813.68, "word": " في", "probability": 0.8173828125}, {"start": 813.68, "end": 814.06, "word": " الشهر", "probability": 0.9910481770833334}, {"start": 814.06, "end": 814.58, "word": " الأول", "probability": 0.98681640625}, {"start": 814.58, "end": 815.86, "word": " زي", "probability": 0.5914306640625}, {"start": 815.86, "end": 815.94, "word": " ما", "probability": 0.92919921875}, {"start": 815.94, "end": 816.06, "word": " احنا", "probability": 0.8388671875}, {"start": 816.06, "end": 816.6, "word": " شايفين", "probability": 0.982177734375}, {"start": 816.6, "end": 816.96, "word": " by", "probability": 0.5078125}, {"start": 816.96, "end": 817.18, "word": " the", "probability": 0.92138671875}, {"start": 817.18, "end": 817.56, "word": " end", "probability": 0.90673828125}, {"start": 817.56, "end": 817.84, "word": " of", "probability": 0.982421875}, {"start": 817.84, "end": 818.0, "word": " the", "probability": 0.8984375}, {"start": 818.0, "end": 818.36, "word": " first", "probability": 0.9072265625}, {"start": 818.36, "end": 818.82, "word": " month", "probability": 0.9169921875}, {"start": 818.82, "end": 819.52, "word": " the", "probability": 0.541015625}, {"start": 819.52, "end": 819.9, "word": " imperial", "probability": 0.2498779296875}, {"start": 819.9, "end": 820.24, "word": " is", "probability": 0.90966796875}, {"start": 820.24, "end": 821.28, "word": " about", "probability": 0.9267578125}, {"start": 821.28, "end": 821.84, "word": " one", "probability": 0.662109375}, {"start": 821.84, "end": 823.24, "word": " واحدة", "probability": 0.7451171875}, {"start": 823.24, "end": 823.38, "word": " على", "probability": 0.6982421875}, {"start": 823.38, "end": 824.18, "word": " عشرة", "probability": 0.9072265625}, {"start": 824.18, "end": 824.48, "word": " of", "probability": 0.9140625}, {"start": 824.48, "end": 824.86, "word": " an", "probability": 0.7734375}, {"start": 824.86, "end": 825.34, "word": " inch", "probability": 0.96728515625}, {"start": 825.34, "end": 826.12, "word": " عشر", "probability": 0.936767578125}, {"start": 826.12, "end": 826.72, "word": " انش", "probability": 0.776123046875}, {"start": 826.72, "end": 827.46, "word": " زي", "probability": 0.9365234375}, {"start": 827.46, "end": 827.54, "word": " ما", "probability": 0.962890625}, {"start": 827.54, "end": 827.68, "word": " احنا", "probability": 0.9508463541666666}, {"start": 827.68, "end": 828.12, "word": " شايفين", "probability": 0.9930419921875}, {"start": 828.12, "end": 828.5, "word": " كيف", "probability": 0.811279296875}, {"start": 828.5, "end": 828.96, "word": " في", "probability": 0.7509765625}, {"start": 828.96, "end": 829.38, "word": " داخل", "probability": 0.8138020833333334}, {"start": 829.38, "end": 829.82, "word": " الرحم", "probability": 0.939453125}, {"start": 829.82, "end": 830.62, "word": " مش", "probability": 0.96826171875}, {"start": 830.62, "end": 831.16, "word": " مبين", "probability": 0.9173177083333334}, {"start": 831.16, "end": 831.96, "word": " لكن", "probability": 0.880859375}, {"start": 831.96, "end": 832.2, "word": " لو", "probability": 0.97509765625}, {"start": 832.2, "end": 832.48, "word": " جينا", "probability": 0.9835611979166666}, {"start": 832.48, "end": 833.0, "word": " نفصل", "probability": 0.7928059895833334}, {"start": 833.0, "end": 833.48, "word": " أكتر", "probability": 0.890625}, {"start": 833.48, "end": 834.02, "word": " هلاجي", "probability": 0.786376953125}, {"start": 834.02, "end": 834.52, "word": " انه", "probability": 0.777587890625}, {"start": 834.52, "end": 834.88, "word": " في", 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أو", "probability": 0.6142578125}, {"start": 850.74, "end": 852.12, "word": " البرتقال", "probability": 0.95498046875}, {"start": 852.12, "end": 856.42, "word": " وفي", "probability": 0.577392578125}, {"start": 856.42, "end": 856.72, "word": " هذه", "probability": 0.9072265625}, {"start": 856.72, "end": 857.26, "word": " الفترة", "probability": 0.98974609375}, {"start": 857.26, "end": 858.3, "word": " بيبدأ", "probability": 0.9241943359375}, {"start": 858.3, "end": 858.92, "word": " القلب", "probability": 0.99560546875}, {"start": 858.92, "end": 859.82, "word": " ينبط", "probability": 0.9141845703125}], "temperature": 1.0}, {"id": 35, "seek": 88750, "start": 863.88, "end": 887.5, "text": "زي ما احنا شايفين كيف صورة حقيقية للجنين في خلال الشهر الأول، لاحظوا كيف؟ وهذه مكبرة ألاف المرات، مكبرة ألاف المرات في الشهر التاني، the embryo is about one inch length طوله تقريبا واحد إنش", "tokens": [11622, 1829, 19446, 1975, 5016, 8315, 13412, 995, 33911, 9957, 9122, 33911, 20328, 13063, 3660, 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{"start": 883.74, "end": 884.3, "word": " inch", "probability": 0.76416015625}, {"start": 884.3, "end": 885.08, "word": " length", "probability": 0.73974609375}, {"start": 885.08, "end": 885.9, "word": " طوله", "probability": 0.8395182291666666}, {"start": 885.9, "end": 886.5, "word": " تقريبا", "probability": 0.98857421875}, {"start": 886.5, "end": 887.08, "word": " واحد", "probability": 0.95068359375}, {"start": 887.08, "end": 887.5, "word": " إنش", "probability": 0.74609375}], "temperature": 1.0}, {"id": 36, "seek": 91786, "start": 888.2, "end": 917.86, "text": "has a distinct slightly webbed fingers تبدأ شكل الأصابع الإيدين تبدأ تظهر شوية شوية veins are clearly visible الأوردة واضحة ومرئية the heart has divided into right and left chambers القلب في هذه العمر منقسم إلى جزئين الجزء الأيمن والجزء الأيسر", "tokens": [12438, 257, 10644, 4748, 3670, 2883, 7350, 6055, 44510, 10721, 13412, 28820, 16247, 9381, 16758, 3615, 33688, 25708, 9957, 6055, 44510, 10721, 6055, 19913, 3224, 2288, 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الحجم five months عند خمس شهور a protective coating called vernix", "tokens": [15040, 5016, 19913, 14407, 9122, 33911, 21542, 7435, 2304, 6055, 3555, 3615, 3224, 20328, 9640, 4032, 4117, 33911, 30767, 7578, 19446, 11331, 4117, 1829, 8315, 28242, 5551, 7435, 3224, 11622, 3660, 25724, 38251, 44650, 30544, 3660, 44381, 6055, 11622, 3215, 18513, 8717, 2304, 2407, 11296, 8978, 21542, 7435, 2304, 1732, 2493, 43242, 16490, 2304, 3794, 13412, 3224, 13063, 257, 16314, 20163, 1219, 35793, 970], "avg_logprob": -0.15096153846153845, "compression_ratio": 1.3588235294117648, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1085.5, "end": 1086.46, "word": "لاحظوا", "probability": 0.931396484375}, {"start": 1086.46, "end": 1087.02, "word": " كيف", "probability": 0.958984375}, {"start": 1087.02, "end": 1087.92, "word": " الحجم", "probability": 0.9723307291666666}, {"start": 1087.92, "end": 1088.82, "word": " تبعه", "probability": 0.69580078125}, {"start": 1088.82, "end": 1089.06, "word": " 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reflexively cause secretion of oxytocin مجرد ما يصير عملية ال stretch في عنق الرحم تبدأ يفرز هرمون ال oxytocin", "tokens": [3555, 2655, 44510, 10721, 23032, 3555, 3615, 995, 18871, 4587, 34892, 35571, 7251, 2655, 41779, 3615, 4724, 8592, 28820, 9122, 3555, 13546, 10874, 28259, 2423, 39184, 1300, 1336, 830, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 10874, 3215, 9640, 34892, 35571, 4032, 8978, 18871, 4587, 34892, 35571, 8983, 6987, 4032, 4724, 1829, 9381, 13546, 1211, 16095, 6055, 1863, 21292, 3224, 597, 23802, 3413, 3082, 4054, 313, 295, 5976, 4328, 905, 259, 3714, 7435, 2288, 3215, 19446, 7251, 9381, 13546, 6225, 42213, 10632, 2423, 5985, 8978, 18871, 4587, 34892, 35571, 6055, 44510, 10721, 7251, 5172, 2288, 11622, 8032, 2288, 2304, 11536, 2423, 5976, 4328, 905, 259], "avg_logprob": -0.15566038284099326, "compression_ratio": 1.5895196506550218, "no_speech_prob": 4.0471553802490234e-05, "words": [{"start": 1938.31, "end": 1939.03, "word": "بتبدأ", "probability": 0.8929443359375}, 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reflexively", "probability": 0.683837890625}, {"start": 1955.49, "end": 1956.41, "word": " cause", "probability": 0.60888671875}, {"start": 1956.41, "end": 1957.19, "word": " secretion", "probability": 0.9521484375}, {"start": 1957.19, "end": 1957.51, "word": " of", "probability": 0.970703125}, {"start": 1957.51, "end": 1958.35, "word": " oxytocin", "probability": 0.94140625}, {"start": 1958.35, "end": 1959.95, "word": " مجرد", "probability": 0.97265625}, {"start": 1959.95, "end": 1960.17, "word": " ما", "probability": 0.96728515625}, {"start": 1960.17, "end": 1960.85, "word": " يصير", "probability": 0.95751953125}, {"start": 1960.85, "end": 1961.29, "word": " عملية", "probability": 0.98779296875}, {"start": 1961.29, "end": 1961.47, "word": " ال", "probability": 0.79541015625}, {"start": 1961.47, "end": 1961.95, "word": " stretch", "probability": 0.4482421875}, {"start": 1961.95, "end": 1963.01, "word": " في", "probability": 0.95458984375}, {"start": 1963.01, "end": 1963.69, "word": " عنق", "probability": 0.995361328125}, {"start": 1963.69, "end": 1964.11, "word": " الرحم", "probability": 0.986572265625}, {"start": 1964.11, "end": 1965.29, "word": " تبدأ", "probability": 0.810302734375}, {"start": 1965.29, "end": 1965.71, "word": " يفرز", "probability": 0.9410400390625}, {"start": 1965.71, "end": 1966.25, "word": " هرمون", "probability": 0.9486083984375}, {"start": 1966.25, "end": 1966.59, "word": " ال", "probability": 0.90771484375}, {"start": 1966.59, "end": 1967.45, "word": " oxytocin", "probability": 0.8348388671875}], "temperature": 1.0}, {"id": 79, "seek": 199656, "start": 1968.94, "end": 1996.56, "text": "من الـ posterior pituitary gland الـ oxytocin فيديته انه بيزود انقباضات ال muscles اللي موجودة في جدار الرحم وبيعمل توسع لعنق الرحم اذا بيوسع قناة الولادة وبيزود انقباضات الرحم في عملية الولادة بيمر او بتمر في ثلاث مراحل", "tokens": [27842, 2423, 39184, 33529, 10147, 1983, 822, 43284, 2423, 39184, 5976, 4328, 905, 259, 8978, 16254, 47395, 16472, 3224, 4724, 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dilatation of the cervix مجرد ما ييجي الرأس تجاه الرحم بيبدأ عملية ال stretching للرحم وبتبدأ تتوسع قناة الولادات", "tokens": [6027, 29973, 5016, 37977, 16247, 12610, 7578, 3233, 472, 13672, 7578, 39894, 8592, 42213, 11504, 267, 399, 295, 264, 39543, 970, 3714, 7435, 2288, 3215, 19446, 7251, 1829, 7435, 1829, 34892, 10721, 3794, 6055, 7435, 40294, 34892, 35571, 4724, 1829, 44510, 10721, 6225, 42213, 10632, 2423, 19632, 24976, 2288, 35571, 46599, 2655, 44510, 10721, 6055, 2655, 41779, 3615, 12174, 8315, 3660, 2423, 12610, 18513, 9307], "avg_logprob": -0.20655776063601175, "compression_ratio": 1.4156626506024097, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 1997.14, "end": 1997.84, "word": "المرحلة", "probability": 0.72943115234375}, {"start": 1997.84, "end": 1998.38, "word": " الأولى", "probability": 0.9757486979166666}, {"start": 1998.38, "end": 1998.78, "word": " stage", "probability": 0.244384765625}, {"start": 1998.78, "end": 1999.12, "word": " one", "probability": 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الرحم", "probability": 0.902587890625}, {"start": 2009.12, "end": 2010.22, "word": " بيبدأ", "probability": 0.9036865234375}, {"start": 2010.22, "end": 2010.58, "word": " عملية", "probability": 0.9734700520833334}, {"start": 2010.58, "end": 2010.72, "word": " ال", "probability": 0.7587890625}, {"start": 2010.72, "end": 2011.28, "word": " stretching", "probability": 0.73486328125}, {"start": 2011.28, "end": 2012.82, "word": " للرحم", "probability": 0.767822265625}, {"start": 2012.82, "end": 2013.8, "word": " وبتبدأ", "probability": 0.81817626953125}, {"start": 2013.8, "end": 2014.36, "word": " تتوسع", "probability": 0.937255859375}, {"start": 2014.36, "end": 2014.76, "word": " قناة", "probability": 0.96875}, {"start": 2014.76, "end": 2015.44, "word": " الولادات", "probability": 0.858154296875}], "temperature": 1.0}, {"id": 81, "seek": 204549, "start": 2016.39, "end": 2045.49, "text": "Contraction are greatest and cervix open completely بزيد عملية الإنقباضات لعضلات الرحم تتوسع قناة الرحم وبتفتح كاملا حيث أنها تسمح بمرور الرأس المرحلة التانية بيبدأ يظهر رأس الجنين أو رأس الطفل خلال عملية الولادة", "tokens": [29821, 26766, 366, 6636, 293, 39543, 970, 1269, 2584, 4724, 11622, 25708, 6225, 42213, 10632, 33688, 1863, 4587, 3555, 46958, 9307, 5296, 3615, 11242, 1211, 9307, 34892, 35571, 6055, 2655, 41779, 3615, 12174, 8315, 3660, 34892, 35571, 46599, 2655, 5172, 2655, 5016, 9122, 10943, 15040, 11331, 1829, 12984, 14739, 11296, 6055, 38251, 5016, 4724, 29973, 13063, 34892, 10721, 3794, 9673, 2288, 5016, 37977, 16712, 7649, 10632, 4724, 1829, 44510, 10721, 7251, 19913, 3224, 2288, 12602, 10721, 3794, 25724, 1863, 9957, 34051, 12602, 10721, 3794, 41950, 5172, 1211, 16490, 1211, 6027, 6225, 42213, 10632, 2423, 12610, 18513, 3660], "avg_logprob": -0.09956951340546413, "compression_ratio": 1.5585585585585586, "no_speech_prob": 3.230571746826172e-05, "words": [{"start": 2016.39, "end": 2017.15, "word": "Contraction", "probability": 0.652587890625}, {"start": 2017.15, "end": 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2201.93, "end": 2202.55, "word": " اللي", "probability": 0.89111328125}, {"start": 2202.55, "end": 2202.85, "word": " هو", "probability": 0.90185546875}, {"start": 2202.85, "end": 2203.07, "word": " ان", "probability": 0.5380859375}, {"start": 2203.07, "end": 2203.33, "word": " عمل", "probability": 0.9560546875}, {"start": 2203.33, "end": 2203.93, "word": " عشانه", "probability": 0.8837890625}, {"start": 2203.93, "end": 2205.77, "word": " وبيفقد", "probability": 0.8470458984375}, {"start": 2205.77, "end": 2206.37, "word": " وظيفته", "probability": 0.9912109375}, {"start": 2206.37, "end": 2207.57, "word": " كفحص", "probability": 0.9786376953125}, {"start": 2207.57, "end": 2208.11, "word": " ممكن", "probability": 0.986328125}, {"start": 2208.11, "end": 2209.85, "word": " يفيدنا", "probability": 0.903564453125}, {"start": 2209.85, "end": 2211.79, "word": " بيفحص", "probability": 0.8909912109375}, {"start": 2211.79, "end": 2212.23, "word": " طبعا", "probability": 0.9678955078125}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/e0Je6309y2A_raw.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/e0Je6309y2A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ac9c429eb6bf8206e5614ee8a2badf1dc1346316
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/e0Je6309y2A_raw.srt
@@ -0,0 +1,2132 @@
+1
+00:00:00,000 --> 00:00:03,220
+الله بركاته هنتكلم في محاضرتنا اليوم ان شاء الله
+
+2
+00:00:03,220 --> 00:00:07,280
+رب العالمين عن ال reflexes المقصود بال reflexes
+
+3
+00:00:07,280 --> 00:00:13,360
+اللي هي المنعكسات العصبية لو جينا نتطلع على ال
+
+4
+00:00:13,360 --> 00:00:17,440
+definitions of reflexes شو المقصود بالreflexes؟
+
+5
+00:00:20,100 --> 00:00:24,060
+كتعريف reflexes are involuntary movements or
+
+6
+00:00:24,060 --> 00:00:28,240
+actions some movements are spontaneous occurring
+
+7
+00:00:28,240 --> 00:00:32,920
+as a part of the baby usual activity others are
+
+8
+00:00:32,920 --> 00:00:37,920
+responses to certain action generally reflexes
+
+9
+00:00:37,920 --> 00:00:41,860
+will be integrated or suppressed by the age of
+
+10
+00:00:41,860 --> 00:00:49,180
+nine to twelve months reflexes هي عبارة عن حركاتلا
+
+11
+00:00:49,180 --> 00:00:55,610
+إيرادية involuntary movementsأو actions أو تصرفات
+
+12
+00:00:55,610 --> 00:01:00,670
+مش بالضرورة تكون movement some movements are
+
+13
+00:01:00,670 --> 00:01:05,810
+spontaneous بعض هذه الحركات تلقائية occurring as a
+
+14
+00:01:05,810 --> 00:01:10,010
+part of the baby's usual activity هي جزء من النشاط
+
+15
+00:01:10,010 --> 00:01:13,770
+الطبيعي للطفل من ال normal activity اللي موجود عند
+
+16
+00:01:13,770 --> 00:01:19,470
+الطفل others are responses to certain actionsو
+
+17
+00:01:19,470 --> 00:01:25,490
+البعض الآخر منها عشان يتم لازم بيحتاج stimulus
+
+18
+00:01:25,490 --> 00:01:30,770
+بيحتاج مثير على
+
+19
+00:01:30,770 --> 00:01:37,390
+سبيل المثال لو احنا جينا لأخمس القدم نيجي نعمل
+
+20
+00:01:37,390 --> 00:01:46,700
+scratching ل soul of the foot نعمل عمليةتنبيه أو
+
+21
+00:01:46,700 --> 00:01:52,840
+استثاره لأخمس القدم للطفل هلاجي فيه ردة فعل موجودة
+
+22
+00:01:52,840 --> 00:01:58,960
+إذا هذه هي المقصود ب stimulus إنه لازم يكون في
+
+23
+00:01:58,960 --> 00:02:03,580
+مثير لازم يكون في حركة أنا عملتها وبناء عليها صار
+
+24
+00:02:03,580 --> 00:02:10,180
+في عندي ردة فعل من الطفل generally reflexes will
+
+25
+00:02:10,180 --> 00:02:14,160
+be integrated or suppressed by the age of 9 to 12
+
+26
+00:02:14,160 --> 00:02:14,600
+months
+
+27
+00:02:17,410 --> 00:02:23,610
+أغلب ال reflexes بحلول الشهر التاسع إلى الشهر
+
+28
+00:02:23,610 --> 00:02:29,820
+الثاني عشربتكون يا إما اختفت يا إما حلم حلها
+
+29
+00:02:29,820 --> 00:02:34,560
+Reflexes أخرى اتطورت هذا ال Reflexes أو هذا ال
+
+30
+00:02:34,560 --> 00:02:37,420
+Reflexes قعدنا نشوف ان شاء الله رب العالمين خلال
+
+31
+00:02:37,420 --> 00:02:42,900
+دراستنا لهذا الموضوع بعض الأمثلة اللي بتحكي عن ال
+
+32
+00:02:42,900 --> 00:02:49,160
+Reflexes ومتى ممكن تظهر ومتى ممكن تختفي و البعض
+
+33
+00:02:49,160 --> 00:02:55,980
+الآخر متى ممكن يتطور لشيء آخرلو جينا نطلع و نشوف
+
+34
+00:02:55,980 --> 00:03:03,660
+شو اللي بيخلي ال reflex اتم بدنا نفهم ال anatomy
+
+35
+00:03:03,660 --> 00:03:05,260
+لـ
+
+36
+00:03:07,110 --> 00:03:11,330
+الـ spinal cord أو الـ spinal reflex في الغالب هذا
+
+37
+00:03:11,330 --> 00:03:16,170
+الجزء اللي موجود أمامي هو قطاع عرضي في ال spinal
+
+38
+00:03:16,170 --> 00:03:20,490
+cord segment من ال spinal cord احنا بنعرف ان ال
+
+39
+00:03:20,490 --> 00:03:28,390
+spinal cord بتكون من 31 segment تقريبا من هذه منهم
+
+40
+00:03:28,390 --> 00:03:29,970
+تمانية
+
+41
+00:03:32,280 --> 00:03:44,040
+8 أجزاء عنقية و 12 فقرة خاصة بالصدرية 5 قطانية و 5
+
+42
+00:03:44,040 --> 00:03:52,300
+sacral و 1 coccyx هذه الـ segments اللي موجودة من
+
+43
+00:03:52,300 --> 00:03:57,160
+الداخل لو جينا نطلع عليها هنلاقيها انها تتكون من
+
+44
+00:03:57,160 --> 00:04:03,200
+طبقتين أساسيةالطبقة الداخلية اللي عاملة زي حرف ال
+
+45
+00:04:03,200 --> 00:04:08,500
+H بالشكل هذا اللي موجود أمامنا والطبقة الخارجية
+
+46
+00:04:08,500 --> 00:04:13,480
+اللي بيسموها اللي لونها أفتح شوية هذه الطبقة
+
+47
+00:04:13,480 --> 00:04:17,500
+الداخلية زي ما احنا شايفين لونها غامق شوية والطبقة
+
+48
+00:04:17,500 --> 00:04:23,480
+الخارجية لونها أفتح الطبقة الداخلية اللي لونها
+
+49
+00:04:23,480 --> 00:04:26,100
+غامق تسمى gray matter
+
+50
+00:04:28,670 --> 00:04:36,550
+والطبقة الخارجية هذه تسمى white matter gray matter
+
+51
+00:04:36,550 --> 00:04:43,690
+لأنها عبارة عن تجمع لخلايا العصبية اللي موجودة في
+
+52
+00:04:43,690 --> 00:04:48,630
+الحبل الشوكي والخلايا تحتوي على أنوية الخلايا
+
+53
+00:04:48,630 --> 00:04:55,470
+فتعطيها اللون الداكن في حين أن الجزء الخارجي اللي
+
+54
+00:04:55,470 --> 00:05:02,710
+نسميه white matterهذا طبعا بيحتوي على الـ axons
+
+55
+00:05:02,710 --> 00:05:07,610
+والـ axons عليها طبقة تسمى الـ myelin sheet غلاف
+
+56
+00:05:07,610 --> 00:05:17,350
+للـ axons فبيعطيها اللون الأبيض أو اللون الأفتح في
+
+57
+00:05:17,350 --> 00:05:24,440
+داخلالـ Grameter زي ما احنا شايفين في عندنا هذا
+
+58
+00:05:24,440 --> 00:05:29,400
+الجزء بيسموه anterior horn cell و هذا الجزء بيسموه
+
+59
+00:05:29,400 --> 00:05:33,480
+anterior horn cell والجزء الخلفي بيسموه posterior
+
+60
+00:05:33,480 --> 00:05:38,940
+horn cell posterior horn cell الآن الـ anterior
+
+61
+00:05:38,940 --> 00:05:43,820
+horn cell هذا اللي أمامنا هذا بيحتوي على الخلايا
+
+62
+00:05:43,820 --> 00:05:50,200
+اللي مسئولة عن الجهاز أو عن الحركةالـ motor action
+
+63
+00:05:50,200 --> 00:05:56,320
+عشان هيك بنسميه motor neuron الخلايا العصبية بيروح
+
+64
+00:05:56,320 --> 00:06:01,940
+العصب منها بينتقل لحد ما يصل ال effector organ
+
+65
+00:06:01,940 --> 00:06:07,480
+اللي هو عبارة عن عضلة اللي هيصير فيها الانقباض في
+
+66
+00:06:07,480 --> 00:06:13,740
+حين ان الجزء الخلفي زي ما احنا شايفين بيتصل
+
+67
+00:06:15,250 --> 00:06:19,770
+بحاجة يسموها sensory neuron والـ sensory neuron
+
+68
+00:06:19,770 --> 00:06:26,070
+هذه بتنتهي في الجلد في الغالب وفيها مستقبلات الـ
+
+69
+00:06:26,070 --> 00:06:31,890
+receptors شو اللي بيصير في حالة ال reflex ال
+
+70
+00:06:31,890 --> 00:06:36,790
+reflex لما بنيجي بنعمل reflex بنعمل stimulus بنعمل
+
+71
+00:06:36,790 --> 00:06:42,070
+scratch أو بنعمل وخز في مكان معين على الجلب
+
+72
+00:06:42,070 --> 00:06:49,030
+الإشارة هذهبتنتقل في الـ Sensory Neuron في الـ
+
+73
+00:06:49,030 --> 00:06:52,850
+Sensory Neuron زي ما احنا شايفين في عندى Sensory
+
+74
+00:06:52,850 --> 00:06:57,510
+Cell Body او Dorsal Root Ganglion بيسموها هذه في
+
+75
+00:06:57,510 --> 00:07:04,670
+الاناتومي تنتقل للإشارة اللى انا عملتها الإشارة
+
+76
+00:07:04,670 --> 00:07:09,330
+العصبية ال stimulus اللى انا عملته المثير من خلال
+
+77
+00:07:09,330 --> 00:07:15,350
+Sensory Neuron في الـ Dorsal Rootأو الـ Sensory
+
+78
+00:07:15,350 --> 00:07:22,430
+Afferent وبيروح للـ Posterior Horse Cell بين الـ
+
+79
+00:07:22,430 --> 00:07:26,770
+Posterior Horse Cell و الـ Anterior Horse Cell في
+
+80
+00:07:26,770 --> 00:07:32,950
+موجود عندى وصلة Association Neuron أو Interneuron
+
+81
+00:07:33,310 --> 00:07:39,390
+هذه الوصلة بتنقل الإشارة العصبية أو بتنفصل الإشارة
+
+82
+00:07:39,390 --> 00:07:43,650
+العصبية جزء منها بيطلع للـ brain للـ high center
+
+83
+00:07:43,650 --> 00:07:49,250
+وجزء الآخر بيروح على مين؟ على ال motor neuron أو
+
+84
+00:07:49,250 --> 00:07:54,280
+ال motor cellsوبينتقل لخلال الـ motor neuron
+
+85
+00:07:54,280 --> 00:08:00,180
+وبيروح على ال effector organ وبيعمل ردة الفعل اللي
+
+86
+00:08:00,180 --> 00:08:04,700
+احنا بنشوفها عند الطفل يعني لو فرضنا انه انا ال
+
+87
+00:08:04,700 --> 00:08:10,900
+stimulus كانت عبارة عن وخزة دبوس ووخزة الدبوس هاد
+
+88
+00:08:10,900 --> 00:08:16,720
+انتقلت ل ال posterior heart cellعند الـ Posterior
+
+89
+00:08:16,720 --> 00:08:20,520
+Horsel قلنا إن قسمة الإشارة هذه جزء منها راح للـ
+
+90
+00:08:20,520 --> 00:08:24,840
+Brain للـ High Center عشان يقولوا شو اللي صار وجزء
+
+91
+00:08:24,840 --> 00:08:29,740
+الآخر راح على الـ Anterior Horsel على الـ Effector
+
+92
+00:08:29,740 --> 00:08:35,540
+Organ وعمل الإنقباضة اللي عبارة عن سحب الإيد أو
+
+93
+00:08:35,540 --> 00:08:40,980
+سحب الرجل عن مكان واخذة الدبوس أو عن الدبوس هذه
+
+94
+00:08:40,980 --> 00:08:48,410
+باختصار الـ Reflex Arcنحكي عن reflex arc مش
+
+95
+00:08:48,410 --> 00:08:52,510
+بالتفصيل اللي يفترض انه احنا نحكيه في ال anatomy و
+
+96
+00:08:52,510 --> 00:08:57,470
+ال neuro anatomy فقط فكرة عشان نتعرف على ال reflex
+
+97
+00:08:57,470 --> 00:09:04,370
+arc و كيف بتنتقل ال reflexes و شو بلزم لل reflexes
+
+98
+00:09:04,370 --> 00:09:12,220
+عشان احنا نحفز هذه ال reflexesbenefits of infant
+
+99
+00:09:12,220 --> 00:09:17,480
+reflexes primative reflexes شو الهدف وشو الفائدة
+
+100
+00:09:17,480 --> 00:09:22,760
+اللي احنا بنستفيدها من وجود ال primitive reflexes
+
+101
+00:09:22,760 --> 00:09:28,020
+او ال infant reflexes
+
+102
+00:09:30,420 --> 00:09:34,260
+أول حاجة الـ Reflexes هذه قولنا إنه إحنا بنستخدمها
+
+103
+00:09:34,260 --> 00:09:41,640
+كنوع من أنواع الفحوصات للطفل أول ما ينولد و بعد
+
+104
+00:09:41,640 --> 00:09:48,900
+فترة من ولادته عشان نتعرف على الطفل تبعنا هل هو
+
+105
+00:09:49,610 --> 00:09:54,450
+طبيعي من ناحية حركية ولا في عنده مشكلة يعني
+
+106
+00:09:54,450 --> 00:09:58,690
+knowledge of normal and abnormal reflexes response
+
+107
+00:09:58,690 --> 00:10:03,130
+and their effect upon motor development which is
+
+108
+00:10:03,130 --> 00:10:07,430
+needed to identify normal brain and nerve activity
+
+109
+00:10:07,430 --> 00:10:13,790
+إذن هذه ال reflexesبتخليني أتعرف على الطفل اللي
+
+110
+00:10:13,790 --> 00:10:19,630
+قدامي هل يعاني من مشاكل في ال brain أو في ال
+
+111
+00:10:19,630 --> 00:10:24,690
+nervous system و هل سيعاني في المستقبل من motor
+
+112
+00:10:24,690 --> 00:10:29,230
+development problems ولا لأ مشاكل في عمليات النمو
+
+113
+00:10:29,230 --> 00:10:35,090
+النقطة التانية provide a basis for evaluation in
+
+114
+00:10:35,090 --> 00:10:40,120
+the diagnosis and treatment of cerebral palsyإذن
+
+115
+00:10:40,120 --> 00:10:43,800
+كتير من الحالات اللي بيعانوا من cerebral palsy
+
+116
+00:10:43,800 --> 00:10:48,500
+اللي مقصود بيها الشلل الدماغي بيكون في عندهم مشاكل
+
+117
+00:10:48,500 --> 00:10:54,800
+في الحركة و هذه المشاكل ناتجة عن خلل في ال
+
+118
+00:10:54,800 --> 00:10:58,930
+cerebrum أو في ال cerebellumإذا في خلل في الـ
+
+119
+00:10:58,930 --> 00:11:04,170
+brain عملية التقييم اللي أنا بعملها من خلال الـ
+
+120
+00:11:04,170 --> 00:11:08,890
+reflexes بتحددلي شو المشكلة اللي موجودة و بتسهل
+
+121
+00:11:08,890 --> 00:11:13,350
+علي و بتساعدني في عملية التشخيص و عملية العلاج
+
+122
+00:11:13,350 --> 00:11:18,430
+اللي أنا بدي أقوم فيها لهذا الطفل essential and
+
+123
+00:11:18,430 --> 00:11:22,580
+normal development responses to these reflexesIt
+
+124
+00:11:22,580 --> 00:11:25,800
+prepares the child for progressive development
+
+125
+00:11:25,800 --> 00:11:30,560
+such as rolling over, sitting,
+
+126
+00:11:30,940 --> 00:11:35,700
+crawling and standing إذن هذه الـ Reflexes هي كمان
+
+127
+00:11:35,700 --> 00:11:42,220
+تعتبر الأساس لعمليات التطور و النمو الحركي اللي
+
+128
+00:11:42,220 --> 00:11:47,480
+بتكون موجودة عند الطفل فحلاجي أنهأغلب ال
+
+129
+00:11:47,480 --> 00:11:52,020
+activities و أغلب النشاطات هي بدايتها كانت عبارة
+
+130
+00:11:52,020 --> 00:11:56,500
+عن ردات فعل أو عبارة عن reflexes كان الطفل بيقوم
+
+131
+00:11:56,500 --> 00:12:01,580
+فيها بعد هيك صارت نوع من ال functional activities
+
+132
+00:12:01,580 --> 00:12:07,520
+زي ال rolling عملية التقلم لليمين و لليسار ال
+
+133
+00:12:07,520 --> 00:12:12,540
+sitting الجلوس ال crawling ال standing هي هذه كانت
+
+134
+00:12:12,540 --> 00:12:18,600
+مبنية فيه أساسها على ال reflexesلو كان في هذه الـ
+
+135
+00:12:18,600 --> 00:12:23,540
+Reflexes فيها خلل من البداية هيكون في الوظائف هذه
+
+136
+00:12:23,540 --> 00:12:29,680
+الموجودة الجلوس والزحف والوقوف والمشي هيكون فيها
+
+137
+00:12:29,680 --> 00:12:34,440
+خلل في المستقبل gaining control over the body of
+
+138
+00:12:34,440 --> 00:12:40,240
+the child بتساعد الطفل انه يتحكم في جسمه سواء كان
+
+139
+00:12:40,240 --> 00:12:45,680
+في جلوس سواء كان في بعض ال activitiesAt birth
+
+140
+00:12:45,680 --> 00:12:50,180
+approximately 30 primitive reflexes these
+
+141
+00:12:50,180 --> 00:12:54,580
+primitive reflexes better must disappear and
+
+142
+00:12:54,580 --> 00:12:59,680
+equilibrium reactions must appear كتير من ال
+
+143
+00:12:59,680 --> 00:13:04,450
+reflexes اللي بتكون موجودة عند الأطفالأو عند
+
+144
+00:13:04,450 --> 00:13:08,910
+الولادة هي حوالي تلاتين reflex أو reflex اللي
+
+145
+00:13:08,910 --> 00:13:15,070
+بتكون موجودة عند الولادة تلاتين reflex وهذه تختفي
+
+146
+00:13:15,070 --> 00:13:23,690
+أو يجب أن تختفي أو تتطور إلى reflex أخرى تختفي هذه
+
+147
+00:13:23,690 --> 00:13:30,390
+ال reflex و تظهر reflex أخرى infant vs lifespan
+
+148
+00:13:30,390 --> 00:13:36,150
+reflex لو جينا نطلععلى ال infant reflexes اللي
+
+149
+00:13:36,150 --> 00:13:40,250
+بينولد فيها الطفل مقابل ال reflexes اللي بتكون
+
+150
+00:13:40,250 --> 00:13:46,090
+موجودة طول الحياة يعني الطفل بينولد ب reflexes و
+
+151
+00:13:46,090 --> 00:13:49,990
+بعض هذه ال reflexes بتختفي و البعض الآخر بيضلوا
+
+152
+00:13:49,990 --> 00:13:57,720
+ماشي معاه مدى الحياة على سبيل المثالأغلب ال infant
+
+153
+00:13:57,720 --> 00:14:04,160
+reflexes ما بتطولش زيادة عن سنة يعني كلها بحلول
+
+154
+00:14:04,160 --> 00:14:08,480
+السن الأولى كل ال reflexes بحلول السن الأولى
+
+155
+00:14:08,480 --> 00:14:12,420
+بتختفي infant reflexes may not completely
+
+156
+00:14:12,420 --> 00:14:16,760
+disappear بعض ال reflexes هذه ممكن ما تختفيش
+
+157
+00:14:16,760 --> 00:14:21,430
+بالكاملmay be inhabited by maturing central
+
+158
+00:14:21,430 --> 00:14:26,230
+nervous system ممكن يصير في إلها تثبيت من خلال
+
+159
+00:14:26,230 --> 00:14:29,570
+عملية نمو ال nervous system و ال central nervous
+
+160
+00:14:29,570 --> 00:14:33,930
+system may be integrated into new movements ممكن
+
+161
+00:14:33,930 --> 00:14:42,580
+يتم تطورها لحركات أخرى جديدةreflexes that endure
+
+162
+00:14:42,580 --> 00:14:48,580
+are called life span reflexes ال reflexes اللي
+
+163
+00:14:48,580 --> 00:14:54,960
+هتظلها مستمرة مع الشخص طول الحياة هذي بيسموها life
+
+164
+00:14:54,960 --> 00:14:59,820
+span reflexes زي إيش عندي مثلا في ال life span
+
+165
+00:14:59,820 --> 00:15:03,980
+reflexes ال breathing reflex swallowing reflex
+
+166
+00:15:05,330 --> 00:15:12,090
+منعكس التنفس ومنعكس البلق هذه طبعا كامثلة ل
+
+167
+00:15:12,090 --> 00:15:17,330
+reflexes ممكن تظلها ماشية معايا طول الحياة role of
+
+168
+00:15:17,330 --> 00:15:19,850
+reflexes in developing future movement
+
+169
+00:15:23,080 --> 00:15:29,280
+على وظيفة ال reflexes ودورها في تطور الجهاز الحركي
+
+170
+00:15:29,280 --> 00:15:33,840
+و الوظيفي عند الطفل زي ما قلنا ان هذه ال reflexes
+
+171
+00:15:33,840 --> 00:15:43,060
+بتكون في البداية كحركات لا إرادية لا وظيفيةلكن
+
+172
+00:15:43,060 --> 00:15:50,820
+الطفل خلال حياته و تطوره بيعتمد على هذه ال
+
+173
+00:15:50,820 --> 00:16:00,020
+reflexes في تطور وجود وظائف أخرى على سبيل المثال
+
+174
+00:16:00,020 --> 00:16:06,160
+الـ crawling reflex الزحف .. منعكس الزحف اللي
+
+175
+00:16:06,160 --> 00:16:13,180
+بيكون موجود عند ال infantsهيستفيد منه في المستقبل
+
+176
+00:16:13,180 --> 00:16:18,060
+بـ Crawling Reflex يعني كمان الطفل لما يكبر بيقدر
+
+177
+00:16:18,060 --> 00:16:23,460
+يزحف من خلال اعتماده في الأساس على الـ Crawling
+
+178
+00:16:23,460 --> 00:16:28,360
+Reflex اللي كان موجود في البداية Labyrinthine
+
+179
+00:16:28,360 --> 00:16:34,520
+Reflexهذا نوع من أنواع الـ Reflexes وهذا هيساعد في
+
+180
+00:16:34,520 --> 00:16:39,620
+الـ upright posture هيساعد الطفل يكون في عنده
+
+181
+00:16:39,620 --> 00:16:46,860
+الوقوف بشكل معتدل والجلوس بشكل معتدل ال upright
+
+182
+00:16:46,860 --> 00:16:54,000
+posture Balmary grasp هذا كنوع .. كreflex انه انا
+
+183
+00:16:54,000 --> 00:16:59,510
+لما بقى اجي بقى امسك ايد الطفل الصغيروبأعمل
+
+184
+00:16:59,510 --> 00:17:04,290
+scratching لراحة اليد هلاجي إنه صار في عندى
+
+185
+00:17:04,290 --> 00:17:10,830
+grasping كردّة فعل في المستقبل بيصير لما بده يمسك
+
+186
+00:17:10,830 --> 00:17:15,670
+أي حاجة هي هذه الوظيفة ال grasping كانت مبنية على
+
+187
+00:17:15,670 --> 00:17:20,930
+ال palmar grasping reflex ال stepping reflex
+
+188
+00:17:20,930 --> 00:17:29,140
+بيعتمد أو بيتطور للمستقبل على عملية ال walkingلو
+
+189
+00:17:29,140 --> 00:17:33,820
+كان في عندي خلل في الـ Crawling، في الابرنثين، في
+
+190
+00:17:33,820 --> 00:17:37,880
+الـbalmar، في الـstepping، هيكون في عندي خلل في
+
+191
+00:17:37,880 --> 00:17:41,780
+هذه الوظائف يعني لو جينا على سبيل المثال، قلتلكوا
+
+192
+00:17:41,780 --> 00:17:50,360
+إن أنا في عندي طفل في أثناء الـassessment تبعته في
+
+193
+00:17:50,360 --> 00:17:53,840
+أول ثلاث شهور، كان في عنده مشكلة في الـstepping
+
+194
+00:17:53,840 --> 00:17:59,240
+reflexوين المشكلة المتوقع انها تصير عنده خلال
+
+195
+00:17:59,240 --> 00:18:04,440
+تطوره حيكون في عندي مشكلة في عملية ال walking في
+
+196
+00:18:04,440 --> 00:18:09,860
+المستقبل rule of the reflexes in the survival الان
+
+197
+00:18:09,860 --> 00:18:16,520
+لو جينا نتطلع على دور ال reflexes و أهميتها في
+
+198
+00:18:16,520 --> 00:18:23,880
+البقاء و المحافظة على حياة الإنسانزي ما قلنا إنه
+
+199
+00:18:23,880 --> 00:18:27,700
+في عندي أنا life اسمها reflexes و protective
+
+200
+00:18:27,700 --> 00:18:32,480
+reflexes هذه بتحافظ على حياة الإنسان human infant
+
+201
+00:18:32,480 --> 00:18:41,380
+essentially helpless أول ما ينولد الطفل الصغير من
+
+202
+00:18:41,380 --> 00:18:51,630
+عمر يوم لحد تقريبا سنةهو بيحتاج مساعدة الآخرين
+
+203
+00:18:51,630 --> 00:18:57,330
+بشكل كبير جدا في الأكل في الشرب في كل شيء وبالتالي
+
+204
+00:18:57,330 --> 00:19:04,070
+ال reflexes هذه جزء منها بساعد هذا الطفل على أنه
+
+205
+00:19:04,070 --> 00:19:09,390
+يحمي حاله و يكون و يكون نوع من الحياة زي ما حكينا
+
+206
+00:19:09,390 --> 00:19:14,850
+في عندنا human infantreflexes وقولنا أن الطفل
+
+207
+00:19:14,850 --> 00:19:20,190
+بيكون في أول سنة معتمد على الآخرين كليا في كل شئ
+
+208
+00:19:20,190 --> 00:19:24,830
+وفي عندي primitive reflexes occur during gestation
+
+209
+00:19:24,830 --> 00:19:30,990
+or at birth and most are repressed by six months
+
+210
+00:19:30,990 --> 00:19:35,380
+of ageفي عندي ال primitive reflexes و بعض هذه ال
+
+211
+00:19:35,380 --> 00:19:39,960
+primitive reflexes ممكن تكون موجودة او بدأت موجودة
+
+212
+00:19:39,960 --> 00:19:45,800
+في مرحلة الحمل و بعضها الاخر ممكن انوجد عند
+
+213
+00:19:45,800 --> 00:19:50,180
+الولادة و أغلب هذه ال reflexes ال primitive
+
+214
+00:19:50,180 --> 00:19:56,740
+reflexes repressed by age of six months هتختفي عند
+
+215
+00:19:56,740 --> 00:20:02,690
+عمر ست شهورprimitive reflexes are important for
+
+216
+00:20:02,690 --> 00:20:07,710
+protection, nutrition and survival حلاجي ان ال
+
+217
+00:20:07,710 --> 00:20:12,650
+primitive reflexes مهم جدا لعملية الحماية و
+
+218
+00:20:12,650 --> 00:20:17,450
+المحافظة على حياة الشخص للتخديع a protective
+
+219
+00:20:17,450 --> 00:20:22,210
+reflex على سبيل المثال لما نيجي احنا نحط ادينا
+
+220
+00:20:22,210 --> 00:20:28,600
+قدام شخص على عينه هيكون فيه نوع من اغماض العينو
+
+221
+00:20:28,600 --> 00:20:33,780
+اغلاقها هذا الاغلاق هو ردة فعل كنوع من الحماية
+
+222
+00:20:33,780 --> 00:20:38,480
+بيسموه protective reflex في عندى nutrition لما
+
+223
+00:20:38,480 --> 00:20:42,920
+بنجيب نلاقي الطفل انه في عملية البلأ هذا nutrition
+
+224
+00:20:42,920 --> 00:20:51,070
+reflex ال survival reflex زي التنفسلو لوجود التنفس
+
+225
+00:20:51,070 --> 00:20:57,330
+مش هيصير في عندي أنا البقاء، إذا الحياة و استمرار
+
+226
+00:20:57,330 --> 00:21:05,650
+الحياة بيعتمد على ال reflexes بشكل كبير جدا ال
+
+227
+00:21:05,650 --> 00:21:08,730
+role of reflexes in developing future movement
+
+228
+00:21:08,730 --> 00:21:15,030
+الآن شو دور هذه ال reflexes في تطور الحركات
+
+229
+00:21:15,030 --> 00:21:20,900
+الوظيفية اللي موجودة عند الأشخاص؟الـ postural
+
+230
+00:21:20,900 --> 00:21:24,220
+reflexes are related to the development of later
+
+231
+00:21:24,220 --> 00:21:28,780
+voluntary movement هلاجي أنه ال reflexes زي ما
+
+232
+00:21:28,780 --> 00:21:31,680
+قلنا في عندنا primitive reflexes في عندنا survival
+
+233
+00:21:31,680 --> 00:21:35,820
+reflexes في عندنا كمان تقسيم أخرى بيسموها postural
+
+234
+00:21:35,820 --> 00:21:40,040
+reflexes هي ما بتتعلق بال postural بتتعلق بال
+
+235
+00:21:40,040 --> 00:21:46,410
+trunk هذه ال reflexesفي الغالب هنلاقيها بتتطور و
+
+236
+00:21:46,410 --> 00:21:50,910
+بتساعد في عملية ال voluntary movement وتطور
+
+237
+00:21:50,910 --> 00:21:57,490
+الحركات الإيرادية اللي موجودة عند الإنسانreflexes
+
+238
+00:21:57,490 --> 00:22:01,770
+integrated modified and incorporated into more
+
+239
+00:22:01,770 --> 00:22:06,190
+complex pattern to form voluntary movement بعض ال
+
+240
+00:22:06,190 --> 00:22:13,150
+reflexes ممكن يصير لها دمج تعطيني reflexes أخر
+
+241
+00:22:13,150 --> 00:22:17,170
+ممكن يصير لها modification يتعدل هذا ال reflex و
+
+242
+00:22:17,170 --> 00:22:22,370
+يصير عليه تطور ممكن يصير فيه دمج لهذا ال reflex مع
+
+243
+00:22:22,370 --> 00:22:30,410
+reflex أخر كما هوعشان في النهاية تساعد في تطور
+
+244
+00:22:30,410 --> 00:22:37,170
+الحركة والوظيفة للإنسان automatic movements is
+
+245
+00:22:37,170 --> 00:22:43,190
+practice for future voluntary movement وهدي طبعا
+
+246
+00:22:43,190 --> 00:22:47,830
+يعني لو جينا بتطلعنا احنا على طفل عمره تلت شهور
+
+247
+00:22:47,830 --> 00:22:55,010
+تقريباأو أقل شوية هلاجي ان الطفل في العمر هذا و
+
+248
+00:22:55,010 --> 00:23:01,030
+رقبناه بشكل دقيق هلاجي انه بيحرك اديه و بيحرك
+
+249
+00:23:01,030 --> 00:23:06,510
+رجليه حركات لا إرادية سموها automatic movement
+
+250
+00:23:06,510 --> 00:23:11,650
+حركات اوتوماتيكية تلقائية هذه الحركات عبارة عن
+
+251
+00:23:11,650 --> 00:23:18,870
+تمرينوهذا التمرين بدي استفيد منه انه بيقوي عضلات
+
+252
+00:23:18,870 --> 00:23:23,070
+ال upper و ال lower limbs عشان يصير في عنده حركة
+
+253
+00:23:23,070 --> 00:23:29,230
+إرادية تكون هذه العضلات جاهزة للوظيفة تبعتها إلا
+
+254
+00:23:29,230 --> 00:23:35,410
+صناعتي أخليها
+
+255
+00:23:35,410 --> 00:23:40,990
+إحيا حياتي و دنيتي فيها
+
+256
+00:23:44,210 --> 00:23:47,070
+بعضهم يعتقدون أن الـ Reflexes ليسوا مرتبطين بـ
+
+257
+00:23:47,070 --> 00:23:51,910
+Future Movement Development في بعض التوجهات أو بعض
+
+258
+00:23:51,910 --> 00:23:56,850
+العلماء بيعتقدوا أن الـ Reflexes هذه مايلها أي
+
+259
+00:23:56,850 --> 00:24:02,650
+علاقة بالـ Motor Development لكن المثبت حتى الآن
+
+260
+00:24:02,650 --> 00:24:09,130
+كتير منالعلماء بيعتقدوا عكس الكلام هذا انه
+
+261
+00:24:09,130 --> 00:24:13,370
+بيعتقدوا ان ال reflexes لها دور كبير جدا في عملية
+
+262
+00:24:13,370 --> 00:24:19,390
+النمو الحركي types
+
+263
+00:24:19,390 --> 00:24:23,530
+of reflexes اللي ممكن نشوفها احنا reflexes can be
+
+264
+00:24:23,530 --> 00:24:29,400
+divided as survival reflexو هدول ال reflexes
+
+265
+00:24:29,400 --> 00:24:34,600
+survival reflexes aid survival by helping an
+
+266
+00:24:34,600 --> 00:24:40,760
+infant deal with threats to the body هتساعد الطفل
+
+267
+00:24:40,760 --> 00:24:46,020
+انه يتعامل مع التهديدات الخارجية و يحمي نفسه من
+
+268
+00:24:46,020 --> 00:24:52,460
+خلالها على سبيل المثالزي ما حكينا قبل شوية فى
+
+269
+00:24:52,460 --> 00:24:56,000
+عندنا ال breathing reflex من ال protective reflex
+
+270
+00:24:56,000 --> 00:25:01,500
+و ال survival reflex فى عندى ال eye blank reflex
+
+271
+00:25:01,500 --> 00:25:05,700
+ال protective eye reflex فى عند ال sucking reflex
+
+272
+00:25:05,700 --> 00:25:09,760
+فى عند ال swallowing reflex هذه كلها عبارة عن
+
+273
+00:25:09,760 --> 00:25:12,040
+survival reflexes
+
+274
+00:25:15,710 --> 00:25:18,550
+وفي عندنا الـ Primitive Reflexes وقلنا لـ
+
+275
+00:25:18,550 --> 00:25:26,790
+Primitive Reflexes ان غالبيتها بتتم اختفاء عند عمر
+
+276
+00:25:26,790 --> 00:25:37,130
+9 شهور لحد 12 شهر بحد أقصى ابقى
+
+277
+00:25:37,130 --> 00:25:41,770
+نيجي نتطلع على بعض الـ Reflexes نشوف هذه الـ
+
+278
+00:25:41,770 --> 00:25:42,410
+Reflexes
+
+279
+00:25:44,790 --> 00:25:50,410
+وكيف ممكن أنها تساعد في البقاء على الحياة على سبيل
+
+280
+00:25:50,410 --> 00:25:55,650
+المثال ال breathing reflex ال breathing reflex ايش
+
+281
+00:25:55,650 --> 00:25:58,230
+اللي بيصير في ال breathing reflex لو نجي نطلع
+
+282
+00:25:58,230 --> 00:26:01,550
+هلاجى انه عنده repetitive inhalation and
+
+283
+00:26:01,550 --> 00:26:05,950
+exhalation او expiration هو عملية شهيق و زفير
+
+284
+00:26:05,950 --> 00:26:10,410
+متكررةالـ duration تبعتها طبعا هذا permanent
+
+285
+00:26:10,410 --> 00:26:16,750
+reflex بيظله long life أو lifespan reflex provide
+
+286
+00:26:16,750 --> 00:26:23,810
+oxygen and expel carbon dioxide وهذا اللي بنشوفه
+
+287
+00:26:23,810 --> 00:26:28,790
+عند الجميع وشو وظيفة الجهاز التنفس وشو وظيفة
+
+288
+00:26:28,790 --> 00:26:37,010
+التنفس في العملية التنفسبيكون في عندى انا معدل
+
+289
+00:26:37,010 --> 00:26:44,150
+معين لالـ oxygen في داخل الخلايا وفي معدل لثاني
+
+290
+00:26:44,150 --> 00:26:50,370
+أكسيد الكربون مجرد ما يزيد معدل ثاني أكسيد الكربون
+
+291
+00:26:50,370 --> 00:26:59,350
+في داخل الجسم بحفظ الجسم انه ياخد inspiration ياخد
+
+292
+00:26:59,350 --> 00:27:06,720
+زهق شهيق ولمّا يزيدخلّيني أقول طبعا بيتبعوا عملية
+
+293
+00:27:06,720 --> 00:27:12,700
+الزفير اللي بيتخلص منها في عملية أو بتخلص من ال
+
+294
+00:27:12,700 --> 00:27:15,920
+waste products أو من ثاني أكسيد الكربون اللي موجود
+
+295
+00:27:15,920 --> 00:27:23,080
+ال eye blink reflex closing or blinking of the eye
+
+296
+00:27:24,250 --> 00:27:29,990
+عشان نحكي عن الـ Eye Blink Reflex نكون عارفين إنه
+
+297
+00:27:29,990 --> 00:27:36,150
+عبارة عن إغلاق العين نتيجة وجود تهديد على العين
+
+298
+00:27:36,150 --> 00:27:41,270
+protect the eye from a bright light or foreign
+
+299
+00:27:41,270 --> 00:27:47,170
+object وهذه طبعاً بنلاقيها هي عبارة عن حماية للعين
+
+300
+00:27:47,170 --> 00:27:54,200
+منالـ foreign body إذا أنا جربت على العين بـ
+
+301
+00:27:54,200 --> 00:27:59,020
+foreign body إيدي أو جلم أو أي إن كان، حيصير إغلاق
+
+302
+00:27:59,020 --> 00:28:04,900
+للعين أو لو سلطت ضوء مباشر في داخل العين، حيصير في
+
+303
+00:28:04,900 --> 00:28:11,340
+عندي أنا عملية الـ blinking أو
+
+304
+00:28:11,340 --> 00:28:18,810
+ال closing للعين بابيلاري reflexوالتركيز على
+
+305
+00:28:18,810 --> 00:28:26,850
+الشعارات لإضافة ضوء وضوء لظلمةو هذا ال reflex
+
+306
+00:28:26,850 --> 00:28:34,430
+بنشوفه بشكل كبير جدا انه لو انا سلطت ضوء في بؤبق
+
+307
+00:28:34,430 --> 00:28:40,350
+العين هلاجي انه انقبض بؤبق العين بشكل كبير جدا
+
+308
+00:28:40,350 --> 00:28:45,330
+عشان يقلل من كمية الضوء الداخل للعين في حين انه في
+
+309
+00:28:45,330 --> 00:28:51,110
+الظل أو في الظلمة هلاجي انهبقبق العين توسع لأكبر
+
+310
+00:28:51,110 --> 00:28:55,410
+قدر ممكن عشان يسمح بمرور الضوء ويمكن الشخص من
+
+311
+00:28:55,410 --> 00:29:00,850
+الرؤية هو هذا كمان mainly protective eye reflexes
+
+312
+00:29:00,850 --> 00:29:05,550
+ال routing reflex شو اللي بيصير في ال routing
+
+313
+00:29:05,550 --> 00:29:10,590
+reflex turning the head toward the tactile touch
+
+314
+00:29:10,590 --> 00:29:17,350
+or stimulus to the cheek لو أنا جيت لمست خد الطفل
+
+315
+00:29:17,350 --> 00:29:26,780
+وعملتحركة بسيطة تكتال تتش هلاجى ان الطفل شو
+
+316
+00:29:26,780 --> 00:29:33,800
+بيعمل بدير وجهه تجاه هذه الإشارة و بيحاول انه ياخد
+
+317
+00:29:33,800 --> 00:29:38,260
+الشيء اللي موجود في المكان اللي عمله stimulation
+
+318
+00:29:38,260 --> 00:29:45,580
+طبعا هذه الإشارة هي عبارة عنتنبيه للطفل إنه فيه
+
+319
+00:29:45,580 --> 00:29:51,400
+أكل جاي وخصوصا باللاحظ كتير من الأمهات لما بدها
+
+320
+00:29:51,400 --> 00:29:57,620
+تردع ابنها بس بتعمل touch لجزء من الخد أو لخده
+
+321
+00:29:57,620 --> 00:30:02,580
+فبندير وجهه الطفل تجاه هذه الإشارة عشان ياخد
+
+322
+00:30:02,580 --> 00:30:05,180
+المصاصة أو ياخد الرضعة
+
+323
+00:30:08,610 --> 00:30:13,370
+طبعا هذا ال reflex بيظل لفترة few weeks after
+
+324
+00:30:13,370 --> 00:30:21,230
+delivery بعد هيك بيتحول او بينتقل الى ال voluntary
+
+325
+00:30:21,230 --> 00:30:27,450
+head down الى عملية .. الى
+
+326
+00:30:27,450 --> 00:30:34,710
+عملية ازاحة او لف الرأس بشكل إرادي ال sucking
+
+327
+00:30:34,710 --> 00:30:41,060
+reflex suckingAny object placed into the mouth
+
+328
+00:30:41,060 --> 00:30:46,960
+وهذا طبعا بيلاحظه عند الأطفال لو إيش محطينا في ثم
+
+329
+00:30:46,960 --> 00:30:53,380
+الطفل في أول أشهر بيبدأ عملية sucking له أو مص له
+
+330
+00:30:53,380 --> 00:30:59,850
+بشكل تلقائيgradually modified by experience past
+
+331
+00:30:59,850 --> 00:31:05,150
+few weeks after delivery وبتم تطوره لحد ما يصير
+
+332
+00:31:05,150 --> 00:31:08,610
+انه عنده القدرة على انه هذا الشيء بيعجبه او ما
+
+333
+00:31:08,610 --> 00:31:09,370
+بيعجبه
+
+334
+00:31:11,620 --> 00:31:16,620
+إذا بيعجبه بيبدأ عملية ال sucking مابيعجبه بيتوقف
+
+335
+00:31:16,620 --> 00:31:23,060
+عنها لكن كبدأ في أول أسابيع أي شيء بنحطه في فم
+
+336
+00:31:23,060 --> 00:31:27,320
+الطفل بيبدأ عملية ال sucking allows the child to
+
+337
+00:31:27,320 --> 00:31:31,440
+take in a nutrient هذا ال reflex هو اللي بسمح
+
+338
+00:31:31,440 --> 00:31:37,520
+للطفل بعملية التغذية وبساهم في عملية التغذية
+
+339
+00:31:37,520 --> 00:31:44,150
+swallowing reflexزي ما حكينا إنه permanent reflex
+
+340
+00:31:44,150 --> 00:31:49,890
+لأن عملية البلع بتظل شغالة لطول الحياة which allow
+
+341
+00:31:49,890 --> 00:31:54,470
+the child to take in nutrients الأكل اللي أخده عن
+
+342
+00:31:54,470 --> 00:31:59,630
+طريق ال sucking بدي يبلعه عن طريق ال reflex عن
+
+343
+00:31:59,630 --> 00:32:08,530
+طريق اللي هو ال swallowing reflex ال
+
+344
+00:32:08,530 --> 00:32:12,730
+primitive reflexes are involuntaryPredictable
+
+345
+00:32:12,730 --> 00:32:17,350
+Changes in Muscle Tone in Response to Sensory
+
+346
+00:32:17,350 --> 00:32:21,790
+Input الآن في هذه الـBrightened Reflexes حلاقي انه
+
+347
+00:32:21,790 --> 00:32:26,110
+صار بحتاج عندي يكون في عندي Sensory Stimuli
+
+348
+00:32:26,110 --> 00:32:30,470
+Sensory Input لازم أعمل stimulation عشان في
+
+349
+00:32:30,470 --> 00:32:34,410
+النهاية أشوف ردة الفعل في العضلات وشو نوع ال
+
+350
+00:32:34,410 --> 00:32:39,990
+contraction اللي ممكن يكون عند العضلاتأول reflex
+
+351
+00:32:39,990 --> 00:32:46,950
+هنحكي فيه بابنسكي reflex في البابنسكي reflex لو
+
+352
+00:32:46,950 --> 00:32:53,770
+جينا نطلع على ال response هلاجي أن الطفل هيصير في
+
+353
+00:32:53,770 --> 00:33:00,530
+عنده fanning يفرد أصابع رجله بشكل عام و curling of
+
+354
+00:33:00,530 --> 00:33:06,030
+the toes when the bottom of the foot is struck لو
+
+355
+00:33:06,030 --> 00:33:14,440
+أنا جيت اعملت بمفتاحاستميلاش لأخمس القدم هلاقي ان
+
+356
+00:33:14,440 --> 00:33:22,540
+الطفل فرد أصابع رجليه و ثنعهم لتحت شوية نتيجة ال
+
+357
+00:33:22,540 --> 00:33:28,850
+stimulus اللي عملتها اناهذا الـ Reflex بيختفي عند
+
+358
+00:33:28,850 --> 00:33:34,210
+8 شهور إلى سنة presence and later disappearance of
+
+359
+00:33:34,210 --> 00:33:38,690
+this response is normal هذا الـ Reflex طبيعي جدا
+
+360
+00:33:38,690 --> 00:33:47,230
+أن يكون موجود في أولسنة تقريبا و يختفي بعد السنة
+
+361
+00:33:47,230 --> 00:33:55,170
+طبعا اختفائه بيجي مكانه reflex بيسموه plantar
+
+362
+00:33:55,170 --> 00:33:59,650
+reflex ال
+
+363
+00:33:59,650 --> 00:34:04,390
+reflex التاني اللي احنا هنشوفه Palmer grasping
+
+364
+00:34:04,390 --> 00:34:16,450
+reflexبارمال بالمار راسبين رفليكس بارمال
+
+365
+00:34:16,450 --> 00:34:20,470
+بالمار
+
+366
+00:34:20,470 --> 00:34:28,250
+راسبين رفليكس بارمال
+
+367
+00:34:28,250 --> 00:34:34,370
+بالمار راسبين رفليكس بارمال بالمار راسبين رفليكس
+
+368
+00:34:34,370 --> 00:34:34,570
+بارمال بالمار بالمار بالمار بالمار بالمار بالمار
+
+369
+00:34:34,570 --> 00:34:34,610
+بالمار بالمار بالمار بالمار بالمار بالمار بالمار
+
+370
+00:34:34,610 --> 00:34:34,610
+بالمار بالمار بالمار بالمار بالمار بالمار بالمار
+
+371
+00:34:34,610 --> 00:34:34,610
+بالمار بالمار بالمار بالمار بالمار بالمار بالمار
+
+372
+00:34:34,610 --> 00:34:34,610
+بالمار بالمار بالمار بالمار بالمار بالمار بالمار
+
+373
+00:34:34,610 --> 00:34:34,610
+بالمار بالمار بالمار بالمار بالمار بالمار بالمار
+
+374
+00:34:34,610 --> 00:34:35,230
+بالمار بالمار بالمار بالمار بالمار بالمار بالمار
+
+375
+00:34:35,230 --> 00:34:38,300
+بالمار بالمار بالمار بالمارانقباض في إيده في
+
+376
+00:34:38,300 --> 00:34:43,640
+أصابعه يتني أصابعه بيحاول إنه يمسك هذا ال object
+
+377
+00:34:43,640 --> 00:34:49,920
+اللي عمل stimulation هذا ال reflex بيختفي عن تلاتة
+
+378
+00:34:49,920 --> 00:34:56,360
+إلى أربع شهور وبتم استبداله بالقبضة أو مسكة
+
+379
+00:34:56,360 --> 00:35:02,070
+الأشياء بقراتهيعني مش بحاجة لأنه انا اعمل
+
+380
+00:35:02,070 --> 00:35:07,170
+scratching بعد الأربع شهور لأ مجرد ما احط الجلم في
+
+381
+00:35:07,170 --> 00:35:13,950
+إيد الطفل ممكن يعمل grasping له ويمسكه presence
+
+382
+00:35:13,950 --> 00:35:16,950
+and later disappearance is a sign of normal
+
+383
+00:35:16,950 --> 00:35:21,630
+development إذا وجوده واختفائه عند أربع شهور هي
+
+384
+00:35:21,630 --> 00:35:25,030
+جزء من عملية ال normal development اللي بتكون
+
+385
+00:35:25,030 --> 00:35:28,830
+موجودة ال moral reflex
+
+386
+00:35:31,870 --> 00:35:36,130
+هو طبعا من الـ postural reflex تقريبا اللي بتكون
+
+387
+00:35:36,130 --> 00:35:41,710
+موجودة شو اللي بيصير في ال moral reflex sudden
+
+388
+00:35:41,710 --> 00:35:45,610
+change in the head position will cause the child
+
+389
+00:35:45,610 --> 00:35:50,850
+to throw his arms outward and arch the back and
+
+390
+00:35:50,850 --> 00:35:56,150
+then bring his hands toward each other لو أنا جيت
+
+391
+00:35:56,150 --> 00:36:02,530
+عملت support مسكت الطفلو جاعته على أيدي بطريقة
+
+392
+00:36:02,530 --> 00:36:05,450
+معينة ان احنا نشوف بعض الفيديوهات ان شاء الله
+
+393
+00:36:05,450 --> 00:36:11,550
+بالعالمين لهذا ال reflexes و تركت الطفل و عملت له
+
+394
+00:36:11,550 --> 00:36:16,480
+sub part لل head تبعهوفجأة رخيت ال support عن ال
+
+395
+00:36:16,480 --> 00:36:22,360
+head وانا ماسك الطفل هلاجى ان الطفل فرض ايديه his
+
+396
+00:36:22,360 --> 00:36:28,860
+arms outward و بعد هيك جدامهم لقدام شوية كنوع من
+
+397
+00:36:28,860 --> 00:36:32,440
+الحماية هذا ال reflex اللى هو ال moral reflex
+
+398
+00:36:32,440 --> 00:36:38,120
+بيختفي عن تلاتى الى اربع شهوروبعد ذلك يتم استبداله
+
+399
+00:36:38,120 --> 00:36:43,880
+بشيء يسمى startle reflex يتم استبدال ال reflex بال
+
+400
+00:36:43,880 --> 00:36:49,220
+startle reflex presence of the reflex after four
+
+401
+00:36:49,220 --> 00:36:52,260
+months of age is an indication of abnormal
+
+402
+00:36:52,260 --> 00:36:58,300
+development وجود هذا ال reflex بعد أربع شهور يعني
+
+403
+00:36:58,300 --> 00:37:02,920
+أن هناك مشكلة في ال development الموجود عند الطفل
+
+404
+00:37:07,180 --> 00:37:14,780
+الـ swimming reflex an infant if immersed in water
+
+405
+00:37:14,780 --> 00:37:19,600
+will display active movement of the arms and legs
+
+406
+00:37:19,600 --> 00:37:25,040
+and will hold his or her breath وهذا لو جينا احنا
+
+407
+00:37:25,040 --> 00:37:28,820
+الطفل عمره أيام
+
+408
+00:37:31,020 --> 00:37:35,960
+لحد اربع الى ست شهور طفل حديث الولادة لحد عمر اربع
+
+409
+00:37:35,960 --> 00:37:39,880
+شهور لست شهور و جيت انا رميته في الميه غمرته في
+
+410
+00:37:39,880 --> 00:37:47,380
+الميه ردت فعل الطفل الطبيعي ان هو بيكتم نفسه و
+
+411
+00:37:47,380 --> 00:37:54,300
+بيعمل حركات في اديه و في رجليه كنوع من الاسباحة
+
+412
+00:37:54,300 --> 00:37:59,290
+هذا بيسموه swimming reflexهذا الـ reflex بيختفي
+
+413
+00:37:59,290 --> 00:38:03,990
+عند 4 إلى 6 شهور presence and later disappearance
+
+414
+00:38:03,990 --> 00:38:08,190
+is a sign of normal development وجود هذا الـ
+
+415
+00:38:08,190 --> 00:38:12,250
+reflex واختفاءه بعد مرحلة معينة هو شيء طبيعي
+
+416
+00:38:17,610 --> 00:38:21,930
+وهنا بنحكي عن infant held upright with feet
+
+417
+00:38:21,930 --> 00:38:26,430
+touching the surface will step as walking لو جيت
+
+418
+00:38:26,430 --> 00:38:33,250
+أنا مسكت الطفل من تحت قبطاته وخلت رجليه ومشت رجليه
+
+419
+00:38:33,250 --> 00:38:38,110
+يعمل stimulation لل desk اللي موجود او للصرير
+
+420
+00:38:38,110 --> 00:38:43,970
+وسبته وعملت له support اليوم هيعمل بعض الخطوات
+
+421
+00:38:43,970 --> 00:38:50,120
+كأنه بيمشيهذا ال reflex بيختفي عند 8 أسابيع يعني
+
+422
+00:38:50,120 --> 00:38:56,440
+عند شهرين قبل شهرين بيكون موجود وبعد شهرين بيختفي
+
+423
+00:38:56,440 --> 00:39:04,050
+هذا ال reflex واختفائه شيء طبيعيالعائلات اللي
+
+424
+00:39:04,050 --> 00:39:07,330
+بتبقى مركزة و الأمهات اللي مركزة مع نمو الطفل
+
+425
+00:39:07,330 --> 00:39:11,090
+بتقول انه قبل شهرين كان يصلب ع رجله و يعمل خطوات
+
+426
+00:39:11,090 --> 00:39:16,250
+لكن بعد الشهرين بطل يقدر يعمل لأ هذا شئ طبيعي انه
+
+427
+00:39:16,250 --> 00:39:21,630
+يكون موجود من ال reflexes اللي بتكون موجودة كمان
+
+428
+00:39:21,630 --> 00:39:24,830
+بنشوفها ال primitive reflexes
+
+429
+00:39:26,960 --> 00:39:31,980
+asymmetrical tonic neck reflex وهو من الـ postural
+
+430
+00:39:31,980 --> 00:39:37,500
+reflex اللي احنا بنحكي عنها و ال asymmetrical
+
+431
+00:39:37,500 --> 00:39:43,360
+tonic neck reflex when the head of the infant is
+
+432
+00:39:43,360 --> 00:39:48,220
+turned to one side, the hand at the side extends
+
+433
+00:39:48,220 --> 00:39:52,980
+and the opposite leg flicks لو جينا احنا طلعنا في
+
+434
+00:39:52,980 --> 00:40:01,240
+الطفلوعملنا عملية turning للـ head لجهة one side
+
+435
+00:40:01,240 --> 00:40:09,600
+على سبيل المثال اليمين اليد اليمين هتفرد في
+
+436
+00:40:09,600 --> 00:40:15,540
+المقابل ايده او رجله الشمال هيصير فيها reflection
+
+437
+00:40:15,540 --> 00:40:22,310
+طبعا هذا ال reflexبيكون موجود عند أربع إلى ست شهور
+
+438
+00:40:22,310 --> 00:40:29,250
+وبيختفي لحد أربع أو ست شهور بعدها بيختفي ومتقولنا
+
+439
+00:40:29,250 --> 00:40:34,350
+إنه هذه العملية وجوده واختفائه جزء من الـnormal
+
+440
+00:40:34,350 --> 00:40:40,370
+development في reflex آخر بيسموه symmetrical tonic
+
+441
+00:40:40,370 --> 00:40:46,410
+neck reflex الطفل طبعا بيكون في هذه الحالة brown
+
+442
+00:40:46,410 --> 00:40:54,530
+position على وجهه نايمعلى ال therapist بيكون حاطة
+
+443
+00:40:54,530 --> 00:41:01,330
+arms flex and legs as well as هلاجى أنه إيديه
+
+444
+00:41:01,330 --> 00:41:06,890
+ورجليه بيتنوا بنفس الكيفية وبنفس الشكل positive
+
+445
+00:41:06,890 --> 00:41:12,590
+reaction normal up to four to six weeks الآن هنحكى
+
+446
+00:41:12,590 --> 00:41:17,650
+عن tonic labyrinthine reflex لكن خلّينا أنه
+
+447
+00:41:17,650 --> 00:41:22,720
+parachute reactionبتصور إن هدولة هيكون في
+
+448
+00:41:22,720 --> 00:41:25,120
+الفيديوهات إن شاء الله رب العالمين اللي هنزلهم
+
+449
+00:41:25,120 --> 00:41:28,760
+هيكونوا مرتبطين مع المحاضرة روابط لفيديوهات ال
+
+450
+00:41:28,760 --> 00:41:34,400
+reflexes بتشرحهم بشكل أفضل primitive reflexes and
+
+451
+00:41:34,400 --> 00:41:39,820
+how they affect performance
+
+452
+00:41:39,820 --> 00:41:44,260
+لو جينا تطلعنا على ال primitive reflexes وكيف
+
+453
+00:41:44,260 --> 00:41:47,880
+بيأثروا على ال performance تبع الشخص evidence
+
+454
+00:41:47,880 --> 00:41:52,320
+suggestthat when a cluster of primitive reflexes
+
+455
+00:41:52,320 --> 00:41:55,860
+is still present beyond the normal age of
+
+456
+00:41:55,860 --> 00:41:59,120
+inhibition they may interfere with academic
+
+457
+00:41:59,120 --> 00:42:03,480
+performance and prevent a child from reaching his
+
+458
+00:42:03,480 --> 00:42:07,860
+or her potential in the education حلاجي أن وجود
+
+459
+00:42:07,860 --> 00:42:09,580
+مجموعة من ال reflexes
+
+460
+00:42:12,650 --> 00:42:15,630
+أكتر من الوجد اللي يفترض أنها تكون موجودة فيه،
+
+461
+00:42:15,630 --> 00:42:20,030
+يعني يفترض أن هذا الـreflex اختفى، لكن جينات طالعة
+
+462
+00:42:20,030 --> 00:42:25,950
+حلجي موجود، هذا هيأثر على عملية التحصيل العلمي
+
+463
+00:42:25,950 --> 00:42:31,450
+والأكاديمي عند الطفل، على سبيل المثال samples of
+
+464
+00:42:35,030 --> 00:42:38,210
+reflexes are associated with specific learning
+
+465
+00:42:38,210 --> 00:42:42,950
+problems لو جينا تطلعنا على ال asymmetrical tonic
+
+466
+00:42:42,950 --> 00:42:49,310
+neck reflex وكيف هيأثر على سلوك الطفل لو كان في
+
+467
+00:42:49,310 --> 00:42:55,570
+عندي طفل ال asymmetrical tonic neck reflex موجود
+
+468
+00:42:55,570 --> 00:43:00,990
+عنده أكثرأو خلّيني أقول إنه موجود في الوجد اللي
+
+469
+00:43:00,990 --> 00:43:05,730
+يفترض أنه يكون اختفى فيه هذا هيأثر على الطفل
+
+470
+00:43:05,730 --> 00:43:10,340
+بطريقة معينةchildren manifest in the following
+
+471
+00:43:10,340 --> 00:43:16,200
+ways هنلاقي أن الأطفال اللي كانوا بيعانوا من بقاء
+
+472
+00:43:16,200 --> 00:43:19,520
+ال asymmetrical tonic neck reflex أكتر من المدة
+
+473
+00:43:19,520 --> 00:43:23,100
+الطبيعية هنلاقي أنه في عندهم مشاكل في ال
+
+474
+00:43:23,100 --> 00:43:29,180
+handwriting بيقدرش يمسك الجلم و يكتب بالشكل السليم
+
+475
+00:43:29,180 --> 00:43:34,080
+written ideas not reflecting intelligenceالشغلات
+
+476
+00:43:34,080 --> 00:43:40,460
+اللي بيكتبها مابتعكسش مدى ذكاؤه بالضبط poor hand
+
+477
+00:43:40,460 --> 00:43:47,440
+and eye coordination في عنده مشكلة في عملية
+
+478
+00:43:47,440 --> 00:43:52,100
+التناسخ ما بين إيده و ما بين عينه يعني ممكن نلاقيه
+
+479
+00:43:52,100 --> 00:43:57,520
+بيكتب في أول سطر أول كلمة في أول سطر و آخر كلمة
+
+480
+00:43:57,520 --> 00:43:59,400
+نزلت على السطر الأخير
+
+481
+00:44:02,040 --> 00:44:06,260
+Dislike of sport or classlessness at ball games
+
+482
+00:44:06,260 --> 00:44:10,720
+بيحبش الرياضة ولا بيحب حصة الرياضة Difficulty
+
+483
+00:44:10,720 --> 00:44:15,160
+distinguishing left from right بيلاقي صعوبة في أنه
+
+484
+00:44:15,160 --> 00:44:19,940
+يفرق بين الجهة اليمين والجهة الشمال من جسمه Losing
+
+485
+00:44:19,940 --> 00:44:24,320
+their place on the page when reading بتوه كتير لما
+
+486
+00:44:24,320 --> 00:44:30,500
+بيكون بيقرأ في كتاب أو في مكانممكن يلخبط ويضيع
+
+487
+00:44:30,500 --> 00:44:37,300
+مكان القراءة تبعته فبتلاقيه يتبع بالاصبع يعني
+
+488
+00:44:37,300 --> 00:44:44,880
+difficulty distinguishing left from right حلاجة
+
+489
+00:44:44,880 --> 00:44:48,880
+انه لو كان بدي يقرا بدون ما يأشر بعيناه زي ما احنا
+
+490
+00:44:48,880 --> 00:44:52,980
+بنقول يتبع بعيناه سهل جدا انه يتوه عن المكان اللي
+
+491
+00:44:52,980 --> 00:44:54,160
+كان بيقرا فيه
+
+492
+00:44:58,580 --> 00:45:03,300
+if tonic-labyrinthine reflex is persist إذا كنا
+
+493
+00:45:03,300 --> 00:45:09,940
+بنحكي عن الـ asymmetrical tonic neck reflex لو كان
+
+494
+00:45:09,940 --> 00:45:13,900
+موجود، شو هيعمل؟ الآن نتطلع على الـ tonic
+
+495
+00:45:13,900 --> 00:45:17,810
+-labyrinthine reflex شو هيعمل؟child tend to
+
+496
+00:45:17,810 --> 00:45:22,850
+reverse letters or numbers الطفل بيبدأ يعكس الأحرف
+
+497
+00:45:22,850 --> 00:45:27,110
+والأرقام بيكتب السابعة زي التمانية بدل التمانية
+
+498
+00:45:27,110 --> 00:45:31,350
+يعني باللغة العربية بنلاقي أنه كتب سبعة و الفتحة
+
+499
+00:45:31,350 --> 00:45:37,710
+تبعتها ده تحت بيكتب أربعة بدل ما يكتبها على اليمين
+
+500
+00:45:37,710 --> 00:45:42,250
+الفتحة تبعتها بيكتبها على الجهة اليسرى skipping
+
+501
+00:45:42,250 --> 00:45:46,500
+over words or skipping a line while readingبفط
+
+502
+00:45:46,500 --> 00:45:52,020
+كلمات و بفط أسطر أحيانا في أثناء القراءة تبعته
+
+503
+00:45:52,020 --> 00:45:55,960
+orientation and spatial difficulties with direct
+
+504
+00:45:55,960 --> 00:46:00,280
+impact on his or her concept of time understanding
+
+505
+00:46:00,280 --> 00:46:04,680
+and giving direction or math ability في عنده مشكلة
+
+506
+00:46:04,680 --> 00:46:09,820
+في عملية تحديد الأماكن وتحديد بعض المسائل الرياضية
+
+507
+00:46:09,820 --> 00:46:17,140
+وسهل جدا أنه يتوه في مكان معينTravel sickness ده
+
+508
+00:46:17,140 --> 00:46:22,080
+السفر يمكن يكون في عنده مشكلة في السفر بيحبش السفر
+
+509
+00:46:22,080 --> 00:46:29,230
+و بيمرض لما بده يسافر سواء كان في bus أو غيرهالـ
+
+510
+00:46:29,230 --> 00:46:32,990
+symmetrical tonic neck reflex still persists إذا
+
+511
+00:46:32,990 --> 00:46:35,650
+كان هذا الـ symmetrical tonic neck reflex موجود
+
+512
+00:46:35,650 --> 00:46:40,330
+هلاجى إن الطفل في عنده بعض الأعراض إنه لما بديجي
+
+513
+00:46:40,330 --> 00:46:44,190
+يكتب هلاجيه lean down over the page و ال writing
+
+514
+00:46:44,190 --> 00:46:50,270
+هلاجيه نام فوق الدفتر تبعه أثناء الكتابة have
+
+515
+00:46:50,270 --> 00:46:54,290
+difficulty copying from blackboard لما بديجي ينسخ
+
+516
+00:46:54,290 --> 00:47:00,110
+عن اللوح بيقعد فترة طويلةو بيكون في عنده مشكلة في
+
+517
+00:47:00,110 --> 00:47:03,790
+النسخ عن اللوح و ممكن ينمسح اللوح مرة و مرتين هو
+
+518
+00:47:03,790 --> 00:47:12,570
+ما مش مخلص أول مرة فوضى
+
+519
+00:47:12,570 --> 00:47:16,470
+و في الأكل إذا
+
+520
+00:47:16,470 --> 00:47:22,770
+زي ما حكينا في عندهمسي eating or spillage فوضوي في
+
+521
+00:47:22,770 --> 00:47:28,290
+عملية الأكل بشروط كتير في الأكل spend a long time
+
+522
+00:47:28,290 --> 00:47:32,030
+doing homework عملية كتابة واجب ممكن يقعد من أول
+
+523
+00:47:32,030 --> 00:47:36,390
+النهار لآخر النهار و هو بيكتب في الواجب have poor
+
+524
+00:47:36,390 --> 00:47:41,850
+concentration and poor attention to task بيركزش في
+
+525
+00:47:41,850 --> 00:47:47,430
+الواجبات، بيركزش في الأمور اللي بتنطلب منهavoid
+
+526
+00:47:47,430 --> 00:47:52,670
+sport و بيحاول يبعد عن الرياضة هيك احنا بنكون
+
+527
+00:47:52,670 --> 00:47:59,070
+خلصنا ان شاء الله رب العالمين لكن مهم جدا اتبعوا
+
+528
+00:47:59,070 --> 00:48:02,670
+الفيديوهات اللي ان شاء الله رب العالمين هارفقها لل
+
+529
+00:48:02,670 --> 00:48:08,120
+reflex بالذات كل reflex يعني ممكن يكون مد توقفنص
+
+530
+00:48:08,120 --> 00:48:13,120
+دقيقة او اقل او اكتر المهم ان انتوا تتبعوا هذه ال
+
+531
+00:48:13,120 --> 00:48:17,460
+reflexes عشان تفهموها و تشوفوا ردات الفعل بشكل
+
+532
+00:48:17,460 --> 00:48:22,140
+افضل و اللي عنده بعد هيك اي استفسار يحضره ان شاء
+
+533
+00:48:22,140 --> 00:48:24,960
+الله رب العالمين للقاء مباشر بنتكلم فيه
+
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/m26vrl8oTz4_postprocess.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/m26vrl8oTz4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..72509cc971b422b591de5a722eb457adfcb0c136
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/m26vrl8oTz4_postprocess.srt
@@ -0,0 +1,1004 @@
+1
+00:00:00,000 --> 00:00:04,720
+السلام عليكم زي ما حكينا المرة الماضية عن أهمية
+
+2
+00:00:04,720 --> 00:00:09,460
+human growth and development وحكينا إنه كتير من
+
+3
+00:00:09,460 --> 00:00:15,560
+صناع القرار العلماء أولو اهتمام كبير جدا بعملية ال
+
+4
+00:00:15,560 --> 00:00:19,520
+growth and development من ساعة ال time of
+
+5
+00:00:19,520 --> 00:00:24,980
+conception لحد ال time of death يعني زي ما حكينا
+
+6
+00:00:24,980 --> 00:00:30,050
+قبل هيك from womb to tombهذه كلها طبعا سموها عملية
+
+7
+00:00:30,050 --> 00:00:36,430
+ال life span cycle و life span cycle بتحتوي على
+
+8
+00:00:36,430 --> 00:00:42,270
+عدة مراحل المراحل هذه زي ما جسموها العلماء طبعا في
+
+9
+00:00:42,270 --> 00:00:48,490
+بعض الاختلاف بيكون حسب المراجعthey are typically
+
+10
+00:00:48,490 --> 00:00:53,670
+divided into the following categories prenatal
+
+11
+00:00:53,670 --> 00:00:58,390
+period which start from conception to the time of
+
+12
+00:00:58,390 --> 00:01:03,830
+birth the infancy period which start from time of
+
+13
+00:01:03,830 --> 00:01:08,690
+birth until one year and some resources some
+
+14
+00:01:08,690 --> 00:01:13,130
+references said until two years بعض المصادر بتقول
+
+15
+00:01:13,130 --> 00:01:18,220
+لحد سنتين ممكن نعتبر هذه الفترةهى عبارة عن فترة
+
+16
+00:01:18,220 --> 00:01:25,400
+infancy period ال early childhood من حد سن سنة او
+
+17
+00:01:25,400 --> 00:01:31,920
+سنتين حسب المرجع اللى احنا بنتبعه لحد ست سنوات
+
+18
+00:01:31,920 --> 00:01:36,600
+طبعا فترة ال early childhood تنجسم كمان pre
+
+19
+00:01:36,600 --> 00:01:41,660
+kindergarten stage مرحلة رياض الأطفال او مرحلة ما
+
+20
+00:01:41,660 --> 00:01:46,150
+قبل المدارس لحد مرحلة ما قبل المدارسال late
+
+21
+00:01:46,150 --> 00:01:51,570
+childhood من سن من سن ستة لاتناشر سنة ال
+
+22
+00:01:51,570 --> 00:01:56,270
+adolescence period من اتناش لحد عشرين في بعض الكتب
+
+23
+00:01:56,270 --> 00:02:01,670
+ممكن تحكي لحد تمانتاش early adulthood نحكي من حد
+
+24
+00:02:01,670 --> 00:02:08,410
+او من سن عشرين لاربعين سنةمد ال adulthood من 40 ل
+
+25
+00:02:08,410 --> 00:02:16,470
+65 سنة ال late adulthood من 65 لحد نهاية العمر او
+
+26
+00:02:16,470 --> 00:02:20,550
+الى ما شاء الله لو جينا نطلع على مرحلة ال prenatal
+
+27
+00:02:20,550 --> 00:02:23,050
+development ال prenatal development اللي هتلاقيها
+
+28
+00:02:23,050 --> 00:02:29,390
+بتتقسم الى ثلاث مراحل أساسية ال germinal stage ال
+
+29
+00:02:29,390 --> 00:02:36,640
+embryonic stage الفيتل stageو الـ prenatal period
+
+30
+00:02:36,640 --> 00:02:43,140
+start from conception and end with birth until the
+
+31
+00:02:43,140 --> 00:02:48,140
+time of birth أو until birth إذن لما بنحكي على
+
+32
+00:02:48,140 --> 00:02:55,130
+prenatal developmentهي عبارة عن الفترة اللي بتبدأ
+
+33
+00:02:55,130 --> 00:03:01,630
+من ساعة الإخصاب للبويضة لحد ساعة الولادة و بتتقسم
+
+34
+00:03:01,630 --> 00:03:08,170
+إلى تلت مراحل أساسية ال germinal stage اللي بتبدأ
+
+35
+00:03:08,170 --> 00:03:12,330
+من ال time of conception لحد عشرة إلى أربعة عشر
+
+36
+00:03:12,330 --> 00:03:17,950
+يوم أو لحد اسبوعينemperionic stage من أسبوعين لحد
+
+37
+00:03:17,950 --> 00:03:24,210
+تمان أسابيع ال fetal stage من تمان أسابيع لحد وقت
+
+38
+00:03:24,210 --> 00:03:31,670
+الولادة as individuals pass through these life
+
+39
+00:03:31,670 --> 00:03:32,290
+stages
+
+40
+00:03:35,460 --> 00:03:39,020
+type of growth and development occur في أثناء
+
+41
+00:03:39,020 --> 00:03:44,280
+عملية growth and development بيمر الإنسان بعدة
+
+42
+00:03:44,280 --> 00:03:50,320
+تغيرات ممكن نشوفها على صعيد ال physical على صعيد
+
+43
+00:03:50,320 --> 00:03:56,320
+ال mental على صعيد ال emotional و النقطة الرابعة
+
+44
+00:03:56,320 --> 00:04:01,700
+على صعيد ال social إذا في عندي أربع نقاط أساسية
+
+45
+00:04:01,700 --> 00:04:08,100
+اللي احنابدنا ندرسها في عملية الـ change أو عملية
+
+46
+00:04:08,100 --> 00:04:13,540
+الـ growth and development اللي بتصير في ال human
+
+47
+00:04:13,540 --> 00:04:18,720
+being أول مرحلة أو ال dimension الأول اللي قلنا
+
+48
+00:04:18,720 --> 00:04:24,710
+عنه ال physical و اللي تتناولعملية النمو الـ
+
+49
+00:04:24,710 --> 00:04:28,870
+biological change سواء كان زيادة في الطول زيادة في
+
+50
+00:04:28,870 --> 00:04:35,190
+الوزن كل هذه عبارة عن examples of physical
+
+51
+00:04:35,190 --> 00:04:44,240
+developmentو ممكن قياسها بالميزان الوزن الطول ممكن
+
+52
+00:04:44,240 --> 00:04:49,900
+نشوف جداش طول الإنسان و جداش معدل انه اللي بيكون
+
+53
+00:04:49,900 --> 00:04:55,700
+فيه الـmental أو الـ cognitive development اللي
+
+54
+00:04:55,700 --> 00:05:00,540
+بتشمل عملية ال learning بتشمل solving problems
+
+55
+00:05:00,540 --> 00:05:07,160
+بتشمل الإصدار القرارات أو اتخاذ الأحكام بحقكأشياء
+
+56
+00:05:07,160 --> 00:05:12,600
+معينة وبتتطور مع العمر ومع التقدم في العمر ومع
+
+57
+00:05:12,600 --> 00:05:18,650
+الخبرات اللي بيكتسبها في حياة الإنسانemotional
+
+58
+00:05:18,650 --> 00:05:22,870
+which refer to feelings and include dealing with
+
+59
+00:05:22,870 --> 00:05:27,310
+love, hate, joy, fear, excitement and other
+
+60
+00:05:27,310 --> 00:05:31,450
+similar feelings إذا عملية ال emotional هي ما
+
+61
+00:05:31,450 --> 00:05:38,370
+يتناوله أو عملية ال development كيف الإنسان بينمو
+
+62
+00:05:38,370 --> 00:05:44,350
+عنده شعور الحب والكره الخوف كل هذه الأمور كيف ممكن
+
+63
+00:05:44,350 --> 00:05:49,840
+تصير إليها عملية التطورسأقوم بالتركيز على الـ
+
+64
+00:05:49,840 --> 00:05:53,320
+social
+
+65
+00:05:54,890 --> 00:06:01,330
+development of social relationship تكون العلاقات
+
+66
+00:06:01,330 --> 00:06:05,590
+الإجتماعية زي ال friendship الصداقة وغيرها من
+
+67
+00:06:05,590 --> 00:06:09,130
+العلاقات سواء كان على مستوى العمل على مستوى الأسرة
+
+68
+00:06:09,130 --> 00:06:14,210
+كل هذه طبعا ضمن ال social development أو ال social
+
+69
+00:06:14,210 --> 00:06:18,190
+change اللي احنا هنتطلعله و هندرسه في العملية ال
+
+70
+00:06:18,190 --> 00:06:23,650
+developmentمثلًا، يمكن أن يتكلم طفل بطريقة مختلفة
+
+71
+00:06:23,650 --> 00:06:31,870
+مع والده أنه يتكلم مع صديق أو صديق طفل. كل مرحلة
+
+72
+00:06:31,870 --> 00:06:38,810
+تحتوي على خصيصها ومهارات تطورية محددة التي يجب أن
+
+73
+00:06:38,810 --> 00:06:39,370
+يتعلمها الشخص.
+
+74
+00:06:41,910 --> 00:06:45,950
+إذا لو جينا نتطلع كمثال في عملية الـ development
+
+75
+00:06:45,950 --> 00:06:51,090
+لـ social relationship هي عملية أو هي العلاقة
+
+76
+00:06:51,090 --> 00:06:56,370
+الاجتماعية ما بين المراهق أو الطفل أو الشخص في
+
+77
+00:06:56,370 --> 00:07:01,410
+مرحلة المراهقة و ما بين عائلته و ما بين أصدقائه
+
+78
+00:07:01,410 --> 00:07:06,030
+هلاجي أنه في عملية أو في العلاقة اللي بتكون موجودة
+
+79
+00:07:06,030 --> 00:07:11,890
+بينه و بين أصدقائه بيتصرف بطريقة مختلفة عن تصرفه
+
+80
+00:07:12,000 --> 00:07:17,160
+مابين و بين والده لان نجي لمرحلة ال prenatal
+
+81
+00:07:17,160 --> 00:07:21,020
+development و هنتطلع نتطرق ل ال prenatal
+
+82
+00:07:21,020 --> 00:07:25,800
+development بشيء من التفصيل ال prenatal
+
+83
+00:07:25,800 --> 00:07:29,340
+development زي ما حكينا ان احنا بنقسمها إلى ثلاث
+
+84
+00:07:29,340 --> 00:07:36,540
+مراحل أساسيةالمرحلة الأولى بتبدأ من ساعة الإخصاب
+
+85
+00:07:36,540 --> 00:07:41,380
+الـ time of conception لحد عشرة إلى أربعة عشر يوم
+
+86
+00:07:41,380 --> 00:07:46,640
+هذه سميناها ال germinal stage المرحلة التانية اللي
+
+87
+00:07:46,640 --> 00:07:52,160
+هي ال embryonic stage واللي بتبدأ مناربعتاشر يوم
+
+88
+00:07:52,160 --> 00:07:57,560
+او اسبوعين لحد تمان اسابيع و المرحلة التالتة اللى
+
+89
+00:07:57,560 --> 00:08:04,700
+تسمى fetal stage from eight weeks to birth من حد
+
+90
+00:08:04,700 --> 00:08:11,680
+تمان اسابيع لحد الولادة كل هذه طبعا تسمى fetal
+
+91
+00:08:11,680 --> 00:08:15,800
+stage from
+
+92
+00:08:15,800 --> 00:08:21,840
+conception to birthفي تقسيم تانية بتقول انه من
+
+93
+00:08:21,840 --> 00:08:29,260
+ساعة الإخصاب لحد الولادة طبعا بيمر الجنين في مراحل
+
+94
+00:08:29,260 --> 00:08:36,890
+مرحلة الـzygote ومرحلة ال embryo ومرحلة ال fetusلو
+
+95
+00:08:36,890 --> 00:08:43,910
+جينا نسقط هذه المعلومات أو التسمية على المعلومات
+
+96
+00:08:43,910 --> 00:08:47,630
+اللى موجودة عندنا هلاجى مرحلة الـ Zygote هي مرحلة
+
+97
+00:08:47,630 --> 00:08:52,570
+الـ germinal stage اللى بتبدأ من ال time of
+
+98
+00:08:52,570 --> 00:08:58,690
+conception لحد 14 يوم مرحلة ال embryo هلاجيها
+
+99
+00:08:58,690 --> 00:09:05,890
+بتبدأ من أسبوعين لحد 8 أسابيعمرحلة ال fetus او ال
+
+100
+00:09:05,890 --> 00:09:11,510
+fetal stage هنجيها بتبدأ من تمان أسابيع لحد
+
+101
+00:09:11,510 --> 00:09:16,710
+الولادة شو اللي بيميز مرحلة ال zygote او ال
+
+102
+00:09:16,710 --> 00:09:21,010
+germinal stage يقولنا ان هي بتبدأ من ال time of
+
+103
+00:09:21,010 --> 00:09:30,980
+conceptionوجدت الإخصاب لحد 10 days أو 14 days لحد
+
+104
+00:09:30,980 --> 00:09:35,360
+أسبوعين من عشر أيام إلى أسبوعين أو إلى أربعتاشر
+
+105
+00:09:35,360 --> 00:09:40,020
+يوم period of rapid cell divisionوهذه ما يميز
+
+106
+00:09:40,020 --> 00:09:46,200
+مرحلة الزيجوت او الانقسام السريع للخلايا two weeks
+
+107
+00:09:46,200 --> 00:09:50,940
+later when the zygote is implanted in the wall of
+
+108
+00:09:50,940 --> 00:09:58,760
+the uterus تنتهي مجرد ما يصير فيه غمر او زراعة
+
+109
+00:09:58,760 --> 00:10:04,700
+للزيجوت او انغمار الزيجوت في جدار الرحل
+
+110
+00:10:04,700 --> 00:10:12,570
+blastocyste خلال مرحلة الزيجوتبيمر بعدة مراحل زى
+
+111
+00:10:12,570 --> 00:10:18,850
+ما حكينا او في بعض التغيرات اللى بتكون موجودة من
+
+112
+00:10:18,850 --> 00:10:23,450
+ضمنها مرحلة بيسموها ال blastocyst اللى هي عدد او
+
+113
+00:10:23,450 --> 00:10:28,050
+يميزها ان عدد خلاياها بيكون من ستين الى سبعين خلية
+
+114
+00:10:28,050 --> 00:10:33,440
+وهذا طبعا بتكون في اليوم الرابعو في الـ Plastocyst
+
+115
+00:10:33,440 --> 00:10:38,240
+هنلاقي فيها حاجة نسميها Embryonic Disc في المستقبل
+
+116
+00:10:38,240 --> 00:10:46,780
+هيكون ال organism أو جسم الطفل ال outer ring اللي
+
+117
+00:10:46,780 --> 00:10:52,540
+هيكون ال umbilical cord البلسنتاimplantation
+
+118
+00:10:52,540 --> 00:11:01,920
+between days 7 and 9 days عملية زراعة القرص هذا او
+
+119
+00:11:01,920 --> 00:11:05,840
+البلاستوست في جدار الرحم ما بين اليوم السابع
+
+120
+00:11:05,840 --> 00:11:13,660
+والعاشر اذا زي ما حكينا period
+
+121
+00:11:13,660 --> 00:11:17,500
+of zygote بيكون في عندي انا في البلاستوست مرحلة
+
+122
+00:11:17,500 --> 00:11:19,000
+البلاستوست
+
+123
+00:11:21,110 --> 00:11:26,570
+حاجة بنسميها الـ Empirionic Disc و ال outer ring
+
+124
+00:11:26,570 --> 00:11:30,470
+لو جينا نتطلع الآن في الصورة اللي موجودة أمامنا
+
+125
+00:11:30,470 --> 00:11:36,230
+مرحلة التكوين بدأت سيرا عندي
+
+126
+00:11:39,010 --> 00:11:44,950
+ال امبريونك ديسك هاي ال outer ring وهاي في عندي
+
+127
+00:11:44,950 --> 00:11:52,290
+انا طبعا ال disk اللي موجود في الداخل لحد مرحلة
+
+128
+00:11:52,290 --> 00:11:59,090
+implementation في ال wall of the uterus عملية
+
+129
+00:11:59,090 --> 00:12:04,930
+زراعته تحت جدار او في جدار الرحمة
+
+130
+00:12:07,460 --> 00:12:12,760
+إذا لو جينا نطلع على مرحلة ال
+
+131
+00:12:12,760 --> 00:12:17,540
+time of conception او
+
+132
+00:12:17,540 --> 00:12:23,540
+مرحلة إزاي جوت حالة جيه انه بتبدأ من عملية ال time
+
+133
+00:12:23,540 --> 00:12:29,060
+of conception و جابلها بيسبقها عملية ال ovulation
+
+134
+00:12:29,060 --> 00:12:35,400
+و بتمشي في ال valopian tube لحد ما يصير عملية ال
+
+135
+00:12:35,400 --> 00:12:42,260
+fertilizationفي الـ valvian cube و بتبدأ عملية
+
+136
+00:12:42,260 --> 00:12:48,940
+الانقسام السريع للخلايا من خلية واحدة صار خليتين
+
+137
+00:12:48,940 --> 00:12:57,940
+اربعة ست تمانية16 و هلو مجرة لحد ما تصل في اليوم
+
+138
+00:12:57,940 --> 00:13:03,140
+الرابع زي ما قلنا 60 إلى 70 خلية في اليوم الرابع
+
+139
+00:13:03,140 --> 00:13:08,180
+بتوصل عددها 60 إلى 70 خلية و بتكون عندى
+
+140
+00:13:10,860 --> 00:13:14,700
+الـ blastocyst اللي بتكون من الـ embryonic disk
+
+141
+00:13:14,700 --> 00:13:19,240
+اللي هيعطيني في المستقبل ال organism و ال outer
+
+142
+00:13:19,240 --> 00:13:27,480
+ring الخارجي هذا هو اللي هيعطيني أو هيتكون منه ال
+
+143
+00:13:27,480 --> 00:13:31,040
+umbilical cord في المستقبل
+
+144
+00:13:34,570 --> 00:13:39,630
+بلاستوسيست قامت بإستعمال نفسها داخل الاندومتريام
+
+145
+00:13:39,630 --> 00:13:46,250
+وقامت بتنمية بسرعة بينما تصبح عيونها مختلفة إلى
+
+146
+00:13:46,250 --> 00:13:49,350
+عيون تدعم الاندومتريام إلى عيون تدعم الاندومتريام
+
+147
+00:13:49,350 --> 00:13:54,130
+إلى عيون تدعم الاندومتريام إذا المرحلة من 12 إلى
+
+148
+00:13:54,130 --> 00:13:57,930
+14 يوم اللي مرحلة استعمال
+
+149
+00:14:01,150 --> 00:14:05,150
+emperionic disk او زيجوت in the wall of the uterus
+
+150
+00:14:05,150 --> 00:14:12,010
+وبتبدأ عملية ال differentiation للخلايا وزي ما
+
+151
+00:14:12,010 --> 00:14:18,190
+قلنا انه ال outer ring هذا بيصير مسئول عن او
+
+152
+00:14:18,190 --> 00:14:24,830
+هيتكون منه ال embolical cord البلسنتا وال inner
+
+153
+00:14:24,830 --> 00:14:27,730
+disk اللي هيعطيني جسمي
+
+154
+00:14:30,230 --> 00:14:34,930
+الـ fetus أو جسم الجنين في المستقبل وجسم الجنين
+
+155
+00:14:34,930 --> 00:14:41,610
+بتبدأ تتنوع الخلايا وتتشكل الخلايا بحيث يصير واضح
+
+156
+00:14:41,610 --> 00:14:46,610
+من الخلايا اللي هتكون مسئولة عن الجهاز الهضمي من
+
+157
+00:14:46,610 --> 00:14:50,670
+الخلايا اللي هتكون مسئولة عن نمو الجهاز العضلي من
+
+158
+00:14:50,670 --> 00:14:54,590
+الخلايا اللي هتكون مسئولة أو هتتطور في المستقبل
+
+159
+00:14:54,590 --> 00:15:02,630
+لتكوين الجهاز العضليالان زى ما حكينا كمان مرة the
+
+160
+00:15:02,630 --> 00:15:06,630
+blastocyst having implanted itself deep within the
+
+161
+00:15:06,630 --> 00:15:14,330
+endometrium هتنغرس هذه او الزيجوت في جدار الرحم
+
+162
+00:15:17,100 --> 00:15:20,840
+proceed to grow rapidly while its cells become
+
+163
+00:15:20,840 --> 00:15:24,300
+differentiated into embryonic and supporting cells
+
+164
+00:15:24,300 --> 00:15:28,680
+مين اللي هيكون في عندي ال embryonic cell اللي
+
+165
+00:15:28,680 --> 00:15:33,320
+هتعطيني جسم الجنين ومين اللي هتكون شغلات تساعد جسم
+
+166
+00:15:33,320 --> 00:15:37,260
+الجنين على النمو زي ال embolical cord وزي
+
+167
+00:15:37,260 --> 00:15:41,800
+البلاسنتا اللي احنا بسميها المشيمة أو الخلاصة
+
+168
+00:15:44,680 --> 00:15:54,840
+الـ embryonic disk بتكون من ثلاث طبقات أساسية طبقة
+
+169
+00:15:54,840 --> 00:16:02,160
+الاكتودانو طبقة الميزودانو طبقة الاندودانو يعني لو
+
+170
+00:16:02,160 --> 00:16:07,100
+جينا نطلع احنا هاي ال blastocyst اللي موجود أمامي
+
+171
+00:16:07,100 --> 00:16:12,260
+الآن وكيف بدأ ال outer ring يتشكل
+
+172
+00:16:16,100 --> 00:16:23,680
+لحد ما صار فيها عندي بشكل واضح ال embryonic disk
+
+173
+00:16:23,680 --> 00:16:29,120
+الان ال embryonic disk بيتكون من ثلاث طبقات أساسية
+
+174
+00:16:29,120 --> 00:16:34,520
+طبقة اللي لبرا زي ما احنا شايفينها هذه طبقة
+
+175
+00:16:34,520 --> 00:16:41,920
+الectodermالطبقة اللى فى المنتصف طبقة ال mesoderm
+
+176
+00:16:41,920 --> 00:16:47,760
+والطبقة الداخلية هذه كلها بيسموها طبقة ال endoderm
+
+177
+00:16:47,760 --> 00:16:54,100
+الان كل طبقة من الطبقات هذه هتكون هي نوع خلايا
+
+178
+00:16:54,100 --> 00:17:04,090
+مخصص لنمو عدة أجهزة فى الجسمعلى سبيل المثال طبقة
+
+179
+00:17:04,090 --> 00:17:08,770
+الـectoderm اللي هي الطبقة الخارجية هلاجيها مسؤولة
+
+180
+00:17:08,770 --> 00:17:18,770
+عن تكوين nervous system and skin الـfast
+
+181
+00:17:18,770 --> 00:17:24,610
+development of nervous system and skin طبقة الوسطى
+
+182
+00:17:26,030 --> 00:17:31,190
+ميزودان حلجية مسئولة عن development of skeleton،
+
+183
+00:17:31,190 --> 00:17:35,590
+نمو الجهاز
+
+184
+00:17:35,590 --> 00:17:43,960
+العضلي بالاضافة إلى الcirculation تبع الجسمأما
+
+185
+00:17:43,960 --> 00:17:48,840
+طبقة ال endoderm فهي مسئولة عن تكوين الأحشاء
+
+186
+00:17:48,840 --> 00:17:53,780
+الداخلية و أجهزة الجسم الداخلية زي الجهاز الهضمي
+
+187
+00:17:53,780 --> 00:17:57,320
+ال digestive system زي ال respiratory system ال
+
+188
+00:17:57,320 --> 00:18:03,920
+lungs ال urinary tract او tract الجهاز البولي
+
+189
+00:18:07,090 --> 00:18:13,650
+السلب البريونيكي أصبح أكتر مختلفًا لإنشاء مصادر من
+
+190
+00:18:13,650 --> 00:18:21,000
+العديد من أسلوب الجسمكل ما زاد النمو كل ما اتقدم
+
+191
+00:18:21,000 --> 00:18:26,440
+عمر الـ Zygote في النمو كل ما زاد عملية التخصيص
+
+192
+00:18:26,440 --> 00:18:30,080
+للخلايا بحيث ان خلايا تصبح مسئولة عن الجهاز
+
+193
+00:18:30,080 --> 00:18:33,800
+العصبي، خلايا تصبح مسئولة عن الأضافر، خلايا تصبح
+
+194
+00:18:33,800 --> 00:18:41,760
+مسئولة عن الجلد، خلايا تصبح مسئولة عن الشعر،هتبدأ
+
+195
+00:18:41,760 --> 00:18:47,340
+كل ما زاد عمر الجنين كل ما زاد تخصص الخلايا و كل
+
+196
+00:18:47,340 --> 00:18:52,900
+ما صار النواة لكل أجهزة الجسم موجودة بعد هيك بيصير
+
+197
+00:18:52,900 --> 00:18:59,440
+عملية النمو في عدد الخلايا و في حجمها لحد ما يكتمل
+
+198
+00:18:59,440 --> 00:19:04,640
+نمو الجنين كامل او نجي لمرحلة تانية هي مرحلة
+
+199
+00:19:04,640 --> 00:19:07,360
+period of empire
+
+200
+00:19:12,610 --> 00:19:21,070
+تبدأ من الاسبوع التالت نهاية الأسبوع التاني
+
+201
+00:19:23,880 --> 00:19:30,360
+أزاي؟ الآن في هذه المرحلة شو أهم ما يميزها؟ body
+
+202
+00:19:30,360 --> 00:19:35,120
+parts are formed during this period تبدأ تتكون
+
+203
+00:19:35,120 --> 00:19:41,860
+أعضاء الجسم لكن مش كاملة النضوج أو كاملة النمو for
+
+204
+00:19:41,860 --> 00:19:45,320
+the first eight weeks a process of differentiation
+
+205
+00:19:45,320 --> 00:19:52,870
+occur إذا باكتمالالتامن أسابيع أو الشهرين بتكون
+
+206
+00:19:52,870 --> 00:19:59,150
+طبعا عملية ال differentiation تميز الخلايا اكتملت
+
+207
+00:19:59,150 --> 00:20:05,490
+تماما this is the embryonicperiod when the cells
+
+208
+00:20:05,490 --> 00:20:09,490
+of the blastocyst which are very similar divide
+
+209
+00:20:09,490 --> 00:20:14,990
+rapidly over and over again to produce not only
+
+210
+00:20:14,990 --> 00:20:19,750
+bigger embryo but also multiplicity of cell type
+
+211
+00:20:23,620 --> 00:20:31,400
+بتتميز إنه في عندي زيادة في عدد الخلايا بالاضافة
+
+212
+00:20:31,400 --> 00:20:36,440
+إلى زيادة في حجم الخلايا الخاصة بالجنين وهذا
+
+213
+00:20:36,440 --> 00:20:42,600
+المرحلة طبعا ال Embryical cord يبدأ
+
+214
+00:20:42,600 --> 00:20:48,200
+تشكل عشان يربط ما بين ال embryo و ال placenta بربط
+
+215
+00:20:48,200 --> 00:20:54,600
+الجنين بالمشيمةemperio rest in the ammonium filled
+
+216
+00:20:54,600 --> 00:21:00,780
+with amniotic fluid هنلاقي ان مكان ال emperio في
+
+217
+00:21:00,780 --> 00:21:08,960
+كيس موجود sack which the sack consist of two
+
+218
+00:21:08,960 --> 00:21:17,760
+layersطبقة الداخلية من الامنيون هي عبارة عن ساك
+
+219
+00:21:17,760 --> 00:21:24,040
+عبارة
+
+220
+00:21:24,040 --> 00:21:31,160
+عن كيس سعت أو بيحتوي على سبعمية ملي لتر تقريبا نص
+
+221
+00:21:31,160 --> 00:21:36,420
+لتر او اكتر شوية من الامنيوتك فلود من السائل
+
+222
+00:21:36,420 --> 00:21:42,080
+الأميني اللي بيسبح فيهالجنين طبعا هذا باكتمال
+
+223
+00:21:42,080 --> 00:21:49,380
+مرحلة الحمل أو عند الشهر التاسع بيكون حجم الـ
+
+224
+00:21:49,380 --> 00:21:54,500
+amniotic fluid حوالي 700 ملي لترممكن اكتر شوية
+
+225
+00:21:54,500 --> 00:21:59,060
+ممكن اقل حسب الحجم this is a valuable protection
+
+226
+00:21:59,060 --> 00:22:02,900
+for the fetus both during its development and
+
+227
+00:22:02,900 --> 00:22:07,160
+during the early stage of labor وظيفة ال amniotic
+
+228
+00:22:07,160 --> 00:22:11,420
+fluid ان هو بيعطي نوع من الحماية او بيعطي نوع من
+
+229
+00:22:11,420 --> 00:22:16,700
+الحماية للجنين سواء كان في مرحلة النمو مرحلة ال
+
+230
+00:22:16,700 --> 00:22:23,810
+developmentأو في مرحلة الولادة و بتكون علامة و
+
+231
+00:22:23,810 --> 00:22:31,810
+انذار لعملية الولادة في مرحلة ال protectionأو
+
+232
+00:22:31,810 --> 00:22:35,670
+خلّيني أقول إنه بيشتغل ك protection في مرحلة الحمل
+
+233
+00:22:35,670 --> 00:22:42,070
+أو during the fetal stage هلاجي إنه الطفل أو
+
+234
+00:22:42,070 --> 00:22:47,230
+الجنين لو اتعرض لأي ضرب أو الأم اتعرضت لأي ضرب
+
+235
+00:22:47,230 --> 00:22:54,090
+أثناء فترة الحمل بيمتصها السائل الأمينيوما قبل
+
+236
+00:22:54,090 --> 00:22:59,430
+الولادة هلاجة ان هذا السائل صار فيه leakage او
+
+237
+00:22:59,430 --> 00:23:10,230
+عملية انفجار ل ال ammoniumساك أو الكيس هذا وبيطلع
+
+238
+00:23:10,230 --> 00:23:15,830
+منه السائل الأميني وهذا معناه علامة أنه أجى موعد
+
+239
+00:23:15,830 --> 00:23:20,690
+الولادة ونوع من الحماية لأن الطفل لو كانت المي هذه
+
+240
+00:23:20,690 --> 00:23:25,570
+مش موجودة حواليه هتأد إلى مضاعفات وممكن تأد إلى
+
+241
+00:23:25,570 --> 00:23:33,210
+الوفاة ال outer layer of الساك بسموها القريون
+
+242
+00:23:34,410 --> 00:23:47,510
+الكوريون مرتبط بجدار الرحم الكوريون
+
+243
+00:23:47,510 --> 00:23:57,170
+مرتبط
+
+244
+00:23:57,170 --> 00:24:00,470
+بجدار الرحم
+
+245
+00:24:04,760 --> 00:24:11,840
+منطقة الكوريون هي اللى هتنمو بشكل سريع و هتكون
+
+246
+00:24:11,840 --> 00:24:17,720
+عندى الـ placenta of the fetus وهي اللى هتعمل ال
+
+247
+00:24:17,720 --> 00:24:23,200
+machine او هيتكون منها ال machine اللى هتكون حلقة
+
+248
+00:24:23,200 --> 00:24:27,930
+الوصل ما بين الجنين و ما بين ال motherالمرة اللى
+
+249
+00:24:27,930 --> 00:24:29,890
+جاى ان شاء الله رب العالمين محاضرة جاى ان شاء الله
+
+250
+00:24:29,890 --> 00:24:33,970
+رب العالمين هنحكي عن الـ placenta وعن ال
+
+251
+00:24:33,970 --> 00:24:37,330
+circulation of blood inside the placenta
+
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@@ -0,0 +1,1004 @@
+1
+00:00:00,000 --> 00:00:04,720
+السلام عليكم زي ما حكينا المرة الماضية عن أهمية
+
+2
+00:00:04,720 --> 00:00:09,460
+human growth and development وحكينا إنه كتير من
+
+3
+00:00:09,460 --> 00:00:15,560
+صناع القرار العلماء أولو اهتمام كبير جدا بعملية ال
+
+4
+00:00:15,560 --> 00:00:19,520
+growth and development من ساعة ال time of
+
+5
+00:00:19,520 --> 00:00:24,980
+conception لحد ال time of death يعني زي ما حكينا
+
+6
+00:00:24,980 --> 00:00:30,050
+قبل هيك from womb to tombهذه كلها طبعا سموها عملية
+
+7
+00:00:30,050 --> 00:00:36,430
+ال life span cycle و life span cycle بتحتوي على
+
+8
+00:00:36,430 --> 00:00:42,270
+عدة مراحل المراحل هذه زي ما جسموها العلماء طبعا في
+
+9
+00:00:42,270 --> 00:00:48,490
+بعض الاختلاف بيكون حسب المراجعthey are typically
+
+10
+00:00:48,490 --> 00:00:53,670
+divided into the following categories prenatal
+
+11
+00:00:53,670 --> 00:00:58,390
+period which start from conception to the time of
+
+12
+00:00:58,390 --> 00:01:03,830
+birth the infancy period which start from time of
+
+13
+00:01:03,830 --> 00:01:08,690
+birth until one year and some resources some
+
+14
+00:01:08,690 --> 00:01:13,130
+references said until two years بعض المصادر بتقول
+
+15
+00:01:13,130 --> 00:01:18,220
+لحد سنتين ممكن نعتبر هذه الفترةهى عبارة عن فترة
+
+16
+00:01:18,220 --> 00:01:25,400
+infancy period ال early childhood من حد سن سنة او
+
+17
+00:01:25,400 --> 00:01:31,920
+سنتين حسب المرجع اللى احنا بنتبعه لحد ست سنوات
+
+18
+00:01:31,920 --> 00:01:36,600
+طبعا فترة ال early childhood تنجسم كمان pre
+
+19
+00:01:36,600 --> 00:01:41,660
+kindergarten stage مرحلة رياض الأطفال او مرحلة ما
+
+20
+00:01:41,660 --> 00:01:46,150
+قبل المدارس لحد مرحلة ما قبل المدارسال late
+
+21
+00:01:46,150 --> 00:01:51,570
+childhood من سن من سن ستة لاتناشر سنة ال
+
+22
+00:01:51,570 --> 00:01:56,270
+adolescence period من اتناش لحد عشرين في بعض الكتب
+
+23
+00:01:56,270 --> 00:02:01,670
+ممكن تحكي لحد تمانتاش early adulthood نحكي من حد
+
+24
+00:02:01,670 --> 00:02:08,410
+او من سن عشرين لاربعين سنةمد ال adulthood من 40 ل
+
+25
+00:02:08,410 --> 00:02:16,470
+65 سنة ال late adulthood من 65 لحد نهاية العمر او
+
+26
+00:02:16,470 --> 00:02:20,550
+الى ما شاء الله لو جينا نطلع على مرحلة ال prenatal
+
+27
+00:02:20,550 --> 00:02:23,050
+development ال prenatal development اللي هتلاقيها
+
+28
+00:02:23,050 --> 00:02:29,390
+بتتقسم الى ثلاث مراحل أساسية ال germinal stage ال
+
+29
+00:02:29,390 --> 00:02:36,640
+embryonic stage الفيتل stageو الـ prenatal period
+
+30
+00:02:36,640 --> 00:02:43,140
+start from conception and end with birth until the
+
+31
+00:02:43,140 --> 00:02:48,140
+time of birth أو until birth إذن لما بنحكي على
+
+32
+00:02:48,140 --> 00:02:55,130
+prenatal developmentهي عبارة عن الفترة اللي بتبدأ
+
+33
+00:02:55,130 --> 00:03:01,630
+من ساعة الإخصاب للبويضة لحد ساعة الولادة و بتتقسم
+
+34
+00:03:01,630 --> 00:03:08,170
+إلى تلت مراحل أساسية ال germinal stage اللي بتبدأ
+
+35
+00:03:08,170 --> 00:03:12,330
+من ال time of conception لحد عشرة إلى أربعة عشر
+
+36
+00:03:12,330 --> 00:03:17,950
+يوم أو لحد اسبوعينemperionic stage من أسبوعين لحد
+
+37
+00:03:17,950 --> 00:03:24,210
+تمان أسابيع ال fetal stage من تمان أسابيع لحد وقت
+
+38
+00:03:24,210 --> 00:03:31,670
+الولادة as individuals pass through these life
+
+39
+00:03:31,670 --> 00:03:32,290
+stages
+
+40
+00:03:35,460 --> 00:03:39,020
+type of growth and development occur في أثناء
+
+41
+00:03:39,020 --> 00:03:44,280
+عملية growth and development بيمر الإنسان بعدة
+
+42
+00:03:44,280 --> 00:03:50,320
+تغيرات ممكن نشوفها على صعيد ال physical على صعيد
+
+43
+00:03:50,320 --> 00:03:56,320
+ال mental على صعيد ال emotional و النقطة الرابعة
+
+44
+00:03:56,320 --> 00:04:01,700
+على صعيد ال social إذا في عندي أربع نقاط أساسية
+
+45
+00:04:01,700 --> 00:04:08,100
+اللي احنابدنا ندرسها في عملية الـ change أو عملية
+
+46
+00:04:08,100 --> 00:04:13,540
+الـ growth and development اللي بتصير في ال human
+
+47
+00:04:13,540 --> 00:04:18,720
+being أول مرحلة أو ال dimension الأول اللي قلنا
+
+48
+00:04:18,720 --> 00:04:24,710
+عنه ال physical و اللي تتناولعملية النمو الـ
+
+49
+00:04:24,710 --> 00:04:28,870
+biological change سواء كان زيادة في الطول زيادة في
+
+50
+00:04:28,870 --> 00:04:35,190
+الوزن كل هذه عبارة عن examples of physical
+
+51
+00:04:35,190 --> 00:04:44,240
+developmentو ممكن قياسها بالميزان الوزن الطول ممكن
+
+52
+00:04:44,240 --> 00:04:49,900
+نشوف جداش طول الإنسان و جداش معدل انه اللي بيكون
+
+53
+00:04:49,900 --> 00:04:55,700
+فيه الـmental أو الـ cognitive development اللي
+
+54
+00:04:55,700 --> 00:05:00,540
+بتشمل عملية ال learning بتشمل solving problems
+
+55
+00:05:00,540 --> 00:05:07,160
+بتشمل الإصدار القرارات أو اتخاذ الأحكام بحقكأشياء
+
+56
+00:05:07,160 --> 00:05:12,600
+معينة وبتتطور مع العمر ومع التقدم في العمر ومع
+
+57
+00:05:12,600 --> 00:05:18,650
+الخبرات اللي بيكتسبها في حياة الإنسانemotional
+
+58
+00:05:18,650 --> 00:05:22,870
+which refer to feelings and include dealing with
+
+59
+00:05:22,870 --> 00:05:27,310
+love, hate, joy, fear, excitement and other
+
+60
+00:05:27,310 --> 00:05:31,450
+similar feelings إذا عملية ال emotional هي ما
+
+61
+00:05:31,450 --> 00:05:38,370
+يتناوله أو عملية ال development كيف الإنسان بينمو
+
+62
+00:05:38,370 --> 00:05:44,350
+عنده شعور الحب والكره الخوف كل هذه الأمور كيف ممكن
+
+63
+00:05:44,350 --> 00:05:49,840
+تصير إليها عملية التطورسأقوم بالتركيز على الـ
+
+64
+00:05:49,840 --> 00:05:53,320
+social
+
+65
+00:05:54,890 --> 00:06:01,330
+development of social relationship تكون العلاقات
+
+66
+00:06:01,330 --> 00:06:05,590
+الإجتماعية زي ال friendship الصداقة وغيرها من
+
+67
+00:06:05,590 --> 00:06:09,130
+العلاقات سواء كان على مستوى العمل على مستوى الأسرة
+
+68
+00:06:09,130 --> 00:06:14,210
+كل هذه طبعا ضمن ال social development أو ال social
+
+69
+00:06:14,210 --> 00:06:18,190
+change اللي احنا هنتطلعله و هندرسه في العملية ال
+
+70
+00:06:18,190 --> 00:06:23,650
+developmentمثلًا، يمكن أن يتكلم طفل بطريقة مختلفة
+
+71
+00:06:23,650 --> 00:06:31,870
+مع والده أنه يتكلم مع صديق أو صديق طفل. كل مرحلة
+
+72
+00:06:31,870 --> 00:06:38,810
+تحتوي على خصيصها ومهارات تطورية محددة التي يجب أن
+
+73
+00:06:38,810 --> 00:06:39,370
+يتعلمها الشخص.
+
+74
+00:06:41,910 --> 00:06:45,950
+إذا لو جينا نتطلع كمثال في عملية الـ development
+
+75
+00:06:45,950 --> 00:06:51,090
+لـ social relationship هي عملية أو هي العلاقة
+
+76
+00:06:51,090 --> 00:06:56,370
+الاجتماعية ما بين المراهق أو الطفل أو الشخص في
+
+77
+00:06:56,370 --> 00:07:01,410
+مرحلة المراهقة و ما بين عائلته و ما بين أصدقائه
+
+78
+00:07:01,410 --> 00:07:06,030
+هلاجي أنه في عملية أو في العلاقة اللي بتكون موجودة
+
+79
+00:07:06,030 --> 00:07:11,890
+بينه و بين أصدقائه بيتصرف بطريقة مختلفة عن تصرفه
+
+80
+00:07:12,000 --> 00:07:17,160
+مابين و بين والده لان نجي لمرحلة ال prenatal
+
+81
+00:07:17,160 --> 00:07:21,020
+development و هنتطلع نتطرق ل ال prenatal
+
+82
+00:07:21,020 --> 00:07:25,800
+development بشيء من التفصيل ال prenatal
+
+83
+00:07:25,800 --> 00:07:29,340
+development زي ما حكينا ان احنا بنقسمها إلى ثلاث
+
+84
+00:07:29,340 --> 00:07:36,540
+مراحل أساسيةالمرحلة الأولى بتبدأ من ساعة الإخصاب
+
+85
+00:07:36,540 --> 00:07:41,380
+الـ time of conception لحد عشرة إلى أربعة عشر يوم
+
+86
+00:07:41,380 --> 00:07:46,640
+هذه سميناها ال germinal stage المرحلة التانية اللي
+
+87
+00:07:46,640 --> 00:07:52,160
+هي ال embryonic stage واللي بتبدأ مناربعتاشر يوم
+
+88
+00:07:52,160 --> 00:07:57,560
+او اسبوعين لحد تمان اسابيع و المرحلة التالتة اللى
+
+89
+00:07:57,560 --> 00:08:04,700
+تسمى fetal stage from eight weeks to birth من حد
+
+90
+00:08:04,700 --> 00:08:11,680
+تمان اسابيع لحد الولادة كل هذه طبعا تسمى fetal
+
+91
+00:08:11,680 --> 00:08:15,800
+stage from
+
+92
+00:08:15,800 --> 00:08:21,840
+conception to birthفي تقسيم تانية بتقول انه من
+
+93
+00:08:21,840 --> 00:08:29,260
+ساعة الإخصاب لحد الولادة طبعا بيمر الجنين في مراحل
+
+94
+00:08:29,260 --> 00:08:36,890
+مرحلة الـzygote ومرحلة ال embryo ومرحلة ال fetusلو
+
+95
+00:08:36,890 --> 00:08:43,910
+جينا نسقط هذه المعلومات أو التسمية على المعلومات
+
+96
+00:08:43,910 --> 00:08:47,630
+اللى موجودة عندنا هلاجى مرحلة الـ Zygote هي مرحلة
+
+97
+00:08:47,630 --> 00:08:52,570
+الـ germinal stage اللى بتبدأ من ال time of
+
+98
+00:08:52,570 --> 00:08:58,690
+conception لحد 14 يوم مرحلة ال embryo هلاجيها
+
+99
+00:08:58,690 --> 00:09:05,890
+بتبدأ من أسبوعين لحد 8 أسابيعمرحلة ال fetus او ال
+
+100
+00:09:05,890 --> 00:09:11,510
+fetal stage هنجيها بتبدأ من تمان أسابيع لحد
+
+101
+00:09:11,510 --> 00:09:16,710
+الولادة شو اللي بيميز مرحلة ال zygote او ال
+
+102
+00:09:16,710 --> 00:09:21,010
+germinal stage يقولنا ان هي بتبدأ من ال time of
+
+103
+00:09:21,010 --> 00:09:30,980
+conceptionوجدت الإخصاب لحد 10 days أو 14 days لحد
+
+104
+00:09:30,980 --> 00:09:35,360
+أسبوعين من عشر أيام إلى أسبوعين أو إلى أربعتاشر
+
+105
+00:09:35,360 --> 00:09:40,020
+يوم period of rapid cell divisionوهذه ما يميز
+
+106
+00:09:40,020 --> 00:09:46,200
+مرحلة الزيجوت او الانقسام السريع للخلايا two weeks
+
+107
+00:09:46,200 --> 00:09:50,940
+later when the zygote is implanted in the wall of
+
+108
+00:09:50,940 --> 00:09:58,760
+the uterus تنتهي مجرد ما يصير فيه غمر او زراعة
+
+109
+00:09:58,760 --> 00:10:04,700
+للزيجوت او انغمار الزيجوت في جدار الرحل
+
+110
+00:10:04,700 --> 00:10:12,570
+blastocyste خلال مرحلة الزيجوتبيمر بعدة مراحل زى
+
+111
+00:10:12,570 --> 00:10:18,850
+ما حكينا او في بعض التغيرات اللى بتكون موجودة من
+
+112
+00:10:18,850 --> 00:10:23,450
+ضمنها مرحلة بيسموها ال blastocyst اللى هي عدد او
+
+113
+00:10:23,450 --> 00:10:28,050
+يميزها ان عدد خلاياها بيكون من ستين الى سبعين خلية
+
+114
+00:10:28,050 --> 00:10:33,440
+وهذا طبعا بتكون في اليوم الرابعو في الـ Plastocyst
+
+115
+00:10:33,440 --> 00:10:38,240
+هنلاقي فيها حاجة نسميها Embryonic Disc في المستقبل
+
+116
+00:10:38,240 --> 00:10:46,780
+هيكون ال organism أو جسم الطفل ال outer ring اللي
+
+117
+00:10:46,780 --> 00:10:52,540
+هيكون ال umbilical cord البلسنتاimplantation
+
+118
+00:10:52,540 --> 00:11:01,920
+between days 7 and 9 days عملية زراعة القرص هذا او
+
+119
+00:11:01,920 --> 00:11:05,840
+البلاستوست في جدار الرحم ما بين اليوم السابع
+
+120
+00:11:05,840 --> 00:11:13,660
+والعاشر اذا زي ما حكينا period
+
+121
+00:11:13,660 --> 00:11:17,500
+of zygote بيكون في عندي انا في البلاستوست مرحلة
+
+122
+00:11:17,500 --> 00:11:19,000
+البلاستوست
+
+123
+00:11:21,110 --> 00:11:26,570
+حاجة بنسميها الـ Empirionic Disc و ال outer ring
+
+124
+00:11:26,570 --> 00:11:30,470
+لو جينا نتطلع الآن في الصورة اللي موجودة أمامنا
+
+125
+00:11:30,470 --> 00:11:36,230
+مرحلة التكوين بدأت سيرا عندي
+
+126
+00:11:39,010 --> 00:11:44,950
+ال امبريونك ديسك هاي ال outer ring وهاي في عندي
+
+127
+00:11:44,950 --> 00:11:52,290
+انا طبعا ال disk اللي موجود في الداخل لحد مرحلة
+
+128
+00:11:52,290 --> 00:11:59,090
+implementation في ال wall of the uterus عملية
+
+129
+00:11:59,090 --> 00:12:04,930
+زراعته تحت جدار او في جدار الرحمة
+
+130
+00:12:07,460 --> 00:12:12,760
+إذا لو جينا نطلع على مرحلة ال
+
+131
+00:12:12,760 --> 00:12:17,540
+time of conception او
+
+132
+00:12:17,540 --> 00:12:23,540
+مرحلة إزاي جوت حالة جيه انه بتبدأ من عملية ال time
+
+133
+00:12:23,540 --> 00:12:29,060
+of conception و جابلها بيسبقها عملية ال ovulation
+
+134
+00:12:29,060 --> 00:12:35,400
+و بتمشي في ال valopian tube لحد ما يصير عملية ال
+
+135
+00:12:35,400 --> 00:12:42,260
+fertilizationفي الـ valvian cube و بتبدأ عملية
+
+136
+00:12:42,260 --> 00:12:48,940
+الانقسام السريع للخلايا من خلية واحدة صار خليتين
+
+137
+00:12:48,940 --> 00:12:57,940
+اربعة ست تمانية16 و هلو مجرة لحد ما تصل في اليوم
+
+138
+00:12:57,940 --> 00:13:03,140
+الرابع زي ما قلنا 60 إلى 70 خلية في اليوم الرابع
+
+139
+00:13:03,140 --> 00:13:08,180
+بتوصل عددها 60 إلى 70 خلية و بتكون عندى
+
+140
+00:13:10,860 --> 00:13:14,700
+الـ blastocyst اللي بتكون من الـ embryonic disk
+
+141
+00:13:14,700 --> 00:13:19,240
+اللي هيعطيني في المستقبل ال organism و ال outer
+
+142
+00:13:19,240 --> 00:13:27,480
+ring الخارجي هذا هو اللي هيعطيني أو هيتكون منه ال
+
+143
+00:13:27,480 --> 00:13:31,040
+umbilical cord في المستقبل
+
+144
+00:13:34,570 --> 00:13:39,630
+بلاستوسيست قامت بإستعمال نفسها داخل الاندومتريام
+
+145
+00:13:39,630 --> 00:13:46,250
+وقامت بتنمية بسرعة بينما تصبح عيونها مختلفة إلى
+
+146
+00:13:46,250 --> 00:13:49,350
+عيون تدعم الاندومتريام إلى عيون تدعم الاندومتريام
+
+147
+00:13:49,350 --> 00:13:54,130
+إلى عيون تدعم الاندومتريام إذا المرحلة من 12 إلى
+
+148
+00:13:54,130 --> 00:13:57,930
+14 يوم اللي مرحلة استعمال
+
+149
+00:14:01,150 --> 00:14:05,150
+emperionic disk او زيجوت in the wall of the uterus
+
+150
+00:14:05,150 --> 00:14:12,010
+وبتبدأ عملية ال differentiation للخلايا وزي ما
+
+151
+00:14:12,010 --> 00:14:18,190
+قلنا انه ال outer ring هذا بيصير مسئول عن او
+
+152
+00:14:18,190 --> 00:14:24,830
+هيتكون منه ال embolical cord البلسنتا وال inner
+
+153
+00:14:24,830 --> 00:14:27,730
+disk اللي هيعطيني جسمي
+
+154
+00:14:30,230 --> 00:14:34,930
+الـ fetus أو جسم الجنين في المستقبل وجسم الجنين
+
+155
+00:14:34,930 --> 00:14:41,610
+بتبدأ تتنوع الخلايا وتتشكل الخلايا بحيث يصير واضح
+
+156
+00:14:41,610 --> 00:14:46,610
+من الخلايا اللي هتكون مسئولة عن الجهاز الهضمي من
+
+157
+00:14:46,610 --> 00:14:50,670
+الخلايا اللي هتكون مسئولة عن نمو الجهاز العضلي من
+
+158
+00:14:50,670 --> 00:14:54,590
+الخلايا اللي هتكون مسئولة أو هتتطور في المستقبل
+
+159
+00:14:54,590 --> 00:15:02,630
+لتكوين الجهاز العضليالان زى ما حكينا كمان مرة the
+
+160
+00:15:02,630 --> 00:15:06,630
+blastocyst having implanted itself deep within the
+
+161
+00:15:06,630 --> 00:15:14,330
+endometrium هتنغرس هذه او الزيجوت في جدار الرحم
+
+162
+00:15:17,100 --> 00:15:20,840
+proceed to grow rapidly while its cells become
+
+163
+00:15:20,840 --> 00:15:24,300
+differentiated into embryonic and supporting cells
+
+164
+00:15:24,300 --> 00:15:28,680
+مين اللي هيكون في عندي ال embryonic cell اللي
+
+165
+00:15:28,680 --> 00:15:33,320
+هتعطيني جسم الجنين ومين اللي هتكون شغلات تساعد جسم
+
+166
+00:15:33,320 --> 00:15:37,260
+الجنين على النمو زي ال embolical cord وزي
+
+167
+00:15:37,260 --> 00:15:41,800
+البلاسنتا اللي احنا بسميها المشيمة أو الخلاصة
+
+168
+00:15:44,680 --> 00:15:54,840
+الـ embryonic disk بتكون من ثلاث طبقات أساسية طبقة
+
+169
+00:15:54,840 --> 00:16:02,160
+الاكتودانو طبقة الميزودانو طبقة الاندودانو يعني لو
+
+170
+00:16:02,160 --> 00:16:07,100
+جينا نطلع احنا هاي ال blastocyst اللي موجود أمامي
+
+171
+00:16:07,100 --> 00:16:12,260
+الآن وكيف بدأ ال outer ring يتشكل
+
+172
+00:16:16,100 --> 00:16:23,680
+لحد ما صار فيها عندي بشكل واضح ال embryonic disk
+
+173
+00:16:23,680 --> 00:16:29,120
+الان ال embryonic disk بيتكون من ثلاث طبقات أساسية
+
+174
+00:16:29,120 --> 00:16:34,520
+طبقة اللي لبرا زي ما احنا شايفينها هذه طبقة
+
+175
+00:16:34,520 --> 00:16:41,920
+الectodermالطبقة اللى فى المنتصف طبقة ال mesoderm
+
+176
+00:16:41,920 --> 00:16:47,760
+والطبقة الداخلية هذه كلها بيسموها طبقة ال endoderm
+
+177
+00:16:47,760 --> 00:16:54,100
+الان كل طبقة من الطبقات هذه هتكون هي نوع خلايا
+
+178
+00:16:54,100 --> 00:17:04,090
+مخصص لنمو عدة أجهزة فى الجسمعلى سبيل المثال طبقة
+
+179
+00:17:04,090 --> 00:17:08,770
+الـectoderm اللي هي الطبقة الخارجية هلاجيها مسؤولة
+
+180
+00:17:08,770 --> 00:17:18,770
+عن تكوين nervous system and skin الـfast
+
+181
+00:17:18,770 --> 00:17:24,610
+development of nervous system and skin طبقة الوسطى
+
+182
+00:17:26,030 --> 00:17:31,190
+ميزودان حلجية مسئولة عن development of skeleton،
+
+183
+00:17:31,190 --> 00:17:35,590
+نمو الجهاز
+
+184
+00:17:35,590 --> 00:17:43,960
+العضلي بالاضافة إلى الcirculation تبع الجسمأما
+
+185
+00:17:43,960 --> 00:17:48,840
+طبقة ال endoderm فهي مسئولة عن تكوين الأحشاء
+
+186
+00:17:48,840 --> 00:17:53,780
+الداخلية و أجهزة الجسم الداخلية زي الجهاز الهضمي
+
+187
+00:17:53,780 --> 00:17:57,320
+ال digestive system زي ال respiratory system ال
+
+188
+00:17:57,320 --> 00:18:03,920
+lungs ال urinary tract او tract الجهاز البولي
+
+189
+00:18:07,090 --> 00:18:13,650
+السلب البريونيكي أصبح أكتر مختلفًا لإنشاء مصادر من
+
+190
+00:18:13,650 --> 00:18:21,000
+العديد من أسلوب الجسمكل ما زاد النمو كل ما اتقدم
+
+191
+00:18:21,000 --> 00:18:26,440
+عمر الـ Zygote في النمو كل ما زاد عملية التخصيص
+
+192
+00:18:26,440 --> 00:18:30,080
+للخلايا بحيث ان خلايا تصبح مسئولة عن الجهاز
+
+193
+00:18:30,080 --> 00:18:33,800
+العصبي، خلايا تصبح مسئولة عن الأضافر، خلايا تصبح
+
+194
+00:18:33,800 --> 00:18:41,760
+مسئولة عن الجلد، خلايا تصبح مسئولة عن الشعر،هتبدأ
+
+195
+00:18:41,760 --> 00:18:47,340
+كل ما زاد عمر الجنين كل ما زاد تخصص الخلايا و كل
+
+196
+00:18:47,340 --> 00:18:52,900
+ما صار النواة لكل أجهزة الجسم موجودة بعد هيك بيصير
+
+197
+00:18:52,900 --> 00:18:59,440
+عملية النمو في عدد الخلايا و في حجمها لحد ما يكتمل
+
+198
+00:18:59,440 --> 00:19:04,640
+نمو الجنين كامل او نجي لمرحلة تانية هي مرحلة
+
+199
+00:19:04,640 --> 00:19:07,360
+period of empire
+
+200
+00:19:12,610 --> 00:19:21,070
+تبدأ من الاسبوع التالت نهاية الأسبوع التاني
+
+201
+00:19:23,880 --> 00:19:30,360
+أزاي؟ الآن في هذه المرحلة شو أهم ما يميزها؟ body
+
+202
+00:19:30,360 --> 00:19:35,120
+parts are formed during this period تبدأ تتكون
+
+203
+00:19:35,120 --> 00:19:41,860
+أعضاء الجسم لكن مش كاملة النضوج أو كاملة النمو for
+
+204
+00:19:41,860 --> 00:19:45,320
+the first eight weeks a process of differentiation
+
+205
+00:19:45,320 --> 00:19:52,870
+occur إذا باكتمالالتامن أسابيع أو الشهرين بتكون
+
+206
+00:19:52,870 --> 00:19:59,150
+طبعا عملية ال differentiation تميز الخلايا اكتملت
+
+207
+00:19:59,150 --> 00:20:05,490
+تماما this is the embryonicperiod when the cells
+
+208
+00:20:05,490 --> 00:20:09,490
+of the blastocyst which are very similar divide
+
+209
+00:20:09,490 --> 00:20:14,990
+rapidly over and over again to produce not only
+
+210
+00:20:14,990 --> 00:20:19,750
+bigger embryo but also multiplicity of cell type
+
+211
+00:20:23,620 --> 00:20:31,400
+بتتميز إنه في عندي زيادة في عدد الخلايا بالاضافة
+
+212
+00:20:31,400 --> 00:20:36,440
+إلى زيادة في حجم الخلايا الخاصة بالجنين وهذا
+
+213
+00:20:36,440 --> 00:20:42,600
+المرحلة طبعا ال Embryical cord يبدأ
+
+214
+00:20:42,600 --> 00:20:48,200
+تشكل عشان يربط ما بين ال embryo و ال placenta بربط
+
+215
+00:20:48,200 --> 00:20:54,600
+الجنين بالمشيمةemperio rest in the ammonium filled
+
+216
+00:20:54,600 --> 00:21:00,780
+with amniotic fluid هنلاقي ان مكان ال emperio في
+
+217
+00:21:00,780 --> 00:21:08,960
+كيس موجود sack which the sack consist of two
+
+218
+00:21:08,960 --> 00:21:17,760
+layersطبقة الداخلية من الامنيون هي عبارة عن ساك
+
+219
+00:21:17,760 --> 00:21:24,040
+عبارة
+
+220
+00:21:24,040 --> 00:21:31,160
+عن كيس سعت أو بيحتوي على سبعمية ملي لتر تقريبا نص
+
+221
+00:21:31,160 --> 00:21:36,420
+لتر او اكتر شوية من الامنيوتك فلود من السائل
+
+222
+00:21:36,420 --> 00:21:42,080
+الأميني اللي بيسبح فيهالجنين طبعا هذا باكتمال
+
+223
+00:21:42,080 --> 00:21:49,380
+مرحلة الحمل أو عند الشهر التاسع بيكون حجم الـ
+
+224
+00:21:49,380 --> 00:21:54,500
+amniotic fluid حوالي 700 ملي لترممكن اكتر شوية
+
+225
+00:21:54,500 --> 00:21:59,060
+ممكن اقل حسب الحجم this is a valuable protection
+
+226
+00:21:59,060 --> 00:22:02,900
+for the fetus both during its development and
+
+227
+00:22:02,900 --> 00:22:07,160
+during the early stage of labor وظيفة ال amniotic
+
+228
+00:22:07,160 --> 00:22:11,420
+fluid ان هو بيعطي نوع من الحماية او بيعطي نوع من
+
+229
+00:22:11,420 --> 00:22:16,700
+الحماية للجنين سواء كان في مرحلة النمو مرحلة ال
+
+230
+00:22:16,700 --> 00:22:23,810
+developmentأو في مرحلة الولادة و بتكون علامة و
+
+231
+00:22:23,810 --> 00:22:31,810
+انذار لعملية الولادة في مرحلة ال protectionأو
+
+232
+00:22:31,810 --> 00:22:35,670
+خلّيني أقول إنه بيشتغل ك protection في مرحلة الحمل
+
+233
+00:22:35,670 --> 00:22:42,070
+أو during the fetal stage هلاجي إنه الطفل أو
+
+234
+00:22:42,070 --> 00:22:47,230
+الجنين لو اتعرض لأي ضرب أو الأم اتعرضت لأي ضرب
+
+235
+00:22:47,230 --> 00:22:54,090
+أثناء فترة الحمل بيمتصها السائل الأمينيوما قبل
+
+236
+00:22:54,090 --> 00:22:59,430
+الولادة هلاجة ان هذا السائل صار فيه leakage او
+
+237
+00:22:59,430 --> 00:23:10,230
+عملية انفجار ل ال ammoniumساك أو الكيس هذا وبيطلع
+
+238
+00:23:10,230 --> 00:23:15,830
+منه السائل الأميني وهذا معناه علامة أنه أجى موعد
+
+239
+00:23:15,830 --> 00:23:20,690
+الولادة ونوع من الحماية لأن الطفل لو كانت المي هذه
+
+240
+00:23:20,690 --> 00:23:25,570
+مش موجودة حواليه هتأد إلى مضاعفات وممكن تأد إلى
+
+241
+00:23:25,570 --> 00:23:33,210
+الوفاة ال outer layer of الساك بسموها القريون
+
+242
+00:23:34,410 --> 00:23:47,510
+الكوريون مرتبط بجدار الرحم الكوريون
+
+243
+00:23:47,510 --> 00:23:57,170
+مرتبط
+
+244
+00:23:57,170 --> 00:24:00,470
+بجدار الرحم
+
+245
+00:24:04,760 --> 00:24:11,840
+منطقة الكوريون هي اللى هتنمو بشكل سريع و هتكون
+
+246
+00:24:11,840 --> 00:24:17,720
+عندى الـ placenta of the fetus وهي اللى هتعمل ال
+
+247
+00:24:17,720 --> 00:24:23,200
+machine او هيتكون منها ال machine اللى هتكون حلقة
+
+248
+00:24:23,200 --> 00:24:27,930
+الوصل ما بين الجنين و ما بين ال motherالمرة اللى
+
+249
+00:24:27,930 --> 00:24:29,890
+جاى ان شاء الله رب العالمين محاضرة جاى ان شاء الله
+
+250
+00:24:29,890 --> 00:24:33,970
+رب العالمين هنحكي عن الـ placenta وعن ال
+
+251
+00:24:33,970 --> 00:24:37,330
+circulation of blood inside the placenta
+
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..455cefc67adce83a91c8b18120acca068b14dc4c
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM.srt
@@ -0,0 +1,1814 @@
+1
+00:00:00,440 --> 00:00:05,140
+السلام عليكم و رحمة الله و بركاته اليوم هنتكلم في
+
+2
+00:00:05,140 --> 00:00:09,680
+موضوع آخر في موضوع the human growth and 
+
+3
+00:00:09,680 --> 00:00:15,720
+development هنتكلم عن special aspects of
+
+4
+00:00:15,720 --> 00:00:22,340
+development خلال 
+
+5
+00:00:22,340 --> 00:00:27,430
+حديثنا عن الـ special aspects of development هنتكلم
+
+6
+00:00:27,430 --> 00:00:31,690
+شوية هنتكلم عن the development of the teeth و كيف
+
+7
+00:00:31,690 --> 00:00:36,350
+بتكون عند الأطفال و كيف بتكون عند الكبار طبعا بشكل
+
+8
+00:00:36,350 --> 00:00:42,770
+سريع the human has 20 primary and 32 permanent
+
+9
+00:00:42,770 --> 00:00:47,470
+teeth developed from the interaction of the oral
+
+10
+00:00:47,470 --> 00:00:51,810
+epithelial cells بداية لو جينا نتطلع بنعرف أنه
+
+11
+00:00:51,810 --> 00:00:57,560
+الإنسان في عنده في فترة الطفولة بيكون عنده حوالي
+
+12
+00:00:57,560 --> 00:01:03,020
+عشرين سن primary teeth هذا طبعا بيسموها الأسنان
+
+13
+00:01:03,020 --> 00:01:08,340
+اللبنية وفي عنا اثنين و ثلاثين permanent teeth
+
+14
+00:01:08,340 --> 00:01:12,740
+موجودين لو جينا نطلع على the development of the
+
+15
+00:01:12,740 --> 00:01:16,700
+teeth نطلع على the stages of the teeth هنلاقي في
+
+16
+00:01:16,700 --> 00:01:21,180
+عندي three main stages of development هذا الـ three
+
+17
+00:01:21,180 --> 00:01:29,840
+main stages بعد مرحلة مرحلة ثالثة
+
+18
+00:01:29,840 --> 00:01:30,020
+مرحلة
+
+19
+00:01:36,510 --> 00:01:45,930
+الشمس تزداد و تزداد و تزداد و تزداد و تزداد و
+
+20
+00:01:45,930 --> 00:01:56,630
+تزداد و تزداد و تزداد و تزداد و تزداد
+
+21
+00:01:56,630 --> 00:02:05,510
+و تزداد و تزداد و تزداد
+
+22
+00:02:14,380 --> 00:02:19,480
+وهذا طبعا عملية الـ differentiation تبدأ توضح مرحلة
+
+23
+00:02:19,480 --> 00:02:24,620
+اللي بديه يكون فيها الـ bell stage وشو هي المراحل
+
+24
+00:02:24,620 --> 00:02:28,660
+اللي بيكون فيها الـ bell stage لو جينا نطلع الآن
+
+25
+00:02:28,660 --> 00:02:36,450
+على الصورة اللي أمامنا وكيف ممكن يتكون السن حلاجة
+
+26
+00:02:36,450 --> 00:02:40,710
+أن الـ root formation and cementogenesis continue
+
+27
+00:02:40,710 --> 00:02:44,690
+until a functional tooth and its supporting
+
+28
+00:02:44,690 --> 00:02:47,890
+structures are fully developed as the crown are
+
+29
+00:02:47,890 --> 00:02:51,830
+formed and mineralized the root of the teeth begin
+
+30
+00:02:51,830 --> 00:03:00,790
+to form مجرد ما يبدأ التاج يتكون تبدأ تصير عملية
+
+31
+00:03:00,790 --> 00:03:02,070
+الـ mineralization
+
+32
+00:03:10,030 --> 00:03:15,510
+مجرد ما يتكون تاج السن ويصير فيه عملية الـ
+
+33
+00:03:15,510 --> 00:03:19,430
+Mineralization فيه هتبدأ الـ roots of the teeth
+
+34
+00:03:19,430 --> 00:03:25,470
+begin to form جذور السن تبدأ تتكون بشكل آخر بعد أن
+
+35
+00:03:25,470 --> 00:03:29,560
+تكون الـ roots classified ، السبارة تنتشر of the
+
+36
+00:03:29,560 --> 00:03:33,340
+teeth اللي بتشتغل الشغل خانية نقول the cementum
+
+37
+00:03:33,340 --> 00:03:41,040
+and periodontal ligament والغ لربون تتكون تتكون
+
+38
+00:03:41,040 --> 00:03:44,400
+كل هذه المكونات تبدأ تتكون تتكون تتكون تتكون
+
+39
+00:03:44,400 --> 00:03:46,380
+تتكون تتكون تتكون تتكون تتكون تتكون تتكون
+
+40
+00:03:46,380 --> 00:03:49,060
+تتكون تتكون تتكون تتكون تتكون تتكون تتكون
+
+41
+00:03:49,060 --> 00:03:50,440
+تتكون تتكون تتكون تتكون تتكون تتكون تتكون
+
+42
+00:03:50,440 --> 00:04:01,740
+تتكون تتكون تتكون تتكون تتكون تتكو
+
+43
+00:04:03,520 --> 00:04:11,900
+الآن لو جينا نتطلع على هذه المراحل هنلاقي أنه من
+
+44
+00:04:11,900 --> 00:04:15,400
+البداية هنلاقي أنه في عندي صار في عندي إبيثيليام
+
+45
+00:04:15,400 --> 00:04:23,160
+موجود و نواة السن الخلايا الأساسية في عملية
+
+46
+00:04:23,160 --> 00:04:27,900
+differentiation of the teeth هنلاقي أنه صار في عندي
+
+47
+00:04:27,900 --> 00:04:32,080
+dental mesenchyme as the crown are formed and
+
+48
+00:04:32,080 --> 00:04:35,460
+mineralized the root of the teeth begin to form
+
+49
+00:04:35,460 --> 00:04:42,700
+مجرد ما يصير عندي تاج السن يتكون ويصير فيه تكلس
+
+50
+00:04:42,700 --> 00:05:05,900
+ابتدأ الجذور تبعات السن تتكون عندما يتكون
+
+51
+00:05:05,900 --> 00:05:12,460
+الانسجة الداعمة للسن مثل السمنطم الـ periodontal
+
+52
+00:05:12,460 --> 00:05:23,640
+ligament  الالفولار كل هذه تبدأ تتكون مجرد ما
+
+53
+00:05:23,640 --> 00:05:29,980
+يكتمل نمو السن بيبدأ يشق طريقه من خلال اللثة و
+
+54
+00:05:29,980 --> 00:05:36,100
+يطلع في تجويف الفم root formation و cementogenesis
+
+55
+00:05:36,100 --> 00:05:42,020
+تستمر حتى يتم تكوين tooth و تعمل تعمل تعمل تعمل
+
+56
+00:05:42,020 --> 00:05:47,700
+تعمل تعمل تعمل تعمل
+
+57
+00:05:48,330 --> 00:05:52,770
+هذه التفاصيل تستمر لحد ما يصبح لدي functional
+
+58
+00:05:52,770 --> 00:05:59,750
+tooth وهذا يشمل استمرار التطور في الـ supporting
+
+59
+00:05:59,750 --> 00:06:03,830
+structures اللي موجودة حوالين الـ teeth لو جينا
+
+60
+00:06:03,830 --> 00:06:09,830
+نتطلع على مراحل تطور الـ tooth هنلاقي المرحلة
+
+61
+00:06:09,830 --> 00:06:16,210
+الأولى عملية الـ initiation وهذا طبعا في الـ epithelium
+
+62
+00:06:16,210 --> 00:06:20,310
+الحلاجي صار في عندي الـ dental mesenchymal cells هذه
+
+63
+00:06:20,310 --> 00:06:24,850
+بدت تتشكل وصير differentiation لها بعد هيك صار
+
+64
+00:06:24,850 --> 00:06:31,570
+عندي الـ dental placode صار تقريبا مكان السن بده
+
+65
+00:06:31,570 --> 00:06:38,710
+يطلع الآن الـ dental mesenchymal بيبدأ يصير له
+
+66
+00:06:38,710 --> 00:06:46,200
+طبعا تكونو يبدأ يصير فيه development وهذا يسمى
+
+67
+00:06:46,200 --> 00:06:53,460
+مرحلة الـ bud stage المرحلة الثانية مرحلة الـ cap
+
+68
+00:06:53,460 --> 00:07:02,640
+stage تبدأ طبعا شكل السن يتغطى و يأخذ بعد ذلك
+
+69
+00:07:02,640 --> 00:07:06,260
+مرحلة الـ bell stage شكل الجرس
+
+70
+00:07:09,430 --> 00:07:15,490
+مجرد ما تتقوى هذه و يتقوى الجذور في داخل اللثة
+
+71
+00:07:15,490 --> 00:07:20,650
+طبعا بيصير عملية زي ما احنا شايفين الـ root الـ
+
+72
+00:07:20,650 --> 00:07:25,390
+surrounding tissue اللي موجود حوالين السن بيصير في
+
+73
+00:07:25,390 --> 00:07:29,310
+عندي عملية الـ eruption و أثناء عملية الـ eruption
+
+74
+00:07:29,310 --> 00:07:34,470
+هنلاقي أن عملية the development of the root استمرت الـ
+
+75
+00:07:34,470 --> 00:07:38,680
+development of the surrounding structures استمرت لحد
+
+76
+00:07:38,680 --> 00:07:42,900
+ما يصير في عندي functional tooth لحد ما يصير في
+
+77
+00:07:42,900 --> 00:07:48,660
+عندي functional tooth ثلاث مراحل الـ bud stage زي ما
+
+78
+00:07:48,660 --> 00:07:53,800
+احنا شايفين كمرحلة اللي هي البروز هذه مرحلة الـ cap
+
+79
+00:07:53,800 --> 00:07:59,220
+stage بدأ يتشكل شكل السن مرحلة الـ bell stage هذه
+
+80
+00:07:59,220 --> 00:08:06,300
+الثلاث مراحل ما قبل الـ eruption of the tooth ما قبل
+
+81
+00:08:06,300 --> 00:08:11,280
+بزوغ السن بعد هي عمر مرحلة الـ eruption ومرحلة
+
+82
+00:08:11,280 --> 00:08:16,940
+تقوية دور السن من خلال the development of the bone
+
+83
+00:08:16,940 --> 00:08:20,900
+this is also subject to a wide range of variation
+
+84
+00:08:20,900 --> 00:08:24,780
+teething in the lower jaw mandibular usually
+
+85
+00:08:24,780 --> 00:08:29,680
+precedes that in the upper jaw maxillary by one to
+
+86
+00:08:29,680 --> 00:08:36,420
+two months بنعرف أن عملية التسنين بتبدأ في الـ
+
+87
+00:08:36,420 --> 00:08:40,540
+mandibular jaw في الـ lower part of the jaw في
+
+88
+00:08:40,540 --> 00:08:45,520
+الفتق السفلي قبل ما يبدأ تطلع الأسنان في الفتق
+
+89
+00:08:45,520 --> 00:08:50,500
+العلوي حوالي الفاصل ما بينهم من شهر إلى شهرين
+
+90
+00:08:50,500 --> 00:08:57,640
+تقريبا عند الغالبية لكن مش بالضرورة تكون عند الجميع
+
+91
+00:08:57,640 --> 00:09:01,600
+بنفس القدر ممكن يكون في بعض الشواذ لهذه القاعدة
+
+92
+00:09:22,800 --> 00:09:28,920
+في الـ mandibular jaw القواطع الجانبية حيث يظهرون
+
+93
+00:09:28,920 --> 00:09:35,880
+من 7 إلى 9 أشهر في الـ maxillary jaw الفك العلوي
+
+94
+00:09:35,880 --> 00:09:41,920
+من 8 إلى 11 شهر باقي الأسنان تقريبا نفس الشيء و
+
+95
+00:09:41,920 --> 00:09:47,080
+نفس المدة إذا الاختلاف في الـ central incisors و
+
+96
+00:09:47,080 --> 00:09:53,760
+الـ lateral incisors الـ permanent teeth أو الـ
+
+97
+00:09:53,760 --> 00:09:57,500
+secondary teeth هنلاقي أن الـ central في الـ
+
+98
+00:09:57,500 --> 00:10:01,540
+permanent teeth هنلاقي أن الـ central incisors
+
+99
+00:10:01,540 --> 00:10:07,500
+بيبدأ عملية التبديل تبعها بشكل مختلف عن عملية ظهور
+
+100
+00:10:07,500 --> 00:10:13,560
+الـ primary هنلاقي أن الـ upper jaw أو الـ maxillary
+
+101
+00:10:13,560 --> 00:10:21,440
+jaw تظهر في الأسنان عند أو بتبدأ تتساقط الأسنان
+
+102
+00:10:21,440 --> 00:10:28,460
+المتبدلة في الـ upper jaw من 6 إلى 7 وفي الـ lower jaw
+
+103
+00:10:28,460 --> 00:10:35,260
+من 7 إلى 8 سنوات الـ lateral incisors من 7 إلى 8 في
+
+104
+00:10:35,260 --> 00:10:42,080
+الـ upper jaw 8 إلى 9 في الـ lower jaw الـ canines
+
+105
+00:10:42,080 --> 00:10:47,740
+الانياب من 9 إلى 11 في الـ upper من 11 إلى 12 في الـ
+
+106
+00:10:47,740 --> 00:10:55,070
+lower jaw ملاحظ أن عملية تبديل الأسنان في الـ upper
+
+107
+00:10:55,070 --> 00:10:59,750
+jaw تبدأ قبل الـ lower jaw تبديل الأسنان الدائمة
+
+108
+00:10:59,750 --> 00:11:05,430
+لكن ظهور الأسنان اللبنية في الـ lower jaw تبدأ قبل
+
+109
+00:11:05,430 --> 00:11:09,570
+الـ upper jaw هذه المقاطع اللي نحكيها في موضوع
+
+110
+00:11:09,570 --> 00:11:11,370
+the development of the teeth
+
+111
+00:11:14,100 --> 00:11:17,760
+الـ maturity أو الـ maturity of the bone أو الـ
+
+112
+00:11:17,760 --> 00:11:22,380
+bone age حلاجة أن skeletal maturity أو الـ bone
+
+113
+00:11:22,380 --> 00:11:26,700
+age is a maturation process which occurs in bones
+
+114
+00:11:26,700 --> 00:11:30,880
+in the form of appearance, progression in size and
+
+115
+00:11:30,880 --> 00:11:34,920
+eventual fusion of epiphyseal centers with the
+
+116
+00:11:34,920 --> 00:11:39,200
+metaphyses of bone ففي عملية الـ development of
+
+117
+00:11:39,200 --> 00:11:45,360
+the bone هذه اللي بنستفيد منها في عملية التعرف على
+
+118
+00:11:45,360 --> 00:11:52,080
+عمر الشخص اللي أمامنا من خلال نمو العظم اللي بيكون
+
+119
+00:11:52,080 --> 00:11:56,300
+موجود ومن خلال البروزات العظمية اللي بيكون موجودة
+
+120
+00:11:56,300 --> 00:12:00,460
+normally bone age corresponds to the age of the
+
+121
+00:12:00,460 --> 00:12:06,560
+child في الوضع الطبيعي هنلاقي أن عمر العظم أو العمر
+
+122
+00:12:06,560 --> 00:12:26,790
+العظمي the bone age هو يناسب عمر الطفل في بعض
+
+123
+00:12:26,790 --> 00:12:32,370
+الحالات اللي بتكون فيها مشاكل وإعاقة
+
+124
+00:12:32,370 --> 00:12:37,320
+في عملية النمو هنلاقي أن العمر العظمي بيختلف عن
+
+125
+00:12:37,320 --> 00:12:42,180
+العمر الحقيقي للطفل وهذا بنشوفه في حالات مشاكل 
+
+126
+00:12:42,180 --> 00:12:46,540
+الغدد الصماء زي مشكلة الـ hypothyroidism
+
+127
+00:12:46,540 --> 00:12:51,760
+evaluation of bone age كيف نقيم الـ bone age if the
+
+128
+00:12:51,760 --> 00:12:56,580
+newborn and infancy in the newborn and in the
+
+129
+00:12:56,580 --> 00:13:00,880
+infancy the ossified centers around the knee joint
+
+130
+00:13:00,880 --> 00:13:06,710
+are well developed. Absence of these centers means a
+
+131
+00:13:06,710 --> 00:13:11,090
+delay in the bone age. يعني لو جينا احنا و نشوف شو
+
+132
+00:13:11,090 --> 00:13:16,090
+اللي ممكن نستفيده من الـ bone age لو طلعنا على صورة
+
+133
+00:13:16,090 --> 00:13:21,930
+أشعة خاصة بـ newborn هلاقي أن الـ ossified centers
+
+134
+00:13:21,930 --> 00:13:27,070
+مراكز التكلس اللي حوالين الركبة بتتطور تكون
+
+135
+00:13:27,070 --> 00:13:33,170
+موجودة. لكن عدم وجودها في مرحلة الـ Newborn و الـ
+
+136
+00:13:33,170 --> 00:13:40,930
+Infancy سيكون هناك خلل في عملية النمو العظمي للطفل
+
+137
+00:13:41,960 --> 00:13:47,200
+يعني لو جينا أخدنا صورة أشعة لطفل لمنطقة الرقبة
+
+138
+00:13:47,200 --> 00:13:52,760
+يفترض أن يكون في حياته حياته حياته حياته حياته
+
+139
+00:13:52,760 --> 00:13:54,160
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+140
+00:13:54,160 --> 00:13:56,100
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+141
+00:13:56,100 --> 00:13:59,500
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+142
+00:13:59,500 --> 00:13:59,520
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+143
+00:13:59,520 --> 00:13:59,640
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+144
+00:13:59,640 --> 00:14:09,740
+حياته حياته
+
+145
+00:14:09,740 --> 00:14:17,410
+رونتجين جرام of the hand and wrist في مرحلة
+
+146
+00:14:17,410 --> 00:14:26,330
+الطفولة ممكن يتقيم مراكز التعظم أو مراكز العظم في
+
+147
+00:14:26,330 --> 00:14:31,530
+مرحلة الطفولة ممكن تقييم العظم من خلال أشعة أو صور
+
+148
+00:14:31,530 --> 00:14:36,880
+الأشعة. رونتجين جرام for the hand and wrist عامة بين
+
+149
+00:14:36,880 --> 00:14:42,840
+عامين و عامين و عامين. يوجد كربل بون بيرجر بين
+
+150
+00:14:42,840 --> 00:14:48,440
+اثنين إلى ست سنوات. يفترض أنه كل سنة تتكلس عندي
+
+151
+00:14:48,440 --> 00:14:52,880
+عظمة من عضمات الكربل بون اللي موجودة. احنا بنعرف
+
+152
+00:14:52,880 --> 00:14:58,260
+أنه في عندي two rows of carpal bone. في عندي صفين
+
+153
+00:14:58,260 --> 00:15:04,270
+من الـ Carpal bone. إذن هدول الصفين من العظم هم
+
+154
+00:15:04,270 --> 00:15:07,910
+اللي هيحددوا in adolescence and late childhood.
+
+155
+00:15:07,910 --> 00:15:12,630
+evaluation of bone age is more complicated. في
+
+156
+00:15:12,630 --> 00:15:17,970
+مرحلة المراهقة، مرحلة الـ late childhood. هلاقي أن
+
+157
+00:15:17,970 --> 00:15:23,390
+عملية التشخيص وعملية التقييم للعمر العظمي أكثر
+
+158
+00:15:23,390 --> 00:15:28,890
+تعقيدًا. وفي 
+
+159
+00:15:28,890 --> 00:15:37,770
+الغالب يتم النظر لعملية التقاء وتحول الـ cartilage
+
+160
+00:15:37,770 --> 00:15:39,950
+والابيفسيز إلى joints.
+
+161
+00:15:47,860 --> 00:15:55,880
+عشان نحدد مشكلة أو عمر العظم في مرحلة الطفولة
+
+162
+00:15:55,880 --> 00:16:01,500
+والطفولة المتأخرة ومرحلة الـ adolescence يستخدم
+
+163
+00:16:02,380 --> 00:16:07,140
+Atlas. بيسموه Greulich & Pyle atlas أو Tanner atlas.
+
+164
+00:16:07,140 --> 00:16:11,600
+طبعًا هذه يستخدم في تحديد العمر العام.
+
+165
+00:16:11,600 --> 00:16:14,780
+Respiratory rate, heart rate and blood pressure.
+
+166
+00:16:14,780 --> 00:16:18,440
+The following table shows the average heart rate,
+
+167
+00:16:19,220 --> 00:16:22,780
+respiratory rate and blood pressure at different
+
+168
+00:16:22,780 --> 00:16:27,250
+periods of a child. طبعًا هذا الجدول يوضح بعض
+
+169
+00:16:27,250 --> 00:16:33,850
+القراءات لضغط الدم والتنفس ومعدل ضربات
+
+170
+00:16:33,850 --> 00:16:41,490
+القلب عند الأطفال في مراحل متعددة. هلاقي مثلًا لـ
+
+171
+00:16:41,490 --> 00:16:46,570
+newborn. الـ heart rate 130, blood pressure 80 لـ 60.
+
+172
+00:16:46,570 --> 00:16:52,610
+الـ respiratory rate 55. عند 6 شهور. الـ heart rate
+
+173
+00:16:52,610 --> 00:16:57,000
+120. الـ blood pressure 80 لـ 60. الـ respiratory
+
+174
+00:16:57,000 --> 00:17:04,200
+rate 40. عند one year. الـ heart rate 110.
+
+175
+00:17:04,200 --> 00:17:07,960
+blood pressure 80 لـ 60. الـ respiratory rate
+
+176
+00:17:07,960 --> 00:17:14,060
+35. عند أربع سنوات. 100 على 60.
+
+177
+00:17:14,060 --> 00:17:21,340
+عند عشر سنوات. 90 heart rate, 100 على 65 blood
+
+178
+00:17:21,340 --> 00:17:25,440
+pressure. 20 respiratory rate. عند الـ puberty
+
+179
+00:17:25,440 --> 00:17:32,660
+بيصير ضغط الدم مستقر 110 على 70. الـ heart rate
+
+180
+00:17:32,660 --> 00:17:40,040
+تقريبًا 85. والـ respiratory rate يكون 20. القلب بيكون
+
+181
+00:17:40,040 --> 00:17:46,760
+نوعًا ما أكبر في مرحلة
+
+182
+00:17:46,760 --> 00:17:51,900
+الأطفال،
+
+183
+00:17:51,900 --> 00:17:59,490
+more rounded and horizontal. السماعة الأبكسية في
+
+184
+00:17:59,490 --> 00:18:05,870
+الأطفال موجودة في الأراضي الرابعة للضلع الأيسر.
+
+185
+00:18:05,870 --> 00:18:13,490
+لو جينا نسمع الـ cardiac بيت أو الـ apex بيت بدنا نحط
+
+186
+00:18:13,490 --> 00:18:21,870
+السماعة على الأراضي الرابعة جنب الضلع لبرا شوية.
+
+187
+00:18:23,790 --> 00:18:27,930
+رديولوجيًا، الـ cardiographic أو الـ cardiothoracic
+
+188
+00:18:27,930 --> 00:18:36,650
+ريشيو هو حوالي 0.6 مقارنة بالـ 0.5 في الكبير. يعني
+
+189
+00:18:36,650 --> 00:18:44,790
+معدل أو نسبة حجم القلب في الطفل بالنسبة للجسم 0.6.
+
+190
+00:18:44,790 --> 00:18:54,460
+لكن الـ cardiothoracic نسبة القلب بالنسبة للصدر أو الـ
+
+191
+00:18:54,460 --> 00:19:01,280
+thoracic space 0.6 في حين أنه مع الكبير 0.5. لأن
+
+192
+00:19:01,280 --> 00:19:03,820
+نجي نطلع على بعض المشاكل.
+
+193
+00:19:11,630 --> 00:19:18,710
+أول هذه المشاكل سنجدها على موضوع الـ scoliosis. هو
+
+194
+00:19:18,710 --> 00:19:24,010
+عملية الانحناء الجانبي للعمود الفقري.
+
+195
+00:19:27,530 --> 00:19:31,570
+A curvature of the spine that can occur in
+
+196
+00:19:31,570 --> 00:19:36,110
+adolescents and young children. It is a lateral
+
+197
+00:19:36,110 --> 00:19:41,630
+curvature of the spine.
+
+198
+00:19:47,880 --> 00:19:51,520
+Early diagnosis and appropriate management of care.
+
+199
+00:19:51,520 --> 00:19:58,540
+التشخيص السليم والسريع، التشخيص المبكر لهذه العملية
+
+200
+00:19:58,540 --> 00:20:04,340
+أو لهذه الحالة بيساعد في عملية العلاج. بيساعد أن
+
+201
+00:20:04,340 --> 00:20:08,880
+نقدم appropriate management و prevent the need of
+
+202
+00:20:08,880 --> 00:20:13,380
+surgery. ويمنع اللجوء إلى العمليات الجراحية.
+
+203
+00:20:20,400 --> 00:20:26,360
+بشكلٍ مستقيم. الآن في حالة الـ scoliosis اللي يسمونه
+
+204
+00:20:26,360 --> 00:20:30,560
+باللغة العربية الجنف. هلاقي أنه صار في عندي انحناء
+
+205
+00:20:30,560 --> 00:20:36,020
+جانبي، lateral curvature of the spine. ممكن يكون
+
+206
+00:20:36,020 --> 00:20:42,680
+طبعًا في منطقة الـ thoracic area. من المشاكل اللي
+
+207
+00:20:42,680 --> 00:20:49,180
+ممكن نشوفها عند الأطفال. حاجة بيسموها Spina Bifida.
+
+208
+00:20:49,180 --> 00:20:56,360
+فتق في العمود الفقري وحبل الشوكي. وهذا طبعًا بيكون
+
+209
+00:20:56,360 --> 00:21:02,580
+نتيجة خلل في عملية الـ development. لو جينا نتطلع
+
+210
+00:21:02,580 --> 00:21:06,630
+احنا بشكل عام هنلاقي أنه زي ما احنا شايفين في
+
+211
+00:21:06,630 --> 00:21:11,270
+الصورة هذه في عندي أنا spinal cord ماشي في الـ
+
+212
+00:21:11,270 --> 00:21:15,750
+spinal canal. حوالين الـ spinal cord فيه موجود الـ
+
+213
+00:21:15,750 --> 00:21:23,190
+meninges، الأغشية الـ pia mater والـ dura mater والـ
+
+214
+00:21:23,190 --> 00:21:29,490
+arachnoid mater. كل هذه طبعًا موجودة. الآن لما يكون
+
+215
+00:21:29,490 --> 00:21:34,350
+في عندي حاجة يسموها Spina Bifida، فتق في العمود
+
+216
+00:21:34,350 --> 00:21:39,770
+الفقري، ممكن يكون أحد ثلاث حالات. يا إما يكون Spina
+
+217
+00:21:39,770 --> 00:21:47,230
+Bifida Occulta، أو يكون Spina Bifida Manifesta، و
+
+218
+00:21:47,230 --> 00:21:51,650
+Spina Bifida Manifesta تنقسم إلى Meningocele أو
+
+219
+00:21:51,650 --> 00:21:56,670
+Myelomeningocele. الآن لو جينا نتطلع على الـ Spina
+
+220
+00:21:56,670 --> 00:22:00,910
+Bifida Occulta، شو معنى كلمة Occulta؟ Occulta
+
+221
+00:22:00,910 --> 00:22:07,150
+مخفية. زي ما احنا شايفين في الصورة هذه مش مبين في
+
+222
+00:22:07,150 --> 00:22:13,240
+الـ skin أي مشاكل ومش مبين أي بروزات. لكن لو جينا
+
+223
+00:22:13,240 --> 00:22:20,040
+نتطلع هلاقي أنه في المنطقة هذه في خلل في فراغ
+
+224
+00:22:20,040 --> 00:22:24,460
+موجود عندي في الفقرات، العمود الفقري في
+
+225
+00:22:24,460 --> 00:22:29,980
+الـ vertebral column. ونتيجة وجود الفراغ هذه هلاقي
+
+226
+00:22:29,980 --> 00:22:36,080
+أن الجلد في المنطقة هذه مشدود للأسفل.
+
+227
+00:22:39,090 --> 00:22:42,910
+وفي المنطقة هذه التجويف اللي موجود هتلاقي أنه حاجة
+
+228
+00:22:42,910 --> 00:22:48,150
+بتنبت شعر بيسموها hair follicle. مجموعة من الشعر
+
+229
+00:22:48,150 --> 00:22:53,070
+من بصيلات الشعر بتنمو في هذه المنطقة، في هذه
+
+230
+00:22:53,070 --> 00:22:57,050
+الحالة طبعًا بيسموها Spina Bifida Occulta. وعملية
+
+231
+00:22:57,050 --> 00:23:01,610
+علاجها سهل لأن مافي مكونات خارجها.
+
+232
+00:23:04,240 --> 00:23:09,860
+من الـ vertebral column أو من الـ spine وبالتالي
+
+233
+00:23:09,860 --> 00:23:15,700
+عملية العلاج ممكن تكون سهلة وجزء من العمليات أو
+
+234
+00:23:15,700 --> 00:23:20,480
+جزء من الحلقة. طبعًا في الدول المتقدمة بتتم تشخيص
+
+235
+00:23:20,480 --> 00:23:25,060
+هذه المشكلة في الرحم، وبتتم عمل عملية جراحية في داخل
+
+236
+00:23:25,060 --> 00:23:30,400
+الرحم وإغلاق هذه الفتحة قبل الولادة من الـ vertebra
+
+237
+00:23:31,370 --> 00:23:35,430
+and/or the spinal cord of the fetus does not
+
+238
+00:23:35,430 --> 00:23:39,210
+develop properly. It is one of the most common
+
+239
+00:23:39,210 --> 00:23:46,200
+birth defects. واحدة من المشاكل الأكثر شيوعًا مع
+
+240
+00:23:46,200 --> 00:23:51,520
+الأطفال. Occurring in two out of one thousand babies.
+
+241
+00:23:51,520 --> 00:23:56,600
+من كل ألف طفل في عندنا اثنين ممكن يصابوا بهذا الـ
+
+242
+00:23:56,600 --> 00:24:00,280
+diagnosis أو هذه الحالة. While the condition is
+
+243
+00:24:00,280 --> 00:24:03,320
+permanent, early treatment is urged to avoid
+
+244
+00:24:03,320 --> 00:24:07,740
+further spinal and neurological damage. وكونوا أن
+
+245
+00:24:07,740 --> 00:24:15,600
+العملية أو التشخيص هذا Permanent. يفضل أن اكتشافه
+
+246
+00:24:15,600 --> 00:24:21,880
+مبكرًا ومنع حدوثه قبل ما يسيء تمامًا. إذا قلنا في الـ
+
+247
+00:24:21,880 --> 00:24:26,560
+Spina Bifida في عندنا نوعين رئيسيين. Spina Bifida
+
+248
+00:24:26,560 --> 00:24:31,700
+Occulta و Spina Bifida Manifesta. عرفنا شو هي Spina
+
+249
+00:24:31,700 --> 00:24:36,680
+Bifida Occulta. أن نجي لـ Spina Bifida Manifesta.
+
+250
+00:24:37,400 --> 00:24:41,440
+كلمة Manifesta معناها ظاهرة. زي ما احنا شايفين. 
+
+251
+00:24:41,440 --> 00:24:46,120
+بالشكل هذا الـ spinal bifida manifesta بتنقسم إلى
+
+252
+00:24:46,120 --> 00:24:48,920
+قسمين في عندنا meningocel و في عندنا
+
+253
+00:24:48,920 --> 00:24:55,980
+meningomyelocele في حالة لما يكون meningocel هلاقي 
+
+254
+00:24:55,980 --> 00:25:03,680
+أن الـ spinal cord موجود في القناع العضمي الطبيعي
+
+255
+00:25:04,420 --> 00:25:11,580
+في حين أن الأغشية المحيطة به وجزء من السائل صار
+
+256
+00:25:11,580 --> 00:25:16,360
+فيه انبعاج إلى الخارج كيس خارجي زي ما احنا شايفين
+
+257
+00:25:16,360 --> 00:25:22,620
+هذا طبعا بيسموها مننجوسيل في حين أن النوع الثاني
+
+258
+00:25:22,620 --> 00:25:29,500
+الثاني من هذه بيسموه مننجومايلوسيل هلاقي أن الـ
+
+259
+00:25:29,500 --> 00:25:37,520
+مننجيز الأغشية وجزء من الـ spinal cord كمان موجود
+
+260
+00:25:37,520 --> 00:25:42,540
+عشان يسموها meningomyelocele عملية الوقاية منه
+
+261
+00:25:42,540 --> 00:25:50,260
+ممكن تتم في فترة الحمل وإعطاء الأم الحامل الحديد
+
+262
+00:25:50,260 --> 00:25:56,580
+والفوليك أسيد بشكل منتظم في فترة الحمل الأولى الآن
+
+263
+00:25:56,580 --> 00:26:00,320
+نجي للمشكلة الثانية اللي موجودة congenital
+
+264
+00:26:00,320 --> 00:26:01,600
+developmental disorders
+
+265
+00:26:05,310 --> 00:26:10,990
+أو developmental hip dislocation إيه لها اسم قديم
+
+266
+00:26:10,990 --> 00:26:15,250
+بيسموه congenital hip dislocation CDH لكن الاسم
+
+267
+00:26:15,250 --> 00:26:17,730
+الحديث بيسموه developmental dislocation
+
+268
+00:26:17,730 --> 00:26:25,950
+developmental dislocation of the hip DDH كلنا احنا
+
+269
+00:26:25,950 --> 00:26:32,870
+بنعرف في الـ anatomy of the pelvis الـ pelvis بتكون
+
+270
+00:26:33,990 --> 00:26:40,990
+من two halves one half to the right one half to 
+
+271
+00:26:40,990 --> 00:26:47,090
+the left جزء أيمن النصف هذه العظمة هذه بيسموها
+
+272
+00:26:47,090 --> 00:26:53,380
+coxy bone كل هذا النصف بيسموه الـ coxy الاثنين مع
+
+273
+00:26:53,380 --> 00:26:58,600
+بعض بيسموهم اوس كوكسي لو جينا ناخد جانب واحد
+
+274
+00:26:58,600 --> 00:27:05,560
+الـ coxy bone أو الـ coxy هلاقي بتكون من ثلاث عظام
+
+275
+00:27:05,560 --> 00:27:11,240
+أساسية الـ ilium زي ما احنا شايفين هذا الجزء الأساسي
+
+276
+00:27:11,240 --> 00:27:17,700
+الـ ischium وفي عندنا الـ pubic area أو الـ pubic bone
+
+277
+00:27:17,700 --> 00:27:24,480
+هي الثلاث عظام الثلاث عظام هذه مع بعض بتلتحم و
+
+278
+00:27:24,480 --> 00:27:31,600
+بتكون تجويف بيسموه الـ acetabulum الحق الـ acetabulum
+
+279
+00:27:31,600 --> 00:27:36,240
+الـ acetabulum هذا هو اللي بيعمل articulation مع
+
+280
+00:27:36,240 --> 00:27:44,840
+الـ head of femur مع رأس عظمة الفخد وبيسموه هذا طبعا 
+
+281
+00:27:44,840 --> 00:27:49,700
+الـ hip joint كله بيسموه hip joint إذا الـ acetabulum
+
+282
+00:27:49,700 --> 00:27:56,320
+اللي موجود مع الـ head of femur في كثير من الحالات
+
+283
+00:27:56,320 --> 00:28:02,840
+نتيجة خلل معين أو نتيجة مشاكل في عملية الولادة
+
+284
+00:28:02,840 --> 00:28:10,190
+بيصير عملية dislocation بيطلع الـ head of the hip من
+
+285
+00:28:10,190 --> 00:28:13,930
+الـ Acetabulum زي ما احنا شايفين كيف الصورة هذه
+
+286
+00:28:13,930 --> 00:28:21,010
+الـ head of femur مش في الـ Acetabulum مكانه هذه
+
+287
+00:28:21,010 --> 00:28:25,390
+الحالة بيسموها الـ
+
+288
+00:28:25,390 --> 00:28:31,110
+developmental dislocation of the hip DDH وممكن أن
+
+289
+00:28:31,110 --> 00:28:34,890
+عملية الـ dislocation تصير before
+
+290
+00:28:36,490 --> 00:28:42,030
+birth قبل الولادة وممكن تكون during birth أو
+
+291
+00:28:42,030 --> 00:28:50,730
+shortly after birth أو بعد الولادة بمدة قصيرة من
+
+292
+00:28:50,730 --> 00:28:53,950
+المشاكل اللي بتكون موجودة كمان في عندنا حاجة يسميها
+
+293
+00:28:53,950 --> 00:28:58,650
+congenital coxa vara congenital coxa vara شو
+
+294
+00:28:58,650 --> 00:29:04,970
+المقصود بـ congenital coxa vara كلنا بنعرف أن هذه
+
+295
+00:29:04,970 --> 00:29:11,310
+عظمة الـ hip أو عظمة الفخد الـ femur زي ما احنا
+
+296
+00:29:11,310 --> 00:29:16,590
+شايفين تتكون من الـ head of femur الـ neck of femur
+
+297
+00:29:16,590 --> 00:29:19,630
+في عندي الـ greater trochanter في عندنا الـ lesser
+
+298
+00:29:19,630 --> 00:29:24,810
+trochanter وفي عندي الـ shaft of the femur و تحته
+
+299
+00:29:24,810 --> 00:29:28,990
+بتعمل articulation مع الـ knee الآن زي ما احنا
+
+300
+00:29:28,990 --> 00:29:33,470
+شايفين الـ neck of femur مع الـ shaft of femur بتكون
+
+301
+00:29:33,470 --> 00:29:43,970
+عندي زاوية الزاوية هذه طبعا لها مقياس معين يفترض
+
+302
+00:29:43,970 --> 00:29:52,230
+أنه يكون هذا المقياس طبعا عند الـ male بيختلف عن الـ
+
+303
+00:29:52,230 --> 00:29:58,230
+female any condition in which the neck shaft angle
+
+304
+00:29:58,230 --> 00:30:03,070
+الزاوية
+
+305
+00:30:03,070 --> 00:30:10,120
+هذه less than normal which is about one hundred
+
+306
+00:30:10,120 --> 00:30:15,020
+twenty five degrees إذا كانت أقل من مية وخمسة وعشرين 
+
+307
+00:30:15,020 --> 00:30:22,600
+معناه أن هذه الحالة بيسموها كوكسا فارة إذا
+
+308
+00:30:22,600 --> 00:30:27,340
+كانت أقل من مية وخمسة وعشرين لاحظوا المية وخمسة
+
+309
+00:30:27,340 --> 00:30:30,240
+وعشرين تعتبر طبيعي من مية وعشرين لمية وخمسة وثلاثين
+
+310
+00:30:30,240 --> 00:30:30,720
+  
+311
+00:30:33,320 --> 00:30:38,620
+الأقل من مائة وعشرين تعتبر حالة مرضية بيسموها
+
+312
+00:30:38,620 --> 00:30:44,820
+الكوكسافارة الزاوية هذه أقل وهلاقي الشخص اللي عنده
+
+313
+00:30:44,820 --> 00:30:50,340
+هذه المشكلة بيمشي بمشي بيسموها ماشية البطة ماشية
+
+314
+00:30:50,340 --> 00:30:57,400
+البطة إذا كانت أكبر من مائة وخمسة وثلاثين الزاوية
+
+315
+00:30:57,400 --> 00:31:00,160
+زي ما احنا شايفينه في الصورة هذه بيسموها
+
+316
+00:31:00,160 --> 00:31:01,560
+الكوكسافارة
+
+317
+00:31:04,430 --> 00:31:13,430
+الحالة الثانية أو عرض ثاني ممكن يكون موجود مع الناس 
+
+318
+00:31:13,430 --> 00:31:20,330
+اللي عندهم مشاكل في الـ bone حاجة يسموها Leg Calve 
+
+319
+00:31:20,330 --> 00:31:27,050
+Perthes disease it is an osteo or it is
+
+320
+00:31:27,050 --> 00:31:31,190
+osteochondritis of the epiphysis of the femoral
+
+321
+00:31:31,190 --> 00:31:37,500
+head هلاقي أن الـ Leg Calve Perthes صار فيه الـ femoral
+
+322
+00:31:37,500 --> 00:31:44,180
+head وهو طبعا الـ epiphysis هذا صار فيه نوع من الـ
+
+323
+00:31:44,180 --> 00:31:51,320
+inflammation أوستيوكندريتس نتيجة الـ osteochondritis
+
+324
+00:31:51,320 --> 00:31:56,320
+صار فيه عندي ونتيجة الـ weight bearing صار فيه عندي 
+
+325
+00:31:56,320 --> 00:32:04,350
+destruction للـ growth center اللي موجود عملية نمو 
+
+326
+00:32:04,350 --> 00:32:09,370
+في هذا الطرف وفي هذه الحالة سيصبح عند الطفل مشكلة
+
+327
+00:32:09,370 --> 00:32:14,290
+أنه لا يكبر ولا يصبح لديه عملية نمو في هذا الطرف
+
+328
+00:32:14,290 --> 00:32:22,230
+الحل لهم أنهم دائما بيخلوا الطفل يركب جهاز يمنع
+
+329
+00:32:22,230 --> 00:32:28,050
+عملية التحميل على الطرف في أثناء الوقوف والمشي
+
+330
+00:32:28,050 --> 00:32:34,000
+ويفضل لهم دائما الراحة لحد ما تتعالج مشكلة الـ 
+
+331
+00:32:34,000 --> 00:32:38,740
+Osteochondritis slipped capital femoral epiphysis
+
+332
+00:32:38,740 --> 00:32:44,420
+وهذا طبعا هلاقي أن في بعض الحالات زي ما احنا شايفين
+
+333
+00:32:44,420 --> 00:32:47,960
+في الصورة اللي موجودة هي الـ normal head of femur
+
+334
+00:32:47,960 --> 00:32:56,280
+هي الـ normal place لها وهنا صار في عندي slipping
+
+335
+00:32:56,280 --> 00:33:04,610
+صار إزاحة للـ head of femur وهذه الحالات تكون في
+
+336
+00:33:04,610 --> 00:33:08,690
+الغالب ناتجة عن developmental hip abnormalities
+
+337
+00:33:08,690 --> 00:33:12,390
+ممكن يكون فيها fractures أو bosses traumatic
+
+338
+00:33:12,390 --> 00:33:17,630
+abnormalities الـ adolescent hip pain ممكن يكون
+
+339
+00:33:17,630 --> 00:33:24,970
+واحد من الأعراض الموجودة ممكن تكون سبب من أسبابها
+
+340
+00:33:24,970 --> 00:33:30,440
+للـ tumors الـ Malignancies الأورام اللي بتكون
+
+341
+00:33:30,440 --> 00:33:37,220
+موجودة في المنطقة من الأعراض أو من الـ syndromes
+
+342
+00:33:37,220 --> 00:33:40,220
+اللي ممكن تكون موجودة والأمراض اللي بتكون موجودة
+
+343
+00:33:40,220 --> 00:33:44,840
+بتأثر على عملية الـ development neuromuscular
+
+344
+00:33:44,840 --> 00:33:50,500
+diseases في عندنا الـ cerebral palsy الشلل الدماغي
+
+345
+00:33:50,500 --> 00:33:54,480
+كلمة cerebral palsy it's a term used
+
+346
+00:33:59,510 --> 00:34:03,850
+body movement and muscle coordination هي مصطلح
+
+347
+00:34:03,850 --> 00:34:11,990
+بيستخدم لتوصيف مجموعة من الأعراض اللي بتأثر على
+
+348
+00:34:11,990 --> 00:34:17,390
+عملية الـ coordination وعملية الـ movement في الـ
+
+349
+00:34:17,390 --> 00:34:23,970
+upper و lower limbs ممكن تأثر على الـ Cognitive
+
+350
+00:34:23,970 --> 00:34:28,750
+Function كمان It is caused by damage to one or
+
+351
+00:34:28,750 --> 00:34:33,590
+more specific areas of the brain ممكن يكون السبب
+
+352
+00:34:33,590 --> 00:34:38,850
+تبعها إصابة منطقة أو أكثر من الـ brain usually
+
+353
+00:34:38,850 --> 00:34:43,110
+occurring during fetal development or infancy في
+
+354
+00:34:43,110 --> 00:34:50,680
+الغالب تكون في مرحلة الحمل نتيجة تعرض الأم لعدة
+
+355
+00:34:50,680 --> 00:34:56,500
+عوامل ممكن تكون سبب في مشاكل development of the
+
+356
+00:34:56,500 --> 00:35:04,160
+fetus مشاكل ممكن تؤدي إلى تشوهات وممكن تؤدي إلى
+
+357
+00:35:04,160 --> 00:35:10,420
+خلل في normal development of the brain of the
+
+358
+00:35:10,420 --> 00:35:17,340
+child it also can occur before during or shortly
+
+359
+00:35:17,340 --> 00:35:18,740
+following birth
+
+360
+00:35:22,520 --> 00:35:28,580
+وهذا قلنا نتيجة أن الأم تتعرض لـ teratogens تتعرض
+
+361
+00:35:28,580 --> 00:35:33,780
+لعوامل ممكن عوامل كيميائية ممكن أدوية ممكن تلوثات
+
+362
+00:35:33,780 --> 00:35:38,140
+كلها ممكن تؤثر على عملية النمو زي ممكن أم تتعرض
+
+363
+00:35:38,140 --> 00:35:43,980
+لأشعة في فترة الحمل ممكن يكون سبب من أسباب الـ
+
+364
+00:35:43,980 --> 00:35:49,060
+cerebral palsy هذا في مرحلة الحمل during birth
+
+365
+00:35:49,060 --> 00:35:50,220
+أثناء الولادة
+
+366
+00:35:54,560 --> 00:35:59,360
+أو نتيجة عملية الولادة الـ forceps delivery صار
+
+367
+00:35:59,360 --> 00:36:04,480
+فيه damage أو بعد الولادة لمدة تقريبا سنتين أي
+
+368
+00:36:04,480 --> 00:36:09,680
+traumatic brain injury أو أي إصابة في الدماغ يشخص
+
+369
+00:36:09,680 --> 00:36:15,840
+الطفل على أنه cerebral palsy cerebral palsy is
+
+370
+00:36:15,840 --> 00:36:18,460
+neither progressive nor communicable
+
+371
+00:36:24,130 --> 00:36:30,690
+هو مش مرض معد ومش مرض متطور يعني خلينا نقول أنه
+
+372
+00:36:30,690 --> 00:36:37,270
+خلاص صارت المشكلة بتظلها زي ما هي لكن ممكن يصير
+
+373
+00:36:37,270 --> 00:36:41,310
+تبعيات نتيجة قلة الاهتمام قلة العلاج الطبيعي اللي
+
+374
+00:36:41,310 --> 00:36:46,010
+بيكون موجود ممكن تتضاعف أو يصير مضاعفات لهذه
+
+375
+00:36:46,010 --> 00:36:51,800
+الحالة لكن وضع الدماغ بيظل زي ما هو it's important
+
+376
+00:36:51,800 --> 00:36:54,980
+to know that cerebral palsy is not a disease, it
+
+377
+00:36:54,980 --> 00:36:59,720
+is not contagious and does not get worse, يعني مش 
+
+378
+00:36:59,720 --> 00:37:06,500
+مرض معدي، ما بيصير تغير في ال brain، يعني ما بيصير 
+
+379
+00:37:06,500 --> 00:37:11,120
+زيادة في نسبة الخلايا المدمرة في ال brain، لأ بتظل 
+
+380
+00:37:11,120 --> 00:37:21,860
+تابعة الأطفال اللي بيولدوا بـ Cerebral Palsy هيدلوا 
+
+381
+00:37:21,860 --> 00:37:27,980
+طول عمره مع Cerebral Palsy. Cerebral Palsy هو شخص 
+
+382
+00:37:27,980 --> 00:37:29,900
+مُصاب من غلطة 
+
+383
+00:37:32,140 --> 00:37:37,140
+control motor function particularly muscle control
+
+384
+00:37:37,140 --> 00:37:41,420
+and coordination. الأشخاص اللي عندهم مشاكل السيربرا 
+
+385
+00:37:41,420 --> 00:37:45,960
+البنسي هيكون في عندهم مشاكل حركية motor هيكون في 
+
+386
+00:37:45,960 --> 00:37:50,460
+عندهم functional problems هيكون على سبيل المثال 
+
+387
+00:37:50,460 --> 00:37:53,740
+disturbance في ال gate في ال mobility في ال
+
+388
+00:37:53,740 --> 00:37:58,230
+balance. هيكون في عندهم involuntary movement طبعا 
+
+389
+00:37:58,230 --> 00:38:00,950
+الموضوع السليبرال بالسي إن شاء الله رب العالمين
+
+390
+00:38:00,950 --> 00:38:05,490
+هتدرسوه بشيء من التفصيل خلال السنوات القادمة مع 
+
+391
+00:38:05,490 --> 00:38:09,690
+دراسة كل الأطفال من المشاكل اللي بتكون موجودة foot
+
+392
+00:38:09,690 --> 00:38:14,490
+ankle disorders وها ت طبعا من المشاكل اللي بنشوفها 
+
+393
+00:38:14,490 --> 00:38:18,910
+في مراحل ولادة ممكن الطفل ينولد بحاجة يسموها club
+
+394
+00:38:18,910 --> 00:38:25,570
+foot زي ما احنا شايفين كيف ال club food ال club 
+
+395
+00:38:25,570 --> 00:38:32,950
+food هي عبارة عن تلبس equinovarus التشوه 
+
+396
+00:38:32,950 --> 00:38:40,030
+اللي موجود هنا طبعا هو ال club food أو ممكن تكون 
+
+397
+00:38:40,030 --> 00:38:46,410
+تلبس calcaneovalgus صارت طلعت بدل ما هي كفة القدم 
+
+398
+00:38:46,410 --> 00:38:49,470
+داخل 
+
+399
+00:38:49,470 --> 00:38:55,200
+لجوا ممكن تكون خلعة لبرا تالي بس كالكينيو فالجاس 
+
+400
+00:38:55,200 --> 00:39:00,120
+طبعا احنا بنحكي عن تالي بس ال foot و calcaneus
+
+401
+00:39:00,120 --> 00:39:06,250
+اللي هي ال bones of the foot ممكن يكون في عنا 
+
+402
+00:39:06,250 --> 00:39:11,110
+بيسبلانس أو الـ flat foot زي ما احنا شايفين اللي 
+
+403
+00:39:11,110 --> 00:39:17,530
+هو إن قوس القدم مش موجود التقوس اللي موجود في 
+
+404
+00:39:17,530 --> 00:39:22,210
+القدم في الوضع الطبيعي، هذه بيسموها بيسبلانس أو 
+
+405
+00:39:22,210 --> 00:39:28,010
+flat foot من المشاكل اللي بتكون موجودة كمان الـ 
+
+406
+00:39:28,010 --> 00:39:31,930
+down syndrome ال down syndrome طبعا هو عبارة عن 
+
+407
+00:39:31,930 --> 00:39:41,010
+mental retardation و degree of various ال down
+
+408
+00:39:41,010 --> 00:39:48,050
+syndrome هو الخلل جيني ممكن يكون خلل في الجينات It
+
+409
+00:39:48,050 --> 00:39:52,410
+is a chromosomal disorder caused by presence of
+
+410
+00:39:52,410 --> 00:39:57,770
+all or part of an extra 21st chromosome، خلل في 
+
+411
+00:39:57,770 --> 00:40:04,830
+الـ Chromosome رقم 21. The
+
+412
+00:40:04,830 --> 00:40:07,970
+condition is characterized by combination of major
+
+413
+00:40:07,970 --> 00:40:10,190
+and minor differences in structure
+
+414
+00:40:19,430 --> 00:40:25,210
+أكثر ما يميزهم شكل الوجه وكيف ممكن تكون طبعا
+
+415
+00:40:25,210 --> 00:40:28,370
+بالإضافة 
+
+416
+00:40:28,370 --> 00:40:34,070
+لأن احنا بنحكي على بعض 
+
+417
+00:40:34,070 --> 00:40:37,050
+المشاكل اللي ممكن تكون موجودة في عملية ال
+
+418
+00:40:37,050 --> 00:40:45,430
+development طبعاً لعملية الفحص ونتعرف 
+
+419
+00:40:45,430 --> 00:40:53,050
+على الطفل في فترة الحمل ممكن من خلال سحب عينة من 
+
+420
+00:40:53,050 --> 00:41:00,090
+ال fluid amniotic fluid اللي حوالين الجنين طبعا 
+
+421
+00:41:00,090 --> 00:41:02,590
+هذه الحالة بسموها amniocentesis
+
+422
+00:41:06,350 --> 00:41:12,410
+وهذا طبعا ممكن ينعمل فحص during birth during
+
+423
+00:41:12,410 --> 00:41:18,570
+pregnancy أو at birth. لو جينا نطلع على ال down
+
+424
+00:41:18,570 --> 00:41:24,730
+syndrome هلاقي ان في عندهم بعض ال features اللي 
+
+425
+00:41:24,730 --> 00:41:28,510
+بتكون موجودة. Small number have severe to profound
+
+426
+00:41:28,510 --> 00:41:34,020
+mental disability. جزء منهم ممكن يكون في عنده إعاقة 
+
+427
+00:41:34,020 --> 00:41:37,620
+عقلية شديدة. The incidence of Down syndrome is
+
+428
+00:41:37,620 --> 00:41:44,500
+estimated 1 لكل 800 أو ألف بيرت 1 من كل 800 إلى 
+
+429
+00:41:44,500 --> 00:41:56,280
+1000 ولادة ممكن ينولد Down syndrome من 
+
+430
+00:41:56,280 --> 00:42:01,980
+الأعراض اللي بيكون موجودة عندهم طبعا الـ features
+
+431
+00:42:01,980 --> 00:42:05,340
+Down syndrome may also appear in people with a
+
+432
+00:42:05,340 --> 00:42:09,480
+standard set of chromosomes including microgenia
+
+433
+00:42:09,480 --> 00:42:16,480
+and abnormally small chin and unusually round face
+
+434
+00:42:16,480 --> 00:42:22,100
+protruding or oversized tongue and almond shape
+
+435
+00:42:22,100 --> 00:42:30,520
+of the eyes. هلاقي انه اللسان حجم كبير أو بارز ممكن 
+
+436
+00:42:30,520 --> 00:42:35,100
+يكون طبعا العينين
+
+437
+00:42:35,100 --> 00:42:45,380
+بحاجة بيسموها الـ almond shape شكل اللوزة وفي 
+
+438
+00:42:45,380 --> 00:42:50,960
+حاجة بيسموها الـ epicanthic fold of the eyelid. شرط 
+
+439
+00:42:50,960 --> 00:42:57,680
+العين بتكون عينهم مشروطة. هذه هي تقريبا أهم الأعراض 
+
+440
+00:42:57,680 --> 00:43:02,570
+اللي بتكون موجودة من ضمن المشاكل اللي بتكون موجودة
+
+441
+00:43:02,570 --> 00:43:06,130
+معهم و يديروا بالهم مع هؤلاء الناس طبعا higher
+
+442
+00:43:06,130 --> 00:43:10,730
+risk of congenital heart defects gastroesophageal
+
+443
+00:43:10,730 --> 00:43:14,650
+reflux disease recurrent ear infections
+
+444
+00:43:14,650 --> 00:43:21,890
+obstructive sleep apnea thyroid dysfunction. أهم 
+
+445
+00:43:21,890 --> 00:43:26,430
+الأعراض باختصار الـ Oriental eye tongue protrusion
+
+446
+00:43:27,690 --> 00:43:34,070
+العين طبعا كيف شكلها بروز اللسان short arms and
+
+447
+00:43:34,070 --> 00:43:40,910
+legs simian crease طبعا إيديهم فيها fold واحد 
+
+448
+00:43:40,910 --> 00:43:46,250
+الخطوط اللي موجودة في الإيد internal organs
+
+449
+00:43:46,250 --> 00:43:50,190
+congenital heart defect في الغالب في ممكن يكون 
+
+450
+00:43:50,190 --> 00:43:51,530
+فيهم مشاكل في القلب
+
+451
+00:43:56,180 --> 00:44:01,960
+ممكن يكون في عندهم stenosis أو narrowing في blood
+
+452
+00:44:01,960 --> 00:44:09,060
+vessels. هذه تقريبا أهم الأعراض اللي بتكون موجودة 
+
+453
+00:44:09,060 --> 00:44:17,960
+عند ال down syndrome. باقي ال syndromes مش كتير مهم 
+
+454
+00:44:17,960 --> 00:44:18,700
+لنا
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM_postprocess.srt b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..09417649143bbfd55ac2a9493aa44ffae48d7958
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM_postprocess.srt
@@ -0,0 +1,1816 @@
+1
+00:00:00,440 --> 00:00:05,140
+السلام عليكم و رحمة الله و بركاته اليوم هنتكلم في
+
+2
+00:00:05,140 --> 00:00:09,680
+موضوع اخر في موضوع development human growth and
+
+3
+00:00:09,680 --> 00:00:15,720
+development هنتكلم عن special aspects of
+
+4
+00:00:15,720 --> 00:00:22,340
+development خلال
+
+5
+00:00:22,340 --> 00:00:27,430
+حديثنا عنالـ special aspects of development هنتكلم
+
+6
+00:00:27,430 --> 00:00:31,690
+شوية هنتكلم عن ال development of the teeth و كيف
+
+7
+00:00:31,690 --> 00:00:36,350
+بتكون عند الأطفال و كيف بتكون عند الكبار طبعا بشكل
+
+8
+00:00:36,350 --> 00:00:42,770
+سريع ال human has 20 primary and 32 permanent
+
+9
+00:00:42,770 --> 00:00:47,470
+teeth developed from the interaction of the oral
+
+10
+00:00:47,470 --> 00:00:51,810
+epithelial cells بداية لو جينا نتطلع بنعرف انه
+
+11
+00:00:51,810 --> 00:00:57,560
+الإنسان في عندهفي فترة الطفولة بيكون عنده حوالي
+
+12
+00:00:57,560 --> 00:01:03,020
+عشرين سن primary teeth هذا طبعا بيسموها الأسنان
+
+13
+00:01:03,020 --> 00:01:08,340
+اللبنية وفي عنا اتنين و تلاتين permanent teeth
+
+14
+00:01:08,340 --> 00:01:12,740
+موجودين لو جينا نطلع على ال development of the
+
+15
+00:01:12,740 --> 00:01:16,700
+teeth نطلع على ال stages of the teeth هنلاقي في
+
+16
+00:01:16,700 --> 00:01:21,180
+عندي three main stages of development هذا ال three
+
+17
+00:01:21,180 --> 00:01:29,840
+main stagesبعد مرحلة مرحلة تالتة
+
+18
+00:01:29,840 --> 00:01:30,020
+مرحلة
+
+19
+00:01:36,510 --> 00:01:45,930
+الشمس تزداد و تزداد و تزداد و تزداد و تزداد و
+
+20
+00:01:45,930 --> 00:01:56,630
+تزداد و تزداد و تزداد و تزداد و تزداد
+
+21
+00:01:56,630 --> 00:02:05,510
+و تزداد و تزداد و تزداد
+
+22
+00:02:14,380 --> 00:02:19,480
+وهذا طبعا عملية الـ differentiation تبدأ توضح مرحل
+
+23
+00:02:19,480 --> 00:02:24,620
+اللي بديه يكون فيها ال bell stage وشو هي المراحل
+
+24
+00:02:24,620 --> 00:02:28,660
+اللي بيكون فيها ال bell stage لو جينا نبطلع الآن
+
+25
+00:02:28,660 --> 00:02:36,450
+على الصورة اللي أمامنا وكيف ممكنيتكون السن حلاجة
+
+26
+00:02:36,450 --> 00:02:40,710
+ان الـ root formation and cementogenesis continue
+
+27
+00:02:40,710 --> 00:02:44,690
+until a functional tooth and its supporting
+
+28
+00:02:44,690 --> 00:02:47,890
+structures are fully developed as the crown are
+
+29
+00:02:47,890 --> 00:02:51,830
+formed and mineralized the root of the teeth begin
+
+30
+00:02:51,830 --> 00:03:00,790
+to form مجرد ما يبدأ التاج يتكون تبدأ يصير عملية
+
+31
+00:03:00,790 --> 00:03:02,070
+ال mineralization
+
+32
+00:03:10,030 --> 00:03:15,510
+مجرد ما يتكون التاج السن ويصير فيه عملية الـ
+
+33
+00:03:15,510 --> 00:03:19,430
+Mineralization فيه هتبدأ ال roots of the teeth
+
+34
+00:03:19,430 --> 00:03:25,470
+begin to form جذور السن تبدأ تتكون بشكل اخر بعد ان
+
+35
+00:03:25,470 --> 00:03:29,560
+تكون ال roots classified ، السبارة تنتشرof the
+
+36
+00:03:29,560 --> 00:03:33,340
+teeth اللي بتشتغل الشغل خانيا نقول the cementum
+
+37
+00:03:33,340 --> 00:03:41,040
+bredباريو دينتال ليجامين والغ لربون تتكوّن تتكوّن
+
+38
+00:03:41,040 --> 00:03:44,400
+كل هذه المكونات تبدأ تتكوّن تتكوّن تتكوّن تتكوّن
+
+39
+00:03:44,400 --> 00:03:46,380
+تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن
+
+40
+00:03:46,380 --> 00:03:49,060
+تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن
+
+41
+00:03:49,060 --> 00:03:50,440
+تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن
+
+42
+00:03:50,440 --> 00:04:01,740
+تتكوّن تتكوّن تتكوّن تتكوّن تتكوّن تتكو
+
+43
+00:04:03,520 --> 00:04:11,900
+الان لو جينا نتطلع على هذه المراحل هلاجي انه من
+
+44
+00:04:11,900 --> 00:04:15,400
+البداية هلاجي انه في عندي صار في عندي ابثاليم
+
+45
+00:04:15,400 --> 00:04:23,160
+موجود و نواة السن الخلايا الأساسية في عملية
+
+46
+00:04:23,160 --> 00:04:27,900
+differentiation of the teethهلاجي انه صار في عندي
+
+47
+00:04:27,900 --> 00:04:32,080
+missing climb as the crown are formed and
+
+48
+00:04:32,080 --> 00:04:35,460
+mineralized the root of the teeth begin to fall
+
+49
+00:04:35,460 --> 00:04:42,700
+مجرد ما يصير عندي تاج السن يتكون ويصير فيه تكلس
+
+50
+00:04:42,700 --> 00:05:05,900
+ابتدأ الجذور تبعات السن تتكونعندما يتكوّن
+
+51
+00:05:05,900 --> 00:05:12,460
+الانسجة التدعيم للسن مثل السمنطم البرودنتال
+
+52
+00:05:12,460 --> 00:05:23,640
+ليجامنت الالفولاركل هذه تبدأ تتكونمجرد ما
+
+53
+00:05:23,640 --> 00:05:29,980
+يكتمل نمو السن بيبدأ يشق طريقه من خلال اللثة و
+
+54
+00:05:29,980 --> 00:05:36,100
+يطلع في تجويف الفم روت فورميشن و سيمينتوجينيس
+
+55
+00:05:36,100 --> 00:05:42,020
+تستمر حتى يتم تطبيق التوث و تعمل تعمل تعمل تعمل
+
+56
+00:05:42,020 --> 00:05:47,700
+تعمل تعمل تعمل تعمل
+
+57
+00:05:48,330 --> 00:05:52,770
+هذه التفاصيل تستمر لحد ما يصبح لدي functional
+
+58
+00:05:52,770 --> 00:05:59,750
+tooth وهذا يشمل استمرار التطور في الـ supporting
+
+59
+00:05:59,750 --> 00:06:03,830
+structures اللي موجودة حوالين الـ teeth لو جينا
+
+60
+00:06:03,830 --> 00:06:09,830
+نتطلع على مراحل تطور الـ tooth هلاقي المرحلة
+
+61
+00:06:09,830 --> 00:06:16,210
+الأولى عملية ال initiationوهذا طبعا في الابيثيليام
+
+62
+00:06:16,210 --> 00:06:20,310
+الحلاجي صار في عندي ال missing chymal cells هذه
+
+63
+00:06:20,310 --> 00:06:24,850
+بدت تتشكل وصير differentiation لها بعد هيك صار
+
+64
+00:06:24,850 --> 00:06:31,570
+عندي ال dental placode صار تقريبا مكان السن بده
+
+65
+00:06:31,570 --> 00:06:38,710
+يطلع الان ال dental missing chymal بيبدأ يصير له
+
+66
+00:06:38,710 --> 00:06:46,200
+طبعا تكونو يبدأ يصير فيه development وهذا يسمى
+
+67
+00:06:46,200 --> 00:06:53,460
+مرحلة ال bud stage المرحلة التانية مرحلة ال cab
+
+68
+00:06:53,460 --> 00:07:02,640
+stage تبدأ طبعا شكل السن يتغطى و يأخذ بعد ذلك
+
+69
+00:07:02,640 --> 00:07:06,260
+مرحلة ال bell stage شكل الجرس
+
+70
+00:07:09,430 --> 00:07:15,490
+مجرد ما تتقوى هذه و يتقوى الجذور في داخل اللثة
+
+71
+00:07:15,490 --> 00:07:20,650
+طبعا بيصير عملية زي ما احنا شايفين الـ root الـ
+
+72
+00:07:20,650 --> 00:07:25,390
+subparting tissue اللي موجود حوالين السن بيصير في
+
+73
+00:07:25,390 --> 00:07:29,310
+عندي عملية ال eruption و أثناء عملية ال eruption
+
+74
+00:07:29,310 --> 00:07:34,470
+هلاجي ان عملية development of the root استمرت ال
+
+75
+00:07:34,470 --> 00:07:38,680
+development of the subparting structures استمرتلحد
+
+76
+00:07:38,680 --> 00:07:42,900
+ما يصير في عندي functional tooth لحد ما يصير في
+
+77
+00:07:42,900 --> 00:07:48,660
+عندي functional tooth تلت مراحل ال bud stage زي ما
+
+78
+00:07:48,660 --> 00:07:53,800
+احنا شايفين كمرحلة اللي هي البروز هذه مرحلة ال cab
+
+79
+00:07:53,800 --> 00:07:59,220
+stage بدأ يتشكل شكل السن مرحلة ال bell stage هذه
+
+80
+00:07:59,220 --> 00:08:06,300
+التلت مراحل ما قبل ال eruption of the tooth ما قبل
+
+81
+00:08:06,300 --> 00:08:11,280
+بزوغ السنبعد هي عمر مرحلة الـ eruption ومرحلة
+
+82
+00:08:11,280 --> 00:08:16,940
+تقوية دور السن من خلال development of the bone
+
+83
+00:08:16,940 --> 00:08:20,900
+this is also subject to a side range of variation
+
+84
+00:08:20,900 --> 00:08:24,780
+teething in the lower jaw mandibular usually
+
+85
+00:08:24,780 --> 00:08:29,680
+proceed that in the upper jaw maxillary by one to
+
+86
+00:08:29,680 --> 00:08:36,420
+two months بنعرف ان عملية التسنينبتبدأ في الـ
+
+87
+00:08:36,420 --> 00:08:40,540
+mandibular jaw في ال lower part of the jaw في
+
+88
+00:08:40,540 --> 00:08:45,520
+الفتق السفلي قبل ما يبدأ تطلع الأسنان في الفتق
+
+89
+00:08:45,520 --> 00:08:50,500
+العلوي حوالي الفاصل ما بينهم من شهر إلى شهرين
+
+90
+00:08:50,500 --> 00:08:57,640
+تقريباعند الغالبية لكن مش بالضرورة تكون عند الجميع
+
+91
+00:08:57,640 --> 00:09:01,600
+بنفس القدر ممكن يكون في بعض الشواذل هذه القاعدة
+
+92
+00:09:22,800 --> 00:09:28,920
+في الـ mandibular jaw القواطع الجانبية حيث يظهرون
+
+93
+00:09:28,920 --> 00:09:35,880
+من 7 إلى 9 أشهر في الـ maxillary jaw الفك العلوي
+
+94
+00:09:35,880 --> 00:09:41,920
+من 8 إلى 11 شهر باقي الأسنان تقريبا نفس الشيء و
+
+95
+00:09:41,920 --> 00:09:47,080
+نفس المدة إذا الإختلاف في الـ central incisors و
+
+96
+00:09:47,080 --> 00:09:53,760
+ال lateral incisors الـ permanent teethأو الـ
+
+97
+00:09:53,760 --> 00:09:57,500
+secondary teeth هلاجي انه الـ central في ال
+
+98
+00:09:57,500 --> 00:10:01,540
+permanent teeth هلاجي انه ال central incisors
+
+99
+00:10:01,540 --> 00:10:07,500
+بيبدأ عملية التبديل تبعها بشكل مختلف عن عملية ظهور
+
+100
+00:10:07,500 --> 00:10:13,560
+ال primary هلاجي ان ال upper jaw او ال maxillary
+
+101
+00:10:13,560 --> 00:10:21,440
+jaw تظهر في الأسنان عندأو بتبدأ تتساقط الأسنان
+
+102
+00:10:21,440 --> 00:10:28,460
+متبدل في ال upper jaw من 6 إلى 7 وفي ال lower jaw
+
+103
+00:10:28,460 --> 00:10:35,260
+من 7 إلى 8 سنوات ال lateral incisors من 7 إلى 8 في
+
+104
+00:10:35,260 --> 00:10:42,080
+ال upper jaw 8 إلى 9 في ال lower jaw ال canines
+
+105
+00:10:42,080 --> 00:10:47,740
+الأنياب من 9 إلى 11 في ال upper من 11 إلى 12 في ال
+
+106
+00:10:47,740 --> 00:10:55,070
+lower jawملاحظ ان عملية تبديل الأسنان في ال upper
+
+107
+00:10:55,070 --> 00:10:59,750
+jaw تبدأ قبل ال lower jaw تبديل الأسنان الدائمة
+
+108
+00:10:59,750 --> 00:11:05,430
+لكن ظهور الأسنان اللبانية في ال lower jaw تبدأ قبل
+
+109
+00:11:05,430 --> 00:11:09,570
+ال upper jaw هذه المقاط اللي نحكيها في موضوع
+
+110
+00:11:09,570 --> 00:11:11,370
+development of the teeth
+
+111
+00:11:14,100 --> 00:11:17,760
+الـ maturity أو الـ maturity of the bone أو الـ
+
+112
+00:11:17,760 --> 00:11:22,380
+bone age حلّجة إن ciclical maturity أو الـ bone
+
+113
+00:11:22,380 --> 00:11:26,700
+age is a maturation process which occurs in bones
+
+114
+00:11:26,700 --> 00:11:30,880
+in the form of appearance, progression in size and
+
+115
+00:11:30,880 --> 00:11:34,920
+eventual fusion of epiphysis centers with the
+
+116
+00:11:34,920 --> 00:11:39,200
+metaphysics of bone ففي عملية الـ development of
+
+117
+00:11:39,200 --> 00:11:45,360
+the boneهذه اللي بنستفيد منها في عملية التعرف على
+
+118
+00:11:45,360 --> 00:11:52,080
+عمر الشخص اللي أمامنا من خلال نمو العظم اللي بيكون
+
+119
+00:11:52,080 --> 00:11:56,300
+موجود ومن خلال البروزات العظمية اللي بيكون موجودة
+
+120
+00:11:56,300 --> 00:12:00,460
+normally born age correspond to the age of the
+
+121
+00:12:00,460 --> 00:12:06,560
+child في الوضع الطبيعي هلاجي أن عمر العظم أو العمر
+
+122
+00:12:06,560 --> 00:12:26,790
+العظمي ال born ageهو يناسب عمر الطفل في بعض
+
+123
+00:12:26,790 --> 00:12:32,370
+الحالات اللي بتكون فيها مشاكل وإعاقة
+
+124
+00:12:32,370 --> 00:12:37,320
+في عملية النموهلاجي ان العمر العظمى بيختلف عن
+
+125
+00:12:37,320 --> 00:12:42,180
+العمر الحقيقي للطفل وهذا بنشوفه في حالات مشاكل
+
+126
+00:12:42,180 --> 00:12:46,540
+الغدد الصماء زي مشكلة الـ hypothyroidism
+
+127
+00:12:46,540 --> 00:12:51,760
+evaluation of bone age كيف نقيم ال bone age if the
+
+128
+00:12:51,760 --> 00:12:56,580
+newborn and infancy in the newborn and in the
+
+129
+00:12:56,580 --> 00:13:00,880
+infancy the ossified centers around the knee joint
+
+130
+00:13:00,880 --> 00:13:06,710
+are well developedabsence of these centers means a
+
+131
+00:13:06,710 --> 00:13:11,090
+delay in the bond age يعني لو جينا احنا و نشوف شو
+
+132
+00:13:11,090 --> 00:13:16,090
+اللي ممكن نستفيده من ال bond age لو طلعنا على صورة
+
+133
+00:13:16,090 --> 00:13:21,930
+أشعة خاصة بـ newborn هلاجئ ان الـ ossified centers
+
+134
+00:13:21,930 --> 00:13:27,070
+مراكز التكلس اللي حوالين النيجان بتتطور تكون
+
+135
+00:13:27,070 --> 00:13:33,170
+موجودة لكن عدم وجودهافي مرحلة الـ Newborn و الـ
+
+136
+00:13:33,170 --> 00:13:40,930
+Infancy سيكون هناك خلل في عملية النمو العظمي للطفل
+
+137
+00:13:41,960 --> 00:13:47,200
+يعني لو جينا أخدنا صورة أشعة لطفل لمنطقة الرقبة
+
+138
+00:13:47,200 --> 00:13:52,760
+يفترض أن يكون في حياته حياته حياته حياته حياته
+
+139
+00:13:52,760 --> 00:13:54,160
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+140
+00:13:54,160 --> 00:13:56,100
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+141
+00:13:56,100 --> 00:13:59,500
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+142
+00:13:59,500 --> 00:13:59,520
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+143
+00:13:59,520 --> 00:13:59,640
+حياته حياته حياته حياته حياته حياته حياته حياته
+
+144
+00:13:59,640 --> 00:14:09,740
+حياته حياته
+
+145
+00:14:09,740 --> 00:14:17,410
+حرونتين جرام of the hand and wrist في مرحلة
+
+146
+00:14:17,410 --> 00:14:26,330
+الطفولة ممكن يتقيم مراكز التعقم أو مراكز العظم في
+
+147
+00:14:26,330 --> 00:14:31,530
+مرحلة الطفولة ممكن تقييم العظم من خلال أشعة أو صور
+
+148
+00:14:31,530 --> 00:14:36,880
+الأشعة رونتين جرام for the hand and wristعامة بين
+
+149
+00:14:36,880 --> 00:14:42,840
+عامين و عامين و عامين يوجد كربل بون بيرجر بين
+
+150
+00:14:42,840 --> 00:14:48,440
+اتنين الى ست سنوات يفترض انه كل سنة تتكلس عندي
+
+151
+00:14:48,440 --> 00:14:52,880
+عضمة من عضمات الكربل بون اللي موجودة احنا بنعرف
+
+152
+00:14:52,880 --> 00:14:58,260
+انه في عندي two rows of karbal bone في عندي صفين
+
+153
+00:14:58,260 --> 00:15:04,270
+منالـ Carbal bone إذن هدولة الصفين من العظم هم
+
+154
+00:15:04,270 --> 00:15:07,910
+اللي هيحددوا in adolescence and late childhood
+
+155
+00:15:07,910 --> 00:15:12,630
+evaluation of bone age is more complicated في
+
+156
+00:15:12,630 --> 00:15:17,970
+مرحلة المرافقة مرحلة ال late childhood هلاجي ان
+
+157
+00:15:17,970 --> 00:15:23,390
+عمليةالتشخيص وعملية التقييم للعمر العظمى اكتر
+
+158
+00:15:23,390 --> 00:15:28,890
+تعقيدا وفي
+
+159
+00:15:28,890 --> 00:15:37,770
+الغالب يتم النظر لعملية التقام وتحول الـ cartilage
+
+160
+00:15:37,770 --> 00:15:39,950
+والابيفسيز الى joints
+
+161
+00:15:47,860 --> 00:15:55,880
+عشان نحدد مشكلة أو عمر العضم في مرحلة التفولة
+
+162
+00:15:55,880 --> 00:16:01,500
+والتفولة المتأخرة ومرحلة الـ adolescence يستخدم
+
+163
+00:16:02,380 --> 00:16:07,140
+Atlas بيسموه grillage and bile atlas أو tenor
+
+164
+00:16:07,140 --> 00:16:11,600
+atlas طبعا هذه يستخدم في تحديد الأمر العام
+
+165
+00:16:11,600 --> 00:16:14,780
+Respiratory rate, heart rate and blood pressure
+
+166
+00:16:14,780 --> 00:16:18,440
+The following table shows the average heart rate,
+
+167
+00:16:19,220 --> 00:16:22,780
+respiratory rate and blood pressure at different
+
+168
+00:16:22,780 --> 00:16:27,250
+periods of a childطبعا هذا الجدول يوضح بعض
+
+169
+00:16:27,250 --> 00:16:33,850
+القراءات لضغط الدم والرسبيراتورية ومعدل ضربات
+
+170
+00:16:33,850 --> 00:16:41,490
+القلق عند الأطفال في مراحل متعددة هلاجي مثلا لـ
+
+171
+00:16:41,490 --> 00:16:46,570
+newborn ال heart rate 130 blood pressure 80 ل 60
+
+172
+00:16:46,570 --> 00:16:52,610
+ال respiratory rate 55 عند 6 شهور ال heart rate
+
+173
+00:16:52,610 --> 00:16:57,000
+120الـ blood pressure تمانين لستين ال respiratory
+
+174
+00:16:57,000 --> 00:17:04,200
+rate أربعين عند one year ال heart rate مية و عشرين
+
+175
+00:17:04,200 --> 00:17:07,960
+blood pressure تمانين لستين ال respiratory rate
+
+176
+00:17:07,960 --> 00:17:14,060
+خمسة و تلاتين عند أربع سنوات مية تمانين على ستين
+
+177
+00:17:14,060 --> 00:17:21,340
+عند عشر سنوات تسعينهارد ريت 100 على 65 blood
+
+178
+00:17:21,340 --> 00:17:25,440
+pressure 20 respiratory rate عند ال bio parity
+
+179
+00:17:25,440 --> 00:17:32,660
+بصير ضغط الدم مستقر 110 على 70 ال heart rate
+
+180
+00:17:32,660 --> 00:17:40,040
+تقريبا 85 وال respiratory rate يكون 20القلب بيكون
+
+181
+00:17:40,040 --> 00:17:46,760
+نوعا ما أكبر في مرحلة
+
+182
+00:17:46,760 --> 00:17:51,900
+الأطفال،
+
+183
+00:17:51,900 --> 00:17:59,490
+more rounded and horizontalالسماعة الابكسية في
+
+184
+00:17:59,490 --> 00:18:05,870
+الأطفال موجودة في الاراضي الأربعية اللاترى للنبل
+
+185
+00:18:05,870 --> 00:18:13,490
+لو جينا نسمع الاريكال بيت او الابكس بيت بدنا نحط
+
+186
+00:18:13,490 --> 00:18:21,870
+السماعة على الاراضي الأربعية جنب النبل لبرا شوية
+
+187
+00:18:23,790 --> 00:18:27,930
+رديولوجيا الـ cardiographic او الـ cardiothoracic
+
+188
+00:18:27,930 --> 00:18:36,650
+ريشو هو حوالي 0.6 مقارنة بالـ 0.5 في الاخر يعني
+
+189
+00:18:36,650 --> 00:18:44,790
+معدل او نسبة حجم القلب في الطفل بالنسبة للجسم 0.6
+
+190
+00:18:44,790 --> 00:18:54,460
+لكن ال cardiothoracic نسبة القلب بالنسبة للأو الـ
+
+191
+00:18:54,460 --> 00:19:01,280
+Forensic Space 0.6 في حين أنه مع القضال 0.5 لأن
+
+192
+00:19:01,280 --> 00:19:03,820
+نجي نطلع على بعض المشاكل
+
+193
+00:19:11,630 --> 00:19:18,710
+أول هذه المشاكل سنجد على موضوع الـ scoliosis هو
+
+194
+00:19:18,710 --> 00:19:24,010
+عملية الانحناء الجانبي للعمود الفقري
+
+195
+00:19:27,530 --> 00:19:31,570
+A curvature of the spine that can occur in
+
+196
+00:19:31,570 --> 00:19:36,110
+adolescents and young children it is a lateral
+
+197
+00:19:36,110 --> 00:19:41,630
+curvature of the spine
+
+198
+00:19:47,880 --> 00:19:51,520
+Early diagnosis and appropriate management of care
+
+199
+00:19:51,520 --> 00:19:58,540
+تشخيص السليم والسريع التشخيص المبكر لهذه العملية
+
+200
+00:19:58,540 --> 00:20:04,340
+أو لهذه الحالة بيساعد في عملية العلاج بيساعد أن
+
+201
+00:20:04,340 --> 00:20:08,880
+نقدم appropriate management و prevent the need of
+
+202
+00:20:08,880 --> 00:20:13,380
+surgery ويمنع اللجوء إلى العمليات الجراحية
+
+203
+00:20:20,400 --> 00:20:26,360
+بشكل مستقيم الان في حالة الـ scoliosis اللي يسمونه
+
+204
+00:20:26,360 --> 00:20:30,560
+باللغة العربية الجنف حلاجي انه صار في عندي انحناء
+
+205
+00:20:30,560 --> 00:20:36,020
+جانبي lateral curvature of the spine ممكن يكون
+
+206
+00:20:36,020 --> 00:20:42,680
+طبعا في منطقة الـ thoracic area من المشاكل اللي
+
+207
+00:20:42,680 --> 00:20:49,180
+ممكن نشوفها عند الأطفالحاجة بيسموها Spina Bifida
+
+208
+00:20:49,180 --> 00:20:56,360
+فتق في العمود الفقري و حبل الشوكة وهذا طبعا بيكون
+
+209
+00:20:56,360 --> 00:21:02,580
+نتيجة خلل في عملية ال development لو جينا نتطلع
+
+210
+00:21:02,580 --> 00:21:06,630
+احنا بشكل عامهنلاقي انه زي ما احنا شايفين في
+
+211
+00:21:06,630 --> 00:21:11,270
+الصورة هذه في عندي انا spinal cord ماشي في ال
+
+212
+00:21:11,270 --> 00:21:15,750
+spinal canal حوالين ال spinal cord فيه موجود ال
+
+213
+00:21:15,750 --> 00:21:23,190
+meninges الأغشية ال biomatter و ال durameter و ال
+
+214
+00:21:23,190 --> 00:21:29,490
+arachnoid matter كل هذه طبعا موجودة الآن لما يكون
+
+215
+00:21:29,490 --> 00:21:34,350
+في عندي حاجة يسموها spinal bifidaفتق في العمود
+
+216
+00:21:34,350 --> 00:21:39,770
+الفقري ممكن يكون أحد ثلاث حالات يا إما يكون Spina
+
+217
+00:21:39,770 --> 00:21:47,230
+Bifida Occulta أو يكون Spina Bifida Manifesta و
+
+218
+00:21:47,230 --> 00:21:51,650
+Spina Bifida Manifesta تنجسم إلى Meningocel أو
+
+219
+00:21:51,650 --> 00:21:56,670
+Meningomyelocelالان لو جينا نتطلع على الـ Spina
+
+220
+00:21:56,670 --> 00:22:00,910
+Bifida Occulta شو معناه كلمة Occulta؟ Occulta
+
+221
+00:22:00,910 --> 00:22:07,150
+مخفية زي ما احنا شايفين في الصورة هذه مش مبين في
+
+222
+00:22:07,150 --> 00:22:13,240
+ال skin اي مشاكلومش مبين اي بروزات لكن لو جينا
+
+223
+00:22:13,240 --> 00:22:20,040
+نتطلع هلاجى انه في المنطقة هذه في خلل في فراغ
+
+224
+00:22:20,040 --> 00:22:24,460
+موجود عندى في الفقرات العمود الفقري في
+
+225
+00:22:24,460 --> 00:22:29,980
+الـvertebral column ونتيجة وجود الفراغ هذه هلاجى
+
+226
+00:22:29,980 --> 00:22:36,080
+ان الجلد في المنطقة هذه مشدود للأسفل
+
+227
+00:22:39,090 --> 00:22:42,910
+وفي المنطقة هذه التجويف اللي موجود هتلاقي انه حاجة
+
+228
+00:22:42,910 --> 00:22:48,150
+بتنبط الشعر بيسموها hair follicle مجموعة من الشعر
+
+229
+00:22:48,150 --> 00:22:53,070
+من بواصلات الشعر بتنمو في هذه المنطقة في هذه
+
+230
+00:22:53,070 --> 00:22:57,050
+الحالة طبعا بيسموها Spina Bifida Occulta وعملية
+
+231
+00:22:57,050 --> 00:23:01,610
+علاجها سهل لأن مافي مكونات خارجها
+
+232
+00:23:04,240 --> 00:23:09,860
+من الـ vertebral column أو من الـ spine وبالتالي
+
+233
+00:23:09,860 --> 00:23:15,700
+عملية العلاج ممكن تكون سهلة وجزء من العمليات أو
+
+234
+00:23:15,700 --> 00:23:20,480
+جزء من الحلقة طبعا في الدول المتقدمة بتتم تشكيز
+
+235
+00:23:20,480 --> 00:23:25,060
+هذه المشكلة في الرحم وبتم عمل عملية جراحية في داخل
+
+236
+00:23:25,060 --> 00:23:30,400
+الرحم وإغلاق هذه الفتحة قبل الولادة من ال vertebra
+
+237
+00:23:31,370 --> 00:23:35,430
+and or the spinal cord of the fetus does not
+
+238
+00:23:35,430 --> 00:23:39,210
+develop properly it is one of the most common
+
+239
+00:23:39,210 --> 00:23:46,200
+birth defects واحدة من المشاكلالأكثر شيوعا مع
+
+240
+00:23:46,200 --> 00:23:51,520
+الأطفال occurring in two out of one thousand baby
+
+241
+00:23:51,520 --> 00:23:56,600
+من كل الف طفل في عندنا اتنين ممكن يصابوا بهذا ال
+
+242
+00:23:56,600 --> 00:24:00,280
+diagnosis او هذه الحالة while the condition is
+
+243
+00:24:00,280 --> 00:24:03,320
+permanent early treatment is urged to avoid
+
+244
+00:24:03,320 --> 00:24:07,740
+further spinal and neurological damage وكونوا انه
+
+245
+00:24:07,740 --> 00:24:15,600
+العملية او التشخيص هذاPermanent يفضل انه اكتشافه
+
+246
+00:24:15,600 --> 00:24:21,880
+مبكرا ومنى حدوثه قبل ما يسيء تماما اذا قلنا في الـ
+
+247
+00:24:21,880 --> 00:24:26,560
+Spina Bifida في عيننا نوعين رئيسيين Spina Bifida
+
+248
+00:24:26,560 --> 00:24:31,700
+Occulta و Spina Bifida Manifesta عرفنا شوهي Spina
+
+249
+00:24:31,700 --> 00:24:36,680
+Bifida Occulta ان انا نجي ل Spina Bifida Manifesta
+
+250
+00:24:37,400 --> 00:24:41,440
+كلمة Manifesta معناها ظاهرة زي ما احنا شايفين
+
+251
+00:24:41,440 --> 00:24:46,120
+بالشكل هذا ال spinal bifida manifesta بتنقسم إلى
+
+252
+00:24:46,120 --> 00:24:48,920
+قسمين في عندنا meningocel و في عندنا
+
+253
+00:24:48,920 --> 00:24:55,980
+meningomyelocele في حالة لما يكون meningocel هلاجى
+
+254
+00:24:55,980 --> 00:25:03,680
+ان ال spinal cord موجود في القناع العضمي الطبيعي
+
+255
+00:25:04,420 --> 00:25:11,580
+في حين أن الأغشية المحيطة بيه وجزء من السائل صار
+
+256
+00:25:11,580 --> 00:25:16,360
+فيه اندعاج إلى الخارج كيس خارجي زي ما احنا شايفين
+
+257
+00:25:16,360 --> 00:25:22,620
+هذا طبعا بيسموها مننجو سيل في حين أن النوع التاني
+
+258
+00:25:22,620 --> 00:25:29,500
+تاني من هذه بيسموه مننجو مايلوسيل هلاقي ان ال
+
+259
+00:25:29,500 --> 00:25:37,520
+مننجيز الأغشيةوجزء من الـ spinal cord كمان موجود
+
+260
+00:25:37,520 --> 00:25:42,540
+عشان يسموها meningomyelocyte عملية الوقاية منه
+
+261
+00:25:42,540 --> 00:25:50,260
+ممكن تتم في فترة الحمل وإعطاء الأم الحامل الحديد
+
+262
+00:25:50,260 --> 00:25:56,580
+والفولك أسد بشكل منتظم في فترة الحمل الأولى الآن
+
+263
+00:25:56,580 --> 00:26:00,320
+نجي للمشكلة التانية اللي موجودة congenital
+
+264
+00:26:00,320 --> 00:26:01,600
+developmental disorders
+
+265
+00:26:05,310 --> 00:26:10,990
+أو developmental hip dislocation إيه لها اسم قديم
+
+266
+00:26:10,990 --> 00:26:15,250
+بيسموه congenital hip dislocation CDH لكن الإسم
+
+267
+00:26:15,250 --> 00:26:17,730
+الحديث بيسموه developmental dislocation
+
+268
+00:26:17,730 --> 00:26:25,950
+developmental dislocation of the hip DDH كلنا احنا
+
+269
+00:26:25,950 --> 00:26:32,870
+بنعرف في ال anatomy of the pelvis ال pelvis بتكون
+
+270
+00:26:33,990 --> 00:26:40,990
+من two halves one half to the right one half to
+
+271
+00:26:40,990 --> 00:26:47,090
+the left جزء أيمن النصف هذا العضمة هذه بيسموها
+
+272
+00:26:47,090 --> 00:26:53,380
+coxy bone كل هذا النصف بيسموه ال coxyالاتنين مع
+
+273
+00:26:53,380 --> 00:26:58,600
+بعض بيسموهم اوس كوكسي لو جينا ناخد جانب واحد
+
+274
+00:26:58,600 --> 00:27:05,560
+الكوكسي بون او الكوكسي هلاجيه بتكون من تلت عضمات
+
+275
+00:27:05,560 --> 00:27:11,240
+أساسية الاليام زي ما احنا شايفين هذا الجزر الأساسي
+
+276
+00:27:11,240 --> 00:27:17,700
+الاسكياموفي عيننا الـ pubic area أو الـ pubic bone
+
+277
+00:27:17,700 --> 00:27:24,480
+هي التلت عضمات التلت عضمات هذه مع بعض بتلتحم و
+
+278
+00:27:24,480 --> 00:27:31,600
+بتكون تجويف بسموه ال acetabulum الحق ال acetabulum
+
+279
+00:27:31,600 --> 00:27:36,240
+ال acetabulum هذا هو اللي بدي يعمل articulation مع
+
+280
+00:27:36,240 --> 00:27:44,840
+ال head of femur مع رأس عضمة الفخدوبيسموه هذا طبعا
+
+281
+00:27:44,840 --> 00:27:49,700
+الـ hip joint كله بيسموه hip joint إذا الستابلون
+
+282
+00:27:49,700 --> 00:27:56,320
+اللي موجود مع ال head of femur في كتير من الحالات
+
+283
+00:27:56,320 --> 00:28:02,840
+نتيجة خلل معين أو نتيجة مشاكل في عملية الولادة
+
+284
+00:28:02,840 --> 00:28:10,190
+بيصير عملية dislocation بيطلع ال head of the hipمن
+
+285
+00:28:10,190 --> 00:28:13,930
+الـ Acetabulum زي ما احنا شايفين كيف الصورة هذه
+
+286
+00:28:13,930 --> 00:28:21,010
+الـ head of فيمر مش في ال Acetabulum مكانه هذه
+
+287
+00:28:21,010 --> 00:28:25,390
+الحالة بيسموها الـ
+
+288
+00:28:25,390 --> 00:28:31,110
+developmental dislocation of the head DDH وممكن ان
+
+289
+00:28:31,110 --> 00:28:34,890
+عملية ال dislocation صير before
+
+290
+00:28:36,490 --> 00:28:42,030
+birth قبل الولادة وممكن تكون during birth او
+
+291
+00:28:42,030 --> 00:28:50,730
+shortly after birth او بعد الولادة بمدة قصيرة من
+
+292
+00:28:50,730 --> 00:28:53,950
+المشاكل اللي بتكون موجودة كمان في عنا حاجة يسميها
+
+293
+00:28:53,950 --> 00:28:58,650
+congenital coaxivara congenital coaxivara شو
+
+294
+00:28:58,650 --> 00:29:04,970
+المقصود بال congenital coaxivara كلنا بنعرف ان هذه
+
+295
+00:29:04,970 --> 00:29:11,310
+عضمةالـ hip أو عظمة الفخد الـ femur زي ما احنا
+
+296
+00:29:11,310 --> 00:29:16,590
+شايفين تتكون من ال head of femur ال neck of femur
+
+297
+00:29:16,590 --> 00:29:19,630
+فى عندى ال greater trochanter فى عندنا ال lesser
+
+298
+00:29:19,630 --> 00:29:24,810
+trochanter وفى عندى الشافت of the femur و تحته
+
+299
+00:29:24,810 --> 00:29:28,990
+بتعمل articulation مع النجوم الآن زي ما احنا
+
+300
+00:29:28,990 --> 00:29:33,470
+شايفين ال neck of femur مع الشافت of femur بتكون
+
+301
+00:29:33,470 --> 00:29:43,970
+عندى زاويةالزاوية هذه طبعاً لها مقياس معين يفترض
+
+302
+00:29:43,970 --> 00:29:52,230
+انه يكون هذا القياس طبعاً عند ال male بيختلف عن ال
+
+303
+00:29:52,230 --> 00:29:58,230
+female any condition in which the neck shaft angle
+
+304
+00:29:58,230 --> 00:30:03,070
+الزاوية
+
+305
+00:30:03,070 --> 00:30:10,120
+هذهless than normal which is about one hundred
+
+306
+00:30:10,120 --> 00:30:15,020
+twenty five degrees اذا كانت أقل من مية و خمسة و
+
+307
+00:30:15,020 --> 00:30:22,600
+عشرين معناه ان هذا الحالة بيسموها ككسة فارقة اذا
+
+308
+00:30:22,600 --> 00:30:27,340
+كانت أقل من مية و خمسة و عشرين لاحظوا المية و خمسة
+
+309
+00:30:27,340 --> 00:30:30,240
+و عشرين تعتبر طبيعي من مية و عشرين لمية و خمسة و
+
+310
+00:30:30,240 --> 00:30:30,720
+تلاتين
+
+311
+00:30:33,320 --> 00:30:38,620
+الأقل من مائة و عشرين تعتبر حالة مرضية بيسموها
+
+312
+00:30:38,620 --> 00:30:44,820
+الكوكسافارة الزاوية هذه أقل و هلاج الشخص اللي عنده
+
+313
+00:30:44,820 --> 00:30:50,340
+هذا المشكلة بيمشي بمشي بيسموها ماشية البطة ماشية
+
+314
+00:30:50,340 --> 00:30:57,400
+البطة إذا كانت أكبر من مائة و خمس و تلاتين الزاوية
+
+315
+00:30:57,400 --> 00:31:00,160
+زي ما احنا شايفينه في الصورة هذه بيسموها
+
+316
+00:31:00,160 --> 00:31:01,560
+الكوكسافارة
+
+317
+00:31:04,430 --> 00:31:13,430
+الحال التاني أو عرض تاني ممكن يكون موجود مع الناس
+
+318
+00:31:13,430 --> 00:31:20,330
+اللي عندهم مشاكل في الـ bone حاجة يسموها leg calf
+
+319
+00:31:20,330 --> 00:31:27,050
+birth disease it is an osteo or it is
+
+320
+00:31:27,050 --> 00:31:31,190
+osteochondritis of the epiphysis of the femoral
+
+321
+00:31:31,190 --> 00:31:37,500
+headسأجد أن الـ Leg Calve Herpes صار فيه الفيمورال
+
+322
+00:31:37,500 --> 00:31:44,180
+هيد وهو طبعا الابيفسيز هذا صار فيه نوع من ال
+
+323
+00:31:44,180 --> 00:31:51,320
+inflammation أوستيوكندريتس نتيجة الاستيوكندريتس
+
+324
+00:31:51,320 --> 00:31:56,320
+صار فيه عندي ونتيجة ال wet bearing صار فيه عندي
+
+325
+00:31:56,320 --> 00:32:04,350
+destruction لل growth center اللي موجودعاملية نمو
+
+326
+00:32:04,350 --> 00:32:09,370
+في هذا الطرف وفي هذه الحالة سيصبح عند الطفل مشكلة
+
+327
+00:32:09,370 --> 00:32:14,290
+انه لا يكبر و لا يصبح لديه عملية نمو في هذا الطرف
+
+328
+00:32:14,290 --> 00:32:22,230
+الحل لهم انهم دايما بيخلوا الطفل بركبه جهاز يمنع
+
+329
+00:32:22,230 --> 00:32:28,050
+عملية التحميل على الطرف في أثناء الوقوف والمشي
+
+330
+00:32:28,050 --> 00:32:34,000
+ويفضل لهم دايماالراحة لحد ما تتعالج مشكلة الـ
+
+331
+00:32:34,000 --> 00:32:38,740
+Osteochondritis slipped capital femoral epiphysis
+
+332
+00:32:38,740 --> 00:32:44,420
+وهذا طبعا حلاجي ان في بعض الحلات زي ما احنا شايفين
+
+333
+00:32:44,420 --> 00:32:47,960
+في الصورة اللي موجودة هي ال normal head of femur
+
+334
+00:32:47,960 --> 00:32:56,280
+هي ال normal place لها وهنا صار في عندي slipping
+
+335
+00:32:56,280 --> 00:33:04,610
+صار ازاحةللـ head of femur وهذه الحالات تكون في
+
+336
+00:33:04,610 --> 00:33:08,690
+الغالب ناتجة عن developmental hip abnormalities
+
+337
+00:33:08,690 --> 00:33:12,390
+ممكن يكون فيها fractures أو bosses traumatic
+
+338
+00:33:12,390 --> 00:33:17,630
+abnormalities ال adolescent hip pain ممكن يكون
+
+339
+00:33:17,630 --> 00:33:24,970
+واحد من الأعراض الموجودة ممكن تكون سبب من أسبابها
+
+340
+00:33:24,970 --> 00:33:30,440
+لل tumorsالـ Malignancies الأورام اللي بتكون
+
+341
+00:33:30,440 --> 00:33:37,220
+موجودة في المنطقة من الأعراض أو من الـ syndromes
+
+342
+00:33:37,220 --> 00:33:40,220
+اللي ممكن تكون موجودة و الأمراض اللي بتكون موجودة
+
+343
+00:33:40,220 --> 00:33:44,840
+بتأثر على عملية الـ development Neomuscular
+
+344
+00:33:44,840 --> 00:33:50,500
+diseases في عندنا الـ cerebral palsy الشلة الدماني
+
+345
+00:33:50,500 --> 00:33:54,480
+كلمة cerebral palsy it's a term used
+
+346
+00:33:59,510 --> 00:34:03,850
+body movement and muscle coordination هي مصطلح
+
+347
+00:34:03,850 --> 00:34:11,990
+بيستخدم لتوصيف مجموعة من الأعراض اللي بتأثر على
+
+348
+00:34:11,990 --> 00:34:17,390
+عملية ال coordination وعملية ال movement في ال
+
+349
+00:34:17,390 --> 00:34:23,970
+upper و lower limbs ممكن تأثر علىالـ Cognitive
+
+350
+00:34:23,970 --> 00:34:28,750
+Function كمان It is caused by damage to one or
+
+351
+00:34:28,750 --> 00:34:33,590
+more specific areas of the brain ممكن يكون السبب
+
+352
+00:34:33,590 --> 00:34:38,850
+تبعها إصابة ممتقة أو أكتر من الـ brain usually
+
+353
+00:34:38,850 --> 00:34:43,110
+occurring during fatal development or infancy في
+
+354
+00:34:43,110 --> 00:34:50,680
+الغالب تكون في مرحلة الحمل نتيجة تعرض الأم لـعدة
+
+355
+00:34:50,680 --> 00:34:56,500
+عوامل ممكن تكون سبب في مشاكل development of the
+
+356
+00:34:56,500 --> 00:35:04,160
+fetus مشاكل ممكن تؤدي إلى تشوهات وممكن تؤدي إلى
+
+357
+00:35:04,160 --> 00:35:10,420
+خلل في normal development of the brain of the
+
+358
+00:35:10,420 --> 00:35:17,340
+child it also can occur before during or shortly
+
+359
+00:35:17,340 --> 00:35:18,740
+following birth
+
+360
+00:35:22,520 --> 00:35:28,580
+وهذا قلنا نتيجة ان الأم تتعرض لتراتوجينز تتعرض
+
+361
+00:35:28,580 --> 00:35:33,780
+لعوامل ممكن عوامل كيميائية ممكن أدوية ممكن تلميثات
+
+362
+00:35:33,780 --> 00:35:38,140
+كلها ممكن تأثر على عملية النمو زي ممكن أم تتعرض
+
+363
+00:35:38,140 --> 00:35:43,980
+لأشعة في فترة الحمل ممكن يكون سبب من أسباب الـ
+
+364
+00:35:43,980 --> 00:35:49,060
+cerebral palsy هذا في مرحلة الحمل during birth
+
+365
+00:35:49,060 --> 00:35:50,220
+أثناء الولادة
+
+366
+00:35:54,560 --> 00:35:59,360
+أو نتيجة عملية الولادة الـ forceps delivery صار
+
+367
+00:35:59,360 --> 00:36:04,480
+فيه damage أو بعد الولادة لمدة تقريبا سنتين اي
+
+368
+00:36:04,480 --> 00:36:09,680
+traumatic brain injury او اي إصابة في الدماغ يشخص
+
+369
+00:36:09,680 --> 00:36:15,840
+الطفل على انه cerebral palsy cerebral palsy is
+
+370
+00:36:15,840 --> 00:36:18,460
+neither progressive nor communicable
+
+371
+00:36:24,130 --> 00:36:30,690
+هو مش مرض معدي ومش مرض متطور يعني خلّينا نقول أنه
+
+372
+00:36:30,690 --> 00:36:37,270
+خلاص صارت المشكلة بتظلها زي ما هي لكن ممكن يصير
+
+373
+00:36:37,270 --> 00:36:41,310
+تبعيات نتيجة قلة الاهتمام قلة العلاج الطبيعي اللي
+
+374
+00:36:41,310 --> 00:36:46,010
+بيكون موجود ممكن تتضاعف أو يصير مضاعفات لهذه
+
+375
+00:36:46,010 --> 00:36:51,800
+الحالة لكن وضع الدماغ بيظل زي ما هوit's important
+
+376
+00:36:51,800 --> 00:36:54,980
+to know that cerebral palsy is not a disease، it
+
+377
+00:36:54,980 --> 00:36:59,720
+is not contagious and does not get worse، يعني مش
+
+378
+00:36:59,720 --> 00:37:06,500
+مرض معدي، مابصيرش تغير في ال brain، يعني مابصيرش
+
+379
+00:37:06,500 --> 00:37:11,120
+زيادة في نسبة الخلايا المدمرة في ال brain، لأ بتظل
+
+380
+00:37:11,120 --> 00:37:21,860
+تابعةالأطفال اللي بيولد بـ Cerebral Palsy هيدلوا
+
+381
+00:37:21,860 --> 00:37:27,980
+طول عمره مع Cerebral Palsy Cerebral Palsy هو شخص
+
+382
+00:37:27,980 --> 00:37:29,900
+مخصص من غلطة
+
+383
+00:37:32,140 --> 00:37:37,140
+control motor function particularly muscle control
+
+384
+00:37:37,140 --> 00:37:41,420
+and coordination الأشخاص اللي عندهم مشاكل السيربرا
+
+385
+00:37:41,420 --> 00:37:45,960
+البنسي هيكون في عندهم مشاكل حركية motor هيكون في
+
+386
+00:37:45,960 --> 00:37:50,460
+عندهم functional problems هيكون على سبيل المثال
+
+387
+00:37:50,460 --> 00:37:53,740
+disturbance في ال gate في ال mobility في ال
+
+388
+00:37:53,740 --> 00:37:58,230
+balance هيكون في عندهم involuntary movementطبعا
+
+389
+00:37:58,230 --> 00:38:00,950
+الموضوع السليبرال بالسي ان شاء الله رب العالمين
+
+390
+00:38:00,950 --> 00:38:05,490
+هتدرسوه بشيء من التفصيل خلال السنوات القادمة مع
+
+391
+00:38:05,490 --> 00:38:09,690
+دراسة كل الأطفال من المشاكل اللي بتكون موجودة foot
+
+392
+00:38:09,690 --> 00:38:14,490
+ankle disorders وهات طبعا من المشاكل اللي بنشوفها
+
+393
+00:38:14,490 --> 00:38:18,910
+في مراحل ولادة ممكن الطفل ينولد حاجة يسموها club
+
+394
+00:38:18,910 --> 00:38:25,570
+foot زي ما احنا شايفينكيف ال club food ال club
+
+395
+00:38:25,570 --> 00:38:32,950
+food هي عبارة عن تلبس equinovirus التشوق
+
+396
+00:38:32,950 --> 00:38:40,030
+اللي موجود هنا طبعا هو ال club food أو ممكن تكون
+
+397
+00:38:40,030 --> 00:38:46,410
+تلبس calcinevalgas صار طلعت بدل ما هي كفة القدم
+
+398
+00:38:46,410 --> 00:38:49,470
+داخل
+
+399
+00:38:49,470 --> 00:38:55,200
+لجواممكن تكون خلعة لبرا تالي بس كالكينيو فالجاس
+
+400
+00:38:55,200 --> 00:39:00,120
+طبعا احنا بنحكي عن تالي بس ال foot و calcaneus
+
+401
+00:39:00,120 --> 00:39:06,250
+اللي هي ال bones of the footممكن يكون في عنا
+
+402
+00:39:06,250 --> 00:39:11,110
+بيسبلانس أو الـ flat foot زي ما احنا شايفين اللي
+
+403
+00:39:11,110 --> 00:39:17,530
+هو إن عدام الارش مش موجود التقوس اللي موجود في
+
+404
+00:39:17,530 --> 00:39:22,210
+القدم في الوضع الطبيعي، هذه بيسموها بيسبلانس أو
+
+405
+00:39:22,210 --> 00:39:28,010
+flat footمن المشاكل اللي بتكون موجودة كمان الـ
+
+406
+00:39:28,010 --> 00:39:31,930
+down syndrome ال down syndrome طبعا هو عبارة عن
+
+407
+00:39:31,930 --> 00:39:41,010
+mental retardation و degree of various ال down
+
+408
+00:39:41,010 --> 00:39:48,050
+syndrome هو الخلل جيني ممكن يكون خلل في الجيناتIt
+
+409
+00:39:48,050 --> 00:39:52,410
+is a chromosomal disorder caused by presence of
+
+410
+00:39:52,410 --> 00:39:57,770
+all or part of an extra 21st chromosome، خلل في
+
+411
+00:39:57,770 --> 00:40:04,830
+الـChromosome رقم 21 The
+
+412
+00:40:04,830 --> 00:40:07,970
+condition is characterized by combination of major
+
+413
+00:40:07,970 --> 00:40:10,190
+and minor differences in structure
+
+414
+00:40:19,430 --> 00:40:25,210
+أكتر ما يميزهم شكل الوجه وكيف ممكن تكون طبعا
+
+415
+00:40:25,210 --> 00:40:28,370
+بالإضافة
+
+416
+00:40:28,370 --> 00:40:34,070
+لأن احنا بنحكي على بعض
+
+417
+00:40:34,070 --> 00:40:37,050
+المشاكل اللي ممكن تكون موجودة في عملية ال
+
+418
+00:40:37,050 --> 00:40:45,430
+developmentطبعاً لعملية الفحص ونتعرف
+
+419
+00:40:45,430 --> 00:40:53,050
+على الطفل في فترة الحمل ممكن من خلال سحب عينة من
+
+420
+00:40:53,050 --> 00:41:00,090
+ال fluid amniotic fluid اللي حوالين الجنين طبعا
+
+421
+00:41:00,090 --> 00:41:02,590
+هذه الحالة بسموها amniocentesis
+
+422
+00:41:06,350 --> 00:41:12,410
+وهذا طبعا ممكن ينعمل فحص during birth during
+
+423
+00:41:12,410 --> 00:41:18,570
+pregnancy او at birth لو جينا نطلع على ال down
+
+424
+00:41:18,570 --> 00:41:24,730
+syndrome هلاجي ان في عندهم بعض ال features اللي
+
+425
+00:41:24,730 --> 00:41:28,510
+بتكون موجودة small number have severe to profound
+
+426
+00:41:28,510 --> 00:41:34,020
+mental disabilityجزء منهم ممكن يكون في عنده إعاقة
+
+427
+00:41:34,020 --> 00:41:37,620
+عقلية شديدة The incidence of Down syndrome is
+
+428
+00:41:37,620 --> 00:41:44,500
+estimated 1 لكل 800 أو ألف بيرت 1 من كل 800 إلى
+
+429
+00:41:44,500 --> 00:41:56,280
+1000 ولادة ممكن ينولد Down syndrome من
+
+430
+00:41:56,280 --> 00:42:01,980
+الأعراض اللي بيكون موجودة عندهم طبعاالـ features
+
+431
+00:42:01,980 --> 00:42:05,340
+Down syndrome may also appear in people with a
+
+432
+00:42:05,340 --> 00:42:09,480
+standard set of chromosomes including microgenia
+
+433
+00:42:09,480 --> 00:42:16,480
+and abnormally small chin and unusually round face
+
+434
+00:42:16,480 --> 00:42:22,100
+protruding or oversized tongue and element shape
+
+435
+00:42:22,100 --> 00:42:30,520
+of the eyes هلاجي انه اللسان حجم كبير او بارزممكن
+
+436
+00:42:30,520 --> 00:42:35,100
+يكون طبعا العينين
+
+437
+00:42:35,100 --> 00:42:45,380
+حاجة بيسموها الـ element shape شكل اللوزة وفي
+
+438
+00:42:45,380 --> 00:42:50,960
+حاجة بيسموها الـ epicanthic fold of the eyelid شرط
+
+439
+00:42:50,960 --> 00:42:57,680
+العين بتكون عينهم مشروطة هذه هي تقريبا أهم الأعراض
+
+440
+00:42:57,680 --> 00:43:02,570
+اللي بتكون موجودةمن ضمن المشاكل اللي بتكون موجودة
+
+441
+00:43:02,570 --> 00:43:06,130
+معهم و يديروا بالهم مع هؤلاء الناس طبعا higher
+
+442
+00:43:06,130 --> 00:43:10,730
+risk of congenital heart defects gastroesophageal
+
+443
+00:43:10,730 --> 00:43:14,650
+reflux disease recurrent hair infections
+
+444
+00:43:14,650 --> 00:43:21,890
+obstructive sleep apnea thyroid dysfunction أهم
+
+445
+00:43:21,890 --> 00:43:26,430
+الأعراض باختصار الـ Oriental eye tongue protrusion
+
+446
+00:43:27,690 --> 00:43:34,070
+العين طبعا كيف شكلها بروز اللسان short arms and
+
+447
+00:43:34,070 --> 00:43:40,910
+legs simian crease طبعا إيديهم فيها fold واحد
+
+448
+00:43:40,910 --> 00:43:46,250
+الخطوط اللي موجودة في الإيد internal organs
+
+449
+00:43:46,250 --> 00:43:50,190
+congenital heart defect في الغالب في ممكن يكون
+
+450
+00:43:50,190 --> 00:43:51,530
+فيهم مشاكل في القلب
+
+451
+00:43:56,180 --> 00:44:01,960
+ممكن يكون في عندهم stenosis أو narrowing في blood
+
+452
+00:44:01,960 --> 00:44:09,060
+vessels هذه تقريبا أهم الأعراض اللي بتكون موجودة
+
+453
+00:44:09,060 --> 00:44:17,960
+عند ال down syndrome باق ال syndromes مش كتير مهم
+
+454
+00:44:17,960 --> 00:44:18,700
+لنا
+
diff --git a/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM_raw.json b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4ff50a1eb8a8d6612f8459288b9785a973cfdedb
--- /dev/null
+++ b/PL9fwy3NUQKwYNsXbJilO-1J-jzYLneHBY/xhPLNbIwUqM_raw.json
@@ -0,0 +1 @@
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"start": 314.72, "end": 316.58, "text": "كل هذه تبدأ تتكون", "tokens": [28820, 29538, 6055, 44510, 10721, 6055, 2655, 30544], "avg_logprob": -0.3133680555555556, "compression_ratio": 0.7948717948717948, "no_speech_prob": 0.0, "words": [{"start": 314.72, "end": 315.02, "word": "كل", "probability": 0.49609375}, {"start": 315.02, "end": 315.28, "word": " هذه", "probability": 0.6123046875}, {"start": 315.28, "end": 315.92, "word": " تبدأ", "probability": 0.7438151041666666}, {"start": 315.92, "end": 316.58, "word": " تتكون", "probability": 0.8701171875}], "temperature": 1.0}, {"id": 15, "seek": 34770, "start": 318.04, "end": 347.7, "text": "مجرد ما يكتمل نمو السن بيبدأ يشق طريقه من خلال اللثة و يطلع في تجويف الفم روت فورميشن و سيمينتوجينيس تستمر حتى يتم تطبيق التوث و تعمل تعمل تعمل تعمل تعمل تعمل تعمل تعمل", "tokens": [2304, 7435, 2288, 3215, 19446, 7251, 4117, 39237, 1211, 8717, 2304, 2407, 21136, 1863, 4724, 1829, 44510, 10721, 7251, 8592, 4587, 23032, 16572, 4587, 3224, 9154, 16490, 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"end": 511.52, "word": " بنعرف", "probability": 0.7640787760416666}, {"start": 511.52, "end": 511.76, "word": " ان", "probability": 0.419921875}, {"start": 511.76, "end": 513.34, "word": " عملية", "probability": 0.8876953125}, {"start": 513.34, "end": 514.06, "word": " التسنين", "probability": 0.8736572265625}], "temperature": 1.0}, {"id": 22, "seek": 53116, "start": 514.58, "end": 531.16, "text": "بتبدأ في الـ mandibular jaw في ال lower part of the jaw في الفتق السفلي قبل ما يبدأ تطلع الأسنان في الفتق العلوي حوالي الفاصل ما بينهم من شهر إلى شهرين تقريبا", "tokens": [3555, 2655, 44510, 10721, 8978, 2423, 39184, 7411, 897, 1040, 18162, 8978, 2423, 3126, 644, 295, 264, 18162, 8978, 27188, 2655, 4587, 21136, 5172, 20292, 12174, 36150, 19446, 7251, 44510, 10721, 6055, 9566, 1211, 3615, 16247, 3794, 1863, 7649, 8978, 27188, 2655, 4587, 18863, 1211, 45865, 11331, 2407, 6027, 1829, 27188, 33546, 1211, 19446, 49374, 16095, 9154, 13412, 3224, 2288, 30731, 13412, 3224, 2288, 9957, 6055, 4587, 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"word": " the", "probability": 0.8251953125}, {"start": 519.5, "end": 519.8, "word": " jaw", "probability": 0.953125}, {"start": 519.8, "end": 520.54, "word": " في", "probability": 0.83349609375}, {"start": 520.54, "end": 521.34, "word": " الفتق", "probability": 0.7416178385416666}, {"start": 521.34, "end": 522.04, "word": " السفلي", "probability": 0.955078125}, {"start": 522.04, "end": 522.58, "word": " قبل", "probability": 0.79052734375}, {"start": 522.58, "end": 523.14, "word": " ما", "probability": 0.89013671875}, {"start": 523.14, "end": 523.64, "word": " يبدأ", "probability": 0.7447916666666666}, {"start": 523.64, "end": 524.04, "word": " تطلع", "probability": 0.871826171875}, {"start": 524.04, "end": 524.64, "word": " الأسنان", "probability": 0.9764404296875}, {"start": 524.64, "end": 524.84, "word": " في", "probability": 0.91015625}, {"start": 524.84, "end": 525.52, "word": " الفتق", "probability": 0.9903971354166666}, {"start": 525.52, "end": 526.2, "word": " العلوي", "probability": 0.9763997395833334}, {"start": 526.2, "end": 527.14, "word": " حوالي", "probability": 0.8427734375}, {"start": 527.14, "end": 528.56, "word": " الفاصل", "probability": 0.86572265625}, {"start": 528.56, "end": 528.72, "word": " ما", "probability": 0.875}, {"start": 528.72, "end": 529.0, "word": " بينهم", "probability": 0.8603515625}, {"start": 529.0, "end": 529.28, "word": " من", "probability": 0.86962890625}, {"start": 529.28, "end": 529.7, "word": " شهر", "probability": 0.9933268229166666}, {"start": 529.7, "end": 529.94, "word": " إلى", "probability": 0.78076171875}, {"start": 529.94, "end": 530.5, "word": " شهرين", "probability": 0.994140625}, {"start": 530.5, "end": 531.16, "word": " تقريبا", "probability": 0.9884765625}], "temperature": 1.0}, {"id": 23, "seek": 54160, "start": 532.74, "end": 541.6, "text": "عند الغالبية لكن مش بالضرورة تكون عند الجميع بنفس القدر ممكن يكون في بعض الشواذل هذه القاعدة", "tokens": [3615, 41260, 6024, 118, 6027, 3555, 10632, 44381, 37893, 20666, 11242, 2288, 13063, 3660, 6055, 30544, 43242, 25724, 2304, 40228, 44945, 36178, 25062, 3215, 2288, 3714, 43020, 7251, 30544, 8978, 45030, 11242, 25124, 2407, 45636, 1211, 29538, 25062, 995, 22488, 3660], "avg_logprob": -0.2446056469565346, "compression_ratio": 1.5, "no_speech_prob": 0.0168609619140625, "words": [{"start": 532.74, "end": 533.12, "word": "عند", "probability": 0.522216796875}, {"start": 533.12, "end": 533.88, "word": " الغالبية", "probability": 0.95966796875}, {"start": 533.88, "end": 534.34, "word": " لكن", "probability": 0.63623046875}, {"start": 534.34, "end": 534.9, "word": " مش", "probability": 0.50830078125}, {"start": 534.9, "end": 535.66, "word": " بالضرورة", "probability": 0.90537109375}, {"start": 535.66, "end": 536.14, "word": " تكون", "probability": 0.932373046875}, {"start": 536.14, "end": 536.52, "word": " عند", "probability": 0.9521484375}, {"start": 536.52, "end": 537.64, "word": " الجميع", "probability": 0.99072265625}, {"start": 537.64, "end": 538.14, "word": " بنفس", "probability": 0.98291015625}, {"start": 538.14, "end": 538.78, "word": " القدر", "probability": 0.9855143229166666}, {"start": 538.78, "end": 539.12, "word": " ممكن", "probability": 0.8798828125}, {"start": 539.12, "end": 539.42, "word": " يكون", "probability": 0.959716796875}, {"start": 539.42, "end": 539.6, "word": " في", "probability": 0.80078125}, {"start": 539.6, "end": 540.12, "word": " بعض", "probability": 0.9765625}, {"start": 540.12, "end": 540.78, "word": " الشواذل", "probability": 0.71441650390625}, {"start": 540.78, "end": 541.0, "word": " هذه", "probability": 0.54443359375}, {"start": 541.0, "end": 541.6, "word": " القاعدة", "probability": 0.825439453125}], "temperature": 1.0}, {"id": 24, "seek": 59202, "start": 562.8, "end": 592.02, "text": "في الـ mandibular jaw القواطع الجانبية حيث يظهرون من 7 إلى 9 أشهر في الـ maxillary jaw الفك العلوي من 8 إلى 11 شهر باقي الأسنان تقريبا نفس الشيء و نفس المدة إذا الإختلاف في الـ central incisors و ال lateral incisors الـ permanent teeth", "tokens": [41185, 2423, 39184, 7411, 897, 1040, 18162, 25062, 2407, 41193, 3615, 25724, 7649, 3555, 10632, 11331, 1829, 12984, 7251, 19913, 3224, 2288, 11536, 9154, 1614, 30731, 1722, 5551, 8592, 3224, 2288, 8978, 2423, 39184, 11469, 46367, 18162, 27188, 4117, 18863, 1211, 45865, 9154, 1649, 30731, 2975, 13412, 3224, 2288, 4724, 995, 38436, 16247, 3794, 1863, 7649, 6055, 4587, 16572, 3555, 995, 8717, 36178, 25124, 1829, 38207, 4032, 8717, 36178, 9673, 41891, 11933, 15730, 33688, 46456, 15040, 5172, 8978, 2423, 39184, 5777, 834, 271, 830, 4032, 2423, 25128, 834, 271, 830, 2423, 39184, 10996, 7798], "avg_logprob": -0.2373355247472462, "compression_ratio": 1.5855855855855856, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 562.8, "end": 563.06, "word": "في", "probability": 0.2427978515625}, {"start": 563.06, "end": 563.24, "word": " الـ", "probability": 0.624267578125}, {"start": 563.24, "end": 563.84, "word": " mandibular", "probability": 0.7752278645833334}, {"start": 563.84, "end": 564.22, "word": " jaw", "probability": 0.947265625}, {"start": 564.22, "end": 566.08, "word": " القواطع", "probability": 0.91015625}, {"start": 566.08, "end": 566.9, "word": " الجانبية", "probability": 0.9757080078125}, {"start": 566.9, "end": 567.54, "word": " حيث", "probability": 0.738037109375}, {"start": 567.54, "end": 568.92, "word": " يظهرون", "probability": 0.73994140625}, {"start": 568.92, "end": 569.14, "word": " من", "probability": 0.78271484375}, {"start": 569.14, "end": 569.74, "word": " 7", "probability": 0.445068359375}, {"start": 569.74, "end": 570.16, "word": " إلى", "probability": 0.84375}, {"start": 570.16, "end": 570.66, "word": " 9", "probability": 0.99169921875}, {"start": 570.66, "end": 571.66, "word": " أشهر", "probability": 0.9853515625}, {"start": 571.66, "end": 573.24, "word": " في", "probability": 0.76953125}, {"start": 573.24, "end": 573.5, "word": " الـ", "probability": 0.534912109375}, {"start": 573.5, "end": 574.02, "word": " maxillary", "probability": 0.834716796875}, {"start": 574.02, "end": 574.44, "word": " jaw", "probability": 0.953125}, {"start": 574.44, "end": 575.32, "word": " الفك", "probability": 0.9306640625}, {"start": 575.32, "end": 575.88, "word": " العلوي", "probability": 0.953125}, {"start": 575.88, "end": 576.26, "word": " من", "probability": 0.95556640625}, {"start": 576.26, "end": 576.66, "word": " 8", "probability": 0.96142578125}, {"start": 576.66, "end": 576.92, "word": " إلى", "probability": 0.9775390625}, {"start": 576.92, "end": 577.32, "word": " 11", "probability": 0.98388671875}, {"start": 577.32, "end": 577.88, "word": " شهر", "probability": 0.9759114583333334}, {"start": 577.88, "end": 578.96, "word": " باقي", "probability": 0.765625}, {"start": 578.96, "end": 579.46, "word": " الأسنان", "probability": 0.9561767578125}, {"start": 579.46, "end": 580.4, "word": " تقريبا", "probability": 0.9271484375}, {"start": 580.4, "end": 580.9, "word": " نفس", "probability": 0.957275390625}, {"start": 580.9, "end": 581.76, "word": " الشيء", "probability": 0.97509765625}, {"start": 581.76, "end": 581.92, "word": " و", "probability": 0.900390625}, {"start": 581.92, "end": 582.2, "word": " نفس", "probability": 0.70703125}, {"start": 582.2, "end": 582.76, "word": " المدة", "probability": 0.640380859375}, {"start": 582.76, "end": 582.96, "word": " إذا", "probability": 0.5537109375}, {"start": 582.96, "end": 583.64, "word": " الإختلاف", "probability": 0.880126953125}, {"start": 583.64, "end": 584.38, "word": " في", "probability": 0.40966796875}, {"start": 584.38, "end": 585.38, "word": " الـ", "probability": 0.683349609375}, {"start": 585.38, "end": 585.9, "word": " central", "probability": 0.6904296875}, {"start": 585.9, "end": 586.74, "word": " incisors", "probability": 0.908203125}, {"start": 586.74, "end": 587.08, "word": " و", "probability": 0.7861328125}, {"start": 587.08, "end": 587.18, "word": " ال", "probability": 0.51025390625}, {"start": 587.18, "end": 587.54, "word": " lateral", "probability": 0.431396484375}, {"start": 587.54, "end": 588.66, "word": " incisors", "probability": 0.9723307291666666}, {"start": 588.66, "end": 591.08, "word": " الـ", "probability": 0.745849609375}, {"start": 591.08, "end": 591.4, "word": " permanent", "probability": 0.424072265625}, {"start": 591.4, "end": 592.02, "word": " teeth", "probability": 0.900390625}], "temperature": 1.0}, {"id": 25, "seek": 61910, "start": 593.32, "end": 619.1, "text": "أو الـ secondary teeth هلاجي انه الـ central في ال permanent teeth هلاجي انه ال central incisors بيبدأ عملية التبديل تبعها بشكل مختلف عن عملية ظهور ال primary هلاجي ان ال upper jaw او ال maxillary jaw تظهر في الأسنان عند", "tokens": [10721, 2407, 2423, 39184, 11396, 7798, 8032, 15040, 7435, 1829, 16472, 3224, 2423, 39184, 5777, 8978, 2423, 10996, 7798, 8032, 15040, 7435, 1829, 16472, 3224, 2423, 5777, 834, 271, 830, 4724, 1829, 44510, 10721, 6225, 42213, 10632, 16712, 44510, 26895, 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596.48, "end": 596.88, "word": " central", "probability": 0.701171875}, {"start": 596.88, "end": 597.38, "word": " في", "probability": 0.2841796875}, {"start": 597.38, "end": 597.5, "word": " ال", "probability": 0.95947265625}, {"start": 597.5, "end": 597.84, "word": " permanent", "probability": 0.7119140625}, {"start": 597.84, "end": 598.26, "word": " teeth", "probability": 0.90966796875}, {"start": 598.26, "end": 598.74, "word": " هلاجي", "probability": 0.9228515625}, {"start": 598.74, "end": 599.12, "word": " انه", "probability": 0.864501953125}, {"start": 599.12, "end": 600.14, "word": " ال", "probability": 0.96826171875}, {"start": 600.14, "end": 600.6, "word": " central", "probability": 0.3505859375}, {"start": 600.6, "end": 601.54, "word": " incisors", "probability": 0.9261067708333334}, {"start": 601.54, "end": 602.2, "word": " بيبدأ", "probability": 0.8333740234375}, {"start": 602.2, "end": 602.62, "word": " عملية", "probability": 0.9853515625}, {"start": 602.62, "end": 603.22, "word": " التبديل", "probability": 0.8181966145833334}, {"start": 603.22, "end": 603.84, "word": " تبعها", "probability": 0.83428955078125}, {"start": 603.84, "end": 604.62, "word": " بشكل", "probability": 0.9762369791666666}, {"start": 604.62, "end": 605.84, "word": " مختلف", "probability": 0.9921875}, {"start": 605.84, "end": 606.32, "word": " عن", "probability": 0.98291015625}, {"start": 606.32, "end": 607.0, "word": " عملية", "probability": 0.9781901041666666}, {"start": 607.0, "end": 607.5, "word": " ظهور", "probability": 0.896240234375}, {"start": 607.5, "end": 607.94, "word": " ال", "probability": 0.94091796875}, {"start": 607.94, "end": 608.5, "word": " primary", "probability": 0.87353515625}, {"start": 608.5, "end": 610.8, "word": " هلاجي", "probability": 0.9766845703125}, {"start": 610.8, "end": 611.02, "word": " ان", "probability": 0.7255859375}, {"start": 611.02, "end": 611.84, "word": " ال", "probability": 0.69677734375}, {"start": 611.84, "end": 612.24, "word": " upper", "probability": 0.80078125}, {"start": 612.24, "end": 612.6, "word": " jaw", "probability": 0.96142578125}, {"start": 612.6, "end": 612.9, "word": " او", "probability": 0.822998046875}, {"start": 612.9, "end": 613.04, "word": " ال", "probability": 0.80029296875}, {"start": 613.04, "end": 613.56, "word": " maxillary", "probability": 0.732177734375}, {"start": 613.56, "end": 613.98, "word": " jaw", "probability": 0.93359375}, {"start": 613.98, "end": 614.92, "word": " تظهر", "probability": 0.9949951171875}, {"start": 614.92, "end": 615.36, "word": " في", "probability": 0.96484375}, {"start": 615.36, "end": 618.24, "word": " الأسنان", "probability": 0.9334716796875}, {"start": 618.24, "end": 619.1, "word": " عند", "probability": 0.822265625}], "temperature": 1.0}, {"id": 26, "seek": 64855, "start": 619.72, "end": 648.56, "text": "أو بتبدأ تتساقط الأسنان متبدل في ال upper jaw من 6 إلى 7 وفي ال lower jaw من 7 إلى 8 سنوات ال lateral incisors من 7 إلى 8 في ال upper jaw 8 إلى 9 في ال 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"end": 903.81, "word": " العظم", "probability": 0.92138671875}, {"start": 903.81, "end": 904.27, "word": " هم", "probability": 0.773193359375}, {"start": 904.27, "end": 904.51, "word": " اللي", "probability": 0.98388671875}, {"start": 904.51, "end": 905.45, "word": " هيحددوا", "probability": 0.802490234375}, {"start": 905.45, "end": 905.65, "word": " in", "probability": 0.305419921875}, {"start": 905.65, "end": 906.53, "word": " adolescence", "probability": 0.850830078125}, {"start": 906.53, "end": 906.99, "word": " and", "probability": 0.94091796875}, {"start": 906.99, "end": 907.27, "word": " late", "probability": 0.7998046875}, {"start": 907.27, "end": 907.91, "word": " childhood", "probability": 0.9599609375}, {"start": 907.91, "end": 909.25, "word": " evaluation", "probability": 0.8486328125}, {"start": 909.25, "end": 909.87, "word": " of", "probability": 0.9580078125}, {"start": 909.87, "end": 910.21, "word": " bone", "probability": 0.78564453125}, {"start": 910.21, "end": 910.61, "word": " age", "probability": 0.9072265625}, {"start": 910.61, "end": 910.89, "word": " is", "probability": 0.93310546875}, {"start": 910.89, "end": 911.29, "word": " more", "probability": 0.9423828125}, {"start": 911.29, "end": 912.15, "word": " complicated", "probability": 0.93310546875}, {"start": 912.15, "end": 912.63, "word": " في", "probability": 0.82763671875}, {"start": 912.63, "end": 913.23, "word": " مرحلة", "probability": 0.98876953125}, {"start": 913.23, "end": 914.43, "word": " المرافقة", "probability": 0.9644775390625}, {"start": 914.43, "end": 915.59, "word": " مرحلة", "probability": 0.941650390625}, {"start": 915.59, "end": 915.75, "word": " ال", "probability": 0.55224609375}, {"start": 915.75, "end": 915.87, "word": " late", "probability": 0.35888671875}, {"start": 915.87, "end": 917.23, "word": " childhood", "probability": 0.97900390625}, {"start": 917.23, "end": 917.83, "word": " هلاجي", "probability": 0.697509765625}, {"start": 917.83, "end": 917.97, "word": " ان", "probability": 0.39794921875}, {"start": 917.97, "end": 918.51, "word": " عملية", "probability": 0.7332356770833334}], "temperature": 1.0}, {"id": 38, "seek": 93995, "start": 919.45, "end": 939.95, "text": "التشخيص وعملية التقييم للعمر العظمى اكتر تعقيدا وفي الغالب يتم النظر لعملية التقام وتحول الـ cartilage والابيفسيز الى joints", "tokens": [6027, 2655, 8592, 9778, 1829, 9381, 4032, 25957, 1211, 10632, 16712, 38436, 32640, 24976, 25957, 2288, 18863, 19913, 2304, 7578, 1975, 4117, 2655, 2288, 37279, 4587, 25708, 995, 4032, 41185, 6024, 118, 6027, 3555, 7251, 39237, 28239, 19913, 2288, 5296, 25957, 1211, 10632, 16712, 4587, 10943, 34683, 5016, 12610, 2423, 39184, 5467, 48066, 16070, 16758, 1829, 36178, 1829, 11622, 2423, 7578, 19949], "avg_logprob": -0.3283730253340706, "compression_ratio": 1.4726027397260273, "no_speech_prob": 3.9577484130859375e-05, "words": [{"start": 919.45, "end": 920.23, "word": "التشخيص", "probability": 0.8583170572916666}, {"start": 920.23, "end": 920.93, "word": " وعملية", "probability": 0.92626953125}, {"start": 920.93, "end": 921.73, "word": " التقييم", "probability": 0.9607747395833334}, {"start": 921.73, "end": 922.29, "word": " للعمر", "probability": 0.9339192708333334}, {"start": 922.29, "end": 922.79, "word": " العظمى", "probability": 0.833251953125}, {"start": 922.79, "end": 923.39, "word": " اكتر", "probability": 0.7515869140625}, {"start": 923.39, "end": 924.29, "word": " تعقيدا", "probability": 0.8455810546875}, {"start": 924.29, "end": 928.89, "word": " وفي", "probability": 0.3785400390625}, {"start": 928.89, "end": 930.87, "word": " الغالب", "probability": 0.9700927734375}, {"start": 930.87, "end": 931.21, "word": " يتم", "probability": 0.602294921875}, {"start": 931.21, "end": 931.73, "word": " النظر", "probability": 0.9532877604166666}, {"start": 931.73, "end": 932.55, "word": " لعملية", "probability": 0.9140625}, {"start": 932.55, "end": 933.49, "word": " التقام", "probability": 0.8707682291666666}, {"start": 933.49, "end": 935.39, "word": " وتحول", "probability": 0.7706705729166666}, {"start": 935.39, "end": 936.89, "word": " الـ", "probability": 0.423828125}, {"start": 936.89, "end": 937.77, "word": " cartilage", "probability": 0.39215087890625}, {"start": 937.77, "end": 939.01, "word": " والابيفسيز", "probability": 0.4627278645833333}, {"start": 939.01, "end": 939.47, "word": " الى", "probability": 0.673583984375}, {"start": 939.47, "end": 939.95, "word": " joints", "probability": 0.54736328125}], "temperature": 1.0}, {"id": 39, "seek": 96150, "start": 947.86, "end": 961.5, "text": "عشان نحدد مشكلة أو عمر العضم في مرحلة التفولة والتفولة المتأخرة ومرحلة الـ adolescence يستخدم", "tokens": [3615, 8592, 7649, 8717, 24401, 3215, 37893, 28820, 3660, 34051, 6225, 29973, 18863, 11242, 2304, 8978, 3714, 2288, 5016, 37977, 16712, 5172, 12610, 3660, 16070, 2655, 5172, 12610, 3660, 9673, 2655, 10721, 34740, 3660, 4032, 29973, 5016, 37977, 2423, 39184, 21383, 25434, 7251, 14851, 9778, 40448], "avg_logprob": -0.2987034473013371, "compression_ratio": 1.4, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 947.86, "end": 949.26, "word": "عشان", "probability": 0.7050374348958334}, {"start": 949.26, "end": 950.48, "word": " نحدد", "probability": 0.8995768229166666}, {"start": 950.48, "end": 951.34, "word": " مشكلة", "probability": 0.7338053385416666}, {"start": 951.34, "end": 951.5, "word": " أو", "probability": 0.5244140625}, {"start": 951.5, "end": 953.02, "word": " عمر", "probability": 0.8828125}, {"start": 953.02, "end": 953.54, "word": " العضم", "probability": 0.7529296875}, {"start": 953.54, "end": 954.14, "word": " في", "probability": 0.52490234375}, {"start": 954.14, "end": 954.92, "word": " مرحلة", "probability": 0.913818359375}, {"start": 954.92, "end": 955.88, "word": " التفولة", "probability": 0.80450439453125}, {"start": 955.88, "end": 957.2, "word": " والتفولة", "probability": 0.670263671875}, {"start": 957.2, "end": 958.62, "word": " المتأخرة", "probability": 0.90712890625}, {"start": 958.62, "end": 959.36, "word": " ومرحلة", "probability": 0.897705078125}, {"start": 959.36, "end": 959.52, "word": " الـ", "probability": 0.4417724609375}, {"start": 959.52, "end": 960.24, "word": " adolescence", "probability": 0.750244140625}, {"start": 960.24, "end": 961.5, "word": " يستخدم", "probability": 0.972900390625}], "temperature": 1.0}, {"id": 40, "seek": 98404, "start": 962.38, "end": 984.04, "text": "Atlas بيسموه grillage and bile atlas أو tenor atlas طبعا هذه يستخدم في تحديد الأمر العام Respiratory rate, heart rate and blood pressure The following table shows the average heart rate, respiratory rate and blood pressure at different periods of a child", "tokens": [18684, 7743, 4724, 1829, 38251, 2407, 3224, 16492, 609, 293, 18729, 412, 7743, 34051, 2064, 284, 412, 7743, 23032, 3555, 3615, 995, 29538, 7251, 14851, 9778, 40448, 8978, 6055, 5016, 16254, 3215, 16247, 29973, 18863, 10943, 5015, 9501, 4745, 3314, 11, 1917, 3314, 293, 3390, 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"end": 968.26, "word": " طبعا", "probability": 0.957275390625}, {"start": 968.26, "end": 968.46, "word": " هذه", "probability": 0.467529296875}, {"start": 968.46, "end": 969.04, "word": " يستخدم", "probability": 0.8980712890625}, {"start": 969.04, "end": 969.68, "word": " في", "probability": 0.87451171875}, {"start": 969.68, "end": 970.42, "word": " تحديد", "probability": 0.98681640625}, {"start": 970.42, "end": 971.08, "word": " الأمر", "probability": 0.88232421875}, {"start": 971.08, "end": 971.6, "word": " العام", "probability": 0.5107421875}, {"start": 971.6, "end": 972.42, "word": " Respiratory", "probability": 0.7566731770833334}, {"start": 972.42, "end": 972.84, "word": " rate,", "probability": 0.96240234375}, {"start": 973.06, "end": 973.28, "word": " heart", "probability": 0.8115234375}, {"start": 973.28, "end": 973.7, "word": " rate", "probability": 0.95751953125}, {"start": 973.7, "end": 974.02, "word": " and", "probability": 0.7861328125}, {"start": 974.02, "end": 974.32, "word": " blood", "probability": 0.94384765625}, {"start": 974.32, "end": 974.78, "word": " pressure", "probability": 0.92578125}, {"start": 974.78, "end": 975.8, "word": " The", "probability": 0.2000732421875}, {"start": 975.8, "end": 976.22, "word": " following", "probability": 0.87841796875}, {"start": 976.22, "end": 976.6, "word": " table", "probability": 0.875}, {"start": 976.6, "end": 977.0, "word": " shows", "probability": 0.90869140625}, {"start": 977.0, "end": 977.22, "word": " the", "probability": 0.90380859375}, {"start": 977.22, "end": 977.64, "word": " average", "probability": 0.76953125}, {"start": 977.64, "end": 977.98, "word": " heart", "probability": 0.92724609375}, {"start": 977.98, "end": 978.44, "word": " rate,", "probability": 0.96484375}, {"start": 979.22, "end": 979.62, "word": " respiratory", "probability": 0.9013671875}, {"start": 979.62, "end": 980.36, "word": " rate", "probability": 0.95751953125}, {"start": 980.36, "end": 980.82, "word": " and", 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[9566, 3555, 3615, 995, 23758, 2423, 7435, 3215, 12610, 7251, 2407, 11242, 5016, 45030, 11242, 25062, 2288, 16606, 9307, 5296, 11242, 17082, 9566, 32748, 2304, 16070, 2288, 3794, 21292, 2288, 9307, 13063, 10632, 4032, 2304, 22488, 1211, 48812, 25513, 9307, 25062, 1211, 4587, 43242, 16247, 9566, 5172, 6027, 8978, 3714, 23557, 5016, 1211, 44650, 22488, 41891, 8032, 15040, 7435, 1829, 50113, 15040, 5296, 39184, 32928, 2423, 1917, 3314, 19966, 3390, 3321, 4688, 5296, 4060, 2423, 27038, 3314, 12330, 43242, 1386, 13412, 3224, 13063, 2423, 1917, 3314, 10411], "avg_logprob": -0.29900567402893846, "compression_ratio": 1.4954954954954955, "no_speech_prob": 3.635883331298828e-06, "words": [{"start": 984.67, "end": 985.01, "word": "طبعا", "probability": 0.7957763671875}, {"start": 985.01, "end": 985.23, "word": " هذا", "probability": 0.5361328125}, {"start": 985.23, "end": 985.63, "word": " الجدول", "probability": 0.744384765625}, {"start": 985.63, "end": 986.35, "word": " يوضح", "probability": 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عن تلبس equinovirus التشوق اللي موجود هنا طبعا هو ال club food أو ممكن تكون تلبس calcinevalgas صار طلعت بدل ما هي كفة القدم داخل لجوا", "tokens": [4117, 33911, 2423, 6482, 1755, 2423, 6482, 1755, 39896, 6225, 3555, 9640, 3660, 18871, 6055, 46152, 3794, 1267, 2982, 85, 9619, 16712, 8592, 30543, 13672, 1829, 3714, 29245, 23328, 34105, 23032, 3555, 3615, 995, 31439, 2423, 6482, 1755, 34051, 3714, 43020, 6055, 30544, 6055, 46152, 3794, 2104, 66, 533, 3337, 10549, 20328, 9640, 23032, 1211, 34268, 47525, 1211, 19446, 39896, 9122, 5172, 3660, 25062, 40448, 11778, 47283, 1211, 5296, 7435, 14407], "avg_logprob": -0.3322482779622078, "compression_ratio": 1.5321637426900585, "no_speech_prob": 2.1278858184814453e-05, "words": [{"start": 2302.73, "end": 2303.17, "word": "كيف", "probability": 0.763427734375}, {"start": 2303.17, "end": 2303.61, "word": " ال", "probability": 0.31982421875}, {"start": 2303.61, "end": 2303.99, "word": " club", "probability": 0.830078125}, {"start": 2303.99, "end": 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2460.09, "end": 2460.39, "word": " هذه", "probability": 0.6572265625}, {"start": 2460.39, "end": 2460.77, "word": " الحالة", "probability": 0.9488932291666666}, {"start": 2460.77, "end": 2461.23, "word": " بسموها", "probability": 0.8466796875}, {"start": 2461.23, "end": 2462.59, "word": " amniocentesis", "probability": 0.8345703125}], "temperature": 1.0}, {"id": 99, "seek": 248955, "start": 2466.35, "end": 2489.55, "text": "وهذا طبعا ممكن ينعمل فحص during birth during pregnancy او at birth لو جينا نطلع على ال down syndrome هلاجي ان في عندهم بعض ال features اللي بتكون موجودة small number have severe to profound mental disability", "tokens": [2407, 3224, 15730, 23032, 3555, 3615, 995, 3714, 43020, 7251, 1863, 25957, 1211, 6156, 5016, 9381, 1830, 3965, 1830, 16120, 1975, 2407, 412, 3965, 45164, 10874, 1829, 8315, 8717, 9566, 1211, 3615, 15844, 2423, 760, 19371, 8032, 15040, 7435, 1829, 16472, 8978, 43242, 16095, 45030, 11242, 2423, 4122, 13672, 1829, 39894, 30544, 3714, 29245, 23328, 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"probability": 0.6719970703125}, {"start": 2474.13, "end": 2474.71, "word": " at", "probability": 0.95458984375}, {"start": 2474.71, "end": 2475.13, "word": " birth", "probability": 0.97802734375}, {"start": 2475.13, "end": 2475.61, "word": " لو", "probability": 0.82568359375}, {"start": 2475.61, "end": 2475.89, "word": " جينا", "probability": 0.9695638020833334}, {"start": 2475.89, "end": 2476.41, "word": " نطلع", "probability": 0.8572998046875}, {"start": 2476.41, "end": 2476.73, "word": " على", "probability": 0.28857421875}, {"start": 2476.73, "end": 2478.25, "word": " ال", "probability": 0.814453125}, {"start": 2478.25, "end": 2478.57, "word": " down", "probability": 0.45849609375}, {"start": 2478.57, "end": 2479.27, "word": " syndrome", "probability": 0.65283203125}, {"start": 2479.27, "end": 2481.09, "word": " هلاجي", "probability": 0.62384033203125}, {"start": 2481.09, "end": 2481.27, "word": " ان", "probability": 0.73193359375}, {"start": 2481.27, "end": 2481.49, "word": " في", "probability": 0.5380859375}, {"start": 2481.49, "end": 2482.05, "word": " عندهم", "probability": 0.9853515625}, {"start": 2482.05, "end": 2483.25, "word": " بعض", "probability": 0.984375}, {"start": 2483.25, "end": 2483.49, "word": " ال", "probability": 0.95263671875}, {"start": 2483.49, "end": 2484.19, "word": " features", "probability": 0.8505859375}, {"start": 2484.19, "end": 2484.73, "word": " اللي", "probability": 0.87060546875}, {"start": 2484.73, "end": 2485.13, "word": " بتكون", "probability": 0.88671875}, {"start": 2485.13, "end": 2485.83, "word": " موجودة", "probability": 0.979736328125}, {"start": 2485.83, "end": 2486.41, "word": " small", "probability": 0.487060546875}, {"start": 2486.41, "end": 2486.91, "word": " number", "probability": 0.94677734375}, {"start": 2486.91, "end": 2487.23, "word": " have", "probability": 0.91650390625}, {"start": 2487.23, "end": 2487.75, "word": " severe", "probability": 0.93310546875}, {"start": 2487.75, "end": 2488.01, "word": " to", "probability": 0.943359375}, {"start": 2488.01, "end": 2488.51, "word": " profound", "probability": 0.98095703125}, {"start": 2488.51, "end": 2488.85, "word": " mental", "probability": 0.875}, {"start": 2488.85, "end": 2489.55, "word": " disability", "probability": 0.88671875}], "temperature": 1.0}, {"id": 100, "seek": 251966, "start": 2490.12, "end": 2519.66, "text": "جزء منهم ممكن يكون في عنده إعاقة عقلية شديدة The incidence of Down syndrome is estimated 1 لكل 800 أو ألف بيرت 1 من كل 800 إلى 1000 ولادة ممكن ينولد Down syndrome من الأعراض اللي بيكون موجودة عندهم طبعا", "tokens": [7435, 11622, 38207, 9154, 16095, 3714, 43020, 7251, 30544, 8978, 43242, 3224, 11933, 3615, 995, 28671, 6225, 4587, 1211, 10632, 13412, 16254, 41891, 440, 41726, 295, 9506, 19371, 307, 14109, 502, 5296, 28820, 13083, 34051, 5551, 46538, 4724, 13546, 2655, 502, 9154, 28242, 13083, 30731, 9714, 49429, 41891, 3714, 43020, 7251, 1863, 12610, 3215, 9506, 19371, 9154, 16247, 3615, 2288, 46958, 13672, 1829, 4724, 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2516.28, "end": 2516.84, "word": " الأعراض", "probability": 0.89453125}, {"start": 2516.84, "end": 2517.02, "word": " اللي", "probability": 0.873779296875}, {"start": 2517.02, "end": 2517.28, "word": " بيكون", "probability": 0.7691243489583334}, {"start": 2517.28, "end": 2518.52, "word": " موجودة", "probability": 0.9239501953125}, {"start": 2518.52, "end": 2519.18, "word": " عندهم", "probability": 0.57550048828125}, {"start": 2519.18, "end": 2519.66, "word": " طبعا", "probability": 0.9815673828125}], "temperature": 1.0}, {"id": 101, "seek": 254858, "start": 2521.02, "end": 2548.58, "text": "الـ features Down syndrome may also appear in people with a standard set of chromosomes including microgenia and abnormally small chin and unusually round face protruding or oversized tongue and element shape of the eyes هلاجي انه اللسان حجم كبير او بارز", "tokens": [6027, 39184, 4122, 9506, 19371, 815, 611, 4204, 294, 561, 365, 257, 3832, 992, 295, 45228, 3009, 4532, 1766, 654, 293, 47104, 379, 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"word": " shape", "probability": 0.89697265625}, {"start": 2542.1, "end": 2542.52, "word": " of", "probability": 0.97314453125}, {"start": 2542.52, "end": 2542.66, "word": " the", "probability": 0.85009765625}, {"start": 2542.66, "end": 2542.98, "word": " eyes", "probability": 0.90625}, {"start": 2542.98, "end": 2543.5, "word": " هلاجي", "probability": 0.6328125}, {"start": 2543.5, "end": 2543.9, "word": " انه", "probability": 0.5726318359375}, {"start": 2543.9, "end": 2545.04, "word": " اللسان", "probability": 0.9591471354166666}, {"start": 2545.04, "end": 2546.56, "word": " حجم", "probability": 0.9915364583333334}, {"start": 2546.56, "end": 2547.08, "word": " كبير", "probability": 0.9933268229166666}, {"start": 2547.08, "end": 2548.06, "word": " او", "probability": 0.57318115234375}, {"start": 2548.06, "end": 2548.58, "word": " بارز", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 102, "seek": 257898, "start": 2549.98, "end": 2578.98, "text": "ممكن يكون طبعا العينين حاجة بيسموها الـ element shape شكل اللوزة وفي حاجة بيسموها الـ epicanthic fold of the eyelid شرط العين بتكون عينهم مشروطة هذه هي تقريبا أهم الأعراض اللي بتكون موجودة", "tokens": [2304, 43020, 7251, 30544, 23032, 3555, 3615, 995, 2423, 3615, 9957, 9957, 11331, 26108, 3660, 4724, 1829, 38251, 2407, 11296, 2423, 39184, 4478, 3909, 13412, 28820, 13672, 2407, 11622, 3660, 4032, 41185, 11331, 26108, 3660, 4724, 1829, 38251, 2407, 11296, 2423, 39184, 2388, 8914, 392, 299, 4860, 295, 264, 39386, 13412, 2288, 9566, 18863, 9957, 39894, 30544, 6225, 9957, 16095, 37893, 32887, 9566, 3660, 29538, 39896, 6055, 4587, 16572, 3555, 995, 5551, 16095, 16247, 3615, 2288, 46958, 13672, 1829, 39894, 30544, 3714, 29245, 23328, 3660], "avg_logprob": -0.22474564178738482, "compression_ratio": 1.6243386243386244, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2549.98, "end": 2550.52, "word": "ممكن", "probability": 0.7802734375}, {"start": 2550.52, "end": 2550.82, "word": " يكون", "probability": 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0.9140625}], "temperature": 1.0}, {"id": 104, "seek": 263153, "start": 2607.69, "end": 2631.53, "text": "العين طبعا كيف شكلها بروز اللسان short arms and legs simian crease طبعا إيديهم فيها fold واحد الخطوط اللي موجودة في الإيد internal organs congenital heart defect في الغالب في ممكن يكون فيهم مشاكل في القلب", "tokens": [6027, 3615, 9957, 23032, 3555, 3615, 995, 9122, 33911, 13412, 28820, 11296, 4724, 32887, 11622, 13672, 3794, 7649, 2099, 5812, 293, 5668, 1034, 952, 30098, 23032, 3555, 3615, 995, 11933, 1829, 16254, 16095, 8978, 11296, 4860, 36764, 24401, 33962, 9566, 2407, 9566, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 33688, 25708, 6920, 20659, 416, 1766, 1686, 1917, 16445, 8978, 6024, 118, 6027, 3555, 8978, 3714, 43020, 7251, 30544, 8978, 16095, 37893, 995, 28820, 8978, 25062, 46152], "avg_logprob": -0.18293425402083954, "compression_ratio": 1.4926829268292683, "no_speech_prob": 2.0265579223632812e-06, "words": [{"start": 2607.69, "end": 2608.37, "word": "العين", "probability": 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2627.33, "word": " congenital", "probability": 0.91552734375}, {"start": 2627.33, "end": 2627.69, "word": " heart", "probability": 0.92333984375}, {"start": 2627.69, "end": 2628.09, "word": " defect", "probability": 0.93359375}, {"start": 2628.09, "end": 2628.47, "word": " في", "probability": 0.748046875}, {"start": 2628.47, "end": 2629.03, "word": " الغالب", "probability": 0.963623046875}, {"start": 2629.03, "end": 2629.51, "word": " في", "probability": 0.650390625}, {"start": 2629.51, "end": 2629.95, "word": " ممكن", "probability": 0.813720703125}, {"start": 2629.95, "end": 2630.19, "word": " يكون", "probability": 0.9423828125}, {"start": 2630.19, "end": 2630.47, "word": " فيهم", "probability": 0.47943115234375}, {"start": 2630.47, "end": 2630.95, "word": " مشاكل", "probability": 0.9910481770833334}, {"start": 2630.95, "end": 2631.11, "word": " في", "probability": 0.9736328125}, {"start": 2631.11, "end": 2631.53, "word": " القلب", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 105, "seek": 265870, "start": 2636.18, "end": 2658.7, "text": "ممكن يكون في عندهم stenosis أو narrowing في blood vessels هذه تقريبا أهم الأعراض اللي بتكون موجودة عند ال down syndrome باق ال syndromes مش كتير مهم لنا", "tokens": [2304, 43020, 7251, 30544, 8978, 43242, 16095, 28031, 8211, 34051, 9432, 278, 8978, 3390, 20117, 29538, 6055, 4587, 16572, 3555, 995, 5551, 16095, 16247, 3615, 2288, 46958, 13672, 1829, 39894, 30544, 3714, 29245, 23328, 3660, 43242, 2423, 760, 19371, 4724, 995, 4587, 2423, 15198, 4397, 279, 37893, 9122, 2655, 13546, 3714, 16095, 5296, 8315], "avg_logprob": -0.2866477164355191, "compression_ratio": 1.3674698795180722, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 2636.18, "end": 2636.64, "word": "ممكن", "probability": 0.76806640625}, {"start": 2636.64, "end": 2636.9, "word": " يكون", "probability": 0.959716796875}, {"start": 2636.9, "end": 2637.04, "word": " في", "probability": 0.236328125}, {"start": 2637.04, "end": 2637.58, "word": " 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/1d3CViIAlTw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/1d3CViIAlTw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..67622314ce2b55147737985e46331f813ae3cdf7
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/1d3CViIAlTw.srt
@@ -0,0 +1,1943 @@
+1
+00:00:20,690 --> 00:00:26,270
+السلام عليكم اليوم سوف نتكلم عن القصة 14 ولكن قبل 
+
+2
+00:00:26,270 --> 00:00:30,150
+أن نبدأ القصة 14 يمكننا أن نتكلم عن المواضيع
+
+3
+00:00:30,150 --> 00:00:38,250
+المقدمة ما لدينا هنا لدينا قائمة مواضيع تختار من
+
+4
+00:00:38,250 --> 00:00:43,110
+22 مواضيع هذه 
+
+5
+00:00:43,110 --> 00:00:50,850
+المواضيع مواضيع التصميم هدول أيش موضوعات هندسية إذا
+
+6
+00:00:50,850 --> 00:00:59,110
+كنت لأي نوع أو لأسباب تريد أن تختار أشياء أخرى فقط
+
+7
+00:00:59,110 --> 00:01:09,690
+دعني أعرف الموضوع وهو بخير عليك أن تجمع فريق فريق
+
+8
+00:01:09,690 --> 00:01:15,350
+يستخدم من 3 إلى 4 طلاب يعني من ثلاثة إلى أربعة في
+
+9
+00:01:15,350 --> 00:01:22,010
+الفريق تبعكم the presentation should be around ten
+
+10
+00:01:22,010 --> 00:01:29,130
+minutes for the team ten minutes around two and a
+
+11
+00:01:29,130 --> 00:01:33,770
+half minutes for each of you or يعني three minutes
+
+12
+00:01:33,770 --> 00:01:39,580
+for each لو كان الفريق من ثلاثة فهذه عشر دقائق لل
+
+13
+00:01:39,580 --> 00:01:43,980
+presentation فأنت بدك تبحث في الموضوع و تعطي صورة
+
+14
+00:01:43,980 --> 00:01:47,880
+يمكن هذا حاجة تتكلم عنها later بس أقل شيء بدك you
+
+15
+00:01:47,880 --> 00:01:54,160
+need to select a topic by the 18th of this month
+
+16
+00:01:54,160 --> 00:01:59,940
+يعني مارس 18 مارس بدكون كل هيتكم already اخترتوا
+
+17
+00:01:59,940 --> 00:02:04,060
+الفريق تبعكم اللي بده يشتغل معاكم ممكن اليوم ممكن
+
+18
+00:02:04,060 --> 00:02:09,670
+بكرا بس متى متى تقرروا تقرروا الفريق ثلاثة لاربع
+
+19
+00:02:09,670 --> 00:02:15,570
+بنات فقط، كويس؟ الآن ما إنما قررتوا الفريق تبعكم و
+
+20
+00:02:15,570 --> 00:02:19,910
+قررتوا ال topic تبعتولي email confirming ليش؟ لأن
+
+21
+00:02:19,910 --> 00:02:26,890
+احنا الفريق لأنه ممكن تختاروا topic out in two لأن
+
+22
+00:02:26,890 --> 00:02:31,750
+هذا ده بنطلع علينا تقريبا كل group بيطلعلها one
+
+23
+00:02:31,750 --> 00:02:37,570
+topic فبدي كل .. بديش حد يكرر ال topic الآن هدولة
+
+24
+00:02:37,570 --> 00:02:42,210
+هحطهم بالأسود ال topics اللي get selected هيصيروا
+
+25
+00:02:42,210 --> 00:02:46,790
+باللون الأحمر متى ما وصلوا اللون الأحمر خلاص معناته
+
+26
+00:02:46,790 --> 00:02:53,050
+هذا topic is out of the question كويس؟ فهذه الفكرة
+
+27
+00:02:53,050 --> 00:02:57,170
+الموجودة عندنا الكويس سؤال عليها
+
+28
+00:03:02,420 --> 00:03:09,440
+العرض تقريبا أخر فصل هيكون، يعني أخر تقريبا
+
+29
+00:03:09,440 --> 00:03:16,260
+أسبوعين في الفصل بتتم عملية العرض، كويس؟ يعني أخر
+
+30
+00:03:16,260 --> 00:03:22,640
+أسبوعين في الفصل .. أيوة في structure هنتكلم عنه
+
+31
+00:03:23,480 --> 00:03:27,380
+يعني هتكلم عن ال structure تبع ال presentation إيش
+
+32
+00:03:27,380 --> 00:03:31,740
+لازم تحتوي؟ كيف لازم تشتغلوا تعملوا presentation؟
+
+33
+00:03:31,740 --> 00:03:36,200
+إيش الشغلات؟ كيف بدكم تحكوا؟ كيف اللي بيخجلن فيكم
+
+34
+00:03:36,200 --> 00:03:44,420
+بدهم يظبطوا حالهم؟ كل هذا هنحكي عنه في .. في ..
+
+35
+00:03:44,420 --> 00:03:47,160
+لما نتكلم عن ال presentation بس الآن إيش أنت
+
+36
+00:03:47,160 --> 00:03:53,090
+بتعملي؟ reservation لل topic بتحجزي الموضوع تبعكو
+
+37
+00:03:53,090 --> 00:03:57,230
+بتحددي مين الفريق تبعك لإنه في النهاية إيش بتسوي
+
+38
+00:03:57,230 --> 00:04:01,770
+لما اتحدد الفريق تبعك خلاص ببقى عارف هدولة خلصوا و
+
+39
+00:04:01,770 --> 00:04:06,210
+الناس اللي ما لهمش حد هانتهم أنا اللي بسير بحطهم في
+
+40
+00:04:06,210 --> 00:04:12,450
+المجموعات، كويسين هيك؟ احدد الموضوع و المجموعة
+
+41
+00:04:25,210 --> 00:04:29,670
+طيب طيب today as we said we gonna talk about
+
+42
+00:04:29,670 --> 00:04:37,450
+polymers يعني إيش polymers الآن
+
+43
+00:04:37,450 --> 00:04:43,490
+خلّيني أحكي حاجة  ال polymers اللي هو زي ال plastic
+
+44
+00:04:43,490 --> 00:04:49,530
+زي الكوشوك و زي .. في اللي هم أسامي عدة بس خليني
+
+45
+00:04:49,530 --> 00:04:54,610
+الآن احنا بنعطيكي الحاجة العامة هدولة بنسميهم
+
+46
+00:04:54,610 --> 00:04:59,910
+polymers الآن في شغلات تانية الاسم العربي لهم اللي
+
+47
+00:04:59,910 --> 00:05:05,210
+هي poly أيش متعدد Umar أشياء أشياء المتعددة يعني
+
+48
+00:05:05,210 --> 00:05:09,710
+تكوينها بتكلم عن جزيئات متعددة إيش الشغلات
+
+49
+00:05:09,710 --> 00:05:12,750
+الجزيئات المتعددة تتذكروا أنتو لما أنا خدتوا بال
+
+50
+00:05:12,750 --> 00:05:19,010
+biochemistry كيميا الحيوية خدتوا بها .. أخدتوها
+
+51
+00:05:19,010 --> 00:05:24,390
+بالثانوية؟ كيف كان شكل ال structure تبع الجزيئات
+
+52
+00:05:24,390 --> 00:05:29,990
+أو ال molecules؟ كيف كان؟ كبير فهذا الجزئية
+
+53
+00:05:29,990 --> 00:05:35,430
+تكويناتها كبيرة فهي هذه بيسموها فصيلة اللدائن
+
+54
+00:05:35,430 --> 00:05:41,810
+بالعربي أيوة
+
+55
+00:05:41,810 --> 00:05:45,470
+what
+
+56
+00:05:45,470 --> 00:05:49,090
+we gonna talk about today is natural and synthetic
+
+57
+00:05:49,090 --> 00:05:53,950
+polymers thermoplastics and thermosetting plastics
+
+58
+00:05:53,950 --> 00:05:58,350
+هدول النوعين اللي هتكلم عن ال natural و ال
+
+59
+00:05:58,350 --> 00:06:03,820
+synthetic إيش natural؟ طبيعي Synthetic، إيش عكس
+
+60
+00:06:03,820 --> 00:06:11,560
+طبيعي؟ أيوة مصنع، Thermoplastic الـ ال plastic
+
+61
+00:06:11,560 --> 00:06:15,400
+الحراري و Thermosetting plastic اللي هو ال plastic
+
+62
+00:06:15,400 --> 00:06:22,880
+اللي بتتم تصنيعه حراريا، ال plastic اللي مصنع
+
+63
+00:06:22,880 --> 00:06:28,860
+حراريا natural and synthetic polymers الويب بيج تحت
+
+64
+00:06:28,860 --> 00:06:31,540
+من موقع ويب صفحة للدراسات للدراسات للدراسات
+
+65
+00:06:31,540 --> 00:06:34,860
+للدراسات للدراسات للدراسات للدراسات للدراسات
+
+66
+00:06:34,860 --> 00:06:35,220
+للدراسات للدراسات للدراسات للدراسات للدراسات
+
+67
+00:06:35,220 --> 00:06:35,300
+للدراسات للدراسات للدراسات للدراسات للدراسات
+
+68
+00:06:35,300 --> 00:06:36,780
+للدراسات للدراسات للدراسات للدراسات للدراسات
+
+69
+00:06:36,780 --> 00:06:38,020
+للدراسات للدراسات للدراسات للدراسات للدراسات
+
+70
+00:06:38,020 --> 00:06:38,640
+للدراسات للدراسات للدراسات للدراسات للدراسات
+
+71
+00:06:38,640 --> 00:06:43,940
+للدراسات للدراسات
+
+72
+00:06:43,940 --> 00:06:47,160
+للدراسات للدراسات
+
+73
+00:06:53,060 --> 00:06:57,360
+هدولة كل الأسامي يعني شايفين الاسم تبعها حاجة أديش؟
+
+74
+00:06:57,360 --> 00:07:03,100
+هذا أول ما طلعت عليه فكرت أنه Miss Spelt لأن حجم
+
+75
+00:07:03,100 --> 00:07:07,720
+الكلمة أحيانا بتفكريها ملازمة ببعض هي بالغلط it's
+
+76
+00:07:07,720 --> 00:07:10,940
+not surprising that polymers are usually called by
+
+77
+00:07:10,940 --> 00:07:14,480
+their more common names اللي هي إيش ال plastic هذا
+
+78
+00:07:14,480 --> 00:07:18,780
+الاسم بتشوفيهوش إلا حتى في القاموس يعني هاد الكلمة
+
+79
+00:07:18,780 --> 00:07:20,360
+في القاموس مش موجودة
+
+80
+00:07:22,830 --> 00:07:27,730
+هي الاسم الكيميائي تبعها، الآن أطلع مثلها poly
+
+81
+00:07:27,730 --> 00:07:34,810
+متعدد، tetra ثمانية، flora، flora فيها ال fluoride،
+
+82
+00:07:34,810 --> 00:07:38,730
+ethylene، مادة ال ethylene، هذه التكوينة الكيميائية
+
+83
+00:07:38,730 --> 00:07:42,510
+تبعها، الآن لما تيجي تطلع التكوينة الكيميائية
+
+84
+00:07:42,510 --> 00:07:46,850
+ما حدش بيذكرها لما بتحكي هذا الاسم مين بيعرف أنت عن
+
+85
+00:07:46,850 --> 00:07:51,670
+إيش بتتكلمي بس لما تقول plastic كل الناس بتعرفه
+
+86
+00:07:51,670 --> 00:07:57,030
+فعشان هيك أن الاسم المستخدم إيش plastic but what
+
+87
+00:07:57,030 --> 00:08:02,350
+exactly is a polymer or a plastic يعني إيش هذا؟
+
+88
+00:08:02,910 --> 00:08:07,410
+Polymers are compounds made up of several elements
+
+89
+00:08:07,410 --> 00:08:13,310
+that are chemically bound هو معمول من أشياء مختلفة
+
+90
+00:08:13,310 --> 00:08:19,330
+وهدولة إيش اتحدوا مع بعض كيميائيا وزي ما حكيت في
+
+91
+00:08:19,330 --> 00:08:23,150
+الكيميا الحيوية بتشوفوا كيف الاتحادات بتحصل
+
+92
+00:08:23,150 --> 00:08:30,050
+والذرات الآن most compounds consist of large number
+
+93
+00:08:30,050 --> 00:08:34,890
+of tiny molecules الآن لما نيجي نطلع عليها معظم
+
+94
+00:08:34,890 --> 00:08:43,170
+هذه المركبات بتتكون من عدد كبير من جزيئات صغيرة
+
+95
+00:08:43,170 --> 00:08:49,550
+tiny صغيرة جدا لما تقول tiny عن حاجة مثلا tiny toy
+
+96
+00:08:49,550 --> 00:08:55,100
+لعبة صغيرة هذا كثير أصغر من ال small small صغير
+
+97
+00:08:55,100 --> 00:09:06,600
+tiny صغير جدا يعني أيوة صغيرة هي بالعربي زي كذا which
+
+98
+00:09:06,600 --> 00:09:11,140
+it contains just a few atoms كل واحدة منها بتحتوي
+
+99
+00:09:11,140 --> 00:09:17,940
+على ذرات قليلة شايفة كلمة a few بالعدد هذه ال tiny
+
+100
+00:09:17,940 --> 00:09:25,380
+بالجمع على سبيل المثال، ملكية مياه ماء H2O تحتوي
+
+101
+00:09:25,380 --> 00:09:28,740
+على ذرتين هيدروجين و ذرة أكسجين و ذرة أكسجين و ذرة
+
+102
+00:09:28,740 --> 00:09:31,060
+أكسجين و ذرة أكسجين و ذرة أكسجين و ذرة أكسجين و
+
+103
+00:09:31,060 --> 00:09:35,100
+ذرة أكسجين و ذرة أكسجين و ذرة أكسجين و ذرة أكسجين
+
+104
+00:09:35,100 --> 00:09:36,780
+و ذرة أكسجين و ذرة أكسجين و ذرة أكسجين و ذرة
+
+105
+00:09:36,780 --> 00:09:38,640
+أكسجين و ذرة أكسجين و ذرة أكسجين و ذرة أكسجين و
+
+106
+00:09:38,640 --> 00:09:39,880
+ذرة أكسجين و ذرة أكسجين و ذرة أكسجين و ذرة أكسجين
+
+107
+00:09:39,880 --> 00:09:45,620
+و ذرة أكسجين و ذرة أكسجين و تم طيب but the
+
+108
+00:09:45,620 --> 00:09:49,260
+molecules of polymers contain a huge number of
+
+109
+00:09:49,260 --> 00:09:53,180
+atoms joined together in a long chain الفرق بينها
+
+110
+00:09:53,180 --> 00:09:57,240
+هذا إيش ال water شفناها عبارة عن إيش ثلاث ذرات
+
+111
+00:09:57,240 --> 00:10:01,980
+بينما في ال polymers عدد الذرات ال atoms number of
+
+112
+00:10:01,980 --> 00:10:06,160
+atoms is huge كبير طلع على الصورة الموجودة عندها
+
+113
+00:10:06,160 --> 00:10:12,960
+هاي جزء شوفي عدد الذرات اللي عندي كده و هذا كل لون
+
+114
+00:10:12,960 --> 00:10:16,820
+بعطيني من التشكيلة اللي جاي منها ال elements
+
+115
+00:10:16,820 --> 00:10:22,680
+المختلف الآن لما أتكلم على rubber إيش يعني rubber
+
+116
+00:10:22,680 --> 00:10:27,540
+المطاط
+
+117
+00:10:27,540 --> 00:10:35,180
+أيوة طيب الآن في دروس اللغة العربية زمان تكلمنا
+
+118
+00:10:35,180 --> 00:10:40,350
+في السودان في شجر إيش بيعملوا منه؟ أيوة اللي هو
+
+119
+00:10:40,350 --> 00:10:45,550
+الصمغ العربي اللي هي هذه نوع من أنواع المطاط هو
+
+120
+00:10:45,550 --> 00:10:50,550
+شجر الصمغ العربي فالصمغ هذا بيعمل بيصنع منه هذا زي
+
+121
+00:10:50,550 --> 00:10:55,610
+ما هتشوفوا ال rubber thanks to its many uses from
+
+122
+00:10:55,610 --> 00:10:59,730
+rubber bands to car tires is one of the best known
+
+123
+00:10:59,730 --> 00:11:06,280
+polymers هذه تستخدم في العديد من الملاط الملاط
+
+124
+00:11:06,280 --> 00:11:08,840
+اللي بتستخدموها الملاط الصغيرة أو تبعت الشعر أو
+
+125
+00:11:08,840 --> 00:11:14,540
+غيره إلى إطارات السيارات فهو معروف كثير it comes
+
+126
+00:11:14,540 --> 00:11:20,400
+from latex الآن الـ latex هو عبارة عن ايش كلمة 
+
+127
+00:11:20,400 --> 00:11:29,740
+الصمغ وهنا أيوة latex الآن الـ latex هذا هي اسم 
+
+128
+00:11:29,740 --> 00:11:36,040
+خلينا نقول علمي أو للـ plastic أو للمطاط حتى
+
+129
+00:11:36,040 --> 00:11:41,080
+بتشوفوها وين؟ الـ gloves تبعات المستشفيات ايش
+
+130
+00:11:41,080 --> 00:11:48,820
+بيسموهم؟ latex عشان .. عشان .. لها يعني .. أيوة
+
+131
+00:11:48,820 --> 00:11:52,840
+فالآن a natural liquid which comes from rubber
+
+132
+00:11:52,840 --> 00:11:56,680
+trees اللي هو هذا ايش الـ latex؟ اللي هو الصمغ
+
+133
+00:11:56,680 --> 00:12:05,530
+natural liquid أيوة مادة سائلة طبيعية تأتي من شجر
+
+134
+00:12:05,530 --> 00:12:10,650
+المطاط هي الـ latex فأنت ما عليك كلمة rubber و
+
+135
+00:12:10,650 --> 00:12:17,030
+latex و polymer هذول الثلاثة ايش المعنى تبعهم في
+
+136
+00:12:17,030 --> 00:12:22,090
+المضمون واحد rubbers
+
+137
+00:12:22,090 --> 00:12:26,310
+is therefore a natural polymer شايف ايش هنا قال لك
+
+138
+00:12:26,310 --> 00:12:32,240
+الـ rubber المطاط هو ايش هو polymer اللي قلنا ايش
+
+139
+00:12:32,240 --> 00:12:39,320
+هذا، ترجمته polymer لدائن طبيعية however most of
+
+140
+00:12:39,320 --> 00:12:43,860
+the polymers used in industry are not natural but
+
+141
+00:12:43,860 --> 00:12:49,200
+synthetic معظم المطاط المستخدم في الصناعة مصنع مش
+
+142
+00:12:49,200 --> 00:12:56,270
+طبيعي وعادة من مشتقات الـ petrol The term plastic
+
+143
+00:12:56,270 --> 00:12:59,470
+is generally used to refer to synthetic polymers
+
+144
+00:12:59,470 --> 00:13:04,750
+البلاستيك بشكل عام بنعتبره ايه جاي من مش الـ
+
+145
+00:13:04,750 --> 00:13:09,790
+natural polymer or الـ latex جاي من وين؟ من الـ
+
+146
+00:13:09,790 --> 00:13:12,750
+synthetic polymers اللي هي لدى المصنع and other
+
+147
+00:13:12,750 --> 00:13:17,730
+words those that are man-made الـ man-made يعني
+
+148
+00:13:17,730 --> 00:13:24,490
+ايش؟ أيوة الآن الـ synthetic و الـ man .. الـ man made
+
+149
+00:13:24,490 --> 00:13:31,630
+هذول هم مصنع أو صنع الإنسان طيب هلقا احنا هنا بس
+
+150
+00:13:31,630 --> 00:13:35,430
+خليني نرجع هنا شوية عشان نقول لكم ايش الكلمات نأكد
+
+151
+00:13:35,430 --> 00:13:41,070
+عليها الـ plastic و الـ molecules و الـ atoms و الـ
+
+152
+00:13:41,070 --> 00:13:46,890
+ايش و الـ chains ايش الـ chains السلاسل الآن لما
+
+153
+00:13:46,890 --> 00:13:51,090
+أتكلم مالكيوردز اللي هو بتكون من ايش؟ من atoms
+
+154
+00:13:51,090 --> 00:13:56,650
+الآن الـ plastic هو عبارة عن polymer وهنا ايش قلنا
+
+155
+00:13:56,650 --> 00:14:01,270
+يعني بشكل عام الـ rubber و الـ latex هذا natural
+
+156
+00:14:01,270 --> 00:14:05,790
+الآن عندي natural polymers و الـ synthetic polymers
+
+157
+00:14:05,790 --> 00:14:13,250
+اللي هو man-made polymers الآن عندنا نوعين ثانيين
+
+158
+00:14:13,250 --> 00:14:17,810
+بنتكلم عنهم هنا الحصة تستمر في التحقق من نوع الـ
+
+159
+00:14:17,810 --> 00:14:23,530
+polymers نوع الـ polymers نوعي نوعي نوعي نوعي نوعي
+
+160
+00:14:23,530 --> 00:14:27,550
+نوعي نوعي
+
+161
+00:14:28,350 --> 00:14:33,950
+لنوعين هنا two main category thermoplastic اللي هو
+
+162
+00:14:33,950 --> 00:14:39,150
+البلاستيك الحراري can be melted by heat and formed
+
+163
+00:14:39,150 --> 00:14:43,570
+in shape containers called molds الآن احنا ايش
+
+164
+00:14:43,570 --> 00:14:48,650
+بنقول هذا بتسيح بالحرارة هذا النوع وبعدين ايش
+
+165
+00:14:48,650 --> 00:14:54,390
+بنحطه في أوعية لنشكل تعمل الشكل تبعه الأوعية هذه
+
+166
+00:14:54,390 --> 00:14:58,730
+العملية الأوعية بنسميها ايش molds الأوعية اللي
+
+167
+00:14:58,730 --> 00:15:03,950
+بنحط فيها الـ plastic السائح أو السائل قوالب
+
+168
+00:15:03,950 --> 00:15:10,370
+containers قوالب الـ molds هي الشكل للأوعية هذه
+
+169
+00:15:11,970 --> 00:15:16,210
+after the liquid plastic has cooled it sits to
+
+170
+00:15:16,210 --> 00:15:20,250
+form a solid material الآن بعد ما هي تبرد
+
+171
+00:15:20,250 --> 00:15:24,670
+البلاستيك يبرد ايش بتسويها it sits to form ايش
+
+172
+00:15:24,670 --> 00:15:33,410
+يعني تشكل solid material مواد صلبة a thermoplastic
+
+173
+00:15:33,410 --> 00:15:37,170
+is a type of plastic that can be heated and molded
+
+174
+00:15:37,170 --> 00:15:41,950
+numerous times الآن هذه خاصية من خواص الـ
+
+175
+00:15:41,950 --> 00:15:47,790
+thermoplastic ايش هي؟ نقدر نسيحه I can be heated
+
+176
+00:15:47,790 --> 00:15:55,450
+and molded نسيحه ونشكله في قوالب عدة مرات يعني
+
+177
+00:15:55,450 --> 00:16:01,430
+هذا بنفع ينعمله إعادة تدوير أيوة فمين اللي بنعمله
+
+178
+00:16:01,430 --> 00:16:07,750
+إعادة تدوير؟ أيوة الـ thermoplastic Examples of
+
+179
+00:16:07,750 --> 00:16:11,150
+thermoplastic that are common in engineering
+
+180
+00:16:11,150 --> 00:16:18,030
+include هذه أمثلة منها الآن الـ ABC ايش يعني الـ ABC
+
+181
+00:16:18,030 --> 00:16:27,850
+أكريليك أكريليك أكريليك low low نيترال بوتادين ستيرين
+
+182
+00:16:29,620 --> 00:16:36,060
+هذا اسم العلمي لنوع من أنواع الـ plastic في الصناعة
+
+183
+00:16:36,060 --> 00:16:45,860
+بيسموه ABC ABS ABS Stiff and light هذا ايش قوته؟
+
+184
+00:16:45,860 --> 00:16:55,730
+Stiff يعني صعب أن تتميل أو يعني light خفيف يعني في
+
+185
+00:16:55,730 --> 00:17:01,370
+درجة من الصلابة وخفيف use in vehicle body work هذا
+
+186
+00:17:01,370 --> 00:17:06,610
+بيستخدم في أجسام المركبات إذا بتلاحظوها الآن
+
+187
+00:17:06,610 --> 00:17:10,750
+المركبات القديمة كانت ايش الجسم تبعها كله حديد
+
+188
+00:17:10,750 --> 00:17:17,020
+المركبات الحديثة الجسم تبعها مش حديد مواد ثانية هذه
+
+189
+00:17:17,020 --> 00:17:21,400
+هي المادة اللي هي بلاستيكية ABS الموجودة تبع
+
+190
+00:17:21,400 --> 00:17:27,260
+المادة إذا بتلاحظوا خفيفة ومش بتأذي بينما مثلاً
+
+191
+00:17:27,260 --> 00:17:30,560
+السيارات القديمة بتطلع زي الـ tuk-tuk الحديد تبقى
+
+192
+00:17:30,560 --> 00:17:35,460
+كيف؟ جامد الشحن الحديد تبقى .. بس العيب تبقى ثقيلة
+
+193
+00:17:35,460 --> 00:17:41,080
+فهذه بتخلي السيارة مش موفرة للطاقة فلما نخفف الوزن
+
+194
+00:17:41,080 --> 00:17:46,480
+بيصير السيارات موفرة أو بتعطي بنزين يعني أداء أفضل
+
+195
+00:17:46,480 --> 00:17:53,760
+بالنسبة للتر البنزين طيب النوع الثاني ايش هو بالـ
+
+196
+00:17:53,760 --> 00:17:58,560
+بالي كربونيت used to make strong transparent
+
+197
+00:17:58,560 --> 00:18:05,200
+panels and vehicle lights هذا ايش هي قوية تستخدم
+
+198
+00:18:05,200 --> 00:18:09,740
+في صناعة الحاجات الشفافة إجازة .. إجازة الصي ..
+
+199
+00:18:09,740 --> 00:18:13,760
+اللي بتطلع عليه البلاستيك اللي بغطي إجازة السيارات
+
+200
+00:18:13,760 --> 00:18:19,410
+هو من هذا النوع أو الحاجات ال .. ال .. ال .. المواد
+
+201
+00:18:19,410 --> 00:18:24,130
+البلاستيكية الشفافة فبتنبع منها هذه الشغلة وهذه
+
+202
+00:18:24,130 --> 00:18:29,850
+بتلاحظوا مثلاً زي الجناني الجناني مادة شفافة صلبة
+
+203
+00:18:29,850 --> 00:18:35,290
+فهذه بتنبع منها الموجودها الـ PVC هذه موجودة كثير
+
+204
+00:18:35,290 --> 00:18:41,330
+وين بتشوفوها؟ تشوفوا المواسير اللي في البيت؟ كلها
+
+205
+00:18:41,330 --> 00:18:49,310
+من هذه النوعة اللي هي باليفا فينلي كلورايد a
+
+206
+00:18:49,310 --> 00:18:53,650
+cheaper plastic used for window frames and pipes
+
+207
+00:18:57,360 --> 00:19:01,660
+الأرجو كل الحارة هذهك و السكن كلهيته هذه كلهيتها
+
+208
+00:19:01,660 --> 00:19:07,720
+بتلاقيها ايش بكتب عليها PVC فعند الـ ABS الـ
+
+209
+00:19:07,720 --> 00:19:13,500
+polycarbonate و الـ PVC هذه تستخدم إذا بنتطلع عليها
+
+210
+00:19:13,500 --> 00:19:17,340
+هذه
+
+211
+00:19:17,340 --> 00:19:22,940
+تستخدم لأجسام السيارات هذه تستخدم للشفافة هذه
+
+212
+00:19:22,940 --> 00:19:29,260
+تستخدم للمواسير بشكل عام الآن النوع الثاني ايش
+
+213
+00:19:29,260 --> 00:19:31,880
+بنسميها ده ايش سميناها اللي جنوع الأولاني
+
+214
+00:19:31,880 --> 00:19:37,100
+thermoplastic النوع الثاني thermosetting plastic
+
+215
+00:19:37,100 --> 00:19:42,560
+أو sometimes they call it thermostat thermostat
+
+216
+00:19:42,560 --> 00:19:48,740
+اللي هو ايش تبع الحرارة مقياس الحرارة فهم اختصار
+
+217
+00:19:48,740 --> 00:19:51,560
+احنا زي ما حكيت دائماً الهندسة بتحب تستخدم ايش
+
+218
+00:19:53,230 --> 00:19:58,610
+الكلمات الناس مش بتعرفهاش أيوة الآن thermosetting
+
+219
+00:19:58,610 --> 00:20:01,590
+plastic can be heated and molded like
+
+220
+00:20:01,590 --> 00:20:05,830
+thermoplastic فأنت بتقدر تسخنيها بتقدر ايش تعمليها
+
+221
+00:20:05,830 --> 00:20:12,130
+أو تشكليها زي thermoplastic they may also be mixed
+
+222
+00:20:12,130 --> 00:20:16,710
+from cold ingredients ممكن من حاجات باردة تخلطيها
+
+223
+00:20:16,710 --> 00:20:20,690
+however during cooling or mixing a chemical
+
+224
+00:20:20,690 --> 00:20:25,110
+reaction occurs causing the thermosets to cure
+
+225
+00:20:25,110 --> 00:20:29,690
+الآن ايش اللي احنا بنتكلم عنه؟ بنتكلم على الحاجة
+
+226
+00:20:29,690 --> 00:20:35,290
+التالية إنه هذه لما نخلطهم مع بعض بيصير chemical
+
+227
+00:20:35,290 --> 00:20:38,810
+reaction بتعرفوا لما يصير chemical reaction بتقول
+
+228
+00:20:38,810 --> 00:20:43,470
+الـ process irreversible يعني ايش؟ بتقدريش ترجعيها
+
+229
+00:20:43,470 --> 00:20:52,190
+ثاني صح؟ فالـ thermosets بتختلف عن الـ thermoplastic
+
+230
+00:20:52,190 --> 00:20:57,070
+فإنه هذا during the cooling a chemical reaction
+
+231
+00:20:57,070 --> 00:21:02,930
+occur causing the thermosets to cure ايش cure؟ طب
+
+232
+00:21:02,930 --> 00:21:06,530
+ايش cure بالعامية؟
+
+233
+00:21:06,530 --> 00:21:13,370
+أيوة cure .. لما الواحد بدك يشفى بيقول ايش؟ a cure
+
+234
+00:21:13,370 --> 00:21:16,370
+مثلاً you take medicine to cure of your home a
+
+235
+00:21:16,370 --> 00:21:23,910
+disease بتعالجي الآن هنا بتختلف هذه ايش بمعناها
+
+236
+00:21:23,910 --> 00:21:28,590
+أنه بتشكل وخلصنا يعني بتصبح الشكل تبعها أخذت
+
+237
+00:21:28,590 --> 00:21:36,230
+الوضع النهائي أيوة الآن هذه بتنفعش تطلعها this mean
+
+238
+00:21:36,230 --> 00:21:40,470
+هاي cure they sit permanently يعني ايش بيصير لهم؟
+
+239
+00:21:41,650 --> 00:21:47,350
+يعني بيصيرش .. بتصل للوضع النهائي اللي هو ال .. ال
+
+240
+00:21:47,350 --> 00:21:52,710
+.. المستدام اللي هو الدائم and cannot be molded
+
+241
+00:21:52,710 --> 00:21:58,350
+again لأن هذه بتمشي إعادة تشكيلها ثاني خلاص هي مرة
+
+242
+00:21:58,350 --> 00:22:03,720
+واحدة انعملت فيها if a thermoset is heated after
+
+243
+00:22:03,720 --> 00:22:10,060
+curing it will burn لو أنا بدي أعمل .. بدي أعمل ..
+
+244
+00:22:10,060 --> 00:22:15,500
+أسخنها بعد هذا ايش بدي يصير فيها بدها تنحرق هذا زي
+
+245
+00:22:15,500 --> 00:22:20,180
+الشمع شوف الشمع لما تسويه ايش بتسويه لما بدك
+
+246
+00:22:20,180 --> 00:22:28,470
+تسيحيه ايش بيصير له بنحرق، مظبوط؟ طيب examples of
+
+247
+00:22:28,470 --> 00:22:34,890
+thermosets used in engineering are epoxy resins
+
+248
+00:22:34,890 --> 00:22:40,610
+used for strong adhesives ايش يعني strong
+
+249
+00:22:40,610 --> 00:22:46,590
+adhesives؟ epoxy بتشوفوا كلمة epoxy مين فيكم
+
+250
+00:22:46,590 --> 00:22:50,910
+بتطلعوا على الصمغ اللي بتشتروه اللي بيسموه ايش صمغ
+
+251
+00:22:50,910 --> 00:22:58,690
+الأمير؟ أه أيه ولا إزيك؟ إيش هذا بتسويفه؟ طيب
+
+252
+00:22:58,690 --> 00:23:05,570
+الآن هذا لما تسويف بتقدر تعيد استخدامه؟ هذا نوع من
+
+253
+00:23:05,570 --> 00:23:12,610
+أنواع الthermosets كويس؟  الadhesive اللي هي إيش
+
+254
+00:23:12,610 --> 00:23:16,350
+الصمغ أنواع الصمغ اللي .. اللي .. اللي .. اللي ..
+
+255
+00:23:16,350 --> 00:23:16,550
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+256
+00:23:16,550 --> 00:23:16,750
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+257
+00:23:16,750 --> 00:23:17,610
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+258
+00:23:17,610 --> 00:23:18,150
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+259
+00:23:18,150 --> 00:23:18,310
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+260
+00:23:18,310 --> 00:23:18,350
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+261
+00:23:18,350 --> 00:23:18,530
+اللي .. اللي .. اللي .. الل
+
+262
+00:23:22,210 --> 00:23:29,770
+هنا نوع التاني polyimides
+
+263
+00:23:29,770 --> 00:23:34,090
+strong and flexible used as insulators in some
+
+264
+00:23:34,090 --> 00:23:38,310
+electrical cables الآن بعض الكوابل يمكن بتشوفوها
+
+265
+00:23:38,310 --> 00:23:44,030
+هادي كتير طنجرة تبعت الكهربا بتلاقي المنطقة السخنة
+
+266
+00:23:44,030 --> 00:23:49,690
+محطوط عليها مادة صح؟ مظبوط؟ plastic ماحنا بتتكلم عن
+
+267
+00:23:49,690 --> 00:23:54,590
+الplastic المادة هاي بتلاقيها ساحة وملزقة لو جيتي
+
+268
+00:23:54,590 --> 00:24:00,990
+بدك تسيحيها ما فيش إمكانية لا تحرقيها صح؟ فبتخرب
+
+269
+00:24:00,990 --> 00:24:08,070
+الآن ال .. ال .. بعض المناطق تطلع عندك شاحن تبع
+
+270
+00:24:08,070 --> 00:24:12,710
+الكهربا تبع الlaptop ولا أي حاجة تلاقي في جزئية
+
+271
+00:24:12,710 --> 00:24:17,900
+منها ملزقة حاجة مادة بلاستيكية بس البلاستيكية
+
+272
+00:24:17,900 --> 00:24:22,160
+بتقدريش تفكيها هذه هي النوع اللي احنا بنسميه الـ
+
+273
+00:24:22,160 --> 00:24:27,300
+polyimides اللي عنده نوع البلاستيك هذا نوع
+
+274
+00:24:27,300 --> 00:24:31,040
+البلاستيك هذا بيختلف عن البلاستيك التاني في إيش أنه
+
+275
+00:24:31,040 --> 00:24:37,140
+هذا مقاوم يعني بيعمل insulation يعني بيعمل عزل
+
+276
+00:24:37,140 --> 00:24:43,900
+كهربائي لأن هذه مع الحرارة كتير من هذه الشغلات إيش
+
+277
+00:24:43,900 --> 00:24:48,350
+بيصير فيهالو جربتوا الأنواع اللي قبل ما تصل لهذه
+
+278
+00:24:48,350 --> 00:24:52,170
+الformula لكي عرفتوا إيش الموجود زمان كانت هذه
+
+279
+00:24:52,170 --> 00:24:57,990
+أكتر منطقة بيكون فيها الخراب هي منطقة هائلة لإن في
+
+280
+00:24:57,990 --> 00:25:02,730
+عندك كهربا و حرارة فكل فترة اللي في البيت بيقصه و
+
+281
+00:25:02,730 --> 00:25:08,030
+بيسوي من جديد و
+
+282
+00:25:08,030 --> 00:25:18,880
+أنت كمهندسات ممكن بتشتغل جزء منها أه أه أيوة طيب
+
+283
+00:25:18,880 --> 00:25:25,540
+القهد عندنا هذه عرفتوا إيش النوعين هنا؟ epoxy resins
+
+284
+00:25:25,540 --> 00:25:29,800
+وهنا polyimides هدول النوعين هذه إيش
+
+285
+00:25:29,800 --> 00:25:35,420
+بتستخدم؟ هذه للصمغ السريع وهذه بتستخدم لإيش؟
+
+286
+00:25:35,420 --> 00:25:40,940
+للعوازل الكهربائية لأن two more categories for
+
+287
+00:25:40,940 --> 00:25:47,040
+polymers are engineering plastics and elastomers
+
+288
+00:25:47,620 --> 00:25:51,680
+engineering plastics هاي نوع وفيه elastomers النوع
+
+289
+00:25:51,680 --> 00:25:56,260
+التاني طيب إيش هاي engineering plastics are mostly
+
+290
+00:25:56,260 --> 00:26:00,480
+thermoplastic that are especially strong such as
+
+291
+00:26:00,480 --> 00:26:07,260
+ABC, ABS and polycarbonate فهم هدولة النوع ال
+
+292
+00:26:07,260 --> 00:26:11,700
+engineering plastic اللي هو نوعه thermoplastic
+
+293
+00:26:11,700 --> 00:26:19,920
+الآن هو شبيه بمين؟ بالـ strong يعني هو قوي كتير
+
+294
+00:26:19,920 --> 00:26:25,380
+وشبيه بالـ ABS و الـ polycarbonate اللي موجود عندي
+
+295
+00:26:25,380 --> 00:26:31,600
+طيب elastomers is very elastic polymers which can
+
+296
+00:26:31,600 --> 00:26:34,800
+be stretched by force to at least twice their
+
+297
+00:26:34,800 --> 00:26:41,100
+original length شوفوا المغيط هي نوع مغض هذه كلمة
+
+298
+00:26:41,100 --> 00:26:48,200
+elastic Elast Marine أو مغط فهذا اللي عندنا هو ال
+
+299
+00:26:48,200 --> 00:26:52,220
+plastic اللي بمغط لأقل إشي twice its size يعني
+
+300
+00:26:52,220 --> 00:26:57,120
+الحجم تبعها مرتين بنفس الوقت بعدها برجع لنفس
+
+301
+00:26:57,120 --> 00:27:02,660
+المغيطة لما تسحبيها الأصل ترجع لنفسه ولا بتبطل
+
+302
+00:27:02,660 --> 00:27:07,650
+إليها استخدام it was their original link and then
+
+303
+00:27:07,650 --> 00:27:11,550
+can return to its original link when the force is
+
+304
+00:27:11,550 --> 00:27:17,890
+removed يعني هذه بعد ما تسحب القوة المقطاة ترجعي
+
+305
+00:27:17,890 --> 00:27:22,890
+تاني برجع للحجم الطبيعي تبعه يعني هذه ال elastomers
+
+306
+00:27:22,890 --> 00:27:26,710
+اللي هي المغيطة الplastic المغطة
+
+307
+00:27:33,680 --> 00:27:39,940
+ما أعرفش أنا ما جربت إنش .. شفتم بس ما جربتم .. بس
+
+308
+00:27:39,940 --> 00:27:42,780
+هدولة إيش في .. لما بدك تشد حاجة بتحطي ..
+
+309
+00:27:42,780 --> 00:27:51,000
+بتستخدميهم طيب الآن لل exercises الكلمات قبل ما
+
+310
+00:27:51,000 --> 00:27:54,460
+نروح عليها بس عشان نأكد على بعض الشغلات إيش اللي
+
+311
+00:27:54,460 --> 00:28:01,160
+عندها؟ thermosets و thermoplastic molds و molded
+
+312
+00:28:01,160 --> 00:28:05,510
+إيش يعني ال mold؟ اللي هي القوالب اللي بتشكل ..
+
+313
+00:28:05,510 --> 00:28:10,830
+بتعطي الشكل ال ABS و ال polycarbonate هدول عرفتهم
+
+314
+00:28:10,830 --> 00:28:15,190
+لإيش ال ABS هده plastic used .. synthetic plastic
+
+315
+00:28:15,190 --> 00:28:20,970
+used for vehicle bodies هده strong و light weight
+
+316
+00:28:20,970 --> 00:28:24,650
+الآن اللي عنده ال polycarbonate هده transparent
+
+317
+00:28:24,650 --> 00:28:31,080
+اللي عنده ال PVC هده بتستخدم لـ ال pipe الـ
+
+318
+00:28:31,080 --> 00:28:35,100
+thermosets اللي هي احنا يقولنا هي اللي هي نعمل ال
+
+319
+00:28:35,100 --> 00:28:42,220
+plastic هذا يعني it get molded once و بعدها خلصناه
+
+320
+00:28:42,220 --> 00:28:47,680
+بدك if you want to reheat it it will burn يعني حتى
+
+321
+00:28:47,680 --> 00:28:53,400
+تنحرج فيها ال cure اللي هي she sit permanently
+
+322
+00:28:53,400 --> 00:28:55,420
+يعني بتشكل نهائي
+
+323
+00:28:58,380 --> 00:29:03,080
+اللي هي هذه النوع اللي بتعطينا نوع من البلاستيكا
+
+324
+00:29:03,080 --> 00:29:08,640
+بتعطينا adhesive ال polyimides اللي هو هذا
+
+325
+00:29:08,640 --> 00:29:15,560
+flexible وبنعمل لل insulators الآن عندي elastomers
+
+326
+00:29:15,560 --> 00:29:19,560
+وال engineering plastic ال engineering plastics
+
+327
+00:29:19,560 --> 00:29:26,280
+اللي هو نفس خواص مين اللي هي الـ thermoplastic
+
+328
+00:29:26,280 --> 00:29:32,380
+واللي عندي elastomers اللي هو الـ اللي عندي نوع
+
+329
+00:29:32,380 --> 00:29:38,600
+منها it's elastic polymer طيب الآن نيجي نطلع على
+
+330
+00:29:38,600 --> 00:29:43,340
+هاي بنهانة circle the correct word to complete the
+
+331
+00:29:43,340 --> 00:29:48,380
+text a lot of rubber is made from latex الآن إيش
+
+332
+00:29:48,380 --> 00:29:54,050
+قلنا ال latex؟ أيوة هذا إيش؟ man-made ولا natural؟
+
+333
+00:29:54,050 --> 00:29:59,910
+أيوة natural polymers which comes from rubber
+
+334
+00:29:59,910 --> 00:30:03,890
+trees however not all rubbers come from trees,
+
+335
+00:30:04,070 --> 00:30:09,510
+synthetic rubber is man-made كلمة synthetic مصنعة
+
+336
+00:30:09,510 --> 00:30:15,400
+فهو لازم يجي تحت خانة إيش؟ ال man-made طيب polymers
+
+337
+00:30:15,400 --> 00:30:20,840
+with similar property to latex plastic also are
+
+338
+00:30:20,840 --> 00:30:24,840
+also polymers like rubber they consist of long
+
+339
+00:30:24,840 --> 00:30:30,880
+chains of إيش؟ atoms long chain of atoms بتكون ..
+
+340
+00:30:30,880 --> 00:30:36,900
+which form extremely large molecules طيب
+
+341
+00:30:41,700 --> 00:30:45,300
+read the extract describing a plastic panel
+
+342
+00:30:45,300 --> 00:30:50,620
+manufacturing process بس
+
+343
+00:30:50,620 --> 00:30:54,280
+خلال القراءة إيش بدنا نفهم؟ بدنا نفهم إيش اللي
+
+344
+00:30:54,280 --> 00:30:58,500
+موجود هنا by this stage of the process عند هذا
+
+345
+00:30:58,500 --> 00:31:05,280
+المرحلة من التصنيع the plastic is solid في هذه
+
+346
+00:31:05,280 --> 00:31:13,780
+المرحلة البلاستيك صلب و بارد
+
+347
+00:31:13,780 --> 00:31:18,440
+كامل يعني هو عادة البلاستيك ده السيح لو بيصيرش صلب
+
+348
+00:31:18,440 --> 00:31:24,640
+إلا يبقى بارد selected panels can now undergo
+
+349
+00:31:24,640 --> 00:31:30,040
+quality control testing الآن عادة في حاجة بنسميها
+
+350
+00:31:30,040 --> 00:31:33,200
+في عملية التصنيع quality control إيش ال quality
+
+351
+00:31:33,200 --> 00:31:34,020
+control؟
+
+352
+00:31:38,360 --> 00:31:43,620
+لأ عملية ضبط الجودة، إيش عملية ضبط الجودة؟ بياخدوا
+
+353
+00:31:43,620 --> 00:31:49,720
+عينات و بيفحصوهم، كويس؟ الآن إنت لما أمك تسوي كيكة
+
+354
+00:31:49,720 --> 00:31:55,460
+ولا تسوي أكلة جديدة، إيش بتقول؟ بتوزع على دويقة و
+
+355
+00:31:55,460 --> 00:32:00,420
+بتقولهم خدوا دوكم، مصبوط؟ ليش؟ بتقولهم إيش رأيكم
+
+356
+00:32:00,420 --> 00:32:08,630
+فيها؟ كويسة خلاص، مش كويسة نرميها على الفدر كويس
+
+357
+00:32:08,630 --> 00:32:13,190
+ففي التصنيع في عندي ال quality control testing فهد
+
+358
+00:32:13,190 --> 00:32:18,610
+بياخدوا عينات و بيفحصوها حد فيكوا شاف صبت بطون؟
+
+359
+00:32:18,610 --> 00:32:26,850
+إيش بيسووا في البيت ليفحصوا البطون؟ بياخدوا مكعبات،
+
+360
+00:32:26,850 --> 00:32:30,950
+المكعبات هذه بيودوها على مختبر زي مختبر الجامعة و
+
+361
+00:32:30,950 --> 00:32:34,910
+بيفحصهم للنوعية الplastic على فكرة عشان أنت
+
+362
+00:32:34,910 --> 00:32:37,830
+بتعرفوا البطون بس بتعرفوش في الplastic في عندنا
+
+363
+00:32:37,830 --> 00:32:41,610
+مختبر في الجامعة بيفحص عينات الplastic لإن في
+
+364
+00:32:41,610 --> 00:32:45,860
+عندنا في غزة مصانع بتصنع plastic بتصنع إيش؟
+
+365
+00:32:45,860 --> 00:32:50,100
+المواسير، بتصنع الكياس اللي بتشوفوهم البيض والصمر
+
+366
+00:32:50,100 --> 00:32:54,260
+و هذه الأنواع ف .. و بتصنع حاجات كثيرة، الآن هذا
+
+367
+00:32:54,260 --> 00:32:57,480
+المصانع المنتج تبعها بياخدوا عشان ده أنا بدي أشتري
+
+368
+00:32:57,480 --> 00:33:01,580
+عينات مثلا لمشروع هذه، باخد عينة و بوديها على
+
+369
+00:33:01,580 --> 00:33:04,660
+المختبر عندنا في الجامعة بفحصوا هذه العينات اللي
+
+370
+00:33:04,660 --> 00:33:09,080
+بلاستيكية و بيعطوا رأي هل هي طبق المواصفات ولا لأ
+
+371
+00:33:09,080 --> 00:33:13,460
+هذا بيسموه ال quality control عادة كل مصنع برا
+
+372
+00:33:13,460 --> 00:33:17,800
+عنده هذه الشغله automatically داخلية يعني مش عشان
+
+373
+00:33:17,800 --> 00:33:22,380
+بيبيع هو بيصنع هو بيصنع و بيفحص عنده و بيشوف إذا
+
+374
+00:33:22,380 --> 00:33:26,660
+هو حسب المواصفات بيطلع حبيها مش حسب المواصفات
+
+375
+00:33:26,660 --> 00:33:31,990
+بيطلع حاش برجعها عنده بيعيد تدويرها في هذا اللي
+
+376
+00:33:31,990 --> 00:33:36,070
+بنقصد فيه quality control testing to check **if** they
+
+377
+00:33:36,070 --> 00:33:39,410
+are strong enough to cope with tough conditions
+
+378
+00:33:39,410 --> 00:33:47,870
+strong enough إيش يعني جوي كافي to cope إيش cope
+
+379
+00:33:47,870 --> 00:33:59,500
+لا cube مكعب cope يعني يتأقلم with tough
+
+380
+00:33:59,500 --> 00:34:03,660
+conditions ايش tough conditions؟ الظروف الصعبة
+
+381
+00:34:03,660 --> 00:34:08,120
+الآن أنت لما تروحي على بلد و نقول can you cope with
+
+382
+00:34:08,120 --> 00:34:12,300
+this situation أو تمر عليكي ظروف صعبة مثلا لا سمح
+
+383
+00:34:12,300 --> 00:34:16,460
+الله حالة وفاة حالة مرض can they cope with this ..
+
+384
+00:34:16,460 --> 00:34:20,640
+الآن لو حد بده يعطيه منح دراسية من الشغلات اللي
+
+385
+00:34:20,640 --> 00:34:24,750
+بفحصوها والأسئلة بتنسأل بيجيها can ال candidate
+
+386
+00:34:24,750 --> 00:34:28,190
+cope with different environment بيئة مختلفة
+
+387
+00:34:28,190 --> 00:34:32,910
+culture different culture طقافة مختلفة إذا بيقدرش
+
+388
+00:34:32,910 --> 00:34:37,790
+بيطلعوش لازم تكون هذه القدرة موجودة فكلمة cope
+
+389
+00:34:37,790 --> 00:34:46,070
+يتأقلم كويس they will be exposed that they will be
+
+390
+00:34:46,070 --> 00:34:51,210
+exposed in news عادة الظروف الصعبة اللي هيبتعرضوا
+
+391
+00:34:51,210 --> 00:34:56,490
+إليها خلال الاستخدام exposed يتعرض إلى in use في
+
+392
+00:34:56,490 --> 00:35:01,390
+خلال الاستخدام tests include tensile testing ايش
+
+393
+00:35:01,390 --> 00:35:05,770
+tensile testing هايها موجودة where narrow length
+
+394
+00:35:05,770 --> 00:35:11,050
+of panels are subjected to high tension loads to
+
+395
+00:35:11,050 --> 00:35:16,370
+check if they do not stretch or fracture الآن ال
+
+396
+00:35:16,370 --> 00:35:21,170
+tension اللي هي الضغط فهي بيحطوا ضغط عالي عليها
+
+397
+00:35:21,170 --> 00:35:30,150
+وشوفوا هل هي stretch بتمغط أو fracture ايش بتنكسر
+
+398
+00:35:30,150 --> 00:35:37,510
+ال fracture .. ال fracture هذا انكسار stretch تمغط
+
+399
+00:35:37,510 --> 00:35:42,910
+لأن هذا فيه مشكلة إذا أنت بتحط عليها تمغط بتصير في
+
+400
+00:35:42,910 --> 00:35:44,570
+هذه الإشكالة
+
+401
+00:35:56,020 --> 00:35:59,660
+more tests are carried out to check the panels 
+
+402
+00:35:59,660 --> 00:36:05,760
+resistance to impact and scratching الآن في فحوصات
+
+403
+00:36:05,760 --> 00:36:08,380
+أخرى الآن السيارات خليني أقولكوا ايش بيعملوا فيه
+
+404
+00:36:08,380 --> 00:36:14,980
+هنا سيارة لما نيجي نفحصوها بيجي بفحصوها لما تصدم في
+
+405
+00:36:14,980 --> 00:36:18,880
+حيطة أو تصدم في حاجة، ايش بيحصل فيها؟ ال impact
+
+406
+00:36:18,880 --> 00:36:22,820
+على ال driver، قداش بيجي، اللي هو السواق، هل
+
+407
+00:36:22,820 --> 00:36:26,540
+السواق بتعرض يعني بيجي ب .. بسرعات معينة، اللي هي
+
+408
+00:36:26,540 --> 00:36:29,460
+السرعات التقليدية، بيجي بضربه، اللي هي، بشوفوا
+
+409
+00:36:29,460 --> 00:36:34,060
+قداش الجسم المقدمة أو السقف قداش مثلا لو بدي ..
+
+410
+00:36:34,440 --> 00:36:39,520
+المقدمة هي كده بتتطعش، بتصل لها ..يعني هل هي
+
+411
+00:36:39,520 --> 00:36:45,020
+الإنسان اللي قاعد و بتتطبق عليه ولا لأ؟ ما هو
+
+412
+00:36:45,020 --> 00:36:50,160
+هدول اللي حطوهم لزيادة الحماية، for safety reason
+
+413
+00:36:51,050 --> 00:36:55,530
+فانتهينا من الشغلات هذه بنسميها ال impact crash
+
+414
+00:36:55,530 --> 00:37:01,190
+لما انتهت هذه high impact crash لأن ضربة هذه
+
+415
+00:37:01,190 --> 00:37:04,970
+الصدمة ال impact تصادم، هذا ما حصل فيها فأول ما
+
+416
+00:37:04,970 --> 00:37:08,510
+بيجي بضربه هنا اللي هي ايش قولنا ال impact
+
+417
+00:37:08,510 --> 00:37:12,570
+resistance to impact اللي هي ضربة ال .. اللي هي و
+
+418
+00:37:12,570 --> 00:37:17,230
+scratching اللي ايش الخدش
+
+419
+00:37:19,070 --> 00:37:24,590
+الخدش أنت الحين بتشوف حاجات كتير اه اه اه هذي ضبط
+
+420
+00:37:24,590 --> 00:37:28,950
+الجودة بياخدوا سيارات جديدة ولات تجريب هذي بيجربوا
+
+421
+00:37:28,950 --> 00:37:32,650
+فيها وانت بتشوفي كل العملية لو بدك تتفرج عليها
+
+422
+00:37:32,650 --> 00:37:36,710
+بتشوفيها قبل ما تشتري أي حاجة لأن الناس اللي
+
+423
+00:37:36,710 --> 00:37:40,070
+بتطلعوا على ال safety بتطلعوا هذي السيارة هذي ايش
+
+424
+00:37:40,070 --> 00:37:43,250
+بتفرج عن التاني قداش سجلت هذه وقداش سجلت هذه
+
+425
+00:37:44,970 --> 00:37:48,050
+فتتطلع على كل هذه العمليات احنا عندنا بتاخد أي
+
+426
+00:37:48,050 --> 00:37:53,630
+حاجة حتى الخطرة بنشتريها بس في البلدان المتقدمة كل
+
+427
+00:37:53,630 --> 00:37:57,350
+شيء بتتطلع عليه أنت دافع فلوسك دافع بدك أفضل شيء
+
+428
+00:37:57,350 --> 00:38:03,730
+للفلوس اللي بتدفعيها طيب and product that fail the
+
+429
+00:38:03,730 --> 00:38:06,210
+test are returned to the beginning of the
+
+430
+00:38:06,210 --> 00:38:10,510
+production process الآن المنتجات اللي بتفشل في هذه
+
+431
+00:38:10,510 --> 00:38:16,940
+عملية الفحص بيرجعوها وين؟ لنقطة البداية melted down
+
+432
+00:38:16,940 --> 00:38:20,780
+and their material is reused يعني بيعملوها ايش؟
+
+433
+00:38:20,780 --> 00:38:26,320
+recycling بيسيحوها وبيعيدوا استخدامها واضحة هذه؟
+
+434
+00:38:26,320 --> 00:38:32,020
+ايش بنعني فيها؟ هذه مصطلح هندسي كامل الآن نجي نطلع
+
+435
+00:38:32,020 --> 00:38:36,360
+ايش الصح وايش الغلط هنا decide whether the
+
+436
+00:38:36,360 --> 00:38:39,320
+sentences below are true or false and correct the
+
+437
+00:38:39,320 --> 00:38:43,820
+false sentences the plastic was heated earlier in
+
+438
+00:38:43,820 --> 00:38:47,040
+the process يعني ال plastic اللي عندنا احنا ايش
+
+439
+00:38:47,040 --> 00:38:52,960
+قولنا هو الآن solid ايوة و cooled فهو أكيد اتسيح
+
+440
+00:38:52,960 --> 00:38:59,280
+قبل the plastic has now set هو الآن أخد الشكل
+
+441
+00:38:59,280 --> 00:39:05,540
+الخالق ف true the plastic is now liquid false ايش
+
+442
+00:39:05,540 --> 00:39:11,480
+هو الآن solid to pass one test the plastic must be
+
+443
+00:39:11,480 --> 00:39:15,840
+an elastomer
+
+444
+00:39:15,840 --> 00:39:24,860
+لأ false صح ايش elastomer؟ تمدد احنا هنا كنا نبحث
+
+445
+00:39:24,860 --> 00:39:31,020
+عنها عشان ما يتمددش مظبوط هنا ايش قولنا عنها does
+
+446
+00:39:31,020 --> 00:39:36,030
+not stretch مظبوط does not break and does not
+
+447
+00:39:36,030 --> 00:39:43,190
+stretch فهو غير قابل طيب the description suggest
+
+448
+00:39:43,190 --> 00:39:47,530
+the plastic is a type of engineering plastic true
+
+449
+00:39:47,530 --> 00:39:53,750
+هو thermoplastic لأن ايش صار له اللي فشل ايش عملنا
+
+450
+00:39:53,750 --> 00:40:00,430
+فيه عاد التدوير قلنا هذا go to reheated and reused
+
+451
+00:40:01,920 --> 00:40:08,200
+طيب the material is thermosetting plastic لسه
+
+452
+00:40:08,200 --> 00:40:13,680
+الحين جاوبنا عليه ايش هو false هو thermoplastic
+
+453
+00:40:13,680 --> 00:40:22,240
+the material is thermoplastic ايوة جابولكوا كل شيء
+
+454
+00:40:22,240 --> 00:40:24,800
+مال أجوبة ماله هذا مش
+
+455
+00:40:41,740 --> 00:40:45,820
+طيب complete the word الحين عندنا احنا puzzle طلع
+
+456
+00:40:45,820 --> 00:40:50,020
+على ال puzzle هايو جاييننا لاحقا شايفينه؟ بدنا
+
+457
+00:40:50,020 --> 00:40:53,740
+نعبي هذا بس الاصل في ال puzzle عشان نسوي وانتوا
+
+458
+00:40:53,740 --> 00:40:58,970
+كل حد فيكوا اشتغل عليه قبل؟ المتقاطعات عادة بيبقى
+
+459
+00:40:58,970 --> 00:41:03,630
+حاجة تبدأ فيها هادي الاصل هادي معبية وانت بتعبي
+
+460
+00:41:03,630 --> 00:41:07,450
+التاني عقبله بس احنا كمهندسين لساتنا beginners
+
+461
+00:41:07,450 --> 00:41:11,730
+يعني مش شاطرين في هذه الشغل اللي معبيها a shorter
+
+462
+00:41:11,730 --> 00:41:20,330
+name for polyvinyl chloride ايش هو؟ PVC PVC
+
+463
+00:41:20,330 --> 00:41:22,230
+PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC
+
+464
+00:41:22,230 --> 00:41:25,980
+PVC PVC PVC PVC PVC PVC PVC بيلو قدنا شاشة تانية
+
+465
+00:41:25,980 --> 00:41:31,420
+حطينا ازاي طيب used for forming melted plastic ال
+
+466
+00:41:31,420 --> 00:41:36,700
+mold إذا بتلاحظوا احنا ايش بنعمل بنشكل فيه الاشياء هي
+
+467
+00:41:36,700 --> 00:41:40,680
+مراجعة اللي احنا حكيناها هذه ال mold بنشكل فيه
+
+468
+00:41:40,680 --> 00:41:45,000
+الشكل الخارجي لل plastic a group of atoms
+
+469
+00:41:45,000 --> 00:41:52,580
+molecules a long chain of atoms polymer ايش اللي
+
+470
+00:41:52,580 --> 00:41:58,560
+polymer قولنا ايش عبارة عن a chain أو a huge chain
+
+471
+00:41:58,560 --> 00:42:03,760
+of atoms الآن ال group of atoms سمنها ال molecules
+
+472
+00:42:03,760 --> 00:42:08,380
+to sit permanently ايش قولنا هذا الكيور مش
+
+473
+00:42:08,380 --> 00:42:13,420
+حاكيناها هي الكيور اللي هي خلاص a very elastic
+
+474
+00:42:13,420 --> 00:42:19,780
+polymer elastomer a plastic that sits permanently
+
+475
+00:42:22,270 --> 00:42:27,410
+thermosets مظبوط thermoset أو thermostat a natural
+
+476
+00:42:27,410 --> 00:42:31,730
+polymer ايش هو؟ rubber بس هنا الكلمة اللي بندور
+
+477
+00:42:31,730 --> 00:42:40,870
+عليها تدخل في الحجم ايش؟ rubber ولا latex rubber
+
+478
+00:42:40,870 --> 00:42:47,730
+هذه طب not natural في
+
+479
+00:42:47,730 --> 00:42:50,990
+ال synthetic بس اللي بندور عليه ايش؟ man-made
+
+480
+00:42:53,620 --> 00:42:58,900
+particles that form molecules .. atoms another
+
+481
+00:42:58,900 --> 00:43:07,140
+word for not natural .. synthetic طيب material
+
+482
+00:43:07,140 --> 00:43:14,580
+used to make rubber .. latex الآن هيك .. بيصير
+
+483
+00:43:14,580 --> 00:43:15,080
+عندكم
+
+484
+00:43:17,650 --> 00:43:21,510
+ما أيوة؟ هيك بيصير عندكم كل المصطلحات اللي بدكم
+
+485
+00:43:21,510 --> 00:43:29,610
+تعرفوها عن ال plastic كويسين هيك؟ قلتوا أي أسئلة؟
+
+486
+00:43:29,610 --> 00:43:30,970
+طيب بنشوف كل مرة 
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/1d3CViIAlTw_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/1d3CViIAlTw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..69f99467b58da6770e8b78c95f30001711f2cc1c
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/1d3CViIAlTw_raw.json
@@ -0,0 +1 @@
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معناته هذا topic is out of the question كويس؟ فهذه الفكرة الموجودة عندنا الكويس سؤال عليها", "tokens": [5172, 44510, 7578, 28242, 4386, 4724, 16254, 8592, 11331, 3215, 7251, 37983, 2288, 2423, 4829, 2423, 7649, 8032, 3215, 12610, 3660, 8032, 5016, 9566, 16095, 20666, 10721, 3794, 23328, 2423, 8378, 13672, 1829, 483, 8209, 8032, 1829, 9381, 13546, 14407, 20666, 1211, 11536, 16247, 5016, 29973, 44650, 7578, 3714, 2407, 36520, 14407, 13672, 11536, 16247, 5016, 29973, 16490, 1211, 33546, 20449, 8315, 47395, 23758, 4829, 307, 484, 295, 264, 1168, 9122, 45865, 3794, 22807, 6156, 3224, 24192, 27188, 4117, 25720, 9673, 29245, 23328, 3660, 43242, 8315, 33251, 45865, 3794, 8608, 33604, 6027, 25894, 11296], "avg_logprob": -0.17779605263157894, "compression_ratio": 1.6681818181818182, "no_speech_prob": 0.0, "words": [{"start": 153.39, "end": 154.07, "word": "فبدى", "probability": 0.6376139322916666}, {"start": 154.07, "end": 154.27, "word": " كل", "probability": 0.3720703125}, {"start": 154.27, 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"text": "و بعدين إيش بنحطه في أوعية لنشكل تعمل الشكل تبعه الأوعية هذه العملية الأوعية بنسميها إيش molds الأوعية اللي بنحط فيها ال plastic السائح أو السائل قوالب containers قوالب ال molds هي الشكل للأوعية هذه", "tokens": [2407, 39182, 9957, 11933, 1829, 8592, 44945, 5016, 9566, 3224, 8978, 34051, 3615, 10632, 5296, 1863, 8592, 28820, 6055, 25957, 1211, 25124, 28820, 6055, 3555, 3615, 3224, 16247, 45367, 10632, 29538, 18863, 42213, 10632, 16247, 45367, 10632, 44945, 38251, 1829, 11296, 11933, 1829, 8592, 48257, 16247, 45367, 10632, 13672, 1829, 44945, 5016, 9566, 8978, 11296, 2423, 5900, 21136, 16373, 5016, 34051, 21136, 16373, 1211, 12174, 2407, 6027, 3555, 17089, 12174, 2407, 6027, 3555, 2423, 48257, 39896, 25124, 28820, 24976, 10721, 45367, 10632, 29538], "avg_logprob": -0.16313244118576958, "compression_ratio": 1.947674418604651, "no_speech_prob": 0.0, "words": [{"start": 887.59, "end": 887.79, "word": "و", "probability": 0.72998046875}, {"start": 887.79, "end": 888.39, "word": " 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الأن نجي نطلع إيش الصح وإيش الغلط هنا decide whether the sentences below are true or false and correct the false sentences", "tokens": [1211, 1863, 47432, 3660, 29739, 28259, 10632, 19057, 760, 293, 641, 2527, 307, 319, 4717, 37495, 22653, 4724, 1829, 25957, 1211, 2407, 11296, 11933, 1829, 8592, 22807, 23363, 4724, 1829, 3794, 1829, 5016, 2407, 11296, 4032, 4724, 1829, 3615, 25708, 14407, 44713, 9778, 3215, 10943, 11296, 4032, 46958, 5016, 3660, 29538, 22807, 11933, 1829, 8592, 44945, 3615, 22653, 8978, 11296, 22807, 29538, 3714, 9381, 9566, 1211, 5016, 8032, 41260, 3794, 1829, 9122, 10943, 1211, 16247, 1863, 8717, 7435, 1829, 8717, 9566, 1211, 3615, 11933, 1829, 8592, 31767, 5016, 4032, 28814, 1829, 8592, 6024, 118, 1211, 9566, 34105, 4536, 1968, 264, 16579, 2507, 366, 2074, 420, 7908, 293, 3006, 264, 7908, 16579], "avg_logprob": -0.1905691899093134, "compression_ratio": 1.588235294117647, "no_speech_prob": 0.0, "words": [{"start": 2294.2999999999997, "end": 2295.22, "word": "لنقطة", 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هذه الشغل اللي معبيها a shorter name for polyvinyl chloride ايش هو? بي بي سي بي بي سي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي", "tokens": [45340, 2655, 4587, 41193, 3615, 9307, 6225, 18513, 3660, 4724, 1829, 3555, 4587, 7578, 11331, 26108, 3660, 6055, 44510, 10721, 8978, 11296, 8032, 995, 16254, 2423, 33546, 1211, 8032, 995, 16254, 20449, 21292, 3224, 4032, 7649, 2655, 39894, 3615, 21292, 16712, 7649, 1829, 6225, 4587, 36150, 3224, 4724, 3794, 1975, 5016, 8315, 9122, 2304, 3224, 41260, 3794, 9957, 5296, 3794, 9307, 8315, 26992, 37495, 22653, 37893, 13412, 41193, 2288, 9957, 8978, 29538, 25124, 17082, 1211, 13672, 1829, 20449, 21292, 11296, 257, 11639, 1315, 337, 6754, 85, 22946, 35434, 1975, 1829, 8592, 31439, 30, 4724, 1829, 4724, 1829, 8608, 1829, 4724, 1829, 4724, 1829, 8608, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 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used for forming melted plastic ال mold اذا بتلاحظوا احنا ايش بنعمل بنشكل فيه الاش هي مراجعة اللي احنا حكيناها هذه ال mold بنشكل فيه الشكل الخارجي لل plastic a group of atoms molecules a long chain of atoms", "tokens": [1211, 2407, 12174, 3215, 8315, 13412, 33599, 3660, 6055, 7649, 10632, 11331, 9566, 1829, 8315, 1975, 11622, 47302, 23032, 1829, 3555, 1143, 337, 15745, 19057, 5900, 2423, 11102, 1975, 15730, 39894, 15040, 5016, 19913, 14407, 1975, 5016, 8315, 1975, 1829, 8592, 44945, 25957, 1211, 44945, 8592, 28820, 8978, 3224, 2423, 33599, 39896, 3714, 2288, 26108, 27884, 13672, 1829, 1975, 5016, 8315, 11331, 4117, 1829, 8315, 11296, 29538, 2423, 11102, 44945, 8592, 28820, 8978, 3224, 25124, 28820, 33962, 9640, 7435, 1829, 24976, 5900, 257, 1594, 295, 16871, 8015, 68, 11570, 257, 938, 5021, 295, 16871], "avg_logprob": -0.24095395458372015, "compression_ratio": 1.669811320754717, "no_speech_prob": 0.0, "words": [{"start": 2484.54, "end": 2484.98, "word": "لو", "probability": 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هذا الكيور مش حاكيناها هي الكيور اللي هي خلاص a very elastic polymer elastomer a plastic that sits permanently", "tokens": [12892, 88, 936, 11933, 1829, 8592, 13672, 1829, 20073, 12174, 12610, 8315, 11933, 1829, 8592, 6225, 3555, 9640, 3660, 18871, 257, 5021, 1975, 2407, 257, 2603, 5021, 295, 16871, 6024, 48506, 2423, 1594, 295, 16871, 8608, 27842, 11296, 2423, 13093, 281, 1394, 24042, 11933, 1829, 8592, 12174, 12610, 8315, 23758, 33251, 1829, 13063, 37893, 11331, 995, 4117, 1829, 8315, 11296, 39896, 33251, 1829, 13063, 13672, 1829, 39896, 16490, 1211, 33546, 257, 588, 17115, 20073, 806, 525, 14301, 257, 5900, 300, 12696, 24042], "avg_logprob": -0.2597891444183258, "compression_ratio": 1.6748768472906403, "no_speech_prob": 0.0, "words": [{"start": 2511.22, "end": 2511.98, "word": "polymer", "probability": 0.7105305989583334}, {"start": 2511.98, "end": 2512.42, "word": " إيش", "probability": 0.6853841145833334}, {"start": 2512.42, "end": 2512.58, "word": " اللي", "probability": 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rubber و لا latex rubber هذه طب not natural في ال synthetic بس اللي بندور عليه ايش؟ man-made", "tokens": [616, 3415, 1385, 3714, 19913, 3555, 2407, 9566, 8810, 329, 302, 1975, 2407, 8810, 39036, 257, 3303, 20073, 1975, 1829, 8592, 31439, 22807, 11593, 4724, 3794, 34105, 33251, 19528, 3660, 13672, 1829, 44945, 3215, 13063, 25894, 11296, 6055, 3215, 9778, 1211, 8978, 21542, 7435, 2304, 1975, 1829, 8592, 22807, 11593, 4032, 20193, 3469, 87, 11593, 29538, 23032, 3555, 406, 3303, 8978, 2423, 23420, 4724, 3794, 13672, 1829, 44945, 3215, 13063, 47356, 1975, 1829, 8592, 22807, 587, 12, 10341], "avg_logprob": -0.22567247099514248, "compression_ratio": 1.6304347826086956, "no_speech_prob": 0.0, "words": [{"start": 2542.27, "end": 2543.19, "word": "thermosets", "probability": 0.6502278645833334}, {"start": 2543.19, "end": 2544.11, "word": " مظبوط", "probability": 0.8763671875}, {"start": 2544.11, "end": 2545.07, "word": " thermoset", "probability": 0.532470703125}, {"start": 2545.07, "end": 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2551.37, "end": 2551.73, "word": " بندور", "probability": 0.8797200520833334}, {"start": 2551.73, "end": 2552.07, "word": " عليها", "probability": 0.961669921875}, {"start": 2552.07, "end": 2552.47, "word": " تدخل", "probability": 0.99072265625}, {"start": 2552.47, "end": 2552.93, "word": " في", "probability": 0.890625}, {"start": 2552.93, "end": 2553.37, "word": " الحجم", "probability": 0.9830729166666666}, {"start": 2553.37, "end": 2555.13, "word": " ايش؟", "probability": 0.8009033203125}, {"start": 2555.13, "end": 2557.37, "word": " rubber", "probability": 0.81494140625}, {"start": 2557.37, "end": 2557.61, "word": " و", "probability": 0.3046875}, {"start": 2557.61, "end": 2557.75, "word": " لا", "probability": 0.88818359375}, {"start": 2557.75, "end": 2558.87, "word": " latex", "probability": 0.85546875}, {"start": 2558.87, "end": 2560.87, "word": " rubber", "probability": 0.461181640625}, {"start": 2560.87, "end": 2562.35, "word": " هذه", "probability": 0.443359375}, {"start": 2562.35, "end": 2562.99, "word": " طب", "probability": 0.826904296875}, {"start": 2562.99, "end": 2563.27, "word": " not", "probability": 0.93310546875}, {"start": 2563.27, "end": 2564.05, "word": " natural", "probability": 0.91455078125}, {"start": 2564.05, "end": 2567.73, "word": " في", "probability": 0.8427734375}, {"start": 2567.73, "end": 2567.89, "word": " ال", "probability": 0.67138671875}, {"start": 2567.89, "end": 2568.33, "word": " synthetic", "probability": 0.75341796875}, {"start": 2568.33, "end": 2568.67, "word": " بس", "probability": 0.9541015625}, {"start": 2568.67, "end": 2568.77, "word": " اللي", "probability": 0.986572265625}, {"start": 2568.77, "end": 2569.13, "word": " بندور", "probability": 0.9189453125}, {"start": 2569.13, "end": 2569.41, "word": " عليه", "probability": 0.96875}, {"start": 2569.41, "end": 2570.15, "word": " ايش؟", "probability": 0.8154296875}, {"start": 2570.15, "end": 2570.51, "word": " man", "probability": 0.56494140625}, {"start": 2570.51, "end": 2570.99, "word": "-made", "probability": 0.77294921875}], "temperature": 1.0}, {"id": 101, "seek": 259508, "start": 2573.62, "end": 2595.08, "text": "particles that form molecules .. atoms another word for not natural .. synthetic طيب material used to make rubber .. latex الان هيك .. بيصير عندكم", "tokens": [6971, 5350, 300, 1254, 13093, 4386, 16871, 1071, 1349, 337, 406, 3303, 4386, 23420, 23032, 1829, 3555, 2527, 1143, 281, 652, 11593, 4386, 3469, 87, 2423, 7649, 39896, 4117, 4386, 4724, 1829, 9381, 13546, 43242, 24793], "avg_logprob": -0.30384289896166, "compression_ratio": 1.1942446043165467, "no_speech_prob": 0.0, "words": [{"start": 2573.62, "end": 2574.44, "word": "particles", "probability": 0.80322265625}, {"start": 2574.44, "end": 2574.82, "word": " that", "probability": 0.92578125}, {"start": 2574.82, "end": 2575.32, "word": " form", "probability": 0.8310546875}, {"start": 2575.32, "end": 2576.42, "word": " molecules", "probability": 0.83251953125}, {"start": 2576.42, "end": 2577.22, "word": " ..", "probability": 0.12408447265625}, {"start": 2577.22, "end": 2578.0, "word": " atoms", "probability": 0.7333984375}, {"start": 2578.0, "end": 2578.9, "word": " another", "probability": 0.5126953125}, {"start": 2578.9, "end": 2579.42, "word": " word", "probability": 0.97412109375}, {"start": 2579.42, "end": 2579.7, "word": " for", "probability": 0.96435546875}, {"start": 2579.7, "end": 2580.02, "word": " not", "probability": 0.84130859375}, {"start": 2580.02, "end": 2580.8, "word": " natural", "probability": 0.88720703125}, {"start": 2580.8, "end": 2582.92, "word": " ..", "probability": 0.47509765625}, {"start": 2582.92, "end": 2584.14, "word": " synthetic", "probability": 0.50146484375}, {"start": 2584.14, "end": 2585.76, "word": " طيب", "probability": 0.8318684895833334}, {"start": 2585.76, "end": 2587.14, "word": " material", "probability": 0.587890625}, {"start": 2587.14, "end": 2587.66, "word": " used", "probability": 0.9189453125}, {"start": 2587.66, "end": 2587.88, "word": " to", "probability": 0.982421875}, {"start": 2587.88, "end": 2588.14, "word": " make", "probability": 0.95166015625}, {"start": 2588.14, "end": 2588.62, "word": " rubber", "probability": 0.935546875}, {"start": 2588.62, "end": 2589.68, "word": " ..", "probability": 0.6884765625}, {"start": 2589.68, "end": 2590.62, "word": " latex", "probability": 0.9306640625}, {"start": 2590.62, "end": 2592.4, "word": " الان", "probability": 0.57220458984375}, {"start": 2592.4, "end": 2592.92, "word": " هيك", "probability": 0.9296875}, {"start": 2592.92, "end": 2593.14, "word": " ..", "probability": 0.424072265625}, {"start": 2593.14, "end": 2594.58, "word": " بيصير", "probability": 0.92724609375}, {"start": 2594.58, "end": 2595.08, "word": " عندكم", "probability": 0.963623046875}], "temperature": 1.0}, {"id": 102, "seek": 261096, "start": 2597.65, "end": 2610.97, "text": "ما أيوة؟ هيك بيصير عندكم كل المصطلحات اللي بدكم تعرفوها عن ال plastic كويسين هيك؟ قلتوا أي أسئلة؟ طيب بنشوف كل مرة", "tokens": [15042, 36632, 2407, 3660, 22807, 39896, 4117, 4724, 1829, 9381, 13546, 43242, 24793, 28242, 9673, 9381, 9566, 1211, 5016, 9307, 13672, 1829, 47525, 24793, 37279, 28480, 2407, 11296, 18871, 2423, 5900, 9122, 45865, 3794, 9957, 39896, 4117, 22807, 12174, 1211, 2655, 14407, 36632, 5551, 3794, 19986, 37977, 22807, 23032, 1829, 3555, 44945, 8592, 38688, 28242, 3714, 25720], "avg_logprob": -0.20622306445549274, "compression_ratio": 1.3793103448275863, "no_speech_prob": 4.827976226806641e-06, "words": [{"start": 2597.65, "end": 2597.83, "word": "ما", "probability": 0.5322265625}, {"start": 2597.83, "end": 2598.87, "word": " أيوة؟", "probability": 0.544036865234375}, {"start": 2598.87, "end": 2599.17, "word": " هيك", "probability": 0.7578125}, {"start": 2599.17, "end": 2599.53, "word": " بيصير", "probability": 0.9337158203125}, {"start": 2599.53, "end": 2599.93, "word": " عندكم", "probability": 0.98291015625}, {"start": 2599.93, "end": 2600.33, "word": " كل", "probability": 0.9814453125}, {"start": 2600.33, "end": 2601.15, "word": " المصطلحات", "probability": 0.9908040364583334}, {"start": 2601.15, "end": 2601.29, "word": " اللي", "probability": 0.872802734375}, {"start": 2601.29, "end": 2601.51, "word": " بدكم", "probability": 0.749755859375}, {"start": 2601.51, "end": 2602.23, "word": " تعرفوها", "probability": 0.9796142578125}, {"start": 2602.23, "end": 2602.99, "word": " عن", "probability": 0.994140625}, {"start": 2602.99, "end": 2603.51, "word": " ال", "probability": 0.951171875}, {"start": 2603.51, "end": 2604.19, "word": " plastic", "probability": 0.81787109375}, {"start": 2604.19, "end": 2605.71, "word": " كويسين", "probability": 0.9100341796875}, {"start": 2605.71, "end": 2607.75, "word": " هيك؟", "probability": 0.9690755208333334}, {"start": 2607.75, "end": 2608.25, "word": " قلتوا", "probability": 0.646026611328125}, {"start": 2608.25, "end": 2608.33, "word": " أي", "probability": 0.697265625}, {"start": 2608.33, "end": 2609.61, "word": " أسئلة؟", "probability": 0.92802734375}, {"start": 2609.61, "end": 2610.09, "word": " طيب", "probability": 0.943359375}, {"start": 2610.09, "end": 2610.49, "word": " بنشوف", "probability": 0.9298502604166666}, {"start": 2610.49, "end": 2610.69, "word": " كل", "probability": 0.45263671875}, {"start": 2610.69, "end": 2610.97, "word": " مرة", "probability": 0.991455078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2611.1768125, "duration_after_vad": 2494.3806249999884}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/2C3Q0vXI7i0.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/2C3Q0vXI7i0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..42cd6d45e92401c6646c81fae5e5583383e80802
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/2C3Q0vXI7i0.srt
@@ -0,0 +1,1871 @@
+1
+00:00:20,750 --> 00:00:27,370
+السلام عليكم اليوم سنتحدث في الحلقة السادسة حول
+
+2
+00:00:27,370 --> 00:00:34,710
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة
+
+3
+00:00:34,710 --> 00:00:36,590
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة
+
+4
+00:00:36,590 --> 00:00:42,350
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة
+
+5
+00:00:42,350 --> 00:00:46,030
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة
+
+6
+00:00:46,030 --> 00:00:48,230
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة
+
+7
+00:00:48,230 --> 00:00:48,270
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة
+
+8
+00:00:48,270 --> 00:00:48,290
+الخرسانة الخرسانة الخرسانة الخرسانة الخرسانة الخر
+
+9
+00:00:48,820 --> 00:00:53,220
+ثلاثة أنواع من مكونات ال .. ال concrete three
+
+10
+00:00:53,220 --> 00:00:57,780
+elements of concrete  نحن نسميها cement, sand,
+
+11
+00:00:58,140 --> 00:01:02,000
+fine aggregate, coarse aggregate  نسميها gravel
+
+12
+00:01:02,000 --> 00:01:06,960
+أو .. or coarse aggregate هذا ال technical term
+
+13
+00:01:06,960 --> 00:01:15,300
+coarse aggregate المصطلح العام اللي هي gravel اللي 
+
+14
+00:01:15,300 --> 00:01:21,070
+هو حصى كويس، الآن ال fine aggregate اللي هو إيش؟
+
+15
+00:01:21,070 --> 00:01:25,610
+اللي هي الحصى الناعم، في .. أيوة، في بلادنا مثلاً 
+
+16
+00:01:25,610 --> 00:01:30,630
+احنا عندنا موجود رمل، في بلاد ثانية بيستخدموا إيش؟
+
+17
+00:01:30,630 --> 00:01:35,290
+الحصى المطحونة عشان هي كان بي .. اه بس في بلاد
+
+18
+00:01:35,290 --> 00:01:39,110
+ثانية يعني المناطق الجبلية ما فيش فيها رمال زي
+
+19
+00:01:39,110 --> 00:01:44,010
+عندنا فإيش بيستخدموا لما ييجوا يطحنوا الحصى أو 
+
+20
+00:01:44,010 --> 00:01:48,090
+يعملوا الحصى بيضل عندهم حاجة مطحونة هذه رمال زي
+
+21
+00:01:48,090 --> 00:01:51,910
+حصى مطحون فهو عشان هي كان الإسم fine aggregate
+
+22
+00:01:51,910 --> 00:02:00,530
+اللي هي حصى دقيقة أو صغيرة concrete mix design
+
+23
+00:02:00,530 --> 00:02:04,250
+cement is a key material in construction زي ما 
+
+24
+00:02:04,250 --> 00:02:09,090
+بتعرفوا يمكن هذا في غزة احنا له وضع خاص بدون cement
+
+25
+00:02:09,090 --> 00:02:15,310
+فش صناعة فش حياة كل شيء بيتوقف مظبوط مش بس احنا
+
+26
+00:02:15,310 --> 00:02:20,310
+بتتكلم على صناعة اللي هي ال construction
+
+27
+00:02:20,310 --> 00:02:27,270
+industrial بتتكلم على everyday aspect of life it
+
+28
+00:02:27,270 --> 00:02:33,410
+consists of very fine powder اللي هو مصحوق يعني
+
+29
+00:02:33,410 --> 00:02:37,890
+دقيق أو ناعم when water is added to cement a
+
+30
+00:02:37,890 --> 00:02:42,230
+chemical reaction occurs and the cement begins to 
+
+31
+00:02:42,230 --> 00:02:46,730
+sets اللي قال لما نحط المي على ال cement إيش
+
+32
+00:02:46,730 --> 00:02:51,790
+بيحصل؟ بيصير تفاعل كيميائي و ال cement بيبدأ يجمد
+
+33
+00:02:52,660 --> 00:02:57,180
+يجمد set اللي هي إيش هذه معناها it start to become
+
+34
+00:02:57,180 --> 00:03:04,960
+solid يعني بتجمد وهذه بتلاحظوها مظبوط يعني لو
+
+35
+00:03:04,960 --> 00:03:10,240
+حاطيته ميه ع سمنت بيصير السمنت زي الحجار بس ينشف
+
+36
+00:03:10,240 --> 00:03:13,340
+يعني بس هو بيبدأ ال reaction بيبدأ على طول و بيبدأ
+
+37
+00:03:13,340 --> 00:03:14,800
+شوية شوية ينشف
+
+38
+00:03:19,740 --> 00:03:26,260
+أكثر أشياء شائعة من الحاجات المشتقات للسمنت هي
+
+39
+00:03:26,260 --> 00:03:42,600
+الخرسانة التي تتكون من سمنت ورمل وحصى
+
+40
+00:03:42,600 --> 00:03:49,740
+ومياه after concrete has set يعني لما تتجمد it
+
+41
+00:03:49,740 --> 00:03:53,600
+needs time to reach its structural strength الـ
+
+42
+00:03:53,600 --> 00:03:57,200
+structural ليه؟ strength اللي هي قوة تبعته
+
+43
+00:03:57,200 --> 00:04:02,420
+الإنشائية الحديد بيحتاج لفترة أو الخرسانة بتحتاج
+
+44
+00:04:02,420 --> 00:04:06,480
+لفترة لتصل للقوة الإنشائية يعني لو جيت الخرسانة
+
+45
+00:04:06,480 --> 00:04:12,200
+صبّيتها ونشفت وفكيت عنها إيش بيصير عليها؟ توقع على
+
+46
+00:04:12,200 --> 00:04:17,710
+طول لازم تأخذ إيش؟أيوة في هذه الإلهان الـ strength
+
+47
+00:04:17,710 --> 00:04:21,110
+needed to perform effectively, generally engineers
+
+48
+00:04:21,110 --> 00:04:25,030
+consider that this strength is reached after 28
+
+49
+00:04:25,030 --> 00:04:33,190
+days, a point called 28 day strength 28 إلهان عادة
+
+50
+00:04:33,190 --> 00:04:39,470
+في بلادنا سبعة أيام لأ مش سبعة بس خد من السابعة
+
+51
+00:04:39,470 --> 00:04:44,290
+لحاجة structure خفيف يعني لعمود حاجة زي هيك لما
+
+52
+00:04:44,290 --> 00:04:59,590
+بدك توصل لسقف قداش مدي يقعد يا أهل المدني العين
+
+53
+00:04:59,590 --> 00:05:05,470
+صغيرة بس لما تيجي تطلع على السطح بياخد حد أدنى من
+
+54
+00:05:05,470 --> 00:05:10,810
+عشر أيام لخمسة عشر يوم، هذا .. هذا مش مدني، بس 
+
+55
+00:05:10,810 --> 00:05:15,970
+الحياة بتعلم زيك، فأنت لو شيلتيه أقل من هيك بيصير
+
+56
+00:05:15,970 --> 00:05:21,390
+تشققات، لأنه هذا heavy، فهذا اللي .. اللي بيحصل فيه
+
+57
+00:05:22,020 --> 00:05:28,840
+Okay فهي المعروف عنده دولياً 28 days هذا للـ
+
+58
+00:05:28,840 --> 00:05:32,920
+typical cement طبعاً في cement أسرع من الثاني بنشفه
+
+59
+00:05:32,920 --> 00:05:34,680
+وهذه أنواع مختلفة
+
+60
+00:05:36,820 --> 00:05:40,040
+concrete mix design concrete mix mix design which
+
+61
+00:05:40,040 --> 00:05:44,280
+is specified by engineers state the proportions of
+
+62
+00:05:44,280 --> 00:05:47,620
+cement fine aggregate and coarse aggregate to be
+
+63
+00:05:47,620 --> 00:05:51,360
+used for specific structures زي ما بتعرف في نسب
+
+64
+00:05:51,360 --> 00:05:56,660
+معينة لها أنتو بتبعين البطون إيش أنواع البطون
+
+65
+00:05:56,660 --> 00:06:03,960
+فاطلنا نعرف فيه قوات في غزة المشهور في عندنا 200
+
+66
+00:06:05,000 --> 00:06:10,580
+هذا بيسموه لأنه ضعيفة .. هذا قبل الصبة ما يبدو يبدو
+
+67
+00:06:10,580 --> 00:06:16,100
+بيحطوا هذه الشغلة، هذه حاجة ضعيفة، نسبة ال cement
+
+68
+00:06:16,100 --> 00:06:23,500
+فيه أقل، في 250 اللي هذا بيستخدموه لل .. مش العمدان
+
+69
+00:06:23,500 --> 00:06:28,100
+بيستخدموه لصبّ السطح أحياناً و أحياناً بيستخدموه
+
+70
+00:06:28,100 --> 00:06:32,800
+للعمدان الأفقية هذه إيش بيسموهم؟ الحزامات ..
+
+71
+00:06:32,800 --> 00:06:37,320
+الحزامات الأرضية بيستخدموهم 250 في 300 هذه أقوى
+
+72
+00:06:37,320 --> 00:06:41,680
+الأنواع الموجودة عندنا في غزة هذا للعمدان و الناس
+
+73
+00:06:41,680 --> 00:06:45,700
+اللي بتعزّ السطح بتستخدم ال 300 منهم بس هذا أقوى
+
+74
+00:06:45,700 --> 00:06:51,650
+إيش موجود اللي هي ال 300 قوته 300 بيسموه طَب الآن
+
+75
+00:06:51,650 --> 00:06:57,470
+for example one two four mix consists of one part
+
+76
+00:06:57,470 --> 00:07:01,370
+cement two parts fine aggregate and four parts
+
+77
+00:07:01,370 --> 00:07:05,650
+coarse aggregate فهي النسب هاي بيحطوها قداش هي
+
+78
+00:07:05,650 --> 00:07:12,090
+بتحدد ال strength level لال concrete كويس for
+
+79
+00:07:12,090 --> 00:07:15,450
+mixing precise quantity a quantity known as
+
+80
+00:07:15,450 --> 00:07:19,690
+batching الآن ال batch اللي هي إيش الخلطة
+
+81
+00:07:21,300 --> 00:07:26,620
+أو العجينة لما بدك تسويها حاجة حاجة فيه الآن زمان
+
+82
+00:07:26,620 --> 00:07:30,620
+يمكن قبل عصر المصانع الباطون إيش كانوا يسووا؟
+
+83
+00:07:30,620 --> 00:07:35,200
+كانوا يخلطوا يدوياً على الأرض، كانوا بيعدوا كام
+
+84
+00:07:35,200 --> 00:07:40,380
+جدالة من هذه النسب بالظبط بيعدوها، الآن إيه بهذه
+
+85
+00:07:40,380 --> 00:07:47,500
+إيش؟ أنه مش دقيقة و اللي بعد بنس أحياناً ما بتلاقي
+
+86
+00:07:47,500 --> 00:07:51,460
+إيش يعني أنت جرب بحالك بتعدّي أي حاجة شوفوا كدهش
+
+87
+00:07:51,460 --> 00:07:58,320
+تركز فيها ف .. فهي ال batch اللي هي الخلطة أو
+
+88
+00:07:58,320 --> 00:08:02,060
+العجينة فهذه اللي بنسميها batching و proportions
+
+89
+00:08:02,060 --> 00:08:07,280
+are measured by weight و عادة ال measurement بتصير
+
+90
+00:08:07,280 --> 00:08:13,720
+بال .. إيش؟ بالوزن القليجي نتطلع لحاجة معينة تصوري
+
+91
+00:08:13,720 --> 00:08:18,760
+عندك مصنع باطون مصنع الباطون إيش بيعمل؟ بدخل كميات
+
+92
+00:08:18,760 --> 00:08:24,180
+السمنت بدي وزنه بشكل دقيق مظبوط الرمل الغيرة لهذه
+
+93
+00:08:24,180 --> 00:08:28,460
+الشغلات لو الأوزان هذه ما كانتش دقيقة إيش بيحصل؟
+
+94
+00:08:28,460 --> 00:08:33,630
+يعني لو حط سمنت بالزيادة إيش بيحصل للمصنع؟ هو بيخسر
+
+95
+00:08:33,630 --> 00:08:39,070
+مصاري مش ماتبتبسك و لو حط رمل بالزيادة الزبون
+
+96
+00:08:39,070 --> 00:08:42,850
+بيزعل لأن الزبون مش هيرضى هيقول ان الباطون الأجيالي
+
+97
+00:08:42,850 --> 00:08:48,450
+ضعيف فهو ال .. ال .. عملية الوزن هذه بتكون دقيقة،
+
+98
+00:08:48,450 --> 00:08:53,890
+الآن كيف بيوزنوا هدول؟ الآن هو بيعيّر، الآن بيديه
+
+99
+00:08:53,890 --> 00:08:58,370
+.. في عنده إيش زي ال cement موجود في الصوبة بيسموه 
+
+100
+00:08:58,370 --> 00:08:59,290
+shalow
+
+101
+00:09:02,350 --> 00:09:05,610
+الصوبة الكبيرة بيعبوا الـ cement فالـ cement بيجي
+
+102
+00:09:05,610 --> 00:09:14,390
+للمصانع كيس بيجي زي .. كوب بيبقى موجود و بيحطوها
+
+103
+00:09:14,390 --> 00:09:19,490
+هناك، الآن هذه بتيجي حسب الفتحة بفتح فيه هناك عنده
+
+104
+00:09:19,490 --> 00:09:25,650
+زي شيء بفتح بوابة بتفتح و بتسكر الهن هو بدي عاير
+
+105
+00:09:25,650 --> 00:09:31,610
+الأصل الأتمة بتصير معايرة هذه الفتحة قداش بتطلع
+
+106
+00:09:31,610 --> 00:09:35,970
+بالثانية قداش الوزن اللي بتطلع و قداش حجم الفتحة
+
+107
+00:09:35,970 --> 00:09:40,690
+لازم يكون عشان هيك الأن هذه طبعاً في العلم تبعنا
+
+108
+00:09:40,690 --> 00:09:44,110
+بدخل الكهربا هنانتوا هناك بدأنا في علم الإيش
+
+109
+00:09:44,110 --> 00:09:48,130
+الهندسة المدنية الآن علم الكهربا علم الكهربا إيش
+
+110
+00:09:48,130 --> 00:09:52,070
+بيسوي بنظم الفتحات و بيجيس بحيث أن يكون ال error
+
+111
+00:09:52,070 --> 00:09:56,330
+أقل شيء ممكن يعني الفتحة اللي بدها تيجي فتحت
+
+112
+00:09:56,330 --> 00:10:00,970
+لهالقد بتنزل هالقد وزن الآن هذه عادة بتكاشي توزن
+
+113
+00:10:00,970 --> 00:10:04,910
+أكثر من اللازم و بتكاشي توزن أقل فبتصير فتحة كبيرة
+
+114
+00:10:04,910 --> 00:10:09,850
+بعدها فتحات صغيرة اللي بتنظم بحيث يصل إن الكمية
+
+115
+00:10:09,850 --> 00:10:13,680
+اللي بدك إياها تدخل نفس الشيء بنعملها للتنيات الحين
+
+116
+00:10:13,680 --> 00:10:18,240
+الماء سهلة جداً ليش؟ لأنه في متر عليها ده أسهل
+
+117
+00:10:18,240 --> 00:10:24,300
+حاجة أنجيزها أدخلها الجدّي بدخل الموجود فيها الآن
+
+118
+00:10:24,300 --> 00:10:27,700
+proportion are measured by weight mix also
+
+119
+00:10:27,700 --> 00:10:32,360
+specified the water cement ratio الآن الحاجات اللي
+
+120
+00:10:32,360 --> 00:10:38,950
+بيجيزوها قداش نسبة الماء للسمنة الآن هذه المجاول
+
+121
+00:10:38,950 --> 00:10:43,930
+بيحب الباطون يفجّعش؟ مين طبعاً ال .. ال .. المدن إيش
+
+122
+00:10:43,930 --> 00:10:52,800
+بيحب المجاول الباطون يفجّعش؟ أيوة ليش؟ أسهل في الشغل
+
+123
+00:10:52,800 --> 00:10:58,760
+الآن هذا طبعاً بيرتب عليه أن القوة بتنزل فهذا اللي
+
+124
+00:10:58,760 --> 00:11:02,280
+بتتكلم عنه ال water cement ratio the amount of
+
+125
+00:11:02,280 --> 00:11:06,060
+water added relative to the amount of cement used
+
+126
+00:11:06,060 --> 00:11:10,560
+excess water reduces the strength of concrete يعني
+
+127
+00:11:10,560 --> 00:11:14,720
+زيادة في الميه بتتنقل so the quantity of water is
+
+128
+00:11:14,720 --> 00:11:19,590
+kept to minimum الأصل فيها الهادى بتضل حجم الميه
+
+129
+00:11:19,590 --> 00:11:24,250
+بتضل أصغر شيء لإن لو لاحظته لما تحطوا ميه كتيرة
+
+130
+00:11:24,250 --> 00:11:27,890
+يمكن هادى بتشوفوها في البيوت عندكم الميه بتطلع من
+
+131
+00:11:27,890 --> 00:11:32,290
+العمود، بتطلعش ميه صافي، بتطلع ميه ما حققش السمنت
+
+132
+00:11:32,290 --> 00:11:36,290
+فمعناه أن السمنت بدل ما يضل جوا وين صار طلع برا
+
+133
+00:11:37,560 --> 00:11:45,420
+ولكن كشجرة تدرس أكثر صعوبة تعمل مع مادة إضافية أو
+
+134
+00:11:45,420 --> 00:11:49,840
+مادة إضافية اسمها بلاستيزر عادة بتستخدمها
+
+135
+00:11:56,580 --> 00:12:01,100
+يعني بتلاقي الحركة بتغلب، الحاجة الثانية يمكن هذه
+
+136
+00:12:01,100 --> 00:12:06,120
+بتشوفوها بس بتتقفوش الهنتوا كتير بتلاقيه بيسموه
+
+137
+00:12:06,120 --> 00:12:10,960
+بعشش البطون عارفين إيش تعشش البطون؟ أيوة، الآن
+
+138
+00:12:10,960 --> 00:12:16,960
+بتلاقي مناطق فاضية مش مغطية أو بتلاقي أن هي فاش
+
+139
+00:12:16,960 --> 00:12:21,100
+بييجي المقاول على طول بيجيبله شوية بطون شوية سمنت
+
+140
+00:12:21,100 --> 00:12:25,160
+و بيلزق حوار عليها عشان ما يتمينس بس هي إيش الأصل
+
+141
+00:12:25,160 --> 00:12:30,640
+فيه في حاجة بيسموها الرجاج أيوة بيحطوه هذا ليش؟
+
+142
+00:12:30,640 --> 00:12:36,340
+عشان بيضلش فراغات فبيحطوه عشان هذا يتخلص من
+
+143
+00:12:36,340 --> 00:12:40,100
+الفراغات ما يصيرش هاي وعادة البطون زي ما حكينا ده
+
+144
+00:12:40,100 --> 00:12:44,480
+كان جامد بتبقى فيه صعوبة في التعامل معاه لهذا السبب
+
+145
+00:12:44,480 --> 00:12:49,200
+بضيفوا إيش ال plasticizer ال plasticizer هي مادة
+
+146
+00:12:49,200 --> 00:12:55,340
+من البلاستيك بتعمل .. بتخلي البطون softer أكتر
+
+147
+00:12:55,340 --> 00:13:00,680
+مرونة يعني في التعامل .. في الهيئة فهو بتخليه مد
+
+148
+00:13:00,680 --> 00:13:04,480
+معهم يعني ما يستوي this helps the concrete to flow
+
+149
+00:13:04,480 --> 00:13:09,660
+more easily بتخلي ال concrete يتحرك بسهولة
+
+150
+00:13:13,610 --> 00:13:21,530
+هي بتخليه بتضيف سيولة إليه بس
+
+151
+00:13:21,530 --> 00:13:26,250
+لأ هي شوف يعني زي ما أحيانا في مواد بتضيفيها تعمل
+
+152
+00:13:26,250 --> 00:13:31,510
+مرونة في الشغل هذا ال plasticizer مادة يمكن
+
+153
+00:13:31,510 --> 00:13:36,310
+أفرجيكوا بالظبط وين بتشوفيها بشكل عملي الآن لما
+
+154
+00:13:36,310 --> 00:13:40,980
+يقصروا أو يبنوا فيه صاروا زمان كانوا يحطوا sheet
+
+155
+00:13:40,980 --> 00:13:46,620
+مظبوط الآن صاروا يجيبوا غلن ويحطوا منه سائل حد
+
+156
+00:13:46,620 --> 00:13:52,180
+فيكوا شافه زي .. زي ال jelly زي دوة ال jelly زي
+
+157
+00:13:52,180 --> 00:13:58,180
+دوة ال jelly بيحطوها هناك هذا بيخليه فيه مرونة فيه
+
+158
+00:13:58,180 --> 00:14:03,680
+و هذا شفتوه و حد بدي يجلي منه بتلاقي لو حد شافه
+
+159
+00:14:03,680 --> 00:14:10,780
+بيتفكر تلك بس هي مادة بلاستيكية يعني بتضطر الخلطة،
+
+160
+00:14:10,780 --> 00:14:16,740
+كويس؟ الآن this helps the concrete to flow easily
+
+161
+00:14:16,740 --> 00:14:19,940
+other adjectives can also be used for example
+
+162
+00:14:19,940 --> 00:14:27,220
+retarder، retarder إيش هي هذه؟ retarded people،
+
+163
+00:14:27,220 --> 00:14:30,300
+retarder عادة هي عملية slow
+
+164
+00:14:32,720 --> 00:14:38,520
+فيه بطق، الآن هذه بتبطق إيش؟ بتعرف البطون بنشفه
+
+165
+00:14:38,520 --> 00:14:43,120
+بسرعة، صح؟ بتبطل عملية تنشيف البطون، هذا ال
+
+166
+00:14:43,120 --> 00:14:50,880
+retarder retarder لما نتكلم على الإنسان retarded
+
+167
+00:14:50,880 --> 00:14:55,900
+people إيش هم؟ الناس اللي تفكيرهم بطيقة بطيقين
+
+168
+00:14:55,900 --> 00:15:02,760
+الاستيعاب فيش حدا فيكم أنا ولا تخافوا أن الناس
+
+169
+00:15:02,760 --> 00:15:06,500
+البطئين الاستيعاب في ناس هدول بتلاقي هموم من خلق
+
+170
+00:15:06,500 --> 00:15:11,480
+زي هيك ب .. يعني في استيعاب بطيء فهدول حتى بيروحوا
+
+171
+00:15:11,480 --> 00:15:15,780
+لمدارس خاصة اللي هي تستوعب أن تتعلمهم
+
+172
+00:15:19,040 --> 00:15:23,180
+الباطون عادة بنشفه بسرعة عشان ما يخلوهش ينشفه
+
+173
+00:15:23,180 --> 00:15:26,620
+بسرعة إيش بيسويه بيضيفي مادة ال retarder هاي
+
+174
+00:15:26,620 --> 00:15:32,640
+بتخليه بطق في التجميد ما
+
+175
+00:15:32,640 --> 00:15:37,160
+هو أنت لما تصفي سطح و تسويكهم عندك بتلاحظ أنك مثلا
+
+176
+00:15:37,160 --> 00:15:41,080
+قداش اللي بيشتغلوا أربع عمال و المعلم تباعهم
+
+177
+00:15:41,080 --> 00:15:45,220
+أحيانا بتلاقي حجم الكمية كبيرة عليهم فبتخافوا
+
+178
+00:15:45,220 --> 00:15:48,380
+ينشفوا بيخرب فهو بيضيفوا هذه المادة على أساس
+
+179
+00:15:48,380 --> 00:15:52,080
+يستوعبه وبعدين لو أنت بتتكلم عن big construction
+
+180
+00:15:52,080 --> 00:15:55,700
+ال big construction بدك هذه الشغلات تبقى أكيد فيه
+
+181
+00:15:55,700 --> 00:15:59,980
+لأنه بتقدريش تلحق على حجم الشغل اللي موجود عندك
+
+182
+00:15:59,980 --> 00:16:03,700
+فأنت بدكيش تخسره أو تصير فيه مشاكل فيه
+
+183
+00:16:07,630 --> 00:16:12,630
+عشان تطول الموضوع؟ اه ايه .. في الآن في سيارات
+
+184
+00:16:12,630 --> 00:16:16,350
+البطون زي ما بتحكي هذا في أنواع كمان شوية هنتكلم
+
+185
+00:16:16,350 --> 00:16:21,250
+عنهم إيش أنواع هذا البطون في بطون بنعمل في الموقع
+
+186
+00:16:21,250 --> 00:16:27,630
+و في بنعمل في مصنع اللي بنعمل في الموقع غير اللي
+
+187
+00:16:27,630 --> 00:16:30,630
+بنعمل في المصنع اللي بنعمل في المصنع ده بتلاحظوا
+
+188
+00:16:30,630 --> 00:16:34,910
+لما تطلع السيارة حد فيكوا شاف الفاتورة تبعت
+
+189
+00:16:34,910 --> 00:16:35,570
+السيارة
+
+190
+00:16:39,120 --> 00:16:44,220
+بتحدد هي بتعطيك الوجد اللي هي طلعت من المصنع لأن
+
+191
+00:16:44,220 --> 00:16:51,620
+هذا لازم يتم استخدامه خلال قداش أيوة
+
+192
+00:16:51,620 --> 00:16:58,060
+فهي ليش لأن هو محطوط له هذه المادة و هي خلاصتها بس
+
+193
+00:16:58,060 --> 00:16:59,080
+خليكم معنا بقى
+
+194
+00:17:02,100 --> 00:17:06,160
+أرتاردر may be added to delay sitting which gives
+
+195
+00:17:06,160 --> 00:17:09,840
+worker more time to pour or replace the concrete
+
+196
+00:17:09,840 --> 00:17:14,220
+يعني بتعطي وقت إضافي للها الآن لما نتكلم عن
+
+197
+00:17:14,220 --> 00:17:18,360
+reinforced concrete اللي هو الخرسانة المسلحة
+
+198
+00:17:19,670 --> 00:17:26,210
+reinforce concrete structures contain steel parts
+
+199
+00:17:26,210 --> 00:17:30,190
+يعني بتعرفوا اللي هي الخرسانة المسلحة فيها إيش
+
+200
+00:17:30,190 --> 00:17:36,570
+الحديد وكل الحديد و الخرسانة فيهم ميزة إيش هم جبل
+
+201
+00:17:36,570 --> 00:17:43,110
+في محاضرات جبل معدل التمدد تبعهم و الانكماش متساوي
+
+202
+00:17:43,110 --> 00:17:49,650
+عشان هيك بيظبطوا مع بعض لما نحطوا Steel
+
+203
+00:17:49,650 --> 00:17:52,690
+reinforcement is needed mainly because concrete is
+
+204
+00:17:52,690 --> 00:17:57,470
+weak in tension تحت الضغط ال concrete لحاله بتشجج
+
+205
+00:17:57,470 --> 00:18:04,510
+مظبوط إذا حطيتك يعني بتدعم العمود أو صبه لفوق
+
+206
+00:18:04,510 --> 00:18:12,150
+وما حطش فيها ولا إيش حديد إيش بيصير فيها بتتشجك و
+
+207
+00:18:12,150 --> 00:18:15,670
+بعدين بتجعل مظبوط وهذا اللي بتحكيه عندي
+
+208
+00:18:27,470 --> 00:18:31,370
+بتتفتت وبتقع as steel is a strong intention
+
+209
+00:18:31,370 --> 00:18:35,310
+reinforced power overcome these weaknesses بنعرف
+
+210
+00:18:35,310 --> 00:18:42,110
+الحديد بتحمل الشد فهو لما نظيفه بيعمل يعني بدعم
+
+211
+00:18:42,110 --> 00:18:47,230
+هذه العملية in order to form the different part of
+
+212
+00:18:47,230 --> 00:18:50,490
+a structure a framework sometimes also called
+
+213
+00:18:50,490 --> 00:18:55,840
+shattering is used عادة إحنا بنحط إيش؟ الـ
+
+214
+00:18:55,840 --> 00:18:59,160
+Framework أو الـ Shattering اللي هي تركيبة بتعرفوا
+
+215
+00:18:59,160 --> 00:19:03,480
+إيش بيسويوا في الحديد بيرمهوش زي هيكا صح؟ بيربطوه
+
+216
+00:19:03,480 --> 00:19:07,160
+و بيحطوا أساور بتعرفوا الأساور تمام؟ البنات
+
+217
+00:19:07,160 --> 00:19:11,380
+المدنية عارفات الأساور إيش هما و بيربطوه على أشكال
+
+218
+00:19:11,380 --> 00:19:17,660
+معينة الآن في حسبة كل مهندسين المدني بيحسبوها قداش
+
+219
+00:19:17,660 --> 00:19:22,260
+عدد أو كمية الحديد اللي لازمة تكون عشان تتحمل
+
+220
+00:19:22,260 --> 00:19:27,470
+الضغط اللي بدي انعمل من هذا this consists of molds
+
+221
+00:19:27,470 --> 00:19:31,750
+of the required size and shape made from steel or
+
+222
+00:19:31,750 --> 00:19:34,590
+timber which are used to contain the concrete
+
+223
+00:19:34,590 --> 00:19:38,910
+until it has cysts الآن عادة لما أنا بدي أعمل إيش
+
+224
+00:19:38,910 --> 00:19:42,970
+بدي أعمل؟ في حاجة بعملها لأي حاجة بدي أعمل فيها
+
+225
+00:19:42,970 --> 00:19:51,130
+أصب فيها؟ إيش اللي بحطه؟ الآن لما بدهاش أصب على
+
+226
+00:19:51,130 --> 00:19:58,410
+السطح إيش بعمله؟ بحط يا خشب يا حديد الآن مثلا
+
+227
+00:19:58,410 --> 00:20:02,790
+الشباك لما بحطه ممكن بدي قوالب القوالب بحطها يا
+
+228
+00:20:02,790 --> 00:20:06,970
+قوالب من خشب يا قوالب من حديد وهي اللي بتشكل الشكل
+
+229
+00:20:06,970 --> 00:20:11,510
+اللي عندي طلع مثلا هنا الحفة شايفها؟ هاي عندي حاطط
+
+230
+00:20:11,510 --> 00:20:15,530
+أنا حفة فعمل decor معين هذا ال decor المعين أحيانا
+
+231
+00:20:15,530 --> 00:20:20,440
+لما يكون شكله غريب قوالب الخشب تسعفنيش بيحط إيش
+
+232
+00:20:20,440 --> 00:20:25,480
+حديد أو بعض الناس بتتذكروا في خشب بيسموه الموزينيت
+
+233
+00:20:25,480 --> 00:20:30,480
+سمعين فيه اللين هذا اللي بتسوي فأنت بتشكل منه شكل
+
+234
+00:20:30,480 --> 00:20:34,380
+بتحطيه في الآخر بتحط البطون فيه بتعطيك الشكل هذا
+
+235
+00:20:34,380 --> 00:20:39,400
+أحيانا بدي قوالب معينة مش موجودة يمكن لو شفتوا
+
+236
+00:20:39,400 --> 00:20:44,980
+مبنى المختبرات العلوم إيش حطوا التفريغ هناك قوالب
+
+237
+00:20:44,980 --> 00:20:50,320
+حتى فلينية اللي حطوها بحيث عملت تشكيل معين لما
+
+238
+00:20:50,320 --> 00:20:56,160
+موجود عندي بس في الآخر بدي حاجة تشيل وبدعمها بإيش؟
+
+239
+00:20:56,160 --> 00:21:00,480
+بالرجلين اللي بنحكي عنهم في بلادنا هذه التقنية
+
+240
+00:21:00,480 --> 00:21:04,020
+موجودة في بلاد غيرنا هتلاقوها مختلفة ويمكن في
+
+241
+00:21:04,020 --> 00:21:09,440
+مطورة وفي أقل مننا في المرة ترجع فهذه .. فهذه الآن
+
+242
+00:21:09,440 --> 00:21:13,860
+ال molds هذه مرت علينا الكلمة صح؟ إيش قلنا عنها؟
+
+243
+00:21:14,790 --> 00:21:22,310
+قوالب هذه كويس؟ when wet concrete is cast or
+
+244
+00:21:22,310 --> 00:21:27,550
+replaced in its final position it is called incito
+
+245
+00:21:27,550 --> 00:21:32,930
+concrete يعني هذه بتقول إيش؟ لما ال concrete اللي
+
+246
+00:21:32,930 --> 00:21:41,550
+هي الخرسانة تبقى wet إيش يعني wet؟ is cast
+
+247
+00:21:41,550 --> 00:21:47,230
+وضعت in its final position is called in-site
+
+248
+00:21:47,230 --> 00:21:51,890
+concrete لما هي تنعمل في الموقع أو تصل للموقف تنصب
+
+249
+00:21:51,890 --> 00:21:55,190
+في الموقع بيسميها in-site concrete هذا الإسم
+
+250
+00:21:55,190 --> 00:22:02,590
+أحفظوه كويس؟ مصطلح هي ال concrete اللي عندي لما 
+
+251
+00:22:02,590 --> 00:22:08,930
+نوصل قبل التوزيعInstead of being cast in situ,
+
+252
+00:22:09,090 --> 00:22:12,830
+reinforced concrete elements can also be precast
+
+253
+00:22:12,830 --> 00:22:18,670
+الـ precast هذي cast at ال factory يعني ال precast
+
+254
+00:22:18,670 --> 00:22:23,650
+هذا البطون اللي بنجيبه من مصانع البطون بيسموه 
+
+255
+00:22:23,650 --> 00:22:27,750
+precast concrete لأنه ايش؟ بيتم خلط وين؟ في المصنع
+
+256
+00:22:27,750 --> 00:22:36,420
+في المصنع فبصل إليك جاهزكويس؟ هذا فارقية بين هذه و
+
+257
+00:22:36,420 --> 00:22:40,800
+هذه الـ
+
+258
+00:22:40,800 --> 00:22:45,460
+in situ هو هذا بيبقى في الموقع، في الموقع، الآن
+
+259
+00:22:45,460 --> 00:22:48,560
+الـ precast وين بيبقى؟ في المصنع
+
+260
+00:22:51,350 --> 00:22:54,210
+طيب then deliver to the construction site ready
+
+261
+00:22:54,210 --> 00:22:57,730
+for assembly عادة بوصلوه بالشاحنات sometimes
+
+262
+00:22:57,730 --> 00:23:02,990
+precast concrete is also pre-stressed ايش بيصيرله؟
+
+263
+00:23:02,990 --> 00:23:08,530
+pre-stressed يعني ال stress ايش هو؟ مضغوطه، هاي
+
+264
+00:23:08,530 --> 00:23:12,890
+بيصيرله ايش؟ يعني ضغط مسبق، بنضغط مسبق يعني كيف
+
+265
+00:23:12,890 --> 00:23:16,650
+هات؟ with pre-stressing tension is applied to the
+
+266
+00:23:16,650 --> 00:23:23,320
+reinforcing bar يعني بيصير شب لمين؟ للحديد المسلح
+
+267
+00:23:23,320 --> 00:23:28,820
+بدل ما يقعد الحديد زي ما هو الحديد بيبقى مشدود ليش
+
+268
+00:23:28,820 --> 00:23:31,860
+هذه؟
+
+269
+00:23:31,860 --> 00:23:39,520
+أيوة ضغط لأن هذا بدك تخليه يجي عشان ما يريحش فأنت
+
+270
+00:23:39,520 --> 00:23:44,900
+بتشديه بيبطل فيه بيبقى 
+
+271
+00:23:44,900 --> 00:23:52,000
+مشدود الشد هذا عشان ما يكونش فيه مجال للتريحةهذا
+
+272
+00:23:52,000 --> 00:23:56,940
+اللي بنحكي فيه فيه
+
+273
+00:23:56,940 --> 00:24:04,050
+الجاذبية إلهاأيوة بيبقى بسيط أبسط من لو كان طبيعي
+
+274
+00:24:04,050 --> 00:24:07,990
+متروك لحاله إذا بتعرفوا أنتم جاذبية خصوصاً لما
+
+275
+00:24:07,990 --> 00:24:11,110
+تتكلموا عن مسافات يمكن تطلعوا على المسافة اللي
+
+276
+00:24:11,110 --> 00:24:15,350
+عندنا هنا أي شيء أكبر من أربعة متر بيصير التأثير
+
+277
+00:24:15,350 --> 00:24:19,790
+تبعه بيزيد و السمك تبع الهاي بيزيد يمكن في لغة
+
+278
+00:24:19,790 --> 00:24:24,790
+المدنية السمك بتتراوح بإيش حسب المسافات كل ما كبرت
+
+279
+00:24:24,790 --> 00:24:30,230
+المسافة كل ما السمك تبع الجسم الخرساني بيزيدأيوة في
+
+280
+00:24:30,230 --> 00:24:33,910
+معادلة عندكم أنا بعرفهاش بس في معادلة بعرفها ده
+
+281
+00:24:33,910 --> 00:24:38,410
+بيصير لإن أنتم اعتبارين الجامعة الإسلامية مشهور
+
+282
+00:24:38,410 --> 00:24:45,690
+عنكم السقف تبعنا دائماً 28 صانط سقفنا البطون خارجين
+
+283
+00:24:45,690 --> 00:24:50,230
+الجامعة دائماً بحبوا سقف البطون تبعنا ما هو كل شيء
+
+284
+00:24:50,230 --> 00:24:55,570
+بحسابه كل صانط بيزيد كوب البطون بيزيد اللي معاك
+
+285
+00:24:55,570 --> 00:24:56,770
+فالتقلبة بيزيد
+
+286
+00:25:00,510 --> 00:25:05,170
+مع تحرير التنسيق يتم تطبيق التنسيق على محطة دفع
+
+287
+00:25:05,170 --> 00:25:08,030
+التنسيق على محطة دفع دفع دفع دفع دفع دفع
+
+288
+00:25:08,030 --> 00:25:11,890
+دفع دفع دفع دفع دفع دفع دفع دفع دفع دفع
+
+289
+00:25:11,890 --> 00:25:12,630
+دفع دفع دفع دفع دفع دفع دفع دفع دفع دفع
+
+290
+00:25:12,630 --> 00:25:19,110
+دفع دفع دفع دفع دفع دفع دفع دفع دفع
+
+291
+00:25:19,110 --> 00:25:24,930
+دفع
+
+292
+00:25:27,080 --> 00:25:34,680
+بعد أن البطون ينصب بيصير مجددين يعني بعد أن البطون
+
+293
+00:25:34,680 --> 00:25:38,200
+ينصب بيصير مجددين يعني بعد أن البطون ينصب بيصير
+
+294
+00:25:38,200 --> 00:25:42,520
+مجددين يعني بعد أن البطون ينصب بيصير مجددين يعني
+
+295
+00:25:42,520 --> 00:25:44,040
+بعد أن البطون ينصب بيصير مجددين يعني بعد أن البطون
+
+296
+00:25:44,040 --> 00:25:47,340
+ينصب بيصير مجددين يعني بعد أن البطون ينصب بيصير
+
+297
+00:25:47,340 --> 00:25:56,530
+مجددين يعني بعد أن ال bending forcing اللي هي ايش
+
+298
+00:25:56,530 --> 00:26:05,010
+القوة تبعت اللي هي بتعمله انحناء اللي هي الجاذبية
+
+299
+00:26:05,010 --> 00:26:09,610
+بشكل أساسي طيب نيجي نتكلم على بعض الكلمات اللي هنا
+
+300
+00:26:09,610 --> 00:26:14,510
+طيب قبل ما نسوي نرجع ثاني عشان نشوف أشهر الكلمات
+
+301
+00:26:14,510 --> 00:26:21,450
+اللي عندي هنا ال cement كلكم عارفينه، كويس؟ الآن
+
+302
+00:26:21,450 --> 00:26:27,070
+لما نتكلم على set، ايش يعني set؟ أيوة، فهنا start
+
+303
+00:26:27,070 --> 00:26:33,010
+become solid مصوا ال cement paste المشتقات الآن،
+
+304
+00:26:33,010 --> 00:26:36,750
+أيوة المشتقات، concrete هي أشهر ايش ايه؟ يعني هاد
+
+305
+00:26:36,750 --> 00:26:41,490
+من اسمها اللي هاد، الآن ال fine aggregate و ال
+
+306
+00:26:41,490 --> 00:26:45,310
+coarse aggregate هدول مهمين ال Fine Aggregate
+
+307
+00:26:45,310 --> 00:26:49,090
+اللي سميناها ال Sand والـ Coarse Aggregate سميناها
+
+308
+00:26:49,090 --> 00:26:53,950
+ال Gravel الآن ال Structural Strength اللي
+
+309
+00:26:53,950 --> 00:26:58,230
+بنتكلم عنه ال time it takes كويسة القوة الإنشائية
+
+310
+00:26:58,230 --> 00:27:02,310
+ال Strength needed to perform effectively الآن في
+
+311
+00:27:02,310 --> 00:27:08,990
+عندي 28 days 28 day strength اللي بنسميهو اكتشف
+
+312
+00:27:08,990 --> 00:27:14,730
+بيوصل ال concrete to its maximum strength أو
+
+313
+00:27:14,730 --> 00:27:20,570
+normal strength الآن mix designs اللي هي قداش النسب
+
+314
+00:27:20,570 --> 00:27:28,030
+نتكلم proportional proportions of cement to sand
+
+315
+00:27:28,030 --> 00:27:32,870
+to gravel or fine aggregate to coarse aggregate
+
+316
+00:27:32,870 --> 00:27:36,090
+اللي عندي ال batching اللي هي قلنا ال proportion
+
+317
+00:27:36,090 --> 00:27:39,970
+of measurement by weight اللي هي الخلطة أو العجينة
+
+318
+00:27:42,100 --> 00:27:47,580
+Water-cement ratio هذه نسبة المياه للاسمنت وهذا
+
+319
+00:27:47,580 --> 00:27:54,340
+ضروري لكل شيء Additives اللي هي المواد اللي عندنا
+
+320
+00:27:54,340 --> 00:27:59,020
+ال plasticizer is an additive used to make
+
+321
+00:27:59,020 --> 00:28:07,400
+concrete soft أيوة الآن لما نتكلم عن ال retarder
+
+322
+00:28:07,400 --> 00:28:08,180
+ايش بتعمل
+
+323
+00:28:12,710 --> 00:28:20,230
+slow setting يعني أو give more time to workers to
+
+324
+00:28:20,230 --> 00:28:25,370
+pour the cement الآن اللي هي retarder الآن لما
+
+325
+00:28:25,370 --> 00:28:30,270
+نتكلم على reinforced concrete نتكلم على ايش؟ بارز
+
+326
+00:28:30,270 --> 00:28:36,750
+آيرن بارز with concrete shattering
+
+327
+00:28:36,750 --> 00:28:43,150
+اللي هي عبارة عن ايش؟ ال framework اللي هي الجسم
+
+328
+00:28:43,150 --> 00:28:50,150
+الجسم اللي بنعمله من ال ايش من ال iron bars في
+
+329
+00:28:50,150 --> 00:28:54,870
+المجسم اللي بنعمله عادة لو حد فيكوا جرب الحديد
+
+330
+00:28:54,870 --> 00:29:00,090
+لحاله هو بيشيل السطح أنتم بتشوفوا .. أنتم اللي
+
+331
+00:29:00,090 --> 00:29:06,720
+بيشوف اللي عنده .. معظمكم شغل في بيتكم حاجة صح؟ إلا
+
+332
+00:29:06,720 --> 00:29:11,280
+اللي اتولدت بشجة وما شافتش شيء ثاني، بس معظم بيوتنا
+
+333
+00:29:11,280 --> 00:29:16,360
+دائماً فيها شغل، ما فيش حد بيشغلش فعلاً، فبتلاحظوا
+
+334
+00:29:16,360 --> 00:29:21,000
+حاجة واحدة إنه في الشغل هات بتشوفوا أحياناً يربطوا
+
+335
+00:29:21,000 --> 00:29:26,240
+الحديد ممكن حد يمشي عليه بدون أي اشكالية بتحمل
+
+336
+00:29:26,240 --> 00:29:30,820
+الوزن بتحمل كل شيء ليش؟ لأن هو اللي بيشيل الباقي
+
+337
+00:29:30,820 --> 00:29:35,480
+فأنت الاصل ايش بنحط؟ نخفف كمية الخرسانة اللي
+
+338
+00:29:35,480 --> 00:29:40,900
+بيشيلها هذا الجسم لأنه في الآخر هيعطيك الشكل اللي
+
+339
+00:29:40,900 --> 00:29:46,800
+بدك إياه فأنت بتخفف الوزن اللي بيحط عليه molds
+
+340
+00:29:46,800 --> 00:29:53,920
+اللي قلنا هي ال shape the general shape we try to
+
+341
+00:29:53,920 --> 00:29:58,380
+pour the concrete in اللي عادة made of either iron
+
+342
+00:29:58,380 --> 00:30:07,060
+or wood cast اللي هي place in site of concrete
+
+343
+00:30:07,060 --> 00:30:13,120
+concrete made at the site كويس؟ الآن precast
+
+344
+00:30:13,120 --> 00:30:18,880
+concrete made at the factory المصنع طيب
+
+345
+00:30:21,060 --> 00:30:29,020
+ال cast اللي هي الصبة هي لأ انخلطت بالموقع يعني
+
+346
+00:30:29,020 --> 00:30:34,340
+الآن لما أنا بدأ ..
+
+347
+00:30:34,340 --> 00:30:37,360
+cast
+
+348
+00:30:37,360 --> 00:30:44,260
+لحالها اللي هي الخلطة بشكل عام أيوة يعني وين
+
+349
+00:30:44,260 --> 00:30:44,960
+بتسوي؟
+
+350
+00:30:48,720 --> 00:30:56,740
+الآن pre-stressing اللي هي عملية نعملها في البطون
+
+351
+00:30:56,740 --> 00:31:02,240
+لما نشد ال iron يعني we stretch the iron bars
+
+352
+00:31:02,240 --> 00:31:04,900
+before pouring in the concrete
+
+353
+00:31:09,280 --> 00:31:14,260
+when somebody gets in a place where he does not
+
+354
+00:31:14,260 --> 00:31:18,300
+feel comfortable يعني لو أنت ت .. يعني تنحشر بمكان
+
+355
+00:31:18,300 --> 00:31:22,080
+و بتحسش براحة بنسميها you're trapped حتى أحياناً
+
+356
+00:31:22,080 --> 00:31:26,800
+مش .. مش ضروري تكون physical بنحكيها لما أنت و حدا
+
+357
+00:31:26,800 --> 00:31:31,460
+using في كلمة حكيتها بنقول you're trapped by your
+
+358
+00:31:31,460 --> 00:31:36,940
+own words أنت صار ايش لك ان حشرت بكلمتك اللي أنت
+
+359
+00:31:36,940 --> 00:31:44,850
+حكيتها أيوة طيب الآن a gravel used in concrete ايش
+
+360
+00:31:44,850 --> 00:31:50,050
+بنسمي ال gravel coarse aggregate sand used in
+
+361
+00:31:50,050 --> 00:31:54,810
+concrete fine aggregate هاي الكلمات بنعيد عليها
+
+362
+00:31:54,810 --> 00:31:58,710
+نهيه الآن powder that enables concrete to set
+
+363
+00:31:58,710 --> 00:32:06,390
+cement mix in concrete accurately batching اللي
+
+364
+00:32:06,390 --> 00:32:11,210
+بنتكلم عنه الآن specification of concrete
+
+365
+00:32:11,210 --> 00:32:17,250
+ingredients mixed design mixed design effective
+
+366
+00:32:17,250 --> 00:32:24,050
+capability of concrete twenty-eight day strength
+
+367
+00:32:24,050 --> 00:32:28,450
+هذا ال effective اللي عندي effect wetness and
+
+368
+00:32:28,450 --> 00:32:32,450
+strength of concrete كلمة wet طلع كلمة wetness
+
+369
+00:32:32,450 --> 00:32:40,090
+معناها ايش؟ فيه .. فيه ماء بنقول ايش؟ water cement
+
+370
+00:32:40,090 --> 00:32:45,070
+ratio different types of chemical put in concrete
+
+371
+00:32:45,070 --> 00:32:50,050
+additives أي حاجة بدو فيها يمكن حتى في الأكل إذا
+
+372
+00:32:50,050 --> 00:32:54,530
+بتلاحظوا على أي شغلة بتشتروها هتلاقي في كلمة
+
+373
+00:32:54,530 --> 00:32:58,250
+additives موجودة فيها أحياناً ايش بيحطوا في الأكل؟
+
+374
+00:32:58,880 --> 00:33:04,320
+أكثر شيء المواد الحافظة فهذا اسم additives هذه
+
+375
+00:33:04,320 --> 00:33:09,480
+الحاجات الزيادة اللي بتنحط هذه بتحط أحياناً حتى لما 
+
+376
+00:33:09,480 --> 00:33:12,400
+عندنا .. احنا في المطاعم بتلاقي الناس أهل المطاعم
+
+377
+00:33:12,400 --> 00:33:17,340
+بيحطوا حاجات برضه من عندهم هدولة بيسموها مشحيات أو 
+
+378
+00:33:17,340 --> 00:33:21,760
+حاجة زي هيكا فهي بتنحطها على الدكتور محمد عودة في
+
+379
+00:33:21,760 --> 00:33:24,740
+زمنته لما قال في حاجات تبعين المطاعم تبعيننا
+
+380
+00:33:24,740 --> 00:33:32,700
+بيحطوها بزيادة ومش صحية طبعا بتعطي طعم بس مش صحية
+
+381
+00:33:32,700 --> 00:33:38,100
+فهذه الـ adjectives لتغيير الطبيعة عادة إذا 
+
+382
+00:33:38,100 --> 00:33:41,820
+بتلاحظوا هنا بنحط إيش؟ بنحط طبيعة الـ concrete إيش
+
+383
+00:33:41,820 --> 00:33:46,160
+بيصير له؟ بتجمد بسرعة أو بيبقى أشلين فنغير طبيعته
+
+384
+00:33:46,160 --> 00:33:51,000
+بنضيف الـ adjectives اللي بنحكيها allowed to stay
+
+385
+00:33:51,000 --> 00:33:55,760
+wet for longer retarded makes drier concrete
+
+386
+00:33:55,760 --> 00:33:59,490
+easier to work with. plasticizer
+
+387
+00:34:01,050 --> 00:34:05,710
+طيب الآن هذه الأجوبة نتكلم الآن complete the 
+
+388
+00:34:05,710 --> 00:34:09,690
+textbook extract about a type of prestressed
+
+389
+00:34:09,690 --> 00:34:13,750
+concrete using the words in the box cast framework
+
+390
+00:34:13,750 --> 00:34:18,650
+pouring presetting structural concrete in situ
+
+391
+00:34:18,650 --> 00:34:23,170
+precast reinforcement prestressing techniques
+
+392
+00:34:23,170 --> 00:34:27,130
+العنوان تبعنا in the production of reinforced
+
+393
+00:34:27,130 --> 00:34:30,790
+concrete components the process of إيش؟
+
+394
+00:34:49,890 --> 00:34:55,830
+pre-stressing usually involves holding إيش
+
+395
+00:34:55,830 --> 00:34:56,670
+intention؟
+
+396
+00:35:01,410 --> 00:35:04,530
+reinforcement intention إيش اللي ب .. إيش يقول
+
+397
+00:35:04,530 --> 00:35:10,290
+الحديد هو عبارة عن إيش؟ إيش بيعمل؟ reinforce الـ
+
+398
+00:35:10,290 --> 00:35:14,370
+concrete فده اللي بشده مين؟ بشد الـ concrete ولا
+
+399
+00:35:14,370 --> 00:35:20,950
+الحديد؟ الحديد الحديد ما نشدش الحديد اللي ما نشدش
+
+400
+00:35:20,950 --> 00:35:26,730
+فأنا بشد الحديد الحديد إيش الاسم العلمي له ده قامة
+
+401
+00:35:26,730 --> 00:35:33,850
+مظبوط مش هو بدعم الـ concrete اللي هي الخرسانة فاسم
+
+402
+00:35:33,850 --> 00:35:39,450
+التاني له إيش reinforcement intention  while إيش
+
+403
+00:35:39,450 --> 00:35:40,170
+concrete
+
+404
+00:35:42,770 --> 00:35:45,710
+while إيش بيسوي أنا لما بشده إيش بعمل في الـ
+
+405
+00:35:45,710 --> 00:35:52,330
+concrete بعدها بنزله مظبوط عملية الصبة اللي تنزلها
+
+406
+00:35:52,330 --> 00:35:57,530
+هي بيسميها pouring placing كويس؟
+
+407
+00:35:59,240 --> 00:36:03,840
+هذه الطريقة الـ pre-stressing تسمى pre-tension pre-
+
+408
+00:36:03,840 --> 00:36:07,260
+tensioning عندما يتم استخدام الضغط قبل أن يتم 
+
+409
+00:36:07,260 --> 00:36:12,080
+إصلاح المجلد وهذه هي جواب حدي هذا وهذه هذه جواب
+
+410
+00:36:12,080 --> 00:36:19,920
+حوية هنا تلاتة هي هذا يعني إذا كنت تقرأ الفقرة
+
+411
+00:36:19,920 --> 00:36:26,270
+بشكل هذا ستجد الفقرة مجاوبة لك هذا ما نقوله. التقنية
+
+412
+00:36:26,270 --> 00:36:37,110
+عادة تستخدم في إصدار مجزم من الأرض التي
+
+413
+00:36:37,110 --> 00:36:43,930
+تكون صغيرة كمية لتعمل في خلف محطة ويمكن أن تكون
+
+414
+00:36:43,930 --> 00:36:48,070
+قمت بتجهيزها في المصنع
+
+415
+00:36:52,140 --> 00:36:58,660
+من المصنع بيسموها precast الموجود a less common
+
+416
+00:36:58,660 --> 00:37:03,060
+prestressing technique is post tensioning apply
+
+417
+00:37:03,060 --> 00:37:07,260
+tension after the concrete has set لأن عندي طريقة
+
+418
+00:37:07,260 --> 00:37:11,080
+تانية ليش بيسموها post
+
+419
+00:37:12,340 --> 00:37:15,740
+Post-tensioning احنا كان عندنا pre-tensioning لما
+
+420
+00:37:15,740 --> 00:37:19,080
+أنا بشد و بصب هنا الـ post-tensioning إيش بيعمل؟
+
+421
+00:37:19,080 --> 00:37:22,860
+apply tension after the concrete has set يعني بعد ما
+
+422
+00:37:22,860 --> 00:37:28,560
+يجمد الحديد بشد هذا الـ post هذا this is more
+
+423
+00:37:28,560 --> 00:37:31,500
+suitable for large elements especially long beams
+
+424
+00:37:31,500 --> 00:37:35,100
+which cannot be transported and therefore need to
+
+425
+00:37:35,100 --> 00:37:43,040
+be poured إيش الحاجات اللي بتنتقلش وين بأعمل لها
+
+426
+00:37:43,040 --> 00:37:48,560
+الصبة؟ في الموقع، إيش يقولنا في الموقع؟ in situ
+
+427
+00:37:48,560 --> 00:37:53,400
+can't be transported الحاجات اللي can't be
+
+428
+00:37:53,400 --> 00:37:57,700
+transported وين بتكون؟ on the site، مظبوط فكلمة
+
+429
+00:37:57,700 --> 00:38:04,080
+inside بنقول in situ بتجاوب عنها in situ
+
+430
+00:38:16,890 --> 00:38:21,170
+العمدان الطويلة before the concrete is poured,
+
+431
+00:38:21,350 --> 00:38:24,830
+ducts usually plastic tubes are placed inside
+
+432
+00:38:26,740 --> 00:38:31,280
+framework عادة إيش بيسووا هذه فيها بيحطوا مواصير
+
+433
+00:38:31,280 --> 00:38:36,840
+من الـ plastic والآن جوه المواصير بتبقى إيش الحديد
+
+434
+00:38:36,840 --> 00:38:41,840
+اللي بده الشد كويس فهي بيحطوا المواصير فيها لجوه
+
+435
+00:38:41,840 --> 00:38:48,860
+الآن الـ framework اللي هو إيش المجسم تبعي along the
+
+436
+00:38:48,860 --> 00:38:52,540
+length of the beam these ducts الـ duct اللي هي ..
+
+437
+00:38:52,540 --> 00:38:59,520
+contain steel cables هدول بنحط إيش فيهم؟ كوابل من
+
+438
+00:38:59,520 --> 00:39:03,740
+الستيل الآن هذا الـ cable عشان إنه .. هاي بيشدوه
+
+439
+00:39:03,740 --> 00:39:09,580
+فإيش بيصير؟ العمود بيظله مشدود فيها after the 
+
+440
+00:39:09,580 --> 00:39:15,300
+concrete has been إيش؟ cast بعد ما ينصب and has
+
+441
+00:39:15,300 --> 00:39:20,210
+gained sufficient structural strength صار له قوة
+
+442
+00:39:20,210 --> 00:39:23,750
+The cables are put in tension using jacks at
+
+443
+00:39:23,750 --> 00:39:28,050
+either end of the beam وهذه بتشوفوها في جثور بشكل
+
+444
+00:39:28,050 --> 00:39:34,250
+أساسي هاي
+
+445
+00:39:34,250 --> 00:39:39,390
+هذا الشكل تبعهم شايفين كيف؟ هذا بنحطه بعده بإيش؟
+
+446
+00:39:39,390 --> 00:39:43,090
+بنشد اللي عندك this is only possible because the
+
+447
+00:39:43,090 --> 00:39:47,590
+cables are free to move within the duct it is not
+
+448
+00:39:47,590 --> 00:39:51,490
+possible with pretension reinforcing bar which are
+
+449
+00:39:51,490 --> 00:39:57,190
+held fast by the hard concrete surrounding them
+
+450
+00:39:57,190 --> 00:40:00,790
+the end of the cables are then permanently
+
+451
+00:40:00,790 --> 00:40:04,690
+anchored at either end of the beam إيش يعني
+
+452
+00:40:04,690 --> 00:40:05,470
+anchored؟
+
+453
+00:40:07,720 --> 00:40:13,420
+رباطور الـ anchor man اللي عادة إيش بشد الفريق تبعه
+
+454
+00:40:13,420 --> 00:40:20,820
+بتعرفوه هذه الآن في عندي خليني أجيبكوا إيش معنى
+
+455
+00:40:20,820 --> 00:40:25,780
+anchor بالظبط الآن بتعرفوا في مسابقات الجارية
+
+456
+00:40:25,780 --> 00:40:33,320
+التتابع بيبقى الفريق من كام واحد؟ أربعة تقريبا سواء
+
+457
+00:40:33,320 --> 00:40:38,000
+في الصباحة أو في الجري، صح؟ الآن الـ anchor person
+
+458
+00:40:38,000 --> 00:40:42,420
+إيش بيسوي؟ هو اللي بيجي set the pace لمن؟ لكل اللي
+
+459
+00:40:42,420 --> 00:40:50,370
+وراة، لو أجي أول شخص هذا كان في المؤخرة اللي بعده
+
+460
+00:40:50,370 --> 00:40:56,370
+صعب يعمله أي حاجة ولو كانت في المقدمة هو هذا أحسن
+
+461
+00:40:56,370 --> 00:41:00,790
+واحد الباقين بتتبعه وراه فهذا بيسموه anchor man
+
+462
+00:41:00,790 --> 00:41:05,490
+اللي هو الشخص اللي بيسحب الكل هذه الكلمة فـ anchor
+
+463
+00:41:05,490 --> 00:41:11,650
+اللي هو بيشد الكل في هذا المجال هذا عند chapter 16
+
+464
+00:41:11,650 --> 00:41:19,670
+المرة الجاية المحاضرة الجاية المحاضرة الجاية بنتكلم
+
+465
+00:41:19,670 --> 00:41:25,230
+على seventeen وهدولة بتبقى لحد آخر محاضرة جاية هو
+
+466
+00:41:25,230 --> 00:41:29,030
+اللي داخل في النصفة بعد هيك بنتكلم على
+
+467
+00:41:29,030 --> 00:41:34,330
+presentations آخر أسبوع يوم الأربعاء أيوه و بنبدأ في
+
+468
+00:41:34,330 --> 00:41:38,650
+الجزء الثاني من المادة بيعطيكوا العافية
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/3BCXCLdWrNY_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/3BCXCLdWrNY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b8a451d5a3f53bb3d8fde473dedc5652f56cbdc1
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/3BCXCLdWrNY_raw.srt
@@ -0,0 +1,1624 @@
+1
+00:00:20,840 --> 00:00:29,440
+السلام عليكم اليوم سنتحدث عن القرن 15 القرن 15
+
+2
+00:00:29,440 --> 00:00:36,220
+يتعامل عن مادة المنورات والسيراميكا إيش مينرالز؟
+
+3
+00:00:36,220 --> 00:00:42,180
+مرت عليك كلمة مينرالز؟ إيش هي؟ شفتوها في اللي إيش؟
+
+4
+00:00:42,180 --> 00:00:48,260
+في الميه صح؟ إيش بنقول عنها؟ مينرال و water صح؟
+
+5
+00:00:48,260 --> 00:00:55,250
+فإيش مينرال؟أيوة معدل معادل ceramics بتعرفوا ال
+
+6
+00:00:55,250 --> 00:01:03,250
+ceramics أيوة طيب what
+
+7
+00:01:03,250 --> 00:01:06,450
+we gonna talk about two sections in section one
+
+8
+00:01:06,450 --> 00:01:10,550
+minerals and ceramics engineering material و
+
+9
+00:01:10,550 --> 00:01:15,590
+الحاجة التانية glass اللي هو إيش الزجاج الزجاج
+
+10
+00:01:15,590 --> 00:01:22,500
+بيجي تحت أيه ال minerals ولا ال ceramicsلأ الزجاج
+
+11
+00:01:22,500 --> 00:01:27,580
+تحت ليش؟ minerals and ceramics engineering
+
+12
+00:01:27,580 --> 00:01:32,220
+material a mineral is a natural inorganic material
+
+13
+00:01:32,220 --> 00:01:41,300
+natural يعني إيش؟ طبيعي، inorganic غير عضوي، أيوة
+
+14
+00:01:41,300 --> 00:01:43,080
+العضوي organic
+
+15
+00:01:45,690 --> 00:01:51,430
+one that is not living يعني الغير عضوى which is
+
+16
+00:01:51,430 --> 00:01:56,310
+found in the ground often within rocks يعني هو
+
+17
+00:01:56,310 --> 00:02:01,270
+عادة وين بنلاقيه؟ في الصخور موجود minerals are
+
+18
+00:02:01,270 --> 00:02:09,050
+quite pure يعني ايش pure؟ quite pure صافية او نقية
+
+19
+00:02:09,050 --> 00:02:14,900
+جداRocks on the other hand can be mixtures of
+
+20
+00:02:14,900 --> 00:02:20,740
+several minerals الصخور تبقى خليط من المعادن
+
+21
+00:02:20,740 --> 00:02:28,240
+المختلفة، مظبوط؟ الشيخ أخدته في الثانوية and may
+
+22
+00:02:28,240 --> 00:02:35,640
+also contain previously organic materials وممكن
+
+23
+00:02:35,640 --> 00:02:41,140
+الصخور يكون فيها مواد عضويةExamples of minerals
+
+24
+00:02:41,140 --> 00:02:48,100
+include different types of ore يعني إيش ال ore؟
+
+25
+00:02:48,100 --> 00:02:54,360
+طيب بتعرفوا أنتوا لو ما نيجي نحفر في الأرض إيش
+
+26
+00:02:54,360 --> 00:02:59,500
+بنطلع من الأرض؟ زي النفط، زي الحديد، زي غير إيش
+
+27
+00:02:59,500 --> 00:03:06,100
+بنسميها؟ أيوة، فال ore معناها إيش؟ خام، المواد
+
+28
+00:03:06,100 --> 00:03:16,790
+الخامة فهمتوا إيش ore؟فانا بجيب الكل ها طيب form
+
+29
+00:03:16,790 --> 00:03:21,030
+of which metal can be extracted such as iron or
+
+30
+00:03:21,030 --> 00:03:25,210
+non-metallic minerals include الآن ال non-metallic
+
+31
+00:03:25,210 --> 00:03:30,570
+ال ore متالك صح اللي
+
+32
+00:03:30,570 --> 00:03:34,370
+بدي أتكلم عليه iron ore متالك ال non-metallic زي
+
+33
+00:03:34,370 --> 00:03:40,580
+إيش ال diamond إيش ال diamondالماس an extremely
+
+34
+00:03:40,580 --> 00:03:45,680
+hard form of carbon زي ما بتعرف الماس ايش؟ carbon
+
+35
+00:03:45,680 --> 00:03:53,320
+صلب جدا، مظبوط؟ طيب which is used as an abrasive
+
+36
+00:03:53,320 --> 00:03:56,600
+very hard and rough material in cutting tools ايش
+
+37
+00:03:56,600 --> 00:03:57,920
+يعني abrasives؟
+
+38
+00:04:00,110 --> 00:04:05,250
+هي مادة صلبة بس عادة في حاجات .. لما بنقطع في حاجة
+
+39
+00:04:05,250 --> 00:04:10,690
+تشوف انتوا الاجزاز بيقطعوه في الاش؟ في المادة،
+
+40
+00:04:10,690 --> 00:04:15,230
+الآن ال tools بيعملولها ال synth بقى حاجات أو بعض
+
+41
+00:04:15,230 --> 00:04:21,170
+الشغلات اللي بدها حفل الحاجات زي الحديد زي غيره
+
+42
+00:04:21,170 --> 00:04:26,070
+المبرد أو براده هاي بيستخدموا كلمة abrasive
+
+43
+00:04:26,640 --> 00:04:32,080
+abrasive اللي هي الحك أو عملية
+
+44
+00:04:32,080 --> 00:04:38,540
+البرادة هذه بنسميها abrasive frequently referred
+
+45
+00:04:38,540 --> 00:04:42,180
+to as industrial diamond when used in engineering
+
+46
+00:04:42,180 --> 00:04:45,520
+هذه المواد اللي بنستخدمها في ال diamond اللي
+
+47
+00:04:45,520 --> 00:04:49,680
+بنستخدمه في عملية القطع بنسميه أيش أو في عملية ال
+
+48
+00:04:49,680 --> 00:04:54,460
+abrasive بنسميه industrial diamond
+
+49
+00:04:57,540 --> 00:05:01,680
+هذا هو ال clay bricks بتعرفوا انتوا مش في بلادنا
+
+50
+00:05:01,680 --> 00:05:07,800
+هذا موجود في مصر الحجر الحراري الحجر الحراري هو
+
+51
+00:05:07,800 --> 00:05:14,060
+حجر مصنوع من أيش؟ من الطينة هنتكلم عنه كمان شوية
+
+52
+00:05:14,060 --> 00:05:20,100
+Silicon found in sand and silica بتعرفيش ال
+
+53
+00:05:20,100 --> 00:05:26,720
+silicon؟هو بالعربي ما هو Silicon؟ طيب Silicon
+
+54
+00:05:26,720 --> 00:05:31,520
+Dioxide اللي هو إيش؟ أكسيد السيليكون اللي يمكن أن
+
+55
+00:05:31,520 --> 00:05:37,760
+يكون محرم بهجة عالية لإصلاح عجزة تعرف لما الرمل أو
+
+56
+00:05:37,760 --> 00:05:43,400
+السيليكون سخن لدرجات حرارة عالية نعمل منه الإجازة
+
+57
+00:05:43,400 --> 00:05:48,870
+عامة في مواد أوريجانية لا متاليةthat have been
+
+58
+00:05:48,870 --> 00:05:53,450
+formed by heating are called ceramics لما نيجي طلع
+
+59
+00:05:53,450 --> 00:05:57,990
+عندها inorganic non-metallic material لما عادة
+
+60
+00:05:57,990 --> 00:06:04,830
+نستخدم الحرارة فيها بنسميها إيش ceramics زي الفخار
+
+61
+00:06:04,830 --> 00:06:09,530
+بتعرف الفخار كل هي كده بتشوفوه الفخار كيف بيعملوه
+
+62
+00:06:09,530 --> 00:06:14,840
+بالطين بالطين بس بعدين إيش بيسووا فيهبسخنوه بحرقوه
+
+63
+00:06:14,840 --> 00:06:22,240
+مظبوط فبصير فخه فهذا هو نوع من ال ceramics glass
+
+64
+00:06:22,240 --> 00:06:25,740
+is therefore a ceramic when materials are heated
+
+65
+00:06:25,740 --> 00:06:28,760
+to extremely high temperature to form ceramics
+
+66
+00:06:28,760 --> 00:06:33,400
+that are glass-like ال ceramics عادة إلها
+
+67
+00:06:33,400 --> 00:06:38,250
+المواصفات زي مواصفات الإجازةthat is with a
+
+68
+00:06:38,250 --> 00:06:41,570
+structure like that of a glass we say they are
+
+69
+00:06:41,570 --> 00:06:45,150
+vitrified
+
+70
+00:06:45,150 --> 00:06:49,990
+vitrified يعني إيش؟ فهذه بتلاقوها موجودة على بعض
+
+71
+00:06:49,990 --> 00:06:53,290
+الأواني
+
+72
+00:06:53,290 --> 00:06:59,410
+vitrified الزجاجية بتلاقيها موجودة لوش بتتذكروا
+
+73
+00:06:59,410 --> 00:07:04,150
+انتوا كل هيتكم بتعرفون في صواني في البيت تبعت ال
+
+74
+00:07:04,150 --> 00:07:10,340
+pyrexأيوة بتلاقيها إيش مكتوب عليها? vitrified أيوة
+
+75
+00:07:10,340 --> 00:07:15,200
+يعني هذه استخدمت درجات حرارة عالية لتعملها إناء
+
+76
+00:07:15,200 --> 00:07:22,940
+أيوة فهذه vitrified اللي بنسميها هذه يعني صارت
+
+77
+00:07:22,940 --> 00:07:29,330
+مواصفات هذه هي مواصفات الجزاز بس في نفس الوقتعن
+
+78
+00:07:29,330 --> 00:07:32,230
+طريق حرارة عالية اقدرنا نعملها زي هيك معناتها
+
+79
+00:07:32,230 --> 00:07:38,060
+بتقدر تستخد .. تستخد .. تتحمل درجات الحرارةCeramic
+
+80
+00:07:38,060 --> 00:07:41,720
+materials are used to make construction materials
+
+81
+00:07:41,720 --> 00:07:45,440
+such as bricks الان ال construction مواد البناء
+
+82
+00:07:45,440 --> 00:07:50,280
+such as bricks اللي هم الحجار اللي عندى they are
+
+83
+00:07:50,280 --> 00:07:56,380
+made from clay اللي هي الطين اللي موجود عندنا and
+
+84
+00:07:56,380 --> 00:08:02,240
+are then fired in a client ايش يعني fired؟ بتم
+
+85
+00:08:02,240 --> 00:08:09,070
+حرقهم عملية الحرق في ال client اللي في فرنعملية
+
+86
+00:08:09,070 --> 00:08:15,470
+الحرق في الفرن بيسميها fired in a clay كويس؟ that
+
+87
+00:08:15,470 --> 00:08:18,590
+is heated to a high temperature in an industrial
+
+88
+00:08:18,590 --> 00:08:25,150
+oven clay can also be vitrified for example in ..
+
+89
+00:08:25,150 --> 00:08:29,670
+to make waterproof pipes أحيانا بنعمل إيش؟
+
+90
+00:08:29,670 --> 00:08:38,860
+بنستخدمها لنعمل؟ إيش ال water proof؟ اللي هي أيوةو
+
+91
+00:08:38,860 --> 00:08:46,220
+الـ vibes اللي هي إيش أنا بيب الموجودة عندنا فالآن
+
+92
+00:08:46,220 --> 00:08:50,160
+لما نيجي خليني بس لهنا أهم شغلات اللي اتكلم عليها
+
+93
+00:08:50,160 --> 00:08:54,200
+اتكلمنا على ال minerals و قولنا ال minerals هي
+
+94
+00:08:54,200 --> 00:08:59,730
+عبارة عن إيش؟inorganic materials و هاد ال
+
+95
+00:08:59,730 --> 00:09:05,750
+inorganic ممكن تكون metals و non-metals كويس؟ الآن
+
+96
+00:09:05,750 --> 00:09:11,610
+هان اتكلمنا على ال ore و ال ore قلنا عبارة عن ايش؟
+
+97
+00:09:11,610 --> 00:09:16,090
+مواد خام نخرجها من الأرض اللى عندى او من بين
+
+98
+00:09:16,090 --> 00:09:19,550
+الصخور اللى موجودة عندنا اتكلمنا ع ال diamond و ال
+
+99
+00:09:19,550 --> 00:09:25,550
+diamond هو a form of hearthard form of carbon وهذا
+
+100
+00:09:25,550 --> 00:09:30,950
+يعني abrasive لأنه صلب جدا فيستخدم العمليات القطع
+
+101
+00:09:30,950 --> 00:09:37,850
+cutting material and في هذا الحالة بنسميه
+
+102
+00:09:37,850 --> 00:09:39,390
+industrial diamond
+
+103
+00:09:42,220 --> 00:09:48,040
+السيليكون قولنا يعمل منه السيليكا ال ceramic و ال
+
+104
+00:09:48,040 --> 00:09:51,460
+ceramic بنعمل by applying high temperature ال
+
+105
+00:09:51,460 --> 00:09:56,760
+temperature الموجود عندك لما احنا نعمله heating to
+
+106
+00:09:56,760 --> 00:09:59,820
+high temperature بنسمي هذه العملية عملية ايش?
+
+107
+00:10:00,820 --> 00:10:05,100
+vitrifying او بنسمي المادة vitrified
+
+108
+00:10:08,460 --> 00:10:12,580
+الإيش؟ Klein اللي هو الفرن هذا اللي بن .. ال Klein
+
+109
+00:10:12,580 --> 00:10:21,580
+عادة فرن بيستخدم لحرق أو ..
+
+110
+00:10:21,580 --> 00:10:31,130
+ال إيش؟ Clay هذيكClay .. Clay طين و ال Klein هذه
+
+111
+00:10:31,130 --> 00:10:37,790
+.. هذه بتبقى فرن كبير صناعي بيستخدنوه لحرق المواد
+
+112
+00:10:37,790 --> 00:10:44,770
+زي مثلا الحجار زي السمنتز زي غيره فهذا يستخدم في
+
+113
+00:10:44,770 --> 00:10:46,650
+هذا المصانع الموجودة
+
+114
+00:10:49,500 --> 00:10:55,640
+الان نتكلم عن عصير عصير عصير عصير عصير عصير عصير
+
+115
+00:10:55,640 --> 00:10:57,000
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+116
+00:10:57,000 --> 00:11:01,160
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+117
+00:11:01,160 --> 00:11:08,900
+عصير عصير عصير عصير عصير
+
+118
+00:11:12,260 --> 00:11:16,940
+الـ technical advisor عادة بيبقى في ال structure
+
+119
+00:11:16,940 --> 00:11:23,940
+تبع المؤسسات الصناعية في حد بيستعينوا
+
+120
+00:11:23,940 --> 00:11:29,720
+فيهم خبراء فخبير تقني بيسموه technical advisor هو
+
+121
+00:11:29,720 --> 00:11:34,700
+البرشد في هذا المجال فهو for a glass manufacturer
+
+122
+00:11:34,700 --> 00:11:40,750
+اللي هي لأحدى مصانع الزجاجفهو giving a briefing
+
+123
+00:11:40,750 --> 00:11:47,710
+بيعطي زي نبدة أو بيعطي ملخص to a group of
+
+124
+00:11:47,710 --> 00:11:50,990
+engineers at a trade .. trade fair ايش ال trade
+
+125
+00:11:50,990 --> 00:11:53,530
+fair سمعتوا فيه؟
+
+126
+00:11:57,930 --> 00:12:02,510
+بيعملوا معارض تجارية trade fair معارض تجاري
+
+127
+00:12:02,510 --> 00:12:06,510
+فالمعارض التجارية إيش بيعملوا فيها؟ بيقدموا
+
+128
+00:12:06,510 --> 00:12:10,990
+المنتجات الجديدة للناس يعني عادة لما تشوفوا احنا
+
+129
+00:12:10,990 --> 00:12:14,690
+عندنا لإن الدنيا و سكرة علينا بنشوف إيش هذه الجزء
+
+130
+00:12:14,690 --> 00:12:21,260
+الجزء لما أي مؤسسات كل سنة نعمل مؤسسات إلهامعرض
+
+131
+00:12:21,260 --> 00:12:25,460
+سنوي أو معارض سنوية مثلا على سبيل المثال كانوا
+
+132
+00:12:25,460 --> 00:12:29,360
+كتير من اللي عندنا الصناعين اللي عندنا بطلع اللي
+
+133
+00:12:29,360 --> 00:12:32,620
+بيشتغلوا في ال boya بتعرف ال boya كل سنة إيش
+
+134
+00:12:32,620 --> 00:12:35,960
+بيحصللها؟ في تطوير مستمر إذا بتطلع على ال boya
+
+135
+00:12:35,960 --> 00:12:39,380
+اللي كانت مستخدمة قبل عشر سنين و ال boya المستخدمة
+
+136
+00:12:39,380 --> 00:12:44,630
+الآن تختلف تماماطب كيف هدول اللي عندنا الصناعة و
+
+137
+00:12:44,630 --> 00:12:47,350
+الناس اللي بتشتغل بتعرف فيها لازم يروحوا هاد
+
+138
+00:12:47,350 --> 00:12:52,270
+المعارض يعرفوا إيش هذه كيف ممكن استخدامها، إيش
+
+139
+00:12:52,270 --> 00:12:55,430
+ميزاتها عن اللي قبل عشان يقدروا يبيعوها للناس،
+
+140
+00:12:55,430 --> 00:12:58,710
+يوصولهم إيها نفس الشيء اللي أنت بتروحي في صناعة
+
+141
+00:12:58,710 --> 00:13:02,190
+الألمانيا و في الصناعات اللي .. كل سنة بروح على
+
+142
+00:13:02,190 --> 00:13:06,330
+المعارض كان احنا عندنا في عندنا في المنطقة معرضين
+
+143
+00:13:06,330 --> 00:13:12,600
+رئيسيينواحد بنعمل في مصر للهندسة بكل أو لهندسة
+
+144
+00:13:12,600 --> 00:13:16,180
+البناء وواحد بنعمل في الأردن كل سنة كانوا بطلع
+
+145
+00:13:16,180 --> 00:13:20,240
+المهندسين من عندنا والمقاومين بروحوا عادي للمعارضة
+
+146
+00:13:20,240 --> 00:13:24,320
+يشوفوا أيش جديد فيها في عالم التقنية وفي عالم
+
+147
+00:13:24,320 --> 00:13:30,090
+الاشيالان في ال .. في ال .. في المجال العلمي في
+
+148
+00:13:30,090 --> 00:13:33,150
+المؤتمرات السنوية اللي بتسير على مستوى العالم مثلا
+
+149
+00:13:33,150 --> 00:13:36,970
+في التقصص الفلاني في اتنين او تلاتة هدول معروفين
+
+150
+00:13:36,970 --> 00:13:41,250
+كل الناس اللي بتشتغل في هذا المجال بتيجي عليهالان
+
+151
+00:13:41,250 --> 00:13:46,390
+في الصناعات برضه ال .. كل إشي يقدم، بتشوفوا تجارنا
+
+152
+00:13:46,390 --> 00:13:51,510
+بروح ع الصين، ع المعارض، مظبوط اسمع فيهم، بروحوا
+
+153
+00:13:51,510 --> 00:13:54,690
+يشتريوا، الحين هم إيش بروحوا؟ بتفرجوا إيش اللي
+
+154
+00:13:54,690 --> 00:14:01,190
+بنعرض، فال fairs هذه هي عادة مكان ل ..يعرف إيش
+
+155
+00:14:01,190 --> 00:14:05,970
+جديد فلما حد بدى يعمل إيش جديد بعرض لهم هذا بيسميه
+
+156
+00:14:05,970 --> 00:14:09,950
+ال briefing بعرضهم إيش ميزة هذه الشغلة إيش جديد
+
+157
+00:14:09,950 --> 00:14:14,090
+فيها كيف بدهم يعرفوا الزباين عليها أو كيف بدهم
+
+158
+00:14:14,090 --> 00:14:18,770
+يستخدموها فهو بيبقى أخد فكرة كاملة أو المهندسة أو
+
+159
+00:14:18,770 --> 00:14:22,150
+المهندسة أخدت فكرة كاملة لكيف تشرح هذه الشغلة
+
+160
+00:14:22,150 --> 00:14:27,010
+لغيرها بيجيش يقرأ لحاله وده لهم أية سؤالة طبعا
+
+161
+00:14:27,010 --> 00:14:31,490
+بيسأله في هذا المجلد عرفتوا إيش ال fairفي ال fair
+
+162
+00:14:31,490 --> 00:14:36,830
+طبعا بختلف من حاجة للتانية الان sheets of glass
+
+163
+00:14:36,830 --> 00:14:41,790
+which are obviously flat and thin are called float
+
+164
+00:14:41,790 --> 00:14:47,570
+glass الحين الجزاز بيعملوه على شكل ايش ورق sheets
+
+165
+00:14:47,570 --> 00:14:55,310
+او شرائح الشرائح هذه بتبقى رقيقة ايش هنا هي flat
+
+166
+00:14:55,310 --> 00:15:01,490
+and thin بتبقى مستوية و رقيقةهذه بيسموها إيش float
+
+167
+00:15:01,490 --> 00:15:07,230
+glass فلو سألنا عن float glass هي sheet of glass
+
+168
+00:15:07,230 --> 00:15:13,110
+that are flat and thin كويس؟
+
+169
+00:15:13,110 --> 00:15:19,250
+طيب this refers to the manufacturing technique
+
+170
+00:15:19,250 --> 00:15:24,370
+where molten glass is floated on molten tin الآن
+
+171
+00:15:24,370 --> 00:15:31,290
+إيش بنسكب molten؟ إيش معناه؟ حكيناها قبلسائل أو
+
+172
+00:15:31,290 --> 00:15:37,050
+دائب يعني هو على شكل liquid مصهور هي الكلمة الأصحى
+
+173
+00:15:37,050 --> 00:15:41,030
+liquid على شكل سائل فهذا بنسميه molten glass
+
+174
+00:15:41,030 --> 00:15:44,610
+floating on molten tin اللي هي إيه؟ يا إما تنك يا
+
+175
+00:15:44,610 --> 00:15:52,120
+إما خرصين أو اللهان على طبقة دائبةطيب to produce
+
+176
+00:15:52,120 --> 00:15:56,500
+flat sheets usually after float .. float glass has
+
+177
+00:15:56,500 --> 00:16:01,080
+been formed it's annealed يعني إيش annealed هنا
+
+178
+00:16:01,080 --> 00:16:06,620
+تطلع عليها it's left to cool slowly الآن عملية ال
+
+179
+00:16:06,620 --> 00:16:13,680
+annealing هذه هي الجزاز الآن هو كان سائل مادة
+
+180
+00:16:13,680 --> 00:16:19,110
+سائلةأو من صاهرة الآن هي بدها تبرد شوية شوية هذه
+
+181
+00:16:19,110 --> 00:16:24,650
+العملية اسمها annealing لسبب لأنه لها مواصفات كويس
+
+182
+00:16:24,650 --> 00:16:28,710
+هنا ايش المواصفات تبعتها but if it's left in this
+
+183
+00:16:28,710 --> 00:16:32,410
+state and the glass later get broken it breaks
+
+184
+00:16:32,410 --> 00:16:36,670
+into dangerous sharp pieces تلاقي بعض الأجزاز من
+
+185
+00:16:36,670 --> 00:16:40,800
+حد ما يتكسر ايش بتصير؟القطع تبعته لأ، القطع
+
+186
+00:16:40,800 --> 00:16:45,040
+بتلاقيها sharp حادة وعلى طول هاد أي حد بمسك أي إشي
+
+187
+00:16:45,040 --> 00:16:50,300
+بتجرح في نوع تاني من الجزاز بتفتفت زي ال .. الرز
+
+188
+00:16:50,300 --> 00:16:57,000
+أو حاجات زي .. هاش جدا بتلاقيه بتفتفت .. يعني يمكن
+
+189
+00:16:57,000 --> 00:17:00,780
+بعرفش حدا فيكوا شافه ولا لأ الجزاز السيارة الخلفي
+
+190
+00:17:00,780 --> 00:17:06,100
+أو الشباك لما يتفتفت الشباك الجانبي كيف بتفتفت؟
+
+191
+00:17:06,100 --> 00:17:12,630
+بيصير صغير صغيرمش يعني .. بتحسهوش sharp زي الحاجات
+
+192
+00:17:12,630 --> 00:17:17,010
+مثل المرايا، المرايا لو انكسرت إيش بتلاقي شارحها؟
+
+193
+00:17:17,010 --> 00:17:21,010
+Sharp، هاد التاني بتلاقيه خفيف، الآن الإجزاز
+
+194
+00:17:21,010 --> 00:17:28,810
+الأمامي لو انكسر تبع السيارة إيش بيصير؟ بشجق يعني
+
+195
+00:17:28,810 --> 00:17:32,810
+لو انكسر، لو حد كسره و السيارة ماشية، بضرب حد من
+
+196
+00:17:32,810 --> 00:17:38,180
+حواليه؟بيضلوا مكانه هذا الانواع تلت انواع اجازة
+
+197
+00:17:38,180 --> 00:17:42,780
+عندك كويس ال annealed glass هذا ال glass الاش
+
+198
+00:17:42,780 --> 00:17:48,840
+heated and cooled slowly هذا ايش المواصفات تبعه it
+
+199
+00:17:48,840 --> 00:17:52,440
+broken into sharp ده بتطلع هنا
+
+200
+00:17:55,820 --> 00:18:00,740
+sharp pieces وهذا dangerous اللي عندي كويس large
+
+201
+00:18:00,740 --> 00:18:05,720
+sharp pieces هدولها حادة هذا بيسمي ايش a nailed
+
+202
+00:18:05,720 --> 00:18:12,620
+glass for most engineering and architecture uses a
+
+203
+00:18:12,620 --> 00:18:18,560
+nailed glass is unsuitable مش مناسب لأن هذا خطر
+
+204
+00:18:18,560 --> 00:18:24,910
+على الناس اللي حواليهwe need to use what we call
+
+205
+00:18:24,910 --> 00:18:32,590
+safety glass اللي هو الزجاج اللي هو آمن، الزجاج
+
+206
+00:18:32,590 --> 00:18:39,020
+الآمن بتحب أنه لما نتفات فات مايعملشالتشوهات يمكن
+
+207
+00:18:39,020 --> 00:18:42,720
+حتى لاحظتوها انتوا ايام الحروب شبابيك كانت لما انت
+
+208
+00:18:42,720 --> 00:18:47,700
+تتكسر تأذي اكتر من ايش من هذا بس طلعت شبابيك
+
+209
+00:18:47,700 --> 00:18:51,680
+السيارات اللي هي مصممة safe ايش بيصير فيها حتى لما
+
+210
+00:18:51,680 --> 00:18:57,960
+تتكسر وانت في السيارة بسركيش بتيجي الحبيبات
+
+211
+00:18:57,960 --> 00:19:02,620
+صغيرة صغيرةفبتقديش هذا اللي ورا اللي هو مش مصمم
+
+212
+00:19:02,620 --> 00:19:07,600
+انه ايش انه ينضرب يعني ال .. الامام هو اللي مصمم
+
+213
+00:19:07,600 --> 00:19:12,300
+لهذا لأنه انت يعني بتلاحظوهاش كتير بس عادة و انت
+
+214
+00:19:12,300 --> 00:19:15,980
+ماشي ع الشارع احيانا السيارة اللي قدام تدعس على
+
+215
+00:19:15,980 --> 00:19:19,640
+حجر بطير الحجر على الشباك اللي انت .. و انت ماشي
+
+216
+00:19:19,640 --> 00:19:24,160
+فهذا بتلاقي اش بيسوي بيكسر الاجزاز بس الاجزاز
+
+217
+00:19:24,160 --> 00:19:29,960
+بتفتفتش او بيقديش بهذه الشغلةلأنه بصنع من ايش؟
+
+218
+00:19:29,960 --> 00:19:34,860
+safety glass، هنا عندي unnailed glass وهنا ايش؟
+
+219
+00:19:34,860 --> 00:19:38,340
+safety glass one type of safety glass is toughened
+
+220
+00:19:38,340 --> 00:19:45,140
+glass هذا نوع منه بيسموه toughened glass يعني زجاج
+
+221
+00:19:45,140 --> 00:19:52,160
+مقوة toughened glass هم نوعين ونوع ال safety glass
+
+222
+00:19:52,160 --> 00:19:57,690
+له نوعينواحد بنسميه toughened glass also called
+
+223
+00:19:57,690 --> 00:20:03,970
+tempered glass و ال tempered glass هي نفس الشغلة
+
+224
+00:20:03,970 --> 00:20:08,190
+إيش هذا مواصفاته as the term suggests the glass is
+
+225
+00:20:08,190 --> 00:20:12,270
+tempered if heated and kept hot for a certain time
+
+226
+00:20:12,270 --> 00:20:18,090
+يعني هذا قلنا بنسخنه وبعده بيخليه برد شوي شوي ال
+
+227
+00:20:18,090 --> 00:20:24,240
+annealed هذا بنسخنه و بيخليه ساخن لفترة معينةto
+
+228
+00:20:24,240 --> 00:20:27,320
+change its structure هذا لما نسخنه زي هيك ال
+
+229
+00:20:27,320 --> 00:20:35,120
+structure تبعه بتغير then if tempered glass is
+
+230
+00:20:35,120 --> 00:20:40,540
+broken it shatters it shatters تتفتفت هي معناه
+
+231
+00:20:40,540 --> 00:20:47,170
+shatters it breaks into tiny piecesجزيئات صغيرة
+
+232
+00:20:47,170 --> 00:20:51,750
+صغيرة زي ما قلتلكوا لو حد شاف سيارة سيارة الشباك
+
+233
+00:20:51,750 --> 00:20:55,570
+الخلفي تبع السيارة لما نيتفات فات بتلاقيه شقف
+
+234
+00:20:55,570 --> 00:20:59,010
+صغيرة صغيرة حتى لما بدك تنظفيه من السيارة تطلع
+
+235
+00:20:59,010 --> 00:21:02,910
+عينك و أنت تدور عليهم و تبقى لك تنظف لشهر بعد ما
+
+236
+00:21:02,910 --> 00:21:10,230
+.. او شهرين بعد ما تعملي هذه الشغلهذه الميزة تبعد
+
+237
+00:21:10,230 --> 00:21:13,050
+كثير من الميزة التي تنتج من خلال عصر طويل و صحيح
+
+238
+00:21:13,050 --> 00:21:23,370
+عند تحطم عصر طويل و صحيح
+
+239
+00:21:23,370 --> 00:21:30,240
+عند تحطم عصر طويلthe disadvantage of toughen glass
+
+240
+00:21:30,240 --> 00:21:34,460
+is that it cannot withstand impact from small
+
+241
+00:21:34,460 --> 00:21:38,360
+objects such as flying stone طبعا لو أجالها حجر
+
+242
+00:21:38,360 --> 00:21:44,010
+طاير تتحملوش هذي بتتفتفت بسرعةواللي شاف عارف هذه
+
+243
+00:21:44,010 --> 00:21:47,930
+الشغلة مجربها يعني، في السيارات مصر عم يتقل
+
+244
+00:21:47,930 --> 00:21:52,210
+الإجازة، من حجر طاير ماشي في الشارع أو ولد بيخبطله
+
+245
+00:21:52,210 --> 00:21:56,250
+حجر بتلاقيه زي هيك أو كبير بيخبطله حجر على السيارة
+
+246
+00:21:56,250 --> 00:22:03,740
+بتلاقيه فت فت بشكل واضحطيب so for instance that
+
+247
+00:22:03,740 --> 00:22:09,300
+makes it unsuitable for vehicle windscreen الشباك
+
+248
+00:22:09,300 --> 00:22:14,360
+الأمامي بيسميه windscreen او windshield ايش اسمه
+
+249
+00:22:14,360 --> 00:22:19,240
+هذا اللي بتستخدمه windscreen وممكن نسميه wind
+
+250
+00:22:23,540 --> 00:22:29,480
+windshield هدولة نفس الشغلة اللي هي الشباك الأمامي
+
+251
+00:22:29,480 --> 00:22:34,220
+ال windshield و windscreen إيش معناته هذا هو مواجه
+
+252
+00:22:34,220 --> 00:22:38,520
+للإيش للهواء يعني هذا بدي يتحمل ضغط أكتر لإن
+
+253
+00:22:38,520 --> 00:22:45,500
+السيارة و هي ماشي هذا جزء من body تبع حصار so in
+
+254
+00:22:45,500 --> 00:22:50,800
+cases where impact إيش ال impact؟ قلنا تصادم لأ
+
+255
+00:22:50,800 --> 00:22:58,980
+هذا ال impact صدمةالصدمة ال impact are a problem
+
+256
+00:22:58,980 --> 00:23:02,420
+another type of safety glass بنسميه laminated
+
+257
+00:23:02,420 --> 00:23:05,660
+glass لان عندي safety glass عندي نوعين
+
+258
+00:23:10,760 --> 00:23:18,300
+Laminated glass is made by
+
+259
+00:23:18,300 --> 00:23:21,660
+laminating glass with a polymer
+
+260
+00:23:30,230 --> 00:23:34,850
+إيش بتلاقي في النص عشان هيك بتفتفتش لو طلعت على
+
+261
+00:23:34,850 --> 00:23:38,050
+الشباك الأمام تبقى السيارة فيها مادة زي ال plastic
+
+262
+00:23:38,050 --> 00:23:43,470
+في النص فهي بساوية sandwich في النص المادة شجة
+
+263
+00:23:43,470 --> 00:23:49,560
+glass من الشجة ها و الشجة التانية فيها glassمع الـ
+
+264
+00:23:49,560 --> 00:23:53,640
+Polymer في كلمة أخرى، تصنع عجزة ومقالة Polymer مع
+
+265
+00:23:53,640 --> 00:23:58,640
+مقالة Polymer في الموسيقى ومقالات عجزة في جميع
+
+266
+00:23:58,640 --> 00:24:04,020
+الجانحين فإن فرصة الحصول على مادة ملزقة ليست فقط
+
+267
+00:24:04,020 --> 00:24:10,500
+.. إنها قوية جدًا، مجموعات العجزة مجموعة Polymer
+
+268
+00:24:10,500 --> 00:24:11,920
+يعني مجموعة ملزقة
+
+269
+00:24:15,330 --> 00:24:18,730
+they are struck to the polymer, so if the glass
+
+270
+00:24:18,730 --> 00:24:22,670
+does break, the broken pieces are held together
+
+271
+00:24:22,670 --> 00:24:26,790
+and don't fly يعني هذا لو انكسر وهذا بتلاحظوه
+
+272
+00:24:26,790 --> 00:24:32,210
+بتلاقي ايش هو بتشجج او بنكسر بس بتطيرش حاجة منه
+
+273
+00:24:32,210 --> 00:24:37,990
+بيضله موجود هذا بيأديش الناس اللي قاعدة، مظبوط؟ اه
+
+274
+00:24:37,990 --> 00:24:42,670
+طب ليش مانعمل شبابيكنا منه؟ التأكل فعال يعني
+
+275
+00:24:47,380 --> 00:24:51,400
+طيب الان شوفنا ايش الأنواع هذا اتكلمنا على three
+
+276
+00:24:51,400 --> 00:24:56,280
+kinds of glass ايش هم او type of glass ايش .. un
+
+277
+00:24:56,280 --> 00:25:01,140
+-nailed glass safety glass وفيه يقولنا نوعين فيه
+
+278
+00:25:01,140 --> 00:25:06,980
+ايش هو toughened او tampered glass و laminated
+
+279
+00:25:06,980 --> 00:25:11,760
+glass الفرق بين ال .. ال un-nailed و ال safety ان
+
+280
+00:25:11,760 --> 00:25:16,790
+ال un-nailed it get heatedand get cooled down
+
+281
+00:25:16,790 --> 00:25:21,150
+slowly بينما a toughened glass get heated for a
+
+282
+00:25:21,150 --> 00:25:25,850
+period of time stays heated بعد هيك ايش it cooled
+
+283
+00:25:25,850 --> 00:25:29,750
+down التافند
+
+284
+00:25:29,750 --> 00:25:33,070
+و ال .. التافند و ال .. و ال ايش annealed?
+
+285
+00:25:34,490 --> 00:25:40,280
+laminated?tempered نفس الاسم tempered and
+
+286
+00:25:40,280 --> 00:25:44,340
+toughened هي نفس الاسم الان ال laminated في عندى
+
+287
+00:25:44,340 --> 00:25:51,460
+polymer layer in the middle كويس فهي bounded يعني
+
+288
+00:25:51,460 --> 00:25:55,950
+ال polymer و ال glass boundedto each other الان
+
+289
+00:25:55,950 --> 00:26:01,670
+الاختلاف هذا الاختلاف فيها ال poly .. ال .. ال ..
+
+290
+00:26:01,670 --> 00:26:05,670
+laminated glass في عندى polymer plus ايش؟ glass
+
+291
+00:26:05,670 --> 00:26:10,250
+bounded together they form a sandwich sandwich في
+
+292
+00:26:10,250 --> 00:26:14,230
+عندى polymer in the middle two layer of glass on
+
+293
+00:26:14,230 --> 00:26:19,330
+each sideالان exercise fifteen one decide whether
+
+294
+00:26:19,330 --> 00:26:22,930
+the sentences below are true or false then change
+
+295
+00:26:22,930 --> 00:26:26,330
+one word in each of the false sentences to correct
+
+296
+00:26:26,330 --> 00:26:31,510
+them Minerals are organic, false أيش قلنا؟
+
+297
+00:26:31,510 --> 00:26:36,870
+inorganic Minerals can be found in rocks, true
+
+298
+00:26:36,870 --> 00:26:42,410
+Silica is a compound containing siliconصحيحة
+
+299
+00:26:42,410 --> 00:26:48,790
+مصارعين يمكن أن يكونوا متاليك أو لا متاليك صحيحة
+
+300
+00:26:48,790 --> 00:26:56,390
+مصارع دايمون عامل مصارع متاليك لا متاليك لا متاليك
+
+301
+00:26:56,390 --> 00:27:04,310
+لأنه قلنا دايمون هو نوع من كربون طيب لكي تصبح
+
+302
+00:27:04,310 --> 00:27:10,150
+مصارع كراميكا المواد يجب أن تكون محفظة خاطئ
+
+303
+00:27:14,110 --> 00:27:20,190
+ال glass اللي ايش glass .. glass-like مظبوط هو ال
+
+304
+00:27:20,190 --> 00:27:26,670
+glass اللي بيصيره verified مظبوط مش ال ceramic طيب
+
+305
+00:27:26,670 --> 00:27:33,290
+ال clay can be fired to produce material with a
+
+306
+00:27:33,290 --> 00:27:37,770
+glass-like structure true الفخار مواصفته زي
+
+307
+00:27:37,770 --> 00:27:43,170
+مواصفات ايش؟ ال glass مظبوط هذه بتشوفوه في الحياة
+
+308
+00:27:43,170 --> 00:27:48,760
+تبعتناطيب use the words and expressions in the box
+
+309
+00:27:48,760 --> 00:27:52,180
+to describe each photo you will need to use some
+
+310
+00:27:52,180 --> 00:27:58,460
+words more than once الان هذا ايش هو ايش هو بالظبط
+
+311
+00:27:58,460 --> 00:28:06,660
+هذا هذا ال exhaust تبع السيارة الأمامي ايوة هنا هي
+
+312
+00:28:06,660 --> 00:28:13,490
+broken نوع هذا ايش laminated glass ايش كمانSafety
+
+313
+00:28:13,490 --> 00:28:19,410
+glass و إيش هذا windscreen مظبوط هذا شايفين كيف
+
+314
+00:28:19,410 --> 00:28:28,730
+إيش مفتفت كيف زي إيش زي السكر أو الرز أو الحبيبات
+
+315
+00:28:28,730 --> 00:28:35,410
+الصغيرة tiny pieces هذا إيش هو toughened و
+
+316
+00:28:35,410 --> 00:28:39,010
+tempered و هو قولنا نوع من أنواع إيش ال safety
+
+317
+00:28:39,010 --> 00:28:44,380
+glass هذا تطلعوا كيف شكلههذا زي اللي بتشوفوه عادي
+
+318
+00:28:44,380 --> 00:28:51,500
+ايوة sharp edges هذا بنسميه annealed glass اللي هو
+
+319
+00:28:51,500 --> 00:28:56,740
+شايفين كيف الشكل تبعه؟ هذا اللي بنشوفه العادي اللي
+
+320
+00:28:56,740 --> 00:29:01,000
+احنا بنستخدمه
+
+321
+00:29:01,000 --> 00:29:07,060
+طيب سمعتوا في حاجة اسمها water bullet proof glass؟
+
+322
+00:29:07,060 --> 00:29:16,600
+ايش يعني؟اسمعتوا فيه؟ طيب،
+
+323
+00:29:16,600 --> 00:29:20,420
+الآن هي .. إيش بنقولها؟ complete the article about
+
+324
+00:29:20,420 --> 00:29:24,320
+bulletproof glass for .. from a science and
+
+325
+00:29:24,320 --> 00:29:28,860
+technology magazine using words from B sometimes
+
+326
+00:29:28,860 --> 00:29:33,340
+more than one word is possible الآن ممكن أكتر من
+
+327
+00:29:33,340 --> 00:29:37,940
+كلمة بس طالع اسمعوا إيش اللي حاكيهاbullet proof is
+
+328
+00:29:37,940 --> 00:29:41,420
+a loosely used word suggesting something is
+
+329
+00:29:41,420 --> 00:29:45,720
+totally unbreakable
+
+330
+00:29:45,720 --> 00:29:49,980
+اللي عندي، الآن هو بقول bullet proof هو إيش؟
+
+331
+00:29:49,980 --> 00:29:56,760
+loosely used word، يعني إيش loosely؟ لأ، هي هذه
+
+332
+00:29:56,760 --> 00:30:01,990
+slangيعني هو مصطلح إيش بيقول يعني ال bullet proof
+
+333
+00:30:01,990 --> 00:30:08,870
+اللي هو كلمة المقاوم للرصاص هو مصطلح يستخدم يعني
+
+334
+00:30:08,870 --> 00:30:14,090
+مش بدي أقول بتوسع بستخدم زيادة عن حده يعني مش
+
+335
+00:30:14,090 --> 00:30:19,650
+واقعي بعبارة تانية loosely used word يعني هي
+
+336
+00:30:19,650 --> 00:30:24,930
+متجاوز في استخدام الكلمة كويس في تجاوز في استخدام
+
+337
+00:30:24,930 --> 00:30:31,480
+الكلمة يعني أنا مش مستخدمهامعناها الحقيقي هي مصطلح
+
+338
+00:30:31,480 --> 00:30:36,180
+أنه فيه تجاوز وهذا بتنحكم lose the use word يعني
+
+339
+00:30:36,180 --> 00:30:41,460
+أنت أحيانا بتحكي الكلمة مش مبالغ فيها مبالغ فيها
+
+340
+00:30:41,460 --> 00:30:47,560
+زي ما بيقول تسليم انت مبالغ في الكلمة but
+
+341
+00:30:47,560 --> 00:30:53,300
+technicallyspeaking how accurate is the term
+
+342
+00:30:53,300 --> 00:30:58,440
+bullet proof glass يعني من ناحية التقنية مدى دقة
+
+343
+00:30:58,440 --> 00:31:06,070
+هذا المصطلح outside of Hollywood moviesCan glass
+
+344
+00:31:06,070 --> 00:31:10,950
+really stop bullets يعني بعيدا عن أفلام هولووود
+
+345
+00:31:10,950 --> 00:31:17,910
+قداش الجزاز بيقدر يوقف الرصاص؟ أيوة بعيدا عن
+
+346
+00:31:17,910 --> 00:31:23,730
+المفالقة اللي بتحكي هانقولها The answer is not on
+
+347
+00:31:23,730 --> 00:31:30,910
+its own but if several .. إيش .. if glass are
+
+348
+00:31:30,910 --> 00:31:37,520
+sandwich إيش اللي أحنا بنعمله؟Layers او sheets
+
+349
+00:31:37,520 --> 00:31:43,340
+احنا حاطينا طبقات من الاجزاز كويس هنا اللي بنحكيها
+
+350
+00:31:43,340 --> 00:31:46,740
+Sandwich
+
+351
+00:31:46,740 --> 00:31:51,140
+اللي هي اتجمعت مع بعض يعني with a high strength
+
+352
+00:31:51,140 --> 00:31:58,460
+polymer معه polymer بقوة عالية to form ايش؟ a
+
+353
+00:31:58,460 --> 00:32:02,980
+glass to
+
+354
+00:32:02,980 --> 00:32:12,160
+formlaminated okay laminated glass كويس طيب أنا
+
+355
+00:32:12,160 --> 00:32:16,380
+عارف بس عشان هيكوديا كنت تعودوا عليها laminated
+
+356
+00:32:16,380 --> 00:32:18,740
+glass bullet resistance
+
+357
+00:32:21,520 --> 00:32:26,000
+if not completely bullet proof barrier can be
+
+358
+00:32:26,000 --> 00:32:31,400
+obtained عادة لو احنا جمعنا خلينا نقول ال glass
+
+359
+00:32:31,400 --> 00:32:36,520
+اللي هو طبقات من الزجاج وفيه polymer قوي plastic
+
+360
+00:32:36,520 --> 00:32:41,060
+قوي في النص وهذا بتلاقي الدروع اللي هي الواقع من
+
+361
+00:32:41,060 --> 00:32:45,880
+الرصاص هي عبارة عن ايش polymers بس حواليها بدل ما
+
+362
+00:32:45,880 --> 00:32:51,990
+يكون glassحديد وبتبقى أنواع خفيفة يعني من الحديد
+
+363
+00:32:51,990 --> 00:32:57,550
+فبتلاقي هذا .. بس هذا ال bullet proof بيسمي bullet
+
+364
+00:32:57,550 --> 00:32:59,270
+proof chest
+
+365
+00:33:02,100 --> 00:33:07,280
+اللي عندى chest jacket هادى تختلف عن ال bullet
+
+366
+00:33:07,280 --> 00:33:12,820
+proof glass ال glass بنعمل طبقات كبيرة من الزجاج
+
+367
+00:33:12,820 --> 00:33:16,800
+يعني خلّيني أقول toughened أو الزجاج laminated
+
+368
+00:33:16,800 --> 00:33:23,120
+وفيه طبقات polymer قوية هذا اللي بنحكيها طيب the
+
+369
+00:33:23,120 --> 00:33:26,520
+technology of sandwiching polymer and glass is
+
+370
+00:33:26,520 --> 00:33:33,970
+nothing unusualcar windscreen are made by الكلمة
+
+371
+00:33:33,970 --> 00:33:37,650
+اللي كررتها كتير bonding اللي هي ال bonding لما
+
+372
+00:33:37,650 --> 00:33:43,270
+الحاجتين يتلزجهم بعض أو يتحدوا مع بعض glass to a
+
+373
+00:33:43,270 --> 00:33:49,370
+polymer such as BVB هذه نوع من أنواع ال plastic
+
+374
+00:33:49,370 --> 00:33:54,910
+القويto form a type of safety glass unlike the
+
+375
+00:33:54,910 --> 00:33:58,990
+other main type of safety glass ايش هنا بنقول
+
+376
+00:33:58,990 --> 00:34:02,770
+toughened أو tempered glass اللي هي النوع التاني
+
+377
+00:34:02,770 --> 00:34:08,410
+laminated glass remains intact on breaking يعني كل
+
+378
+00:34:08,410 --> 00:34:14,850
+أنواع ال glass الأخرى بتتفتفت لما ايش او يعني ايش
+
+379
+00:34:14,850 --> 00:34:19,950
+بنقول عنها كلمة scattered لما ايش يصير لها
+
+380
+00:34:19,950 --> 00:34:24,880
+breakingهذه بتضل ايش بتقول لما ينكسر الاجزاز
+
+381
+00:34:24,880 --> 00:34:31,380
+بيضلوا together يعني intact .. intact بيضلوا يعيش
+
+382
+00:34:31,380 --> 00:34:33,580
+مع بعضه
+
+383
+00:34:36,770 --> 00:34:41,770
+طيب intact if a stone hits a window screen even
+
+384
+00:34:41,770 --> 00:34:46,230
+though a small section of the glass on the outside
+
+385
+00:34:46,230 --> 00:34:50,750
+may crack, the polymer behind it will stop the
+
+386
+00:34:50,750 --> 00:34:54,730
+stone and also ensure the entire piece of glass
+
+387
+00:34:54,730 --> 00:35:02,660
+does not shatter يعني بتتفتشتتفتفتش هي يعني لو
+
+388
+00:35:02,660 --> 00:35:06,520
+انكسر من برا بيظل ال polymer ماسكه و بيضمن ان هذا
+
+389
+00:35:06,520 --> 00:35:13,960
+ما ينكسرشbullet resistance
+
+390
+00:35:13,960 --> 00:35:18,540
+glass uses the same principle but must be much
+
+391
+00:35:18,540 --> 00:35:22,540
+tougher يعني نفس الفكرة بيستخدمها bullet proof
+
+392
+00:35:22,540 --> 00:35:29,960
+glass a stronger polymer is therefore used often
+
+393
+00:35:29,960 --> 00:35:35,000
+polycarbonate as well as greater .. بتتذكر مرة
+
+394
+00:35:35,000 --> 00:35:40,110
+فاتة اتكلمنا عن polycarbonateقولنا هذا نوع من الـ
+
+395
+00:35:40,110 --> 00:35:44,950
+polymers القوى البلاستيكو المقوى as well as
+
+396
+00:35:44,950 --> 00:35:52,050
+greater number of layers أو sheets of glass and
+
+397
+00:35:52,050 --> 00:35:55,890
+polymers يعني هذا إيش اللي بيعملوا بالظبط بيحط
+
+398
+00:35:55,890 --> 00:36:00,070
+طبقات مش طبقة طبقات من ال polymers ال polymers
+
+399
+00:36:00,070 --> 00:36:04,890
+الآن بدنا إياه مقوة اللي هو قولنا النوع اللي إيش
+
+400
+00:36:04,890 --> 00:36:10,140
+polymer carbonateهذا من القوي و نعمل طبقات في
+
+401
+00:36:10,140 --> 00:36:15,840
+الآخر هذا بنقول أنه لو أجت له رصاصة بتحملها طبعا
+
+402
+00:36:15,840 --> 00:36:21,740
+حسب نوع الرصاصة رصاصة الأيام هذه بيخزغ الحديد مش
+
+403
+00:36:21,740 --> 00:36:28,900
+بس الإجازة اللي هو ال uranium enriched bullets هذه
+
+404
+00:36:28,900 --> 00:36:35,360
+بتدخل على كل شي في طريقة طيب هيك بنبقى chapter 15
+
+405
+00:36:36,670 --> 00:36:43,750
+خلصنا او المحاضرة الجاية احنا النصف عنكم داخل
+
+406
+00:36:43,750 --> 00:36:44,610
+ستاشر وسبعة
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/9QmZQ18Yl5w_postprocess.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/9QmZQ18Yl5w_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b44bfbbe88fff9a7b33017c1fc3768ee677783c1
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/9QmZQ18Yl5w_postprocess.srt
@@ -0,0 +1,2248 @@
+1
+00:00:20,770 --> 00:00:26,470
+السلام عليكم اليوم سنكتشف حلقة ثلاثة حلقة ثلاثة
+
+2
+00:00:26,470 --> 00:00:31,430
+تتكلم عن نقاط التصميم التصميم التصميم التصميم
+
+3
+00:00:31,430 --> 00:00:32,250
+التصميم التصميم التصميم التصميم التصميم التصميم
+
+4
+00:00:32,250 --> 00:00:37,310
+التصميم التصميم التصميم التصميم التصميم التصميم
+
+5
+00:00:37,310 --> 00:00:41,470
+التصميم التصميم التصميم التصميم التصميم التصميم
+
+6
+00:00:41,470 --> 00:00:41,690
+التصميم التصميم التصميم التصميم التصميم التصميم
+
+7
+00:00:41,690 --> 00:00:45,710
+التصميم التصميم التصميم التصميم التصميم التصميم
+
+8
+00:00:45,710 --> 00:00:49,170
+التصميم التصميم التصميم التصميم التصميم التصميم
+
+9
+00:00:49,170 --> 00:00:54,080
+التصمdesign objectives if you look the webpage
+
+10
+00:00:54,080 --> 00:00:58,600
+below is from a manufacturing company company's
+
+11
+00:00:58,600 --> 00:01:03,740
+intranet إيش الفرق بين ال internet و ال intranet؟
+
+12
+00:01:03,740 --> 00:01:10,680
+حد بتعرف؟ ال internet كلكم بتعرفوها صح؟ ال
+
+13
+00:01:10,680 --> 00:01:14,960
+intranet الآن الشبكة الداخلية تبعت الجامعة بنسميها
+
+14
+00:01:14,960 --> 00:01:22,060
+intranet اللي هي شبكة داخلية بالمؤسسةمش بـ مفتوحة
+
+15
+00:01:22,060 --> 00:01:26,900
+للناس التانية عرفتوا إيش الفرق بينها؟ هي كلمة
+
+16
+00:01:26,900 --> 00:01:32,220
+جديدة عليكم الـ Intranet اللي هي كلمة موجودة ..
+
+17
+00:01:32,220 --> 00:01:36,060
+يعني هي يقصد فيها الـ Internet مفتوحة لكل العالم،
+
+18
+00:01:36,060 --> 00:01:41,580
+صح؟ الـ Intranet مفتوحة لداخل المؤسسةيعني لو جيت
+
+19
+00:01:41,580 --> 00:01:45,620
+تتفرجتي على حاجة بس موجودة داخل الجامعة الإسلامية
+
+20
+00:01:45,620 --> 00:01:50,640
+من برا بتشوفيهاش فهي هذه شبكة الـ Intranet و عادة
+
+21
+00:01:50,640 --> 00:01:54,980
+بيبقى عليها حماية على اساس اللي برا مايدخلوش عليها
+
+22
+00:01:54,980 --> 00:01:58,400
+فهذه لها sharing file، objectives، أي حاجة بدك
+
+23
+00:01:58,400 --> 00:02:04,180
+تعمليها، تعمليها داخلها فليش اتطلع company design
+
+24
+00:02:04,180 --> 00:02:08,100
+procedure، design brief عرفنا احنا ايش ال design
+
+25
+00:02:08,100 --> 00:02:13,360
+brief، صح؟الأن بنكمل a design brief for the
+
+26
+00:02:13,360 --> 00:02:17,760
+proposed product should be drawn up by the project
+
+27
+00:02:17,760 --> 00:02:21,100
+engineer طيب ال design brief اللي هي الملفة
+
+28
+00:02:21,100 --> 00:02:27,420
+proposed product إيش يعني؟ ال product عارفين إيش
+
+29
+00:02:27,420 --> 00:02:32,580
+ال product؟ المنتج و ال proposed المقترح المقترح
+
+30
+00:02:32,580 --> 00:02:39,450
+المنتج المقترح should be drawn up إيش drawn up؟لأ
+
+31
+00:02:39,450 --> 00:02:43,450
+مش رسم الان
+
+32
+00:02:43,450 --> 00:02:48,170
+طلعت drawn up by the project engineer الان هي
+
+33
+00:02:48,170 --> 00:02:54,450
+بتجمع او تحدد هذا .. هذا المقصود فيها مش المقصود
+
+34
+00:02:54,450 --> 00:02:59,810
+فيها انه نرسمها okay عادة هي كلمة drawn up هي
+
+35
+00:02:59,810 --> 00:03:04,090
+بتفكر .. بتاخد .. بتاخد كلمة الرسم بس هي ككلة
+
+36
+00:03:04,090 --> 00:03:09,830
+بنحدد المعالم تحدد المعالم فيهاthis should consist
+
+37
+00:03:09,830 --> 00:03:13,910
+of a detailed list of technical objectives شايف ال
+
+38
+00:03:13,910 --> 00:03:21,150
+objective بترتسم ولا بتم تحديدها؟ ايوة ف drawn up
+
+39
+00:03:21,150 --> 00:03:23,410
+اللي هي تحدد determinant
+
+40
+00:03:28,020 --> 00:03:30,600
+this should consist of a detailed list of
+
+41
+00:03:30,600 --> 00:03:33,600
+technical objectives which the design team must
+
+42
+00:03:33,600 --> 00:03:39,020
+work to in order to produce a design solution يعني
+
+43
+00:03:39,020 --> 00:03:43,780
+هدول المحددات أو ال constraints هذا من ضمنها ال
+
+44
+00:03:43,780 --> 00:03:47,700
+constraints إيش هي المحددات عادة لما بدي أعمل أي
+
+45
+00:03:47,700 --> 00:03:51,480
+مشروع أو بدي أنتج أي إشي بديش أقول هو بدي أنتج
+
+46
+00:03:51,480 --> 00:03:55,440
+حاجة بتشتغل لكل إشي إذا بدي أعمل حاجة بتشتغل لكل
+
+47
+00:03:55,440 --> 00:04:00,390
+إشي بقدرش أعمل حاجةفلازم أحط محددات و هنتكلم عن
+
+48
+00:04:00,390 --> 00:04:05,050
+المحددات كمان شوية إيش هي بس لازم نحط constraints
+
+49
+00:04:05,050 --> 00:04:11,270
+كويس to produce a design solution اللي هي حل أو هي
+
+50
+00:04:11,270 --> 00:04:16,050
+تصميم يعني design objectives إيش اللي ممكن يكون
+
+51
+00:04:16,050 --> 00:04:20,750
+فيها؟ key elements of the design brief هدول إيش؟
+
+52
+00:04:20,750 --> 00:04:24,830
+مكونات design brief function إيش ال function؟
+
+53
+00:04:26,980 --> 00:04:31,660
+الوظيفة إيش الغرض من ال product هذا وظيفة ال
+
+54
+00:04:31,660 --> 00:04:37,400
+product ال product intended use لإيش بدي استخدمه
+
+55
+00:04:37,400 --> 00:04:44,180
+intend إيش النية في الاستخدام use استخدام what is
+
+56
+00:04:44,180 --> 00:04:49,440
+it is designed to do إيش هي صممة لتعمل including
+
+57
+00:04:49,440 --> 00:04:53,860
+performance targets إيش ال performance targets
+
+58
+00:04:56,050 --> 00:04:59,970
+يعني أهداف أداء في الأداء في حاجة أنا بدي إياها
+
+59
+00:04:59,970 --> 00:05:05,010
+تعمل إيه من ناحية ال strength المتانة إنها بتنكسرش
+
+60
+00:05:05,010 --> 00:05:12,550
+power قوة قوية من ناحية durability تتحمل عرفتوا
+
+61
+00:05:12,550 --> 00:05:19,290
+إيش بتلاقي هدول strength متانةpower قوة يعني إنها
+
+62
+00:05:19,290 --> 00:05:23,870
+جوية بتقدر تعملها ال durability إنها لو يعني
+
+63
+00:05:23,870 --> 00:05:28,730
+بتتحمل الغابرة بتتحمل الضرب، بتتحمل الصغار يلعبوا
+
+64
+00:05:28,730 --> 00:05:32,730
+فيها، بتتحمل الكبار يوجعوها، كل هذه في تحمل إنها
+
+65
+00:05:32,730 --> 00:05:38,490
+بتخربش، يمكن كل كشتريته حاجات صينية، مظبوط؟ رخيصة،
+
+66
+00:05:38,490 --> 00:05:45,120
+بس إيش؟ أي حاجة اللي هي خربانةفى حاجات بتلاقيها
+
+67
+00:05:45,120 --> 00:05:50,200
+منتجات نوعية اعلى بتلاقيها ايش؟ بتتحمل يعني لو
+
+68
+00:05:50,200 --> 00:05:53,360
+وجعت حاجة ازا صغيرة اي ايش بتتحمل فيها فهذا
+
+69
+00:05:53,360 --> 00:05:57,840
+المتكلمة فال function اللي هي الوظيفة تبعتها اللي
+
+70
+00:05:57,840 --> 00:06:02,120
+هي what it is intended for او what it is designed
+
+71
+00:06:02,120 --> 00:06:06,380
+to do هذه لازم نفهمها ايش الحاجة التانية؟
+
+72
+00:06:06,380 --> 00:06:12,820
+constraintsلو انا بدي اعمل حلول تشتغل لكل شي بتنفع
+
+73
+00:06:12,820 --> 00:06:16,500
+في كل الظروف تصبتش مع الدنيا فلازم يكون عندي
+
+74
+00:06:16,500 --> 00:06:20,740
+constraints limit on the design for example it
+
+75
+00:06:20,740 --> 00:06:24,200
+must not exceed a maximum size or weight limit
+
+76
+00:06:24,200 --> 00:06:28,120
+يعني بقدرش مثلا ان انا بدي أسوي جهاز remote زي هيك
+
+77
+00:06:28,120 --> 00:06:33,860
+بقدرش أعمله هالجد بطل remote صح؟ ببطل أقدر أشيله
+
+78
+00:06:35,240 --> 00:06:39,960
+بدي يكون حجمه معقول ووزنه معقول نفس الشيء يعني هذا
+
+79
+00:06:39,960 --> 00:06:44,920
+لو كان كله steel تقيل اللي بيظل ماشي .. ماسك فترة
+
+80
+00:06:44,920 --> 00:06:49,620
+بتتعب إيده فلازم يكون خفيف وحجمه معقول بينمسك هيه
+
+81
+00:06:49,620 --> 00:06:54,900
+بالإيد زي نفس الشيء الجلم الحاجات الخارج .. فكل
+
+82
+00:06:54,900 --> 00:06:59,260
+إشي فيه إلها design اللي أنا بدي أصمم ساعة بنفعش
+
+83
+00:06:59,260 --> 00:07:03,140
+أعملها هالقدةو ساعت حقط و أقول هذه بدي أحطها ماحدش
+
+84
+00:07:03,140 --> 00:07:07,520
+فيكوا هيشوفها إلا بده نضور فلازم يكون حجمها كبير و
+
+85
+00:07:07,520 --> 00:07:10,600
+في نفس الوقت اللي بدي أعلقها حجمها بدي يكون خفيف
+
+86
+00:07:10,600 --> 00:07:15,300
+فهذا بحدد المواد اللي ممكن أشتغل منها فهذه ال
+
+87
+00:07:15,300 --> 00:07:17,440
+constraints ال constraints التاني مثلا في غزة
+
+88
+00:07:17,440 --> 00:07:21,460
+الحين كل واحد بدي أشتري أي إيش جديد بسأل سؤال صار
+
+89
+00:07:21,460 --> 00:07:26,710
+إيش؟قداشي بتستهلك كهربا صح؟ صرنا نسأل هذا السؤال
+
+90
+00:07:26,710 --> 00:07:30,710
+فانت .. هذا constraints الآن لو أنا بدي أجيب أي
+
+91
+00:07:30,710 --> 00:07:35,530
+أجهزة بجيب أطلع عليها إيش هو قداشي بتسحبها فهذه ال
+
+92
+00:07:35,530 --> 00:07:39,110
+constraints أو بدي أصمم أي منتج بدي أصمم بهذا
+
+93
+00:07:39,110 --> 00:07:44,050
+comparative target إيش ال comparative ال
+
+94
+00:07:44,050 --> 00:07:49,190
+constraints اللي هي إيش محدديات أو
+
+95
+00:07:49,190 --> 00:07:55,870
+شروطال competitive targets إيش هي؟ أهداف مقارنية،
+
+96
+00:07:55,870 --> 00:07:59,430
+يعني لما أنا بدي أجي بدي أقارن في منتجات أخرى،
+
+97
+00:07:59,430 --> 00:08:03,310
+بانفعش أجي أعمل حاجة هذه في السوق حقها الآن خمس
+
+98
+00:08:03,310 --> 00:08:06,630
+شكل، أجي أروح أعمل حاجة بسبعة شكل و أتوقع أنها
+
+99
+00:08:06,630 --> 00:08:15,200
+هتمشي، صح؟ فلازم تكون سعري مقاربللمنتج الموجود في
+
+100
+00:08:15,200 --> 00:08:19,560
+السوق بنفس الشي جوته مقاربة إليها how well the
+
+101
+00:08:19,560 --> 00:08:22,260
+product should perform compared with existing
+
+102
+00:08:22,260 --> 00:08:28,380
+models يعني كيف هذا المنتج بد يكون أدائه مقارة
+
+103
+00:08:28,380 --> 00:08:32,780
+بالمنتج الحالي الموجود في السوق existing models
+
+104
+00:08:32,780 --> 00:08:36,960
+اللي هي النماذج الموجودة competing product already
+
+105
+00:08:36,960 --> 00:08:40,880
+in the market or the current model that the new
+
+106
+00:08:40,880 --> 00:08:46,260
+product will replaceيعني المنتج اللي موجود في
+
+107
+00:08:46,260 --> 00:08:52,420
+السوق هي current competing product اللي هي
+
+108
+00:08:52,420 --> 00:08:57,240
+المنتجات المنافسة اللي هي موجودة حاليا في السوق أو
+
+109
+00:08:57,240 --> 00:09:00,160
+current model أو ال model الحالي دات ال new
+
+110
+00:09:00,160 --> 00:09:04,240
+product و ال replace اللي هي المنتج الجديد اللي
+
+111
+00:09:04,240 --> 00:09:08,740
+بده يسوي أحيانا كتير من الشركات تبقى عندها منتج
+
+112
+00:09:08,740 --> 00:09:15,540
+تروح تطلع منتج جديدبيحققش الأداء بنفس الطريقة زي
+
+113
+00:09:15,540 --> 00:09:19,380
+المنتج القديم يمكن شركات ال Pepsi و Coca Cola في
+
+114
+00:09:19,380 --> 00:09:24,400
+أمريكا كل فترة بيحاولوا يحسنوا على المنتج نوع جديد
+
+115
+00:09:24,400 --> 00:09:28,720
+أحيانا كتير برجع للمنتج اللي قبله ليش؟ لأن الناس
+
+116
+00:09:28,720 --> 00:09:33,560
+ماقبلتش على المنتج الجديد بالشكل المطلوب فنفس
+
+117
+00:09:33,560 --> 00:09:37,960
+الشيء هذا مثلا انتوا بعض منكم استخدم Windowsمش كل
+
+118
+00:09:37,960 --> 00:09:43,000
+نسخة جديدة الناس بترتاع عليها في نسخ انت بتضلك
+
+119
+00:09:43,000 --> 00:09:46,380
+ماشي عن نسخة القديمة لما يجبروك تروحي النسخة
+
+120
+00:09:46,380 --> 00:09:50,540
+الجديدة لإيش لأن النسخة القديمة فيها ميزات الجديدة
+
+121
+00:09:50,540 --> 00:09:55,580
+مش موجودة فيها أحيانا بتحس هذا الشخص فهذه من ال ..
+
+122
+00:09:55,580 --> 00:10:00,480
+اللي أنت بدك تفكر فيها as في ال design brief تبعات
+
+123
+00:10:00,480 --> 00:10:01,880
+ال element الموجودة
+
+124
+00:10:05,300 --> 00:10:10,260
+design features ايش ال design features ايش
+
+125
+00:10:10,260 --> 00:10:15,520
+features المزايا او الميزايا اللي هي ايش اللي
+
+126
+00:10:15,520 --> 00:10:18,320
+بيميز specific things that the new design must
+
+127
+00:10:18,320 --> 00:10:24,080
+have for example rechargeable battery a led with a
+
+128
+00:10:24,080 --> 00:10:29,380
+lock عادة ال lock اللي هي مفتاح او قفل وال led
+
+129
+00:10:29,380 --> 00:10:33,120
+غطاية احيانا المنتج بده غطاية احيانا حاجة تانية
+
+130
+00:10:33,120 --> 00:10:38,400
+بتتطلع عليها الشكلاحيانا بيعطيكي ميزة طلع الجوالات
+
+131
+00:10:38,400 --> 00:10:43,900
+على سبيل المثال كل جوال نسخة جديدة فيه ميزة عن
+
+132
+00:10:43,900 --> 00:10:49,890
+اللي قبل صح تخليكي ترمي القديم تقولي بده جديدمن ال
+
+133
+00:10:49,890 --> 00:10:54,530
+design من ال application من ال operating system ال
+
+134
+00:10:54,530 --> 00:11:01,290
+bandwidth تبعه كل هذه الشغلات الحجم الممري ميزات
+
+135
+00:11:01,290 --> 00:11:04,590
+التصوير مثلا ميزات انه بتقدر تستخدميها ل activity
+
+136
+00:11:04,590 --> 00:11:09,410
+تانية كل هذه بتخليها فيها فيه new features عادة
+
+137
+00:11:09,410 --> 00:11:13,090
+يمكن اكتر اشي بتقدر تلاحظه في هذه التغيرات اللي هي
+
+138
+00:11:13,090 --> 00:11:16,870
+الجوالاتمن نسخة لتانية بتلاقي ال features زادت
+
+139
+00:11:16,870 --> 00:11:20,670
+بشكل كبير لحتى الآن صار الجوال يعني لو احنا عندنا
+
+140
+00:11:20,670 --> 00:11:27,730
+الجيل الرابع او التالت من يعني من خليني اقول من ال
+
+141
+00:11:27,730 --> 00:11:33,790
+communication system اللي هو احنا لجينا حالة جوال
+
+142
+00:11:33,790 --> 00:11:40,340
+في كل شيء بخصنامن محاضراتك لل homework لكل حاجة و
+
+143
+00:11:40,340 --> 00:11:43,540
+هو communication and computer center ماشي معاك
+
+144
+00:11:43,540 --> 00:11:47,080
+جوالات الحديثة في العالم هي كانت تستخدمها هي كل
+
+145
+00:11:47,080 --> 00:11:52,120
+إشي بدك إياه موجود فيه نيجي نتكلم عن ال budget إيش
+
+146
+00:11:52,120 --> 00:11:56,940
+ال budget؟ الميزاني وهذا مهمة دايما ال cost limit
+
+147
+00:11:56,940 --> 00:12:00,580
+that must not be exceeded in order to make the
+
+148
+00:12:00,580 --> 00:12:06,300
+designed cost effective دايما بدي المنتج تبعيdo
+
+149
+00:12:06,300 --> 00:12:13,660
+كفاءة اقتصادية او مالية cost effective يعني في
+
+150
+00:12:13,660 --> 00:12:18,600
+جدوة مالية من وراها يعني بجيش اجي حاجة بقول هي
+
+151
+00:12:18,600 --> 00:12:24,200
+ثمنها غالي كتير مقارة بغيرها او مقارة بالخدمات
+
+152
+00:12:24,200 --> 00:12:27,980
+بتلاقي الاقبال عليها بقل وهذه بتحصل كتير في
+
+153
+00:12:27,980 --> 00:12:31,560
+المنتجات اللي بتشوفوها انا بدي اجيب بدي نزل حاجة
+
+154
+00:12:31,560 --> 00:12:36,850
+جديدة سعرها عاليالزباين تبعها غلال، هل أنا هذا
+
+155
+00:12:36,850 --> 00:12:40,550
+اللي بدي اياه و لا لأ؟ اللي انا لأ ممكن، تبعين
+
+156
+00:12:40,550 --> 00:12:43,770
+الإدارة تسنين شافت، لما لا خدناها أحيان أنا بدي
+
+157
+00:12:43,770 --> 00:12:48,490
+ناس بهذا النوع، أسوي، بس أنا ببقى عارف أدخل على
+
+158
+00:12:48,490 --> 00:12:52,630
+إيش، إذا أنا بدي أعمل mass production أو أنا بدي
+
+159
+00:12:52,630 --> 00:12:56,310
+أعمل شئ للكل، هذه اللي بدي أطلع فيها
+
+160
+00:12:59,340 --> 00:13:03,940
+تكلمنا قبل شوية عن ال design objectives شفنا ال
+
+161
+00:13:03,940 --> 00:13:07,620
+design objectives بتكون في ال design brief مظبوط
+
+162
+00:13:07,620 --> 00:13:11,460
+شفنا إيش المكونات تبعتها الآن نروح لل design
+
+163
+00:13:11,460 --> 00:13:15,140
+calculation كيف أنا بدي أعمل الحسبات design
+
+164
+00:13:15,140 --> 00:13:18,920
+information is shown on a drawing and written in
+
+165
+00:13:18,920 --> 00:13:22,780
+specifications ال design information معلومات
+
+166
+00:13:22,780 --> 00:13:29,260
+التصميم بتبقى موجودة على الرسوماتوموجودة في ال ..
+
+167
+00:13:29,260 --> 00:13:35,560
+إيش؟ إيش ال specification؟ المواصفات، كويس؟ الآن
+
+168
+00:13:35,560 --> 00:13:41,600
+أنتوا سنة أولى، بكرا بتروحوا على المختبرات، صح؟ أي
+
+169
+00:13:41,600 --> 00:13:45,480
+حاجة بقولك اطلع ال specification sheet لتشوفي إيش
+
+170
+00:13:45,480 --> 00:13:49,640
+المواصفات تبع هذا الجهاز أو تبع القطعة الإلكترونية
+
+171
+00:13:49,640 --> 00:13:53,880
+أو غيرها، ليش؟لأنه فيها هذه المعلومات اللي حطها،
+
+172
+00:13:53,880 --> 00:13:57,600
+مين اللي بيحطها؟ المهندسين، انت عندك في البيت
+
+173
+00:13:57,600 --> 00:14:02,740
+شريتي جهاز جديد، أيش بتعمله؟ بفتح ال specification
+
+174
+00:14:02,740 --> 00:14:06,600
+sheet، تفتحته، مش بيجي معه ورقة، دليل، الدليل هذا
+
+175
+00:14:06,600 --> 00:14:11,240
+بتفتحيه، بتطلع عليه، هذا بتفكروا مين اللي بيكتبه؟
+
+176
+00:14:11,240 --> 00:14:16,230
+أنتم، مش حد تانيالـ engineers فهي هذه design
+
+177
+00:14:16,230 --> 00:14:19,910
+specifications documents which describe the
+
+178
+00:14:19,910 --> 00:14:23,950
+materials, sizes and technical requirements of the
+
+179
+00:14:23,950 --> 00:14:27,450
+components لأن specification هذه تبعت ال design مش
+
+180
+00:14:27,450 --> 00:14:30,910
+تبعت ال final product هذه اللي بتروح لمين؟
+
+181
+00:14:30,910 --> 00:14:35,710
+للمهندسين والمهندسات عشان يصمموا فهذه بيكون فيها
+
+182
+00:14:35,710 --> 00:14:41,900
+إيش نوع ال material اللي بدها تستخدمقداش الأحجام
+
+183
+00:14:41,900 --> 00:14:45,920
+and technical requirement of the components يمكن
+
+184
+00:14:45,920 --> 00:14:51,580
+أبسط حاجة تطلعوا على خريطة بيت بتلاقي هذا محدد
+
+185
+00:14:51,580 --> 00:14:55,980
+فيها خريطة البيت محدد إيش نوع الحديد، قداش ثمكه
+
+186
+00:14:56,940 --> 00:15:03,080
+قداش الأحجام تبعته كل هذه ويمكن العمدان و هدول وين
+
+187
+00:15:03,080 --> 00:15:08,320
+يربط صلوك وين يعمل أساور كل هذه بتلاقيها موجودة في
+
+188
+00:15:08,320 --> 00:15:12,860
+القارطة مفصلة ال mechanical نفس الشي ال electrical
+
+189
+00:15:12,860 --> 00:15:16,520
+نفس الشغلات إيش ال components وقداش حجمها كل هدول
+
+190
+00:15:16,520 --> 00:15:21,060
+بتلاقوها موجودة في ال specification عشان إيه أنا
+
+191
+00:15:21,060 --> 00:15:24,620
+أعرف أو اللي بديه يصمم يعرف إيش اللي بدي استخدمه
+
+192
+00:15:24,620 --> 00:15:30,450
+في هذا المجالin order to specify this detailed
+
+193
+00:15:30,450 --> 00:15:38,550
+information an engineer must evaluate عشان المهندس
+
+194
+00:15:38,550 --> 00:15:44,790
+يعني يوصف هذه المعلومات التفصيلية an engineer must
+
+195
+00:15:44,790 --> 00:15:51,410
+evaluate إيش يعني evaluate؟ يقيم، كويس؟إيش يقيم
+
+196
+00:15:51,410 --> 00:15:55,470
+إيش يعني this is identify and calculate معنى
+
+197
+00:15:55,470 --> 00:16:02,690
+التقييم هذا أنه بده يتعرف ويحدد كويس أنا بدي يعني
+
+198
+00:16:02,690 --> 00:16:08,710
+يحدد ويحسب هي evaluate بدي أحدد ايه شو ال loads و
+
+199
+00:16:08,710 --> 00:16:12,790
+ال loads عندى اللي هي عبارة عن إيش forces في ال
+
+200
+00:16:12,790 --> 00:16:17,410
+mechanical ال loads هي عبارة عن إيش forces في ال
+
+201
+00:16:17,410 --> 00:16:21,590
+mechanical engineeringأو بال static و ال dynamic
+
+202
+00:16:21,590 --> 00:16:25,610
+اللي هتمر عليكوا .. تبعين المدني .. تبعين العمارة
+
+203
+00:16:25,610 --> 00:16:29,510
+هتمر عليكوا مادة .. مادتين واحدة static و واحدة
+
+204
+00:16:29,510 --> 00:16:35,390
+dynamics هدول بتعاملوا مع ال forces فهدول إيش؟ مرت
+
+205
+00:16:35,390 --> 00:16:39,330
+عليكوا بالثانوية القوة و ال .. إيش ال loads؟
+
+206
+00:16:39,330 --> 00:16:44,090
+بسميها في العربي؟ ماعرفش زمان مرت .. أحمال ..
+
+207
+00:16:44,090 --> 00:16:49,110
+الأحمال و القوةفهدولة اللي هنتكلم .. هتلاقيها
+
+208
+00:16:49,110 --> 00:16:53,570
+موجودة فلازم يعني .. يعني خلينا نقول يحدد إيش هذه
+
+209
+00:16:53,570 --> 00:16:58,630
+الأحمال و القوة و يحسبها عشان يقدر يحدد القطوات
+
+210
+00:16:58,630 --> 00:17:02,130
+دلوقتي that key components will have to carry الآن
+
+211
+00:17:02,130 --> 00:17:06,810
+أنا لو بدي أحط شيء و بيجي عليه حمل بدي أضمن أن
+
+212
+00:17:06,810 --> 00:17:09,750
+الحمل اللي بيجي عليه هذا ال components بيقدر
+
+213
+00:17:09,750 --> 00:17:15,140
+يتحمله صح؟يعني لما نعمل درج مثلا على سبيل المثال و
+
+214
+00:17:15,140 --> 00:17:20,480
+اقول الدرج بدي يمشي عليه عشر أشخاص، بدي يتحمل عشر
+
+215
+00:17:20,480 --> 00:17:24,560
+أشخاص، الأسنصير إيش بتلاقي محدد فيه؟ قديش عدد
+
+216
+00:17:24,560 --> 00:17:30,720
+الحمولة، صح؟ الوزن، لو أنت جوزت الوزن إيش بيسوي؟
+
+217
+00:17:31,240 --> 00:17:35,680
+هذا .. هذا التسوير وانه مش تشتغلش هذا من ال safety
+
+218
+00:17:35,680 --> 00:17:40,080
+من عناصر الأمان نحن هنتكلم عنها لاحقا فهو .. بس هو
+
+219
+00:17:40,080 --> 00:17:44,660
+لو طلع بالوزن الزائد ممكن ينقطع و يجعب في الناس
+
+220
+00:17:44,660 --> 00:17:50,040
+اللي حاملها فهذا من ال design اللي بنتكلم عليه فهو
+
+221
+00:17:50,040 --> 00:17:55,220
+بدك تشوفي قداش كل إشي بقدر يتحمل to do this the
+
+222
+00:17:55,220 --> 00:18:00,360
+engineer needs to determine to determine يعني إيش
+
+223
+00:18:00,360 --> 00:18:07,900
+نقوليحدد أيوة identify the different loads then
+
+224
+00:18:07,900 --> 00:18:14,780
+quantify them يعني إيش quantify them؟ فيه qualify
+
+225
+00:18:14,780 --> 00:18:21,800
+و quantify ال qualitative يعملها يكمم يعني يحدد
+
+226
+00:18:21,800 --> 00:18:28,540
+الكمية و quantify يحدد العددcalculate them in
+
+227
+00:18:28,540 --> 00:18:35,280
+number form يحولها لأعداد quantified usually each
+
+228
+00:18:35,280 --> 00:18:39,540
+load is quantified based on a worst case scenario
+
+229
+00:18:39,540 --> 00:18:45,960
+ايش يعني worst case scenario؟ أسوأ حالة انت لما
+
+230
+00:18:45,960 --> 00:18:51,740
+تيجي تصمم أي اشي بتصمميش للحالات ليه؟أفضل الحالات
+
+231
+00:18:51,740 --> 00:18:58,280
+بتصمم؟ لأ أسوأ الحالات كهندسة هذا شغلنا كمهندسات و
+
+232
+00:18:58,280 --> 00:19:03,040
+مهندسين بنصطلع عيش أسوأ حالة و بنشتغل عليها و مش
+
+233
+00:19:03,040 --> 00:19:07,280
+بس بنسوي هذا و بنضيف شوية احتياط و أنا هنقولهليش؟
+
+234
+00:19:07,280 --> 00:19:12,080
+لأنه دايما ال safety أهم عنصر عندك هندسة، يمكن أنا
+
+235
+00:19:12,080 --> 00:19:17,060
+بقول من عيب اللي بدرس هندسة أو بتدرس هندسة، خمس
+
+236
+00:19:17,060 --> 00:19:20,680
+سنين بتخليك أول ماتروح أي مكان عينك بتشوف الغلط و
+
+237
+00:19:20,680 --> 00:19:25,340
+اللي بيأذي الناس، على طول بتقولي هذه ماتعملش هندسة
+
+238
+00:19:25,340 --> 00:19:30,390
+و هيك، ليش؟ هذا بتسير في الدم تبعناwe breed
+
+239
+00:19:30,390 --> 00:19:35,570
+safety، بتصير عندنا كل شي بتعلق بال safety تبعت
+
+240
+00:19:35,570 --> 00:19:43,570
+الناس، هذا شغل لك هندسةطيب usually each load is
+
+241
+00:19:43,570 --> 00:19:47,390
+quantified based on a worst case scenario in other
+
+242
+00:19:47,390 --> 00:19:50,750
+words engineer will .. the engineer will allow for
+
+243
+00:19:50,750 --> 00:19:56,250
+maximum load يعني هو بده يسمح allow for يسمح لإيش
+
+244
+00:19:56,250 --> 00:20:03,210
+ال maximum load أكتر أكبر اللي هي أكبر حمل ممكن
+
+245
+00:20:03,670 --> 00:20:08,310
+such as an aircraft making a very hard landing
+
+246
+00:20:08,310 --> 00:20:16,730
+بتعرف الطيارة أسوأ إش فيها لما تنزل إيش؟ التعبير
+
+247
+00:20:16,730 --> 00:20:21,030
+اللي بتتكلم فيه إيش هنا؟Hard Landing أو Crash
+
+248
+00:20:21,030 --> 00:20:26,230
+Landing انها بتنزل واستضام يعني عدى الطيارة كيف
+
+249
+00:20:26,230 --> 00:20:30,210
+بتنزل؟ بتنزل شوية شوية approach ال ground و لما
+
+250
+00:20:30,210 --> 00:20:32,910
+تنزل في ال ground بتنزل smooth و بتظلها ماشية
+
+251
+00:20:32,910 --> 00:20:38,590
+بسرعة لحدين تتوطى لحدين توصل لسرعة السيارات يعني و
+
+252
+00:20:38,590 --> 00:20:42,370
+بعدها بتوطى زي كده، الأسوأ أشياء لما الطيارة تيجي
+
+253
+00:20:42,370 --> 00:20:47,000
+و ترتطم ارتطام في الأرض و بتظلها ماشية تزحلجهذا
+
+254
+00:20:47,000 --> 00:20:50,900
+ايش بيسموها crash landing او hard landing هذا
+
+255
+00:20:50,900 --> 00:20:55,160
+بتحصل وقتيش في الطوارئ.الان تحت هذه الظروف ايش بدي
+
+256
+00:20:55,160 --> 00:20:59,620
+اعمل؟ مدهاش الطيارة تتقسم او تتكسر ل pieces فال
+
+257
+00:20:59,620 --> 00:21:03,540
+design بيشتغل على انه انا كمهندس بدي مسئول عن ال
+
+258
+00:21:03,540 --> 00:21:07,720
+design ان الطيارة تظل one piece و ال passenger
+
+259
+00:21:07,720 --> 00:21:12,340
+قاعدين في الكراسي و مايصيرش لهم حاجة يعني يكون ال
+
+260
+00:21:12,340 --> 00:21:18,840
+.. خليني اقول ال ..حجم الضرر خفيف جدا، فهذا
+
+261
+00:21:18,840 --> 00:21:25,020
+تصميمنا كمهندسين و مهندسات لازم نتطلع عليه or a
+
+262
+00:21:25,020 --> 00:21:29,040
+bridge being hit by extremely high winds طلعوا
+
+263
+00:21:29,040 --> 00:21:33,600
+الجسر، لو أنا مصمم جسر، و الجسر أجاله ريح، إيش
+
+264
+00:21:33,600 --> 00:21:40,830
+بيعمل فيه؟ بيصير يحرك فيهالان الجسورة في العالم في
+
+265
+00:21:40,830 --> 00:21:44,090
+عدة تكنولوجيا بتشتغل عليها في تكنولوجيا بيسموها
+
+266
+00:21:44,090 --> 00:21:48,750
+suspended bridges اللي هي جسور المعلقة بتبقى الجسر
+
+267
+00:21:48,750 --> 00:21:53,430
+عبارة مثلا عن خشب او حديد ومشدود شد يعني من عملي
+
+268
+00:21:53,430 --> 00:21:56,970
+ممكن شوفتوا اذا حدا فيكوا تطلع على مثلا الجسر اللي
+
+269
+00:21:56,970 --> 00:22:01,950
+موجود على قناة السويسة في عمودين كبار و العمودين
+
+270
+00:22:01,950 --> 00:22:06,270
+هذول مشدودات بسلوك حديد في قواعد كبيرة مربوطة في
+
+271
+00:22:06,270 --> 00:22:11,670
+الأرضالان لو روحت على بلاد تانية في أحيان جبلين
+
+272
+00:22:11,670 --> 00:22:15,490
+بيبقوا كبار وعليات بدهم يعملوا طريق بينهم بيعملوا
+
+273
+00:22:15,490 --> 00:22:19,030
+suspended bridge ال bridge طبعا كل ما ارتفعت في
+
+274
+00:22:19,030 --> 00:22:24,170
+العلو كل ما صار الرياح حجمها ايش اكبر بكتير فالان
+
+275
+00:22:24,170 --> 00:22:28,130
+هذه بدك تشديها في أمريكا كانت مليانة على سبيل
+
+276
+00:22:28,130 --> 00:22:33,910
+المثال جسورةيمكن طولها طويل، فوق الكلوات بتلاقي،
+
+277
+00:22:33,910 --> 00:22:37,350
+صورة في المي و هيك، و هذا ما شابه، الآن هذه بتبقى
+
+278
+00:22:37,350 --> 00:22:41,650
+مصممة أنه لو أجالنا high winds يعني قداش الريح
+
+279
+00:22:41,650 --> 00:22:46,170
+اللي ممكن تجيهنا، سرعتها، بيقولوا مثلا أقصى اشي 40
+
+280
+00:22:46,170 --> 00:22:52,240
+كيلو في الساعة، بتصمميش كمهندسة على 40بديك تصمم
+
+281
+00:22:52,240 --> 00:22:55,580
+تقول طيب لو في الطوارئ أجتنا هيك كداش بدي أصير
+
+282
+00:22:55,580 --> 00:22:59,240
+عندهم بتعمل تصميمك في هذا المجال الان لو أجت
+
+283
+00:22:59,240 --> 00:23:04,280
+بالفعل ريح في ضرف مرة في السنة او في كل عشر او
+
+284
+00:23:04,280 --> 00:23:08,040
+خمستاشر سنة بيصير الشيء يعني بتتذكروا كلهيتنا لما
+
+285
+00:23:08,040 --> 00:23:13,800
+غرقت غزة قبل كم من سنة بصبوط؟ الان انت لما بديك
+
+286
+00:23:13,800 --> 00:23:18,240
+تصممه لو بدي أصمم نظام المجاري اللي عندي بصممها
+
+287
+00:23:18,240 --> 00:23:23,380
+لحاجة تيجي زي هيكالأن معظم السنوات مش هتيجي بهذا
+
+288
+00:23:23,380 --> 00:23:27,280
+الحجم بس لو أجته بهذا الحجم ببقى أنا مستعد هذا
+
+289
+00:23:27,280 --> 00:23:31,440
+اللي بنتكلم عليه allow for maximum load or worst
+
+290
+00:23:31,440 --> 00:23:37,880
+case scenario هذا اللي بنتكلم عليه طيب after
+
+291
+00:23:37,880 --> 00:23:41,400
+maximum load have been quantified an engineer will
+
+292
+00:23:41,400 --> 00:23:46,340
+apply a factor of safety طب أنا حددت أسوأ حالة،
+
+293
+00:23:46,340 --> 00:23:50,570
+الآن أنا بضيف حاجة زيادة كمانكل مهندسينا في
+
+294
+00:23:50,570 --> 00:23:53,950
+المباني تبعتنا بيعملوا زي هيكا، كل مهندسي اللي
+
+295
+00:23:53,950 --> 00:23:58,290
+عندنا، يعني انت تطلع للتسليح في المباني عندنا أكتر
+
+296
+00:23:58,290 --> 00:24:02,730
+بكتير من المطلوب، يعني انت مطلوب مثلا خليني اقول
+
+297
+00:24:02,730 --> 00:24:10,190
+بدى حجم السياق مثلا تمانية في العمود، القطر تبعه
+
+298
+00:24:10,190 --> 00:24:14,130
+خليني اقول عشرة ملي بيحط اربعتاشر ملي، لأن هذا
+
+299
+00:24:14,130 --> 00:24:19,780
+بتضيف تكلفةبس في عنصر safety أعلى يعني لو أجى
+
+300
+00:24:19,780 --> 00:24:24,000
+زلزال تتحمل أكتر يمكن في بلادنا في احنا ماشي زلزال
+
+301
+00:24:24,000 --> 00:24:27,960
+في قصف يا جنبك يا جنب المنطقة اللي جنبك فبيهز
+
+302
+00:24:27,960 --> 00:24:33,700
+المبنى فانت فدك المبنى يتحمل هذه الهزال هذا بنسميه
+
+303
+00:24:33,700 --> 00:24:40,660
+ايش factor safety يعني هذا او safety margin بنضيف
+
+304
+00:24:40,660 --> 00:24:47,180
+يعني حاجةللأمانها this is an extra margin to make
+
+305
+00:24:47,180 --> 00:24:50,600
+the components strong enough to carry loads that
+
+306
+00:24:50,600 --> 00:24:53,920
+are higher than the worst case scenario هذا يعني
+
+307
+00:24:53,920 --> 00:24:59,200
+حتى الأسوأ بتقدر تتحملها في هذا المجال وهذا
+
+308
+00:24:59,200 --> 00:25:02,940
+بتلاقيها في كل إشي مثلا بقولك ال maximum هالجد بس
+
+309
+00:25:02,940 --> 00:25:07,900
+لو اتعدى تحصلش إشي صح؟ انت لما تشتري علبة لبن إيش
+
+310
+00:25:07,900 --> 00:25:13,200
+مكتوب عليها? expiration date مظبوط؟الان لو جيت
+
+311
+00:25:13,200 --> 00:25:18,640
+بعدها بيوم، بيومين، كويسة، التلاجات شغالة، خليني
+
+312
+00:25:18,640 --> 00:25:21,660
+أقول، بتلاقيها كويسة ماحصلش فيها إشي، يعني لو
+
+313
+00:25:21,660 --> 00:25:25,000
+خدتيني بتبقى كويسة الأدوية على سبيل المثال، كل
+
+314
+00:25:25,000 --> 00:25:28,800
+الأدوية الأجنبية فيها expiration date، الآن
+
+315
+00:25:28,800 --> 00:25:32,540
+الأدوية الأجنبية عادة في ست أشهر معاك بعد ال
+
+316
+00:25:32,540 --> 00:25:38,120
+expiration date صالحةأدوياتنا يالا يالا بتحصل ..
+
+317
+00:25:38,120 --> 00:25:41,800
+بس هذه معلومة يعني أجل ثمان كانوا في الجامعة
+
+318
+00:25:41,800 --> 00:25:46,800
+بيعطوا أدوية زي هيكة بتيجي ضايلها شهرين أو شهر و
+
+319
+00:25:46,800 --> 00:25:51,780
+تخلص صلاحيتها فشكوا الطلاب فاحنا أيامها كنا بنسوي
+
+320
+00:25:51,780 --> 00:25:57,040
+عليها فلأ لقينا هاد دايما فيها اللي هي إيش عندنا
+
+321
+00:25:57,040 --> 00:26:01,740
+factor of safety أو safety margins حاجة مسموحة
+
+322
+00:26:01,740 --> 00:26:07,900
+أكتر من الموجودةعلى سبيل المثال، فاكتره 1.5 يزيد
+
+323
+00:26:07,900 --> 00:26:12,520
+عملية تحميل مجموعات يمكن أن تحمل 50% بعد أن كان
+
+324
+00:26:12,520 --> 00:26:16,580
+هذا فاكتره فيه، فإنجنير سيقوم بتصميم المجموعات
+
+325
+00:26:16,580 --> 00:26:21,200
+التي هي تتخيل صميمها المطلوب يعني بعد ما يدخل هذه
+
+326
+00:26:21,200 --> 00:26:28,340
+الفاكتره بأمان، فالإنجنير يجب أن يقوم بتصميم يعني
+
+327
+00:26:28,340 --> 00:26:32,380
+يعطي الحجم المطلوب للمواد المطلوبة في هذا المجال
+
+328
+00:26:32,960 --> 00:26:36,080
+فانت بعد ما تاخد ايش بيطلع ال worst case scenario
+
+329
+00:26:36,080 --> 00:26:41,120
+بضيفله ايش factor of safety بيصير عندي بقدر بعدها
+
+330
+00:26:41,120 --> 00:26:46,160
+احسب المطلوب سواء من المواد او ثمكها او حجمها هنا
+
+331
+00:26:46,160 --> 00:26:51,300
+بنتكلم عن ال size engineers طلعوا هذا على هذا اللي
+
+332
+00:26:51,300 --> 00:26:54,940
+دايما احنا بنحصل فيه اذا انا بضيف كل هدول ايش هذا
+
+333
+00:26:54,940 --> 00:27:00,890
+هضيف؟تكلفة وهذا اللي بتتكلم عنها engineers are
+
+334
+00:27:00,890 --> 00:27:04,870
+sometimes .. sometimes criticized because they
+
+335
+00:27:04,870 --> 00:27:11,650
+over design things over design يعني إيش؟ بحطه أكتر
+
+336
+00:27:11,650 --> 00:27:16,710
+من ما هو مطلوب وهذه تطلعه لأي حد بتطلع على الخرائط
+
+337
+00:27:16,710 --> 00:27:21,170
+طبيعات بيوت نهان كله بحكي هذا الكلمة أنت بتحطه
+
+338
+00:27:21,170 --> 00:27:29,330
+أكتر بكتير من المطلوبالمشكلة بزيد التكلفة يعني على
+
+339
+00:27:29,330 --> 00:27:35,110
+رأي الناس أجت ب .. بتذكر في تعبير اللي هي بال ..
+
+340
+00:27:35,110 --> 00:27:40,770
+يعني المباني الموفرة الطاقة، ذاكرينها؟ efficient
+
+341
+00:27:40,770 --> 00:27:47,450
+energy buildings، إيش هذه بتلاحظوا؟ في بتنحط فيها
+
+342
+00:27:47,450 --> 00:27:51,610
+إيش؟ الحجر اللي بنحطه على الحيطة مش حجر عاديفي ..
+
+343
+00:27:51,610 --> 00:27:55,910
+بيبقى في في النص طبقة عازلة، يعني مثلا حجر أبو
+
+344
+00:27:55,910 --> 00:28:01,030
+عشرين بنحط في النص طبقة يا فالين يا طبقة عازلة طب
+
+345
+00:28:01,030 --> 00:28:05,070
+هذه بتخلي الحرارة اللي جوا جوا و ال .. يعني سواء
+
+346
+00:28:05,070 --> 00:28:10,550
+في الشتاء البيت دافي و في الصيف بارد لإن بتعزل
+
+347
+00:28:10,550 --> 00:28:15,760
+الطبقة الخارجية طب ليش ما بنستخدم هذه؟تكلفة بتزيد
+
+348
+00:28:15,760 --> 00:28:20,080
+في ناس يعني مثلا الحجر بدل ما يبنوه واحد عشرين
+
+349
+00:28:20,080 --> 00:28:23,560
+بيبنوا اتنين عشرة و بدل ما يحطوا يعني حد ادنى
+
+350
+00:28:23,560 --> 00:28:27,240
+بيسيبوا فترة بيسيبوا خمسة سانتا او عشرة تقريبا
+
+351
+00:28:27,240 --> 00:28:32,360
+فراغ بين الحجرين أساس هذه عازلة بدون ما يحطوا فيها
+
+352
+00:28:32,360 --> 00:28:36,520
+أي شيء بتعمل لسه أولا لا بتدخل رطوبة على البيت من
+
+353
+00:28:36,520 --> 00:28:42,040
+برا ولا بتسوي نوعا ما عزل بس في تكلفة في الصناعة
+
+354
+00:28:42,040 --> 00:28:49,160
+في المادةأحسن .. أحسن .. بس ماحدش بيستخدمها لإن في
+
+355
+00:28:49,160 --> 00:28:53,040
+الآخر الناس بدها تسكن الاخر خلينا في غزة لو أنا
+
+356
+00:28:53,040 --> 00:28:58,780
+عملت اقصارة ولا حجر قدسي؟ الاقصارة أرخص بس الحجر
+
+357
+00:28:58,780 --> 00:29:04,020
+القدسي أحسن بعزل كل عوامل التعريع عن البيت بس ..
+
+358
+00:29:04,020 --> 00:29:08,040
+وكل بيعمل عزل كامل الرغم من أن هي كانت جليل اللي
+
+359
+00:29:08,040 --> 00:29:12,400
+بيستخدموه في البيوت الخاصة تاكلوا فعلالما تكلفة
+
+360
+00:29:12,400 --> 00:29:16,520
+هاي فهي نتكلم engineers are sometimes criticized
+
+361
+00:29:16,520 --> 00:29:19,660
+because they over design thing and excessive
+
+362
+00:29:19,660 --> 00:29:25,440
+factor of safety بضيفوا عناصر زيادة عن الطبيعي
+
+363
+00:29:25,440 --> 00:29:32,220
+which increases costs وهذا طبيعي ان التكلفة هتزيد
+
+364
+00:29:32,220 --> 00:29:36,140
+however according to Murphy's law عرفوا إيش
+
+365
+00:29:36,140 --> 00:29:42,570
+Murphy's law الترجمة مش هتعطيك حقهميرفز لاوش بيقول
+
+366
+00:29:42,570 --> 00:29:48,730
+هو قانون يعني بيقول أي حاجة سيئة ممكن تحصل اتوقعي
+
+367
+00:29:48,730 --> 00:29:55,230
+هتحصل هتحصل هيك ميرفز لاوش anything can go wrong
+
+368
+00:29:55,230 --> 00:30:00,710
+will go wrong يعني أي شيء تتوقعي يعني انت بتقولي
+
+369
+00:30:00,710 --> 00:30:04,870
+انا اليوم جاية هذابتلاقيك مثلا حريصة تجيب ال
+
+370
+00:30:04,870 --> 00:30:09,390
+homework تبعك، مظبوط، تعمل احتياطك و كل شي حاطه زي
+
+371
+00:30:09,390 --> 00:30:13,570
+هيك و بتيجي ع الجامعة و مش جاي بقى، اه اليوم عندي
+
+372
+00:30:13,570 --> 00:30:17,870
+إشي مهمممكن تصير .. خلّيني أقول قاعد باشتغل على
+
+373
+00:30:17,870 --> 00:30:21,490
+الكمبيوتر و بدي أخلص ال .. ال presentation تبعتي و
+
+374
+00:30:21,490 --> 00:30:26,670
+كل حاجة .. الكهربا ضايلها نص ساعة .. إيش .. بس
+
+375
+00:30:26,670 --> 00:30:30,030
+ممكن تقطع .. أضرب .. تلاقي .. تبقى حد تفكر بإيه ده
+
+376
+00:30:30,030 --> 00:30:34,770
+بتقطع .. هاي Murphy's Law .. انه .. يعني كل إشي ..
+
+377
+00:30:34,770 --> 00:30:38,070
+هاي .. الآن إيش الترجمة إلو فيش ترجمة .. هو اسمه
+
+378
+00:30:38,070 --> 00:30:39,450
+Murphy's Law .. قانون Murphy
+
+379
+00:30:42,430 --> 00:30:46,530
+فهو هادى دايما الكلام اللى بتكلم عليه اتوقعى يعنى
+
+380
+00:30:46,530 --> 00:30:51,170
+عبارة تانية اتوقع الأسبوع يحصل في أصعب الأوقات و
+
+381
+00:30:51,170 --> 00:30:56,410
+هادى بتحصل حتى دايما بتلاقي .. لأ حتى بتحصل أنا
+
+382
+00:30:56,410 --> 00:31:00,950
+مثلا بتلاقيه أحيانا كثير يعنى بشتغل على document و
+
+383
+00:31:00,950 --> 00:31:06,210
+اللى بشتغل فيها ساعتين مثلا و مناش فريقىو .. و ..
+
+384
+00:31:06,210 --> 00:31:09,150
+يعني و زي ما بيقولوا بشكلها ال computer زيادة عن
+
+385
+00:31:09,150 --> 00:31:12,390
+اللازم، تتوقع أن ال computer .. ماتتوقعش أن ال
+
+386
+00:31:12,390 --> 00:31:14,770
+computer يصير أي حاجة، فجأة بتشوف أن ال computer
+
+387
+00:31:14,770 --> 00:31:19,890
+ضارب، ف .. و انت ما .. مافيش عندك وقت كتير، يعني
+
+388
+00:31:19,890 --> 00:31:24,010
+ال due date مثلا بكرا، بدك تسلمي، مافيش ما .. بدك
+
+389
+00:31:24,010 --> 00:31:29,910
+الحين تشتغل بدون عجل، زي ما بيقولونهطيب، this
+
+390
+00:31:29,910 --> 00:31:33,270
+suggests that built-in phrases and expressions
+
+391
+00:31:33,270 --> 00:31:37,530
+often used in engineering based on the safest
+
+392
+00:31:37,530 --> 00:31:41,150
+method to hold up a trouser is a sensible
+
+393
+00:31:41,150 --> 00:31:44,170
+approach، الآن احنا جيبنا كلمتين، ميرفيز لوه،
+
+394
+00:31:44,170 --> 00:31:48,610
+والآن تطلعوا، الناس لما تلبس بنطلون عشان تضمنوا ما
+
+395
+00:31:48,610 --> 00:31:55,050
+يسحلش، أيش بتعمل؟بتحطوا كشاط، مظبوط؟ نحكي هذا لأنه
+
+396
+00:31:55,050 --> 00:31:59,150
+.. الآن في حاجة تانية بيعملوها، في .. هذه موجودة
+
+397
+00:31:59,150 --> 00:32:02,990
+بتشوفيها، في بلادنا مالهاش سعبية، عند المصريين
+
+398
+00:32:02,990 --> 00:32:07,510
+موجودة و عند البريطانيين موجودة، الربطات تبعات
+
+399
+00:32:07,510 --> 00:32:11,770
+البنطلون، عند الصغار الحملات، انت بتحطوها للصغار،
+
+400
+00:32:11,770 --> 00:32:16,430
+مظبوط؟ بتحط .. تلاقيها أحيانا، الحملات للصغار عشان
+
+401
+00:32:16,430 --> 00:32:21,330
+إيش؟يعني حتى في الظروف اللي هيما يسحلش بالمرة،
+
+402
+00:32:21,330 --> 00:32:25,690
+فهذا التعبير أنه احنا بنحط الاحتياط built-in
+
+403
+00:32:25,690 --> 00:32:31,510
+braces اكشات وحملات عشان البنطالو مايسحلش، فهذا
+
+404
+00:32:31,510 --> 00:32:35,750
+التعبير اللي نقصد فيه أنه عشان ال design تبعنا في
+
+405
+00:32:35,750 --> 00:32:41,630
+كل الحلات مايحصلش أي خلال فيه، فاحنا بنحط حاجة
+
+406
+00:32:41,630 --> 00:32:47,390
+شبيهة بالاكشات وحملات في ال designكويس عشان هذه
+
+407
+00:32:47,390 --> 00:32:51,410
+تصبط مع أن هذا مايلحقناش ميرفيز لو مايحصلش عندنا
+
+408
+00:32:51,410 --> 00:32:57,690
+فبنحط هذه الشغلانة و هذه expression often used in
+
+409
+00:32:57,690 --> 00:33:01,730
+engineering based on the safest method for holding
+
+410
+00:33:01,730 --> 00:33:06,110
+up a treasure هذه أكتر طريقة فيها أمان أن البنطلون
+
+411
+00:33:06,110 --> 00:33:11,150
+مايسحلش تحط الشاط جوي و حملات خلاص حتى الولد
+
+412
+00:33:11,150 --> 00:33:16,310
+الصغير لو ماليش بدي أعمل هيك بيسحل بقدر يسحلطيب
+
+413
+00:33:16,310 --> 00:33:23,650
+هذي is a sensible approach, إيش sensible؟ يعني
+
+414
+00:33:23,650 --> 00:33:31,300
+مناسب، طريقة مناسبةطيب نيجي نتكلم على ال .. اللي
+
+415
+00:33:31,300 --> 00:33:35,300
+عندى complete the sentences from technical
+
+416
+00:33:35,300 --> 00:33:39,160
+conversation using the words in the box نتكلم على
+
+417
+00:33:39,160 --> 00:33:41,940
+.. نتطلع على ال words إيش اللي عندى budget,
+
+418
+00:33:42,760 --> 00:33:46,920
+constraints, cost of effective design exceed
+
+419
+00:33:46,920 --> 00:33:51,560
+existing function feature proposed of course money
+
+420
+00:33:51,560 --> 00:33:57,750
+is limited يعني عادةالمصاري دايما في أي اشي محدودة
+
+421
+00:33:57,750 --> 00:34:05,550
+مافيش عندى bank مفتوح في هذا cost limitations are
+
+422
+00:34:05,550 --> 00:34:12,580
+always ايش؟ دايما ال cost ايش؟ cost limitationأيوة
+
+423
+00:34:12,580 --> 00:34:17,600
+ال cost limitation دايما في .. is .. is always a
+
+424
+00:34:17,600 --> 00:34:22,320
+constraint دايما في أي شيء التكلفة دايما تعد
+
+425
+00:34:22,320 --> 00:34:26,680
+constraint في أي design لأن ماحدش بيقولك روحي صممي
+
+426
+00:34:26,680 --> 00:34:32,100
+و أنا ماعنديش .. عندك ميزانية مفتوحة دايما بيقولك
+
+427
+00:34:32,100 --> 00:34:37,350
+في حدود هلقد صح؟ انت بتروح تشتري حاجةبتقولي أنا
+
+428
+00:34:37,350 --> 00:34:40,870
+قبل ما تطلع من البيت أنا حدودي هلقد، محدد أقداش
+
+429
+00:34:40,870 --> 00:34:44,990
+ميزانيتك فكتصميم دايما عندك بده يكون حدود
+
+430
+00:34:44,990 --> 00:34:52,530
+constraints but some finance is available إيش has
+
+431
+00:34:52,530 --> 00:34:58,930
+been allocated for design phase؟ إيش هنا اللي
+
+432
+00:34:58,930 --> 00:35:02,290
+دايما نحطها؟ إيش اللي قلت لما تروح انتي إيش
+
+433
+00:35:02,290 --> 00:35:07,460
+بتعملي؟ بتحط إيش؟ميزانية قبل أي حاجة فدائما عندي
+
+434
+00:35:07,460 --> 00:35:11,340
+budget a budget has been allocated ما حد ما
+
+435
+00:35:11,340 --> 00:35:16,920
+allocated انه تم تخصيصها allocated allocated تم
+
+436
+00:35:16,920 --> 00:35:21,320
+تخصيصها has been allocated for a preliminary
+
+437
+00:35:21,320 --> 00:35:26,520
+design phase a total of thirty five thousand
+
+438
+00:35:26,520 --> 00:35:33,840
+dollar but we must not ish that amountexceed مش
+
+439
+00:35:33,840 --> 00:35:40,120
+لازم نتجاوز عنها ال
+
+440
+00:35:40,120 --> 00:35:46,680
+budget ميزانية ال constraints شروط او محددات ال a
+
+441
+00:35:46,680 --> 00:35:53,240
+exceed اللي هي تجاوز طيب هنا بنتكلم على obviously
+
+442
+00:35:53,910 --> 00:36:00,050
+إذا كان علينا أن ندفع 80 باون على جزء من كل مصدر
+
+443
+00:36:00,050 --> 00:36:06,450
+للجهاز و المصدر يتسلل لـ 70 دولار فهو ليس مصدر
+
+444
+00:36:06,450 --> 00:36:11,890
+تصميم يعني لو أنا روحت بدي أشتري .. بدي أعمل تصميم
+
+445
+00:36:11,890 --> 00:36:16,890
+لجهاز .. الجهاز بيكلف 80 شيكل و روحت في السوق
+
+446
+00:36:16,890 --> 00:36:22,850
+وجدوا بنبيعه بـ 70 شيكل تصميمي إيش صار؟ is notcost
+
+447
+00:36:22,850 --> 00:36:31,250
+effective يعني فش فيه جدوة مالية من وراه لإن الناس
+
+448
+00:36:31,250 --> 00:36:34,650
+مش هتاخدوا أولا product جديد، الحاجة التانية، في
+
+449
+00:36:34,650 --> 00:36:44,750
+حاجة أرخص منه طيب the age of the detector is to
+
+450
+00:36:44,750 --> 00:36:51,730
+locate underground cables by giving audio feedback
+
+451
+00:36:53,680 --> 00:37:02,260
+the function of detector ايش ال detector لأ
+
+452
+00:37:02,260 --> 00:37:10,360
+الان ايش ال sensor ايوة اللي هو المجس ال detector
+
+453
+00:37:10,360 --> 00:37:19,260
+اللي هو مجس بس لمين للمعدن detect okay to locate
+
+454
+00:37:19,260 --> 00:37:24,950
+underground cables ال underground cables ايشإيش
+
+455
+00:37:24,950 --> 00:37:28,930
+underground؟ تحت الأرض، الكوابل الموجودة تحت
+
+456
+00:37:28,930 --> 00:37:34,450
+الأرض، الآن لو حد بدي .. بدي .. يعني وظيفة الجهاز
+
+457
+00:37:34,450 --> 00:37:40,330
+هذا، المجس اللي هو بتطلع على حديد الكوابل اللي تحت
+
+458
+00:37:40,330 --> 00:37:47,390
+الأرض by giving audio feedback، بيعطي رسالة صوتية،
+
+459
+00:37:47,390 --> 00:37:53,230
+يعني بتشوفوا أنتوا؟اللي في الأفلام الجهاز هذا لما
+
+460
+00:37:53,230 --> 00:37:58,910
+نمشي و نلاقي حد يداشي بيعمل بزمة وهذا اللي بنحكي
+
+461
+00:37:58,910 --> 00:38:02,890
+فيه هذا هو هذا ال function بس هنا عشان نقولك إيش
+
+462
+00:38:02,890 --> 00:38:08,490
+معناه function وظيفة الجهاز أنه يحدد فيه معدن تحت
+
+463
+00:38:08,490 --> 00:38:15,270
+ويعطي صوت since it is it's to be used in a noisy
+
+464
+00:38:15,270 --> 00:38:23,620
+environmentairphone is unimportant since it's
+
+465
+00:38:23,620 --> 00:38:31,120
+designed to be used in a noisy environment عادة
+
+466
+00:38:31,120 --> 00:38:36,400
+هذا الجهاز بيروح في شارع مظبوط انت بتطلعي
+
+467
+00:38:36,400 --> 00:38:40,340
+underground cable underground cable في شارع مش
+
+468
+00:38:40,340 --> 00:38:45,880
+معقول انت تمسكيه و بدك تسمعيزي ان انت ماسك جوالك و
+
+469
+00:38:45,880 --> 00:38:49,540
+بتتكلم في الشارع عادة مش دايما بتسمع في الصيارات
+
+470
+00:38:49,540 --> 00:38:55,360
+فالسمعات ال earphones هنا اين روحنا ال .. ال
+
+471
+00:38:55,360 --> 00:38:59,820
+earphones هي ايش سماعات الأدن اللي بنحطها بالأديان
+
+472
+00:38:59,820 --> 00:39:09,880
+earphones is an important ايش feature ايش ميزة طيب
+
+473
+00:39:09,880 --> 00:39:16,860
+forare these already on the market؟ هل هدولة في ال
+
+474
+00:39:16,860 --> 00:39:22,840
+market؟ are they إيش product؟
+
+475
+00:39:22,840 --> 00:39:26,960
+existing existing بتيجي، انت ضال عندك كل كلماتك،
+
+476
+00:39:26,960 --> 00:39:30,640
+إيش كيف احنا كنا بنعمل كلمة بحطها بشوف راكبة ولا
+
+477
+00:39:30,640 --> 00:39:34,580
+لأ؟ الآن ضال اللي عندى لما اتشط بهدي راحت و هدي
+
+478
+00:39:34,580 --> 00:39:41,320
+راحت و هدي راحت و هدي راحت و هدي راحت هدي ضلكهذه
+
+479
+00:39:41,320 --> 00:39:46,680
+راحت هذا ضلت ال propose وال existing الأخر واحدة
+
+480
+00:39:46,680 --> 00:39:50,680
+طيب الآن لو حطينا are they propose product ولا or
+
+481
+00:39:50,680 --> 00:39:56,260
+are we talking about propose product are these
+
+482
+00:39:56,260 --> 00:39:59,000
+already on the market بنسأل هل هم في ال market
+
+483
+00:39:59,000 --> 00:40:04,640
+هدول موجودين في ال market are they current product
+
+484
+00:40:05,330 --> 00:40:11,170
+بنقول طيب هل هما منتج حالي or are we talking about
+
+485
+00:40:11,170 --> 00:40:15,430
+product that we are still that are still under
+
+486
+00:40:15,430 --> 00:40:18,550
+development still under development بتقولي هذه
+
+487
+00:40:18,550 --> 00:40:23,790
+إيش؟ هي propose لأنه تحت لساتها تحت التطوير
+
+488
+00:40:23,790 --> 00:40:27,930
+فمعناته هي مقترح فلهذا السبب باختار هنا propose
+
+489
+00:40:27,930 --> 00:40:33,470
+وهنا existing القالية هذه اللي بنفكر فيها فكر فيها
+
+490
+00:40:33,470 --> 00:40:38,340
+لما انت تشتغلي في الحلليش أنا قاعد ب .. بعودكم
+
+491
+00:40:38,340 --> 00:40:44,000
+عليها انك دايما اتعودي ماتستعجليش في الإجابة لأ
+
+492
+00:40:44,000 --> 00:40:47,940
+خدي هاي و قولي لو حطيتها أنا طب هاد بتقد المعنى و
+
+493
+00:40:47,940 --> 00:40:57,840
+على فكرة و أنت بت grip بتحس فيها طيب هاد
+
+494
+00:40:57,840 --> 00:41:02,480
+يقولنا خلصنا
+
+495
+00:41:02,480 --> 00:41:02,900
+من هاد
+
+496
+00:41:06,950 --> 00:41:09,650
+choose the correct word from the brackets to
+
+497
+00:41:09,650 --> 00:41:12,970
+complete the sentences يعني هذا بدنا الكلمة
+
+498
+00:41:12,970 --> 00:41:16,930
+الصحيحة من بين الموجودين the types of flow that
+
+499
+00:41:16,930 --> 00:41:23,110
+will be encountered must .. إيش يعني encountered؟
+
+500
+00:41:23,110 --> 00:41:25,410
+the type of flow that will be encountered
+
+501
+00:41:25,410 --> 00:41:29,790
+encountered
+
+502
+00:41:29,790 --> 00:41:36,250
+بنواجهها أو faced must be designed ولا determined
+
+503
+00:41:38,170 --> 00:41:41,790
+أيوة يعني ال type of forces we encounter بنواجهها
+
+504
+00:41:41,790 --> 00:41:47,050
+لأ مش بنصممها بنحددها determined maximum loads are
+
+505
+00:41:47,050 --> 00:41:51,990
+based on predicted ايش يعني predicted المتوقعة
+
+506
+00:41:51,990 --> 00:41:55,770
+predicted specification ولا worst case scenario
+
+507
+00:41:55,770 --> 00:42:02,340
+شايفين على طول سرته صار حق تمشي فيهاon top of
+
+508
+00:42:02,340 --> 00:42:06,560
+maximum loads additional safety margins are
+
+509
+00:42:06,560 --> 00:42:12,080
+factored in او in size يعني بنحسب حسابها ولا بنحجم
+
+510
+00:42:12,080 --> 00:42:16,660
+احنا قولنا التحجيم بيجي اخر اشي بعد ما نسويه for
+
+511
+00:42:16,660 --> 00:42:20,620
+cost reasons components shouldn't be over designed
+
+512
+00:42:20,620 --> 00:42:23,960
+ولا quantified over designed
+
+513
+00:42:25,530 --> 00:42:28,790
+التعامل بالتعامل بالتعامل بالتعامل بالمجموعات يمكن
+
+514
+00:42:28,790 --> 00:42:34,110
+أن يكون تسمى بـ Built and braces factor of safety
+
+515
+00:42:34,110 --> 00:42:39,050
+approach الـ factor of .. اللي هي .. أيوة .. اللي
+
+516
+00:42:39,050 --> 00:42:44,850
+هي احنا ايش قلنا عنه؟ أيوة، عفوزيكم quantifying
+
+517
+00:42:44,850 --> 00:42:48,510
+ولا sizing components يعني تخطيط مجموعاتهم؟
+
+518
+00:42:48,510 --> 00:42:52,770
+مجموعات .. مجموعات بروح مع مين؟ مع الـ size
+
+519
+00:42:58,190 --> 00:43:02,950
+طيب replace the underlying words and expressions
+
+520
+00:43:02,950 --> 00:43:07,310
+with alternative words and expressions from اللي
+
+521
+00:43:07,310 --> 00:43:13,430
+هي اللي مر علينا جزئية A أو B most engineering
+
+522
+00:43:13,430 --> 00:43:17,930
+designs make provision for excessive or abnormal
+
+523
+00:43:17,930 --> 00:43:22,170
+operating conditions إيش making provisions؟ إيش
+
+524
+00:43:22,170 --> 00:43:23,050
+أحنا بنعمل؟
+
+525
+00:43:25,700 --> 00:43:30,320
+allow for عادة احنا بنعمل most engineer allow for
+
+526
+00:43:30,320 --> 00:43:34,940
+excessive or abnormal operating يعني إيش allow for
+
+527
+00:43:34,940 --> 00:43:41,340
+بنسمح مرت علينا هذا الكلمة من هناك طيب ذكرتك
+
+528
+00:43:41,340 --> 00:43:49,220
+provision إيش هنا أحيانا انت يعني make provision
+
+529
+00:43:49,220 --> 00:43:59,230
+انت بتعملي زي احتياطOkay تسمحي for excessive تعمل
+
+530
+00:43:59,230 --> 00:44:02,550
+احتياط انت ايش بتسمحي يعني هذا the critical
+
+531
+00:44:02,550 --> 00:44:07,310
+question is how much of a two percent of extra
+
+532
+00:44:07,310 --> 00:44:11,390
+size or capacity ايش يعني percentage of extra size
+
+533
+00:44:11,390 --> 00:44:18,350
+or capacity؟ مرت علينا ليش؟ factor of safety،
+
+534
+00:44:18,350 --> 00:44:22,890
+مظبوط؟ طيب should be applied without adding too
+
+535
+00:44:22,890 --> 00:44:30,000
+much of a marginover desire طيب four calculate an
+
+536
+00:44:30,000 --> 00:44:34,120
+amount four إيش قلنا عندنا هذه quantify لما ت
+
+537
+00:44:34,120 --> 00:44:37,840
+calculate an amount بدنا نعمل حوله لأرقام هذه
+
+538
+00:44:37,840 --> 00:44:42,920
+quantify for this figure it's critical to assess
+
+539
+00:44:42,920 --> 00:44:45,700
+the consequence of technical of a technical
+
+540
+00:44:45,700 --> 00:44:51,080
+failure where the stakes إيش يعني ال stakes are
+
+541
+00:44:51,080 --> 00:44:55,740
+highمرد عليك كلمة ال steak مش ال steak اللي
+
+542
+00:44:55,740 --> 00:45:00,100
+بناكلها المخاطر
+
+543
+00:45:00,100 --> 00:45:05,720
+ال stakes المخاطر مرتفعة in applications such as
+
+544
+00:45:05,720 --> 00:45:11,680
+aviations ايش aviations لأ ال aviation عالم
+
+545
+00:45:11,680 --> 00:45:18,280
+الطيران okay designing for the most extreme
+
+546
+00:45:18,280 --> 00:45:23,240
+situation ايش ال most extreme worst case scenario
+
+547
+00:45:23,590 --> 00:45:29,390
+is clearly critical on safety ground on the face
+
+548
+00:45:29,390 --> 00:45:37,010
+of it the result of this may seem costly عادة لما
+
+549
+00:45:37,010 --> 00:45:43,770
+نحمل بيقول هذه ممكن تكون تكلفة عالية but where the
+
+550
+00:45:43,770 --> 00:45:48,270
+human implications and expense of failure are
+
+551
+00:45:48,270 --> 00:45:54,750
+serious ايش يعني human implication؟النتائج البشرية
+
+552
+00:45:54,750 --> 00:45:59,350
+أو اللي بترتب على الإنسان يعني على حالة الإنسان
+
+553
+00:45:59,350 --> 00:46:06,750
+expense of failure تكلفة الفشل are serious خطرة a
+
+554
+00:46:06,750 --> 00:46:10,670
+high level of expenditure aimed at accident
+
+555
+00:46:10,670 --> 00:46:18,660
+prevention إيش accident prevention مانعالحوادث can
+
+556
+00:46:18,660 --> 00:46:22,840
+be considered financially viable ايش يعني
+
+557
+00:46:22,840 --> 00:46:30,500
+financially viable يعني التكلفة ال financial ..
+
+558
+00:46:30,500 --> 00:46:36,900
+المالي يعني التكلفة المالية ده جدوة ايش احنا قلنا
+
+559
+00:46:36,900 --> 00:46:42,440
+عندها هذه cost effective هذه الموجودة عندنا
+
+560
+00:46:46,630 --> 00:46:50,970
+و هيك خلصنا ال chapter المرة الجاية بنشتغل عاربعة
+
+561
+00:46:50,970 --> 00:46:55,570
+بس هيك بنبقى خلصنا الوحدة الأولى اللي هي بتتكلم عن
+
+562
+00:46:55,570 --> 00:46:55,950
+إيش
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/EwbY24Yuo2c_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/EwbY24Yuo2c_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..643c2d2e95d4369978a866026653ed84e4c341b5
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/EwbY24Yuo2c_raw.srt
@@ -0,0 +1,1156 @@
+1
+00:00:20,650 --> 00:00:27,010
+السلام عليكم اليوم سوف نتحدث عن ميكانيكا أسطورية
+
+2
+00:00:27,010 --> 00:00:42,550
+حدث 32 حدث 32 حدث 32 حدث 32 حدث 32
+
+3
+00:00:42,550 --> 00:00:42,550
+حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32
+
+4
+00:00:42,550 --> 00:00:42,630
+حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32
+
+5
+00:00:42,630 --> 00:00:42,710
+حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32
+
+6
+00:00:42,710 --> 00:00:42,710
+حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32 حدث 32
+
+7
+00:00:42,710 --> 00:00:43,250
+حدث 32 حدث 32 حدث 32 حدث 32 حدث 33 حدث 33 حدث 33
+
+8
+00:00:43,250 --> 00:00:43,250
+حدث 33 حدث 34 حدث 34 حدث 34 حدث 35 حدث 35 حدث 35
+
+9
+00:00:43,250 --> 00:00:48,850
+حدث 35 حدث 35 حدث
+
+10
+00:00:49,540 --> 00:00:59,000
+مكتب شويه ايه الكلام المفضل او قد يكون مفضل او
+
+11
+00:00:59,000 --> 00:00:59,400
+مفضل او مفضل او مفضل او مفضل او مفضل او مفضل او
+
+12
+00:00:59,400 --> 00:00:59,980
+مفضل او مفضل او مفضل او مفضل او مفضل او مفضل او
+
+13
+00:00:59,980 --> 00:01:00,440
+مفضل او مفضل او مفضل او مفضل او مفضل او مفضل او
+
+14
+00:01:00,440 --> 00:01:01,420
+مفضل او مفضل او مفضل او مفضل او مفضل او مفضل او
+
+15
+00:01:01,420 --> 00:01:04,920
+مفضل او مفضل او مفضل او مفضل او مفضل او مفضل او
+
+16
+00:01:04,920 --> 00:01:12,400
+مفضل او مفضل
+
+17
+00:01:12,400 --> 00:01:16,740
+او مفض
+
+18
+00:01:17,890 --> 00:01:23,750
+frames and trusses ال frame اللي هو ايش ال هيكل و
+
+19
+00:01:23,750 --> 00:01:26,850
+ال truss اللي عارفينه اللي احنا بنسميه بالعامية ال
+
+20
+00:01:26,850 --> 00:01:31,990
+truss ايش ال truss الحين لما انت مشي انت في ممر
+
+21
+00:01:31,990 --> 00:01:39,070
+ايش بتلاقي او بلكون ايش اللي ها بيسموه truss الان
+
+22
+00:01:39,070 --> 00:01:46,000
+سقف الكرميد اللي هو حاجة بنسميها دي ال trussاللي
+
+23
+00:01:46,000 --> 00:01:50,140
+هي الحماية، هنتكلم عنه .. كشفة يا انت .. لأ لأ مش
+
+24
+00:01:50,140 --> 00:01:56,500
+الكشفة .. هه ده .. هنتكلم عنها، لاتجلجوش .. الآن
+
+25
+00:01:56,500 --> 00:01:57,940
+لما نتكلم على ..
+
+26
+00:02:02,380 --> 00:02:06,860
+Statically determinate structure when a structure
+
+27
+00:02:06,860 --> 00:02:11,960
+member that is part of the structure is loaded in
+
+28
+00:02:11,960 --> 00:02:15,760
+certain direction يعني لما يكون عندنا ال structure
+
+29
+00:02:15,760 --> 00:02:23,240
+محمل باتجاه معين ال load will cause reaction يعني
+
+30
+00:02:23,240 --> 00:02:28,100
+لو أجت قوة على حاجة هيصير الهيش ردت فعلالان ردة
+
+31
+00:02:28,100 --> 00:02:33,020
+الفعل هذا يعني ان طاقة أخرى متساوية للوضع ستعمل في
+
+32
+00:02:33,020 --> 00:02:38,800
+الاتجاه المعكس لكل فعل رد فعل مساوء في المقدار
+
+33
+00:02:38,800 --> 00:02:43,400
+معكس في الاتجاه هذا اللي بيحكينا ان هي كويس ال
+
+34
+00:02:43,400 --> 00:02:47,540
+reaction will counteract resist the load and stop
+
+35
+00:02:47,540 --> 00:02:51,320
+the member from moving يعني هذه القوة لما نيجي
+
+36
+00:02:51,320 --> 00:02:58,300
+نحطها مش هتخلي الجسم أو العضو هذا يتحركwhen the
+
+37
+00:02:58,300 --> 00:03:02,700
+loads and reactions acting in members are equal
+
+38
+00:03:02,700 --> 00:03:07,700
+لما هذا يكون الأحمال وردود الأفعال تبعتها أو
+
+39
+00:03:07,700 --> 00:03:13,360
+التفاعل معها القوة المضادة لها متساوية، إيش اللي
+
+40
+00:03:13,360 --> 00:03:17,620
+بيحصل؟ we say it is in equilibrium عملية إيش؟
+
+41
+00:03:17,620 --> 00:03:23,490
+اتزيانstructures that are designed not to move to
+
+42
+00:03:23,490 --> 00:03:26,510
+stay in equilibrium are called statically
+
+43
+00:03:26,510 --> 00:03:29,690
+determined structures يعني اللي statically
+
+44
+00:03:29,690 --> 00:03:32,210
+determined structure هم ال structure in
+
+45
+00:03:32,210 --> 00:03:36,530
+equilibrium يعني بتتحركش لا بريح ولا بتتحرك بالقوة
+
+46
+00:03:36,530 --> 00:03:41,490
+اللي بتنضغط عليه هذا بنقول عنه إيش؟ أيوة
+
+47
+00:03:41,490 --> 00:03:46,250
+statically determined structure كويس؟
+
+48
+00:03:48,330 --> 00:04:02,030
+resultant forces and the center of gravity عادة
+
+49
+00:04:02,030 --> 00:04:09,030
+أي هيكل بيحمل
+
+50
+00:04:09,030 --> 00:04:16,990
+أحمال مختلفةفي سواء من ناحية ال magnitude أو من
+
+51
+00:04:16,990 --> 00:04:21,130
+ناحية الاتجاه اللي بتيجي عليه to calculate the
+
+52
+00:04:21,130 --> 00:04:23,830
+results of these different components فهذا خدتوها
+
+53
+00:04:23,830 --> 00:04:27,770
+بالفيزيا component forces and engineer can
+
+54
+00:04:27,770 --> 00:04:32,370
+calculate a resultant force or resultants يعني في
+
+55
+00:04:32,370 --> 00:04:36,750
+العادة احنا ك .. خدتوها بال statistics في الثانوية
+
+56
+00:04:36,750 --> 00:04:42,890
+بالفيزيا صح؟فيزيا الف أخدتها انت في عندي قوة
+
+57
+00:04:42,890 --> 00:04:47,850
+مختلفة جاي بدأ أجيب المحصلة تبعتها باجيب حاجة
+
+58
+00:04:47,850 --> 00:04:52,070
+اتجاه المحصلة في الاتجاه العمودي والعمودي والأفقي
+
+59
+00:04:52,070 --> 00:04:56,250
+وبعدين باجيب المحصلة تبعت التنتين تطلع في أي اتجاه
+
+60
+00:04:56,250 --> 00:05:01,230
+بس لازم أحدد النقطة اللي عندها بتطلاق كل هذه القوة
+
+61
+00:05:01,230 --> 00:05:04,210
+اللي بنقول ال center of gravity أو ال center اللي
+
+62
+00:05:04,210 --> 00:05:11,050
+عندي لهذه الشغلةone of the main forces exerted in
+
+63
+00:05:11,050 --> 00:05:14,810
+structure is gravity احنا في كل شي في عندنا
+
+64
+00:05:14,810 --> 00:05:17,470
+الجاذبية الأرضية
+
+65
+00:05:21,560 --> 00:05:28,900
+Okay ال gravity this acts vertically downward اللي
+
+66
+00:05:28,900 --> 00:05:33,380
+هي يعني عادة ال gravity بتيجي إيش عمودي في اتجاه
+
+67
+00:05:33,380 --> 00:05:38,640
+الأسفل هذه و دايما هذه بنحسب حسابها بشكل .. بدك
+
+68
+00:05:38,640 --> 00:05:43,730
+تشوف التفاصيل بتروح على ال chapter 9الجاذبية تتعرض
+
+69
+00:05:43,730 --> 00:05:49,970
+لكل درّة لجاذبها لكل إشي لكل درّة لها تتعرض
+
+70
+00:05:49,970 --> 00:05:54,410
+للجاذبية However, to simplify their calculation
+
+71
+00:05:54,410 --> 00:05:57,410
+engineers assumed that gravity exerted an
+
+72
+00:05:57,410 --> 00:06:01,510
+imaginary point called the center of gravity الآن
+
+73
+00:06:01,510 --> 00:06:04,470
+ال center of gravity اللي بنتكلم عليه هي نقطة إيش
+
+74
+00:06:04,470 --> 00:06:10,230
+imaginary pointقندق نقطة فرضية احنا بنفرضها هي على
+
+75
+00:06:10,230 --> 00:06:14,850
+أرض الواقع كل جزئية في الجسم أو كل ضرر إلها هذه بس
+
+76
+00:06:14,850 --> 00:06:19,130
+احنا بنقول ككل بدنا نقول هي هذه نقطة الجاذبية
+
+77
+00:06:19,130 --> 00:06:23,370
+تبعتنا اللي بنتكلم عنهاDepending on the shape of
+
+78
+00:06:23,370 --> 00:06:27,330
+the object, this point may be inside the object, a
+
+79
+00:06:27,330 --> 00:06:32,750
+cross-sectional area or outside the cross
+
+80
+00:06:32,750 --> 00:06:35,770
+-sectional area يعني ممكن نقطة الجاذبية الأرضية
+
+81
+00:06:35,770 --> 00:06:39,990
+هذه اللي بنقول عنها افتراضية تبقى جوا المساحة
+
+82
+00:06:39,990 --> 00:06:44,470
+العرضية لل object أو تبقى خارجها ككل طب كيف ده
+
+83
+00:06:44,470 --> 00:06:49,230
+هتكون خارجها؟ طالع على شكلها هنا بسهولة بنقول وين
+
+84
+00:06:49,230 --> 00:06:55,590
+جاية؟ في النصهنا جوا وهنا اشطلعت برا فهذه بتعطيك
+
+85
+00:06:55,590 --> 00:07:02,230
+example كيف انها ممكن تكون برا الان
+
+86
+00:07:02,230 --> 00:07:08,890
+لما نتكلم عن ال frames and traces ال frame is made
+
+87
+00:07:08,890 --> 00:07:14,330
+from a number of relative ten members عادة ال
+
+88
+00:07:14,330 --> 00:07:19,400
+frame .. خليكم معايا يا بناتالـ frame هو عبارة عن
+
+89
+00:07:19,400 --> 00:07:22,920
+إيش؟ طلع أنت الحماية اللي بتنعمل على الشباك، هذا
+
+90
+00:07:22,920 --> 00:07:29,360
+بنسميه frame الدرج، شاحط الحديد اللي على شاحط
+
+91
+00:07:29,360 --> 00:07:35,380
+الدرج، هذا بنسميه frame هو إطار، بتقدر تعتبريه، بس
+
+92
+00:07:35,380 --> 00:07:43,720
+عادة المقصد الهندسي فيه هو إطار من الأعضاء تبعينه،
+
+93
+00:07:43,720 --> 00:07:49,140
+إيش بنقول عنه الـ tin، ارفعةexample are bicycle
+
+94
+00:07:49,140 --> 00:07:54,620
+frames البسكاليت الإطار تبعت البسكاليت steel frame
+
+95
+00:07:54,620 --> 00:08:00,420
+building اللي هي تبعات البنايات members of a frame
+
+96
+00:08:00,420 --> 00:08:04,560
+can form a complex shape often with many triangles
+
+97
+00:08:04,560 --> 00:08:09,620
+called lattices الآن عادة ليكون ال frame قوي إيش
+
+98
+00:08:09,620 --> 00:08:15,080
+لازم أعمله على شكل متلتات لو أنا جيت عملت frame
+
+99
+00:08:15,080 --> 00:08:23,790
+كالتاليأبناء تقلقوا معاه بدون صوت جانبي هذا
+
+100
+00:08:23,790 --> 00:08:27,990
+frame لو جيت ضغطت عليه إيش ال frame هذا بدي يحصل
+
+101
+00:08:27,990 --> 00:08:35,470
+له؟ بسوقش، بالطعش، مظبوط هذا بيصير .. بتلاقوه على
+
+102
+00:08:35,470 --> 00:08:41,030
+طول بيحصل، مظبوط؟ لأدعمه إيش بعمل؟ لو حطيت موتلة
+
+103
+00:08:41,030 --> 00:08:49,360
+تاعت هنا إيش بيحصل له؟ بتجوىهذا القصد فيه اللي
+
+104
+00:08:49,360 --> 00:08:53,460
+عندي، الآن هذه هي simple structure، structure
+
+105
+00:08:53,460 --> 00:08:57,340
+deformed under load، هنا عملت لإيش؟ adding cross
+
+106
+00:08:57,340 --> 00:09:01,520
+members اللي هي .. اللي .. اللي هي استفن ده إيش؟
+
+107
+00:09:01,520 --> 00:09:05,220
+ال structure اللي .. اللي موجود عندك
+
+108
+00:09:09,220 --> 00:09:14,820
+Okay members of the frame can form a complex shape
+
+109
+00:09:14,820 --> 00:09:18,860
+often with many triangles called lattices اللاتيس
+
+110
+00:09:18,860 --> 00:09:23,080
+هذا هي ال triangular shape the advantage of
+
+111
+00:09:23,080 --> 00:09:29,380
+triangles is that they are stiff ايش يعني stiff
+
+112
+00:09:29,380 --> 00:09:36,240
+لما الواحد stiff arm بتمدي ايدك زي هيكو بت ..
+
+113
+00:09:36,240 --> 00:09:40,720
+بتمشي .. حد مقدر يجرب منك؟ هذا بيسميها stiff arm
+
+114
+00:09:40,720 --> 00:09:47,610
+مشدودة ال aid مشدودة stiff armفهدولة بيعملوا
+
+115
+00:09:47,610 --> 00:09:50,650
+الحديد stiff يعني إيش؟ ال stiff arm تنطع جيش
+
+116
+00:09:50,650 --> 00:09:55,770
+ممدودة مشدودة مش مطعوجة فهي لما تحطيها زي هيكة و
+
+117
+00:09:55,770 --> 00:09:59,990
+بتزجي حد لو كانت متنية و بتزجي حد لو فيه force
+
+118
+00:09:59,990 --> 00:10:03,910
+بيجيش بالسيارة تنتنى بس لو كانت زي هيكة ماحدش
+
+119
+00:10:03,910 --> 00:10:10,190
+التانية صعبة فهذه الفكرة في ال stiff they strongly
+
+120
+00:10:10,190 --> 00:10:15,130
+resist deformation يعني تقدريش التشوه اللي عندك
+
+121
+00:10:19,330 --> 00:10:25,030
+أنت في ال .. في المعنى .. في المعنى السلبي .. أه
+
+122
+00:10:25,030 --> 00:10:30,310
+استفى الشخص اللي بتلاقيه أحيانا بيقول عنه اللي
+
+123
+00:10:30,310 --> 00:10:38,310
+بيغيرشيعني مخ و بكف زي هيك بس في ال .. برضه في
+
+124
+00:10:38,310 --> 00:10:42,290
+اللغة العامية الموجودة ال stiff أكتر أشي بيسموها
+
+125
+00:10:42,290 --> 00:10:46,170
+ال stiff arm اللي هي إيش الإيد الممدودة اللي بتخلي
+
+126
+00:10:46,170 --> 00:10:51,570
+مسافة بين الأشخاص فال stiff يعني بتعملش أنه يعني
+
+127
+00:10:51,570 --> 00:10:55,930
+خلينا نقول ي lean بت lean أو بتغيرش شكلها هذا ال
+
+128
+00:10:55,930 --> 00:11:01,720
+..اللي بنحكي فيها الـ triangular ال symbols can
+
+129
+00:11:01,720 --> 00:11:06,180
+therefore be used to stiffen or brace a structure
+
+130
+00:11:06,180 --> 00:11:11,440
+يعني لتقوي ال structure أو لتدعم ال structure هذا
+
+131
+00:11:11,440 --> 00:11:16,300
+الهدف منها ال diagram two اللي هتشوفوه ال
+
+132
+00:11:16,300 --> 00:11:19,280
+structure دي فوق اللي شوفناها because the joints
+
+133
+00:11:19,280 --> 00:11:22,760
+between the ten members are weak ال joints اللي هي
+
+134
+00:11:22,760 --> 00:11:28,130
+إيش هذه بنسميها jointأيوة هذه بنسميها joints هدول
+
+135
+00:11:28,130 --> 00:11:34,210
+ال joints الركب و هدول هذه المفاصل هي المفصل
+
+136
+00:11:34,210 --> 00:11:39,950
+المفصل الزوايا تعد ايش مفاصل التقاء اي جسم اي
+
+137
+00:11:39,950 --> 00:11:46,470
+حاجتين بنسميها مفصل فعنا نوعين من المفاصل مفاصل زي
+
+138
+00:11:46,470 --> 00:11:51,090
+احنا ادينا و رجلينا هدول ايش بنسميها لينة بتخلي
+
+139
+00:11:51,090 --> 00:11:58,360
+حركةو في مفاصل مش لينا زي الموجود هنا هذه بنسميها
+
+140
+00:11:58,360 --> 00:12:05,840
+solid joints وهذه بنسميها pin joint ال pin joint
+
+141
+00:12:05,840 --> 00:12:09,780
+اللي هي flexible في flexibility فيها وهذه هنتكلم
+
+142
+00:12:09,780 --> 00:12:15,850
+عنها كمان ساطرينare weak and can flex easily flex
+
+143
+00:12:15,850 --> 00:12:20,530
+أيش يعني بتتحرك بسرعة joints which flex because
+
+144
+00:12:20,530 --> 00:12:23,370
+they are weak or because they are designed to do
+
+145
+00:12:23,370 --> 00:12:28,090
+so اللي هي مصممة زي المفاصل الإنسان مصممة انها
+
+146
+00:12:28,090 --> 00:12:33,610
+تتحرك تكون flexible are called bend joints فعرفتوا
+
+147
+00:12:33,610 --> 00:12:38,110
+إيش ال bend joints؟اللي بتتحرك الان النوع التاني
+
+148
+00:12:38,110 --> 00:12:42,830
+هي lattices which are entirely bent joint and
+
+149
+00:12:42,830 --> 00:12:45,810
+which therefore need cross members to stiffen them
+
+150
+00:12:45,810 --> 00:12:50,350
+are called traces ال traces اللي هي إيش بدهم دعم
+
+151
+00:12:51,560 --> 00:12:55,760
+الـ trust contain two types of members, members
+
+152
+00:12:55,760 --> 00:13:00,140
+that resist tension are called ties في عندى حاجات
+
+153
+00:13:00,140 --> 00:13:07,680
+بقاوم الشد بنسميهم ties وفي حاجات بتقاوم الاشالـ
+
+154
+00:13:07,680 --> 00:13:10,460
+compression اللي بتقاوم ال compression which
+
+155
+00:13:10,460 --> 00:13:14,000
+members that resist compression are called struts
+
+156
+00:13:14,000 --> 00:13:18,340
+الـ struts اللي هي بتقارن ال compression ال ties
+
+157
+00:13:18,340 --> 00:13:23,060
+اللي هي بتقارن ال tension الشد a joint which does
+
+158
+00:13:23,060 --> 00:13:27,520
+not flex is called a rigid joint rigid او solid
+
+159
+00:13:27,520 --> 00:13:34,140
+اللي هي ايش بتتحركش or moments connectionrigid
+
+160
+00:13:34,140 --> 00:13:37,780
+joints are often thick and securely joined for
+
+161
+00:13:37,780 --> 00:13:43,200
+example by weld ايش ال weld قلنا عنه؟
+
+162
+00:13:43,200 --> 00:13:48,620
+اتكلمنا عنه المحاضرة قبل تمانية و عشرين مظبوط؟
+
+163
+00:13:48,620 --> 00:13:53,520
+الحام عملية الحام اللي هي ال weld الآن اتطلع عندى
+
+164
+00:13:53,520 --> 00:14:00,060
+تتذكروا سجوف الكرميد؟ شفتوهم ايش الشكل تبع الحام
+
+165
+00:14:00,060 --> 00:14:05,600
+اللي تبعه؟ زي هيك مظبوط؟الان لو ضغطت هذه joint
+
+166
+00:14:05,600 --> 00:14:09,240
+بنسميها pin joint لو ضغطت عليها ايش بيحصل له هدول
+
+167
+00:14:09,240 --> 00:14:16,120
+هدولة بدها تفرد او هدولة ايش بدهم يسووا الان لو
+
+168
+00:14:16,120 --> 00:14:20,760
+ربطتهم بحاجة من هنا حطيت شكفة خشب او حاجة بهذه هذي
+
+169
+00:14:20,760 --> 00:14:25,960
+بسميها اللي شفتوها ايش يقولوا احنا عندنا straw
+
+170
+00:14:25,960 --> 00:14:32,060
+هدول
+
+171
+00:14:32,890 --> 00:14:38,970
+هذا كله بنسميه trust وهذه اللي بنسميها ال tie طلع
+
+172
+00:14:38,970 --> 00:14:45,070
+على حاجة تانية، لو جيبت هذه كلها موجودة عندنا ال
+
+173
+00:14:45,070 --> 00:14:49,830
+raft تبع الكتب، مظبوط؟ ال raft تبع الكتب، إيش
+
+174
+00:14:49,830 --> 00:14:55,910
+بيحصل له؟ هذا لو حطيت الكتب على هذا، إيش بيحصل
+
+175
+00:14:55,910 --> 00:15:01,210
+لهذا؟ تنطعج،
+
+176
+00:15:01,210 --> 00:15:08,220
+بظبط؟مش هذه بدها تنطعش؟ الان
+
+177
+00:15:08,220 --> 00:15:12,380
+طبيعي لو انت جبت حاجة مش جاوية يعني ممكن طاولات
+
+178
+00:15:12,380 --> 00:15:15,300
+الكمبيوتر اللي بتشوفوها بتنبيع في السوق التجاري
+
+179
+00:15:15,300 --> 00:15:20,480
+هذه good examples مظبوط تطلع عليها بتلاقي هذه على
+
+180
+00:15:20,480 --> 00:15:25,240
+طول بتنطعش ايش بيعملوا؟ بربطوا حاجة هنا لو كانت
+
+181
+00:15:25,240 --> 00:15:31,410
+هذه ارتبطت من فوق هذا بسميه tie ليش؟لأن هذا بيقاوم
+
+182
+00:15:31,410 --> 00:15:36,770
+للشد وهذا بيبقى ايش؟ بالقوام اللي في الداخل، ايوة،
+
+183
+00:15:36,770 --> 00:15:39,810
+هذا الـstrap الآن لو حطيت هاجة تانية زي هذه
+
+184
+00:15:39,810 --> 00:15:43,930
+وحطيتها على اللي عندي تحت، ايش هذه صارت؟ هذه
+
+185
+00:15:43,930 --> 00:15:49,510
+الـstrap وهذه الـtie هذا ال frame الآن، هذه الشجة
+
+186
+00:15:49,510 --> 00:15:53,790
+إيش بيحصل لها؟ هذة will get compressed لو بقى
+
+187
+00:15:53,790 --> 00:15:57,630
+الوزن، هتنضغط، هذه الشجة التانية اللي برا إيش
+
+188
+00:15:57,630 --> 00:16:05,360
+بيصير لها؟ تنشدمظبوط هذه هتصبح tension هان لو حطيت
+
+189
+00:16:05,360 --> 00:16:09,480
+هذه الشكل هان هان عندي tension و هان عندي
+
+190
+00:16:09,480 --> 00:16:15,220
+compression نوع
+
+191
+00:16:15,220 --> 00:16:18,640
+القوة هذه بدها تضغط اللي هان وهذا بدها تسوي اللي
+
+192
+00:16:18,640 --> 00:16:30,010
+موجود هان قولنا ال tie و هان ايش و هان ال strutككل
+
+193
+00:16:30,010 --> 00:16:37,690
+هذا على بعضه بنسميه إيش ال trust أو ال frame كويس؟
+
+194
+00:16:37,690 --> 00:16:40,970
+طيب
+
+195
+00:16:40,970 --> 00:16:46,990
+نيجي الآن complete the explanation using words and
+
+196
+00:16:46,990 --> 00:16:50,970
+expression from a الأول فقرة you will need to
+
+197
+00:16:50,970 --> 00:16:55,320
+change the form of one wordالان انا حاطط لها أجوبة
+
+198
+00:16:55,320 --> 00:16:59,580
+مش حاطط لها سواء على طول هذا المفروض حاطيت لها
+
+199
+00:16:59,580 --> 00:17:06,640
+حركة عشان تختلي and it's statically determined
+
+200
+00:17:06,640 --> 00:17:11,420
+structure each load acting on this structure is
+
+201
+00:17:11,420 --> 00:17:19,780
+إيش؟ وهي موجودة counteracted أظبط counteracted by
+
+202
+00:17:19,780 --> 00:17:25,650
+إيش؟a reaction الان عندي statically determinate
+
+203
+00:17:25,650 --> 00:17:30,450
+ايش يقولنا ال statically determinate نعيد عليها
+
+204
+00:17:30,450 --> 00:17:34,570
+تأكيد عشان أجي و متأخر ال statically determinate
+
+205
+00:17:34,570 --> 00:17:38,090
+structure اللي هو ال structure is in equilibrium
+
+206
+00:17:38,090 --> 00:17:42,710
+and does not move مظبوط الان ال equilibrium ايش
+
+207
+00:17:42,710 --> 00:17:48,540
+عندي عندي load او forces و في عندي counter forceأو
+
+208
+00:17:48,540 --> 00:17:52,800
+load عندها لما اتنين يبقوا متساويين ومتعاكسين في
+
+209
+00:17:52,800 --> 00:17:57,880
+الاتجاه in opposite direction equally in the
+
+210
+00:17:57,880 --> 00:18:01,460
+magnitude is equal and the direction is opposite
+
+211
+00:18:01,460 --> 00:18:06,540
+هذا بنقول it's under equilibrium اللي هي في مرحلة
+
+212
+00:18:06,540 --> 00:18:11,280
+اتزان هذا اللي بنحكي عنه this means the structure
+
+213
+00:18:11,280 --> 00:18:13,460
+always remain in equilibrium
+
+214
+00:18:16,650 --> 00:18:21,330
+الان اتطلع عندى هنا ايش موجود عندى؟ هى ال trust
+
+215
+00:18:21,330 --> 00:18:26,170
+اللى موجود عندى هنا ايش عندى؟ forces لو حطيت مثلا
+
+216
+00:18:26,170 --> 00:18:30,470
+هنا لغاية loads from three supports carrying a
+
+217
+00:18:30,470 --> 00:18:34,690
+large satellite dish هدول ال forces جاي من تلات
+
+218
+00:18:34,690 --> 00:18:39,520
+اماكنمحمول عليهم satellite dish يعني هاد جاي على
+
+219
+00:18:39,520 --> 00:18:43,500
+وين؟ على السطح اللي هاد الان نقطة ال result sense
+
+220
+00:18:43,500 --> 00:18:48,600
+تبعهم وين؟ هاد تكون هاد الان هذا بنقول to analyze
+
+221
+00:18:48,600 --> 00:18:52,520
+دروف structure shown in diagram one and engineer
+
+222
+00:18:52,520 --> 00:18:56,220
+draw diagram two الان diagram two for analysis
+
+223
+00:18:56,220 --> 00:19:01,640
+purposes يعني لهدف التحليل to help make some
+
+224
+00:19:01,640 --> 00:19:06,480
+initial simple calculationIn diagram two, the
+
+225
+00:19:06,480 --> 00:19:09,440
+engineer uses the following assumption and
+
+226
+00:19:09,440 --> 00:19:16,880
+information The three component forces from
+
+227
+00:19:16,880 --> 00:19:20,420
+loads
+
+228
+00:19:20,420 --> 00:19:26,020
+act as a singleresultants محصلة مظبوط في ال
+
+229
+00:19:26,020 --> 00:19:30,420
+diagram اتنين هذه صارت تلاتة واحدة كيف بعملهم بجيب
+
+230
+00:19:30,420 --> 00:19:34,220
+المحصلة تبعتهم resultant force in the top of the
+
+231
+00:19:34,220 --> 00:19:39,560
+frame all joints in the frame are ايش سمناهم هدول
+
+232
+00:19:39,560 --> 00:19:46,780
+ال joints هدولة flexible ولا rigid flexible لو انا
+
+233
+00:19:46,780 --> 00:19:53,620
+ضغط عليهم بتحركوا مظبوطفي هدف نسميه إيش؟ pin
+
+234
+00:19:53,620 --> 00:20:00,260
+joints ال joints قلنا المفصل ال pin اللي هي مفصل
+
+235
+00:20:00,260 --> 00:20:06,220
+flexible flexible joints can flex so the frame
+
+236
+00:20:06,220 --> 00:20:13,240
+behaves as إيش قلنا؟truss مظبوط الان اللي قلنا ال
+
+237
+00:20:13,240 --> 00:20:17,380
+trust اللي هو إيش عندي frame with flexible joint
+
+238
+00:20:17,380 --> 00:20:25,900
+أو pin joint مش rigid اللي عندي دي إيش of دروف
+
+239
+00:20:25,900 --> 00:20:32,000
+structure حاجة من تلت كلمات the center of a
+
+240
+00:20:32,000 --> 00:20:36,700
+gravity of دروف structure shown in redاللي انتوا
+
+241
+00:20:36,700 --> 00:20:39,880
+شايفينه هنا not including the satellite dish is
+
+242
+00:20:39,880 --> 00:20:43,880
+exactly halfway between the two supports يعني اللي
+
+243
+00:20:43,880 --> 00:20:48,500
+هي في النص أجا هاي
+
+244
+00:20:48,500 --> 00:20:56,500
+الخمسة الان in diagram two which of the members
+
+245
+00:20:56,500 --> 00:21:02,140
+are ties and which are struts اللي هنا ال a هذي
+
+246
+00:21:02,140 --> 00:21:10,040
+ايش هي هذيStraight هدى Straight هدى Tie هدول
+
+247
+00:21:10,040 --> 00:21:14,700
+الشغلات بدكوا تعرفوها لأن هدى من الشغلات السهلة
+
+248
+00:21:14,700 --> 00:21:21,080
+طيب choose the correct word from the bracket to
+
+249
+00:21:21,080 --> 00:21:25,280
+complete the sentences بدنا الكلمة الصحى traces
+
+250
+00:21:25,280 --> 00:21:32,700
+are frameworks or ties ايش ال trace framework with
+
+251
+00:21:32,700 --> 00:21:39,810
+ايشقول لو دي flexible أو joint أو pin joints،
+
+252
+00:21:39,810 --> 00:21:43,850
+مظبوط؟ طيب ال connection between members which
+
+253
+00:21:43,850 --> 00:21:50,190
+flexes is called؟ pin joint مش rigid، كويس؟ Struts
+
+254
+00:21:50,190 --> 00:21:54,510
+are designed to resist compression ولا tension؟
+
+255
+00:21:54,510 --> 00:22:00,530
+compression طلع عند ال tie إيش؟ ال tie اللي هي
+
+256
+00:22:00,530 --> 00:22:06,010
+عملية ال إيش؟ ال tension، أيوةهذه عملية ال tension
+
+257
+00:22:06,010 --> 00:22:11,430
+بنسميها ال tie و ال compression ال stress و ال
+
+258
+00:22:11,430 --> 00:22:16,650
+trust اللي هو بيحمل التنتين كويس by adding cross
+
+259
+00:22:16,650 --> 00:22:20,490
+member frames is embraced و لا being joined making
+
+260
+00:22:20,490 --> 00:22:25,010
+it stiffer embraced embraced اللي هي إيش قلنا عنها
+
+261
+00:22:25,010 --> 00:22:33,790
+embraced اللي هي لما نقول عنه إيش بيعمللناstiffen
+
+262
+00:22:33,790 --> 00:22:43,050
+و brace نفس الشيء لما نعمل ال stiffen هاي طيب الآن
+
+263
+00:22:43,050 --> 00:22:47,030
+ده بنطلع احنا ايش اللي مرن علينا الكلمات في هنا
+
+264
+00:22:47,030 --> 00:22:52,750
+اتكلمنا في ال chapter هاي على ال structural
+
+265
+00:22:52,750 --> 00:22:59,100
+mechanicsتكلمنا فيه على .. أولا قلنا لما ال frame
+
+266
+00:22:59,100 --> 00:23:04,820
+اللي عندي is statically determinant structure إيش
+
+267
+00:23:04,820 --> 00:23:10,780
+معناته؟ ال structure is under equilibrium and not
+
+268
+00:23:10,780 --> 00:23:13,440
+moving طب لما يكون under equilibrium إيش اللي
+
+269
+00:23:13,440 --> 00:23:17,600
+عندي؟ عندي two different forces أو two different
+
+270
+00:23:17,600 --> 00:23:23,850
+loadsof equal magnitude and opposite direction act
+
+271
+00:23:23,850 --> 00:23:29,390
+على ال frame الموجود هنا الأن اتكلمنا برضه على
+
+272
+00:23:29,390 --> 00:23:36,090
+حاجة تانية بعدها هذا اتكلمنا على الجزئية هذهال
+
+273
+00:23:36,090 --> 00:23:39,990
+gravity و ال center of gravity ال gravity هي احدى
+
+274
+00:23:39,990 --> 00:23:43,790
+ال forces بتأثر على كل شيء و دايما احنا بتكون
+
+275
+00:23:43,790 --> 00:23:47,950
+downward و ممكن انتوا بتعرفوها كيف تحسبوها اللي هي
+
+276
+00:23:47,950 --> 00:23:53,030
+بتساوي M في G مظبوط؟ اقولكوا في الفيزياء مرت
+
+277
+00:23:53,030 --> 00:23:58,310
+عليكوا ال G اللي هي A ال A اللي هي بس في ال .. في
+
+278
+00:23:58,310 --> 00:24:04,180
+ال gravity كدهش بتساوي؟تسعة point تمانية واحد
+
+279
+00:24:04,180 --> 00:24:08,160
+meter squared per second مظبوط او meter per second
+
+280
+00:24:08,160 --> 00:24:12,520
+squared الان اللي عندي هذه اللي بنتطلع عليها الان
+
+281
+00:24:12,520 --> 00:24:18,520
+لما نيجي بعد هيك اتكلمنا على ال structure with
+
+282
+00:24:18,520 --> 00:24:22,280
+different joint قولنا ال joints لما تكون flexible
+
+283
+00:24:22,280 --> 00:24:27,780
+بنسميها pin joint و لما تبقى hard او solid بنسميها
+
+284
+00:24:27,780 --> 00:24:33,000
+ايش rigid jointsالان اتكلمنا على ال structure تبعه
+
+285
+00:24:33,000 --> 00:24:37,440
+ده ال structure الموجود عندى with flexible او بين
+
+286
+00:24:37,440 --> 00:24:43,680
+joint سمناه traces او trace الان اللى عندى في ال
+
+287
+00:24:43,680 --> 00:24:48,940
+trace عندى فيه member ده ال member members resist
+
+288
+00:24:48,940 --> 00:24:53,840
+compression سمناهم ايش؟ stress و ده عملوا
+
+289
+00:24:53,840 --> 00:25:00,670
+resisting لل tension سمناهم ايش؟ tieهكذا خلصنا
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c18eabf02cfa18c1002e8e3a85a5459a8195537b
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw.srt
@@ -0,0 +1,1171 @@
+1
+00:00:21,850 --> 00:00:24,850
+سنتحدث اليوم عن القصة الخامسة 
+
+2
+00:00:24,850 --> 00:00:25,510
+ 
+
+3
+00:00:25,510 --> 00:00:25,730
+ 
+
+4
+00:00:25,730 --> 00:00:26,330
+ 
+
+5
+00:00:26,330 --> 00:00:28,010
+ 
+
+6
+00:00:28,010 --> 00:00:30,630
+ 
+
+7
+00:00:30,630 --> 00:00:31,150
+ 
+
+8
+00:00:31,150 --> 00:00:31,710
+ 
+
+9
+00:00:31,710 --> 00:00:40,270
+ 
+
+10
+00:00:40,270 --> 00:00:46,660
+الخامسة the distances between the holes
+
+11
+00:00:46,660 --> 00:00:50,540
+can be shown as running dimensions or as chain 
+
+12
+00:00:50,540 --> 00:00:56,340
+dimensions الآن احنا إيش بنتكلم عن؟ تعرفوا في 
+
+13
+00:00:56,340 --> 00:00:59,880
+العلم القديم يمكن هذا اللي ماحدش فيكم بشوف ال
+
+14
+00:00:59,880 --> 00:01:05,980
+American sport في عندهم chain اللي هو إيش زي مقياس
+
+15
+00:01:05,980 --> 00:01:08,880
+أنتوا الآن ال meter اللي عندنا في البيت أكبر إيش؟
+
+16
+00:01:08,880 --> 00:01:15,030
+قداش؟خمسة متر، مظبوط؟ لو عندي حاجة طولها عشرين 
+
+17
+00:01:15,030 --> 00:01:20,350
+متر، إيش بده أعمل فيه؟ بده أجيس الخمسة متر، خمسة
+
+18
+00:01:20,350 --> 00:01:23,530
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+19
+00:01:23,530 --> 00:01:25,210
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+20
+00:01:25,210 --> 00:01:26,470
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+21
+00:01:26,470 --> 00:01:30,050
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+22
+00:01:30,050 --> 00:01:38,210
+متر، خمسة متر، خمسة متر، خمسة متر، خمسةكويس ال
+
+23
+00:01:38,210 --> 00:01:41,830
+chain اللي هو إيش هو زي ال chain اللي هو عبارة عن
+
+24
+00:01:41,830 --> 00:01:49,230
+سلك أو حبل بس ال chain اللي هو إيش هو هو بتبقى 
+
+25
+00:01:49,230 --> 00:01:55,070
+بتشوف السلسلة السلسلة زي العقد إيش هذا سلسلة هذا
+
+26
+00:01:55,070 --> 00:02:00,250
+بيسموه chain فهو بيبقى قياس مثلا في ال American
+
+27
+00:02:00,250 --> 00:02:05,610
+sport في chain عشرة متر عشرة yardفبيجرسوا فيه كل
+
+28
+00:02:05,610 --> 00:02:09,210
+عشرة يارد بيحطوا من نقطة البداية لنقطة النهاية هاي
+
+29
+00:02:09,210 --> 00:02:12,970
+العشرة يارد و بيسحبوا هاي الان ال chain لو انه
+
+30
+00:02:12,970 --> 00:02:17,970
+plastic ممكن يمد صح او ينكمش بس لما انه بنقول 
+
+31
+00:02:17,970 --> 00:02:24,590
+chain حديد الحديد بيمدش صح فهنا بتكلم على ال chain 
+
+32
+00:02:24,590 --> 00:02:27,610
+dimensions or running dimension ال running
+
+33
+00:02:27,610 --> 00:02:33,150
+dimension اللي هو بيظله ساحب يعني مقياس طويل In
+
+34
+00:02:33,150 --> 00:02:37,250
+both cases, the center line aligned through the
+
+35
+00:02:37,250 --> 00:02:41,190
+center of the holes is measured is marked down and
+
+36
+00:02:41,190 --> 00:02:44,870
+the distances between the center lines are given
+
+37
+00:02:44,870 --> 00:02:49,150
+عادة لما تقيس مسافة بين ال hole اللي هو إيش
+
+38
+00:02:51,820 --> 00:02:56,880
+حفرة الحفرة عادة شكلها إيش بيبقى دائرة أو لو كانت
+
+39
+00:02:56,880 --> 00:03:01,120
+مربعة بدي أجسمها في النص في نقطة اللي هي منتصف
+
+40
+00:03:01,120 --> 00:03:05,320
+الحفرة بجيس من منتصف الحفرة هذا بسميها ال center
+
+41
+00:03:05,320 --> 00:03:09,320
+of the hole لمنتصف الحفرة التانية عشان أجيس
+
+42
+00:03:09,320 --> 00:03:13,780
+المسافة بينهمكويس يعني لما في حفرتين بدي اجيس
+
+43
+00:03:13,780 --> 00:03:17,900
+مسافة المسافة بين الحفرتين لازم اجيس من نص الحفرة
+
+44
+00:03:17,900 --> 00:03:21,760
+اللي هي مركز الحفرة اللي هي ال center لمركز الحفرة
+
+45
+00:03:21,760 --> 00:03:26,680
+التانية ال center التانية هذه بسميها اللي عندى ال
+
+46
+00:03:26,680 --> 00:03:30,520
+distance اللي بداش احتلها ال center line اللي هو
+
+47
+00:03:30,520 --> 00:03:34,860
+الخط اللي بمر فيه في مركز الحفرة ال center اللي
+
+48
+00:03:34,860 --> 00:03:38,800
+موجود distances between center lines are called
+
+49
+00:03:38,800 --> 00:03:45,400
+center to centerThe holes below are at 100mm
+
+50
+00:03:45,400 --> 00:03:50,700
+centers يعني طلع عندى شايف المسافة هان؟ ايش هان
+
+51
+00:03:50,700 --> 00:03:55,940
+اخدت؟ هى من ال center ال center هان هى 100 200 300
+
+52
+00:03:55,940 --> 00:04:00,040
+هدى running dimension لإنه خدت أنا مسافة كلية
+
+53
+00:04:00,040 --> 00:04:03,740
+بينما هان ايش قلت عنها؟ it's chain dimension ايش
+
+54
+00:04:03,740 --> 00:04:10,560
+اخدت؟نفس الشيء ولكن هنا 100 مليمتر 100 مليمتر 100
+
+55
+00:04:10,560 --> 00:04:11,680
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+56
+00:04:11,680 --> 00:04:13,160
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+57
+00:04:13,160 --> 00:04:13,200
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+58
+00:04:13,200 --> 00:04:13,400
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+59
+00:04:13,400 --> 00:04:16,360
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+60
+00:04:16,360 --> 00:04:18,220
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+61
+00:04:18,220 --> 00:04:20,720
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+62
+00:04:20,720 --> 00:04:29,300
+مليمتر 100 مليمترمتساوية الان ال note ال
+
+63
+00:04:29,300 --> 00:04:33,540
+written note ايش بتقولي عندي؟ CC from center to
+
+64
+00:04:33,540 --> 00:04:42,120
+center المسافة كام؟ one hundred millimeter center
+
+65
+00:04:42,120 --> 00:04:47,030
+lines are often used as reference pointsاللي هي
+
+66
+00:04:47,030 --> 00:04:51,550
+مرجعية نقاط مرجعية these can be measured from in
+
+67
+00:04:51,550 --> 00:04:55,150
+order to locate that is give the position of
+
+68
+00:04:55,150 --> 00:05:00,890
+points on components عادة بحطها عشان اعرف مكان
+
+69
+00:05:00,890 --> 00:05:06,730
+locate تحدد الموقع give the position the
+
+70
+00:05:06,730 --> 00:05:10,830
+measurement are offset from the center lines ايش
+
+71
+00:05:10,830 --> 00:05:18,220
+يعني offset؟ لأالان انا بازاحة تنزاح شوية او 
+
+72
+00:05:18,220 --> 00:05:23,280
+shifted في الانجليزي shifted اللي هي ايش يعني هي
+
+73
+00:05:23,280 --> 00:05:27,540
+offset from the center line each is at a certain
+
+74
+00:05:27,540 --> 00:05:32,090
+distance from it and the offsets are measured at a
+
+75
+00:05:32,090 --> 00:05:36,570
+right angle to the center lines at 90 degrees to
+
+76
+00:05:36,570 --> 00:05:39,750
+it يعني عادة لما يقول right at right angle ال
+
+77
+00:05:39,750 --> 00:05:44,050
+right angle الزاوية القائمة اللي هي كام تسعين درجة
+
+78
+00:05:44,050 --> 00:05:49,990
+هذا انتوا خبرة فيها نتكلم الآن على ال grades ايش
+
+79
+00:05:49,990 --> 00:05:55,330
+ال grades؟ شبكة الان دفتر الرسم الهندسي عبارة عن
+
+80
+00:05:55,330 --> 00:06:01,500
+ال grid page صح؟مقسم لخطوط طول و عرض البياني
+
+81
+00:06:01,500 --> 00:06:06,280
+الرسم البياني مظبوط هذا الرسم البياني الان in
+
+82
+00:06:06,280 --> 00:06:10,400
+large designs notably those of structure grids are
+
+83
+00:06:10,400 --> 00:06:15,260
+used for horizontal positioning الان عندى عادة ال
+
+84
+00:06:15,260 --> 00:06:19,600
+grid للتصميمات الكبيرة بتبقى موجودة عشان يحدد
+
+85
+00:06:19,600 --> 00:06:23,760
+المواقع الأفقية ال grid lines have numbers and
+
+86
+00:06:23,760 --> 00:06:29,130
+lettersال grid lines في عندى عمودي و في عندى ايش
+
+87
+00:06:29,130 --> 00:06:36,990
+القفقي و العمودي واحد بعطيه ارقام grid line 123 و
+
+88
+00:06:36,990 --> 00:06:44,210
+التاني بعطيه ايش a,b,c,d و هكذا alphabetically All
+
+89
+00:06:44,210 --> 00:06:47,890
+grid lines are parallel with one another that is
+
+90
+00:06:47,890 --> 00:06:50,550
+they are straight lines and are at regular
+
+91
+00:06:50,550 --> 00:06:54,890
+distances apart كل ال grid lines هدول سواء
+
+92
+00:06:54,890 --> 00:06:58,430
+المجموعة العمودية أو الأفقية متوازية ايش يعني
+
+93
+00:06:58,430 --> 00:07:04,050
+متوازية عبارة عن خطوط مستقيمة على مسافات متساوية
+
+94
+00:07:04,050 --> 00:07:10,130
+مش هيك احنا تعريف التوازي خطين المتوازين ايش خطين 
+
+95
+00:07:10,130 --> 00:07:18,610
+مستقيمين على مسافاتمتساوية في هذا المجال طيب ..
+
+96
+00:07:18,610 --> 00:07:22,470
+الآن بالنسبة إلينا .. يعني إذا بنطلع عليها ال
+
+97
+00:07:22,470 --> 00:07:27,470
+parallel عرفناها طب ال perpendicular اللي هي ال
+
+98
+00:07:27,470 --> 00:07:34,510
+إيش؟ العمودية هذا بشتغل لحاله قلناه طيب ال
+
+99
+00:07:34,510 --> 00:07:38,410
+perpendicular اللي هي العموديين هدولة بتقاطعوا at
+
+100
+00:07:38,410 --> 00:07:42,610
+a right angle صح؟ بيعملوا اتنين right angle
+
+101
+00:07:45,170 --> 00:07:49,630
+طيب letter lines are run parallel with one another
+
+102
+00:07:49,630 --> 00:07:55,130
+and are perpendicular to the numbered lines يعني
+
+103
+00:07:55,130 --> 00:08:00,710
+زي ما حكيت عندى فيه اتجاه عمودي وفيه اتجاه أفقي
+
+104
+00:08:00,710 --> 00:08:05,750
+العمودي ايش مع الأفق ايش بيعملوا زوايا قائمة right
+
+105
+00:08:05,750 --> 00:08:09,470
+angle فبنقول عنهم متعامدين اللي هي perpendicular
+
+106
+00:08:09,470 --> 00:08:17,060
+او بنقول they joined at right angle or right angles
+
+107
+00:08:17,060 --> 00:08:24,440
+at right angles the plan بلغه هذا هنشوف show part
+
+108
+00:08:24,440 --> 00:08:30,060
+of the floor of an office building يعني في مقطع
+
+109
+00:08:30,060 --> 00:08:39,320
+موجود هيفرجينا المستوى الأرضي لبناية بناية خاصة
+
+110
+00:08:39,320 --> 00:08:43,400
+بالمكاتب the perpendicular grid line intersect at
+
+111
+00:08:44,120 --> 00:08:49,100
+يعني intersect at إيش هي معناته؟ تقاطع cross at
+
+112
+00:08:49,100 --> 00:08:53,440
+the centers of the columns تعرف ال column إيش
+
+113
+00:08:53,440 --> 00:08:58,860
+بنسميه؟ العمود الآن أحنا في البيت في عندنا حزامات
+
+114
+00:08:58,860 --> 00:09:04,440
+و فينا أعمدة لتبعين المدني بكرا اللي بتخصصه البيت
+
+115
+00:09:04,440 --> 00:09:09,900
+في عندنا الحزام اللي هو الأفقي العمود اللي هو رأسي
+
+116
+00:09:09,900 --> 00:09:14,710
+ففي عندنا اللي بتحكم في البيتالإحزامات والأعمدة
+
+117
+00:09:14,710 --> 00:09:20,150
+يعني البيت ممكن يقوم على بس الإحزامات والأعمدة، 
+
+118
+00:09:20,150 --> 00:09:26,330
+كويس؟ فهنا لما نقول columns أعمدة an opening hole
+
+119
+00:09:26,330 --> 00:09:30,630
+in the floor is shown using coordinate dimension
+
+120
+00:09:30,630 --> 00:09:32,470
+أيش يعني coordinate dimension؟
+
+121
+00:09:36,180 --> 00:09:41,000
+الإحداثيات كلمة إحداثيات هي تستخدم ال technical
+
+122
+00:09:41,000 --> 00:09:45,880
+word كويس these allow the site engineers to sit
+
+123
+00:09:45,880 --> 00:09:50,480
+out إيش يعني sit out mark the position of يعني
+
+124
+00:09:50,480 --> 00:09:54,960
+يحدد الموقع sit out mark the position of the
+
+125
+00:09:54,960 --> 00:09:58,520
+opening by squaring of the grid line making the 
+
+126
+00:09:58,520 --> 00:10:02,160
+lines that run at right angles to them يعني هنا
+
+127
+00:10:02,160 --> 00:10:08,400
+square off making يعني بيعمل/بيحدد الزوايا القائمة 
+
+128
+00:10:08,400 --> 00:10:12,520
+الموجودة then measuring along these lines using a
+
+129
+00:10:12,520 --> 00:10:18,340
+tape measure إيش الـ tape measure اللي هو الـ متر
+
+130
+00:10:18,340 --> 00:10:24,340
+سمعينه؟ اه ايوه؟
+
+131
+00:10:24,340 --> 00:10:30,440
+الآن في عندي عدة مفردات موجودة هنا دي أوضو لايت
+
+132
+00:10:30,440 --> 00:10:35,700
+إيش هي دي أوضو لايت is an optical device used for
+
+133
+00:10:35,700 --> 00:10:40,040
+measuring angles can be used to square off grid
+
+134
+00:10:40,040 --> 00:10:44,100
+lines accurately الآن هذا جهاز بيقيس الزوايا احنا
+
+135
+00:10:44,100 --> 00:10:48,720
+عادة إيش .. هنقولكوا كيف نقيس الزوايا يمكن هذا ال
+
+136
+00:10:48,720 --> 00:10:51,200
+.. قليل فيكم اللي بيستطيعوا يطلعوا عليهم بيستطيعوا
+
+137
+00:10:51,200 --> 00:10:52,920
+يطلعوا على المجاولين إيش بيستخدموه
+
+138
+00:10:55,630 --> 00:10:59,950
+هذا عند المساحة، اللي ما عنده مساحة إيش بيعمل؟
+
+139
+00:10:59,950 --> 00:11:04,430
+تعرفوا أنتم نظرية فيثاغورس، مظبوط؟ إيش بتقول؟
+
+140
+00:11:04,430 --> 00:11:09,430
+ها هي هذا، ده بنتكلم عليها إيش using؟ Pythagoras
+
+141
+00:11:10,140 --> 00:11:14,060
+theorem اللي هي فيثاغورس إيش بتعمل هات؟ بنقيس
+
+142
+00:11:14,060 --> 00:11:18,520
+مثلًا أنا بعرف لو جبت ستة متر من هنا مع ثمانية متر
+
+143
+00:11:18,520 --> 00:11:23,720
+القطر تبعهم بيكون كام؟ عشرة فبيعملوا زي هيك هناك
+
+144
+00:11:23,720 --> 00:11:28,600
+الـ بناء ما عنده هذا الجهاز إيش بيعمل؟ بيقيس زي هيك و
+
+145
+00:11:28,600 --> 00:11:33,320
+بيحدد بيقول هذه الزاوية بدها مفتوحة أو مسكرة مفتوحة
+
+146
+00:11:33,320 --> 00:11:38,940
+يعني إيش؟ منفرجة صارت مش .. مسكرة إيش صارت؟ صارت
+
+147
+00:11:38,940 --> 00:11:44,260
+ضيقة إنها أقل من تسعين درجة الآن to double check
+
+148
+00:11:44,260 --> 00:11:48,620
+the dimension إيش double check أنا بقيس بس لازم
+
+149
+00:11:48,620 --> 00:11:54,220
+أتأكد من .. في المقاسات double check double check
+
+150
+00:11:54,220 --> 00:11:58,820
+للتأكد okay dimension that is carry out an extra
+
+151
+00:11:58,820 --> 00:12:04,160
+check diagonal measurement can be used as in
+
+152
+00:12:04,160 --> 00:12:09,030
+engineers sketch الـ داياجونال هذه نستخدمها اللي هي
+
+153
+00:12:09,030 --> 00:12:12,810
+القطر اللي حكيت عنه الـ length of the diagonals
+
+154
+00:12:12,810 --> 00:12:17,770
+can be calculated using Pythagoras theorem اللي هي
+
+155
+00:12:17,770 --> 00:12:22,390
+نظرية فيثاغورس وهي عندي الشكل طلع عندي هذا اللي
+
+156
+00:12:22,390 --> 00:12:27,550
+بتعمل لي هاي هذا وهذا parallel هذا وهذا parallel
+
+157
+00:12:27,550 --> 00:12:31,550
+الآن هذا وهذا perpendicular اللي عندي
+
+158
+00:12:34,400 --> 00:12:37,980
+هي هنا اللي بنتكلم عليه الـ إيش الـ diagonal اللي
+
+159
+00:12:37,980 --> 00:12:42,580
+بنحسب المسافة بنقول الجذر التربيعي للقطر إيه؟
+
+160
+00:12:42,580 --> 00:12:47,020
+القطر الأول تربيع والتاني تربيع بيعطينا المسافة
+
+161
+00:12:47,020 --> 00:12:53,750
+الموجودة الـ right angle الآن exercise 5.1 بدنا نبدل
+
+162
+00:12:53,750 --> 00:12:57,370
+هذه الكلمات look at these sentences about the
+
+163
+00:12:57,370 --> 00:13:03,030
+design of ship replace the underlying words and
+
+164
+00:13:03,030 --> 00:13:06,250
+expressions with alternative words and expressions
+
+165
+00:13:06,250 --> 00:13:09,570
+يعني هذا بدنا نبدلهم بإيش؟ بالكلمات اللي احنا
+
+166
+00:13:09,570 --> 00:13:15,170
+غطيناها في اللي عندك الـ handrail is fixed by 115
+
+167
+00:13:15,170 --> 00:13:20,750
+brackets إيش الـ handrail؟ اللي هو الدرابزين
+
+168
+00:13:20,750 --> 00:13:25,050
+الآن اللي عنده مش بيجيب لعب للصغار الآن هذا بيعمل
+
+169
+00:13:25,050 --> 00:13:29,890
+سكة حديد هذا بيسموه الـ hand is fixed by brackets
+
+170
+00:13:29,890 --> 00:13:33,870
+which are one one seventy five millimeter apart
+
+171
+00:13:33,870 --> 00:13:38,190
+between their centers إيش الكلمة اللي بيسموها at
+
+172
+00:13:38,190 --> 00:13:43,310
+لأ بنقول at one seventy five millimeter centers
+
+173
+00:13:43,310 --> 00:13:48,850
+هذا بدلتنا كل الكلمة اللي موجودة عندها the
+
+174
+00:13:48,850 --> 00:13:52,150
+dimensions are measured from the line down the
+
+175
+00:13:52,150 --> 00:13:55,010
+middle of the ship إيش الـ line down the middle؟
+
+176
+00:13:55,010 --> 00:14:01,270
+إيش سميناها؟ الـ center line how far is the widest
+
+177
+00:14:01,270 --> 00:14:05,990
+point of the ship located away from the center
+
+178
+00:14:05,990 --> 00:14:10,930
+line إيش هذه سميناها؟ إيش اللي احنا لما نقولها لما
+
+179
+00:14:10,930 --> 00:14:16,250
+بدي هاي المكان وزحت عنه إيش سميناه؟ offset مظبوط
+
+180
+00:14:17,770 --> 00:14:21,810
+Are the adjacent adjacent linked of the handrail
+
+181
+00:14:21,810 --> 00:14:26,950
+at 90 degree to each other؟ إيش الـ adjacent؟ إيش
+
+182
+00:14:26,950 --> 00:14:32,830
+معناه adjacent؟ طيب بس إيش adjacent السؤال قبل
+
+183
+00:14:32,830 --> 00:14:39,910
+adjacent القريب القرب من أيوه
+
+184
+00:14:39,910 --> 00:14:43,730
+الآن لما الحاجة جنب بعض بنسميها adjacent to each
+
+185
+00:14:43,730 --> 00:14:47,810
+other الحين لما أقول أنت مين و who is adjacent to
+
+186
+00:14:47,810 --> 00:14:53,190
+you بدك تقول زميلتك اللي جنبك القريبة منك فهنا at
+
+187
+00:14:53,190 --> 00:14:57,170
+ninety degree at a ninety degree أو at ninety
+
+188
+00:14:57,170 --> 00:15:01,510
+degrees these dimensions allow you to establish
+
+189
+00:15:01,510 --> 00:15:03,930
+the position of the whole إيش establish the
+
+190
+00:15:03,930 --> 00:15:09,030
+position قولنا locate هذه الكلمات اللي بتيجي عندك
+
+191
+00:15:09,030 --> 00:15:11,010
+locate establish position
+
+192
+00:15:14,470 --> 00:15:22,010
+في إيه؟ في الغالب بالامتحان اه لأ بس هذا أنت لساتك
+
+193
+00:15:22,010 --> 00:15:26,550
+الحين مخلصة تمر عليهم عشان هذه اه وبعدين هذا
+
+194
+00:15:26,550 --> 00:15:32,110
+بيقولك look at الـ .. اللي عندي a and b و replace
+
+195
+00:15:32,110 --> 00:15:36,190
+these words يعني بتحطيهم قدامك ومنها تختاري بس
+
+196
+00:15:36,190 --> 00:15:41,130
+احنا بنحط لك قائمة زي .. بالنسبة لنا زي الموجود هنا
+
+197
+00:15:46,420 --> 00:15:53,680
+of a handrail at each other ممكن تقول hand are
+
+198
+00:15:53,680 --> 00:16:00,440
+adjacent linked ممكن تقول perpendicular to each
+
+199
+00:16:00,440 --> 00:16:05,200
+other بنفع هي perpendicular لأن هي at right angle
+
+200
+00:16:05,200 --> 00:16:08,220
+طيب
+
+201
+00:16:09,430 --> 00:16:12,690
+الآن اللي عندي التاني five two look at these
+
+202
+00:16:12,690 --> 00:16:17,950
+extracts from technical discussion on construction
+
+203
+00:16:17,950 --> 00:16:21,570
+complete these sentences using the words in the
+
+204
+00:16:21,570 --> 00:16:29,630
+box what they mean by extracts extracts
+
+205
+00:16:29,630 --> 00:16:35,950
+هي هذه بتيجي حاجات بالطريق look at extract from
+
+206
+00:16:35,950 --> 00:16:38,590
+technical discussion الـ extract
+
+207
+00:16:41,310 --> 00:16:48,730
+تسمعوا من مقتطفات؟ هي مقتطفات الـ extract في العربية
+
+208
+00:16:48,730 --> 00:16:53,770
+يعني إيش؟ لما أنت تاخد في محادثة تقنية وتاخد
+
+209
+00:16:53,770 --> 00:17:00,150
+أجزاء منها بنسميها إيش؟ مقتطفات according to this
+
+210
+00:17:00,150 --> 00:17:05,690
+drawing إيش؟ it runs along the external wall of
+
+211
+00:17:05,690 --> 00:17:11,320
+this structure أي واحدة بنقول According to this
+
+212
+00:17:11,320 --> 00:17:14,100
+drawing بنفع grid lines ولا intersections
+
+213
+00:17:14,100 --> 00:17:20,020
+parallel perpendicular set out or square up؟ يعني
+
+214
+00:17:20,020 --> 00:17:24,080
+هذا بدك إياها إيش؟ بدك إيش إياها verb، مظبوط؟ إيش
+
+215
+00:17:24,080 --> 00:17:30,800
+من هدول؟ الـ grid line according to this drawing
+
+216
+00:17:30,800 --> 00:17:36,240
+grid line طيب the positions were marked accurately
+
+217
+00:17:36,240 --> 00:17:39,800
+they were إيش؟ by our site engineer
+
+218
+00:17:42,280 --> 00:17:47,740
+إيش هي set out مظبوط إيش قولنا set out checked
+
+219
+00:17:47,740 --> 00:17:55,440
+مظبوط يعني انفحصت في هذا the external wall runs
+
+220
+00:17:55,440 --> 00:18:03,060
+along grid lines one and the internal corridor
+
+221
+00:18:03,060 --> 00:18:07,520
+wall runs along grid line two so the walls are
+
+222
+00:18:07,520 --> 00:18:13,510
+with each other الآن هذا إيش الترقيم؟ أرقام أخدت الـ
+
+223
+00:18:13,510 --> 00:18:16,690
+grid lines أخدت واحد اتنين واحد اتنين إيش بيكونوا
+
+224
+00:18:16,690 --> 00:18:21,130
+parallel لو قلت one and a إيش بيكونوا
+
+225
+00:18:21,130 --> 00:18:26,550
+perpendicular بس one and two معناته إيش بدهم
+
+226
+00:18:26,550 --> 00:18:31,830
+يكونوا parallel خليكم معايا في هذه إذا أعطيتكوا الـ
+
+227
+00:18:31,830 --> 00:18:36,350
+grid lines مرقمين أو alphabetically يعني يا إما
+
+228
+00:18:36,350 --> 00:18:40,070
+مرقمين يا إما in alphabetical order هدول بيكونوا
+
+229
+00:18:40,070 --> 00:18:46,230
+إيش؟ parallel لو أخدت واحد numbered والتاني alphabetic
+
+230
+00:18:46,230 --> 00:18:56,030
+إيش بيكونوا؟ perpendicular واضحة طيب I've
+
+231
+00:18:56,030 --> 00:19:00,350
+marked a cross on the concrete floor showing where
+
+232
+00:19:00,350 --> 00:19:06,830
+the two grid lines الـ cross بيجي وين where دي إيش
+
+233
+00:19:06,830 --> 00:19:10,990
+بيسوي two grid lines إيش بيصير فيهم؟ intersect في
+
+234
+00:19:10,990 --> 00:19:14,890
+التقاطع عادة لما بحط x بحط على نقطة إيه؟ تقاطع
+
+235
+00:19:14,890 --> 00:19:20,990
+كهندسة طيب we need to show the position of the
+
+236
+00:19:20,990 --> 00:19:27,550
+corner of the staircase with coordinate dimensions
+
+237
+00:19:27,550 --> 00:19:34,530
+they should be taken from two grid lines الآن الـ
+
+238
+00:19:34,530 --> 00:19:43,470
+staircase إيش هو؟ تعرف الدرج؟ أيوه السلالم الأهدأ
+
+239
+00:19:43,470 --> 00:19:46,150
+بيقول we need to show the position of the corner
+
+240
+00:19:46,150 --> 00:19:51,170
+الـ position تبع الـ corner إيش بيكون؟ في عند الـ two
+
+241
+00:19:51,170 --> 00:19:56,750
+grid lines إيش معناتهم؟ بتقاطع متعمدين، مظبوط، في
+
+242
+00:19:56,750 --> 00:20:03,330
+hyperpendicular we will use the tidal light to
+
+243
+00:20:03,330 --> 00:20:08,490
+edge the grid lines and mark a ninety degree
+
+244
+00:20:08,490 --> 00:20:13,210
+offset إيش الـ optical light ليش بيستخدم الـ optical
+
+245
+00:20:13,210 --> 00:20:17,750
+light square off اللي هي تطبطب الزوايا
+
+246
+00:20:22,040 --> 00:20:26,760
+طيب الآن الـ match .. match the two parts of the
+
+247
+00:20:26,760 --> 00:20:30,620
+sentences to complete the extract .. extract from
+
+248
+00:20:30,620 --> 00:20:33,960
+a training manual in civil engineering the follow
+
+249
+00:20:33,960 --> 00:20:37,440
+.. the following precautions can help to prevent
+
+250
+00:20:37,440 --> 00:20:42,580
+costly setting out mistakes إيش الـ precaution؟ 
+
+251
+00:20:47,780 --> 00:20:53,380
+الاحتياطات أو دي بدك تقولي ال .. يعني الحاجات اللي
+
+252
+00:20:53,380 --> 00:20:59,060
+بدك تتجنبيها يعني التعليمات ال .. ال .. الأساسية
+
+253
+00:20:59,060 --> 00:21:03,380
+لتجنب المشاكل prevent costly setting out mistakes
+
+254
+00:21:03,380 --> 00:21:09,840
+اللي هي الأخطاء اللي .. اللي هي الأخطاء اللي بتكلف
+
+255
+00:21:09,840 --> 00:21:16,250
+.. اللي بتكلف كثير always use a steel tape measure
+
+256
+00:21:16,250 --> 00:21:21,710
+never a plastic one ليش؟ ايش اللي هاي بيقولك دايما
+
+257
+00:21:21,710 --> 00:21:25,910
+يستخدمي متر معدني مش متر plastic to ensure it
+
+258
+00:21:25,910 --> 00:21:29,090
+doesn't stretch under tension أيوة to ensure it
+
+259
+00:21:29,090 --> 00:21:32,270
+doesn't stretch under tension لو استخدمت plastic
+
+260
+00:21:32,270 --> 00:21:39,810
+ممكن لما أشده يعمل stretch يمط معاه مظبوط فدايما
+
+261
+00:21:39,810 --> 00:21:44,150
+بتلاقي اللي هو أمطارفيش للخياطين اللي بيستخدموا ايش
+
+262
+00:21:44,150 --> 00:21:55,550
+متر جلدي لأن المسافة مش كبيرة حديد
+
+263
+00:21:55,550 --> 00:21:59,650
+بس طويل هو نفسه بس الحجم بدل ما هو الجلد بيبقى
+
+264
+00:21:59,650 --> 00:22:04,620
+هالجلد حجمه و بيسحب فيه هدول المساحة دايما معهم شو
+
+265
+00:22:04,620 --> 00:22:08,460
+اللي عندنا بقى؟ لأ لأ صغير هذا .. هذا .. هذا صغير
+
+266
+00:22:08,460 --> 00:22:11,840
+خمسة متر حده اللي كبير فيه ثلاثة متر و فيه خمسة
+
+267
+00:22:11,840 --> 00:22:16,560
+متر بس ال car car بيوصل لمائة متر فأنت لما بدك تقيس
+
+268
+00:22:16,560 --> 00:22:21,580
+أراضي بيقيسش خمسة متر خمسة بيسحب و بيمشي مظبوط؟ و
+
+269
+00:22:21,580 --> 00:22:24,020
+لو طلعته و أنت ماشيين في السيارات اللي بتلاقيهم
+
+270
+00:22:24,020 --> 00:22:27,400
+بيقيسوا بتلاقي معاه متر و معاه عدة المساحة ال
+
+271
+00:22:27,400 --> 00:22:30,960
+car car اللي عنده هذا هو كبير .. متر كبير يعني زي
+
+272
+00:22:30,960 --> 00:22:36,120
+ما بيقولوه check that both diagonals of the
+
+273
+00:22:36,120 --> 00:22:39,840
+rectangular shape are equal الآن لو جبت أنا
+
+274
+00:22:39,840 --> 00:22:45,040
+المستطيل المستطيل ايش بيميزه المحاور تبعته ايش
+
+275
+00:22:45,040 --> 00:22:49,840
+متساوية هذه المحاور هذه خلينا نقول كل ضلعين متقابلين
+
+276
+00:22:49,840 --> 00:22:53,380
+متساويين والمحاور متساوية يبقى الزوايا تبعته ايش
+
+277
+00:22:53,380 --> 00:22:57,720
+بتكون قائمة قائمة لو ما كان زي هيك بتبقى الزوايا
+
+278
+00:22:57,720 --> 00:23:02,370
+تبعته مش قائمة المساح لما بديه يفرز أرض بيقيس 
+
+279
+00:23:02,370 --> 00:23:07,230
+المسافات وبعده بيقيس المحاور المحور هذا والمحور
+
+280
+00:23:07,230 --> 00:23:10,250
+الاثنين لازم يكونوا متساوين عشان تأخذ مساحة
+
+281
+00:23:10,250 --> 00:23:16,350
+مستطيلة أي واحدة بنقول فيهم هنا الأولى to check
+
+282
+00:23:16,350 --> 00:23:20,590
+the corners are at right angles لما نقول نحن
+
+283
+00:23:20,590 --> 00:23:24,390
+diagonal، diagonal to check the angles measure
+
+284
+00:23:24,390 --> 00:23:27,990
+dimensions in two directions from parallel grid
+
+285
+00:23:27,990 --> 00:23:28,570
+lines
+
+286
+00:23:31,880 --> 00:23:37,000
+to double check measurement إذا جئت عندك خطين
+
+287
+00:23:37,000 --> 00:23:40,540
+متساويين وقست المسافة من هنا والمسافة من الطرف
+
+288
+00:23:40,540 --> 00:23:48,380
+الثاني ايش مضمن أنه هدول ما بيصيرش أخطاء add
+
+289
+00:23:48,380 --> 00:23:54,740
+up chains dimensions give running dimensionsto
+
+290
+00:23:54,740 --> 00:23:58,720
+prevent slight errors being multiplied عشان ال
+
+291
+00:23:58,720 --> 00:24:03,440
+error ما يزيدش عندنا لأنه بيستخدم ال running meter
+
+292
+00:24:03,440 --> 00:24:08,980
+ليؤكد منهم طيب هي كما ننوي نحن جاهزين لل quiz
+
+293
+00:24:08,980 --> 00:24:09,560
+تبعكم 
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw_postprocess.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..461c1deb0a12ad8ab1225c7a9ae1f2c75ae337d5
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw_postprocess.srt
@@ -0,0 +1,1172 @@
+1
+00:00:21,850 --> 00:00:24,850
+سنتحدث اليوم عن القصة الخامسة الخامسة الخامسة
+
+2
+00:00:24,850 --> 00:00:25,510
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+3
+00:00:25,510 --> 00:00:25,730
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+4
+00:00:25,730 --> 00:00:26,330
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+5
+00:00:26,330 --> 00:00:28,010
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+6
+00:00:28,010 --> 00:00:30,630
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+7
+00:00:30,630 --> 00:00:31,150
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+8
+00:00:31,150 --> 00:00:31,710
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+9
+00:00:31,710 --> 00:00:40,270
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+10
+00:00:40,270 --> 00:00:46,660
+الخامسة الخامسة الخthe distances between the holes
+
+11
+00:00:46,660 --> 00:00:50,540
+can be shown as running dimensions or as chain
+
+12
+00:00:50,540 --> 00:00:56,340
+dimensions الآن احنا إيش بنتكلم عن؟ تعرفوا في
+
+13
+00:00:56,340 --> 00:00:59,880
+العلم القديم يمكن هذا اللي ماحدش فيكم بشوف ال
+
+14
+00:00:59,880 --> 00:01:05,980
+America sport في عندهم chain اللي هو إيش زي مقياس
+
+15
+00:01:05,980 --> 00:01:08,880
+أنتوا الآن ال meter اللي عندنا في البيت أكبر إيش؟
+
+16
+00:01:08,880 --> 00:01:15,030
+قداش؟خمسة متر، مظبوط؟ لو عندي حاجة طولها عشرين
+
+17
+00:01:15,030 --> 00:01:20,350
+متر، إيش بده أعمل فيه؟ بده أجيس الخمسة متر، خمسة
+
+18
+00:01:20,350 --> 00:01:23,530
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+19
+00:01:23,530 --> 00:01:25,210
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+20
+00:01:25,210 --> 00:01:26,470
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+21
+00:01:26,470 --> 00:01:30,050
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+22
+00:01:30,050 --> 00:01:38,210
+متر، خمسة متر، خمسة متر، خمسة متر، خمسةكويس ال
+
+23
+00:01:38,210 --> 00:01:41,830
+chain اللي هو إيش هو زي ال chain اللي هو عبارة عن
+
+24
+00:01:41,830 --> 00:01:49,230
+سلك أو حبل بس ال chain اللي هو إيش هو هو بتبقى
+
+25
+00:01:49,230 --> 00:01:55,070
+بتشوف السلسلة السلسلة زي العقد إيش هذا سلسلة هذا
+
+26
+00:01:55,070 --> 00:02:00,250
+بيسموه chain فهو بيبقى قياس مثلا في ال American
+
+27
+00:02:00,250 --> 00:02:05,610
+sport في chain عشرة متر عشرة yardفبيجرسوا فيه كل
+
+28
+00:02:05,610 --> 00:02:09,210
+عشرة يارد بيحطوا من نقطة البداية لنقطة النهاية هاي
+
+29
+00:02:09,210 --> 00:02:12,970
+العشرة يارد و بيسحبوا هاي الان ال chain لو انه
+
+30
+00:02:12,970 --> 00:02:17,970
+plastic ممكن يمد صح او ينكمش بس لما انه بنقول
+
+31
+00:02:17,970 --> 00:02:24,590
+chain حديد الحديد بيمدش صح فهنا بتكلم على ال chain
+
+32
+00:02:24,590 --> 00:02:27,610
+dimensions or running dimension ال running
+
+33
+00:02:27,610 --> 00:02:33,150
+dimension اللي هو بيظله ساحب يعني مقياس طويلIn
+
+34
+00:02:33,150 --> 00:02:37,250
+both cases, the center line aligned through the
+
+35
+00:02:37,250 --> 00:02:41,190
+center of the holes is measured is marked down and
+
+36
+00:02:41,190 --> 00:02:44,870
+the distances between the center lines are given
+
+37
+00:02:44,870 --> 00:02:49,150
+عادة لما تقيس مسافة بين ال hole اللي هو إيش
+
+38
+00:02:51,820 --> 00:02:56,880
+حفرة الحفرة عادة شكلها إيش بيبقى دائرة أو لو كانت
+
+39
+00:02:56,880 --> 00:03:01,120
+مربعة بدي أجسمها في النص في نقطة اللي هي منتصف
+
+40
+00:03:01,120 --> 00:03:05,320
+الحفرة بجيس من منتصف الحفرة هذا بسميها ال center
+
+41
+00:03:05,320 --> 00:03:09,320
+of the hole لمنتصف الحفرة التانية عشان أجيس
+
+42
+00:03:09,320 --> 00:03:13,780
+المسافة بينهمكويس يعني لما في حفرتين بدي اجيس
+
+43
+00:03:13,780 --> 00:03:17,900
+مسافة المسافة بين الحفرتين لازم اجيس من نص الحفرة
+
+44
+00:03:17,900 --> 00:03:21,760
+اللي هي مركز الحفرة اللي هي ال center لمركز الحفرة
+
+45
+00:03:21,760 --> 00:03:26,680
+التانية ال center التانية هذه بسميها اللي عندى ال
+
+46
+00:03:26,680 --> 00:03:30,520
+distance اللي بداش احتلها ال center line اللي هو
+
+47
+00:03:30,520 --> 00:03:34,860
+الخط اللي بمر فيه في مركز الحفرة ال center اللي
+
+48
+00:03:34,860 --> 00:03:38,800
+موجود distances between center lines are called
+
+49
+00:03:38,800 --> 00:03:45,400
+center to centerThe holes below are at 100mm
+
+50
+00:03:45,400 --> 00:03:50,700
+centers يعني طلع عندى شايف المسافة هان؟ ايش هان
+
+51
+00:03:50,700 --> 00:03:55,940
+اخدت؟ هى من ال center ال center هان هى 100 200 300
+
+52
+00:03:55,940 --> 00:04:00,040
+هدى running dimension لإنه خدت أنا مسافة كلية
+
+53
+00:04:00,040 --> 00:04:03,740
+بينما هان ايش قلت عنها؟ it's chain dimension ايش
+
+54
+00:04:03,740 --> 00:04:10,560
+اخدت؟نفس الشيء ولكن هنا 100 مليمتر 100 مليمتر 100
+
+55
+00:04:10,560 --> 00:04:11,680
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+56
+00:04:11,680 --> 00:04:13,160
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+57
+00:04:13,160 --> 00:04:13,200
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+58
+00:04:13,200 --> 00:04:13,400
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+59
+00:04:13,400 --> 00:04:16,360
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+60
+00:04:16,360 --> 00:04:18,220
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+61
+00:04:18,220 --> 00:04:20,720
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+62
+00:04:20,720 --> 00:04:29,300
+100 مليمتر 100 مليمترمتساوية الان ال note ال
+
+63
+00:04:29,300 --> 00:04:33,540
+written note ايش بتقولي عندي؟ CC from center to
+
+64
+00:04:33,540 --> 00:04:42,120
+center المسافة كام؟ one hundred millimeter center
+
+65
+00:04:42,120 --> 00:04:47,030
+lines are often used as reference pointsاللي هي
+
+66
+00:04:47,030 --> 00:04:51,550
+مرجعية نقاط مرجعية these can be measured from in
+
+67
+00:04:51,550 --> 00:04:55,150
+order to locate that is give the position of
+
+68
+00:04:55,150 --> 00:05:00,890
+points on components عادة بحطها عشان اعرف مكان
+
+69
+00:05:00,890 --> 00:05:06,730
+locate تحدد الموقع give the position the
+
+70
+00:05:06,730 --> 00:05:10,830
+measurement are offset from the center lines ايش
+
+71
+00:05:10,830 --> 00:05:18,220
+يعني offset؟ لأالان انا بازاحة تنزاح شوية او
+
+72
+00:05:18,220 --> 00:05:23,280
+shifted في الانجليزي shifted اللي هي ايش يعني هي
+
+73
+00:05:23,280 --> 00:05:27,540
+offset from the center line each is at a certain
+
+74
+00:05:27,540 --> 00:05:32,090
+distance from it and the offsets are measured ata
+
+75
+00:05:32,090 --> 00:05:36,570
+right angle to the center lines at 90 degrees to
+
+76
+00:05:36,570 --> 00:05:39,750
+it يعني عادة لما يقول right at right angle ال
+
+77
+00:05:39,750 --> 00:05:44,050
+right angle الزاوية القائمة اللي هي كام تسعين درجة
+
+78
+00:05:44,050 --> 00:05:49,990
+هذا انتوا خبرة فيها نتكلم الآن على ال grades ايش
+
+79
+00:05:49,990 --> 00:05:55,330
+ال grades؟ شبكة الان دفتر الرسم الهندسي عبارة عن
+
+80
+00:05:55,330 --> 00:06:01,500
+ال grade page صح؟مقسم لخطوط طول و عرض البياني
+
+81
+00:06:01,500 --> 00:06:06,280
+الرسم البياني مظبوط هذا الرسم البياني الان in
+
+82
+00:06:06,280 --> 00:06:10,400
+large designs notably those of structure grids are
+
+83
+00:06:10,400 --> 00:06:15,260
+used for horizontal positioning الان عندى عادة ال
+
+84
+00:06:15,260 --> 00:06:19,600
+grid للتصميمات الكبيرة بتبقى موجودة عشان يحدد
+
+85
+00:06:19,600 --> 00:06:23,760
+المواقع الأفقية ال grid lines have numbers and
+
+86
+00:06:23,760 --> 00:06:29,130
+lettersال grid lines في عندى عمودي و في عندى ايش
+
+87
+00:06:29,130 --> 00:06:36,990
+القفقي و العمودي واحد بعطيه ارقام grid line 123 و
+
+88
+00:06:36,990 --> 00:06:44,210
+التاني بعطيه ايش a,b,c,d و هكذا alphabeticallyAll
+
+89
+00:06:44,210 --> 00:06:47,890
+grid lines are parallel with one another that is
+
+90
+00:06:47,890 --> 00:06:50,550
+they are straight lines and are at regular
+
+91
+00:06:50,550 --> 00:06:54,890
+distances apart كل ال grid lines هدول سواء
+
+92
+00:06:54,890 --> 00:06:58,430
+المجموعة العمودية أو الأفقية متوازية ايش يعني
+
+93
+00:06:58,430 --> 00:07:04,050
+متوازية عبارة عن خطوط مستقيمة على مسافات متساوية
+
+94
+00:07:04,050 --> 00:07:10,130
+مش هيك احنا تعريف التوازي خطين المتوازين ايش خطين
+
+95
+00:07:10,130 --> 00:07:18,610
+مستقيمين على مسافاتمتساوية في هذا المجال طيب ..
+
+96
+00:07:18,610 --> 00:07:22,470
+الآن بالنسبة إلينا .. يعني إذا بنطلع عليها ال
+
+97
+00:07:22,470 --> 00:07:27,470
+parallel عرفناها طب ال perpendicular اللي هي ال
+
+98
+00:07:27,470 --> 00:07:34,510
+إيش؟ العمودية هذا بشتغل لحاله قلناه طيب ال
+
+99
+00:07:34,510 --> 00:07:38,410
+perpendicular اللي هي العموديين هدولة بتقاطعوا at
+
+100
+00:07:38,410 --> 00:07:42,610
+a right angle صح؟ بيعملوا اتنين right angle
+
+101
+00:07:45,170 --> 00:07:49,630
+طيب letter lines are run parallel with one another
+
+102
+00:07:49,630 --> 00:07:55,130
+and are perpendicular to the numbered lines يعني
+
+103
+00:07:55,130 --> 00:08:00,710
+زي ما حكيت عندى فيه اتجاه عمودي وفيه اتجاه أفقي
+
+104
+00:08:00,710 --> 00:08:05,750
+العمودي ايش مع الأفق ايش بيعملوا زوايا قائمة right
+
+105
+00:08:05,750 --> 00:08:09,470
+angle فبنقول عنهم متعامدين اللي هي perpendicular
+
+106
+00:08:09,470 --> 00:08:17,060
+او بنقول they joined atright angle او right angles
+
+107
+00:08:17,060 --> 00:08:24,440
+at right angles the plan بلغه هذا هنشوف show part
+
+108
+00:08:24,440 --> 00:08:30,060
+of the floor of an office building يعني في مقطع
+
+109
+00:08:30,060 --> 00:08:39,320
+موجود هيفرجينا المستوى الأرضي لبناية بناية خاصة
+
+110
+00:08:39,320 --> 00:08:43,400
+بالمكاتب the perpendicular grid line intersect at
+
+111
+00:08:44,120 --> 00:08:49,100
+يعني intersect at إيش هي معناته؟ تقاطع cross at
+
+112
+00:08:49,100 --> 00:08:53,440
+the centers of the columns تعرف ال column إيش
+
+113
+00:08:53,440 --> 00:08:58,860
+بنسميه؟ العمود الآن أحنا في البيت في عندنا حزامات
+
+114
+00:08:58,860 --> 00:09:04,440
+و فينا أعمدة لتبعين المدني بكرا اللي بتخصصه البيت
+
+115
+00:09:04,440 --> 00:09:09,900
+في عندنا الحزام اللي هو الأفقي العمود اللي هو رأسي
+
+116
+00:09:09,900 --> 00:09:14,710
+ففي عندنا اللي بتحكم في البيتالإحزامات والأعمدة
+
+117
+00:09:14,710 --> 00:09:20,150
+يعني البيت ممكن يقوم على بس الإحزامات والأعمدة،
+
+118
+00:09:20,150 --> 00:09:26,330
+كويس؟ فهنا لما نقول columns أعمدة an opening hole
+
+119
+00:09:26,330 --> 00:09:30,630
+in the floor is shown using coordinate dimension
+
+120
+00:09:30,630 --> 00:09:32,470
+أيش يعني coordinate dimension؟
+
+121
+00:09:36,180 --> 00:09:41,000
+الإحداثيات كلمة إحداثيات هي تستخدم ال technical
+
+122
+00:09:41,000 --> 00:09:45,880
+word كويس these allow the site engineers to sit
+
+123
+00:09:45,880 --> 00:09:50,480
+out إيش يعني sit out mark the position of يعني
+
+124
+00:09:50,480 --> 00:09:54,960
+يحدد الموقع sit out mark the position of the
+
+125
+00:09:54,960 --> 00:09:58,520
+opening by squaring of the grid line making the
+
+126
+00:09:58,520 --> 00:10:02,160
+lines that run at right angle to them يعني هنا
+
+127
+00:10:02,160 --> 00:10:08,400
+square of making يعني بيعملبيحدد الزوايا القائمة
+
+128
+00:10:08,400 --> 00:10:12,520
+الموجودة then measuring along these lines using a
+
+129
+00:10:12,520 --> 00:10:18,340
+tape measure ايش ال tape measure اللي هو ال متر
+
+130
+00:10:18,340 --> 00:10:24,340
+سمعينه؟ اه ايوه؟
+
+131
+00:10:24,340 --> 00:10:30,440
+الان في عنديعدة مفردات الموجودة هنا دي اوضو لايت
+
+132
+00:10:30,440 --> 00:10:35,700
+ايش هي دي اوضو لايت is an optical device used for
+
+133
+00:10:35,700 --> 00:10:40,040
+measuring angles can be used to square off grid
+
+134
+00:10:40,040 --> 00:10:44,100
+lines accurately الان هذا جهاز بقييس الزوايا احنا
+
+135
+00:10:44,100 --> 00:10:48,720
+عادة ايش .. هنقولكوا كيف نقيس الزوايا يمكن هذا ال
+
+136
+00:10:48,720 --> 00:10:51,200
+.. قليل فيكم اللي بيستطيعوا تطلع عليهم بيستطيعوا
+
+137
+00:10:51,200 --> 00:10:52,920
+تطلع علي المجاولين ايش بيستخدموه
+
+138
+00:10:55,630 --> 00:10:59,950
+هذا عند المساحة، اللي ماعندوش مساحة إيش بيعمل؟
+
+139
+00:10:59,950 --> 00:11:04,430
+تعرفوا أنتوا نظرية Vita-course، مظبوط؟ إيش بتقول؟
+
+140
+00:11:04,430 --> 00:11:09,430
+ها هي هذا، ده بنتكلم عليها إيش using? Pythagoras
+
+141
+00:11:10,140 --> 00:11:14,060
+theorem اللي هي vita course ايش بتعمل هات؟ بنقيس
+
+142
+00:11:14,060 --> 00:11:18,520
+مثلا انا بعرف لو جيبت ستة متر من هنا مع تمانية متر
+
+143
+00:11:18,520 --> 00:11:23,720
+القطر تبعهم بيكون كام؟ عشرة فبيعملوا زي هيك هناك
+
+144
+00:11:23,720 --> 00:11:28,600
+البنة ماعندوش هذا الجهاز ايش بيعمل؟ بقيس زي هيك و
+
+145
+00:11:28,600 --> 00:11:33,320
+بحدد بيقول هذا الزاوية بدها فاتحة او مسكرة فاتحة
+
+146
+00:11:33,320 --> 00:11:38,940
+يعني ايش؟ منفرجة صارت مش .. مسكرة ايش صارت؟صارت
+
+147
+00:11:38,940 --> 00:11:44,260
+ضيقة إنها أقل من تسعين درجة الان to double check
+
+148
+00:11:44,260 --> 00:11:48,620
+the dimension إيش double check أنا بجيس بس لازم
+
+149
+00:11:48,620 --> 00:11:54,220
+أتأكد من .. في المقسمية double check double check
+
+150
+00:11:54,220 --> 00:11:58,820
+للتأكد okay dimension that is carry out an extra
+
+151
+00:11:58,820 --> 00:12:04,160
+check diagonal measurement can be used as in
+
+152
+00:12:04,160 --> 00:12:09,030
+engineers sketchالدياجونال هذه نستخدمها اللي هي
+
+153
+00:12:09,030 --> 00:12:12,810
+القطر اللي حكيت عنه الـ length of the diagonals
+
+154
+00:12:12,810 --> 00:12:17,770
+can be calculated using Pythagoras theorem اللي هي
+
+155
+00:12:17,770 --> 00:12:22,390
+مقدرية Pythagoras وهي عندي الشكل طلع عندي هذا اللي
+
+156
+00:12:22,390 --> 00:12:27,550
+بتعمللي هاي هذا وهذا parallel هذا وهذا parallel
+
+157
+00:12:27,550 --> 00:12:31,550
+الآن هذا وهذا perpendicular اللي عندي
+
+158
+00:12:34,400 --> 00:12:37,980
+هي هنا اللي بنتكلم عليه ال ايش ال diagonal اللي
+
+159
+00:12:37,980 --> 00:12:42,580
+بنحسب المسافة بنقول الجدر التربيعي للقطر ايه؟
+
+160
+00:12:42,580 --> 00:12:47,020
+القطر الأول تربيع والتاني تربيع بيعطينا المسافة
+
+161
+00:12:47,020 --> 00:12:53,750
+الموجودة ال right angleالان exercise 5.1 بدنا نبدل
+
+162
+00:12:53,750 --> 00:12:57,370
+هذه الكلمات look at these sentences about the
+
+163
+00:12:57,370 --> 00:13:03,030
+design of ship replace the underlying words and
+
+164
+00:13:03,030 --> 00:13:06,250
+expressions with alternative words and expressions
+
+165
+00:13:06,250 --> 00:13:09,570
+يعني هذا بدنا نبدلهم بإيش؟ بالكلمات اللي احنا
+
+166
+00:13:09,570 --> 00:13:15,170
+غطناها في اللي عندك ال handrail is fixed by 115
+
+167
+00:13:15,170 --> 00:13:20,750
+brackets أيش ال handrail؟اللي هو القطار اليدوي
+
+168
+00:13:20,750 --> 00:13:25,050
+الان اللي عنده مش بيجيب لعب للصغار الان هذا بيعمل
+
+169
+00:13:25,050 --> 00:13:29,890
+سكة حديد هذا بيسموه ال hand is fixed by brackets
+
+170
+00:13:29,890 --> 00:13:33,870
+which are one one seventy five millimeter apart
+
+171
+00:13:33,870 --> 00:13:38,190
+between their centers ايش الكلمة اللي بيسموها at
+
+172
+00:13:38,190 --> 00:13:43,310
+لأ بنقول at one seventy five millimeter centers
+
+173
+00:13:43,310 --> 00:13:48,850
+هذا بدلتنا كل الكلمة اللي موجودة عندهاthe
+
+174
+00:13:48,850 --> 00:13:52,150
+dimensions are measured from the line down the
+
+175
+00:13:52,150 --> 00:13:55,010
+middle of the ship إيش ال line down the middle؟
+
+176
+00:13:55,010 --> 00:14:01,270
+إيش سمنها؟ ال center line how far is the widest
+
+177
+00:14:01,270 --> 00:14:05,990
+point of the ship located away from the center
+
+178
+00:14:05,990 --> 00:14:10,930
+line إيش هذه سمنها؟ إيش اللي احنا لما نقولها لما
+
+179
+00:14:10,930 --> 00:14:16,250
+بدي هاي المكان وزحت عنه إيش سميته؟ offset مظبوط
+
+180
+00:14:17,770 --> 00:14:21,810
+Are the adjacent adjacent linked of the handrail
+
+181
+00:14:21,810 --> 00:14:26,950
+at 90 degree to each other؟ إيش ال adjacent؟ إيش
+
+182
+00:14:26,950 --> 00:14:32,830
+معناه adjacent؟ طيب بس إيش adjacent السؤال قبل
+
+183
+00:14:32,830 --> 00:14:39,910
+adjacent القريب القرب من أيوة
+
+184
+00:14:39,910 --> 00:14:43,730
+الآن لما الحاجة جنب بعض بنسميها adjacent to each
+
+185
+00:14:43,730 --> 00:14:47,810
+otherالحين لما اقول انت مين و who is adjacent to
+
+186
+00:14:47,810 --> 00:14:53,190
+you بدك تقول زميلتك اللي جنبك القريبة منك فهنا at
+
+187
+00:14:53,190 --> 00:14:57,170
+ninety degree at a ninety degree او at ninety
+
+188
+00:14:57,170 --> 00:15:01,510
+degrees these dimensions allow you to establish
+
+189
+00:15:01,510 --> 00:15:03,930
+the position of the whole ايش establish the
+
+190
+00:15:03,930 --> 00:15:09,030
+position قولنا locate هذه الكلمات اللي بتيجي عندك
+
+191
+00:15:09,030 --> 00:15:11,010
+locate establish position
+
+192
+00:15:14,470 --> 00:15:22,010
+فى ايه؟ فى الغالب بالامتحان اه لأ بس هذا انت لساتك
+
+193
+00:15:22,010 --> 00:15:26,550
+الحين مخلصة تمر عليهم عشان هذه اه و بعدين هذا
+
+194
+00:15:26,550 --> 00:15:32,110
+بقولك look at ال .. اللي عندي a and b و replace
+
+195
+00:15:32,110 --> 00:15:36,190
+these words يعني بتحطيهم قدامك و منها تختاري بس
+
+196
+00:15:36,190 --> 00:15:41,130
+احنا بنحطلك قائمة زي .. بالنسبة لنا زي الموجود هنا
+
+197
+00:15:46,420 --> 00:15:53,680
+of a handrail at each other ممكن تقول hand are
+
+198
+00:15:53,680 --> 00:16:00,440
+adjacent linked ممكن تقول perpendicular to each
+
+199
+00:16:00,440 --> 00:16:05,200
+other بنفع هي perpendicular لأن هي at right angle
+
+200
+00:16:05,200 --> 00:16:08,220
+طيب
+
+201
+00:16:09,430 --> 00:16:12,690
+الان اللي عندى التانى five two look at these
+
+202
+00:16:12,690 --> 00:16:17,950
+extracts from technical discussion on construction
+
+203
+00:16:17,950 --> 00:16:21,570
+complete these sentences using the words in the
+
+204
+00:16:21,570 --> 00:16:29,630
+box what they mean by extracts extracts
+
+205
+00:16:29,630 --> 00:16:35,950
+هي هذه بتيجي حاجات بالطريق look at extract from
+
+206
+00:16:35,950 --> 00:16:38,590
+technical discussion ال extract
+
+207
+00:16:41,310 --> 00:16:48,730
+تسمعوا من مقتطفات؟ هي مقتطفات ال extract في العرب
+
+208
+00:16:48,730 --> 00:16:53,770
+يعني إيش؟ لما انت تاخد في محادثة تقنية و تاخد
+
+209
+00:16:53,770 --> 00:17:00,150
+أجزاء منها بنسميها إيش؟ مقتطفات according to this
+
+210
+00:17:00,150 --> 00:17:05,690
+drawing إيش؟ it runs along the external wall of
+
+211
+00:17:05,690 --> 00:17:11,320
+this structure أي واحدة بنقولAccording to this
+
+212
+00:17:11,320 --> 00:17:14,100
+drawing بنفع grid lines و لا intersections
+
+213
+00:17:14,100 --> 00:17:20,020
+parallel perpendicular set out or square up؟ يعني
+
+214
+00:17:20,020 --> 00:17:24,080
+هذا بدك إياها إيش؟ بدك إيش إياها verb، مظبوط؟ إيش
+
+215
+00:17:24,080 --> 00:17:30,800
+من هدولة؟ ال grid line according to this drawing
+
+216
+00:17:30,800 --> 00:17:36,240
+grid line طيب the positions were marked accurately
+
+217
+00:17:36,240 --> 00:17:39,800
+they were إيش؟ by our site engineer
+
+218
+00:17:42,280 --> 00:17:47,740
+إيش هي sit out مظبوط إيش قولنا sit out checked
+
+219
+00:17:47,740 --> 00:17:55,440
+مظبوط يعني انفحصا في هذا the external wall runs
+
+220
+00:17:55,440 --> 00:18:03,060
+along grid lines one and the internal corridor
+
+221
+00:18:03,060 --> 00:18:07,520
+wall runs along grid line two so the walls are
+
+222
+00:18:07,520 --> 00:18:13,510
+with each other الآن هذا إيش الترقيم؟أرقام أخدت ال
+
+223
+00:18:13,510 --> 00:18:16,690
+grid lines أخدت واحد اتنين واحد اتنين إيش بيكونوا
+
+224
+00:18:16,690 --> 00:18:21,130
+parallel لو قلت one and a إيش بيكونوا
+
+225
+00:18:21,130 --> 00:18:26,550
+perpendicular بس one and two معناته إيش بدهم
+
+226
+00:18:26,550 --> 00:18:31,830
+يكونوا parallel خليكم معايا في هذه إذا أعطيتكوا ال
+
+227
+00:18:31,830 --> 00:18:36,350
+grid lines مرقمين أو alphabetically يعني يا إما
+
+228
+00:18:36,350 --> 00:18:40,070
+مرقمين يا إما in alphabetical order هدولة بيكونوا
+
+229
+00:18:40,070 --> 00:18:46,230
+إيشبرريل لو أخدت واحد numbered والتاني alphabetic
+
+230
+00:18:46,230 --> 00:18:56,030
+إيش بيكونوا perpendicular واضحة طيب I've
+
+231
+00:18:56,030 --> 00:19:00,350
+marked a cross on the concrete floor showing where
+
+232
+00:19:00,350 --> 00:19:06,830
+the two grid lines ال cross بيجي وين where دي إيش
+
+233
+00:19:06,830 --> 00:19:10,990
+بيسوي two grid lines إيش بيصير فيهمintersect في
+
+234
+00:19:10,990 --> 00:19:14,890
+التقاطع عادة لما بحط x بحط على نقطة ايه؟ تقاطع
+
+235
+00:19:14,890 --> 00:19:20,990
+كهندسة طيب we need to show the position of the
+
+236
+00:19:20,990 --> 00:19:27,550
+corner of the staircase with coordinate dimensions
+
+237
+00:19:27,550 --> 00:19:34,530
+they should be taken from two grid lines الان ال
+
+238
+00:19:34,530 --> 00:19:43,470
+staircase ايش هو؟ تعرف الدرج؟أيوة السلالم الاهدأ
+
+239
+00:19:43,470 --> 00:19:46,150
+بيقول we need to show the position of the corner
+
+240
+00:19:46,150 --> 00:19:51,170
+ال position تبع ال corner إيش بيكون؟ في عند ال two
+
+241
+00:19:51,170 --> 00:19:56,750
+grid lines إيش معناتهم؟ بتقاطع متعمدين، مظبوط، في
+
+242
+00:19:56,750 --> 00:20:03,330
+hyperpendicular we will use the tidal light to
+
+243
+00:20:03,330 --> 00:20:08,490
+edge the grid lines and mark a ninety degree
+
+244
+00:20:08,490 --> 00:20:13,210
+offsetإيش ال order light ليش بيستخدم ال order
+
+245
+00:20:13,210 --> 00:20:17,750
+light square off اللي هي تطبط الزوايا
+
+246
+00:20:22,040 --> 00:20:26,760
+طيب الان ال match .. match the two parts of the
+
+247
+00:20:26,760 --> 00:20:30,620
+sentences to complete the extract .. extract from
+
+248
+00:20:30,620 --> 00:20:33,960
+a training manual in civil engineering the follow
+
+249
+00:20:33,960 --> 00:20:37,440
+.. the following precautions can help to prevent
+
+250
+00:20:37,440 --> 00:20:42,580
+costly sitting out mistakes ايش ال precaution؟
+
+251
+00:20:47,780 --> 00:20:53,380
+الاحتياطات أو دي بدك تقولي ال .. يعني الحاجات اللي
+
+252
+00:20:53,380 --> 00:20:59,060
+بدك تتجنبيها يعني التعليمات ال .. ال .. الاساسية
+
+253
+00:20:59,060 --> 00:21:03,380
+لتجنب المشاكل prevent costly setting out mistakes
+
+254
+00:21:03,380 --> 00:21:09,840
+اللي هي الأخطاء اللي .. اللي هي الأخطاء اللي بتكلف
+
+255
+00:21:09,840 --> 00:21:16,250
+.. اللي بتكلف كثيرalways use a steel tape measure
+
+256
+00:21:16,250 --> 00:21:21,710
+never a plastic one ليش؟ ايش اللي هاي بيقولك دايما
+
+257
+00:21:21,710 --> 00:21:25,910
+يستخدمي متر معدني مش متر plastic to ensure it
+
+258
+00:21:25,910 --> 00:21:29,090
+doesn't stretch under tension ايوة to ensure it
+
+259
+00:21:29,090 --> 00:21:32,270
+doesn't stretch under tension لو استخدمت plastic
+
+260
+00:21:32,270 --> 00:21:39,810
+ممكن لما أشده يعمل stretch يمط معاه مظبوط فدايما
+
+261
+00:21:39,810 --> 00:21:44,150
+بتلاقي اللي هو أمطارفيش للخياطين اللي بيستخدم ايش
+
+262
+00:21:44,150 --> 00:21:55,550
+متر جلدي لأن المسافة مش كبيرة حديد
+
+263
+00:21:55,550 --> 00:21:59,650
+بس طويل هو نفسه بس الحجم بدل ما هو الجد بيبقى
+
+264
+00:21:59,650 --> 00:22:04,620
+هالجد حجمه و بيسحب فيه هدول المساحة دايما معهمشو
+
+265
+00:22:04,620 --> 00:22:08,460
+اللي عندنا بقى؟ لأ لأ صغير هذا .. هذا .. هذا صغير
+
+266
+00:22:08,460 --> 00:22:11,840
+خمسة متر حده اللي كبير فيه تلاتة متر و فيه خمسة
+
+267
+00:22:11,840 --> 00:22:16,560
+متر بس ال car car بوصل لمائة متر فانت لما بدي قيص
+
+268
+00:22:16,560 --> 00:22:21,580
+أراضي بيقيسش خمسة متر خمسة بيسحب و بيمشي مظبوط؟ و
+
+269
+00:22:21,580 --> 00:22:24,020
+لو طلعته و انت ماشيين في السيارات اللي بتلاقيهم
+
+270
+00:22:24,020 --> 00:22:27,400
+بيقيسوا بتلاقيوا معاه متر و معاه عدة المساحة ال
+
+271
+00:22:27,400 --> 00:22:30,960
+car car اللي عنده هذا هو كبير .. متر كبير يعني زي
+
+272
+00:22:30,960 --> 00:22:36,120
+ما بيقولوهcheck that both diagonals of the
+
+273
+00:22:36,120 --> 00:22:39,840
+rectangular shape are equal الأن لو جبت أنا
+
+274
+00:22:39,840 --> 00:22:45,040
+المستطيل المستطيل أيش بيميزه المحاور تبعته أيش
+
+275
+00:22:45,040 --> 00:22:49,840
+متساوية ده المحاور ده خلينا نقول كل ضلعين متقابلين
+
+276
+00:22:49,840 --> 00:22:53,380
+متساويين و المحاور متساوية يبقى الزوايا تبعته أيش
+
+277
+00:22:53,380 --> 00:22:57,720
+بتكون قائمة قائمة لو ما كان زي هيك بتبقى الزوايا
+
+278
+00:22:57,720 --> 00:23:02,370
+تبعته مش قائمة المساح لما بديه يفرز أرضبجيس
+
+279
+00:23:02,370 --> 00:23:07,230
+المسافات وبعده بجيس المحاور المحور هاد والمحور
+
+280
+00:23:07,230 --> 00:23:10,250
+الاتنين لازم يكونوا متساوين عشان تاخد مساحة
+
+281
+00:23:10,250 --> 00:23:16,350
+مستطيلة أي واحدة بنقول فيهم هنا الأولى to check
+
+282
+00:23:16,350 --> 00:23:20,590
+the corners are at right angles لما نقول نحنا
+
+283
+00:23:20,590 --> 00:23:24,390
+diagonal، diagonal to check the angles measure
+
+284
+00:23:24,390 --> 00:23:27,990
+dimensions in two directions from parallel grid
+
+285
+00:23:27,990 --> 00:23:28,570
+lines
+
+286
+00:23:31,880 --> 00:23:37,000
+to double check measurement إذا جيت عندك خطين
+
+287
+00:23:37,000 --> 00:23:40,540
+متساويين وقصت المسافة من هنا والمسافة من الطرف
+
+288
+00:23:40,540 --> 00:23:48,380
+التاني إيش مضمن أنه هدول ما بيصيرش أخطاء add
+
+289
+00:23:48,380 --> 00:23:54,740
+up chains dimensions give running dimensionsto
+
+290
+00:23:54,740 --> 00:23:58,720
+prevent slight errors being multiplied عشان ال
+
+291
+00:23:58,720 --> 00:24:03,440
+error مايزيدش عندنا لأنه بستخدم ال running meter
+
+292
+00:24:03,440 --> 00:24:08,980
+لأكد منهم طيب هي كما بنبغي احنا جاهزين ل ال quiz
+
+293
+00:24:08,980 --> 00:24:09,560
+تبعكم
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..461c1deb0a12ad8ab1225c7a9ae1f2c75ae337d5
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/I-OM6cRV6Nw_raw.srt
@@ -0,0 +1,1172 @@
+1
+00:00:21,850 --> 00:00:24,850
+سنتحدث اليوم عن القصة الخامسة الخامسة الخامسة
+
+2
+00:00:24,850 --> 00:00:25,510
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+3
+00:00:25,510 --> 00:00:25,730
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+4
+00:00:25,730 --> 00:00:26,330
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+5
+00:00:26,330 --> 00:00:28,010
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+6
+00:00:28,010 --> 00:00:30,630
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+7
+00:00:30,630 --> 00:00:31,150
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+8
+00:00:31,150 --> 00:00:31,710
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+9
+00:00:31,710 --> 00:00:40,270
+الخامسة الخامسة الخامسة الخامسة الخامسة الخامسة
+
+10
+00:00:40,270 --> 00:00:46,660
+الخامسة الخامسة الخthe distances between the holes
+
+11
+00:00:46,660 --> 00:00:50,540
+can be shown as running dimensions or as chain
+
+12
+00:00:50,540 --> 00:00:56,340
+dimensions الآن احنا إيش بنتكلم عن؟ تعرفوا في
+
+13
+00:00:56,340 --> 00:00:59,880
+العلم القديم يمكن هذا اللي ماحدش فيكم بشوف ال
+
+14
+00:00:59,880 --> 00:01:05,980
+America sport في عندهم chain اللي هو إيش زي مقياس
+
+15
+00:01:05,980 --> 00:01:08,880
+أنتوا الآن ال meter اللي عندنا في البيت أكبر إيش؟
+
+16
+00:01:08,880 --> 00:01:15,030
+قداش؟خمسة متر، مظبوط؟ لو عندي حاجة طولها عشرين
+
+17
+00:01:15,030 --> 00:01:20,350
+متر، إيش بده أعمل فيه؟ بده أجيس الخمسة متر، خمسة
+
+18
+00:01:20,350 --> 00:01:23,530
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+19
+00:01:23,530 --> 00:01:25,210
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+20
+00:01:25,210 --> 00:01:26,470
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+21
+00:01:26,470 --> 00:01:30,050
+متر، خمسة متر، خمسة متر، خمسة متر، خمسة متر، خمسة
+
+22
+00:01:30,050 --> 00:01:38,210
+متر، خمسة متر، خمسة متر، خمسة متر، خمسةكويس ال
+
+23
+00:01:38,210 --> 00:01:41,830
+chain اللي هو إيش هو زي ال chain اللي هو عبارة عن
+
+24
+00:01:41,830 --> 00:01:49,230
+سلك أو حبل بس ال chain اللي هو إيش هو هو بتبقى
+
+25
+00:01:49,230 --> 00:01:55,070
+بتشوف السلسلة السلسلة زي العقد إيش هذا سلسلة هذا
+
+26
+00:01:55,070 --> 00:02:00,250
+بيسموه chain فهو بيبقى قياس مثلا في ال American
+
+27
+00:02:00,250 --> 00:02:05,610
+sport في chain عشرة متر عشرة yardفبيجرسوا فيه كل
+
+28
+00:02:05,610 --> 00:02:09,210
+عشرة يارد بيحطوا من نقطة البداية لنقطة النهاية هاي
+
+29
+00:02:09,210 --> 00:02:12,970
+العشرة يارد و بيسحبوا هاي الان ال chain لو انه
+
+30
+00:02:12,970 --> 00:02:17,970
+plastic ممكن يمد صح او ينكمش بس لما انه بنقول
+
+31
+00:02:17,970 --> 00:02:24,590
+chain حديد الحديد بيمدش صح فهنا بتكلم على ال chain
+
+32
+00:02:24,590 --> 00:02:27,610
+dimensions or running dimension ال running
+
+33
+00:02:27,610 --> 00:02:33,150
+dimension اللي هو بيظله ساحب يعني مقياس طويلIn
+
+34
+00:02:33,150 --> 00:02:37,250
+both cases, the center line aligned through the
+
+35
+00:02:37,250 --> 00:02:41,190
+center of the holes is measured is marked down and
+
+36
+00:02:41,190 --> 00:02:44,870
+the distances between the center lines are given
+
+37
+00:02:44,870 --> 00:02:49,150
+عادة لما تقيس مسافة بين ال hole اللي هو إيش
+
+38
+00:02:51,820 --> 00:02:56,880
+حفرة الحفرة عادة شكلها إيش بيبقى دائرة أو لو كانت
+
+39
+00:02:56,880 --> 00:03:01,120
+مربعة بدي أجسمها في النص في نقطة اللي هي منتصف
+
+40
+00:03:01,120 --> 00:03:05,320
+الحفرة بجيس من منتصف الحفرة هذا بسميها ال center
+
+41
+00:03:05,320 --> 00:03:09,320
+of the hole لمنتصف الحفرة التانية عشان أجيس
+
+42
+00:03:09,320 --> 00:03:13,780
+المسافة بينهمكويس يعني لما في حفرتين بدي اجيس
+
+43
+00:03:13,780 --> 00:03:17,900
+مسافة المسافة بين الحفرتين لازم اجيس من نص الحفرة
+
+44
+00:03:17,900 --> 00:03:21,760
+اللي هي مركز الحفرة اللي هي ال center لمركز الحفرة
+
+45
+00:03:21,760 --> 00:03:26,680
+التانية ال center التانية هذه بسميها اللي عندى ال
+
+46
+00:03:26,680 --> 00:03:30,520
+distance اللي بداش احتلها ال center line اللي هو
+
+47
+00:03:30,520 --> 00:03:34,860
+الخط اللي بمر فيه في مركز الحفرة ال center اللي
+
+48
+00:03:34,860 --> 00:03:38,800
+موجود distances between center lines are called
+
+49
+00:03:38,800 --> 00:03:45,400
+center to centerThe holes below are at 100mm
+
+50
+00:03:45,400 --> 00:03:50,700
+centers يعني طلع عندى شايف المسافة هان؟ ايش هان
+
+51
+00:03:50,700 --> 00:03:55,940
+اخدت؟ هى من ال center ال center هان هى 100 200 300
+
+52
+00:03:55,940 --> 00:04:00,040
+هدى running dimension لإنه خدت أنا مسافة كلية
+
+53
+00:04:00,040 --> 00:04:03,740
+بينما هان ايش قلت عنها؟ it's chain dimension ايش
+
+54
+00:04:03,740 --> 00:04:10,560
+اخدت؟نفس الشيء ولكن هنا 100 مليمتر 100 مليمتر 100
+
+55
+00:04:10,560 --> 00:04:11,680
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+56
+00:04:11,680 --> 00:04:13,160
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+57
+00:04:13,160 --> 00:04:13,200
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+58
+00:04:13,200 --> 00:04:13,400
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+59
+00:04:13,400 --> 00:04:16,360
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+60
+00:04:16,360 --> 00:04:18,220
+100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100
+
+61
+00:04:18,220 --> 00:04:20,720
+مليمتر 100 مليمتر 100 مليمتر 100 مليمتر 100 مليمتر
+
+62
+00:04:20,720 --> 00:04:29,300
+100 مليمتر 100 مليمترمتساوية الان ال note ال
+
+63
+00:04:29,300 --> 00:04:33,540
+written note ايش بتقولي عندي؟ CC from center to
+
+64
+00:04:33,540 --> 00:04:42,120
+center المسافة كام؟ one hundred millimeter center
+
+65
+00:04:42,120 --> 00:04:47,030
+lines are often used as reference pointsاللي هي
+
+66
+00:04:47,030 --> 00:04:51,550
+مرجعية نقاط مرجعية these can be measured from in
+
+67
+00:04:51,550 --> 00:04:55,150
+order to locate that is give the position of
+
+68
+00:04:55,150 --> 00:05:00,890
+points on components عادة بحطها عشان اعرف مكان
+
+69
+00:05:00,890 --> 00:05:06,730
+locate تحدد الموقع give the position the
+
+70
+00:05:06,730 --> 00:05:10,830
+measurement are offset from the center lines ايش
+
+71
+00:05:10,830 --> 00:05:18,220
+يعني offset؟ لأالان انا بازاحة تنزاح شوية او
+
+72
+00:05:18,220 --> 00:05:23,280
+shifted في الانجليزي shifted اللي هي ايش يعني هي
+
+73
+00:05:23,280 --> 00:05:27,540
+offset from the center line each is at a certain
+
+74
+00:05:27,540 --> 00:05:32,090
+distance from it and the offsets are measured ata
+
+75
+00:05:32,090 --> 00:05:36,570
+right angle to the center lines at 90 degrees to
+
+76
+00:05:36,570 --> 00:05:39,750
+it يعني عادة لما يقول right at right angle ال
+
+77
+00:05:39,750 --> 00:05:44,050
+right angle الزاوية القائمة اللي هي كام تسعين درجة
+
+78
+00:05:44,050 --> 00:05:49,990
+هذا انتوا خبرة فيها نتكلم الآن على ال grades ايش
+
+79
+00:05:49,990 --> 00:05:55,330
+ال grades؟ شبكة الان دفتر الرسم الهندسي عبارة عن
+
+80
+00:05:55,330 --> 00:06:01,500
+ال grade page صح؟مقسم لخطوط طول و عرض البياني
+
+81
+00:06:01,500 --> 00:06:06,280
+الرسم البياني مظبوط هذا الرسم البياني الان in
+
+82
+00:06:06,280 --> 00:06:10,400
+large designs notably those of structure grids are
+
+83
+00:06:10,400 --> 00:06:15,260
+used for horizontal positioning الان عندى عادة ال
+
+84
+00:06:15,260 --> 00:06:19,600
+grid للتصميمات الكبيرة بتبقى موجودة عشان يحدد
+
+85
+00:06:19,600 --> 00:06:23,760
+المواقع الأفقية ال grid lines have numbers and
+
+86
+00:06:23,760 --> 00:06:29,130
+lettersال grid lines في عندى عمودي و في عندى ايش
+
+87
+00:06:29,130 --> 00:06:36,990
+القفقي و العمودي واحد بعطيه ارقام grid line 123 و
+
+88
+00:06:36,990 --> 00:06:44,210
+التاني بعطيه ايش a,b,c,d و هكذا alphabeticallyAll
+
+89
+00:06:44,210 --> 00:06:47,890
+grid lines are parallel with one another that is
+
+90
+00:06:47,890 --> 00:06:50,550
+they are straight lines and are at regular
+
+91
+00:06:50,550 --> 00:06:54,890
+distances apart كل ال grid lines هدول سواء
+
+92
+00:06:54,890 --> 00:06:58,430
+المجموعة العمودية أو الأفقية متوازية ايش يعني
+
+93
+00:06:58,430 --> 00:07:04,050
+متوازية عبارة عن خطوط مستقيمة على مسافات متساوية
+
+94
+00:07:04,050 --> 00:07:10,130
+مش هيك احنا تعريف التوازي خطين المتوازين ايش خطين
+
+95
+00:07:10,130 --> 00:07:18,610
+مستقيمين على مسافاتمتساوية في هذا المجال طيب ..
+
+96
+00:07:18,610 --> 00:07:22,470
+الآن بالنسبة إلينا .. يعني إذا بنطلع عليها ال
+
+97
+00:07:22,470 --> 00:07:27,470
+parallel عرفناها طب ال perpendicular اللي هي ال
+
+98
+00:07:27,470 --> 00:07:34,510
+إيش؟ العمودية هذا بشتغل لحاله قلناه طيب ال
+
+99
+00:07:34,510 --> 00:07:38,410
+perpendicular اللي هي العموديين هدولة بتقاطعوا at
+
+100
+00:07:38,410 --> 00:07:42,610
+a right angle صح؟ بيعملوا اتنين right angle
+
+101
+00:07:45,170 --> 00:07:49,630
+طيب letter lines are run parallel with one another
+
+102
+00:07:49,630 --> 00:07:55,130
+and are perpendicular to the numbered lines يعني
+
+103
+00:07:55,130 --> 00:08:00,710
+زي ما حكيت عندى فيه اتجاه عمودي وفيه اتجاه أفقي
+
+104
+00:08:00,710 --> 00:08:05,750
+العمودي ايش مع الأفق ايش بيعملوا زوايا قائمة right
+
+105
+00:08:05,750 --> 00:08:09,470
+angle فبنقول عنهم متعامدين اللي هي perpendicular
+
+106
+00:08:09,470 --> 00:08:17,060
+او بنقول they joined atright angle او right angles
+
+107
+00:08:17,060 --> 00:08:24,440
+at right angles the plan بلغه هذا هنشوف show part
+
+108
+00:08:24,440 --> 00:08:30,060
+of the floor of an office building يعني في مقطع
+
+109
+00:08:30,060 --> 00:08:39,320
+موجود هيفرجينا المستوى الأرضي لبناية بناية خاصة
+
+110
+00:08:39,320 --> 00:08:43,400
+بالمكاتب the perpendicular grid line intersect at
+
+111
+00:08:44,120 --> 00:08:49,100
+يعني intersect at إيش هي معناته؟ تقاطع cross at
+
+112
+00:08:49,100 --> 00:08:53,440
+the centers of the columns تعرف ال column إيش
+
+113
+00:08:53,440 --> 00:08:58,860
+بنسميه؟ العمود الآن أحنا في البيت في عندنا حزامات
+
+114
+00:08:58,860 --> 00:09:04,440
+و فينا أعمدة لتبعين المدني بكرا اللي بتخصصه البيت
+
+115
+00:09:04,440 --> 00:09:09,900
+في عندنا الحزام اللي هو الأفقي العمود اللي هو رأسي
+
+116
+00:09:09,900 --> 00:09:14,710
+ففي عندنا اللي بتحكم في البيتالإحزامات والأعمدة
+
+117
+00:09:14,710 --> 00:09:20,150
+يعني البيت ممكن يقوم على بس الإحزامات والأعمدة،
+
+118
+00:09:20,150 --> 00:09:26,330
+كويس؟ فهنا لما نقول columns أعمدة an opening hole
+
+119
+00:09:26,330 --> 00:09:30,630
+in the floor is shown using coordinate dimension
+
+120
+00:09:30,630 --> 00:09:32,470
+أيش يعني coordinate dimension؟
+
+121
+00:09:36,180 --> 00:09:41,000
+الإحداثيات كلمة إحداثيات هي تستخدم ال technical
+
+122
+00:09:41,000 --> 00:09:45,880
+word كويس these allow the site engineers to sit
+
+123
+00:09:45,880 --> 00:09:50,480
+out إيش يعني sit out mark the position of يعني
+
+124
+00:09:50,480 --> 00:09:54,960
+يحدد الموقع sit out mark the position of the
+
+125
+00:09:54,960 --> 00:09:58,520
+opening by squaring of the grid line making the
+
+126
+00:09:58,520 --> 00:10:02,160
+lines that run at right angle to them يعني هنا
+
+127
+00:10:02,160 --> 00:10:08,400
+square of making يعني بيعملبيحدد الزوايا القائمة
+
+128
+00:10:08,400 --> 00:10:12,520
+الموجودة then measuring along these lines using a
+
+129
+00:10:12,520 --> 00:10:18,340
+tape measure ايش ال tape measure اللي هو ال متر
+
+130
+00:10:18,340 --> 00:10:24,340
+سمعينه؟ اه ايوه؟
+
+131
+00:10:24,340 --> 00:10:30,440
+الان في عنديعدة مفردات الموجودة هنا دي اوضو لايت
+
+132
+00:10:30,440 --> 00:10:35,700
+ايش هي دي اوضو لايت is an optical device used for
+
+133
+00:10:35,700 --> 00:10:40,040
+measuring angles can be used to square off grid
+
+134
+00:10:40,040 --> 00:10:44,100
+lines accurately الان هذا جهاز بقييس الزوايا احنا
+
+135
+00:10:44,100 --> 00:10:48,720
+عادة ايش .. هنقولكوا كيف نقيس الزوايا يمكن هذا ال
+
+136
+00:10:48,720 --> 00:10:51,200
+.. قليل فيكم اللي بيستطيعوا تطلع عليهم بيستطيعوا
+
+137
+00:10:51,200 --> 00:10:52,920
+تطلع علي المجاولين ايش بيستخدموه
+
+138
+00:10:55,630 --> 00:10:59,950
+هذا عند المساحة، اللي ماعندوش مساحة إيش بيعمل؟
+
+139
+00:10:59,950 --> 00:11:04,430
+تعرفوا أنتوا نظرية Vita-course، مظبوط؟ إيش بتقول؟
+
+140
+00:11:04,430 --> 00:11:09,430
+ها هي هذا، ده بنتكلم عليها إيش using? Pythagoras
+
+141
+00:11:10,140 --> 00:11:14,060
+theorem اللي هي vita course ايش بتعمل هات؟ بنقيس
+
+142
+00:11:14,060 --> 00:11:18,520
+مثلا انا بعرف لو جيبت ستة متر من هنا مع تمانية متر
+
+143
+00:11:18,520 --> 00:11:23,720
+القطر تبعهم بيكون كام؟ عشرة فبيعملوا زي هيك هناك
+
+144
+00:11:23,720 --> 00:11:28,600
+البنة ماعندوش هذا الجهاز ايش بيعمل؟ بقيس زي هيك و
+
+145
+00:11:28,600 --> 00:11:33,320
+بحدد بيقول هذا الزاوية بدها فاتحة او مسكرة فاتحة
+
+146
+00:11:33,320 --> 00:11:38,940
+يعني ايش؟ منفرجة صارت مش .. مسكرة ايش صارت؟صارت
+
+147
+00:11:38,940 --> 00:11:44,260
+ضيقة إنها أقل من تسعين درجة الان to double check
+
+148
+00:11:44,260 --> 00:11:48,620
+the dimension إيش double check أنا بجيس بس لازم
+
+149
+00:11:48,620 --> 00:11:54,220
+أتأكد من .. في المقسمية double check double check
+
+150
+00:11:54,220 --> 00:11:58,820
+للتأكد okay dimension that is carry out an extra
+
+151
+00:11:58,820 --> 00:12:04,160
+check diagonal measurement can be used as in
+
+152
+00:12:04,160 --> 00:12:09,030
+engineers sketchالدياجونال هذه نستخدمها اللي هي
+
+153
+00:12:09,030 --> 00:12:12,810
+القطر اللي حكيت عنه الـ length of the diagonals
+
+154
+00:12:12,810 --> 00:12:17,770
+can be calculated using Pythagoras theorem اللي هي
+
+155
+00:12:17,770 --> 00:12:22,390
+مقدرية Pythagoras وهي عندي الشكل طلع عندي هذا اللي
+
+156
+00:12:22,390 --> 00:12:27,550
+بتعمللي هاي هذا وهذا parallel هذا وهذا parallel
+
+157
+00:12:27,550 --> 00:12:31,550
+الآن هذا وهذا perpendicular اللي عندي
+
+158
+00:12:34,400 --> 00:12:37,980
+هي هنا اللي بنتكلم عليه ال ايش ال diagonal اللي
+
+159
+00:12:37,980 --> 00:12:42,580
+بنحسب المسافة بنقول الجدر التربيعي للقطر ايه؟
+
+160
+00:12:42,580 --> 00:12:47,020
+القطر الأول تربيع والتاني تربيع بيعطينا المسافة
+
+161
+00:12:47,020 --> 00:12:53,750
+الموجودة ال right angleالان exercise 5.1 بدنا نبدل
+
+162
+00:12:53,750 --> 00:12:57,370
+هذه الكلمات look at these sentences about the
+
+163
+00:12:57,370 --> 00:13:03,030
+design of ship replace the underlying words and
+
+164
+00:13:03,030 --> 00:13:06,250
+expressions with alternative words and expressions
+
+165
+00:13:06,250 --> 00:13:09,570
+يعني هذا بدنا نبدلهم بإيش؟ بالكلمات اللي احنا
+
+166
+00:13:09,570 --> 00:13:15,170
+غطناها في اللي عندك ال handrail is fixed by 115
+
+167
+00:13:15,170 --> 00:13:20,750
+brackets أيش ال handrail؟اللي هو القطار اليدوي
+
+168
+00:13:20,750 --> 00:13:25,050
+الان اللي عنده مش بيجيب لعب للصغار الان هذا بيعمل
+
+169
+00:13:25,050 --> 00:13:29,890
+سكة حديد هذا بيسموه ال hand is fixed by brackets
+
+170
+00:13:29,890 --> 00:13:33,870
+which are one one seventy five millimeter apart
+
+171
+00:13:33,870 --> 00:13:38,190
+between their centers ايش الكلمة اللي بيسموها at
+
+172
+00:13:38,190 --> 00:13:43,310
+لأ بنقول at one seventy five millimeter centers
+
+173
+00:13:43,310 --> 00:13:48,850
+هذا بدلتنا كل الكلمة اللي موجودة عندهاthe
+
+174
+00:13:48,850 --> 00:13:52,150
+dimensions are measured from the line down the
+
+175
+00:13:52,150 --> 00:13:55,010
+middle of the ship إيش ال line down the middle؟
+
+176
+00:13:55,010 --> 00:14:01,270
+إيش سمنها؟ ال center line how far is the widest
+
+177
+00:14:01,270 --> 00:14:05,990
+point of the ship located away from the center
+
+178
+00:14:05,990 --> 00:14:10,930
+line إيش هذه سمنها؟ إيش اللي احنا لما نقولها لما
+
+179
+00:14:10,930 --> 00:14:16,250
+بدي هاي المكان وزحت عنه إيش سميته؟ offset مظبوط
+
+180
+00:14:17,770 --> 00:14:21,810
+Are the adjacent adjacent linked of the handrail
+
+181
+00:14:21,810 --> 00:14:26,950
+at 90 degree to each other؟ إيش ال adjacent؟ إيش
+
+182
+00:14:26,950 --> 00:14:32,830
+معناه adjacent؟ طيب بس إيش adjacent السؤال قبل
+
+183
+00:14:32,830 --> 00:14:39,910
+adjacent القريب القرب من أيوة
+
+184
+00:14:39,910 --> 00:14:43,730
+الآن لما الحاجة جنب بعض بنسميها adjacent to each
+
+185
+00:14:43,730 --> 00:14:47,810
+otherالحين لما اقول انت مين و who is adjacent to
+
+186
+00:14:47,810 --> 00:14:53,190
+you بدك تقول زميلتك اللي جنبك القريبة منك فهنا at
+
+187
+00:14:53,190 --> 00:14:57,170
+ninety degree at a ninety degree او at ninety
+
+188
+00:14:57,170 --> 00:15:01,510
+degrees these dimensions allow you to establish
+
+189
+00:15:01,510 --> 00:15:03,930
+the position of the whole ايش establish the
+
+190
+00:15:03,930 --> 00:15:09,030
+position قولنا locate هذه الكلمات اللي بتيجي عندك
+
+191
+00:15:09,030 --> 00:15:11,010
+locate establish position
+
+192
+00:15:14,470 --> 00:15:22,010
+فى ايه؟ فى الغالب بالامتحان اه لأ بس هذا انت لساتك
+
+193
+00:15:22,010 --> 00:15:26,550
+الحين مخلصة تمر عليهم عشان هذه اه و بعدين هذا
+
+194
+00:15:26,550 --> 00:15:32,110
+بقولك look at ال .. اللي عندي a and b و replace
+
+195
+00:15:32,110 --> 00:15:36,190
+these words يعني بتحطيهم قدامك و منها تختاري بس
+
+196
+00:15:36,190 --> 00:15:41,130
+احنا بنحطلك قائمة زي .. بالنسبة لنا زي الموجود هنا
+
+197
+00:15:46,420 --> 00:15:53,680
+of a handrail at each other ممكن تقول hand are
+
+198
+00:15:53,680 --> 00:16:00,440
+adjacent linked ممكن تقول perpendicular to each
+
+199
+00:16:00,440 --> 00:16:05,200
+other بنفع هي perpendicular لأن هي at right angle
+
+200
+00:16:05,200 --> 00:16:08,220
+طيب
+
+201
+00:16:09,430 --> 00:16:12,690
+الان اللي عندى التانى five two look at these
+
+202
+00:16:12,690 --> 00:16:17,950
+extracts from technical discussion on construction
+
+203
+00:16:17,950 --> 00:16:21,570
+complete these sentences using the words in the
+
+204
+00:16:21,570 --> 00:16:29,630
+box what they mean by extracts extracts
+
+205
+00:16:29,630 --> 00:16:35,950
+هي هذه بتيجي حاجات بالطريق look at extract from
+
+206
+00:16:35,950 --> 00:16:38,590
+technical discussion ال extract
+
+207
+00:16:41,310 --> 00:16:48,730
+تسمعوا من مقتطفات؟ هي مقتطفات ال extract في العرب
+
+208
+00:16:48,730 --> 00:16:53,770
+يعني إيش؟ لما انت تاخد في محادثة تقنية و تاخد
+
+209
+00:16:53,770 --> 00:17:00,150
+أجزاء منها بنسميها إيش؟ مقتطفات according to this
+
+210
+00:17:00,150 --> 00:17:05,690
+drawing إيش؟ it runs along the external wall of
+
+211
+00:17:05,690 --> 00:17:11,320
+this structure أي واحدة بنقولAccording to this
+
+212
+00:17:11,320 --> 00:17:14,100
+drawing بنفع grid lines و لا intersections
+
+213
+00:17:14,100 --> 00:17:20,020
+parallel perpendicular set out or square up؟ يعني
+
+214
+00:17:20,020 --> 00:17:24,080
+هذا بدك إياها إيش؟ بدك إيش إياها verb، مظبوط؟ إيش
+
+215
+00:17:24,080 --> 00:17:30,800
+من هدولة؟ ال grid line according to this drawing
+
+216
+00:17:30,800 --> 00:17:36,240
+grid line طيب the positions were marked accurately
+
+217
+00:17:36,240 --> 00:17:39,800
+they were إيش؟ by our site engineer
+
+218
+00:17:42,280 --> 00:17:47,740
+إيش هي sit out مظبوط إيش قولنا sit out checked
+
+219
+00:17:47,740 --> 00:17:55,440
+مظبوط يعني انفحصا في هذا the external wall runs
+
+220
+00:17:55,440 --> 00:18:03,060
+along grid lines one and the internal corridor
+
+221
+00:18:03,060 --> 00:18:07,520
+wall runs along grid line two so the walls are
+
+222
+00:18:07,520 --> 00:18:13,510
+with each other الآن هذا إيش الترقيم؟أرقام أخدت ال
+
+223
+00:18:13,510 --> 00:18:16,690
+grid lines أخدت واحد اتنين واحد اتنين إيش بيكونوا
+
+224
+00:18:16,690 --> 00:18:21,130
+parallel لو قلت one and a إيش بيكونوا
+
+225
+00:18:21,130 --> 00:18:26,550
+perpendicular بس one and two معناته إيش بدهم
+
+226
+00:18:26,550 --> 00:18:31,830
+يكونوا parallel خليكم معايا في هذه إذا أعطيتكوا ال
+
+227
+00:18:31,830 --> 00:18:36,350
+grid lines مرقمين أو alphabetically يعني يا إما
+
+228
+00:18:36,350 --> 00:18:40,070
+مرقمين يا إما in alphabetical order هدولة بيكونوا
+
+229
+00:18:40,070 --> 00:18:46,230
+إيشبرريل لو أخدت واحد numbered والتاني alphabetic
+
+230
+00:18:46,230 --> 00:18:56,030
+إيش بيكونوا perpendicular واضحة طيب I've
+
+231
+00:18:56,030 --> 00:19:00,350
+marked a cross on the concrete floor showing where
+
+232
+00:19:00,350 --> 00:19:06,830
+the two grid lines ال cross بيجي وين where دي إيش
+
+233
+00:19:06,830 --> 00:19:10,990
+بيسوي two grid lines إيش بيصير فيهمintersect في
+
+234
+00:19:10,990 --> 00:19:14,890
+التقاطع عادة لما بحط x بحط على نقطة ايه؟ تقاطع
+
+235
+00:19:14,890 --> 00:19:20,990
+كهندسة طيب we need to show the position of the
+
+236
+00:19:20,990 --> 00:19:27,550
+corner of the staircase with coordinate dimensions
+
+237
+00:19:27,550 --> 00:19:34,530
+they should be taken from two grid lines الان ال
+
+238
+00:19:34,530 --> 00:19:43,470
+staircase ايش هو؟ تعرف الدرج؟أيوة السلالم الاهدأ
+
+239
+00:19:43,470 --> 00:19:46,150
+بيقول we need to show the position of the corner
+
+240
+00:19:46,150 --> 00:19:51,170
+ال position تبع ال corner إيش بيكون؟ في عند ال two
+
+241
+00:19:51,170 --> 00:19:56,750
+grid lines إيش معناتهم؟ بتقاطع متعمدين، مظبوط، في
+
+242
+00:19:56,750 --> 00:20:03,330
+hyperpendicular we will use the tidal light to
+
+243
+00:20:03,330 --> 00:20:08,490
+edge the grid lines and mark a ninety degree
+
+244
+00:20:08,490 --> 00:20:13,210
+offsetإيش ال order light ليش بيستخدم ال order
+
+245
+00:20:13,210 --> 00:20:17,750
+light square off اللي هي تطبط الزوايا
+
+246
+00:20:22,040 --> 00:20:26,760
+طيب الان ال match .. match the two parts of the
+
+247
+00:20:26,760 --> 00:20:30,620
+sentences to complete the extract .. extract from
+
+248
+00:20:30,620 --> 00:20:33,960
+a training manual in civil engineering the follow
+
+249
+00:20:33,960 --> 00:20:37,440
+.. the following precautions can help to prevent
+
+250
+00:20:37,440 --> 00:20:42,580
+costly sitting out mistakes ايش ال precaution؟
+
+251
+00:20:47,780 --> 00:20:53,380
+الاحتياطات أو دي بدك تقولي ال .. يعني الحاجات اللي
+
+252
+00:20:53,380 --> 00:20:59,060
+بدك تتجنبيها يعني التعليمات ال .. ال .. الاساسية
+
+253
+00:20:59,060 --> 00:21:03,380
+لتجنب المشاكل prevent costly setting out mistakes
+
+254
+00:21:03,380 --> 00:21:09,840
+اللي هي الأخطاء اللي .. اللي هي الأخطاء اللي بتكلف
+
+255
+00:21:09,840 --> 00:21:16,250
+.. اللي بتكلف كثيرalways use a steel tape measure
+
+256
+00:21:16,250 --> 00:21:21,710
+never a plastic one ليش؟ ايش اللي هاي بيقولك دايما
+
+257
+00:21:21,710 --> 00:21:25,910
+يستخدمي متر معدني مش متر plastic to ensure it
+
+258
+00:21:25,910 --> 00:21:29,090
+doesn't stretch under tension ايوة to ensure it
+
+259
+00:21:29,090 --> 00:21:32,270
+doesn't stretch under tension لو استخدمت plastic
+
+260
+00:21:32,270 --> 00:21:39,810
+ممكن لما أشده يعمل stretch يمط معاه مظبوط فدايما
+
+261
+00:21:39,810 --> 00:21:44,150
+بتلاقي اللي هو أمطارفيش للخياطين اللي بيستخدم ايش
+
+262
+00:21:44,150 --> 00:21:55,550
+متر جلدي لأن المسافة مش كبيرة حديد
+
+263
+00:21:55,550 --> 00:21:59,650
+بس طويل هو نفسه بس الحجم بدل ما هو الجد بيبقى
+
+264
+00:21:59,650 --> 00:22:04,620
+هالجد حجمه و بيسحب فيه هدول المساحة دايما معهمشو
+
+265
+00:22:04,620 --> 00:22:08,460
+اللي عندنا بقى؟ لأ لأ صغير هذا .. هذا .. هذا صغير
+
+266
+00:22:08,460 --> 00:22:11,840
+خمسة متر حده اللي كبير فيه تلاتة متر و فيه خمسة
+
+267
+00:22:11,840 --> 00:22:16,560
+متر بس ال car car بوصل لمائة متر فانت لما بدي قيص
+
+268
+00:22:16,560 --> 00:22:21,580
+أراضي بيقيسش خمسة متر خمسة بيسحب و بيمشي مظبوط؟ و
+
+269
+00:22:21,580 --> 00:22:24,020
+لو طلعته و انت ماشيين في السيارات اللي بتلاقيهم
+
+270
+00:22:24,020 --> 00:22:27,400
+بيقيسوا بتلاقيوا معاه متر و معاه عدة المساحة ال
+
+271
+00:22:27,400 --> 00:22:30,960
+car car اللي عنده هذا هو كبير .. متر كبير يعني زي
+
+272
+00:22:30,960 --> 00:22:36,120
+ما بيقولوهcheck that both diagonals of the
+
+273
+00:22:36,120 --> 00:22:39,840
+rectangular shape are equal الأن لو جبت أنا
+
+274
+00:22:39,840 --> 00:22:45,040
+المستطيل المستطيل أيش بيميزه المحاور تبعته أيش
+
+275
+00:22:45,040 --> 00:22:49,840
+متساوية ده المحاور ده خلينا نقول كل ضلعين متقابلين
+
+276
+00:22:49,840 --> 00:22:53,380
+متساويين و المحاور متساوية يبقى الزوايا تبعته أيش
+
+277
+00:22:53,380 --> 00:22:57,720
+بتكون قائمة قائمة لو ما كان زي هيك بتبقى الزوايا
+
+278
+00:22:57,720 --> 00:23:02,370
+تبعته مش قائمة المساح لما بديه يفرز أرضبجيس
+
+279
+00:23:02,370 --> 00:23:07,230
+المسافات وبعده بجيس المحاور المحور هاد والمحور
+
+280
+00:23:07,230 --> 00:23:10,250
+الاتنين لازم يكونوا متساوين عشان تاخد مساحة
+
+281
+00:23:10,250 --> 00:23:16,350
+مستطيلة أي واحدة بنقول فيهم هنا الأولى to check
+
+282
+00:23:16,350 --> 00:23:20,590
+the corners are at right angles لما نقول نحنا
+
+283
+00:23:20,590 --> 00:23:24,390
+diagonal، diagonal to check the angles measure
+
+284
+00:23:24,390 --> 00:23:27,990
+dimensions in two directions from parallel grid
+
+285
+00:23:27,990 --> 00:23:28,570
+lines
+
+286
+00:23:31,880 --> 00:23:37,000
+to double check measurement إذا جيت عندك خطين
+
+287
+00:23:37,000 --> 00:23:40,540
+متساويين وقصت المسافة من هنا والمسافة من الطرف
+
+288
+00:23:40,540 --> 00:23:48,380
+التاني إيش مضمن أنه هدول ما بيصيرش أخطاء add
+
+289
+00:23:48,380 --> 00:23:54,740
+up chains dimensions give running dimensionsto
+
+290
+00:23:54,740 --> 00:23:58,720
+prevent slight errors being multiplied عشان ال
+
+291
+00:23:58,720 --> 00:24:03,440
+error مايزيدش عندنا لأنه بستخدم ال running meter
+
+292
+00:24:03,440 --> 00:24:08,980
+لأكد منهم طيب هي كما بنبغي احنا جاهزين ل ال quiz
+
+293
+00:24:08,980 --> 00:24:09,560
+تبعكم
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/J81K1-qcMI0_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/J81K1-qcMI0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9065ea2864dbbd847063bd7e9ce1bc8018484493
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/J81K1-qcMI0_raw.srt
@@ -0,0 +1,1504 @@
+1
+00:00:20,700 --> 00:00:26,880
+اليوم سنتحدث عن القصة الـ 26 قصة الـ 26 تتحدث عن
+
+2
+00:00:26,880 --> 00:00:29,500
+مقارنات ميكانية ميكانية ميكانية ميكانية ميكانية
+
+3
+00:00:29,500 --> 00:00:29,640
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+4
+00:00:29,640 --> 00:00:30,180
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+5
+00:00:30,180 --> 00:00:30,320
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+6
+00:00:30,320 --> 00:00:30,640
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+7
+00:00:30,640 --> 00:00:30,640
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+8
+00:00:30,640 --> 00:00:31,180
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+9
+00:00:31,180 --> 00:00:37,100
+ميكانية ميكانية ميكانية ميكانية ميكانية ميكانية
+
+10
+00:00:37,100 --> 00:00:39,440
+ميكانية مي
+
+11
+00:00:42,310 --> 00:00:46,350
+بالتالي الصورة الموجودة في الصفحة التالية تظهر
+
+12
+00:00:46,350 --> 00:00:50,890
+كمان مقفل أو مقفل اللي بنسميه الحاجة اللي بتربط،
+
+13
+00:00:50,890 --> 00:00:55,750
+الرابط اللي بيربط حاجتين، يا ابنا نربطه بالحم، يا
+
+14
+00:00:55,750 --> 00:01:00,710
+ابنا نربطه بحاجة اندخلها في بعض، هذي بيسموها
+
+15
+00:01:00,710 --> 00:01:06,690
+plugged in، يا اما في برغي، هذي التلت شغلات أو
+
+16
+00:01:06,690 --> 00:01:12,290
+مصمارة، يعني برضه هذا يعاد من ال fastenersor
+
+17
+00:01:12,290 --> 00:01:17,350
+fixing a bolt with a nut البرغي اللي له إيش؟ سمونا
+
+18
+00:01:17,350 --> 00:01:23,070
+هذا بيسميه bolt bolts have threads grooves on the
+
+19
+00:01:23,070 --> 00:01:27,090
+outside of the bolt shaft or shank عادة البرغي إيش
+
+20
+00:01:27,090 --> 00:01:32,470
+إله؟ في حواف مسنونة، كويس؟ الحواف المسنونة هذه
+
+21
+00:01:32,470 --> 00:01:35,910
+اللي هي threads بنسميها الحافة المسنونة و ال
+
+22
+00:01:35,910 --> 00:01:40,360
+grooves اللي هي إيش؟ في حاجة بارز و حاجةنازلة تعرف
+
+23
+00:01:40,360 --> 00:01:44,620
+الحفة إيش بيبقى فيها الحفة الحادة بتلاقيها بارزة
+
+24
+00:01:44,620 --> 00:01:48,420
+وفي جنبها إيش عشان تبين هاي في جنبها إيش منخفض
+
+25
+00:01:48,420 --> 00:01:53,920
+مسافة منخفضة يعني لما تطلع عليه شكل
+
+26
+00:01:53,920 --> 00:02:01,280
+الفرغي الجسم تبعه بيبقى زي هيكا الآن
+
+27
+00:02:01,280 --> 00:02:07,700
+هذه بيبقى في سن إذا خلّينا هذه الراس بشكل عامهنا
+
+28
+00:02:07,700 --> 00:02:12,800
+هذا الجسم بتلاقيه مسنن، مظبوط؟ هذه الحواف .. هذول
+
+29
+00:02:12,800 --> 00:02:16,140
+الحواف بنسميها treads و ال .. و ال grooves اللي هي
+
+30
+00:02:16,140 --> 00:02:19,980
+إيش؟ اللي هي الم .. اللي هان المفرقة، في حاجات ..
+
+31
+00:02:19,980 --> 00:02:26,000
+ايوة المفرقة هذه بنسميها ال shaft أو ال shank هذه
+
+32
+00:02:26,000 --> 00:02:34,240
+بنسميها ال head كويس؟ طيب الإيد هذه، هذه الدراع هي
+
+33
+00:02:34,240 --> 00:02:40,340
+ال shaftwhich runs around the shaft in a helical
+
+34
+00:02:40,340 --> 00:02:43,080
+pattern، helical pattern بتعرفوا إيش؟ ال helical
+
+35
+00:02:43,080 --> 00:02:48,500
+إيش هو؟ شوفوا حفة الدان كيف شكلها، مش دائرة،
+
+36
+00:02:48,500 --> 00:02:52,900
+مائلة، هذا بيسميها helical، أيوة حلزوني
+
+37
+00:02:57,140 --> 00:03:01,000
+The threaded shaft allows a nut which has the
+
+38
+00:03:01,000 --> 00:03:05,540
+threads inside it to be screwed into the bolts
+
+39
+00:03:05,540 --> 00:03:11,660
+.الأن ده بتسمونه إيش فيها مفرقة بنفس الطريقة مصبوط
+
+40
+00:03:11,660 --> 00:03:16,380
+في حواف من الداخل فعشان هيك لما نحطها و نلفها
+
+41
+00:03:16,380 --> 00:03:23,210
+بتركب مع مين؟ مع البرغي اللي موجود عندكBy turning
+
+42
+00:03:23,210 --> 00:03:26,290
+motion, the thread inside to be screwed onto the
+
+43
+00:03:26,290 --> 00:03:29,790
+bolt by turning a turning motion لما نلفها و
+
+44
+00:03:29,790 --> 00:03:37,370
+نحركها بشكل دائري، الناتس عادة تكون لديها نوع من
+
+45
+00:03:37,370 --> 00:03:41,290
+نوعين، حاجة نسميها left hand threadو right hand
+
+46
+00:03:41,290 --> 00:03:48,130
+thread يعني بنقول عنها هذه اللفة بتبقى في اتجاه
+
+47
+00:03:48,130 --> 00:03:53,470
+عقارب الساعة او عكس عقارب الساعة ال right hand هذه
+
+48
+00:03:53,470 --> 00:03:57,510
+screwed by turning them clockwise في اتجاه عقارب
+
+49
+00:03:57,510 --> 00:04:02,270
+الساعة بنسميها دي ايش clockwise او right hand
+
+50
+00:04:02,270 --> 00:04:10,330
+threadand unscrewed by turning them anticlockwise
+
+51
+00:04:10,330 --> 00:04:14,270
+الـ anticlockwise اللي بنسميه عندنا مصطلح معروف ال
+
+52
+00:04:14,270 --> 00:04:16,030
+counter clockwise
+
+53
+00:04:18,000 --> 00:04:22,480
+هي Anti-clockwise وAnti معناتها ضد ده انا بروح في
+
+54
+00:04:22,480 --> 00:04:26,440
+اتجاه اقارب الساعة ايش ضدها عكس اللي هي بيسميها
+
+55
+00:04:26,440 --> 00:04:30,880
+counter clockwise او Anti-clockwise هذا ال Anti ..
+
+56
+00:04:30,880 --> 00:04:39,260
+لما نحزق بنعمل ايش Titan بنعمل Clockwise بنعمل
+
+57
+00:04:39,260 --> 00:04:44,850
+Loosing ده بنعمل ايشanti أو counter clockwise
+
+58
+00:04:44,850 --> 00:04:49,690
+however in some situation left hand threads are
+
+59
+00:04:49,690 --> 00:04:55,070
+used الغالبية ايش؟ right hand، بس في حالات معينة
+
+60
+00:04:55,070 --> 00:05:01,810
+ممكن يكون left hand هذه البرغة اللي بنحكي عنها هي
+
+61
+00:05:01,810 --> 00:05:06,950
+ال thread هي ال shaft هذههذه الـ head الموجودة
+
+62
+00:05:06,950 --> 00:05:11,590
+وهذه اللي سمناها ال nuts هذه سمناها Spanner اللي
+
+63
+00:05:11,590 --> 00:05:16,190
+هو المفك أو المفتاح اللي عندي اللي بنستخدمهان هذه
+
+64
+00:05:16,190 --> 00:05:19,410
+اللي سمناها hex key أو بيسموها allen key اللي
+
+65
+00:05:19,410 --> 00:05:25,150
+بنسميها العفريتاالمفتاح اللي بيدخل في الرأس لما
+
+66
+00:05:25,150 --> 00:05:30,210
+الرأس تبقى مخزوقة بشكل معين بدخل المفتاح فيها فهذا
+
+67
+00:05:30,210 --> 00:05:36,370
+بنسميها اللي هي ال hex key او allen key بتبقى
+
+68
+00:05:36,370 --> 00:05:41,610
+الرأس مفرقة على شكل معين كلكم شفتوه هنا دوة
+
+69
+00:05:48,480 --> 00:05:52,080
+فيه برضه نوع تاني هذا و هي حسب التفريغة الآن هم
+
+70
+00:05:52,080 --> 00:05:55,880
+بتكلموا عنه عين النوع للرأس اللي شكلها تماني
+
+71
+00:05:55,880 --> 00:06:01,720
+hexagonal و التفريغة تمانية اللي بنتكلم عنها هنا
+
+72
+00:06:01,720 --> 00:06:05,800
+most bull bolts have heads with hexagonal
+
+73
+00:06:05,800 --> 00:06:09,920
+perimeter hexagonal heads or hex heads يعني الشكل
+
+74
+00:06:09,920 --> 00:06:17,030
+تبعها شكل الرأس هنا تمانيthese allow a spanner to
+
+75
+00:06:17,030 --> 00:06:21,030
+turn them المفتاح هذا لما بدنا نحزقه بنستخدم
+
+76
+00:06:21,030 --> 00:06:26,030
+المفتاح الموجود heads can also have a hexagonal
+
+77
+00:06:26,030 --> 00:06:32,670
+hole in their top يعني تبقى مفرق فيها زي ثقب على
+
+78
+00:06:32,670 --> 00:06:39,920
+شكل شكل تمانيcalled socket head الصاكت اللي هي إيش
+
+79
+00:06:39,920 --> 00:06:46,200
+الجسم المفرق هي الصاكت اللي بنسميها this allows a
+
+80
+00:06:46,200 --> 00:06:49,700
+hex key or allen key to fit into them يعني لما
+
+81
+00:06:49,700 --> 00:06:54,700
+ندخل المفتاح فيها نقدر نلفه بدونه نقدرش نشتغل هذا
+
+82
+00:06:54,700 --> 00:06:59,020
+طبعا أصعب الأنواع اللي بنشتغل عليها لأن هدولة زي
+
+83
+00:06:59,020 --> 00:07:04,730
+ما حكيت دايما بدك تكون عندك عدة تانية لهذا المجالa
+
+84
+00:07:04,730 --> 00:07:09,310
+nut is screwed into a bolt, a bolt can be screwed
+
+85
+00:07:09,310 --> 00:07:13,950
+into the threaded hole يعني هدا ال nuts عادة إيش
+
+86
+00:07:13,950 --> 00:07:19,870
+بيصير فيها؟ screwed into the bolt يعني بن .. بن ..
+
+87
+00:07:19,870 --> 00:07:28,560
+بن لزجها أو بنلفهابال .. بال .. بالبرغة يعني بن ..
+
+88
+00:07:28,560 --> 00:07:31,640
+بنسويها على البرغة و ال board can be screwed into
+
+89
+00:07:31,640 --> 00:07:36,580
+the threaded hole أحيانا في عندي إيش؟ ثقب و الثقب
+
+90
+00:07:36,580 --> 00:07:41,380
+هذا إيش موجود فيه؟ هو مفرج على شكل إيش؟ مش دايما
+
+91
+00:07:41,380 --> 00:07:44,560
+لازم يكون عندى سمونه أحيانا بدقل في عندي ثقب و
+
+92
+00:07:44,560 --> 00:07:49,820
+الثقب هذا معموله مفرج كده للبرغة يدخل فيه فهدولة
+
+93
+00:07:49,820 --> 00:07:52,900
+برضه نوع تاني من الموجود
+
+94
+00:07:55,670 --> 00:07:58,510
+الآن اضافة تحزين في الجوانت الملعقة الملعقة
+
+95
+00:07:58,510 --> 00:07:59,390
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+96
+00:07:59,390 --> 00:08:00,990
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+97
+00:08:00,990 --> 00:08:03,090
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+98
+00:08:03,090 --> 00:08:03,170
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+99
+00:08:03,170 --> 00:08:03,190
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+100
+00:08:03,190 --> 00:08:05,590
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+101
+00:08:05,590 --> 00:08:05,630
+الملعقة الملعقة الملعقة الملعقة الملعقة الملعقة
+
+102
+00:08:05,630 --> 00:08:10,510
+الملعقة الملعقة الملعقة الملعقة
+
+103
+00:08:10,510 --> 00:08:20,550
+الملعقة الملعقة الملعقة الملعقةأو بسميها ايش
+
+104
+00:08:20,550 --> 00:08:24,710
+turning force انا فيه قوة او عزم ب .. ب .. بعمله
+
+105
+00:08:24,710 --> 00:08:30,770
+لأحزق البرغي as a bolt is tightening, the tension
+
+106
+00:08:30,770 --> 00:08:34,350
+stretching force in its shaft increases اذا
+
+107
+00:08:34,350 --> 00:08:37,710
+بتلاحظوا لما انا أحزق في البرغي حتى ده بتحسوه
+
+108
+00:08:37,710 --> 00:08:42,600
+أحيان بسخنهذا لاحظ هذا الشغل؟ لأن السخون هذا من
+
+109
+00:08:42,600 --> 00:08:46,780
+أيش؟ من قوة الحزق اللي موجود هنا الان هذا بيسوي
+
+110
+00:08:46,780 --> 00:08:53,000
+ضغط ال tension ال tension هذا ممكن يولد حرارة in
+
+111
+00:08:53,000 --> 00:08:56,140
+its shaft increases and the components being
+
+112
+00:08:56,140 --> 00:08:59,160
+bolted together are pressed tightly together ايش
+
+113
+00:08:59,160 --> 00:09:06,320
+اللي بيصير فيهم؟ هم بنحزقه او بنضغطهبشكل جامد مع
+
+114
+00:09:06,320 --> 00:09:13,340
+بعض tightly يعني حزاجة يعني بنحزجوا مع بعض this
+
+115
+00:09:13,340 --> 00:09:18,040
+pressing force is called preload or clamp load هذه
+
+116
+00:09:18,040 --> 00:09:24,240
+اللي بنسميها القوة اللي هي preload القوة الضغطة او
+
+117
+00:09:24,240 --> 00:09:28,440
+ال clamp اللي هي ال clamp ايش بيسميه لما نيجي نحط
+
+118
+00:09:28,440 --> 00:09:34,720
+حاجتين مع بعض بنسميها clampيعني أنا ربطهم في بعض
+
+119
+00:09:34,720 --> 00:09:41,760
+أو ضغطهم على بعض فهذا بيسميها clamp load also if
+
+120
+00:09:41,760 --> 00:09:46,260
+enough preload is applied friction between the
+
+121
+00:09:46,260 --> 00:09:50,340
+components will prevent them sliding in different
+
+122
+00:09:50,340 --> 00:09:55,600
+directions لو أنا حطيت قوة كافية فيهم مش هيروحوا
+
+123
+00:09:55,600 --> 00:10:00,180
+في اتجاهات مختلفة يعني هيظلوا ملزقين مع بعض مافيش
+
+124
+00:10:00,180 --> 00:10:05,410
+حاجة هتروح للتانيthis is an advantage as sliding
+
+125
+00:10:05,410 --> 00:10:11,330
+object decides of bolts to shear force the
+
+126
+00:10:11,330 --> 00:10:14,730
+scissoring force which can cause them to break in
+
+127
+00:10:14,730 --> 00:10:20,510
+steel structure to break عادة لو انا حطيت قوة
+
+128
+00:10:20,510 --> 00:10:25,910
+زيادة عن لازم ايش بدي يحصل فيها؟ بتلاحظ ان البرغي
+
+129
+00:10:25,910 --> 00:10:32,020
+بينكسرأو الجسم بنكسر، في حاجة من التنتين .. واحدة
+
+130
+00:10:32,020 --> 00:10:36,840
+من التنتين هتنكسر، يا البرغي يا الجسم، و هاد بتحصل
+
+131
+00:10:36,840 --> 00:10:41,560
+معنى كتير، بتلاقي حالك بتحسكي .. بتحسكي فجأة و
+
+132
+00:10:41,560 --> 00:10:43,340
+بتفرط اللي أنت بتحسكي فيها
+
+133
+00:10:46,250 --> 00:10:49,930
+الصناعات الصناعية التي تستخدمها قوة قوة عالية
+
+134
+00:10:49,930 --> 00:10:54,350
+لإنقاذ السلاجة هي صناعات صناعة صناعة صناعة صناعة
+
+135
+00:10:54,350 --> 00:10:57,010
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+136
+00:10:57,010 --> 00:10:59,230
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+137
+00:10:59,230 --> 00:11:02,950
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+138
+00:11:02,950 --> 00:11:06,150
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+139
+00:11:06,150 --> 00:11:06,210
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+140
+00:11:06,210 --> 00:11:06,870
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+141
+00:11:06,870 --> 00:11:07,290
+صناعة صناعة صناعة صناعة صناعة صناعة صناعة صناعة
+
+142
+00:11:07,290 --> 00:11:10,390
+صناعة صناعة
+
+143
+00:11:11,930 --> 00:11:15,690
+ضغط عالي لما انت بدي .. لأن ال structure انا ايش
+
+144
+00:11:15,690 --> 00:11:20,470
+بدي؟ بدي أحزق جامد فبديش اي حاجة مثلا تطلعوا على
+
+145
+00:11:20,470 --> 00:11:29,430
+عجل السيارة حدا فيكم شاف كيف بيبقى محزوق؟ فعجل
+
+146
+00:11:29,430 --> 00:11:33,390
+السيارة بتلاقي .. لو كان رخو مش محزوق جامد ايش
+
+147
+00:11:33,390 --> 00:11:38,650
+بيصير؟ العجل بيفلط وانت تصور وانت ماشي العجل يفلط
+
+148
+00:11:41,930 --> 00:11:46,170
+طيب the amount of torque applied to bolts can be
+
+149
+00:11:46,170 --> 00:11:52,530
+adjusted using torque wrench الان في العامية خلينا
+
+150
+00:11:52,530 --> 00:11:57,370
+نقول أي مفتاح بنحذق فيه البراغي شكل ثمانية عند
+
+151
+00:11:57,370 --> 00:12:01,270
+الأمريكان كان بيسموه wrench الان المقصود في ال
+
+152
+00:12:01,270 --> 00:12:04,430
+wrench هان تتذكروا في حاجة بنسميها المفتاح الفرنسي
+
+153
+00:12:05,350 --> 00:12:09,950
+ايوة اللي هو شكله زي هيكه وبتضل نعدل فيه فهذا هو
+
+154
+00:12:09,950 --> 00:12:15,450
+.. ايوة زي ال F مش ال F لأ ال F انجليزي بيسموه ال
+
+155
+00:12:15,450 --> 00:12:20,770
+English ال F زي هيكه وهنا اللي بتحزك الفرنسي اللي
+
+156
+00:12:20,770 --> 00:12:26,050
+هو إيش؟و هنا في عند الحاجة اللى فى النص هذه اللى
+
+157
+00:12:26,050 --> 00:12:30,410
+بيساوي فيها هذا الاش المفتاح الفرنسى هذا اللى
+
+158
+00:12:30,410 --> 00:12:33,610
+بيسموه ال wrench فال wrench هذا اش بتعمل فيه
+
+159
+00:12:33,610 --> 00:12:39,230
+بتحزقه و بتقدر تحس كده ما حزقه مظبوط إذا حدا فيك
+
+160
+00:12:39,230 --> 00:12:45,170
+يجرب فالبنات عادة تقليل اللى بيجرب من فيه أصلا
+
+161
+00:12:45,170 --> 00:12:49,690
+زردية مثل هذا؟ لأ مش زي الزردية هذا مفتاح تانى لون
+
+162
+00:12:49,690 --> 00:12:55,630
+دايما حتى بتلاقيه silver ايوةفهذا هو اللي بنعمل
+
+163
+00:12:55,630 --> 00:13:00,390
+منه a tool which can tighten and loosen bolts هذه
+
+164
+00:13:00,390 --> 00:13:04,030
+اللي احنا بنستخدمها ليش هذه لأن انت بتقدر تعدل
+
+165
+00:13:04,030 --> 00:13:09,690
+الحجم تبعها اللي تتناسب مع حجم الرأس تبع ال bolts
+
+166
+00:13:09,690 --> 00:13:12,850
+ال head of the bolts which indicates how much
+
+167
+00:13:12,850 --> 00:13:16,210
+torque is applied this help to ensure that bolts
+
+168
+00:13:16,210 --> 00:13:21,580
+are tightened enough but notover-tightened torque
+
+169
+00:13:21,580 --> 00:13:26,180
+wrenches الآن اللي بقول إيش هذا بقدر أضمن أنه
+
+170
+00:13:26,180 --> 00:13:31,500
+البرغة هذا انحزت كافي لإن أنت بتحسي بس مش زيادة
+
+171
+00:13:31,500 --> 00:13:37,220
+لإن أنت أخر لحظاتك بتحسي أن أنت وصلتي لإيش ل .. ل
+
+172
+00:13:37,220 --> 00:13:42,520
+.. تقريبا لحدود لإن بتصير إيش الحركة تقيلة جدا
+
+173
+00:13:42,520 --> 00:13:45,280
+جوية جدا بدك force زيادة على اللازم بتعرف أنك
+
+174
+00:13:45,280 --> 00:13:46,880
+وصلتي للنهاية
+
+175
+00:13:49,210 --> 00:13:53,510
+Torque wrenches are also useful for checking that
+
+176
+00:13:53,510 --> 00:13:58,090
+both joints do not work loose يعني هذا إيش لما
+
+177
+00:13:58,090 --> 00:14:02,450
+تيجي تستخدم هذا بتعرف انه لأنه في الإيد لو تيجي
+
+178
+00:14:02,450 --> 00:14:06,250
+مسكتها بتعرف إيش بس لو تحط هذا مجرد ما تحطيه تيجي
+
+179
+00:14:06,250 --> 00:14:12,330
+تحذقه بتعرف هذا مرخية ولا إيش محذوقة work loose
+
+180
+00:14:12,330 --> 00:14:18,290
+يعني إيش مرخية that isthey do not become loose
+
+181
+00:14:18,290 --> 00:14:21,810
+over time يعني لو في شوية رخاوة مع الوقت ايش
+
+182
+00:14:21,810 --> 00:14:26,490
+بتلاقيها رخوة اترخرخت او يمكن بتلاحظوها في اي حاجة
+
+183
+00:14:26,490 --> 00:14:31,630
+موجود السرير فيه مربوط ببراغي لو اطلعته عليه مع
+
+184
+00:14:31,630 --> 00:14:37,050
+الوقت بيصير اترخرخ و بيفك لأن اي حركة هي السيارة
+
+185
+00:14:37,050 --> 00:14:41,050
+يمكن بحكي العجل لو العجل اترخرخ على طول بنكسر
+
+186
+00:14:41,050 --> 00:14:44,750
+بتكسر من التبعات العجال هدول اصلا
+
+187
+00:14:47,220 --> 00:14:51,300
+طيب ال washers اللي حكيتلكوا عنها اللي هي الإسورة
+
+188
+00:14:51,300 --> 00:14:55,720
+أو الدبلة اللي بيحطوها في وين في البرغي الموجود
+
+189
+00:14:55,720 --> 00:14:59,360
+هنا لأن البرغي أحيانا بده حاجة تعزل بينه وبين
+
+190
+00:14:59,360 --> 00:15:03,360
+الجسم اللي بنركبه عليه أو بنلحزق washers are metal
+
+191
+00:15:03,360 --> 00:15:07,440
+discs which fit between the head of the balls or a
+
+192
+00:15:07,440 --> 00:15:10,900
+nut and the components being bolted together ده
+
+193
+00:15:10,900 --> 00:15:16,010
+اللي بيحطها هنا ليش هادى؟ طيبordinary washers
+
+194
+00:15:16,010 --> 00:15:22,390
+called flat washers or plain washers flat washers
+
+195
+00:15:22,390 --> 00:15:30,950
+or plain washers هدوله النوع ال ايش ال typical ال
+
+196
+00:15:30,950 --> 00:15:36,030
+typical اللي هي ال flat اللي هي شكلها دائري بهذا
+
+197
+00:15:36,030 --> 00:15:43,000
+الشكلI have a larger outside diameter than the
+
+198
+00:15:43,000 --> 00:15:46,600
+bolt head or the nut عادة تبقى مساحتهم أكبر من
+
+199
+00:15:46,600 --> 00:15:52,600
+مساحة البرغة و عادة هذه بتعطيني نوعا ما شوية مجال
+
+200
+00:15:52,600 --> 00:15:56,940
+لو البرغة كان حجمه صغير بتحطي هذا بتصبط معاك فيها
+
+201
+00:16:01,690 --> 00:16:05,530
+Wider area is intended to spread the load or
+
+202
+00:16:05,530 --> 00:16:09,230
+distribute the pressure over the surface of the
+
+203
+00:16:09,230 --> 00:16:12,730
+component as the bolt is tightened يعني هذا ايش ال
+
+204
+00:16:12,730 --> 00:16:17,550
+reason اللي بيسويها الدغط اللي بيجي بتوزع على كل
+
+205
+00:16:17,550 --> 00:16:23,750
+المناطق spread the pressure القاعدة تطلع على هذه
+
+206
+00:16:23,750 --> 00:16:31,940
+ايش هيبتلاقيها واضحانة مفتوحة و عادة مش مستويةيعني
+
+207
+00:16:31,940 --> 00:16:35,640
+بتلاقيها إيش؟ في وسع بينهم وبين التانية يعني
+
+208
+00:16:35,640 --> 00:16:39,420
+مابجيش على جبال بعض الآن لما أنا أحزق أحزق أحزق
+
+209
+00:16:39,420 --> 00:16:42,980
+إيش بتصير؟ الشكل تبعها بتتطبق أو الشكل بتبعها
+
+210
+00:16:42,980 --> 00:16:47,920
+بتغير هذه سمنها إيش؟ helical spring washer هذا
+
+211
+00:16:47,920 --> 00:16:51,860
+النوع تبعهم بتسميه spring washer هذه سمنها plain
+
+212
+00:16:51,860 --> 00:16:57,060
+أو flat washer هذه helical spring washer هي مفتوحة
+
+213
+00:16:57,060 --> 00:17:02,800
+من هنا هذه بتلاقيها سميكةيعني الارتفاع تبعها مش
+
+214
+00:17:02,800 --> 00:17:09,360
+متساوي هذي سمنها ايش conical spring washer الان
+
+215
+00:17:09,360 --> 00:17:13,040
+لما انا اجي اضغط بلاقي هذي ايش بيصيرلها compressed
+
+216
+00:17:13,040 --> 00:17:20,000
+تنضغط فهذي بتساوي هذي الان ال springwashers are
+
+217
+00:17:20,000 --> 00:17:24,080
+designed to be compressed الهدف منهم ايش هدولة
+
+218
+00:17:24,080 --> 00:17:28,430
+ينضغطواto allow the amount of preload to be
+
+219
+00:17:28,430 --> 00:17:32,510
+adjusted as the bolts is tightened الآن القوة اللي
+
+220
+00:17:32,510 --> 00:17:35,750
+هذه اللي موجودة عليها إيش بيصير فيها بيصير لها
+
+221
+00:17:35,750 --> 00:17:41,270
+adjusting بيصير لها تعديل تتعدل حسب ما هو مطلوب
+
+222
+00:17:41,270 --> 00:17:47,530
+أحيانا بديكي أحزق كتير في كل شي مربوط أي أي قطعتين
+
+223
+00:17:47,530 --> 00:17:52,370
+mechanical حديد حتى الخشب أحيانا بتلاقي مش هي
+
+224
+00:17:52,370 --> 00:17:59,600
+شكلها هيكأه شكلها زي هيك هدولة موجودين حتى إنت لما
+
+225
+00:17:59,600 --> 00:18:03,920
+تروح تشتري على محل البراغي فبقولك البنات في شغلات
+
+226
+00:18:03,920 --> 00:18:07,360
+كتير بعيدة عنها لو تروحي على محل براغي و بدك تشتري
+
+227
+00:18:07,360 --> 00:18:14,520
+بتلاقي هدولة بالكواه موجودات واشيروش
+
+228
+00:18:14,520 --> 00:18:18,380
+مش هيعرف بقولك بيسموها يا أسورة يا دبلة يا مش عارف
+
+229
+00:18:18,380 --> 00:18:25,430
+إيش in some situationsفي بعض الحالات الـ spring
+
+230
+00:18:25,430 --> 00:18:30,870
+washers يستخدمون لتسمح لسجن يتحرك قليلا لكي يتلاعب
+
+231
+00:18:30,870 --> 00:18:36,170
+الشكس الآن لدينا الشكس ماهي المطاب أو الحركة اللي
+
+232
+00:18:36,170 --> 00:18:41,850
+بسرعة هذه بنسميها شك فاحيانا الموجودة هذه اللي
+
+233
+00:18:41,850 --> 00:18:46,150
+بنحطها ال washer ال spring washer بتخليه يتحمل هذا
+
+234
+00:18:46,150 --> 00:18:51,330
+الشك يعني بتعطيه شوية مرونة ان يتحرك حركة خفيفة
+
+235
+00:18:52,770 --> 00:18:56,070
+common types of spring washer are helical spring
+
+236
+00:18:56,070 --> 00:19:00,330
+washer and conical spring washer اللي احنا اتكلمنا
+
+237
+00:19:00,330 --> 00:19:05,970
+عنهم الان ليجي نتكلم على التمرين اللي موجود الان
+
+238
+00:19:05,970 --> 00:19:10,890
+بشكل عام ايش اللي اتكلمنا عنهم الكلمات اذا بتتطلع
+
+239
+00:19:10,890 --> 00:19:16,090
+عليها اتكلمنا على ال fasteners اللي هي عبارة عن
+
+240
+00:19:16,090 --> 00:19:21,670
+روابط اتكلمنا على ال bolts و ال knots اتكلمنا على
+
+241
+00:19:21,670 --> 00:19:26,910
+الال spanner اللي هو ايش المفتاح اتكلمنا على ايش
+
+242
+00:19:26,910 --> 00:19:32,790
+كمان ال hex او ال allen key اللي هو اللي موجودة
+
+243
+00:19:32,790 --> 00:19:40,250
+اتكلمنا على ال threads انت بتتذكر و الشافت مظبوط
+
+244
+00:19:40,250 --> 00:19:43,730
+الآن الشافت اتكلمنا الشكل تبع ال head ايش قلنا
+
+245
+00:19:43,730 --> 00:19:47,910
+كلاج
+
+246
+00:19:47,910 --> 00:19:55,150
+ايش قلناhexagonal اللي هي تماني الرأس واتكلمنا عنه
+
+247
+00:19:55,150 --> 00:20:02,890
+ممكن تكون هذه يعني ايوة ممكن تكون هي بنستخدمها هاي
+
+248
+00:20:02,890 --> 00:20:08,990
+وممكن تكون ال head هذه عبارة عن hole ال hole شكله
+
+249
+00:20:08,990 --> 00:20:17,370
+hexagonal اتكلمنا بعد هيك على ال forces اتكلمنا
+
+250
+00:20:17,370 --> 00:20:23,210
+على shear forceاتكلمنا على ال tension ده بتتذكروا
+
+251
+00:20:23,210 --> 00:20:28,630
+و اتكلمنا على ال scissor torque او scissor force
+
+252
+00:20:28,630 --> 00:20:33,650
+بعد هيك روحنا على ال washers و قولنا عندنا نوعين
+
+253
+00:20:33,650 --> 00:20:36,890
+من ال washers اللي هي ال plain او ال flat و ال
+
+254
+00:20:36,890 --> 00:20:42,790
+spring و ال spring عندنا فيها نوعين helical و ايش؟
+
+255
+00:20:42,790 --> 00:20:48,670
+ايوةالان نجي طلع على ال ranches ال ranches هدول
+
+256
+00:20:48,670 --> 00:20:54,790
+are well-known example of fasteners صح؟ ال .. ال
+
+257
+00:20:54,790 --> 00:20:59,490
+.. ال ranches ايش هو؟ مش fastener هي tool for a
+
+258
+00:20:59,490 --> 00:21:05,010
+fastener ايش ال fastener؟ ال .. ال bolts مظبوط؟
+
+259
+00:21:05,010 --> 00:21:10,110
+البرغي هو fastener ال .. ال .. ال ranches هو ال ..
+
+260
+00:21:10,110 --> 00:21:15,320
+هو الأداة اللي احنا بنحزك فيها البرغيالرنش اللي هي
+
+261
+00:21:15,320 --> 00:21:21,760
+الأداة المفتاح اللي ايش قلنا عنه ايوة مظبوط in
+
+262
+00:21:21,760 --> 00:21:25,760
+most cases nuts are screwed into balls by turning
+
+263
+00:21:25,760 --> 00:21:30,980
+them anticlockwise Clockwise ال majority قلنا ايش
+
+264
+00:21:30,980 --> 00:21:37,830
+Clockwise المظبوط ال majority clockwiseالـ
+
+265
+00:21:37,830 --> 00:21:40,550
+exception اللي هي counter-clockwise أو anti
+
+266
+00:21:40,550 --> 00:21:45,330
+-clockwise the threaded part of a bolt is the head
+
+267
+00:21:45,330 --> 00:21:51,530
+إيش ال threaded part؟ ال shaft أو الشانك الدراع
+
+268
+00:21:51,530 --> 00:21:57,890
+تبعه، مظبوط؟ ال threads are cut to form hexagonal
+
+269
+00:21:57,890 --> 00:22:04,980
+pattern helical pattern اللي هي إيش؟ الحلدونيمظبوط
+
+270
+00:22:04,980 --> 00:22:09,180
+Allen keys are designed to fit around the head of
+
+271
+00:22:09,180 --> 00:22:14,260
+the bolts ايش ال Allen؟ انتوا مظبوط قولنا هذا اللي
+
+272
+00:22:14,260 --> 00:22:19,240
+بندخلها في الرأس الرأس بتبقى ايش مفرقة فبندخلها
+
+273
+00:22:19,240 --> 00:22:19,660
+فيها
+
+274
+00:22:26,590 --> 00:22:31,110
+الان we got to use the words in the box to fill in
+
+275
+00:22:31,110 --> 00:22:34,410
+the blank in a structural application اللي هي
+
+276
+00:22:34,410 --> 00:22:41,590
+التطبيقات تبعات البناء it is essential to .. إيش؟
+
+277
+00:22:41,590 --> 00:22:46,750
+ال bolts .. tighten the bolts مظبوط؟ لازم نحزق
+
+278
+00:22:46,750 --> 00:22:53,410
+البراغيit is essential to tighten the bolts لازم
+
+279
+00:22:53,410 --> 00:22:59,010
+نحزق .. ضرور نحزق the bolts correctly okay firstly
+
+280
+00:22:59,010 --> 00:23:03,550
+to make sure that joints are held together with
+
+281
+00:23:03,550 --> 00:23:09,950
+the right amount of .. ايش بدنا نحطها؟ ايوة
+
+282
+00:23:09,950 --> 00:23:15,110
+preload مظبوط احنا روحنا ايش عندنا؟ tighten و
+
+283
+00:23:15,110 --> 00:23:20,880
+preload اللي عندهاover time however that does not
+
+284
+00:23:20,880 --> 00:23:25,920
+end secondly to help ensure that the balls do not
+
+285
+00:23:25,920 --> 00:23:33,400
+work loose over time يعني مع الوقت مش هايش يترخخوا
+
+286
+00:23:33,400 --> 00:23:41,640
+work loose طيب however that does not mean to say
+
+287
+00:23:41,640 --> 00:23:46,470
+the tighter the barrelطيب يعني هذا بتقولش أنه لو
+
+288
+00:23:46,470 --> 00:23:51,370
+كان محزوج زيادة على محزوج كتير أفضل if excessive
+
+289
+00:23:51,370 --> 00:23:57,730
+force is used to overtighten لو أنا استخدمت قوة
+
+290
+00:23:57,730 --> 00:24:06,410
+زيادة على لازم لأحزق بزيادة overtighten في
+
+291
+00:24:06,410 --> 00:24:11,050
+كلمة مش عارفينها excessive اللي هي زيادة بزيادة
+
+292
+00:24:11,050 --> 00:24:12,870
+طيب
+
+293
+00:24:16,040 --> 00:24:19,820
+the bolt will no longer be strong enough to
+
+294
+00:24:19,820 --> 00:24:23,320
+transmit the extra load to the joint ايش يعني
+
+295
+00:24:23,320 --> 00:24:31,020
+transmit؟ transmit transmission
+
+296
+00:24:31,020 --> 00:24:38,000
+او transmission ايش هو؟ يرسل transmission انه ينقل
+
+297
+00:24:39,480 --> 00:24:44,840
+transmit the extra load ينقل الحمل الزيادة لمن؟ لل
+
+298
+00:24:44,840 --> 00:24:48,760
+joint ال joint اللي هي ايش؟ المنطقة اللي .. ال ..
+
+299
+00:24:48,760 --> 00:24:54,120
+ال .. الرابط للرابط at this point various problem
+
+300
+00:24:54,120 --> 00:25:00,620
+can occur the shank may begin to twist as it is
+
+301
+00:25:00,620 --> 00:25:05,640
+subject to additional ايش؟ torque الان ايش ال ..
+
+302
+00:25:05,640 --> 00:25:14,070
+الجسم هنا هيبدأ ايش؟twist ايش يعني twist؟ يلوي لما
+
+303
+00:25:14,070 --> 00:25:20,650
+الحاجة تلتوى بنقولها twist فهانقاش لو احنا حاطينا
+
+304
+00:25:20,650 --> 00:25:24,470
+force زيادة ايش .. ايش بيحصل تبقى تلوى تلتوى هذه
+
+305
+00:25:24,470 --> 00:25:29,290
+بعد هيش بيصيرلها تنكسر مظبوط؟ طيب
+
+306
+00:25:31,700 --> 00:25:34,780
+subject to additional torque from the wrench
+
+307
+00:25:34,780 --> 00:25:37,080
+eventually causing the bolts to fail
+
+308
+00:25:37,080 --> 00:25:46,920
+Alternatively,
+
+309
+00:25:48,860 --> 00:25:53,820
+as the bolt is stretcheddue to increasing ايش؟ ايش
+
+310
+00:25:53,820 --> 00:25:58,680
+اللي بيسببها؟ tension in the shank the force will
+
+311
+00:25:58,680 --> 00:26:05,940
+be transmitted to the threads of the bolt and nuts
+
+312
+00:26:07,060 --> 00:26:11,520
+هيقولنا attention إيش اللي بدي أحصل فيها هذه ال
+
+313
+00:26:11,520 --> 00:26:15,460
+load أو الحمل هيروح لمين لل threads ال thread اللي
+
+314
+00:26:15,460 --> 00:26:20,360
+هي ليش السنان تبعات ال balls و تبعات الهاي فهذه
+
+315
+00:26:20,360 --> 00:26:24,700
+ايش بيصير فيها أحيان الأسنان هذه تتكسر كمان
+
+316
+00:26:28,830 --> 00:26:31,810
+potentially causing permanent damage to that
+
+317
+00:26:31,810 --> 00:26:36,790
+thread هاي ايش بيسوي بتخرب أسنان هذه الموجودة
+
+318
+00:26:36,790 --> 00:26:40,030
+permanent damage this will not only make it
+
+319
+00:26:40,030 --> 00:26:48,750
+impossible to subsequently tighten and loosen
+
+320
+00:26:48,750 --> 00:26:54,630
+the boltsOkay normally but also cause tension to
+
+321
+00:26:54,630 --> 00:26:58,490
+be released from the shank as nuts slip reducing
+
+322
+00:26:58,490 --> 00:27:02,290
+preload and compromising the strength of the
+
+323
+00:27:02,290 --> 00:27:05,570
+joints ايش احنا بيحصل عندها لو انا حذاقت و خربت
+
+324
+00:27:05,570 --> 00:27:09,970
+ايش بيصير طفلة مرة بترخي مرة واحدة مظبوط معناته لو
+
+325
+00:27:09,970 --> 00:27:15,210
+رخت مرة واحدةكل إشي خرب بدك تجيبي حاجة برغ جديدة و
+
+326
+00:27:15,210 --> 00:27:19,750
+حاجة جديدة المشكلة كانت لو عندك not مش مشكلة بس لو
+
+327
+00:27:19,750 --> 00:27:23,430
+عندك حاجة مره في الجسم إيش بتسوي خربت السن تبع
+
+328
+00:27:23,430 --> 00:27:29,190
+الجسم بدك ترمي كل هذه بدك تاخديها عند حد عنده إيش
+
+329
+00:27:29,190 --> 00:27:32,630
+بيسموه هدولة تبعات المخارط و يخرطلك فيها حين انت
+
+330
+00:27:32,630 --> 00:27:38,490
+بتصير غلبة كبيرة طيب
+
+331
+00:27:40,450 --> 00:27:45,670
+أحنا هذه بدنا الجزء التالت نتكلم عليه true and
+
+332
+00:27:45,670 --> 00:27:51,930
+false و correct the wrong answer the purpose of
+
+333
+00:27:51,930 --> 00:27:55,250
+all washers is to spread the load from the bolts
+
+334
+00:27:55,250 --> 00:27:59,410
+across the surfaces of the components being bolted
+
+335
+00:27:59,410 --> 00:28:03,850
+together هذا كل ال washers كل هدول هذا لمين بتنعمل
+
+336
+00:28:03,850 --> 00:28:11,140
+بس ال flat أو ال plain الباقيبظبطش فيها ال plain
+
+337
+00:28:11,140 --> 00:28:16,200
+washers are flat ال plain إيش قلنا عنهم؟ شكلهم
+
+338
+00:28:16,200 --> 00:28:23,040
+flat ال spring washer it change shape as a bolt is
+
+339
+00:28:23,040 --> 00:28:27,240
+tightened الشكل تبقى حمقولنا واحدة بتبقى زي هيكة
+
+340
+00:28:27,240 --> 00:28:31,720
+لما تنضغط إيش بيصير أو التانية إيش بيصير بتبقى
+
+341
+00:28:31,720 --> 00:28:34,900
+شكلها منفوخة تنضغط
+
+342
+00:28:36,350 --> 00:28:40,370
+الـ spring washer تأكد من أنه لا مهما كمية قطعة
+
+343
+00:28:40,370 --> 00:28:46,470
+تضغط تبقى كمية الـ preload نفسها مخطئة مخطئة مخطئة
+
+344
+00:28:46,470 --> 00:28:47,770
+مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة
+
+345
+00:28:47,770 --> 00:28:52,890
+مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة
+
+346
+00:28:52,890 --> 00:28:59,530
+مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة
+
+347
+00:28:59,530 --> 00:29:04,570
+مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة مخطئة
+
+348
+00:29:04,570 --> 00:29:09,110
+مخطئة مخطئةfalse ايش بت allow some movement عندى
+
+349
+00:29:09,110 --> 00:29:13,950
+بيصير فيه movement هي أحيانا بتسمحلي بشوية حركة
+
+350
+00:29:13,950 --> 00:29:19,410
+موجودة باللاحظ اليوم الأهم حاجة عرفناها من
+
+351
+00:29:19,410 --> 00:29:24,370
+المصطلحات الجديدة اللى هى ال washers كلكوا عارفين
+
+352
+00:29:24,370 --> 00:29:34,150
+ايش ال washers طب لا الدبلة او السوارة هى ال
+
+353
+00:29:34,150 --> 00:29:42,560
+washersأيوة هذه washer ايش اللي عندنا قلنا ال
+
+354
+00:29:42,560 --> 00:29:48,980
+fasteners هذه اللي هي ايش الآن لما نيجي نتكلم على
+
+355
+00:29:48,980 --> 00:29:55,220
+هاي ال washer و هاي ال bolts وهذه
+
+356
+00:29:55,220 --> 00:30:00,540
+ال head وهذه اللي قلنا عنه الشكل اللي زي هيك
+
+357
+00:30:12,710 --> 00:30:18,630
+أيوة هذا بنسميه Spanner كويس
+
+358
+00:30:18,630 --> 00:30:24,750
+المفتاح هذا هذا سمنها ايش ال wrench ايش اللي عندنا
+
+359
+00:30:24,750 --> 00:30:28,470
+ضال ال allen key ال allen key او ال hex اللي هو
+
+360
+00:30:28,470 --> 00:30:29,410
+الشكل تبعه
+
+361
+00:30:32,890 --> 00:30:37,890
+بتبقى زي هيكة وفيه اليد تبعته وهد عادة بتلاقيها مش
+
+362
+00:30:37,890 --> 00:30:43,050
+واحدة بتلاقي كبشة موجودة مع بعض هي .. هي ايد ويلها
+
+363
+00:30:43,050 --> 00:30:49,370
+اكتر من راس موجودة هاي و مجسات فهد بنسميها ال
+
+364
+00:30:49,370 --> 00:30:54,090
+allen key او ال hex اللي عندى ايش ضال عندى من
+
+365
+00:30:54,090 --> 00:30:58,130
+الكلمات اللي مرت علينا ال torque و ال tension و ال
+
+366
+00:30:58,130 --> 00:31:04,070
+forceطب هاد بتعرفوهم مرت عليكم بالفيزيا وال share
+
+367
+00:31:04,070 --> 00:31:11,490
+force مرت عليكم ضال كلمات معينة ال tread اللي هي
+
+368
+00:31:11,490 --> 00:31:16,570
+إيش؟ الأسنان الأسنان تبعت ال .. أو أحيانا إيش
+
+369
+00:31:16,570 --> 00:31:19,790
+بتلاقيهم ال tread of the tires مرت عليكم أيام ال
+
+370
+00:31:19,790 --> 00:31:27,390
+tires إيش هنا؟عشان تشوفوا جاهزين العجل فيه إله
+
+371
+00:31:27,390 --> 00:31:33,190
+إيش؟ خطوط عليه مظبوط هذه بيسميها ال tread of the
+
+372
+00:31:33,190 --> 00:31:37,370
+tires اللي قال لما العجل يصير قديم ال tread هدولة
+
+373
+00:31:37,370 --> 00:31:44,130
+بينمسحه بيصير العجل بنشر بسرعة مرة تانيةف ال
+
+374
+00:31:44,130 --> 00:31:47,690
+treads اللي هي الأسنان أو الأشكال اللي هات الان
+
+375
+00:31:47,690 --> 00:31:54,790
+helical إيش الحلزوني الموجود عندى hexagonal تمانى
+
+376
+00:31:54,790 --> 00:31:57,470
+هذا بشكل عام معظم الكلمات
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/JSBZUTmDLbE.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/JSBZUTmDLbE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c792eee4b58fdccba144e54fecddcbd026cd47d
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/JSBZUTmDLbE.srt
@@ -0,0 +1,1303 @@
+1
+00:00:20,860 --> 00:00:25,660
+السلام عليكم اليوم سوف نتكلم عن الحلقة التاسعة
+
+2
+00:00:25,660 --> 00:00:31,880
+الحلقة التاسعة تتكلم عن load، stress و strain إيش 
+
+3
+00:00:31,880 --> 00:00:38,640
+يعني ال load؟ الأحمال و stress، الضغط و strain، 
+
+4
+00:00:38,640 --> 00:00:45,010
+الشد، إيش بتأثير الشد؟ خلّينا نقول a load when
+
+5
+00:00:45,010 --> 00:00:48,170
+engineering engineers design a machine or a
+
+6
+00:00:48,170 --> 00:00:51,610
+structure they need to know what forces will be
+
+7
+00:00:51,610 --> 00:00:56,090
+exerted on it يعني لما المهندسين بدهم يصمم مبنى أو 
+
+8
+00:00:56,090 --> 00:01:02,130
+جهاز دايما بتطلعوا قد إيش القوة اللي بدها applied
+
+9
+00:01:02,130 --> 00:01:07,770
+أو exerted اللي إن حطت عليها أو بتضغط عليها إيش هي
+
+10
+00:01:07,770 --> 00:01:11,610
+put pressure on it in engineering forces are
+
+11
+00:01:11,610 --> 00:01:15,760
+called loads في الهندسة وهذا في مجال الهندسة
+
+12
+00:01:15,760 --> 00:01:22,320
+المدنية بشكل أساسي بنسميها أحمال القوة usually
+
+13
+00:01:22,320 --> 00:01:27,380
+several different loads will act on or apply force
+
+14
+00:01:27,380 --> 00:01:30,160
+to عادة في عندي أكتر من قوة تيجي
+
+15
+00:01:33,200 --> 00:01:38,840
+بتفرض حالها على البناء هذا أو على الجهاز الموجود
+
+16
+00:01:38,840 --> 00:01:42,900
+the components in the machine or the members part
+
+17
+00:01:42,900 --> 00:01:46,140
+of a structure a component or member which is
+
+18
+00:01:46,140 --> 00:01:49,680
+designed to carry or bear a load called load
+
+19
+00:01:49,680 --> 00:01:53,620
+bearing components or members الآن ال load bearing
+
+20
+00:01:53,620 --> 00:01:57,920
+اللي هي القطعة أو الجهاز أو جزء من الجهاز اللي إيش
+
+21
+00:01:57,920 --> 00:02:03,420
+بيصير له بنضغط عليه من هذه القوة أو هي اللي بتعمل
+
+22
+00:02:03,420 --> 00:02:09,740
+generation لهذه القوة لتخطيط ما سيحدث عندما يتم
+
+23
+00:02:09,740 --> 00:02:15,040
+تحميل المجموعات الانجنير يتخطيط كمية وكمية تحميط
+
+24
+00:02:15,040 --> 00:02:16,960
+وتعمل أيضًا تعمل تعمل تعمل تعمل تعمل تعمل تعمل
+
+25
+00:02:16,960 --> 00:02:19,500
+تعمل تعمل تعمل تعمل تعمل تعمل تعمل تعمل تعمل
+
+26
+00:02:19,500 --> 00:02:22,320
+تعمل تعمل تعمل تعمل تعمل تعمل تعمل تعمل تعمل
+
+27
+00:02:22,320 --> 00:02:33,600
+تعمل تعمل تمظبوط، إلها magnitude والها direction أو
+
+28
+00:02:33,600 --> 00:02:38,220
+phase زاوية فالزاوية هذا القوة لو .. هاي بدك ..
+
+29
+00:02:38,220 --> 00:02:42,280
+عادة احنا في الهندسة كنا بنشتغل الزاوية الاتجاه
+
+30
+00:02:42,280 --> 00:02:46,180
+العمودي أو الاتجاه الأفقي horizontal أو 
+
+31
+00:02:46,180 --> 00:02:50,680
+vertical ال weight مثلا على سبيل المثال الوزن إيش
+
+32
+00:02:50,680 --> 00:02:55,100
+القوة تبعت وين؟ vertical فهذه .. هذه اللي بنتكلم
+
+33
+00:02:55,100 --> 00:03:00,340
+فيش قوة بتلاقيها جاية بدون اتجاه؟ فهذا اللي بتحكينا
+
+34
+00:03:00,340 --> 00:03:04,260
+يعني عادة احنا بنحسب لهاي ال magnitude و بنطلع على
+
+35
+00:03:04,260 --> 00:03:08,540
+ال phase load is therefore a vector a quantity or
+
+36
+00:03:08,540 --> 00:03:13,640
+vector هي عبارة عن إيش متجهة that is a measurement
+
+37
+00:03:13,640 --> 00:03:17,720
+with both magnitude and direction يعني بالها اتجاه
+
+38
+00:03:17,720 --> 00:03:22,680
+و بالها مقدار أو بالها زاوية و مقدار احنا هذه من
+
+39
+00:03:22,680 --> 00:03:27,550
+الحاجات بعد شوية في الهندسة مسلمات بتصير إنه بتتكلم
+
+40
+00:03:27,550 --> 00:03:35,570
+عن الزاوية نفس لغة ال magnitude this
+
+41
+00:03:35,570 --> 00:03:39,310
+is different to a scalar quantity which has a
+
+42
+00:03:39,310 --> 00:03:42,490
+magnitude only طبعا ال scalar quantity إلها بس
+
+43
+00:03:42,490 --> 00:03:48,190
+magnitude وما بنتكلمش على أي اتجاه هي جهاز هذا ب ..
+
+44
+00:03:48,190 --> 00:03:52,070
+ب .. لو روحتوا لمختبر المواد والتربة أو روحتوا
+
+45
+00:03:52,070 --> 00:03:55,270
+لمختبر ال plastic اللي في الجامعة هذه هتلاقي
+
+46
+00:03:55,270 --> 00:04:00,070
+الجهاز اللي هي apply force أو بتشد عشان تشوف إيش
+
+47
+00:04:00,070 --> 00:04:05,300
+درجة ال .. أو ال quality of the product بيشوفوا قداش
+
+48
+00:04:05,300 --> 00:04:08,940
+درجة التحمل قداش درجة الشد اللي بترجع هاي .. هاي
+
+49
+00:04:08,940 --> 00:04:12,460
+فحص بيسموه مختبر المواد والتربة اللي موجودة في
+
+50
+00:04:12,460 --> 00:04:15,940
+الجامعة فيه الأجهزة اللي بتنفحص فيه المواد
+
+51
+00:04:15,940 --> 00:04:21,780
+الموجودة stress and strain الآن هنجي نسمع إيش ال
+
+52
+00:04:21,780 --> 00:04:25,840
+stress الآن لو أنا جيت مسكت شكوش و دجيته على
+
+53
+00:04:25,840 --> 00:04:31,220
+الطاولة هذه أو جيت على قطعة صغيرة و دجيت عليها في
+
+54
+00:04:31,220 --> 00:04:37,330
+هذه إيش الفرق بين التنتين؟ هلاحظ .. هلاحظ .. أيوة،
+
+55
+00:04:37,330 --> 00:04:42,050
+الآن واحدة هتتحمل واحدة هتتفشفش، مظبوط؟ ال .. ال
+
+56
+00:04:42,050 --> 00:04:48,030
+.. كل ما زادت المساحة كل ما كان التحمل أكبر، كل ما
+
+57
+00:04:48,030 --> 00:04:51,270
+جلت كل ما .. في example اللي بيضربوها، لو أنا جيت
+
+58
+00:04:51,270 --> 00:04:56,630
+cable أو حبل و سحبت فيه حاجة كبيرة، اللي لو كان
+
+59
+00:04:56,630 --> 00:05:00,510
+الحجم كبير تبعه، بيقدر أشيل الشغلة اللي تقيلها، لو
+
+60
+00:05:00,510 --> 00:05:05,760
+كان الحجم صغير، بقطع الحبل طب إيش الفرق بينها؟ طب
+
+61
+00:05:05,760 --> 00:05:09,500
+إن هي نفس الوزن أو نفس القوة الفرق اللي هي إيش؟
+
+62
+00:05:09,500 --> 00:05:13,160
+المساحة اللي بنسميها فهذه بتجيهنا كلمة ال stress
+
+63
+00:05:13,160 --> 00:05:20,580
+ال stress بنتكلم على قوة لمساحة the extract below
+
+64
+00:05:20,580 --> 00:05:23,740
+is from an engineering textbook من كتاب هندسة إيش
+
+65
+00:05:23,740 --> 00:05:27,500
+بتحكيها in a test a thick cable is used to pick up
+
+66
+00:05:27,500 --> 00:05:34,800
+a heavy object يعني كابل سميك احنا سحبنا فيه شيء
+
+67
+00:05:34,800 --> 00:05:40,760
+وزنه ثقيل the cable stretches slightly عادة قبل ما
+
+68
+00:05:40,760 --> 00:05:46,540
+أي حاجة apply force بيصير إيش بيصير له stretching
+
+69
+00:05:46,540 --> 00:05:51,660
+بمد يعني لو أنا جيت لحاجة زي هيك و حطيت عليها حاجة
+
+70
+00:05:51,660 --> 00:05:55,460
+تجيه ليش بلاقيه بيجوص لتحت إذا كان هو حتى جوه
+
+71
+00:05:55,460 --> 00:05:58,500
+بتلاقي التجويسة بتحسيش فيها بس إذا كان حاجة ضعيفة
+
+72
+00:05:58,500 --> 00:06:04,170
+إيش بلاقيها مبينة ملحوظة يعني لو جيت على حبل حطيته
+
+73
+00:06:04,170 --> 00:06:09,330
+و شديته كده اشده و علقتش فيه إيش هلاحظ فيه؟ هينزل
+
+74
+00:06:09,330 --> 00:06:13,030
+من النص و هو كده اشده ماشدود إيش معناته؟ انه هو شد
+
+75
+00:06:13,030 --> 00:06:16,530
+.. صارله شد بزيادة يعني الشكل تبعه أو البعد ..
+
+76
+00:06:16,530 --> 00:06:22,290
+البعد تبعه .. الطول تبعه تغير شوية أو بنقوله صار
+
+77
+00:06:22,290 --> 00:06:26,860
+deformed طيب the cable stretches slightly but lifts
+
+78
+00:06:26,860 --> 00:06:30,560
+the weight يعني بشيل الوزن a second test is done
+
+79
+00:06:30,560 --> 00:06:33,960
+using a thinner cable thinner cable اللي هو إيه؟
+
+80
+00:06:33,960 --> 00:06:39,820
+كابل أرفع one with only half the cross-sectional
+
+81
+00:06:39,820 --> 00:06:44,500
+area of the thick cable يعني أخدنا نص السمك تبعه
+
+82
+00:06:44,500 --> 00:06:49,560
+this time the cable stretches then break الكابل
+
+83
+00:06:49,560 --> 00:06:54,980
+إيش بيصير؟ بمط و بعدين إيش؟ بنقطع why did the
+
+84
+00:06:54,980 --> 00:07:00,260
+thinner cable fail؟ ليش هو؟ فشل الآن not due to a
+
+85
+00:07:00,260 --> 00:07:03,520
+higher load as the weight was the same يعني ال
+
+86
+00:07:03,520 --> 00:07:07,880
+load تبعتي أو الحمل تبعي ما تغيرش طيب هناش بنقول
+
+87
+00:07:07,880 --> 00:07:12,160
+the failure was due to stress هو من إيش؟ السبب
+
+88
+00:07:12,160 --> 00:07:16,800
+الرئيسي لل stress طيب ال stress is force per unit
+
+89
+00:07:16,800 --> 00:07:19,720
+area ال stress اللي احنا بنتكلم عليه هو عبارة عن
+
+90
+00:07:19,720 --> 00:07:25,930
+إيش؟ قوة على المساحة اللي عندي and is measured in
+
+91
+00:07:25,930 --> 00:07:30,710
+newton per square meter or pascals الوحدة تبعته
+
+92
+00:07:30,710 --> 00:07:34,550
+newton per square meter أو pascals the thinner
+
+93
+00:07:34,550 --> 00:07:39,210
+cable was therefore stressed twice as much as the
+
+94
+00:07:39,210 --> 00:07:42,050
+thick cable يعني أنا طلع علاقة اللي هذه العلاقة
+
+95
+00:07:42,050 --> 00:07:47,690
+اللي حطناها هذه proportional اللي هي زادت المساحة
+
+96
+00:07:47,690 --> 00:07:53,400
+نقصت لنص فالتأثير تبع ال stress اضاعف هذا اللي
+
+97
+00:07:53,400 --> 00:07:58,260
+بيصير فيه as the same load was concentrated into
+
+98
+00:07:58,260 --> 00:08:03,160
+the cross-sectional area that was fifty percent
+
+99
+00:08:03,160 --> 00:08:08,550
+smaller الآن concentrated إيش معناته؟ focused أو
+
+100
+00:08:08,550 --> 00:08:13,850
+تركزت focus تركزت وهي concentrated طلع عند الكلمات
+
+101
+00:08:13,850 --> 00:08:17,070
+اللي مرت علينا fail, failure, stressed, 
+
+102
+00:08:17,610 --> 00:08:24,110
+concentrated في اللي قبلها exerted اللي هي إيش
+
+103
+00:08:24,110 --> 00:08:31,850
+applied يعنيها loads اللي هي سميها act on تتفاعل في
+
+104
+00:08:31,850 --> 00:08:36,550
+عندنا carry أو pair نفس الشيء load bearing اللي هي
+
+105
+00:08:36,550 --> 00:08:41,310
+الجسم اللي بتتعرض للهاي عند ال magnitude وعند ال
+
+106
+00:08:41,310 --> 00:08:47,950
+quantity وعند ال scalar quantity طيب نكمل الموضوع
+
+107
+00:08:47,950 --> 00:08:50,890
+اللي عندنا why did the ticker cable stretch but
+
+108
+00:08:50,890 --> 00:08:54,250
+not break when the objects are stretched they
+
+109
+00:08:54,250 --> 00:09:00,050
+deform ال deformation إيش معناتها؟ بتشوه هو مجرد
+
+110
+00:09:00,050 --> 00:09:05,270
+أنه يطول هيتشوه لأنه هيرفع كمان هو بطول و برفع
+
+111
+00:09:05,270 --> 00:09:09,670
+شوية يمكن أبسط حاجة لما نجي نطلع عليها لو خدنا
+
+112
+00:09:09,670 --> 00:09:15,770
+مغيطة خدت مغيطة و سحبتيها إيش بتسوي معاك؟ تتمدد ..
+
+113
+00:09:15,770 --> 00:09:19,870
+تتمدد يعني أو بتمطب تسوي معاك لو راخدتيها بترجع
+
+114
+00:09:19,870 --> 00:09:24,200
+لإيش؟ لنفس الحجم، هذه في حاجة بنسميها، هنتكلم عنها
+
+115
+00:09:24,200 --> 00:09:34,340
+كمان شوية، بنسميها المرونة أو ال elasticity الآن
+
+116
+00:09:34,340 --> 00:09:38,580
+elasticity لو اتكلمنا عنها، الآن لما نيجي نتكلم
+
+117
+00:09:38,580 --> 00:09:45,140
+على لو أخدت Layden و مضطيت، برجع ال factor تبعه
+
+118
+00:09:45,140 --> 00:09:50,920
+بختلف من حاجة للتانية طيب in test the cable
+
+119
+00:09:50,920 --> 00:09:55,500
+extended it increased in length extension can be
+
+120
+00:09:55,500 --> 00:09:58,900
+measured as a change in an object length compared
+
+121
+00:09:58,900 --> 00:10:02,560
+to its original length يعني هذا ال change لما يصير
+
+122
+00:10:02,560 --> 00:10:07,340
+عنده .. هذي نسبة .. قداشة التغير في طوله بالنسبة
+
+123
+00:10:07,340 --> 00:10:15,100
+لإيش؟ لحاجة الأصلية هذا ال .. التغير بنسميها إيش؟
+
+124
+00:10:15,100 --> 00:10:20,810
+strain الـ strain هو بيجيس إيش التغير فيها وفي أنواع
+
+125
+00:10:20,810 --> 00:10:24,930
+له هتطلع إياه according to a law called young's
+
+126
+00:10:24,930 --> 00:10:30,190
+modulus of elasticity stress is proportional to
+
+127
+00:10:30,190 --> 00:10:34,330
+strain الآن ال stress احنا إيش بنلاحظ في علاقة
+
+128
+00:10:34,330 --> 00:10:38,290
+بينه وبين مين ال strain اللي موجود عندي in other
+
+129
+00:10:38,290 --> 00:10:41,630
+words a percentage increase in the stress will
+
+130
+00:10:41,630 --> 00:10:44,770
+cause the same percentage increase in the strain
+
+131
+00:10:44,770 --> 00:10:51,990
+يعني العلاقة طردية كل ما بزود ال stress هيزيد عندي
+
+132
+00:10:51,990 --> 00:10:57,210
+ال strain الموجود however this is only true up to
+
+133
+00:10:57,210 --> 00:11:01,250
+a point called limit of proportionality الآن هذه
+
+134
+00:11:01,250 --> 00:11:03,950
+العلاقة اللي بنقول عنها طردية بنسميها linear
+
+135
+00:11:03,950 --> 00:11:08,770
+region linear لإيش؟ لإن كل ما بزيد هذه بزيد
+
+136
+00:11:08,770 --> 00:11:12,640
+الموجودة بنفس الشيء هذه المنطقة بيسميها ال linear
+
+137
+00:11:12,640 --> 00:11:17,720
+الآن برا المنطقة هذه outside ال limit of 
+
+138
+00:11:17,720 --> 00:11:20,600
+proportionality إيش اللي بيحصل العلاقة بتبطل
+
+139
+00:11:20,600 --> 00:11:23,820
+linear بيصير non-linear يعني الزيادة في ال stress
+
+140
+00:11:23,820 --> 00:11:28,800
+مش هيرافقها نفس الزيادة في ال strain هذا لما
+
+141
+00:11:28,800 --> 00:11:32,640
+تحصل بيسمي هذه المنطقة ال non-linear relationship
+
+142
+00:11:32,640 --> 00:11:38,340
+أو ال non-linear region إذا كانت المادة مضغوطة بشكل
+
+143
+00:11:38,340 --> 00:11:43,740
+كبير، فإنها ستصبح مضغوطة بشكل أعضاء أعضاء.
+
+144
+00:11:49,200 --> 00:11:53,480
+النسبة تبعته أعلى من قبل stress and strain were
+
+145
+00:11:53,480 --> 00:11:58,120
+therefore become disproportionate العلاقة الآن مش
+
+146
+00:11:58,120 --> 00:12:02,520
+طردية زي ما ..يعني مش بنفس النسب اللي كانت نسبية
+
+147
+00:12:02,520 --> 00:12:08,120
+صارت العلاقة ..فيش إشي بحكم يعني يمكن باللغة خلينا
+
+148
+00:12:08,120 --> 00:12:12,640
+..خلينا أعطيكوا حاجة في حد فيكوا ..اخدتوا
+
+149
+00:12:12,640 --> 00:12:16,500
+بالثانوية ال diode ال diode
+
+150
+00:12:19,510 --> 00:12:26,750
+ماش اسمه بالعربي؟ اتناقش؟ لأ ال .. ال diode ايش
+
+151
+00:12:26,750 --> 00:12:31,090
+بتلاحظوا؟ او ال transistor او اي اشى ال transistor
+
+152
+00:12:31,090 --> 00:12:35,570
+على سبيل المثال مار عليكم الان كل ما بزود بالتيار
+
+153
+00:12:35,570 --> 00:12:41,990
+تبع ال base تيار تبع ال collector ايش بحصل فيه؟ لأ
+
+154
+00:12:41,990 --> 00:12:47,450
+بزيد عندي .. بزيد الان
+
+155
+00:12:47,450 --> 00:12:54,070
+عندي علاقة في الترانزيستر اولا في curve عندي هنا هي
+
+156
+00:12:54,070 --> 00:13:02,830
+ال VB أو CE وهنا ال IC كويس ال IC اللي هو التيار
+
+157
+00:13:02,830 --> 00:13:09,950
+تبع مين ال collector صح انا جايبلكوا حاجة الكهربا
+
+158
+00:13:09,950 --> 00:13:17,860
+خلاص بلاش نذهب عنها الآن لما نيجي في أحيانا بال ..
+
+159
+00:13:17,860 --> 00:13:23,100
+بالعلاقات اللي بتصير كل ما بزود تخليني أقول يمكن
+
+160
+00:13:23,100 --> 00:13:31,680
+اطلع على لو جبت cable من النوع ال .. او خليني أقول
+
+161
+00:13:31,680 --> 00:13:37,510
+مطاط حاجة مطاطة بتلاقوها من حبل مطاط طبع النط، طبع
+
+162
+00:13:37,510 --> 00:13:42,450
+غيره، الآن ممكن أحمل فيه وزن معين، حلاحظ إيش بمط
+
+163
+00:13:42,450 --> 00:13:45,850
+معي بدرجة معينة، طب لو ضليتني أزود في الأوزان
+
+164
+00:13:45,850 --> 00:13:51,470
+بلاحظ إيش .. الآن لو حطيت وزن دقيق، إيش بلاحظ؟ ال
+
+165
+00:13:51,470 --> 00:13:56,700
+.. بمط مطة كبيرة مظبوط التشوق اه بس اول كانت نسبية
+
+166
+00:13:56,700 --> 00:14:02,440
+لحد دي حد معين بعد هذا الحد ايش بيصير فش نسبة
+
+167
+00:14:02,440 --> 00:14:06,380
+معقولة وهذا اللي بنتكلم عنه هنا النسبة بطلت
+
+168
+00:14:06,380 --> 00:14:12,060
+متشابهة الان في عند ال type of loads و ال
+
+169
+00:14:12,060 --> 00:14:17,130
+description تبعهم ايش هي ال dead load وفي عندي ال
+
+170
+00:14:17,130 --> 00:14:20,190
+live load هدى فى ال appendix ايش ال dead load؟
+
+171
+00:14:20,190 --> 00:14:24,090
+اللي أنا طالع عندي مبنى هدى المبنى هدى لو مافيش في
+
+172
+00:14:24,090 --> 00:14:32,310
+حده فيه ضغط للإيش للسقف في ضغط الحيطان في هذا كله
+
+173
+00:14:32,310 --> 00:14:37,830
+ضغط هذا الضغط بتغير مع الزمن ال .. الأوزان هذه
+
+174
+00:14:37,830 --> 00:14:42,070
+بتتغيرش مع الزمن، بس الآن العدد تبعكم في هذا
+
+175
+00:14:42,070 --> 00:14:46,470
+القاعة إيش بيصير فيه؟ بتغير مع الوقت، كل محاضرة
+
+176
+00:14:46,470 --> 00:14:50,770
+غير على التانية، ال .. الوزن تبعكم بيسميه live
+
+177
+00:14:50,770 --> 00:14:55,570
+load فهمتوا إيش ال live load؟ بتغير مع الوقت، هذه
+
+178
+00:14:55,570 --> 00:14:58,650
+dead load، ال dead load إيش بيحصل فيها؟
+
+179
+00:15:04,430 --> 00:15:07,990
+الوزن هذا a load whose magnitude can be different
+
+180
+00:15:07,990 --> 00:15:11,850
+at different time usually imposed on put on or
+
+181
+00:15:11,850 --> 00:15:16,170
+machine اللي عندها static loads ايش هذا عنده فيه
+
+182
+00:15:16,170 --> 00:15:21,350
+loads they stay يعني the same remain still still
+
+183
+00:15:21,350 --> 00:15:28,980
+ايش ثابتة ال loads اللي بتضل ثابتة أو ساكنة ده
+
+184
+00:15:28,980 --> 00:15:32,200
+بنتطلع عليها زي إيش اللي .. اللي .. اللي عندها
+
+185
+00:15:32,200 --> 00:15:38,780
+اتطلع عنده لو عنده ال .. المبنى، المبنى التأثير
+
+186
+00:15:38,780 --> 00:15:45,900
+اللي عليه، إيش بيحصل؟ خفيف، تأثير القوة الموجهة
+
+187
+00:15:45,900 --> 00:15:52,590
+عليه بتتغير مثلا نيجي نطلع على الأحمال اللي موجودة
+
+188
+00:15:52,590 --> 00:15:57,030
+عندي هنا بتتغيرش عليه لا أبيض ولا أسود ولا حاجة
+
+189
+00:15:57,030 --> 00:16:03,630
+الآن المبنى نفسه لو في عندي الريح الريح هي إيش قوة
+
+190
+00:16:03,630 --> 00:16:11,020
+الريح هي dynamic ولا static؟ dynamic تتغير لأنه حسب
+
+191
+00:16:11,020 --> 00:16:15,520
+الاتجاه حسب القوة تبعتها فهذه dynamic load
+
+192
+00:16:15,520 --> 00:16:20,460
+بنعتبرها وهذه static
+
+193
+00:16:20,460 --> 00:16:23,940
+load اللي هي اللي عندي في عندي حاجتين في عندي
+
+194
+00:16:23,940 --> 00:16:28,180
+point load و في عندي uniformly distributed load ال
+
+195
+00:16:28,180 --> 00:16:33,560
+point load لما انا اعمل التأثير في نقطة محددة يعني
+
+196
+00:16:33,560 --> 00:16:36,960
+باجي لنقطة و بعمل التأثير تبعها هات ايش بسميها
+
+197
+00:16:36,960 --> 00:16:40,900
+load which is concentrated that is which act on a
+
+198
+00:16:40,900 --> 00:16:44,700
+smaller area باجي ع منطقة معينة و بسويها ال
+
+199
+00:16:44,700 --> 00:16:48,480
+distributed weight ايش هي اللي بتبقى موزعة على
+
+200
+00:16:48,480 --> 00:16:53,980
+المساحة كلها فهات بسميها ايش distributed weight
+
+201
+00:16:53,980 --> 00:17:01,170
+يعني لو انا جيت طرقت هوايا هانالـ force اللي عندي
+
+202
+00:17:01,170 --> 00:17:05,350
+وين جات على المنطقهات بس لو أنا جبت هذه ووزعت حطيت
+
+203
+00:17:05,350 --> 00:17:10,070
+خشبة كبيرة صرت اضغط عليها ككل ايش بيصير انها
+
+204
+00:17:10,070 --> 00:17:13,670
+distributed uniformly distributed weight a load
+
+205
+00:17:13,670 --> 00:17:17,250
+which is spread evenly هذه ليش هنسميها هنستخدمها
+
+206
+00:17:17,250 --> 00:17:22,450
+بالتمرين التانيفانا .. ايوة فانا باجي بعرف فيها
+
+207
+00:17:22,450 --> 00:17:26,750
+إيش هي عشان تعرفوها فيها أنا موجود على صفحة video
+
+208
+00:17:26,750 --> 00:17:30,810
+بتكلم على ال loads أنواعها و بفرجيكوا و بعطيكوا
+
+209
+00:17:30,810 --> 00:17:35,610
+examples و بتكلم في عندي على ال stress و ال strain
+
+210
+00:17:35,610 --> 00:17:41,770
+موجود على صفحة ال video هتفرجوا عليه موجود
+
+211
+00:17:41,770 --> 00:17:43,010
+مطلبات الكلمات
+
+212
+00:17:45,790 --> 00:17:49,410
+الحين هتشوفي .. مش في التمرين اتسنى عليها هتشوفي
+
+213
+00:17:49,410 --> 00:17:53,470
+وين هتلاقي إنتيجها replace the underlying words
+
+214
+00:17:53,470 --> 00:17:56,110
+and expressions with alternative words and
+
+215
+00:17:56,110 --> 00:18:01,810
+expressions from a and appendix اللي عند page 106
+
+216
+00:18:01,810 --> 00:18:06,280
+اللي هي إيش هذي اللي شفتوهن قبل شوية بنستخدم
+
+217
+00:18:06,280 --> 00:18:10,200
+الكلمات طلع عندها if you look at objects around
+
+218
+00:18:10,200 --> 00:18:12,720
+you it's difficult to find something that could
+
+219
+00:18:12,720 --> 00:18:17,020
+not be smashed with a hammer لو طلعت حواليكي مش
+
+220
+00:18:17,020 --> 00:18:22,400
+هتلاقي حاجة بتقدريش تكسريها بالشكوش صح؟ كل حاجة
+
+221
+00:18:22,400 --> 00:18:28,140
+بتتكسر بالشكوش اسأل أخواتك الصغار بيقولولك مافيش
+
+222
+00:18:28,140 --> 00:18:34,320
+شيء متكسرش عندهم طيب but if you lay the hammer down
+
+223
+00:18:34,320 --> 00:18:37,960
+carefully on any of these objects دي إيش force
+
+224
+00:18:37,960 --> 00:18:45,200
+with إيش هذا؟ لو أنا نزلت الشكوش شوية شوية إيش
+
+225
+00:18:45,200 --> 00:18:47,920
+بدها ال force؟ إيش احنا قولنا ال force عبارة عن
+
+226
+00:18:47,920 --> 00:18:54,720
+إيش سمناها؟ load load مظبوط which is put on them
+
+227
+00:18:54,720 --> 00:19:00,930
+إيش بنقول put on؟ exerted أو imposed on ال impose
+
+228
+00:19:00,930 --> 00:19:06,690
+يعني أنا عملتها عليهم أو exerted أنا فردتها عليهم
+
+229
+00:19:06,690 --> 00:19:10,170
+would not be sufficient to cause even the
+
+230
+00:19:10,170 --> 00:19:13,130
+slightest damage this comparison illustrate the
+
+231
+00:19:13,130 --> 00:19:17,030
+difference between them طلع عندي الآن التعبيرات
+
+232
+00:19:17,030 --> 00:19:22,190
+اللي قبل شوية حكيناهم ماذا يسمى moving force which
+
+233
+00:19:22,190 --> 00:19:24,970
+combine mass and moment؟ ماذا يسمى الجسم منها ال
+
+234
+00:19:24,970 --> 00:19:27,770
+moving force؟ ال moving force هي عبارة عن ال
+
+235
+00:19:27,770 --> 00:19:33,710
+dynamic force لأن هي بتتحرك apply a shock ايش
+
+236
+00:19:33,710 --> 00:19:40,910
+الشك؟ ال impulse مظبوط أنا لما نعمل impulse عبارة
+
+237
+00:19:40,910 --> 00:19:45,310
+عن ايش هذه؟ shock الاسم ايش؟ impulse
+
+238
+00:19:48,420 --> 00:19:53,760
+احنا بلغة الكهربا موجودة هذه الامبولز اللي هي أنا
+
+239
+00:19:53,760 --> 00:19:59,900
+لو ال system عندي اعطيها ايش يعني اشاره ان ال
+
+240
+00:19:59,900 --> 00:20:06,480
+magnitude تبعها بنسميها بس at time zero مثلا يعني
+
+241
+00:20:06,480 --> 00:20:11,620
+في .. هذه بس قوة تعطيها في لحظة معينة، هذه بنسميها
+
+242
+00:20:11,620 --> 00:20:15,420
+الشاق، الحين لما حد يخبطك هويا، هذا شاق و أنت
+
+243
+00:20:15,420 --> 00:20:20,240
+ساهر، بيجيب وخبطك على طول و لا بس هويا و بس؟ يعني
+
+244
+00:20:20,240 --> 00:20:25,380
+زي نخزة و بعدين موقف، هذه بنسميها الشاق، لأ هي
+
+245
+00:20:25,380 --> 00:20:31,810
+بطلت شاق هذه الدرب على طول الشك انك اللحظة تبعتها
+
+246
+00:20:31,810 --> 00:20:37,850
+تبقى صغيرة جدا هذه بيسميها الشك فهذه ال moving
+
+247
+00:20:37,850 --> 00:20:43,490
+force هذه سمنها dynamic load وهذه سمنها impulse
+
+248
+00:20:43,490 --> 00:20:49,750
+الآن still force ايش سمنها static load which
+
+249
+00:20:49,750 --> 00:20:53,070
+consists only of an object own mass ايش ال own
+
+250
+00:20:53,070 --> 00:20:59,530
+mass سمنها ال self weight self weight ال own mass
+
+251
+00:20:59,530 --> 00:21:04,250
+يعني لما نتكلم عنها between the two situations ايش 
+
+252
+00:21:04,250 --> 00:21:07,990
+the size of the load ايش سميناها الـ magnitude اللي
+
+253
+00:21:07,990 --> 00:21:13,070
+هو حجم اللي ها load placed on the service is
+
+254
+00:21:13,070 --> 00:21:18,370
+dramatically different ايش placed on exerted أو 
+
+255
+00:21:18,370 --> 00:21:23,170
+imposed on هي
+
+256
+00:21:23,170 --> 00:21:30,430
+نفس الـ put on أو applied on أو applied to نفس
+
+257
+00:21:30,430 --> 00:21:34,790
+الكلام هذا بس احنا بتقول the above comparison
+
+258
+00:21:34,790 --> 00:21:38,350
+illustrated another difference in the way services
+
+259
+00:21:38,350 --> 00:21:43,330
+are pressured ايش يعني pressured؟ ايش سميناها هنا؟
+
+260
+00:21:44,810 --> 00:21:49,510
+loaded when a hammer is laid horizontally on the
+
+261
+00:21:49,510 --> 00:21:54,450
+surface its weight is spread over relatively large
+
+262
+00:21:54,450 --> 00:21:59,490
+area لو انت حطيتي حاجة على سطح horizontal ايش
+
+263
+00:21:59,490 --> 00:22:05,830
+هتلاحظه انه المساحة تبعته أو الوزن تبعه هيروح على
+
+264
+00:22:05,830 --> 00:22:11,330
+المساحة كلها it is therefore applied spread out
+
+265
+00:22:11,330 --> 00:22:18,070
+force ايش سميناها اخر كلمة uniformly distributed load
+
+266
+00:22:18,070 --> 00:22:22,670
+الـ uniformly distributed load إيش معناته؟ أنا وزعت
+
+267
+00:22:22,670 --> 00:22:28,650
+الحمل على المسافة بشكل متساوي، uniform معناته إيش؟
+
+268
+00:22:28,650 --> 00:22:29,890
+منتظم
+
+269
+00:22:32,740 --> 00:22:36,940
+by contrast يعني على النقيض when a hammer hits
+
+270
+00:22:36,940 --> 00:22:40,300
+something only the edge of the hammer head comes
+
+271
+00:22:40,300 --> 00:22:44,000
+into contact with the surface لما حطيت هذه زي هيك
+
+272
+00:22:44,000 --> 00:22:47,820
+خليني أقول هذه شكوش الوزن تبعه توزع على كله لما
+
+273
+00:22:47,820 --> 00:22:52,360
+أجي أضرب ايش بساوي أنا بركز على المنطقة الموجودة
+
+274
+00:22:52,360 --> 00:22:56,400
+عندها in contact with the surface the force
+
+275
+00:22:56,400 --> 00:23:01,750
+therefore is focused ايش قولنا عنها concentrated in
+
+276
+00:23:01,750 --> 00:23:05,630
+a small area applying إيش؟ localized pressure
+
+277
+00:23:05,630 --> 00:23:10,110
+point load إيش قولنا الـ point load؟ اللي هي بتيجي
+
+278
+00:23:10,110 --> 00:23:16,650
+في نقطة معينة الـ uniformly spread load إيش؟ متوزع
+
+279
+00:23:16,650 --> 00:23:20,230
+هدولة كلمتين إيش اللي الحين بدك تفكر فيها؟ الكلمات
+
+280
+00:23:20,230 --> 00:23:24,330
+الـ dynamic إيش حكينا عنه؟ dynamic load moving
+
+281
+00:23:24,330 --> 00:23:31,100
+still الـ اللي هي static load، الآن اتكلمنا على الشغل
+
+282
+00:23:31,100 --> 00:23:34,820
+التاني point load، اللي هي التركيز بيجي في نقطة
+
+283
+00:23:34,820 --> 00:23:38,580
+واحدة uniformly، distributed load اللي هي over،
+
+284
+00:23:38,580 --> 00:23:42,460
+بتوزع على اللي موجود عندنا، هدولة بشكل عام
+
+285
+00:23:42,460 --> 00:23:48,370
+المفرضات اللي احنا نتكلم عنها الآن اتطلع عندي
+
+286
+00:23:48,370 --> 00:23:52,490
+التمرين الثاني complete the technical checklist
+
+287
+00:23:52,490 --> 00:23:59,510
+based on الـ a الآن موزعتهم ايش في الكتاب حاطين الـ a
+
+288
+00:23:59,510 --> 00:24:04,650
+و الـ b و في الصفحة الثانية حاطين ايش الأسئلة اللي
+
+289
+00:24:04,650 --> 00:24:08,510
+عليها هنا بنقدرش نضل نروح و نيجي حطيتهم ايش كل
+
+290
+00:24:08,510 --> 00:24:12,190
+واحدة وراها السؤال اللي عندي which components need
+
+291
+00:24:12,190 --> 00:24:16,190
+to carry load determine what which components are
+
+292
+00:24:16,820 --> 00:24:23,440
+ايش سميناها هذه؟ bearing .. bearing ايش؟ load اللي
+
+293
+00:24:23,440 --> 00:24:27,360
+سميناها هنا which components need to carry load
+
+294
+00:24:27,360 --> 00:24:31,740
+سميناها الـ bearing load هذا الآن طلع عندي what
+
+295
+00:24:31,740 --> 00:24:35,560
+type of load will be carried out carried by each
+
+296
+00:24:35,560 --> 00:24:39,840
+part with which load will remain constant and
+
+297
+00:24:39,840 --> 00:24:42,980
+which will differ depending on the use of
+
+298
+00:24:42,980 --> 00:24:46,500
+circumstances طلع هنا analyzing the type of the
+
+299
+00:24:46,500 --> 00:24:54,480
+load that will ايش ايش قلنا act on exerted on أو
+
+300
+00:24:54,480 --> 00:24:59,380
+impose on on each part أسس ايش اللي عندي أنواع الـ
+
+301
+00:24:59,380 --> 00:25:07,140
+load قلنا في نوعين قلنا عنهم في عندي الـ dead
+
+302
+00:25:07,140 --> 00:25:12,170
+load و الـ live load مظبوط الـ dead ايش قلنا؟ اللي
+
+303
+00:25:12,170 --> 00:25:16,670
+هي الـ structure المتغير الـ live اللي هي انت
+
+304
+00:25:16,670 --> 00:25:23,690
+بتغيره حسب الوقت هذه كتابة مع الوقت هذه متغيرة مع
+
+305
+00:25:23,690 --> 00:25:27,730
+الوقت what amount of load will be exerted in
+
+306
+00:25:27,730 --> 00:25:33,590
+newtons calculate ايش the magnitude of the load as
+
+307
+00:25:35,150 --> 00:25:39,330
+scalar quantity المجموعات التي لديها المجموعات هي
+
+308
+00:25:39,330 --> 00:25:44,270
+عبارة عن scalar quantity لما نتكلم عن الـ vector هو
+
+309
+00:25:44,270 --> 00:25:50,110
+عنده scalar quantity زائد direction اللي عندها in
+
+310
+00:25:50,110 --> 00:25:55,350
+what direction will the load act evaluate the load
+
+311
+00:25:55,350 --> 00:26:01,640
+as لسه حكيناها قبل شوي vector quantities For the
+
+312
+00:26:01,640 --> 00:26:06,960
+materials used, how concentrated can the maximum
+
+313
+00:26:06,960 --> 00:26:10,060
+load be without putting the components under too
+
+314
+00:26:10,060 --> 00:26:13,960
+much pressure? Determine the maximum level of
+
+315
+00:26:13,960 --> 00:26:19,080
+stress that can be carried by materials without
+
+316
+00:26:19,080 --> 00:26:23,130
+causing them to be overloaded over stress هذا
+
+317
+00:26:23,130 --> 00:26:27,370
+stress قلنا اللي هو الـ force per unit area و over
+
+318
+00:26:27,370 --> 00:26:32,510
+stress انه يصير عندها توصل لـ break down أو توصل لـ
+
+319
+00:26:32,510 --> 00:26:37,610
+deformation how much deformation can be expected
+
+320
+00:26:37,610 --> 00:26:41,390
+calculate the percentage of strain قلنا الـ
+
+321
+00:26:41,390 --> 00:26:47,760
+deformation التغير بنسميه ايش الـ strain if
+
+322
+00:26:47,760 --> 00:26:50,940
+something breaks will the assembly collapse
+
+323
+00:26:50,940 --> 00:26:58,440
+dangerously or in a controlled relatively safe way
+
+324
+00:26:58,440 --> 00:27:03,140
+assist the consequence if a component collapse
+
+325
+00:27:03,140 --> 00:27:08,640
+fail fail determining the potential dangers of the
+
+326
+00:27:08,640 --> 00:27:09,820
+failure
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/KGbm6t1qbLk.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/KGbm6t1qbLk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..34e69c1a904f5fff202cc8e5ab0e55060356aa82
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/KGbm6t1qbLk.srt
@@ -0,0 +1,1459 @@
+1
+00:00:20,700 --> 00:00:27,460
+السلام عليكم اليوم سنقوم بتغطية قصتين قصة 36 تتكلم
+
+2
+00:00:27,460 --> 00:00:37,280
+عن النار ودرجة حرارة النار نحن 
+
+3
+00:00:37,280 --> 00:00:43,340
+سنتكلم عن تغيير درجة الحرارة وشكل الأمور النار تتغطى
+
+4
+00:00:46,420 --> 00:00:50,660
+التغيير من الارتفاع والظلالة كما تعلمون التغيير من
+
+5
+00:00:50,660 --> 00:00:59,100
+الارتفاع يتم تقيمه في درجة سلسلة ولكن .. هذه بدها
+
+6
+00:00:59,100 --> 00:01:12,120
+شوية ..
+
+7
+00:01:12,120 --> 00:01:17,600
+هذه بتبقى but heat is energy so it is measured in
+
+8
+00:01:17,600 --> 00:01:22,900
+joules الآن ال temperature is measured in ايش؟
+
+9
+00:01:22,900 --> 00:01:28,320
+degrees Celsius أو degrees Fahrenheit أو ايش؟
+
+10
+00:01:28,320 --> 00:01:32,860
+degrees Kelvin  هدول ال measurement تبعت ال
+
+11
+00:01:32,860 --> 00:01:36,980
+temperature ال measurement تبعت ال heat in joules
+
+12
+00:01:36,980 --> 00:01:41,520
+شايفين الحضور والغياب كيف بيعمل؟ كل الزبائن اللي
+
+13
+00:01:41,520 --> 00:01:49,420
+بيبدو مش ييجوا بييجوا بيعرفوا طيب
+
+14
+00:01:49,420 --> 00:01:54,340
+to calculate the amount of energy needed to raise
+
+15
+00:01:54,340 --> 00:01:56,140
+the temperature of a substance
+
+16
+00:01:59,250 --> 00:02:04,530
+to calculate the amount of energy needed to raise
+
+17
+00:02:04,530 --> 00:02:08,070
+the temperature of a substance you need the
+
+18
+00:02:08,070 --> 00:02:11,330
+specific heat capacity you need to know the mass
+
+19
+00:02:11,330 --> 00:02:14,990
+of the substance being heated عادة لو بده أحسب قد
+
+20
+00:02:14,990 --> 00:02:19,210
+إيش energy لأي شيء بده أعرف قد إيش الوزن
+
+21
+00:02:19,210 --> 00:02:24,220
+تبع الحاجة اللي بدي .. بدي أسخنها و بدي أعرف معامل
+
+22
+00:02:24,220 --> 00:02:28,820
+التمدد الحراري تبعها عشان أعرف قد إيش بتستهلك فهذا
+
+23
+00:02:28,820 --> 00:02:32,480
+اللي بنحكي فيه you need to know the mass of the
+
+24
+00:02:32,480 --> 00:02:35,880
+substance being heated and also the specific heat
+
+25
+00:02:35,880 --> 00:02:39,540
+capacity in other words the amount of energy in
+
+26
+00:02:39,540 --> 00:02:42,540
+joules required to raise the temperature of one
+
+27
+00:02:42,540 --> 00:02:47,080
+kilogram of a substance by one degree Celsius يعني
+
+28
+00:02:47,960 --> 00:02:52,900
+إذا عندي .. إذا عندي ال .. ال .. الوزن تبع المادة
+
+29
+00:02:52,900 --> 00:02:57,840
+باجي بتطلع عليها قداش هيدي بتاخد لأعمى ال raising
+
+30
+00:02:57,840 --> 00:03:04,280
+لهدي المادة one degree Celsius لكل
+
+31
+00:03:04,280 --> 00:03:07,940
+kilogram بعدها الوزن الموجود بضربه في المعامل هي
+
+32
+00:03:07,940 --> 00:03:12,260
+بيعطيني قداش ال .. ال .. ال .. ال heat ال required
+
+33
+00:03:12,260 --> 00:03:17,300
+أيوة قداش ال heat requirement للمطلوبة
+
+34
+00:03:19,630 --> 00:03:23,770
+what happens when substances changing states
+
+35
+00:03:23,770 --> 00:03:27,090
+بتعرفوا ال state of the substance في عندي three
+
+36
+00:03:27,090 --> 00:03:32,530
+stages مظبوط أو three states ايوة كل خبرة فيها
+
+37
+00:03:32,530 --> 00:03:35,670
+خدتوها في الفيزياء وخدتوها مش عارف في أكثر من
+
+38
+00:03:35,670 --> 00:03:39,810
+المادة will heat energy is needed to make a solid
+
+39
+00:03:39,810 --> 00:03:45,230
+melt and become a liquid ال solid melt هنا في I
+
+40
+00:03:45,230 --> 00:03:52,120
+طائرة ال solid melt اللي هي يعني في حاجة مادة solid
+
+41
+00:03:52,120 --> 00:03:57,240
+بدي أعملها liquid بدي أحولها ل state تانية it's
+
+42
+00:03:57,240 --> 00:04:01,340
+also needed to turn liquid into vapor اللي هو ايش
+
+43
+00:04:01,340 --> 00:04:07,100
+اللي هي مادة غازية من مادة سائلة لمادة غازية it
+
+44
+00:04:07,100 --> 00:04:11,380
+takes energy to make a liquid boil so that وهي
+
+45
+00:04:11,380 --> 00:04:18,640
+تتبخر وتتحول لغاز فهي ايش بيصيرلها؟ بيصيرلها تبخر
+
+46
+00:04:18,640 --> 00:04:26,480
+تتحول لغاز That's because melting and evaporation
+
+47
+00:04:26,480 --> 00:04:32,050
+are endothermic processes that means they take a heat
+
+48
+00:04:32,050 --> 00:04:35,550
+energy they need to observe heat from a heat
+
+49
+00:04:35,550 --> 00:04:40,150
+source such as a flame يعني بتاخد حرارة الحرارة
+
+50
+00:04:40,150 --> 00:04:48,090
+بتيجي عادة من ايش؟ أبسط حاجة من لهب أو حاجة شعلة
+
+51
+00:04:48,090 --> 00:04:52,900
+من شعلة ال flame لهب أو شعلة and it's the opposite
+
+52
+00:04:52,900 --> 00:05:00,180
+when a substance cools لما برضه بدي مادة حاجة
+
+53
+00:05:00,180 --> 00:05:07,240
+بتعطيني برودة في هذا المجال as
+
+54
+00:05:07,240 --> 00:05:13,870
+gas condense يعني لما الجاز ايش بيصير فيه بتكتف to
+
+55
+00:05:13,870 --> 00:05:18,310
+.. to .. condense يتكتف to become a liquid or a
+
+56
+00:05:18,310 --> 00:05:21,470
+liquid solidified to become a solid يعني لو جيت
+
+57
+00:05:21,470 --> 00:05:25,810
+أنا حاطط أي مادة سائلة وعرضتها لدرجة برودة ايش
+
+58
+00:05:25,810 --> 00:05:32,010
+بتصير؟ بتتجمد وبتصير على شكل مادة مثلا المي بتصير
+
+59
+00:05:32,010 --> 00:05:37,590
+زي التلج ال .. الزيت بتتحول لسمنة وممكن يتحول
+
+60
+00:05:37,590 --> 00:05:43,110
+لقوالب أي حاجة بتتعرضيها بتصير ايش مادة
+
+61
+00:05:47,230 --> 00:05:52,050
+العدد من الهواتف التي تم تجهيزها أو تجهيزها بقيمة
+
+62
+00:05:52,050 --> 00:05:57,810
+صلبة بدي .. يعني خلّيني أقول بدي أحولها من مادة
+
+63
+00:05:57,810 --> 00:06:03,750
+صلبة أو غازية لمادة سائلة .. لسائلة أو غازية، ايش
+
+64
+00:06:03,750 --> 00:06:08,570
+بدي أعمل؟ بدي أعطيها حرارة، صح؟ ولما أنا بدي
+
+65
+00:06:08,570 --> 00:06:12,950
+أحولها العكس، ايش بدي آخذ؟ بدي أمطص الحرارة عملية
+
+66
+00:06:12,950 --> 00:06:17,310
+emitted، اللي هي ايش؟ اللي هي بتطلع المادة حرارة،
+
+67
+00:06:17,310 --> 00:06:22,480
+يعني ال .. الضوء هذا ايش بيعمل؟ emitting photons
+
+68
+00:06:22,480 --> 00:06:27,260
+يعني بيطلع فوتونات ال element ال observe المادة
+
+69
+00:06:27,260 --> 00:06:31,080
+الصلبة البيضة ايش بتعمل بتعكس المادة الصلبة ايش
+
+70
+00:06:31,080 --> 00:06:36,540
+بتعمل observe ايش بتصير انها بتمطص يعني observe
+
+71
+00:06:36,540 --> 00:06:41,260
+اللي هي امتصاص بتمطص هذه الهاي فإذا لما حاجة بدها
+
+72
+00:06:41,260 --> 00:06:45,500
+تتحول بدها تخزن، حاجة بد .. يعني بدها .. حاجة بدها
+
+73
+00:06:45,500 --> 00:06:49,760
+تتحول .. بدها تطلع الحرارة تبحر، ايش بتعمل؟ emit،
+
+74
+00:06:49,760 --> 00:06:55,320
+emit يعني يطلق observe يعني ايش يمطص هذا اللي
+
+75
+00:06:55,320 --> 00:06:58,620
+بنسويه while a substance changes states in joules
+
+76
+00:06:58,620 --> 00:07:04,160
+per kilogram is called late latent heat عملية هاي
+
+77
+00:07:04,160 --> 00:07:09,760
+ايش اللي بنسميها latent heat عملية سواء الامتصاص
+
+78
+00:07:09,760 --> 00:07:16,560
+أو عملية الإشعاع هذه بنسميها latent heat اللي هو
+
+79
+00:07:16,560 --> 00:07:21,190
+ال heat المتنقل during melting it's called latent
+
+80
+00:07:21,190 --> 00:07:26,370
+heat of fusion لما عملية ال melting سمنا ايش
+
+81
+00:07:26,370 --> 00:07:33,450
+latent heat of fusion and during vaporizing
+
+82
+00:07:33,450 --> 00:07:38,610
+it's called latent heat of vaporization في عندي
+
+83
+00:07:38,610 --> 00:07:44,090
+latent heat of vaporization هد بتحول .. تحويل لغاز
+
+84
+00:07:44,090 --> 00:07:51,450
+latent heat of fusion هد في عملية تحويل لمادة سائلة
+
+85
+00:07:51,450 --> 00:07:56,270
+كويس هاي two terms اللى عندي الباقي المصطلحات اللي
+
+86
+00:07:56,270 --> 00:08:00,330
+مرت عليكم تقريبا عارفين أنتو كلهيتها
+
+87
+00:08:02,760 --> 00:08:05,940
+الـ heat transfer to help understand the transfer
+
+88
+00:08:05,940 --> 00:08:10,760
+homes provide everyday examples في البيوت بتشوفوا
+
+89
+00:08:10,760 --> 00:08:16,420
+أمثلة متعددة لكيف انتقال الحرارة ال heating system
+
+90
+00:08:16,420 --> 00:08:21,620
+in homes often have electric convector heaters
+
+91
+00:08:21,620 --> 00:08:26,160
+عادة خلينا نقول البيوت نحنا الجو اللي عندنا نوعا
+
+92
+00:08:26,160 --> 00:08:32,510
+ما معتدل ففيش عندنا تدفئة بشكل أساسي تدفئة مركزية
+
+93
+00:08:32,510 --> 00:08:36,490
+أو تدفئة للبيوت عندنا شوية صارت الموديل دخل عندنا
+
+94
+00:08:36,490 --> 00:08:40,810
+التبريد مظبوط ال air conditioning دخل عندها بس
+
+95
+00:08:40,810 --> 00:08:46,900
+التدفئة لساتها مش كتير عندنا موجودة بس التقنية
+
+96
+00:08:46,900 --> 00:08:50,700
+واحدة لا اثنتين، يعني ال techniques واحد في هذا
+
+97
+00:08:50,700 --> 00:08:55,880
+المجال these heat .. يعني هنا ال electric .. ال
+
+98
+00:08:55,880 --> 00:08:58,280
+heating system in homes often have electric
+
+99
+00:08:58,280 --> 00:09:02,660
+convectors .. heaters these heat .. heat the air
+
+100
+00:09:02,660 --> 00:09:05,660
+and make it circulate عادة ال air condition زي ما
+
+101
+00:09:05,660 --> 00:09:10,420
+بتسوي .. لو أنا عندي جو بارد ايش بتعمل؟ بتسخن
+
+102
+00:09:10,420 --> 00:09:14,560
+الهواء وبتخليه يدور في ال .. في ال .. في ال .. في
+
+103
+00:09:14,560 --> 00:09:18,610
+البيت هذه احدى الطرق اللي بتنعمل فيها تسخين الهواء
+
+104
+00:09:18,610 --> 00:09:21,950
+وعملية انه يدور في الغرفة هي بتسحب الهواء اللي
+
+105
+00:09:21,950 --> 00:09:26,030
+موجود وبتعيد تسخينه وبتخليه يعمل أو عملية
+
+106
+00:09:26,030 --> 00:09:29,970
+التبريد ايش بتسوي بتبرد الهواء وتدفع برا وبتاخد
+
+107
+00:09:29,970 --> 00:09:38,260
+الهواء السخون تاني عشان يتبرد وهو يتحرك في حركة
+
+108
+00:09:38,260 --> 00:09:44,080
+أولا ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك
+
+109
+00:09:44,080 --> 00:09:45,100
+ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم
+
+110
+00:09:45,100 --> 00:09:45,260
+ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم
+
+111
+00:09:45,260 --> 00:09:46,560
+تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك
+
+112
+00:09:46,560 --> 00:09:46,820
+ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم
+
+113
+00:09:46,820 --> 00:09:51,460
+تتحرك ثم تتحرك ثم
+
+114
+00:09:51,460 --> 00:09:56,780
+تتحرك اللي أنا باخد الهواء البارد أو الهواء السخن و
+
+115
+00:09:56,780 --> 00:10:01,580
+بعكس وأضعه وبعدين بطلقه تاني هذا ال circle
+
+116
+00:10:01,580 --> 00:10:05,080
+الدائرة هاي بتساوي فيها فعملية التبريد أنا باخد
+
+117
+00:10:05,080 --> 00:10:10,790
+الهواء السخن بعمله تبريد وبَرجعه تاني الآن في عملية
+
+118
+00:10:10,790 --> 00:10:16,790
+التدفئة باخد الهواء البارد وبسخنه وبَرجعه تاني
+
+119
+00:10:16,790 --> 00:10:20,730
+على شكل الهواء سخن فبتصير تدفئة أو بتصير تبريد
+
+120
+00:10:20,730 --> 00:10:26,450
+للمكان الموجود this is called convection where
+
+121
+00:10:26,450 --> 00:10:30,390
+warm gas or liquid moves around and dissipate heat
+
+122
+00:10:30,390 --> 00:10:35,130
+transferring it to the rest of the gas or the
+
+123
+00:10:35,130 --> 00:10:38,890
+liquid الآن هذه احدى الطرق في طرق تانية ايش بتعمل
+
+124
+00:10:39,970 --> 00:10:44,770
+تاخد ميه تشوفه أنا بيه بالغاز اللي في البيت، حدا
+
+125
+00:10:44,770 --> 00:10:50,410
+فيكم شافها، ايش بتبقى شكلها؟ الآن لو أنت عندك مش
+
+126
+00:10:50,410 --> 00:10:57,070
+.. الجرة مش مشبوكة مباشرة على الفرن أو على الغاز
+
+127
+00:10:57,070 --> 00:11:01,010
+اللي أنت فيها، بتبقى مثلاً تحت و أنت عاملة خط، الخط
+
+128
+00:11:01,010 --> 00:11:06,820
+إيش نوعه؟ نحاسي صح؟ عادة إيش بيسووا برا؟ بيعملوا خط
+
+129
+00:11:06,820 --> 00:11:12,260
+نحاس هذا للتدفئة، هذا التدفئة عساس التدفئة ال air
+
+130
+00:11:12,260 --> 00:11:16,600
+conditioning إيش بتعمل في الرطوبة في الجو؟ بتغيرها
+
+131
+00:11:17,340 --> 00:11:20,660
+بتصير فيه نوعاً ما جفاف فإنت في ال .. في البيوت
+
+132
+00:11:20,660 --> 00:11:23,860
+اللي بدها تستخدمه لازم إيش تعمل؟ في عندها
+
+133
+00:11:23,860 --> 00:11:29,360
+humidifier اللي هي حاجة بتطلق رطوبة في الجو عشان
+
+134
+00:11:29,360 --> 00:11:33,400
+تحافظ على درجة معينة من الرطوبة، الآن لو أنا أتخلص
+
+135
+00:11:33,400 --> 00:11:38,510
+من هذه المشكلة إيش بعمل؟ بعمل التدفئة في التدفئة
+
+136
+00:11:38,510 --> 00:11:43,050
+الخصوصية بستخدمش الهواء اللي مسخن باجي بعمل
+
+137
+00:11:43,050 --> 00:11:47,610
+أنابيب نحاسية و بلفها حوالين البيت و بدخل فيها مية
+
+138
+00:11:47,610 --> 00:11:52,330
+سخنة و بسوي لها circulation هذا التدفئة الميزة
+
+139
+00:11:52,330 --> 00:11:57,230
+تبعها بتأثرش على الرطوبة في الجو بتغيرهاش فإنت
+
+140
+00:11:57,230 --> 00:12:02,350
+بتعيش ببيئة نوعاً ما طبيعية، هذه بتختلف عن رطوبة
+
+141
+00:12:02,350 --> 00:12:06,910
+الاش .. الجو اللي هي ال .. الهواء نأخذه و نعمله و 
+
+142
+00:12:06,910 --> 00:12:10,170
+نشتغل عليه طيب
+
+143
+00:12:11,520 --> 00:12:14,620
+Alternatively, the heating system in a home may
+
+144
+00:12:14,620 --> 00:12:17,880
+circulate hot water through a radiator. هذه
+
+145
+00:12:17,880 --> 00:12:22,420
+بنعملها the radiators act as a heat exchanger
+
+146
+00:12:22,420 --> 00:12:28,060
+devices that transfer heat in this case from the
+
+147
+00:12:28,060 --> 00:12:34,500
+hot water inside to the cooler air outside الآن
+
+148
+00:12:34,500 --> 00:12:38,570
+هذه بتشوفوها في السيارات الآن السيارة يمكن تعرفوا ال
+
+149
+00:12:38,570 --> 00:12:41,730
+motor السيارة و هو ماجي إيش بيصير له؟ تبقى درجة
+
+150
+00:12:41,730 --> 00:12:44,970
+حرارته كيف؟ عالية عالية يعني لو جيت و حطيت إيدك عليه
+
+151
+00:12:44,970 --> 00:12:48,230
+على طول تنحرق إيدك في هاي كلبسة بتجي تتخبى تحت
+
+152
+00:12:48,230 --> 00:12:54,940
+السيارة في الشتاء بتجي تتخبى تحت السيارة خفيفة الآن
+
+153
+00:12:54,940 --> 00:13:00,860
+إيش بنعمل؟ فيها cooling system و عملية ال cooling
+
+154
+00:13:00,860 --> 00:13:03,600
+إيش بتمر؟ في عندهم الجهاز هذا اللي بيسموه ال
+
+155
+00:13:03,600 --> 00:13:07,520
+radiator إيش هذا بتدخل فيه؟ بتدخل المية و بتلف على
+
+156
+00:13:07,520 --> 00:13:12,740
+قنابيب الآن حوالينها دي في مروحة بت .. بت .. بت ..
+
+157
+00:13:12,740 --> 00:13:15,880
+بت .. بتبت هواها الهواها عبر القنابيب اللي بتلف
+
+158
+00:13:15,880 --> 00:13:19,800
+فيها و في حواليها heat sinks إيش ال heat sinks؟
+
+159
+00:13:20,010 --> 00:13:26,130
+حاجات يعني من مادة خلينا نقول معدنية عادة بتطلعها
+
+160
+00:13:26,130 --> 00:13:30,890
+المية هذا إيش بتسوي؟ بتطلع الحرارة على هذه الشرايح
+
+161
+00:13:30,890 --> 00:13:34,450
+لأن المروحة لما تسوي إيش بتعمل؟ بتبرد هذه الشرايح
+
+162
+00:13:34,450 --> 00:13:39,490
+فبتبرد المية اللي موجودة فيها فبتنزل درجة الحرارة
+
+163
+00:13:39,490 --> 00:13:44,650
+تبع ماتور السيارة فهذه موجودة بشكل مباشر بتقدر
+
+164
+00:13:44,650 --> 00:13:51,030
+تشوفوها بشكل أوضح في هذا المجال هذا حدث من نشطة
+
+165
+00:13:51,030 --> 00:13:58,290
+الهيئة المتحركة من مصدر صلب الهيئة
+
+166
+00:13:58,290 --> 00:14:01,110
+المتحركة من مصدر صلب الهيئة المتحركة من مصدر صلب
+
+167
+00:14:01,110 --> 00:14:02,610
+الهيئة المتحركة من مصدر صلب الهيئة المتحركة من
+
+168
+00:14:02,610 --> 00:14:06,110
+مصدر صلب الهيئة المتحركة من مصدر صلب الهيئة
+
+169
+00:14:06,110 --> 00:14:11,680
+المتحركة من مصدر صلب الآن شفت إيش أنا بقول لكم هات؟
+
+170
+00:14:11,680 --> 00:14:16,000
+قلت هذه الحدايات تبع ال radiator الموجودة الشرايح
+
+171
+00:14:16,000 --> 00:14:21,020
+هذه مع المروحة بتطلع .. هي بتطلع .. المروحة بتسرع
+
+172
+00:14:21,020 --> 00:14:26,700
+عملية خروج هذه الطاقة أو ال heat اللي موجود عنده
+
+173
+00:14:26,700 --> 00:14:31,760
+heat is dissipated by convection هذه الكلمة اللي
+
+174
+00:14:31,760 --> 00:14:35,100
+بدنا نطلع عليها the third way that heat is
+
+175
+00:14:35,100 --> 00:14:39,300
+transferred by radiation this is heat that travel
+
+176
+00:14:39,300 --> 00:14:43,520
+as electromagnetic wave عادة كلمة radiation إيش
+
+177
+00:14:43,520 --> 00:14:49,960
+معناتها؟ الإشعاع، الآن كلمة radiator شوية مبالغ فيها
+
+178
+00:14:49,960 --> 00:14:53,820
+عادة لما أتكلم على radiation معناه تعبر
+
+179
+00:14:53,820 --> 00:14:57,680
+electromagnetic waves اللي بنتكلم فيها فهذا اللي
+
+180
+00:14:57,680 --> 00:15:00,380
+بتحكيها this is heat that travels as
+
+181
+00:15:00,380 --> 00:15:03,440
+electromagnetic wave and example is heat from the
+
+182
+00:15:03,440 --> 00:15:08,120
+sun درجة الحرارة بتجي لما الشمس بتجي عبر
+
+183
+00:15:08,120 --> 00:15:11,340
+electromagnetic waves زي ما اتكلمنا هي photons
+
+184
+00:15:11,340 --> 00:15:15,320
+اللي اتصلنا في هذا المجال so that the radiators
+
+185
+00:15:15,320 --> 00:15:19,620
+that circulate water have a misleading name as
+
+186
+00:15:19,620 --> 00:15:23,880
+they don't really function as radiation يعني اسم
+
+187
+00:15:23,880 --> 00:15:31,000
+ال radiator شوية مبالغ فيه من هذه الناحية الآن نجي
+
+188
+00:15:31,000 --> 00:15:35,420
+نطلع عليهم على ال example الأصل هذه الكلمات
+
+189
+00:15:35,420 --> 00:15:40,500
+الموجودة هنا سهلة علينا when temperature of ice is
+
+190
+00:15:40,500 --> 00:15:47,440
+zero degree it changes إيش state it is to water
+
+191
+00:15:47,440 --> 00:15:54,460
+melts to water لأن هي إيش بيصير فيها تتحول لمية
+
+192
+00:15:54,460 --> 00:15:59,200
+يعني الثلج بيصير مية at one hundred degree water
+
+193
+00:16:00,790 --> 00:16:08,670
+boil أو إيش بيصير له؟ بيبخر أو
+
+194
+00:16:08,670 --> 00:16:15,930
+بيغلي و بتحول ل state when water is إيش to zero
+
+195
+00:16:15,930 --> 00:16:23,730
+degree or below it become ice when water cools to
+
+196
+00:16:23,730 --> 00:16:29,050
+zero degree or below and إيش to become ice
+
+197
+00:16:31,490 --> 00:16:36,610
+solidify إيش يعني solidify؟ تتجمد المية تتجمد
+
+198
+00:16:36,610 --> 00:16:44,930
+بتتحول لإيش؟ لثلج it freezes in gas form water is
+
+199
+00:16:44,930 --> 00:16:56,390
+called steam أو vapor أو water vapor يعني يا ابن
+
+200
+00:16:56,390 --> 00:17:01,450
+نسميه steam ال steam اللي هو إيش؟ البخار و عادة هذا
+
+201
+00:17:01,450 --> 00:17:06,510
+يمكن إن شاء الله بتدخلوا بتشوفوا بتدخلوا تخصصات
+
+202
+00:17:06,510 --> 00:17:11,130
+توصلكم لو تروحوا على محطة الكهربا بتلاقوا عندنا
+
+203
+00:17:11,130 --> 00:17:17,040
+فيه بتسمعوا أنتم فيها كام مولد ولا معلومات عامة
+
+204
+00:17:17,040 --> 00:17:25,980
+سفر أربع مولدات بس اللي موجود عندنا مش أربع ستة
+
+205
+00:17:25,980 --> 00:17:31,300
+الآن اثنين بيشتغلوا بيسموهم على الغاز و كل two
+
+206
+00:17:31,300 --> 00:17:34,580
+units اللي هي one unit بتشتغل على إيش؟ على steam
+
+207
+00:17:34,580 --> 00:17:39,740
+لأنه لما يبردوا محطة الكهربا هيبدها إيش؟ تبريد
+
+208
+00:17:39,740 --> 00:17:42,920
+فعملية التبريد بتشوفوا أنتم إذا محدد مرج من عند
+
+209
+00:17:42,920 --> 00:17:49,460
+البحر عقبال مدينة الظهر إيش فيه؟ في هناك حاجة لمحطة
+
+210
+00:17:49,460 --> 00:17:53,060
+توليد الكهربا بياخدوا المي تبعت البحر و بيودوها
+
+211
+00:17:53,060 --> 00:17:57,420
+على المحطة عشان يبردوا فيها إيش؟ التوربينات تبعت
+
+212
+00:17:57,420 --> 00:18:03,080
+اللي بتولد الكهربا فعملية التبريد هذه بتعمل steam
+
+213
+00:18:03,080 --> 00:18:07,760
+ال steam هذا بتستخدموه ليولدوا فيه إيش؟ كهربا
+
+214
+00:18:07,760 --> 00:18:12,820
+زيادة هذا بيسموها ال combined cycle اللي هي .. أيوة
+
+215
+00:18:12,820 --> 00:18:18,160
+فلكل اثنين فيه unit تالتة اللي هي بتعمل توليد
+
+216
+00:18:18,160 --> 00:18:22,760
+بتستخدم البخار اثنين بيستخدموا الديزل أو الغاز و
+
+217
+00:18:22,760 --> 00:18:27,240
+واحدة بتستخدم البخار فعنا بالضبط ستة units اللي
+
+218
+00:18:27,240 --> 00:18:34,460
+موجودة هذه معلومة عامة طيب between one hundred
+
+219
+00:18:34,460 --> 00:18:37,860
+degree Celsius and three hundred seventy four
+
+220
+00:18:37,860 --> 00:18:43,940
+degree water is إيش؟ a vapor because it's below it
+
+221
+00:18:43,940 --> 00:18:50,540
+.. it's .. إيش .. temperature below إيش ..
+
+222
+00:18:50,540 --> 00:18:54,480
+critical .. it's a critical temperature ال
+
+223
+00:18:54,480 --> 00:18:58,240
+critical temperature بتصير إيش بعدها superheated
+
+224
+00:18:58,240 --> 00:19:06,020
+superheated يعني اتوصل لدرجات أنه اتعدى الحاجات
+
+225
+00:19:06,020 --> 00:19:12,130
+هذه extremely hot water vapor is called superheated
+
+226
+00:19:12,130 --> 00:19:21,890
+وصلنا له على طول طيب
+
+227
+00:19:21,890 --> 00:19:25,050
+نبدأ
+
+228
+00:19:25,050 --> 00:19:34,030
+نعمل matching between a liquid pumped onto a
+
+229
+00:19:34,030 --> 00:19:37,450
+work piece that is being machined to stop it
+
+230
+00:19:37,450 --> 00:19:43,040
+overheating is called إيش؟ coolant بتعرفوا هذه في
+
+231
+00:19:43,040 --> 00:19:48,860
+حاجة يمكن .. خلّيني أعطيكم معلومة ثانية الآن ال ..
+
+232
+00:19:48,860 --> 00:19:50,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+233
+00:19:50,300 --> 00:19:50,880
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+234
+00:19:50,880 --> 00:19:51,700
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+235
+00:19:51,700 --> 00:19:54,940
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+236
+00:19:54,940 --> 00:19:55,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+237
+00:19:55,440 --> 00:19:56,740
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+238
+00:19:56,740 --> 00:19:57,000
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+239
+00:19:57,000 --> 00:19:57,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+240
+00:19:57,280 --> 00:20:02,740
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+241
+00:20:02,740 --> 00:20:06,880
+ال .. ال .. ال
+
+242
+00:20:11,020 --> 00:20:13,860
+بيبقوها هذه ممكن اللي حد شاف اللي حد عنده أبوها
+
+243
+00:20:13,860 --> 00:20:17,180
+سيارة و بديحطلها حاجة و بديعزها بجيب هذا المية
+
+244
+00:20:17,180 --> 00:20:22,120
+سائل لونه زي الأخضر أو الأزرق بيحطه في السيارة لل
+
+245
+00:20:22,120 --> 00:20:25,820
+radiator بيحطش مية لإن مية ميتنا بتخرب ال radiator
+
+246
+00:20:25,820 --> 00:20:31,720
+بسرعة طب كم برد فيها شركة الكهربا؟ هي .. هي .. لأ
+
+247
+00:20:31,720 --> 00:20:36,940
+المية الملحمة هي هذه إيش بيصير فيها، هذه اختلاف،
+
+248
+00:20:36,940 --> 00:20:42,760
+محط الكهربا بدهم كميات مية كبيرة جداً، فبيلزمهم وين
+
+249
+00:20:42,760 --> 00:20:46,700
+هذه متوفرة؟ يا في الأنهار يا في البحار، الآن لما
+
+250
+00:20:46,700 --> 00:20:51,560
+تحطوها إيش بيصير؟ بتتبخر هذه المية، المية لما 
+
+251
+00:20:51,560 --> 00:20:56,130
+تتبخر إيش بتصير؟الـ .. بيضل الملح أيوة بيضل الملح و
+
+252
+00:20:56,130 --> 00:21:01,430
+بعدين المية اللي بتطلع .. بتطلع مية مش يعني مية
+
+253
+00:21:01,430 --> 00:21:06,050
+بحر بيصير مية عادية، فهم إيش بيسووا عشان ما يضروش
+
+254
+00:21:06,050 --> 00:21:10,830
+البحر، بيرجعوا من الملح هذا بخلطوه ثاني و بيرجعوا
+
+255
+00:21:10,830 --> 00:21:16,090
+نسبة مية ملح عشان الأسماك و البحر ما تتأثرش، واحنا 
+
+256
+00:21:16,090 --> 00:21:21,350
+محافظين على البيئة و بنصف بعد غزة فيه، طيب
+
+257
+00:21:22,380 --> 00:21:25,480
+the form of heat transfer that occurs with
+
+258
+00:21:25,480 --> 00:21:31,080
+infrared heat, a form of electromagnetic wave, is
+
+259
+00:21:31,080 --> 00:21:36,260
+called إيش؟ radiation، حد ما تطلع infrared أنت
+
+260
+00:21:36,260 --> 00:21:44,180
+بتعرف إيش الـ infrared؟ الأشعة إيش؟ ultraviolet و
+
+261
+00:21:44,180 --> 00:21:48,830
+infrared، هدول لازم تحفظوهم، أخدتهم بالفيزياء الـ
+
+262
+00:21:48,830 --> 00:21:53,230
+Infrared التحت الحمراء والـ Ultraviolet فوق البنفسجية
+
+263
+00:21:53,230 --> 00:21:58,550
+بنفسه جيه، مظبوط؟ هدول لازم نغرسوا معاكم، فهذه is
+
+264
+00:21:58,550 --> 00:22:03,550
+form of radiation، الـ metal fins اللي هي الـ
+
+265
+00:22:03,550 --> 00:22:07,010
+plates اللي حكينا عندها، هذي إيش؟ around air
+
+266
+00:22:07,010 --> 00:22:10,230
+cooled engine intended to maximize the surface
+
+267
+00:22:10,230 --> 00:22:14,290
+area of the hot engine that is in contact with the
+
+268
+00:22:14,290 --> 00:22:19,190
+cooler air are designed to act as إيش؟ heat sink
+
+269
+00:22:19,190 --> 00:22:23,750
+قلتلكم هذا إيش بتسوي؟ حكيناكوا يا هاد عبارة عن
+
+270
+00:22:23,750 --> 00:22:27,550
+heat sink، و الـ heat sink إيش بوسع المساحة اللي
+
+271
+00:22:27,550 --> 00:22:32,190
+بتشبك عليها، هاد بكرا دي حد فيكوا تخصص كهربا بعض
+
+272
+00:22:32,190 --> 00:22:37,430
+القطع اللي بتسخن بسرعة بنحطلها heat sink، قطعة
+
+273
+00:22:37,430 --> 00:22:42,900
+معدنية حواليها توسع المجال تبع إطلاق الحرارة في
+
+274
+00:22:42,900 --> 00:22:46,160
+الجو، وهذا ده حدث فيك وفتح الكمبيوتر بيلاقوها
+
+275
+00:22:46,160 --> 00:22:51,680
+موجودة جوا الكمبيوتر، هذه القطع هدفها إيش تعمل
+
+276
+00:22:51,680 --> 00:22:55,600
+إطلاق للحرارة بدل ما هي القطع الصغيرة اللي حالها
+
+277
+00:22:55,600 --> 00:23:00,440
+بتطلق بنلحمها بهذه القطع، بتوصل بتصير الحرارة بشكل
+
+278
+00:23:00,440 --> 00:23:10,590
+أكبر وأسرع، heat sink heat heat exchanger وهي برضه
+
+279
+00:23:10,590 --> 00:23:18,190
+بتقدر تعمليها heat sink لأن هي act as both، الآن
+
+280
+00:23:18,190 --> 00:23:22,210
+الوراها إيش بنتكلم، take dense internal walls
+
+281
+00:23:22,210 --> 00:23:25,150
+inside an energy efficient house which are
+
+282
+00:23:25,150 --> 00:23:28,530
+intended to absorb heat energy during the day and
+
+283
+00:23:28,530 --> 00:23:32,470
+store some of it to be emitted at night, function
+
+284
+00:23:32,470 --> 00:23:40,910
+as هي .. هذا الـ heat exchanger الأصل، ليش؟ لأن أنا
+
+285
+00:23:40,910 --> 00:23:45,490
+باخد في الليل، في النهار، و بطلق في الليل، طلعوا
+
+286
+00:23:45,490 --> 00:23:50,270
+عندنا البيوت، البيوت ده حد فيكم لاحظ حاجة واحدة،
+
+287
+00:23:50,270 --> 00:23:54,870
+إيش بنلاحظ؟ الحرارة تبعتنا، البيت، دايما أسأل أختي
+
+288
+00:23:54,870 --> 00:23:59,070
+أختي بيقولك البيت في الليل، يعني في النهار، أقعد
+
+289
+00:23:59,070 --> 00:24:07,120
+تحت فيه شجرة، مش فيه بيت، ليش؟ الشجرة بتمتص حرارة،
+
+290
+00:24:07,120 --> 00:24:11,960
+الآن البيوت بتمتص الحرارة و في الليل بتصير تطلق
+
+291
+00:24:11,960 --> 00:24:16,320
+هذه الحرارة عشان هيك في الليل بتلاقي .. لأ البيت
+
+292
+00:24:16,320 --> 00:24:21,060
+بيضلوا محافظين على الحرارة لـ .. لآخر الليل تقريبا،
+
+293
+00:24:21,060 --> 00:24:25,040
+بتصل كل هايم، بس تطلع برا بتلاقي الجو أبرد بكثير
+
+294
+00:24:25,040 --> 00:24:30,920
+من جوا الهايم، فهي هذه إيش بتصير؟ يعني هي الـ heat
+
+295
+00:24:30,920 --> 00:24:36,460
+sink إيش بيعمل؟ هو يعني مكان لإشعاع على الحرارة
+
+296
+00:24:36,460 --> 00:24:41,310
+هذا الـ heat sink، هذا الـ engineering term تبعها، طيب
+
+297
+00:24:41,310 --> 00:24:45,470
+the soil and rocks on the surface of air remain
+
+298
+00:24:45,470 --> 00:24:48,590
+warm at night and summer due to the principle of
+
+299
+00:24:48,590 --> 00:24:53,330
+إيش؟ thermal inertia اللي أحنا بنحكي عنها لأن هاد
+
+300
+00:24:53,330 --> 00:24:58,330
+إيش بتضلها تمتص وبعدها الإطلاق بتبقى خفيف جدا في
+
+301
+00:24:58,330 --> 00:25:06,990
+هذا المجال ولو إن هاد تلاتة وأربعة فيهم شوية خربطة
+
+302
+00:25:06,990 --> 00:25:14,300
+يعني كويس لإنه الـ .. التلاتة بدك تحطيها C، أربعة
+
+303
+00:25:14,300 --> 00:25:20,340
+حطيها E لأن التلاتة الـ heat هذه الـ plate شغلتها
+
+304
+00:25:20,340 --> 00:25:24,120
+إيش act as a heat sink، وهذه بندرسها احنا في
+
+305
+00:25:24,120 --> 00:25:33,240
+الكهربا، طيب circle the correct words من الموجود
+
+306
+00:25:33,240 --> 00:25:36,600
+هنا condensing boilers are becoming increasingly
+
+307
+00:25:36,600 --> 00:25:43,810
+popular in home لأنهم يستخدمون أكثر من 40% أقل من
+
+308
+00:25:43,810 --> 00:25:45,050
+الغاز التقليدي 
+
+309
+00:25:45,050 --> 00:25:45,610
+التقليدي 
+
+310
+00:25:45,610 --> 00:25:48,430
+التقليدي
+
+311
+00:25:48,430 --> 00:25:50,170
+التقليدي
+
+312
+00:25:50,170 --> 00:25:51,810
+التقليدي
+
+313
+00:25:51,810 --> 00:25:51,910
+التقليدي
+
+314
+00:25:51,910 --> 00:25:55,530
+التقليدي
+
+315
+00:25:55,530 --> 00:25:59,530
+التقليدي
+
+316
+00:25:59,530 --> 00:26:04,830
+التقليدي
+
+317
+00:26:04,830 --> 00:26:13,840
+التقليدي، لأن هذا إيش بيحول من سائل لغاز؟ الـ process
+
+318
+00:26:13,840 --> 00:26:20,280
+endothermic ولا exothermic؟ لأن هذا إيش بتعمل؟
+
+319
+00:26:20,280 --> 00:26:26,120
+endothermic بتاخد، exothermic بتطلع، وهذه بتطلعها،
+
+320
+00:26:26,120 --> 00:26:30,510
+this mean heat is observed ولا emitted؟ emitted
+
+321
+00:26:30,510 --> 00:26:34,350
+لأنها بتطلع and can thus be circulated ولا
+
+322
+00:26:34,350 --> 00:26:38,310
+conducted circulated by the water inside the
+
+323
+00:26:38,310 --> 00:26:42,630
+radiator in the home, a condensing boiler per
+
+324
+00:26:42,630 --> 00:26:49,150
+natural gas to لأن hydrocarbon fuel اللي هو الـ
+
+325
+00:26:49,150 --> 00:26:52,650
+natural gas اللي هو الغاز اللي عندنا to heat or
+
+326
+00:26:52,650 --> 00:26:56,290
+cool water, heat water just like a conventional
+
+327
+00:26:56,290 --> 00:26:59,330
+boiler, however it achieve greater efficiency by
+
+328
+00:26:59,330 --> 00:27:03,830
+recovering energy from water vapor، وهذه بتلاحظوها
+
+329
+00:27:03,830 --> 00:27:08,830
+يمكن حاليا بدت تنتشر في غزة، إيش احنا عندنا تسخين
+
+330
+00:27:08,830 --> 00:27:14,900
+المية بتتم عبر إيش في غزة الغالبية .. يا .. يا
+
+331
+00:27:14,900 --> 00:27:20,060
+السخانات الشمسية يا إما سخانات الكهربا في في غزة
+
+332
+00:27:20,060 --> 00:27:27,680
+الحين صارت سخانات غاز على الغاز و safe و كويسة و
+
+333
+00:27:27,680 --> 00:27:32,240
+بتحسش أنه بتطلع حرارة زي الموجود و بتعطيك نفس
+
+334
+00:27:32,240 --> 00:27:38,660
+المفعول، أنا عند واحد فـ .. فـ .. كويس كتير يعني من
+
+335
+00:27:38,660 --> 00:27:43,250
+.. ما هي في الشتاء الشمس بتعطيكيشي الدرجة اللي بدك
+
+336
+00:27:43,250 --> 00:27:49,170
+إياها، فهذه للشتاء حل .. حل كويس هذا اللي عندي
+
+337
+00:27:49,170 --> 00:27:57,610
+سنتين الحين، فوضع كويس، طيب this is a .. this is a
+
+338
+00:27:57,610 --> 00:28:00,990
+present in the hot waste gas that produced when
+
+339
+00:28:00,990 --> 00:28:04,410
+natural gas is burned in a traditional boiler، ده
+
+340
+00:28:04,410 --> 00:28:08,430
+heat ولا ده temperature energy؟ من حد ما تلاحظ كلمة
+
+341
+00:28:08,430 --> 00:28:14,090
+energy بروح معها إيش؟ heat from the gas which is
+
+342
+00:28:14,090 --> 00:28:20,550
+at 180 degree من حد ما تشوفي رقم بروح معها حد إيش؟
+
+343
+00:28:20,550 --> 00:28:26,280
+degrees Celsius، معناته temperature، 180 درجة أو أكثر
+
+344
+00:28:26,280 --> 00:28:33,060
+ستكون محطمة أو محطمة في الهواء، محطمة لأنها بتطلع
+
+345
+00:28:33,060 --> 00:28:39,440
+هنا By conduction ولا convection؟ convection and
+
+346
+00:28:39,440 --> 00:28:43,260
+the water vapor within it would condense in the
+
+347
+00:28:43,260 --> 00:28:48,190
+outside air but a condensing boiler boiler the hot
+
+348
+00:28:48,190 --> 00:28:52,330
+gas passes through a heat or temperature exchanger
+
+349
+00:28:52,330 --> 00:28:56,370
+مر عليكم قبل شوية اللي هو الـ heat exchanger، this
+
+350
+00:28:56,370 --> 00:29:00,350
+allow heat from the gas to be observed ولا omitted
+
+351
+00:29:00,350 --> 00:29:05,370
+by cool water، observe من حد ما تشوفيه cool water
+
+352
+00:29:05,370 --> 00:29:10,360
+بدي آخذ الذي يرجع إلى النافذة بعد المرور من
+
+353
+00:29:10,360 --> 00:29:16,720
+النافذات في المنزل، الهيئة
+
+354
+00:29:16,720 --> 00:29:17,440
+الهيئة
+
+355
+00:29:17,440 --> 00:29:19,240
+الهيئة
+
+356
+00:29:19,240 --> 00:29:19,860
+الهيئة
+
+357
+00:29:19,860 --> 00:29:21,560
+الهيئة
+
+358
+00:29:21,560 --> 00:29:29,960
+الهيئة
+
+359
+00:29:29,960 --> 00:29:34,240
+الهيئة
+
+360
+00:29:34,240 --> 00:29:41,260
+الهـ Solidify بدي يتحول لمادة صلبة، Condensed بدي
+
+361
+00:29:41,260 --> 00:29:46,300
+يتحول لمادة سائلة، و Vapor اللي هو الغاز، بنروحش من
+
+362
+00:29:46,300 --> 00:29:54,580
+الغاز للصلب، بنروح من الغاز لإيش للسائل، and it is
+
+363
+00:29:54,580 --> 00:29:57,920
+the process that enables significant amount of
+
+364
+00:29:57,920 --> 00:30:00,480
+heat to be transferred due to the principle of
+
+365
+00:30:00,480 --> 00:30:02,580
+latent heat 
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/KGbm6t1qbLk_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/KGbm6t1qbLk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4f3751a5f260ae4f6046154c8788ef13a45aa31f
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/KGbm6t1qbLk_raw.srt
@@ -0,0 +1,1480 @@
+1
+00:00:20,700 --> 00:00:27,460
+السلام عليكم اليوم سنقوم بتغطية 2 قصة قصة 36 تتكلم
+
+2
+00:00:27,460 --> 00:00:37,280
+عن النار وتمبراتور نار وتمبراتور نحن
+
+3
+00:00:37,280 --> 00:00:43,340
+سنتكلم عن تغيير التمبراتور وشكل الأمور نار تتغطى
+
+4
+00:00:46,420 --> 00:00:50,660
+التغيير من الارتفاع والظلالة كما تعلمين التغيير من
+
+5
+00:00:50,660 --> 00:00:59,100
+الارتفاع يتم تقيمه في درجة سلسلة ولكن .. هذه بدها
+
+6
+00:00:59,100 --> 00:01:12,120
+شوية ..
+
+7
+00:01:12,120 --> 00:01:17,600
+هذه بتبقىbut heat is energy so it is measured in
+
+8
+00:01:17,600 --> 00:01:22,900
+joules الان ال temperature is measured in ايش؟
+
+9
+00:01:22,900 --> 00:01:28,320
+degrees Celsius او degrees Fahrenheit او ايش؟
+
+10
+00:01:28,320 --> 00:01:32,860
+degrees Kelvin هدولة ال measurement تبعت ال
+
+11
+00:01:32,860 --> 00:01:36,980
+temperature ال measurement تبعت ال heat in joules
+
+12
+00:01:36,980 --> 00:01:41,520
+شايفين الحضور الغياب كيف بيعمل؟كل الزبائن اللي
+
+13
+00:01:41,520 --> 00:01:49,420
+بيبدو مش ييجوا بييجوا بيعرفوا طيب
+
+14
+00:01:49,420 --> 00:01:54,340
+to calculate the amount of energy needed to raise
+
+15
+00:01:54,340 --> 00:01:56,140
+the temperature of a substance
+
+16
+00:01:59,250 --> 00:02:04,530
+to calculate the amount of energy needed to raise
+
+17
+00:02:04,530 --> 00:02:08,070
+the temperature of a substance you need the
+
+18
+00:02:08,070 --> 00:02:11,330
+specific heat capacity you need to know the mass
+
+19
+00:02:11,330 --> 00:02:14,990
+of the substance being heated عادة لو بده أحسب قد
+
+20
+00:02:14,990 --> 00:02:19,210
+ياش energy لأي شيء بده أعرف قد ياش قد ياش الوزن
+
+21
+00:02:19,210 --> 00:02:24,220
+تبعالحاجة اللي بدي .. بدي أسخنها و بدي أعرف معامل
+
+22
+00:02:24,220 --> 00:02:28,820
+التمدد الحراري تبعها عشان أعرف قد إيش بتستهلك فهذا
+
+23
+00:02:28,820 --> 00:02:32,480
+اللي بنحكي فيه you need to know the mass of the
+
+24
+00:02:32,480 --> 00:02:35,880
+substance being heated and also the specific heat
+
+25
+00:02:35,880 --> 00:02:39,540
+capacity in other words the amount of energy in
+
+26
+00:02:39,540 --> 00:02:42,540
+joules required to raise the temperature of one
+
+27
+00:02:42,540 --> 00:02:47,080
+kilogram of a substance by one degree Celsius يعني
+
+28
+00:02:47,960 --> 00:02:52,900
+إذا عندى .. إذا عندى ال .. ال .. الوزن تبع المادة
+
+29
+00:02:52,900 --> 00:02:57,840
+باجي بتطلع عليها قداش هدى بتاخد لأعمى ال raising
+
+30
+00:02:57,840 --> 00:03:04,280
+لهدى المادة one degree Celsius لكل
+
+31
+00:03:04,280 --> 00:03:07,940
+kilogram بعدها الوزن الموجود بضربه في المعامل هى
+
+32
+00:03:07,940 --> 00:03:12,260
+بيعطينى قداش ال .. ال .. ال .. ال heat ال required
+
+33
+00:03:12,260 --> 00:03:17,300
+أيوة قداش ال heat requirement للمطلوبة
+
+34
+00:03:19,630 --> 00:03:23,770
+what happens when substances changing states
+
+35
+00:03:23,770 --> 00:03:27,090
+بتعرفوا ال state of the substance في عندى three
+
+36
+00:03:27,090 --> 00:03:32,530
+stages مظبوط او three states ايوة كل خبرة فيها
+
+37
+00:03:32,530 --> 00:03:35,670
+خدتوها في الفيزيا وخدتوها مش عارف في اكتر من
+
+38
+00:03:35,670 --> 00:03:39,810
+المادة will heat energy is needed to make a solid
+
+39
+00:03:39,810 --> 00:03:45,230
+melt and become a liquid ال solid melt هنا في I
+
+40
+00:03:45,230 --> 00:03:52,120
+طائرة ال solid melt اللي هي يعني في حاجةمادة solid
+
+41
+00:03:52,120 --> 00:03:57,240
+بدي اعملها liquid بدي احولها ل state تانية it's
+
+42
+00:03:57,240 --> 00:04:01,340
+also needed to turn liquid into vapor اللي هو ايش
+
+43
+00:04:01,340 --> 00:04:07,100
+اللي هي مادة غازية من مادة سائلة لمادة غازية it
+
+44
+00:04:07,100 --> 00:04:11,380
+takes energy to make a liquid boil so thatوهي
+
+45
+00:04:11,380 --> 00:04:18,640
+تتبخر وتتحول لغاز فهي ايش بيصيرلها؟ بيصيرها تبخر
+
+46
+00:04:18,640 --> 00:04:26,480
+تتحول لغاز That's because melting and evaporation
+
+47
+00:04:26,480 --> 00:04:32,050
+are endothermic processthat means they take a heat
+
+48
+00:04:32,050 --> 00:04:35,550
+energy they need to observe heat from a heat
+
+49
+00:04:35,550 --> 00:04:40,150
+source such as a flame يعني بتاخد حرارة الحرارة
+
+50
+00:04:40,150 --> 00:04:48,090
+بتيجي عادة من إيش؟ أبسط حاجة من لهب أو حاجة شعلة
+
+51
+00:04:48,090 --> 00:04:52,900
+من شعلة ال flame لهب أو شعلةand it's the opposite
+
+52
+00:04:52,900 --> 00:05:00,180
+when a substance cools لما برضه بدي مادة حاجة
+
+53
+00:05:00,180 --> 00:05:07,240
+بتعطيني برودة في هذا المجال as
+
+54
+00:05:07,240 --> 00:05:13,870
+gas condense يعني لما الجاز ايش بيصير فيه بتكتفto
+
+55
+00:05:13,870 --> 00:05:18,310
+.. to .. condense يتكتف to become a liquid or a
+
+56
+00:05:18,310 --> 00:05:21,470
+liquid solidified to become a solid يعني لو جيت
+
+57
+00:05:21,470 --> 00:05:25,810
+أنا حاطيت أي مادة سائلة و عرضتها لدرجة برودة إيش
+
+58
+00:05:25,810 --> 00:05:32,010
+بتصير؟ بتتجمد و بتصير على شكل مادة مثلا المي بتصير
+
+59
+00:05:32,010 --> 00:05:37,590
+زي التلج ال .. الزيت بتتحول لسمنة و ممكن يتحول
+
+60
+00:05:37,590 --> 00:05:43,110
+لقوالب أي حاجة بتتعرضيها بتصير إيش مادة
+
+61
+00:05:47,230 --> 00:05:52,050
+العدد من الهواتف التي تم تجهيزها أو تجهيزها بقيمة
+
+62
+00:05:52,050 --> 00:05:57,810
+صلبةبدي .. يعني خلّيني أقول بدي أحولها من مادة
+
+63
+00:05:57,810 --> 00:06:03,750
+صلبة أو غازية لمادة سائة .. لسائلة أو غازية، إيش
+
+64
+00:06:03,750 --> 00:06:08,570
+بدي أعمل؟ بدي أعطيها حرارة، صح؟ ولمّا أنا بدي
+
+65
+00:06:08,570 --> 00:06:12,950
+أحولها العكس، إيش بدي أاخد؟ بدي أمطص الحرارة عملية
+
+66
+00:06:12,950 --> 00:06:17,310
+emitted، اللي هي إيش؟ اللي هي بتطلع المادة حرارة،
+
+67
+00:06:17,310 --> 00:06:22,480
+يعني ال .. الضوء هذا إيش بيعمل؟emitting photons
+
+68
+00:06:22,480 --> 00:06:27,260
+يعني بيطلع فوتونات ال element ال observe المادة
+
+69
+00:06:27,260 --> 00:06:31,080
+الصلبة البيضة ايش بتعمل بتعكس المادة الصلبة ايش
+
+70
+00:06:31,080 --> 00:06:36,540
+بتعمل observe ايش بتصير انها بتمطص يعني observe
+
+71
+00:06:36,540 --> 00:06:41,260
+اللي هي امتصاص بتمطص هذهالهاي فأذا لما حاجة بدها
+
+72
+00:06:41,260 --> 00:06:45,500
+تتحول بدها تخزن، حاجة بد .. يعني بدها .. حاجة بدها
+
+73
+00:06:45,500 --> 00:06:49,760
+تتحول .. بدها تطلع الحرارة تبحر، إيش بتعمل؟ emit،
+
+74
+00:06:49,760 --> 00:06:55,320
+emit يعني يطلقobserve يعني إيش يمطص هذا اللي
+
+75
+00:06:55,320 --> 00:06:58,620
+بنسويه while a substance changes states in joules
+
+76
+00:06:58,620 --> 00:07:04,160
+per kilogram is called late latent heat عملية هاي
+
+77
+00:07:04,160 --> 00:07:09,760
+إيش اللي بنسميها latent heat عملية سواء الامتصاص
+
+78
+00:07:09,760 --> 00:07:16,560
+أو عملية الإشعاع هذه بنسميها latent heat اللي هو
+
+79
+00:07:16,560 --> 00:07:21,190
+ال heat المتنقلduring melting it's called latent
+
+80
+00:07:21,190 --> 00:07:26,370
+heat of fusion لما عملية ال melting سمنا ايش
+
+81
+00:07:26,370 --> 00:07:33,450
+latent heat of fusion and during vaporizing
+
+82
+00:07:33,450 --> 00:07:38,610
+it's called latent heat of vaporizationفي عندى
+
+83
+00:07:38,610 --> 00:07:44,090
+Latin heat of vaporization هد بتحول .. تحويل لغاز
+
+84
+00:07:44,090 --> 00:07:51,450
+Latin heat of fusion هد فى عملية تحويل لمادة سائلة
+
+85
+00:07:51,450 --> 00:07:56,270
+كويس هاي two terms اللى عندى الباقى المصطلحات اللى
+
+86
+00:07:56,270 --> 00:08:00,330
+مرت عليكم تقريبا عارفين انتوا كلهيتها
+
+87
+00:08:02,760 --> 00:08:05,940
+الـ heat transfer to help understand the transfer
+
+88
+00:08:05,940 --> 00:08:10,760
+homes provide everyday examples في البيوت بتشوفوا
+
+89
+00:08:10,760 --> 00:08:16,420
+أمثلة متعددة لكيف انتقال الحرارة ال heating system
+
+90
+00:08:16,420 --> 00:08:21,620
+in homes often have electric convector heaters
+
+91
+00:08:21,620 --> 00:08:26,160
+عادة خلينا نقول البيوت نحنا الجو اللي عندنا نوعا
+
+92
+00:08:26,160 --> 00:08:32,510
+ما معتدل ففيش عندناتدفئة بشكل أساسي تدفئة مركزية
+
+93
+00:08:32,510 --> 00:08:36,490
+أو تدفئة للبيوت عندنا شوية صارت الموديل دخل عندنا
+
+94
+00:08:36,490 --> 00:08:40,810
+التبريد مظبوط ال air conditioning دخل عندها بس
+
+95
+00:08:40,810 --> 00:08:46,900
+التدفئة لساتها مش كتير عندنا موجودةبس التقنية
+
+96
+00:08:46,900 --> 00:08:50,700
+واحدة لا تنتين، يعني ال techniques واحد في هذا
+
+97
+00:08:50,700 --> 00:08:55,880
+المجال these heat .. يعني هنا ال electric .. ال
+
+98
+00:08:55,880 --> 00:08:58,280
+heating system in homes often have electric
+
+99
+00:08:58,280 --> 00:09:02,660
+convectors .. heaters these heat .. heat the air
+
+100
+00:09:02,660 --> 00:09:05,660
+and make it circulate عادة ال air condition زي ما
+
+101
+00:09:05,660 --> 00:09:10,420
+بتسوي .. لو أنا عندي جو بارد إيش بتعمل؟ بتسخن
+
+102
+00:09:10,420 --> 00:09:14,560
+الهواء و بتخليه يدور في ال .. في ال .. في ال .. في
+
+103
+00:09:14,560 --> 00:09:18,610
+البيتهذه احدى الطرق اللى بتنعمل فيها تسخين الهواء
+
+104
+00:09:18,610 --> 00:09:21,950
+وعملية انه بدور في الغرفة هي بتسحب الهواء اللى
+
+105
+00:09:21,950 --> 00:09:26,030
+موجود و بتعيد تسخينه و بتخليه يعمل او فعملية
+
+106
+00:09:26,030 --> 00:09:29,970
+التبريد ايش بتسوي بتبرد الهواء و تدفع برا و بتاخد
+
+107
+00:09:29,970 --> 00:09:38,260
+الهواء الصخون تاني عشان يتبردواوهو يتحرك في حركة
+
+108
+00:09:38,260 --> 00:09:44,080
+أولا ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك
+
+109
+00:09:44,080 --> 00:09:45,100
+ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم
+
+110
+00:09:45,100 --> 00:09:45,100
+تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك
+
+111
+00:09:45,100 --> 00:09:45,260
+ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم
+
+112
+00:09:45,260 --> 00:09:46,560
+تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك
+
+113
+00:09:46,560 --> 00:09:46,820
+ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم تتحرك ثم
+
+114
+00:09:46,820 --> 00:09:51,460
+تتحرك ثم تتحرك ثم
+
+115
+00:09:51,460 --> 00:09:56,780
+تتحاللي أنا باخد الهواء البارد أو الهواء السخن و
+
+116
+00:09:56,780 --> 00:10:01,580
+بعكس و أضعه و بعدين بطلقه تاني هذا ال circle
+
+117
+00:10:01,580 --> 00:10:05,080
+الدائرة هاي بتساوي فيها فعملية التبريد أنا باخد
+
+118
+00:10:05,080 --> 00:10:10,790
+الهواء السخن بعمله تبريد و برجعه تانيالان في عملية
+
+119
+00:10:10,790 --> 00:10:16,790
+التدفئة باخد الهواء البارد و بسخنه و برجعه تاني
+
+120
+00:10:16,790 --> 00:10:20,730
+على شكل الهواء سخن فبتصير تدفئة او بتصير تبريد
+
+121
+00:10:20,730 --> 00:10:26,450
+للمكان الموجود this is called convection where
+
+122
+00:10:26,450 --> 00:10:30,390
+warm gas or liquid moves around and dissipate heat
+
+123
+00:10:30,390 --> 00:10:35,130
+transferring it to the rest of the gas or the
+
+124
+00:10:35,130 --> 00:10:38,890
+liquid الان هذه احدى الطرق في طرق تانية ايش بتعمل
+
+125
+00:10:39,970 --> 00:10:44,770
+تاخد ميه تشوفه أنا بيه بالغاز اللي في البيت، حدا
+
+126
+00:10:44,770 --> 00:10:50,410
+فيكوا شافها، إيش بتبقى شكلها؟ الآن لو أنت عندك مش
+
+127
+00:10:50,410 --> 00:10:57,070
+.. الجرة مش مشبوكة مباشرة على الفرن أو على الغاز
+
+128
+00:10:57,070 --> 00:11:01,010
+اللي أنت فيها، بتبقى مثلا تحت و أنت عاملة خط، الخط
+
+129
+00:11:01,010 --> 00:11:06,820
+إيش نوعه؟نحاسي صح؟ عادة إيش بيسووا برا؟ بيعملوا خط
+
+130
+00:11:06,820 --> 00:11:12,260
+نحاس هاد للتدفئة، هاد التدفئة عساس التدفئة ال air
+
+131
+00:11:12,260 --> 00:11:16,600
+conditioning إيش بتعمل في الرطوبة في الجو؟ بتغيرها
+
+132
+00:11:17,340 --> 00:11:20,660
+بتصير فيه نوعا ما جفاف فانت في ال .. في البيوت
+
+133
+00:11:20,660 --> 00:11:23,860
+اللي بدها تستخدمه لازم إيش تعمل؟ في عندها
+
+134
+00:11:23,860 --> 00:11:29,360
+humidifier اللي هي حاجة بتطلق رطوبة في الجو عشان
+
+135
+00:11:29,360 --> 00:11:33,400
+تحافظ على درجة محينة من الرطوبة، الآن لو أنا اتخلص
+
+136
+00:11:33,400 --> 00:11:38,510
+من هذه المشكلة إيش بعمل؟بعمل التدفئة في التدفئة
+
+137
+00:11:38,510 --> 00:11:43,050
+الخصوصية بستخدمش الهواء اللي مسخّن باجي بعمل
+
+138
+00:11:43,050 --> 00:11:47,610
+أنابيب نحاسية و بلفها حوالين البيت و بدخل فيها ميه
+
+139
+00:11:47,610 --> 00:11:52,330
+سخنة و بسوي لها circulation هذا التدفئة الميزة
+
+140
+00:11:52,330 --> 00:11:57,230
+تبعتها بتأثرش على الرطوبة في الجوبتغيرهاش فانت
+
+141
+00:11:57,230 --> 00:12:02,350
+بتعيش ببيئة نوعا ما طبيعية، هذه بتختلف عن رطوبة
+
+142
+00:12:02,350 --> 00:12:06,910
+الاش .. الجو اللي هي ال .. الهواء ناخده و نعمله و
+
+143
+00:12:06,910 --> 00:12:10,170
+نشتغل عليه طيب
+
+144
+00:12:11,520 --> 00:12:14,620
+Alternatively, the heating system in a home may
+
+145
+00:12:14,620 --> 00:12:17,880
+circulate hot water through a radiator. هذه
+
+146
+00:12:17,880 --> 00:12:22,420
+بنعملها The radiators act as a heat exchanger
+
+147
+00:12:22,420 --> 00:12:28,060
+devices that transfer heat in this case from the
+
+148
+00:12:28,060 --> 00:12:34,500
+hot water inside to the cooler air outside الآن
+
+149
+00:12:34,500 --> 00:12:38,570
+هذه بتشوفوها في السياراتالان السيارة يمكن تعرفه ال
+
+150
+00:12:38,570 --> 00:12:41,730
+motor السيارة و هو ماجي إيش بيصيرله؟ تبقى درجة
+
+151
+00:12:41,730 --> 00:12:44,970
+حرارته كيف؟ عالي عالي يعني لو جيت و حطيت إيدك عليه
+
+152
+00:12:44,970 --> 00:12:48,230
+على طول تنحرق إيدك في هاي كلبسة بتجي تتخبى تحت
+
+153
+00:12:48,230 --> 00:12:54,940
+السيارة في الشتاء بتجي تتخبى تحت السيارة خفيرةالآن
+
+154
+00:12:54,940 --> 00:13:00,860
+إيش بنعمل؟ فيها cooling system وعملية ال cooling
+
+155
+00:13:00,860 --> 00:13:03,600
+إيش بتمر؟ في عندهم الجهاز هذا اللي بيسموه ال
+
+156
+00:13:03,600 --> 00:13:07,520
+radiator إيش هذا بتدخل فيه؟ بتدخل الميه و بتلف على
+
+157
+00:13:07,520 --> 00:13:12,740
+قنابيب الآن حوالينها دي في مروحة بت .. بت .. بت ..
+
+158
+00:13:12,740 --> 00:13:15,880
+بت .. بتبت هواها الهواها عبر القنابيب اللي بتلف
+
+159
+00:13:15,880 --> 00:13:19,800
+فيها و في حواليها heat sinks إيش ال heat sinks؟
+
+160
+00:13:20,010 --> 00:13:26,130
+حاجات يعني من مادة خلينا نقول معدنية عادة بتطلعها
+
+161
+00:13:26,130 --> 00:13:30,890
+الميه هذا ايش بتسوي؟ بتطلع الحرارة على هذه الشرايح
+
+162
+00:13:30,890 --> 00:13:34,450
+لان المروحة لما تسوي ايش بتعمل؟ بتبرد هذه الشرايح
+
+163
+00:13:34,450 --> 00:13:39,490
+فبتبرد الميه اللي موجودة فيها فبتنزل درجة الحرارة
+
+164
+00:13:39,490 --> 00:13:44,650
+تبع ماتور السيارة فهذه موجودة بشكل مباشر بتقدر
+
+165
+00:13:44,650 --> 00:13:51,030
+تشوفوها بشكل أوضح في هذا المجالهذا حدث من نشطة
+
+166
+00:13:51,030 --> 00:13:58,290
+الهيئة المتحركة من مصدر صليد الهيئة
+
+167
+00:13:58,290 --> 00:14:01,110
+المتحركة من مصدر صليد الهيئة المتحركة من مصدر صليد
+
+168
+00:14:01,110 --> 00:14:02,610
+الهيئة المتحركة من مصدر صليد الهيئة المتحركة من
+
+169
+00:14:02,610 --> 00:14:06,110
+مصدر صليد الهيئة المتحركة من مصدر صليد الهيئة
+
+170
+00:14:06,110 --> 00:14:11,680
+المتحركة من مصدر صليدالان شفت ايش انا بقولكوا هات؟
+
+171
+00:14:11,680 --> 00:14:16,000
+قلت هذه الحدايات تبع ال radiator الموجودة الشرايح
+
+172
+00:14:16,000 --> 00:14:21,020
+هذه مع المروحة بتطلع .. هي بتطلع .. المروحة بتسرع
+
+173
+00:14:21,020 --> 00:14:26,700
+عملية خروج هذه الطاقة او ال heat اللي موجود عنده
+
+174
+00:14:26,700 --> 00:14:31,760
+heat is dissipated by convection هذه الكلمة اللي
+
+175
+00:14:31,760 --> 00:14:35,100
+بدنا نطلع عليهاthe third wave that heat is
+
+176
+00:14:35,100 --> 00:14:39,300
+transferred by radiation this is heat that travel
+
+177
+00:14:39,300 --> 00:14:43,520
+as electromagnetic wave عادة كلمة radiation إيش
+
+178
+00:14:43,520 --> 00:14:49,960
+معناتها؟الشاعر، الآن كلمة radiator شوية مبالغ فيها
+
+179
+00:14:49,960 --> 00:14:53,820
+عادة لما اتكلم على radiation معناه تعبر
+
+180
+00:14:53,820 --> 00:14:57,680
+electromagnetic waves اللي بنتكلم فيها فهذا اللي
+
+181
+00:14:57,680 --> 00:15:00,380
+بتحكيها this is heat that travels as
+
+182
+00:15:00,380 --> 00:15:03,440
+electromagnetic wave and example is heat from the
+
+183
+00:15:03,440 --> 00:15:08,120
+sunدرجة الحرارة بتجي لما الشمس بتجي عبر
+
+184
+00:15:08,120 --> 00:15:11,340
+electromagnetic waves زي ما اتكلمنا هي photons
+
+185
+00:15:11,340 --> 00:15:15,320
+اللي اتصلنا في هذا المجال So that the radiators
+
+186
+00:15:15,320 --> 00:15:19,620
+that circulate water have a misleading name as
+
+187
+00:15:19,620 --> 00:15:23,880
+they don't really function as radiation يعني اسم
+
+188
+00:15:23,880 --> 00:15:31,000
+ال radiator شوية مبالغ فيه من هذه الناحيةالان نجي
+
+189
+00:15:31,000 --> 00:15:35,420
+نطلع عليهم على ال example الأصل هذه الكلمات
+
+190
+00:15:35,420 --> 00:15:40,500
+الموجودة هان سهلة علينا when temperature of ice is
+
+191
+00:15:40,500 --> 00:15:47,440
+zero degree it changes ايش state it is to water
+
+192
+00:15:47,440 --> 00:15:54,460
+melts to water لأن هي ايش بيصير فيها تتحول لمية
+
+193
+00:15:54,460 --> 00:15:59,200
+يعني التلج بيصير مية at one hundred degree water
+
+194
+00:16:00,790 --> 00:16:08,670
+boil أو إيش بيصيروله؟ بيبخر أو
+
+195
+00:16:08,670 --> 00:16:15,930
+بيغلي وبتحول ل state when water is إيش to zero
+
+196
+00:16:15,930 --> 00:16:23,730
+degree or below it become ice when water cools to
+
+197
+00:16:23,730 --> 00:16:29,050
+zero degree or below and إيش to become ice
+
+198
+00:16:31,490 --> 00:16:36,610
+solidify ايش يعني solidify؟ تتجمد الميه تتجمد
+
+199
+00:16:36,610 --> 00:16:44,930
+بتتحول لإيش؟ لتلج it freezes in gas form water is
+
+200
+00:16:44,930 --> 00:16:56,390
+called steam او vapor او water vapor يعني يابن
+
+201
+00:16:56,390 --> 00:17:01,450
+نسميه steam ال steam اللي هو إيش؟البخار و عادة هذا
+
+202
+00:17:01,450 --> 00:17:06,510
+يمكن ان شاء الله بتدخلوا بتشوفوا بتدخلوا تخصات
+
+203
+00:17:06,510 --> 00:17:11,130
+توصلكوا لو تروحوا على محطة الكهربا بتلاقوا عندنا
+
+204
+00:17:11,130 --> 00:17:17,040
+فيه بتسمعوا انتوا فيها كام مولدولا معلومات عامة
+
+205
+00:17:17,040 --> 00:17:25,980
+سفر أربع مولدات بس اللي موجود عندنا مش أربع ستة
+
+206
+00:17:25,980 --> 00:17:31,300
+الأن اتنين بيشتغلوا بيسموهم على الغاز وكل two
+
+207
+00:17:31,300 --> 00:17:34,580
+units اللي هي one unit بتشتغل على إيش؟ على steam
+
+208
+00:17:34,580 --> 00:17:39,740
+لأنه لما يبردوا محطة الكهربا هيبدها إيش؟ تبريد
+
+209
+00:17:39,740 --> 00:17:42,920
+فعملية التبريد بتشوفوا أنتوا إذا محدد مرج من عند
+
+210
+00:17:42,920 --> 00:17:49,460
+البحرعقبال مدينة الظهر ايش فيه؟ في هناك حاجة لمحطة
+
+211
+00:17:49,460 --> 00:17:53,060
+توليد الكهربا بياخدوا المي تبعت البحر و بيودوها
+
+212
+00:17:53,060 --> 00:17:57,420
+على المحطة عشان يبردوا فيها ايش؟ التوربينات بتبعت
+
+213
+00:17:57,420 --> 00:18:03,080
+اللي بتولد الكهربا فعملية التبريد هاي بتعمل steam
+
+214
+00:18:03,080 --> 00:18:07,760
+ال steam هات بيستخدموه ليولدوا فيه ايش؟ كهربا
+
+215
+00:18:07,760 --> 00:18:12,820
+زيادة هات بيسموها ال combined cycleاللي هي .. ايوة
+
+216
+00:18:12,820 --> 00:18:18,160
+فلكل تنتين فيه unit تالتة اللي هي بتعمل توليد
+
+217
+00:18:18,160 --> 00:18:22,760
+بتستخدم البخار تنتين بيستخدموا الديزل او الغاز و
+
+218
+00:18:22,760 --> 00:18:27,240
+واحدة بتستخدم البخار فعنا بالظبط ستة units اللي
+
+219
+00:18:27,240 --> 00:18:34,460
+موجودة هاي معلومة عامة طيب between one hundred
+
+220
+00:18:34,460 --> 00:18:37,860
+degree Celsius and three hundred seventy four
+
+221
+00:18:37,860 --> 00:18:43,940
+degree water is ايش؟a vapor because it's below it
+
+222
+00:18:43,940 --> 00:18:50,540
+.. it's .. ايش .. temperature below ايش ..
+
+223
+00:18:50,540 --> 00:18:54,480
+critical .. it's a critical temperature ال
+
+224
+00:18:54,480 --> 00:18:58,240
+critical temperature بتصير ايش بعدها superheated
+
+225
+00:18:58,240 --> 00:19:06,020
+superheated يعني اتوصل لدرجات انه اتعدى الحاجات
+
+226
+00:19:06,020 --> 00:19:12,130
+هذه extremely hot water vapor is calledsuperheated
+
+227
+00:19:12,130 --> 00:19:21,890
+وصلنا له على طول طيب
+
+228
+00:19:21,890 --> 00:19:25,050
+بدنا
+
+229
+00:19:25,050 --> 00:19:34,030
+نعمل matching between a liquid pumped onto a
+
+230
+00:19:34,030 --> 00:19:37,450
+work piece that is being machined to stop it
+
+231
+00:19:37,450 --> 00:19:43,040
+overheating is called ايش؟colant بتعرفوا هذه في
+
+232
+00:19:43,040 --> 00:19:48,860
+حاجة يمكن .. خلّيني أعطيكم معلومة تانية الآن ال ..
+
+233
+00:19:48,860 --> 00:19:50,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+234
+00:19:50,300 --> 00:19:50,880
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+235
+00:19:50,880 --> 00:19:51,700
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+236
+00:19:51,700 --> 00:19:54,940
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+237
+00:19:54,940 --> 00:19:55,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+238
+00:19:55,440 --> 00:19:56,740
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+239
+00:19:56,740 --> 00:19:57,000
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+240
+00:19:57,000 --> 00:19:57,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+241
+00:19:57,280 --> 00:19:57,280
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+242
+00:19:57,280 --> 00:19:57,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+243
+00:19:57,280 --> 00:20:02,740
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+244
+00:20:02,740 --> 00:20:06,880
+ال .. ال .. ال
+
+245
+00:20:11,020 --> 00:20:13,860
+ببقوها هذه ممكن اللي حد شاف اللي حد عنده أبوها
+
+246
+00:20:13,860 --> 00:20:17,180
+سيارة و بديحطلها حاجة و بديعزها بجيب هذا الميه
+
+247
+00:20:17,180 --> 00:20:22,120
+سائل لونه زي الأخضر أو الأزرق بيحطه في السيارة لل
+
+248
+00:20:22,120 --> 00:20:25,820
+radiator بيحطش ميه لإن ميه ميتنا بتخرب ال radiator
+
+249
+00:20:25,820 --> 00:20:31,720
+بسرعة طب كم برد فيها شركة الكهرة؟ هي .. هي ..لأ
+
+250
+00:20:31,720 --> 00:20:36,940
+الميه الملحمة هي هذه إيش بيصير فيها، هذه اختلاف،
+
+251
+00:20:36,940 --> 00:20:42,760
+محط الكهربا بدهم كميات ميه كبيرة جدا، فبيلزمهم وين
+
+252
+00:20:42,760 --> 00:20:46,700
+هذه متوفرة؟ يا في الأنهار يا في البحار، الآن لما
+
+253
+00:20:46,700 --> 00:20:51,560
+تحطوها إيش بيصير؟ بتتبخر هذه الميه، الميه لما
+
+254
+00:20:51,560 --> 00:20:56,130
+تتبخر إيش بتصير؟ال .. بيضل الملح ايوة بيضل الملح و
+
+255
+00:20:56,130 --> 00:21:01,430
+بعدين الميه اللى بتطلع .. بتطلع ميه مش يعني ميه
+
+256
+00:21:01,430 --> 00:21:06,050
+بحر بيصير ميه عادية فهم ايش بيسووا عشان ما يضروش
+
+257
+00:21:06,050 --> 00:21:10,830
+البحر بيرجعوا من الملح هذا بخلطوه تاني و بيرجعوا
+
+258
+00:21:10,830 --> 00:21:16,090
+نسبة ميه ملح عشان الأسماك و البحر ما تتأثرش و احنا
+
+259
+00:21:16,090 --> 00:21:21,350
+محافظين على البيئة و بنصف بعد غزة فيه طيب
+
+260
+00:21:22,380 --> 00:21:25,480
+the form of heat transfer that occurs with
+
+261
+00:21:25,480 --> 00:21:31,080
+infrared heat a form of electromagnetic wave is
+
+262
+00:21:31,080 --> 00:21:36,260
+called إيش؟ radiation حد ما تطلع infrared أنت
+
+263
+00:21:36,260 --> 00:21:44,180
+بتعرف إيش ال infrared؟ الأشعال إيش؟ ultraviolet و
+
+264
+00:21:44,180 --> 00:21:48,830
+infrared هدول لازم تحفظوهم أخدتهم بالفيزياالـ
+
+265
+00:21:48,830 --> 00:21:53,230
+Infrared التحت الحمراء والـ Ultraviolet الفاقل
+
+266
+00:21:53,230 --> 00:21:58,550
+بنفسه جيه، مظبوط؟ هدول لازم نغرسوا معاكم فهذه is
+
+267
+00:21:58,550 --> 00:22:03,550
+form of radiation الـ metal fins اللي هي الـ
+
+268
+00:22:03,550 --> 00:22:07,010
+plates اللي حكينا عندها، هذي إيش؟ around air
+
+269
+00:22:07,010 --> 00:22:10,230
+cooled engine intended to maximize the surface
+
+270
+00:22:10,230 --> 00:22:14,290
+area of the hot engine that is in contact with the
+
+271
+00:22:14,290 --> 00:22:19,190
+cooler air are designed to act as إيش؟heat sink
+
+272
+00:22:19,190 --> 00:22:23,750
+قلتلكم هذا إيش بتسوي؟ حكيناكوا يا هاد عبارة عن
+
+273
+00:22:23,750 --> 00:22:27,550
+heat sink و ال heat sink إيش بوسع المساحة اللي
+
+274
+00:22:27,550 --> 00:22:32,190
+بتشبك عليها هاد بكرا دي حد فيكوا تخصص كهربا بعض
+
+275
+00:22:32,190 --> 00:22:37,430
+القطع اللي بتسخن بسرعة بنحطلها heat sink قطعة
+
+276
+00:22:37,430 --> 00:22:42,900
+معدنية حواليها توسعالمجال تبع اطلاق الحرارة في
+
+277
+00:22:42,900 --> 00:22:46,160
+الجو وهذا ده حدث فيك وفتح الكمبيوتر بيلاقوها
+
+278
+00:22:46,160 --> 00:22:51,680
+موجودة جوا الكمبيوتر هذه القطع هدفها ايش تعمل
+
+279
+00:22:51,680 --> 00:22:55,600
+اطلاق للحرارة بدل ما هي القطع الصغيرة اللي حالها
+
+280
+00:22:55,600 --> 00:23:00,440
+بتطلق بنلحمها بهذه القطع بتوصل بتصير الحرارة بشكل
+
+281
+00:23:00,440 --> 00:23:10,590
+أكبر وأسرع heat sinkheat heat exchanger وهي برضه
+
+282
+00:23:10,590 --> 00:23:18,190
+بتقدر تعمليها heat sink لأن هي act as both الان
+
+283
+00:23:18,190 --> 00:23:22,210
+الوراها ايش بنتكلم take dense internal walls
+
+284
+00:23:22,210 --> 00:23:25,150
+inside an energy efficient house which are
+
+285
+00:23:25,150 --> 00:23:28,530
+intended to absorb heat energy during the day and
+
+286
+00:23:28,530 --> 00:23:32,470
+store some of it to be emitted at night function
+
+287
+00:23:32,470 --> 00:23:40,910
+asهي .. هذا ال heat exchanger الأصل، ليش؟ لأن أنا
+
+288
+00:23:40,910 --> 00:23:45,490
+باخد في الليل، في النهار، و بطلق في الليل، طلعوا
+
+289
+00:23:45,490 --> 00:23:50,270
+عندنا البيوت، البيوت ده حد فيكم لاحظ حاجة واحدة،
+
+290
+00:23:50,270 --> 00:23:54,870
+إيش بنلاحظ؟ الحرارة تبعتنا، البيت، دايما أسأل أختي
+
+291
+00:23:54,870 --> 00:23:59,070
+أختي بيقولك البيت في الليل، يعني في النهار، أقعد
+
+292
+00:23:59,070 --> 00:24:07,120
+تحت فيه شجرة، مش فيه بيت، ليش؟الشجرة بتمطصش حرارة،
+
+293
+00:24:07,120 --> 00:24:11,960
+الآن البيوت بتمطص الحرارة و في الليل بتصير تطلق
+
+294
+00:24:11,960 --> 00:24:16,320
+هذا الحرارة عشان هيك في الليل بتلاقي .. لأ البيت
+
+295
+00:24:16,320 --> 00:24:21,060
+بيضلوا محافظ على الحرارة ل .. لأخر الليل تقريبا،
+
+296
+00:24:21,060 --> 00:24:25,040
+بتصل كل هايم، بس تطلع برا بتلاقي الجو أبرد بكتير
+
+297
+00:24:25,040 --> 00:24:30,920
+من جوا الهايم، فهي هذه إيش بتصير؟يعني هي ال heat
+
+298
+00:24:30,920 --> 00:24:36,460
+sink ايش بيعمل؟ هو يعني مكان للإشعاع على الحرارة
+
+299
+00:24:36,460 --> 00:24:41,310
+هذا ال heat sink هذا ال engineering term تبعهاطيب
+
+300
+00:24:41,310 --> 00:24:45,470
+the soil and rocks on the surface of air remain
+
+301
+00:24:45,470 --> 00:24:48,590
+warm at night and summer due to the principle of
+
+302
+00:24:48,590 --> 00:24:53,330
+إيش؟ thermal inertia اللي أحنا بنحكي عنها لإن هاد
+
+303
+00:24:53,330 --> 00:24:58,330
+إيش بتضالها تمتص و بعدها الإطلاق بتبقى خفيف جدا في
+
+304
+00:24:58,330 --> 00:25:06,990
+هذا المجال ولو إن هاد تلاتة وأربعة فيهم شوية خربط
+
+305
+00:25:06,990 --> 00:25:14,300
+يعني كويس لإنه ال ..التلاتة بدك تحطيها C أربع
+
+306
+00:25:14,300 --> 00:25:20,340
+حطيها E لأن التلاتة ال heat هذه ال plate شغلتها
+
+307
+00:25:20,340 --> 00:25:24,120
+ايش اكت as a heat sink وهذه بندرسها احنا في
+
+308
+00:25:24,120 --> 00:25:33,240
+الكهربا طيب circle the correct words من الموجود
+
+309
+00:25:33,240 --> 00:25:36,600
+هنا condensing boilers are becoming increasingly
+
+310
+00:25:36,600 --> 00:25:43,810
+popular in homeلأنهم يستخدمون اكتر من 40% أقل من
+
+311
+00:25:43,810 --> 00:25:45,050
+الهواء التقليدي التقليدي التقليدي التقليدي
+
+312
+00:25:45,050 --> 00:25:45,610
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+313
+00:25:45,610 --> 00:25:48,430
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+314
+00:25:48,430 --> 00:25:50,170
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+315
+00:25:50,170 --> 00:25:51,810
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+316
+00:25:51,810 --> 00:25:51,810
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+317
+00:25:51,810 --> 00:25:51,910
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+318
+00:25:51,910 --> 00:25:51,910
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+319
+00:25:51,910 --> 00:25:55,530
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+320
+00:25:55,530 --> 00:25:59,530
+التقليدي التقليدي التقليدي التقليدي التقليدي
+
+321
+00:25:59,530 --> 00:26:04,830
+التقليدي
+
+322
+00:26:04,830 --> 00:26:13,840
+التطيب لأن هذا إيش بيحول من سائل لغاز؟ ال process
+
+323
+00:26:13,840 --> 00:26:20,280
+endothermic ولا exothermic؟ لأن هذا إيش بتعمل؟
+
+324
+00:26:20,280 --> 00:26:26,120
+endothermic بتاخد، exothermic بتطلع، وهذه بتطلعها،
+
+325
+00:26:26,120 --> 00:26:30,510
+this mean heat is observed ولا emitted؟emitted
+
+326
+00:26:30,510 --> 00:26:34,350
+لأنها بتطلع and can thus be circulated ولا
+
+327
+00:26:34,350 --> 00:26:38,310
+conducted circulated by the water inside the
+
+328
+00:26:38,310 --> 00:26:42,630
+radiator in the home a condensing boiler per
+
+329
+00:26:42,630 --> 00:26:49,150
+natural gasto لأن hydrocarbon fuel اللي هو ال
+
+330
+00:26:49,150 --> 00:26:52,650
+natural gas اللي هو الغاز اللي عندنا to heat or
+
+331
+00:26:52,650 --> 00:26:56,290
+cool water heat water just like a conventional
+
+332
+00:26:56,290 --> 00:26:59,330
+boiler however it achieve greater efficiency by
+
+333
+00:26:59,330 --> 00:27:03,830
+recovering energy from water vapor وهذه بتلاحظوها
+
+334
+00:27:03,830 --> 00:27:08,830
+يمكن حاليا بدت تنتشر في غزة ايش احنا عندنا تسخين
+
+335
+00:27:08,830 --> 00:27:14,900
+الميه بتتم عبر ايش في غزة الغالبيا .. يا .. يا
+
+336
+00:27:14,900 --> 00:27:20,060
+السخنات الشمسية يا إما سخنات الكهربا في في غزة
+
+337
+00:27:20,060 --> 00:27:27,680
+الحين صارت سخنات غاز على الغاز و safe و كويسة و
+
+338
+00:27:27,680 --> 00:27:32,240
+بتحسيش أنه بتطلع حرارة زي الموجود و بتعطيك نفس
+
+339
+00:27:32,240 --> 00:27:38,660
+المفعول أنا عند واحد ف .. ف .. كويس كتير يعني من
+
+340
+00:27:38,660 --> 00:27:43,250
+..ما هي في الشتاء الشمس بتعطيكيشي الدرجة اللي بدك
+
+341
+00:27:43,250 --> 00:27:49,170
+إياها فهذه للشتاء حل .. حل كويس هذا اللي عندى
+
+342
+00:27:49,170 --> 00:27:57,610
+سنتين الحين فوضع كويس طيب this is a .. this is a
+
+343
+00:27:57,610 --> 00:28:00,990
+present in the hot waste gas that produced when
+
+344
+00:28:00,990 --> 00:28:04,410
+natural gas is burned in a traditional boiler ده
+
+345
+00:28:04,410 --> 00:28:08,430
+heat ولا ده temperature energy؟من حد ما تلاحظ كلمة
+
+346
+00:28:08,430 --> 00:28:14,090
+energy بروح معها إيش؟ heat from the gas which is
+
+347
+00:28:14,090 --> 00:28:20,550
+at 180 degree من حد ما تشوفي رقم بروح معها حد إيش؟
+
+348
+00:28:20,550 --> 00:28:26,280
+degrees Celsius معناته temperature180 درجة أو أكتر
+
+349
+00:28:26,280 --> 00:28:33,060
+ستكون محطمة أو محطمة في الهواء، محطمة لأنها بتطلع
+
+350
+00:28:33,060 --> 00:28:39,440
+هنا By conduction ولا convection؟ convection and
+
+351
+00:28:39,440 --> 00:28:43,260
+the water vapor within it would condense in the
+
+352
+00:28:43,260 --> 00:28:48,190
+outside air but a condensing boilerboiler the hot
+
+353
+00:28:48,190 --> 00:28:52,330
+gas passes through a heat or temperature exchanger
+
+354
+00:28:52,330 --> 00:28:56,370
+مر عليكم قبل شوية اللي هو ال heat exchanger this
+
+355
+00:28:56,370 --> 00:29:00,350
+allow heat from the gas to be observed ولا omitted
+
+356
+00:29:00,350 --> 00:29:05,370
+by cool water observe من حد ما تشوفيه cool water
+
+357
+00:29:05,370 --> 00:29:10,360
+بدي اخدالذي يرجع إلى النافذة بعد المرور من
+
+358
+00:29:10,360 --> 00:29:16,720
+النافذات في المنزل الهيئة الهيئة الهيئة الهيئة
+
+359
+00:29:16,720 --> 00:29:17,440
+الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة
+
+360
+00:29:17,440 --> 00:29:19,240
+الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة
+
+361
+00:29:19,240 --> 00:29:19,860
+الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة
+
+362
+00:29:19,860 --> 00:29:21,560
+الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة
+
+363
+00:29:21,560 --> 00:29:29,960
+الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة
+
+364
+00:29:29,960 --> 00:29:34,240
+الهيئة
+
+365
+00:29:34,240 --> 00:29:41,260
+الهSolidify بدي يتحول لمادة صلبة Condensed بدي
+
+366
+00:29:41,260 --> 00:29:46,300
+يتحول لمادة سائلة و Vapor اللي هو الغاز بنروحش من
+
+367
+00:29:46,300 --> 00:29:54,580
+الغاز للصلب بنروح من الغاز لإيش للسائل and it is
+
+368
+00:29:54,580 --> 00:29:57,920
+the process that enables significant amount of
+
+369
+00:29:57,920 --> 00:30:00,480
+heat to be transferred due to the principle of
+
+370
+00:30:00,480 --> 00:30:02,580
+latent heat
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_postprocess.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..707e24a3d0036e49574d3ca457a35e5fd1aca7d2
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_postprocess.srt
@@ -0,0 +1,1060 @@
+1
+00:00:21,620 --> 00:00:27,320
+السلام عليكم اليوم
+
+2
+00:00:27,320 --> 00:00:32,160
+سنقوم بمقاطع حلقة 12 حلقة 12 تتكلم عن الصناعة
+
+3
+00:00:32,160 --> 00:00:40,800
+ثلاثة جزء من حلقة 12 أولا نتكلم عن الصناعة
+
+4
+00:00:40,800 --> 00:00:46,200
+الكاربون ثانوية نتكلم عن الصناعة الأسلحة ثالثة
+
+5
+00:00:46,200 --> 00:00:52,920
+نتكلم عن الصناعة الكوروجينCarbon Steel ماذا نقصده
+
+6
+00:00:52,920 --> 00:00:59,140
+بـ Carbon Steel؟ هذا إستجابة من مقال في جورنال
+
+7
+00:00:59,140 --> 00:01:02,800
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+8
+00:01:02,800 --> 00:01:02,940
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+9
+00:01:02,940 --> 00:01:03,320
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+10
+00:01:03,320 --> 00:01:03,720
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+11
+00:01:03,720 --> 00:01:06,240
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+12
+00:01:06,240 --> 00:01:12,460
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+13
+00:01:14,300 --> 00:01:18,540
+وأنواع مشتقات الستيل اللي هو أكتر الأنواع الحديد
+
+14
+00:01:18,540 --> 00:01:23,160
+استخدامها technically though this well-known alloy
+
+15
+00:01:23,160 --> 00:01:27,560
+of iron and carbon is not as simple as one might
+
+16
+00:01:27,560 --> 00:01:32,600
+think الفكرة هنا مش بالبساطة اللي بتعتقدوها steel
+
+17
+00:01:32,600 --> 00:01:38,700
+comes in a huge range of different grades الأنواع
+
+18
+00:01:38,700 --> 00:01:43,850
+تبعته والمواصفات مختلفةeach with different
+
+19
+00:01:43,850 --> 00:01:49,110
+characteristics كل واحد له مواصفات مختلفة for the
+
+20
+00:01:49,110 --> 00:01:53,870
+inexperienced it can be difficult to know where to
+
+21
+00:01:53,870 --> 00:01:58,510
+begin للي ما عندهم مش خبرة صعب نعرف من وين نبدأ
+
+22
+00:02:00,010 --> 00:02:05,810
+Carbon steel هذا الوضع الأول، مكان جيد للبدأ هو مع
+
+23
+00:02:05,810 --> 00:02:08,950
+الاتنين الرئيسيين من الصناعة الصناعة الصناعة
+
+24
+00:02:08,950 --> 00:02:10,750
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+25
+00:02:10,750 --> 00:02:11,610
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+26
+00:02:11,610 --> 00:02:12,290
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+27
+00:02:12,290 --> 00:02:12,670
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+28
+00:02:12,670 --> 00:02:12,830
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+29
+00:02:12,830 --> 00:02:13,490
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+30
+00:02:13,490 --> 00:02:13,990
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+31
+00:02:13,990 --> 00:02:14,150
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+32
+00:02:14,150 --> 00:02:17,190
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+33
+00:02:17,190 --> 00:02:24,480
+الصناالان الان لا تحتوي على نسبة معينة لأي نسبة
+
+34
+00:02:24,480 --> 00:02:29,140
+أخرى، نسبة معينة كربونستيل يمكن ان يكون مقاطعًا
+
+35
+00:02:29,140 --> 00:02:34,660
+إلى ثلاثة مقاطع أساسيةعندنا تلات خانات لـ carbon
+
+36
+00:02:34,660 --> 00:02:39,040
+steel إيش همها؟ mild steel the most widely used
+
+37
+00:02:39,040 --> 00:02:42,820
+grade is a low carbon steel which contains up to
+
+38
+00:02:42,820 --> 00:02:47,300
+approximately point three percent of carbon يعني
+
+39
+00:02:47,300 --> 00:02:51,890
+اللي أنا بتطلع عليه هذا ال mild قديش بحتوىثلاثة من
+
+40
+00:02:51,890 --> 00:02:57,090
+عشرة بالمية كربون والباقي ايش؟ ايرن فهذا بنسميه
+
+41
+00:02:57,090 --> 00:03:01,570
+ايش؟ mild steel medium carbon steel contain
+
+42
+00:03:01,570 --> 00:03:07,500
+between approximately point three percentto point
+
+43
+00:03:07,500 --> 00:03:12,540
+six percent carbon يعني من point تلاتة ل point كام
+
+44
+00:03:12,540 --> 00:03:16,300
+ستة carbon high carbon steel contain between
+
+45
+00:03:16,300 --> 00:03:20,300
+approximately point six and one point four percent
+
+46
+00:03:20,300 --> 00:03:24,920
+carbon يعني هذا النسبة تبعته على إشي هذا الأنواع
+
+47
+00:03:24,920 --> 00:03:29,060
+one point four percent carbon الآن بنطلع عليهم هذا
+
+48
+00:03:29,060 --> 00:03:31,940
+التلات أنواع إيش هما mild
+
+49
+00:03:34,300 --> 00:03:39,000
+medium carbon steel و بعدين ايش high carbon steel
+
+50
+00:03:39,000 --> 00:03:42,980
+هدولة التلاتة كل اللي بيحتووا ايش carbons and
+
+51
+00:03:42,980 --> 00:03:46,400
+steel و ال carbon زي ما بتلاحظوا very low
+
+52
+00:03:46,400 --> 00:03:51,400
+quantities يعني لما تتكلم عن تلاتة من العشرة
+
+53
+00:03:51,400 --> 00:03:58,080
+بالمية نسبة يعني كل الف يعني كل كيلو في عليه تلاتة
+
+54
+00:03:58,080 --> 00:04:05,020
+gramهذه حاجة خفيفة جدا و أكتر واحد فيه كل ألف كل
+
+55
+00:04:05,020 --> 00:04:12,180
+كيلو يعني 14 gram برضه هذه النسبة بتبقى خفيفة
+
+56
+00:04:12,180 --> 00:04:17,620
+النوع التاني بنسميه
+
+57
+00:04:17,620 --> 00:04:22,890
+alloy steels الآن نحن بنعرف ال steel إيش نوعهit's
+
+58
+00:04:22,890 --> 00:04:26,930
+an alloy مظبوط مش معنى الكلام انه هذا سمناه alloy
+
+59
+00:04:26,930 --> 00:04:30,570
+steel ات نوع تاني مش alloy لأ هو هى بس التسمية
+
+60
+00:04:30,570 --> 00:04:34,610
+تبعته لإن هذه الأنواع اللي جاية فيه هنا في عيننا
+
+61
+00:04:34,610 --> 00:04:40,660
+othermetals بنحطهم مع الكربون كويس نيجي نطلعها the
+
+62
+00:04:40,660 --> 00:04:44,080
+second main category of steel is alloy steels
+
+63
+00:04:44,080 --> 00:04:48,540
+which consists of iron carbon and one or more
+
+64
+00:04:48,540 --> 00:04:53,500
+alloying material يعني احنا اش بنضيف حاجات اكتر
+
+65
+00:04:53,500 --> 00:04:57,980
+اللي هي واحدة او تنتين من ال material ال alloying
+
+66
+00:04:57,980 --> 00:05:02,800
+material التانية specific grade of the alloying
+
+67
+00:05:02,800 --> 00:05:03,800
+steel include
+
+68
+00:05:09,540 --> 00:05:20,940
+مش صغير طيب
+
+69
+00:05:20,940 --> 00:05:24,280
+ال include ايش اللي عندي ها؟ هاي الأنواع اللي
+
+70
+00:05:24,280 --> 00:05:29,780
+موجودة عندنا نطلع عليهم low alloy steel which
+
+71
+00:05:29,780 --> 00:05:38,060
+contains 90%أو المزيد من الأسلحة وحتى 10% من
+
+72
+00:05:38,060 --> 00:05:45,360
+المواد التجارية مثل اوكروميا نكو مانجانيز
+
+73
+00:05:45,360 --> 00:05:47,680
+موليبيديا
+
+74
+00:05:49,120 --> 00:05:53,780
+Vanadium هدول الأنواع الموجودة اللي بنحطهم فيهم
+
+75
+00:05:53,780 --> 00:05:57,380
+هذا ايش بنسميه low alloying steel لأن في عندي
+
+76
+00:05:57,380 --> 00:06:04,380
+تسعين فالمية iron والباقي alloying materials high
+
+77
+00:06:04,380 --> 00:06:10,720
+strength low alloying steel which contains smaller
+
+78
+00:06:10,720 --> 00:06:15,430
+quantity of the above metalsit's typically less
+
+79
+00:06:15,430 --> 00:06:19,250
+than two percent يعني هدول أقل اللي سمناه high
+
+80
+00:06:19,250 --> 00:06:23,730
+strength low alloying material الآن بيجي النوع
+
+81
+00:06:23,730 --> 00:06:26,890
+التالت اللي بيسميه ال stainless steel كل هيتكم
+
+82
+00:06:26,890 --> 00:06:32,630
+بتعرفوه هذا، مظبوط؟ which contain chromium as well
+
+83
+00:06:32,630 --> 00:06:36,850
+as other metals such as nickel and which do not
+
+84
+00:06:36,850 --> 00:06:40,130
+rust يعني إيش هذا ال stainless steel إيش محصله؟
+
+85
+00:06:41,070 --> 00:06:48,430
+بصديش هاي ال rust ايش معناته يعني صدق tools steals
+
+86
+00:06:48,430 --> 00:06:52,650
+بتعرفوا انتوا لما تيجوا سكاكين او يمكن الحاجات
+
+87
+00:06:52,650 --> 00:06:59,250
+اللي بنقطع فيهم زي تبع المجدحة او المبارد او كل
+
+88
+00:06:59,250 --> 00:07:03,210
+هذه هاتف بيسميها tools steal they contain
+
+89
+00:07:03,210 --> 00:07:07,110
+tungestin and cobalt ال tungestin و ال cobalt
+
+90
+00:07:07,110 --> 00:07:12,360
+هدولة tough material يعني جامدةOkay a widely used
+
+91
+00:07:12,360 --> 00:07:17,340
+grade of tools steel is high-speed steel which is
+
+92
+00:07:17,340 --> 00:07:20,180
+used in cutting tools that operate at a high
+
+93
+00:07:20,180 --> 00:07:23,740
+temperature such as drill bits إيش يعني drill
+
+94
+00:07:23,740 --> 00:07:31,340
+bits؟ لأ بتعرفوا الريش تبعات المجدح؟ هذا بيسموها
+
+95
+00:07:31,340 --> 00:07:35,950
+إيش؟ ال drillbits ما انتوا البنات مش اكتر خبرتكم
+
+96
+00:07:35,950 --> 00:07:41,270
+في هذه الشغلة الشباب هذه الشغلات معظمهم جربوها
+
+97
+00:07:41,270 --> 00:07:44,690
+فالان
+
+98
+00:07:44,690 --> 00:07:48,210
+هذه اللي بنتكلم عنهم فعنا كام نوع من هدول النوع
+
+99
+00:07:48,210 --> 00:07:57,570
+اللي بسميه alloy steel اربع نوع ايش هما low alloy
+
+100
+00:08:02,120 --> 00:08:07,880
+Stainless Steel والرابعة Tools Steel الآن عندنا
+
+101
+00:08:07,880 --> 00:08:11,760
+حاجة بنسميها ال Corrosion إيش هي ال Corrosion؟ هي
+
+102
+00:08:11,760 --> 00:08:20,020
+ال Oxidization أو ال Oxide هي ال Rust إيش يعني؟
+
+103
+00:08:20,020 --> 00:08:26,180
+عملية الصدق عملية الصدق بنسميها عملية أكسدة أو
+
+104
+00:08:26,180 --> 00:08:34,220
+عملية آكل هن التلاتة لنفس المسمةكويس؟ فهنا one
+
+105
+00:08:34,220 --> 00:08:39,060
+weakness of mild steel is that it corrodes its
+
+106
+00:08:39,060 --> 00:08:43,320
+surface progressively deteriorates due to a
+
+107
+00:08:43,320 --> 00:08:48,520
+chemical reaction إيش يعني deteriorates؟
+
+108
+00:08:48,520 --> 00:08:54,520
+الآن خلينا نقول corrodes اللي هي بتتأكلالان due to
+
+109
+00:08:54,520 --> 00:08:58,660
+rates تشوفوا لما الحاجة تبدأ ت .. يعني خلينا نفس
+
+110
+00:08:58,660 --> 00:09:03,680
+الكلمة هي due to rates لما تصير تروح للأسوأ شوية
+
+111
+00:09:03,680 --> 00:09:08,740
+شوية بتتشوه تدهور بتتدهور يعني وضعها بتدهور
+
+112
+00:09:08,740 --> 00:09:13,880
+بيقولها due to rate فهي بتبقى في حالة مثلا معينة و
+
+113
+00:09:13,880 --> 00:09:16,960
+بيصير كل ما فيها شي تراجع بنسميها due to rates
+
+114
+00:09:16,960 --> 00:09:24,420
+اللي عنديهذه الاتفاق تأخذ مقاطع بين الحر في السلطة
+
+115
+00:09:24,420 --> 00:09:31,240
+والهواء في الهواء لتصميم عصيد عصير عصير عصير عصير
+
+116
+00:09:31,240 --> 00:09:33,020
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+117
+00:09:33,020 --> 00:09:33,060
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+118
+00:09:33,060 --> 00:09:38,640
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+119
+00:09:38,640 --> 00:09:38,660
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+120
+00:09:38,660 --> 00:09:42,480
+عصير عصير عصير عصير عصير عصير عصير ع
+
+121
+00:09:45,880 --> 00:09:51,460
+و ال oxidized و ال what و ال corrodes هم في
+
+122
+00:09:51,460 --> 00:09:56,420
+المفقول واحد هو بيكونوا طبقة صدقة
+
+123
+00:10:00,110 --> 00:10:04,650
+في بعض الميثال مثل الألمنيوم، لا يوجد مشكلة في
+
+124
+00:10:04,650 --> 00:10:09,410
+وجود الكروجين لأن مجموعة الحرارة في حول الميثال
+
+125
+00:10:09,410 --> 00:10:15,870
+تبقى صعبة و هذا يمنعها من إتصال أكثر. الآن في
+
+126
+00:10:15,870 --> 00:10:22,490
+الألمنيوم إيش بحصل؟ مش زي صدأ الحديد لأن الصدأ في
+
+127
+00:10:22,490 --> 00:10:27,590
+الحديد إيش بيصير فيه؟ بتاكل و بيصير يجعالألمونة
+
+128
+00:10:27,590 --> 00:10:31,170
+بيعمل الطبقة وبتضالها الطبقة hard فال hardness هذه
+
+129
+00:10:31,170 --> 00:10:36,790
+بيخليش اللي بعدها يصضي فبصير طبقة على الوجه مصضية
+
+130
+00:10:36,790 --> 00:10:40,890
+والباقي مافيش فيه مشكلة ان بتمش عملية التآكل
+
+131
+00:10:40,890 --> 00:10:46,510
+however when mild steel goes rusty the rust on the
+
+132
+00:10:46,510 --> 00:10:51,370
+surface comes off .. comes off ايش؟ يعني زي ما
+
+133
+00:10:51,370 --> 00:10:58,190
+تقول بتجشرأو يعني بسقط يتساقط يتساقط هي التكشير
+
+134
+00:10:58,190 --> 00:11:02,950
+continuously and a new rusty layer forms
+
+135
+00:11:02,950 --> 00:11:09,030
+progressively eating into the metal يعني بتتم أكل
+
+136
+00:11:09,030 --> 00:11:12,870
+الحديد تأكل الحديد و بتلاحظوا انتوا لو عندكم في
+
+137
+00:11:12,870 --> 00:11:17,230
+البيت اي حاجة و احنا في جو غزة ال rust هذا مشكلة
+
+138
+00:11:17,230 --> 00:11:21,590
+كبيرة بتلاقي شوية شوية لما الحديد لحاله يجعب
+
+139
+00:11:21,590 --> 00:11:29,770
+معناته ايش؟بتاكل بسرعة جدا طيب الآن decide whether
+
+140
+00:11:29,770 --> 00:11:34,030
+the sentences below are true or false and correct
+
+141
+00:11:34,030 --> 00:11:38,570
+the false sentences steel is an alloy of iron and
+
+142
+00:11:38,570 --> 00:11:42,930
+carbon true
+
+143
+00:11:42,930 --> 00:11:47,790
+مظبوط مش قولنا المحاضرة اللي فاتت ال steel هو نوع
+
+144
+00:11:47,790 --> 00:11:53,770
+هو alloyهو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+145
+00:11:53,770 --> 00:11:57,250
+هو
+
+146
+00:11:57,250 --> 00:11:57,510
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+147
+00:11:57,510 --> 00:11:57,690
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+148
+00:11:57,690 --> 00:11:57,710
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+149
+00:11:57,710 --> 00:11:58,050
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+150
+00:11:58,050 --> 00:11:58,510
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+151
+00:11:58,510 --> 00:11:59,610
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+152
+00:11:59,610 --> 00:12:01,330
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+153
+00:12:01,330 --> 00:12:01,730
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+154
+00:12:01,730 --> 00:12:03,090
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+155
+00:12:03,090 --> 00:12:12,330
+هو هو هو هو هو هو هو هو هو هو هو هو هو هوهوهوهوه
+
+156
+00:12:15,660 --> 00:12:20,340
+chromium and nickel are used as alloying metal in
+
+157
+00:12:20,340 --> 00:12:26,220
+steel مش قولنا عندنا إيش؟ في كبشة alloying
+
+158
+00:12:26,220 --> 00:12:30,840
+material، هذا .. هذا نوع منهم، كويس؟ low alloy
+
+159
+00:12:30,840 --> 00:12:36,200
+steel contain more chromium than iron، false في
+
+160
+00:12:36,200 --> 00:12:40,560
+أصلا في ال steel كله فيش حاجة أكتر من إيش؟ ال iron
+
+161
+00:12:42,360 --> 00:12:47,820
+الـ stainless steel is an alloy steel true احنا
+
+162
+00:12:47,820 --> 00:12:52,040
+نقول لإيش هو المسمى تبعنا بيجي تحت ال alloy
+
+163
+00:12:52,040 --> 00:12:57,240
+alloying steel أو alloy steels tungsten is added
+
+164
+00:12:57,240 --> 00:13:03,580
+to steel to make it softer false إيش بتعمل harder
+
+165
+00:13:03,580 --> 00:13:09,120
+مش softerhigh speed steel is suitable for making
+
+166
+00:13:09,120 --> 00:13:16,720
+cutting tools that get very hot احنا
+
+167
+00:13:16,720 --> 00:13:22,320
+ايش قلنا اللي بنعمل فيه true مظبوط هو tools نفس
+
+168
+00:13:22,320 --> 00:13:27,720
+الشي ايش cutting tools get very hot فبدك ايش افضل
+
+169
+00:13:27,720 --> 00:13:31,240
+انواع اللي هي high speed steel اللي هي نفس المسمى
+
+170
+00:13:31,240 --> 00:13:40,590
+لمين لل tools steelنفس المسمة اللي بتلاحظ فيه طيب
+
+171
+00:13:40,590 --> 00:13:44,430
+الان complete ال table ال table اللي هابنا نكمله
+
+172
+00:13:44,430 --> 00:13:49,250
+الان عندي ال corroded ال adjective ال noun إيش هو?
+
+173
+00:13:51,810 --> 00:14:00,670
+corrosion مظبوط ال verb? corrode مظبوط طيب ال
+
+174
+00:14:00,670 --> 00:14:02,310
+oxidized
+
+175
+00:14:04,730 --> 00:14:10,890
+oxide مظبوط ال noun oxide صح لما نقول عنه مثلا
+
+176
+00:14:10,890 --> 00:14:18,670
+carbon oxide ذاكرينه فهذا ال noun oxide طيب ال
+
+177
+00:14:18,670 --> 00:14:26,410
+verb oxidize طيب ال هنا go rusty ايش ال verb ممكن
+
+178
+00:14:26,410 --> 00:14:36,110
+يكون كمان rust ال nounrust ال adjective rusty طب
+
+179
+00:14:36,110 --> 00:14:40,170
+خلينا نشوف هنا وين نعبيهم when steel is exposed to
+
+180
+00:14:40,170 --> 00:14:45,450
+air and water it oxidize
+
+181
+00:14:45,450 --> 00:14:52,070
+ايش كمان؟ rust ايش كمان؟ corrodes التلاتة مجوزة
+
+182
+00:14:52,070 --> 00:14:57,470
+التلاتة نفس المعنى هذا يعني بدك الفعل اللي هنا و
+
+183
+00:14:57,470 --> 00:15:03,810
+تحطيه ES او Sطيب a brown red material on the
+
+184
+00:15:03,810 --> 00:15:10,110
+surface of steel is called corrosion التلاتة rust
+
+185
+00:15:10,110 --> 00:15:15,190
+and oxide طيب the strength of steel is reduced if
+
+186
+00:15:15,190 --> 00:15:20,210
+it is نحط ال adjective الآن، إيش ال adjective؟
+
+187
+00:15:20,210 --> 00:15:28,550
+التلاتة، فهي تكون oxidized أو rusty أو corroded
+
+188
+00:15:31,280 --> 00:15:35,920
+هذه الأجابة هنا طيب هنا complete the article about
+
+189
+00:15:35,920 --> 00:15:40,160
+a special type of steel the perennial problem with
+
+190
+00:15:40,160 --> 00:15:44,440
+mild .. إيش
+
+191
+00:15:44,440 --> 00:15:50,480
+الكلمة؟ إيش ال perennial problem؟ اللي مرت عليكم؟
+
+192
+00:15:50,480 --> 00:15:57,060
+المشكلة الدائمة أو الأزالية لمين؟ with mildsteel
+
+193
+00:15:57,060 --> 00:16:02,580
+مظبوط is إتقت إيش when exposed air and water إيش
+
+194
+00:16:02,580 --> 00:16:12,020
+بتصيرلها it rusts or it corrodes or it oxidize طيب
+
+195
+00:16:12,020 --> 00:16:15,920
+generally the only solution is either to apply a
+
+196
+00:16:15,920 --> 00:16:21,660
+protective coating to use or to use another edge
+
+197
+00:16:21,660 --> 00:16:26,920
+of the steelأيوة another grades ال grades يعني في
+
+198
+00:16:26,920 --> 00:16:30,400
+هذا الحالة إيش بنحكي فيه ال type أو variations
+
+199
+00:16:30,400 --> 00:16:35,300
+مظبوط احنا عندنا بعض الأنواع اللي هي يمكن هذه
+
+200
+00:16:35,300 --> 00:16:41,600
+بتشوفوها اللي مين ساكنين قريب للبحر بشكل مباشر إيش
+
+201
+00:16:41,600 --> 00:16:45,120
+بتلاقي عندكوا كل إشي إيش بيصيرله بسرعة
+
+202
+00:16:46,690 --> 00:16:51,310
+كبيرة فلازم كل شي تعمليله يا أما بدك تدهني بشكل
+
+203
+00:16:51,310 --> 00:16:57,090
+دائم أو بدك تجيبي حديد مقلبة مظبوط المقلبة ايش
+
+204
+00:16:57,090 --> 00:17:05,430
+بنعمله بنحط طبقة من ال stainless steel حواليه طيب
+
+205
+00:17:05,430 --> 00:17:11,830
+هنا used ايش قولنا another grade of steel that is
+
+206
+00:17:11,830 --> 00:17:19,660
+resistant toto the rusting process او to corrosion
+
+207
+00:17:19,660 --> 00:17:25,820
+process او to oxidize process the most well-known
+
+208
+00:17:25,820 --> 00:17:30,880
+being ايش steel؟ stainless steel ماحنا قولنا هذا
+
+209
+00:17:30,880 --> 00:17:34,100
+انتوا خبرة فيها stainless steel which contains
+
+210
+00:17:34,100 --> 00:17:38,220
+significant quantity of ايش؟ and often nickel
+
+211
+00:17:38,220 --> 00:17:45,590
+chromium مظبوطعندها طبقة كبيرة بالـ alloy تبع كروم
+
+212
+00:17:45,590 --> 00:17:49,690
+و شوية نيكل there is however an alternative
+
+213
+00:17:49,690 --> 00:17:56,610
+solution so-called weathering needs weathering
+
+214
+00:17:56,610 --> 00:18:00,570
+steel ال weathering steel إيش هذا اللي هو ال steel
+
+215
+00:18:00,570 --> 00:18:04,970
+اللي بتعاوأ اللي يعني خلّيني أقول متأقلم مع الجو
+
+216
+00:18:04,970 --> 00:18:07,210
+كويس؟
+
+217
+00:18:08,200 --> 00:18:11,920
+is a special alloy suitable for outdoor use but
+
+218
+00:18:11,920 --> 00:18:14,720
+rather than being completely protected from
+
+219
+00:18:14,720 --> 00:18:18,540
+corrosion the surface of the steel is allowed to
+
+220
+00:18:18,540 --> 00:18:26,320
+go to go ايش rusty rusty ليش هذا ايش بتخلي انه
+
+221
+00:18:26,320 --> 00:18:31,400
+مسموح ان يصير طبقة من ال rust بس ايش اللي بيعمل ال
+
+222
+00:18:31,400 --> 00:18:37,700
+rust هذا هذا الطبقة hard تسمحش للي بعدهاالطبقات
+
+223
+00:18:37,700 --> 00:18:43,100
+الداخلية سيرلها أكسدها تاني once a layer of إيش
+
+224
+00:18:43,100 --> 00:18:49,680
+has formed on the surface a layer of إيش؟ of rust
+
+225
+00:18:49,680 --> 00:18:58,280
+أو أكسيد أو كروجل okay it stabilizes
+
+226
+00:18:58,280 --> 00:19:02,580
+and forms a hard protective layer إيش
+
+227
+00:19:02,580 --> 00:19:04,300
+stabilizable؟
+
+228
+00:19:07,650 --> 00:19:15,630
+ايش stable بتستقر .. هد بتستقر و بتشكل طبقة hard
+
+229
+00:19:15,630 --> 00:19:22,470
+اللي هي ايش صلبة this layer differs from ordinary
+
+230
+00:19:22,470 --> 00:19:28,050
+iron oxide as it does not continue to eat into the
+
+231
+00:19:28,050 --> 00:19:35,170
+metal هد بتبطلهاش تستمر تاكل في ال metal صوت صوت
+
+232
+00:19:35,170 --> 00:19:42,860
+صوتwhile not everyone may like the rusty look,
+
+233
+00:19:43,420 --> 00:19:46,420
+weathering steel has been widely used in
+
+234
+00:19:46,420 --> 00:19:50,940
+architectures, applications and outdoor sculptures
+
+235
+00:19:50,940 --> 00:19:57,120
+إيش يعني sculpture؟ شايفين هذا المنظر اللي قدامكم؟
+
+236
+00:19:57,120 --> 00:20:04,760
+اللي ع الصورة، الصورة، إيش هذا؟مجسم، مظبوط؟ اه ..
+
+237
+00:20:04,760 --> 00:20:11,020
+ايوة فهذا ال outdoor sculptures اللي هي المجسمات
+
+238
+00:20:11,020 --> 00:20:14,000
+اللي في الآخر معمولة من الحديد بيستخدموها في هذا
+
+239
+00:20:14,000 --> 00:20:17,700
+الشكل احنا في بلادنا مش كتير هذا بتشوفيه بس ببلاد
+
+240
+00:20:17,700 --> 00:20:24,220
+الأوروبا موجود بشكل كتير في كل مكان لو بتشوفيه حتى
+
+241
+00:20:24,220 --> 00:20:26,780
+الشكل المصضي هذا بتشوفيه طبيعي
+
+242
+00:20:31,460 --> 00:20:38,000
+طيب هيك بنبقى خلصنا chapter twelve الان يمكن من
+
+243
+00:20:38,000 --> 00:20:42,260
+الشغلات اللى بنطلع عليهم اول حاجة ال steel عندنا
+
+244
+00:20:42,260 --> 00:20:47,800
+نوعين منه صح عندنا ايش carbon steels و ايش
+
+245
+00:20:47,800 --> 00:20:52,080
+alloying steels ال carbon steel عندنا three grades
+
+246
+00:20:52,080 --> 00:21:00,890
+فيهم ايش هما mild و mediumوهاي هدولة عادة نسبة ال
+
+247
+00:21:00,890 --> 00:21:05,610
+carbon فيهم قداش منخفضة من point three percent لحد
+
+248
+00:21:05,610 --> 00:21:11,110
+ديت one point four الباقي كله ايش iron مافيش عندي
+
+249
+00:21:11,110 --> 00:21:17,490
+any other alloying materials بس carbon and iron ال
+
+250
+00:21:17,490 --> 00:21:22,270
+alloying steels الأنواع التانية بتختلف عن الأربع
+
+251
+00:21:22,270 --> 00:21:25,770
+ايش هم اللوهاد
+
+252
+00:21:25,770 --> 00:21:34,550
+ايش مميزتهانيني برسنت ايرن و تين برسنت ايش؟ ايوة و
+
+253
+00:21:34,550 --> 00:21:40,630
+هذه ايش الأنواع ال alloy اللي بنضيفهم؟ طيب النوع
+
+254
+00:21:40,630 --> 00:21:46,730
+التاني high string
+
+255
+00:21:46,730 --> 00:21:51,570
+ايش هذه؟ نسبة ال alloy قداشر؟ less than two
+
+256
+00:21:51,570 --> 00:21:57,270
+percentالان نوع التالت اللي هي ال stainless steel
+
+257
+00:21:57,270 --> 00:22:01,890
+ال stainless steel قد ايش الميزة تبعته؟ بنضيف ال
+
+258
+00:22:01,890 --> 00:22:06,030
+chromium و بنضيف ايش؟
+
+259
+00:22:06,030 --> 00:22:11,290
+nickels okay الان النوع الرابع ال tools او ال high
+
+260
+00:22:11,290 --> 00:22:17,150
+speed ايش؟ steel هذه اللي بنضيف ايش عندنا؟ ال
+
+261
+00:22:17,150 --> 00:22:21,810
+cobalt و ال ايش؟وال tungsten مظبوط هدول ال hard
+
+262
+00:22:21,810 --> 00:22:25,210
+عشان هم بيبقوا very hard و very tough فبنستخدمهم
+
+263
+00:22:25,210 --> 00:22:30,530
+لل cutting tools لما في حرارة درجة حرارة احتكاك
+
+264
+00:22:30,530 --> 00:22:34,430
+بتعمل درجة حرارة هدول اللي بتحمله درجات الحرارة
+
+265
+00:22:34,430 --> 00:22:34,910
+العالية
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5ebe6efd6f71049fd007816582445da4121b1ded
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_raw.json
@@ -0,0 +1 @@
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"temperature": 1.0}, {"id": 15, "seek": 34768, "start": 332.66, "end": 347.68, "text": "أو المزيد من الأسلحة وحتى 10% من المواد التجارية مثل اوكروميا نكو مانجانيز موليبيديا", "tokens": [10721, 2407, 9673, 11622, 25708, 9154, 16247, 3794, 1211, 5016, 3660, 4032, 33753, 7578, 1266, 4, 9154, 9673, 14407, 3215, 16712, 7435, 9640, 10632, 50113, 1211, 1975, 2407, 37983, 20498, 25528, 8717, 4117, 2407, 3714, 7649, 7435, 7649, 1829, 11622, 3714, 12610, 1829, 21292, 16254, 995], "avg_logprob": -0.6625665045799093, "compression_ratio": 1.4205607476635513, "no_speech_prob": 0.0, "words": [{"start": 332.66, "end": 333.08, "word": "أو", "probability": 0.760986328125}, {"start": 333.08, "end": 333.52, "word": " المزيد", "probability": 0.6155598958333334}, {"start": 333.52, "end": 333.82, "word": " من", "probability": 0.9814453125}, {"start": 333.82, "end": 334.26, "word": " الأسلحة", "probability": 0.6065673828125}, {"start": 334.26, "end": 335.28, "word": " وحتى", "probability": 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ايش بنسميه low alloying steel لأن في عندي تسعين فالمية iron والباقي alloying materials high strength low alloying steel which contains smaller quantity of the above metals", "tokens": [53, 282, 13534, 8032, 3215, 12610, 16247, 1863, 14407, 3615, 9673, 29245, 23328, 3660, 13672, 1829, 44945, 5016, 9566, 16095, 8978, 16095, 23758, 1975, 1829, 8592, 44945, 38251, 1829, 3224, 2295, 37819, 278, 8269, 5296, 33456, 8978, 18871, 16254, 6055, 3794, 3615, 9957, 6156, 45340, 10632, 6497, 16070, 3555, 995, 38436, 37819, 278, 5319, 1090, 3800, 2295, 37819, 278, 8269, 597, 8306, 4356, 11275, 295, 264, 3673, 22548], "avg_logprob": -0.26019021220829175, "compression_ratio": 1.475, "no_speech_prob": 0.0, "words": [{"start": 349.11999999999995, "end": 350.28, "word": "Vanadium", "probability": 0.79052734375}, {"start": 350.28, "end": 350.96, "word": " هدول", "probability": 0.7890625}, {"start": 350.96, "end": 351.48, "word": " الأنواع", "probability": 0.8726806640625}, {"start": 351.48, "end": 352.7, 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"probability": 0.72900390625}, {"start": 357.38, "end": 358.36, "word": " تسعين", "probability": 0.848876953125}, {"start": 358.36, "end": 358.94, "word": " فالمية", "probability": 0.6979166666666666}, {"start": 358.94, "end": 359.86, "word": " iron", "probability": 0.25732421875}, {"start": 359.86, "end": 360.64, "word": " والباقي", "probability": 0.8271484375}, {"start": 360.64, "end": 362.0, "word": " alloying", "probability": 0.77294921875}, {"start": 362.0, "end": 362.78, "word": " materials", "probability": 0.4150390625}, {"start": 362.78, "end": 364.38, "word": " high", "probability": 0.62451171875}, {"start": 364.38, "end": 364.9, "word": " strength", "probability": 0.890625}, {"start": 364.9, "end": 365.22, "word": " low", "probability": 0.91796875}, {"start": 365.22, "end": 365.84, "word": " alloying", "probability": 0.934814453125}, {"start": 365.84, "end": 366.32, "word": " steel", "probability": 0.9296875}, {"start": 366.32, "end": 367.72, "word": " which", "probability": 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هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هوهوهوهوه", "tokens": [3224, 2407, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 31439, 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"probability": 0.93994140625}, {"start": 1267.47, "end": 1268.63, "word": " الباقي", "probability": 0.751953125}, {"start": 1268.63, "end": 1269.07, "word": " كله", "probability": 0.983642578125}, {"start": 1269.07, "end": 1269.41, "word": " ايش", "probability": 0.81591796875}, {"start": 1269.41, "end": 1270.15, "word": " iron", "probability": 0.3740234375}, {"start": 1270.15, "end": 1270.61, "word": " مافيش", "probability": 0.7481282552083334}, {"start": 1270.61, "end": 1271.11, "word": " عندي", "probability": 0.7261962890625}, {"start": 1271.11, "end": 1271.53, "word": " any", "probability": 0.448486328125}, {"start": 1271.53, "end": 1272.69, "word": " other", "probability": 0.68994140625}, {"start": 1272.69, "end": 1273.35, "word": " alloying", "probability": 0.718994140625}, {"start": 1273.35, "end": 1274.17, "word": " materials", "probability": 0.75390625}, {"start": 1274.17, "end": 1274.91, "word": " بس", "probability": 0.968505859375}, {"start": 1274.91, "end": 1275.49, "word": " carbon", "probability": 0.9482421875}, {"start": 1275.49, "end": 1276.09, "word": " and", "probability": 0.91796875}, {"start": 1276.09, "end": 1276.65, "word": " iron", "probability": 0.88818359375}, {"start": 1276.65, "end": 1277.49, "word": " ال", "probability": 0.94384765625}, {"start": 1277.49, "end": 1278.33, "word": " alloying", "probability": 0.9111328125}, {"start": 1278.33, "end": 1278.81, "word": " steels", "probability": 0.6907958984375}, {"start": 1278.81, "end": 1279.39, "word": " الأنواع", "probability": 0.9359130859375}, {"start": 1279.39, "end": 1280.03, "word": " التانية", "probability": 0.9881184895833334}, {"start": 1280.03, "end": 1281.35, "word": " بتختلف", "probability": 0.9690755208333334}, {"start": 1281.35, "end": 1281.63, "word": " عن", "probability": 0.810546875}, {"start": 1281.63, "end": 1282.27, "word": " الأربع", "probability": 0.8077799479166666}, {"start": 1282.27, "end": 1282.53, "word": " ايش", "probability": 0.8126627604166666}, {"start": 1282.53, "end": 1282.75, "word": " هم", "probability": 0.7310791015625}, {"start": 1282.75, "end": 1285.77, "word": " اللوهاد", "probability": 0.5478515625}, {"start": 1285.77, "end": 1286.01, "word": " ايش", "probability": 0.9161783854166666}, {"start": 1286.01, "end": 1286.93, "word": " مميزتها", "probability": 0.9327799479166666}], "temperature": 1.0}, {"id": 51, "seek": 131219, "start": 1287.97, "end": 1312.19, "text": "نيني برسنت ايرن و تين برسنت ايش؟ ايوة و هذه ايش الأنواع ال alloy اللي بنضيفهم؟ طيب النوع التاني high string ايش هذه؟ نسبة ال alloy قداشر؟ less than two percent", "tokens": [1863, 9957, 1829, 4724, 2288, 3794, 29399, 1975, 13546, 1863, 4032, 6055, 9957, 4724, 2288, 3794, 29399, 1975, 1829, 8592, 22807, 1975, 1829, 2407, 3660, 4032, 29538, 1975, 1829, 8592, 16247, 1863, 14407, 3615, 2423, 37819, 13672, 1829, 44945, 11242, 33911, 16095, 22807, 23032, 1829, 3555, 28239, 45367, 16712, 7649, 1829, 1090, 6798, 1975, 1829, 8592, 29538, 22807, 8717, 35457, 3660, 2423, 37819, 12174, 3215, 33599, 2288, 22807, 1570, 813, 732, 3043], "avg_logprob": -0.3424657403606258, "compression_ratio": 1.5151515151515151, "no_speech_prob": 0.0, "words": [{"start": 1287.97, "end": 1288.49, "word": "نيني", "probability": 0.580322265625}, {"start": 1288.49, "end": 1289.17, "word": " برسنت", "probability": 0.7947998046875}, {"start": 1289.17, "end": 1290.45, "word": " ايرن", "probability": 0.5476888020833334}, {"start": 1290.45, "end": 1290.59, "word": " و", "probability": 0.6005859375}, {"start": 1290.59, "end": 1290.83, "word": " تين", "probability": 0.614990234375}, {"start": 1290.83, "end": 1291.43, "word": " برسنت", "probability": 0.946044921875}, {"start": 1291.43, "end": 1291.99, "word": " ايش؟", "probability": 0.7352294921875}, {"start": 1291.99, "end": 1294.27, "word": " ايوة", "probability": 0.6641845703125}, {"start": 1294.27, "end": 1294.55, "word": " و", "probability": 0.455810546875}, {"start": 1294.55, "end": 1294.83, "word": " هذه", "probability": 0.449951171875}, {"start": 1294.83, "end": 1295.09, "word": " ايش", "probability": 0.80029296875}, {"start": 1295.09, "end": 1295.53, "word": " الأنواع", "probability": 0.8515625}, {"start": 1295.53, "end": 1295.67, "word": " ال", "probability": 0.8310546875}, {"start": 1295.67, "end": 1296.03, "word": " alloy", "probability": 0.54931640625}, {"start": 1296.03, "end": 1296.29, "word": " اللي", "probability": 0.830810546875}, {"start": 1296.29, "end": 1297.25, "word": " بنضيفهم؟", "probability": 0.84169921875}, {"start": 1297.25, "end": 1300.15, "word": " طيب", "probability": 0.8580729166666666}, {"start": 1300.15, "end": 1300.63, "word": " النوع", "probability": 0.92431640625}, {"start": 1300.63, "end": 1301.67, "word": " التاني", "probability": 0.9181315104166666}, {"start": 1301.67, "end": 1303.39, "word": " high", "probability": 0.211669921875}, {"start": 1303.39, "end": 1306.73, "word": " string", "probability": 0.333740234375}, {"start": 1306.73, "end": 1306.97, "word": " ايش", "probability": 0.7008463541666666}, {"start": 1306.97, "end": 1307.35, "word": " هذه؟", "probability": 0.45947265625}, {"start": 1307.35, "end": 1307.71, "word": " نسبة", "probability": 0.9807942708333334}, {"start": 1307.71, "end": 1307.85, "word": " ال", "probability": 0.9521484375}, {"start": 1307.85, "end": 1308.19, "word": " alloy", "probability": 0.953125}, {"start": 1308.19, "end": 1310.57, "word": " قداشر؟", "probability": 0.695703125}, {"start": 1310.57, "end": 1310.97, "word": " less", "probability": 0.875}, {"start": 1310.97, "end": 1311.29, "word": " than", "probability": 0.92431640625}, {"start": 1311.29, "end": 1311.57, "word": " two", "probability": 0.71533203125}, {"start": 1311.57, "end": 1312.19, "word": " percent", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 52, "seek": 133873, "start": 1313.57, "end": 1338.73, "text": "الان نوع التالت اللي هي ال stainless steel ال stainless steel قد ايش الميزة تبعته؟ بنضيف ال chromium و بنضيف ايش؟ nickels okay الان النوع الرابع ال tools او ال high speed ايش؟ steel هذه اللي بنضيف ايش عندنا؟ ال cobalt و ال ايش؟", "tokens": [6027, 7649, 8717, 45367, 16712, 6027, 2655, 13672, 1829, 39896, 2423, 24048, 8269, 2423, 24048, 8269, 12174, 3215, 1975, 1829, 8592, 9673, 1829, 11622, 3660, 6055, 3555, 34268, 3224, 22807, 44945, 11242, 33911, 2423, 16209, 2197, 4032, 44945, 11242, 33911, 1975, 1829, 8592, 22807, 30542, 82, 1392, 2423, 7649, 28239, 45367, 34892, 16758, 3615, 2423, 3873, 1975, 2407, 2423, 1090, 3073, 1975, 1829, 8592, 22807, 8269, 29538, 13672, 1829, 44945, 11242, 33911, 1975, 1829, 8592, 43242, 8315, 22807, 2423, 598, 2645, 83, 4032, 2423, 1975, 1829, 8592, 22807], "avg_logprob": -0.216994388719623, "compression_ratio": 1.803191489361702, "no_speech_prob": 0.0, "words": [{"start": 1313.57, "end": 1314.05, "word": "الان", "probability": 0.831787109375}, {"start": 1314.05, "end": 1314.33, "word": " نوع", "probability": 0.848388671875}, {"start": 1314.33, "end": 1315.07, "word": " التالت", "probability": 0.97412109375}, {"start": 1315.07, "end": 1315.55, "word": " اللي", "probability": 0.718017578125}, {"start": 1315.55, "end": 1315.69, "word": " هي", "probability": 0.55810546875}, {"start": 1315.69, "end": 1315.87, "word": " ال", "probability": 0.67236328125}, {"start": 1315.87, "end": 1316.31, "word": " stainless", "probability": 0.7265625}, {"start": 1316.31, "end": 1317.27, "word": " steel", "probability": 0.9423828125}, {"start": 1317.27, "end": 1317.59, "word": " ال", "probability": 0.43603515625}, {"start": 1317.59, "end": 1317.99, "word": " stainless", "probability": 0.92431640625}, {"start": 1317.99, "end": 1318.53, "word": " steel", "probability": 0.92138671875}, {"start": 1318.53, "end": 1318.79, "word": " قد", "probability": 0.7216796875}, {"start": 1318.79, "end": 1319.19, "word": " ايش", "probability": 0.7431640625}, {"start": 1319.19, "end": 1319.79, "word": " الميزة", "probability": 0.7969970703125}, {"start": 1319.79, "end": 1320.77, "word": " تبعته؟", "probability": 0.832177734375}, {"start": 1320.77, "end": 1321.31, "word": " بنضيف", "probability": 0.9580078125}, {"start": 1321.31, "end": 1321.89, "word": " ال", "probability": 0.38623046875}, {"start": 1321.89, "end": 1322.45, "word": " chromium", "probability": 0.89404296875}, {"start": 1322.45, "end": 1322.61, "word": " و", "probability": 0.83056640625}, {"start": 1322.61, "end": 1322.99, "word": " بنضيف", "probability": 0.92431640625}, {"start": 1322.99, "end": 1326.03, "word": " ايش؟", "probability": 0.8385009765625}, {"start": 1326.03, "end": 1326.99, "word": " nickels", "probability": 0.75048828125}, {"start": 1326.99, "end": 1327.31, "word": " okay", "probability": 0.55615234375}, {"start": 1327.31, "end": 1328.21, "word": " الان", "probability": 0.854248046875}, {"start": 1328.21, "end": 1328.57, "word": " النوع", "probability": 0.926513671875}, {"start": 1328.57, "end": 1329.23, "word": " الرابع", "probability": 0.9864908854166666}, {"start": 1329.23, "end": 1330.05, "word": " ال", "probability": 0.83203125}, {"start": 1330.05, "end": 1330.51, "word": " tools", "probability": 0.94677734375}, {"start": 1330.51, "end": 1330.87, "word": " او", "probability": 0.910888671875}, {"start": 1330.87, "end": 1331.01, "word": " ال", "probability": 0.94921875}, {"start": 1331.01, "end": 1331.29, "word": " high", "probability": 0.955078125}, {"start": 1331.29, "end": 1331.85, "word": " speed", "probability": 0.76904296875}, {"start": 1331.85, "end": 1333.43, "word": " ايش؟", "probability": 0.8843994140625}, {"start": 1333.43, "end": 1334.21, "word": " steel", "probability": 0.62353515625}, {"start": 1334.21, "end": 1335.07, "word": " هذه", "probability": 0.2052001953125}, {"start": 1335.07, "end": 1335.39, "word": " اللي", "probability": 0.926025390625}, {"start": 1335.39, "end": 1335.77, "word": " بنضيف", "probability": 0.96923828125}, {"start": 1335.77, "end": 1336.03, "word": " ايش", "probability": 0.966796875}, {"start": 1336.03, "end": 1336.97, "word": " عندنا؟", "probability": 0.861328125}, {"start": 1336.97, "end": 1337.15, "word": " ال", "probability": 0.8466796875}, {"start": 1337.15, "end": 1337.75, "word": " cobalt", "probability": 0.7854817708333334}, {"start": 1337.75, "end": 1337.87, "word": " و", "probability": 0.84375}, {"start": 1337.87, "end": 1337.95, "word": " ال", "probability": 0.53125}, {"start": 1337.95, "end": 1338.73, "word": " ايش؟", "probability": 0.8505859375}], "temperature": 1.0}, {"id": 53, "seek": 135491, "start": 1339.01, "end": 1354.91, "text": "وال tungsten مظبوط هدول ال hard عشان هم بيبقوا very hard و very tough فبنستخدمهم لل cutting tools لما في حرارة درجة حرارة احتكاك بتعمل درجة حرارة هدول اللي بتحمله درجات الحرارة العالية", "tokens": [2407, 6027, 41880, 6266, 3714, 19913, 3555, 2407, 9566, 8032, 3215, 12610, 2423, 1152, 6225, 8592, 7649, 8032, 2304, 4724, 1829, 3555, 4587, 14407, 588, 1152, 4032, 588, 4930, 6156, 3555, 1863, 14851, 9778, 40448, 16095, 24976, 6492, 3873, 5296, 15042, 8978, 11331, 2288, 9640, 3660, 11778, 47341, 3660, 11331, 2288, 9640, 3660, 1975, 33753, 4117, 995, 4117, 39894, 25957, 1211, 11778, 47341, 3660, 11331, 2288, 9640, 3660, 8032, 3215, 12610, 13672, 1829, 39894, 35571, 43761, 11778, 47341, 9307, 21542, 2288, 9640, 3660, 18863, 6027, 10632], "avg_logprob": -0.12320402281722803, "compression_ratio": 1.6480446927374302, "no_speech_prob": 0.0, "words": [{"start": 1339.01, "end": 1339.33, "word": "وال", "probability": 0.769775390625}, {"start": 1339.33, "end": 1340.03, "word": " tungsten", "probability": 0.358154296875}, {"start": 1340.03, "end": 1340.85, "word": " مظبوط", "probability": 0.92724609375}, {"start": 1340.85, "end": 1341.23, "word": " هدول", "probability": 0.8665364583333334}, {"start": 1341.23, "end": 1341.39, "word": " ال", "probability": 0.8994140625}, {"start": 1341.39, "end": 1341.81, "word": " hard", "probability": 0.876953125}, {"start": 1341.81, "end": 1342.37, "word": " عشان", "probability": 0.9710286458333334}, {"start": 1342.37, "end": 1342.47, "word": " هم", "probability": 0.6455078125}, {"start": 1342.47, "end": 1342.77, "word": " بيبقوا", "probability": 0.97080078125}, {"start": 1342.77, "end": 1343.05, "word": " very", "probability": 0.876953125}, {"start": 1343.05, "end": 1343.41, "word": " hard", "probability": 0.92041015625}, {"start": 1343.41, "end": 1343.53, "word": " و", "probability": 0.53125}, {"start": 1343.53, "end": 1343.73, "word": " very", "probability": 0.82421875}, {"start": 1343.73, "end": 1344.09, "word": " tough", "probability": 0.8720703125}, {"start": 1344.09, "end": 1345.21, "word": " فبنستخدمهم", "probability": 0.9815150669642857}, {"start": 1345.21, "end": 1345.53, "word": " لل", "probability": 0.62744140625}, {"start": 1345.53, "end": 1346.07, "word": " cutting", "probability": 0.9345703125}, {"start": 1346.07, "end": 1347.05, "word": " tools", "probability": 0.919921875}, {"start": 1347.05, "end": 1348.31, "word": " لما", "probability": 0.848876953125}, {"start": 1348.31, "end": 1348.55, "word": " في", "probability": 0.8681640625}, {"start": 1348.55, "end": 1349.09, "word": " حرارة", "probability": 0.9468994140625}, {"start": 1349.09, "end": 1349.43, "word": " درجة", "probability": 0.86376953125}, {"start": 1349.43, "end": 1349.99, "word": " حرارة", "probability": 0.9937744140625}, {"start": 1349.99, "end": 1350.53, "word": " احتكاك", "probability": 0.86875}, {"start": 1350.53, "end": 1350.95, "word": " بتعمل", "probability": 0.8662109375}, {"start": 1350.95, "end": 1351.31, "word": " درجة", "probability": 0.9892578125}, {"start": 1351.31, "end": 1351.67, "word": " حرارة", "probability": 0.9879150390625}, {"start": 1351.67, "end": 1352.03, "word": " هدول", "probability": 0.9861653645833334}, {"start": 1352.03, "end": 1352.59, "word": " اللي", "probability": 0.909423828125}, {"start": 1352.59, "end": 1353.27, "word": " بتحمله", "probability": 0.9026692708333334}, {"start": 1353.27, "end": 1353.81, "word": " درجات", "probability": 0.9759114583333334}, {"start": 1353.81, "end": 1354.43, "word": " الحرارة", "probability": 0.98974609375}, {"start": 1354.43, "end": 1354.91, "word": " العالية", "probability": 0.9920247395833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1355.093375, "duration_after_vad": 1283.5574999999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..becb54033311fbfd87760d6a9985596829186a19
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/NGIb7lBLSUw_raw.srt
@@ -0,0 +1,1076 @@
+1
+00:00:21,620 --> 00:00:27,320
+السلام عليكم اليوم
+
+2
+00:00:27,320 --> 00:00:32,160
+سنقوم بمقاطع حلقة 12 حلقة 12 تتكلم عن الصناعة
+
+3
+00:00:32,160 --> 00:00:40,800
+ثلاثة جزء من حلقة 12 أولا نتكلم عن الصناعة
+
+4
+00:00:40,800 --> 00:00:46,200
+الكاربون ثانوية نتكلم عن الصناعة الأسلحة ثالثة
+
+5
+00:00:46,200 --> 00:00:52,920
+نتكلم عن الصناعة الكوروجينCarbon Steel ماذا نقصده
+
+6
+00:00:52,920 --> 00:00:59,140
+بـ Carbon Steel؟ هذا إستجابة من مقال في جورنال
+
+7
+00:00:59,140 --> 00:01:02,800
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+8
+00:01:02,800 --> 00:01:02,940
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+9
+00:01:02,940 --> 00:01:03,320
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+10
+00:01:03,320 --> 00:01:03,720
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+11
+00:01:03,720 --> 00:01:06,240
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+12
+00:01:06,240 --> 00:01:12,460
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+13
+00:01:14,300 --> 00:01:18,540
+وأنواع مشتقات الستيل اللي هو أكتر الأنواع الحديد
+
+14
+00:01:18,540 --> 00:01:23,160
+استخدامها technically though this well-known alloy
+
+15
+00:01:23,160 --> 00:01:27,560
+of iron and carbon is not as simple as one might
+
+16
+00:01:27,560 --> 00:01:32,600
+think الفكرة هنا مش بالبساطة اللي بتعتقدوها steel
+
+17
+00:01:32,600 --> 00:01:38,700
+comes in a huge range of different grades الأنواع
+
+18
+00:01:38,700 --> 00:01:43,850
+تبعته والمواصفات مختلفةeach with different
+
+19
+00:01:43,850 --> 00:01:49,110
+characteristics كل واحد له مواصفات مختلفة for the
+
+20
+00:01:49,110 --> 00:01:53,870
+inexperienced it can be difficult to know where to
+
+21
+00:01:53,870 --> 00:01:58,510
+begin للي ما عندهم مش خبرة صعب نعرف من وين نبدأ
+
+22
+00:02:00,010 --> 00:02:05,810
+Carbon steel هذا الوضع الأول، مكان جيد للبدأ هو مع
+
+23
+00:02:05,810 --> 00:02:08,950
+الاتنين الرئيسيين من الصناعة الصناعة الصناعة
+
+24
+00:02:08,950 --> 00:02:10,750
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+25
+00:02:10,750 --> 00:02:11,610
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+26
+00:02:11,610 --> 00:02:12,290
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+27
+00:02:12,290 --> 00:02:12,670
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+28
+00:02:12,670 --> 00:02:12,830
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+29
+00:02:12,830 --> 00:02:13,490
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+30
+00:02:13,490 --> 00:02:13,990
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+31
+00:02:13,990 --> 00:02:14,150
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+32
+00:02:14,150 --> 00:02:14,150
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+33
+00:02:14,150 --> 00:02:17,190
+الصناعة الصناعة الصناعة الصناعة الصناعة الصناعة
+
+34
+00:02:17,190 --> 00:02:24,480
+الصناالان الان لا تحتوي على نسبة معينة لأي نسبة
+
+35
+00:02:24,480 --> 00:02:29,140
+أخرى، نسبة معينة كربونستيل يمكن ان يكون مقاطعًا
+
+36
+00:02:29,140 --> 00:02:34,660
+إلى ثلاثة مقاطع أساسيةعندنا تلات خانات لـ carbon
+
+37
+00:02:34,660 --> 00:02:39,040
+steel إيش همها؟ mild steel the most widely used
+
+38
+00:02:39,040 --> 00:02:42,820
+grade is a low carbon steel which contains up to
+
+39
+00:02:42,820 --> 00:02:47,300
+approximately point three percent of carbon يعني
+
+40
+00:02:47,300 --> 00:02:51,890
+اللي أنا بتطلع عليه هذا ال mild قديش بحتوىثلاثة من
+
+41
+00:02:51,890 --> 00:02:57,090
+عشرة بالمية كربون والباقي ايش؟ ايرن فهذا بنسميه
+
+42
+00:02:57,090 --> 00:03:01,570
+ايش؟ mild steel medium carbon steel contain
+
+43
+00:03:01,570 --> 00:03:07,500
+between approximately point three percentto point
+
+44
+00:03:07,500 --> 00:03:12,540
+six percent carbon يعني من point تلاتة ل point كام
+
+45
+00:03:12,540 --> 00:03:16,300
+ستة carbon high carbon steel contain between
+
+46
+00:03:16,300 --> 00:03:20,300
+approximately point six and one point four percent
+
+47
+00:03:20,300 --> 00:03:24,920
+carbon يعني هذا النسبة تبعته على إشي هذا الأنواع
+
+48
+00:03:24,920 --> 00:03:29,060
+one point four percent carbon الآن بنطلع عليهم هذا
+
+49
+00:03:29,060 --> 00:03:31,940
+التلات أنواع إيش هما mild
+
+50
+00:03:34,300 --> 00:03:39,000
+medium carbon steel و بعدين ايش high carbon steel
+
+51
+00:03:39,000 --> 00:03:42,980
+هدولة التلاتة كل اللي بيحتووا ايش carbons and
+
+52
+00:03:42,980 --> 00:03:46,400
+steel و ال carbon زي ما بتلاحظوا very low
+
+53
+00:03:46,400 --> 00:03:51,400
+quantities يعني لما تتكلم عن تلاتة من العشرة
+
+54
+00:03:51,400 --> 00:03:58,080
+بالمية نسبة يعني كل الف يعني كل كيلو في عليه تلاتة
+
+55
+00:03:58,080 --> 00:04:05,020
+gramهذه حاجة خفيفة جدا و أكتر واحد فيه كل ألف كل
+
+56
+00:04:05,020 --> 00:04:12,180
+كيلو يعني 14 gram برضه هذه النسبة بتبقى خفيفة
+
+57
+00:04:12,180 --> 00:04:17,620
+النوع التاني بنسميه
+
+58
+00:04:17,620 --> 00:04:22,890
+alloy steels الآن نحن بنعرف ال steel إيش نوعهit's
+
+59
+00:04:22,890 --> 00:04:26,930
+an alloy مظبوط مش معنى الكلام انه هذا سمناه alloy
+
+60
+00:04:26,930 --> 00:04:30,570
+steel ات نوع تاني مش alloy لأ هو هى بس التسمية
+
+61
+00:04:30,570 --> 00:04:34,610
+تبعته لإن هذه الأنواع اللي جاية فيه هنا في عيننا
+
+62
+00:04:34,610 --> 00:04:40,660
+othermetals بنحطهم مع الكربون كويس نيجي نطلعها the
+
+63
+00:04:40,660 --> 00:04:44,080
+second main category of steel is alloy steels
+
+64
+00:04:44,080 --> 00:04:48,540
+which consists of iron carbon and one or more
+
+65
+00:04:48,540 --> 00:04:53,500
+alloying material يعني احنا اش بنضيف حاجات اكتر
+
+66
+00:04:53,500 --> 00:04:57,980
+اللي هي واحدة او تنتين من ال material ال alloying
+
+67
+00:04:57,980 --> 00:05:02,800
+material التانية specific grade of the alloying
+
+68
+00:05:02,800 --> 00:05:03,800
+steel include
+
+69
+00:05:09,540 --> 00:05:20,940
+مش صغير طيب
+
+70
+00:05:20,940 --> 00:05:24,280
+ال include ايش اللي عندي ها؟ هاي الأنواع اللي
+
+71
+00:05:24,280 --> 00:05:29,780
+موجودة عندنا نطلع عليهم low alloy steel which
+
+72
+00:05:29,780 --> 00:05:38,060
+contains 90%أو المزيد من الأسلحة وحتى 10% من
+
+73
+00:05:38,060 --> 00:05:45,360
+المواد التجارية مثل اوكروميا نكو مانجانيز
+
+74
+00:05:45,360 --> 00:05:47,680
+موليبيديا
+
+75
+00:05:49,120 --> 00:05:53,780
+Vanadium هدول الأنواع الموجودة اللي بنحطهم فيهم
+
+76
+00:05:53,780 --> 00:05:57,380
+هذا ايش بنسميه low alloying steel لأن في عندي
+
+77
+00:05:57,380 --> 00:06:04,380
+تسعين فالمية iron والباقي alloying materials high
+
+78
+00:06:04,380 --> 00:06:10,720
+strength low alloying steel which contains smaller
+
+79
+00:06:10,720 --> 00:06:15,430
+quantity of the above metalsit's typically less
+
+80
+00:06:15,430 --> 00:06:19,250
+than two percent يعني هدول أقل اللي سمناه high
+
+81
+00:06:19,250 --> 00:06:23,730
+strength low alloying material الآن بيجي النوع
+
+82
+00:06:23,730 --> 00:06:26,890
+التالت اللي بيسميه ال stainless steel كل هيتكم
+
+83
+00:06:26,890 --> 00:06:32,630
+بتعرفوه هذا، مظبوط؟ which contain chromium as well
+
+84
+00:06:32,630 --> 00:06:36,850
+as other metals such as nickel and which do not
+
+85
+00:06:36,850 --> 00:06:40,130
+rust يعني إيش هذا ال stainless steel إيش محصله؟
+
+86
+00:06:41,070 --> 00:06:48,430
+بصديش هاي ال rust ايش معناته يعني صدق tools steals
+
+87
+00:06:48,430 --> 00:06:52,650
+بتعرفوا انتوا لما تيجوا سكاكين او يمكن الحاجات
+
+88
+00:06:52,650 --> 00:06:59,250
+اللي بنقطع فيهم زي تبع المجدحة او المبارد او كل
+
+89
+00:06:59,250 --> 00:07:03,210
+هذه هاتف بيسميها tools steal they contain
+
+90
+00:07:03,210 --> 00:07:07,110
+tungestin and cobalt ال tungestin و ال cobalt
+
+91
+00:07:07,110 --> 00:07:12,360
+هدولة tough material يعني جامدةOkay a widely used
+
+92
+00:07:12,360 --> 00:07:17,340
+grade of tools steel is high-speed steel which is
+
+93
+00:07:17,340 --> 00:07:20,180
+used in cutting tools that operate at a high
+
+94
+00:07:20,180 --> 00:07:23,740
+temperature such as drill bits إيش يعني drill
+
+95
+00:07:23,740 --> 00:07:31,340
+bits؟ لأ بتعرفوا الريش تبعات المجدح؟ هذا بيسموها
+
+96
+00:07:31,340 --> 00:07:35,950
+إيش؟ ال drillbits ما انتوا البنات مش اكتر خبرتكم
+
+97
+00:07:35,950 --> 00:07:41,270
+في هذه الشغلة الشباب هذه الشغلات معظمهم جربوها
+
+98
+00:07:41,270 --> 00:07:44,690
+فالان
+
+99
+00:07:44,690 --> 00:07:48,210
+هذه اللي بنتكلم عنهم فعنا كام نوع من هدول النوع
+
+100
+00:07:48,210 --> 00:07:57,570
+اللي بسميه alloy steel اربع نوع ايش هما low alloy
+
+101
+00:08:02,120 --> 00:08:07,880
+Stainless Steel والرابعة Tools Steel الآن عندنا
+
+102
+00:08:07,880 --> 00:08:11,760
+حاجة بنسميها ال Corrosion إيش هي ال Corrosion؟ هي
+
+103
+00:08:11,760 --> 00:08:20,020
+ال Oxidization أو ال Oxide هي ال Rust إيش يعني؟
+
+104
+00:08:20,020 --> 00:08:26,180
+عملية الصدق عملية الصدق بنسميها عملية أكسدة أو
+
+105
+00:08:26,180 --> 00:08:34,220
+عملية آكل هن التلاتة لنفس المسمةكويس؟ فهنا one
+
+106
+00:08:34,220 --> 00:08:39,060
+weakness of mild steel is that it corrodes its
+
+107
+00:08:39,060 --> 00:08:43,320
+surface progressively deteriorates due to a
+
+108
+00:08:43,320 --> 00:08:48,520
+chemical reaction إيش يعني deteriorates؟
+
+109
+00:08:48,520 --> 00:08:54,520
+الآن خلينا نقول corrodes اللي هي بتتأكلالان due to
+
+110
+00:08:54,520 --> 00:08:58,660
+rates تشوفوا لما الحاجة تبدأ ت .. يعني خلينا نفس
+
+111
+00:08:58,660 --> 00:09:03,680
+الكلمة هي due to rates لما تصير تروح للأسوأ شوية
+
+112
+00:09:03,680 --> 00:09:08,740
+شوية بتتشوه تدهور بتتدهور يعني وضعها بتدهور
+
+113
+00:09:08,740 --> 00:09:13,880
+بيقولها due to rate فهي بتبقى في حالة مثلا معينة و
+
+114
+00:09:13,880 --> 00:09:16,960
+بيصير كل ما فيها شي تراجع بنسميها due to rates
+
+115
+00:09:16,960 --> 00:09:24,420
+اللي عنديهذه الاتفاق تأخذ مقاطع بين الحر في السلطة
+
+116
+00:09:24,420 --> 00:09:31,240
+والهواء في الهواء لتصميم عصيد عصير عصير عصير عصير
+
+117
+00:09:31,240 --> 00:09:33,020
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+118
+00:09:33,020 --> 00:09:33,060
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+119
+00:09:33,060 --> 00:09:38,640
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+120
+00:09:38,640 --> 00:09:38,640
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+121
+00:09:38,640 --> 00:09:38,660
+عصير عصير عصير عصير عصير عصير عصير عصير عصير عصير
+
+122
+00:09:38,660 --> 00:09:42,480
+عصير عصير عصير عصير عصير عصير عصير ع
+
+123
+00:09:45,880 --> 00:09:51,460
+و ال oxidized و ال what و ال corrodes هم في
+
+124
+00:09:51,460 --> 00:09:56,420
+المفقول واحد هو بيكونوا طبقة صدقة
+
+125
+00:10:00,110 --> 00:10:04,650
+في بعض الميثال مثل الألمنيوم، لا يوجد مشكلة في
+
+126
+00:10:04,650 --> 00:10:09,410
+وجود الكروجين لأن مجموعة الحرارة في حول الميثال
+
+127
+00:10:09,410 --> 00:10:15,870
+تبقى صعبة و هذا يمنعها من إتصال أكثر. الآن في
+
+128
+00:10:15,870 --> 00:10:22,490
+الألمنيوم إيش بحصل؟ مش زي صدأ الحديد لأن الصدأ في
+
+129
+00:10:22,490 --> 00:10:27,590
+الحديد إيش بيصير فيه؟ بتاكل و بيصير يجعالألمونة
+
+130
+00:10:27,590 --> 00:10:31,170
+بيعمل الطبقة وبتضالها الطبقة hard فال hardness هذه
+
+131
+00:10:31,170 --> 00:10:36,790
+بيخليش اللي بعدها يصضي فبصير طبقة على الوجه مصضية
+
+132
+00:10:36,790 --> 00:10:40,890
+والباقي مافيش فيه مشكلة ان بتمش عملية التآكل
+
+133
+00:10:40,890 --> 00:10:46,510
+however when mild steel goes rusty the rust on the
+
+134
+00:10:46,510 --> 00:10:51,370
+surface comes off .. comes off ايش؟ يعني زي ما
+
+135
+00:10:51,370 --> 00:10:58,190
+تقول بتجشرأو يعني بسقط يتساقط يتساقط هي التكشير
+
+136
+00:10:58,190 --> 00:11:02,950
+continuously and a new rusty layer forms
+
+137
+00:11:02,950 --> 00:11:09,030
+progressively eating into the metal يعني بتتم أكل
+
+138
+00:11:09,030 --> 00:11:12,870
+الحديد تأكل الحديد و بتلاحظوا انتوا لو عندكم في
+
+139
+00:11:12,870 --> 00:11:17,230
+البيت اي حاجة و احنا في جو غزة ال rust هذا مشكلة
+
+140
+00:11:17,230 --> 00:11:21,590
+كبيرة بتلاقي شوية شوية لما الحديد لحاله يجعب
+
+141
+00:11:21,590 --> 00:11:29,770
+معناته ايش؟بتاكل بسرعة جدا طيب الآن decide whether
+
+142
+00:11:29,770 --> 00:11:34,030
+the sentences below are true or false and correct
+
+143
+00:11:34,030 --> 00:11:38,570
+the false sentences steel is an alloy of iron and
+
+144
+00:11:38,570 --> 00:11:42,930
+carbon true
+
+145
+00:11:42,930 --> 00:11:47,790
+مظبوط مش قولنا المحاضرة اللي فاتت ال steel هو نوع
+
+146
+00:11:47,790 --> 00:11:53,770
+هو alloyهو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+147
+00:11:53,770 --> 00:11:57,250
+هو
+
+148
+00:11:57,250 --> 00:11:57,510
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+149
+00:11:57,510 --> 00:11:57,690
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+150
+00:11:57,690 --> 00:11:57,710
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+151
+00:11:57,710 --> 00:11:58,050
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+152
+00:11:58,050 --> 00:11:58,050
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+153
+00:11:58,050 --> 00:11:58,510
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+154
+00:11:58,510 --> 00:11:59,610
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+155
+00:11:59,610 --> 00:12:01,330
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+156
+00:12:01,330 --> 00:12:01,730
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+157
+00:12:01,730 --> 00:12:03,090
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+158
+00:12:03,090 --> 00:12:03,090
+هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو هو
+
+159
+00:12:03,090 --> 00:12:12,330
+هو هو هو هو هو هو هو هو هو هو هو هو هو هوهوهوهوه
+
+160
+00:12:15,660 --> 00:12:20,340
+chromium and nickel are used as alloying metal in
+
+161
+00:12:20,340 --> 00:12:26,220
+steel مش قولنا عندنا إيش؟ في كبشة alloying
+
+162
+00:12:26,220 --> 00:12:30,840
+material، هذا .. هذا نوع منهم، كويس؟ low alloy
+
+163
+00:12:30,840 --> 00:12:36,200
+steel contain more chromium than iron، false في
+
+164
+00:12:36,200 --> 00:12:40,560
+أصلا في ال steel كله فيش حاجة أكتر من إيش؟ ال iron
+
+165
+00:12:42,360 --> 00:12:47,820
+الـ stainless steel is an alloy steel true احنا
+
+166
+00:12:47,820 --> 00:12:52,040
+نقول لإيش هو المسمى تبعنا بيجي تحت ال alloy
+
+167
+00:12:52,040 --> 00:12:57,240
+alloying steel أو alloy steels tungsten is added
+
+168
+00:12:57,240 --> 00:13:03,580
+to steel to make it softer false إيش بتعمل harder
+
+169
+00:13:03,580 --> 00:13:09,120
+مش softerhigh speed steel is suitable for making
+
+170
+00:13:09,120 --> 00:13:16,720
+cutting tools that get very hot احنا
+
+171
+00:13:16,720 --> 00:13:22,320
+ايش قلنا اللي بنعمل فيه true مظبوط هو tools نفس
+
+172
+00:13:22,320 --> 00:13:27,720
+الشي ايش cutting tools get very hot فبدك ايش افضل
+
+173
+00:13:27,720 --> 00:13:31,240
+انواع اللي هي high speed steel اللي هي نفس المسمى
+
+174
+00:13:31,240 --> 00:13:40,590
+لمين لل tools steelنفس المسمة اللي بتلاحظ فيه طيب
+
+175
+00:13:40,590 --> 00:13:44,430
+الان complete ال table ال table اللي هابنا نكمله
+
+176
+00:13:44,430 --> 00:13:49,250
+الان عندي ال corroded ال adjective ال noun إيش هو?
+
+177
+00:13:51,810 --> 00:14:00,670
+corrosion مظبوط ال verb? corrode مظبوط طيب ال
+
+178
+00:14:00,670 --> 00:14:02,310
+oxidized
+
+179
+00:14:04,730 --> 00:14:10,890
+oxide مظبوط ال noun oxide صح لما نقول عنه مثلا
+
+180
+00:14:10,890 --> 00:14:18,670
+carbon oxide ذاكرينه فهذا ال noun oxide طيب ال
+
+181
+00:14:18,670 --> 00:14:26,410
+verb oxidize طيب ال هنا go rusty ايش ال verb ممكن
+
+182
+00:14:26,410 --> 00:14:36,110
+يكون كمان rust ال nounrust ال adjective rusty طب
+
+183
+00:14:36,110 --> 00:14:40,170
+خلينا نشوف هنا وين نعبيهم when steel is exposed to
+
+184
+00:14:40,170 --> 00:14:45,450
+air and water it oxidize
+
+185
+00:14:45,450 --> 00:14:52,070
+ايش كمان؟ rust ايش كمان؟ corrodes التلاتة مجوزة
+
+186
+00:14:52,070 --> 00:14:57,470
+التلاتة نفس المعنى هذا يعني بدك الفعل اللي هنا و
+
+187
+00:14:57,470 --> 00:15:03,810
+تحطيه ES او Sطيب a brown red material on the
+
+188
+00:15:03,810 --> 00:15:10,110
+surface of steel is called corrosion التلاتة rust
+
+189
+00:15:10,110 --> 00:15:15,190
+and oxide طيب the strength of steel is reduced if
+
+190
+00:15:15,190 --> 00:15:20,210
+it is نحط ال adjective الآن، إيش ال adjective؟
+
+191
+00:15:20,210 --> 00:15:28,550
+التلاتة، فهي تكون oxidized أو rusty أو corroded
+
+192
+00:15:31,280 --> 00:15:35,920
+هذه الأجابة هنا طيب هنا complete the article about
+
+193
+00:15:35,920 --> 00:15:40,160
+a special type of steel the perennial problem with
+
+194
+00:15:40,160 --> 00:15:44,440
+mild .. إيش
+
+195
+00:15:44,440 --> 00:15:50,480
+الكلمة؟ إيش ال perennial problem؟ اللي مرت عليكم؟
+
+196
+00:15:50,480 --> 00:15:57,060
+المشكلة الدائمة أو الأزالية لمين؟ with mildsteel
+
+197
+00:15:57,060 --> 00:16:02,580
+مظبوط is إتقت إيش when exposed air and water إيش
+
+198
+00:16:02,580 --> 00:16:12,020
+بتصيرلها it rusts or it corrodes or it oxidize طيب
+
+199
+00:16:12,020 --> 00:16:15,920
+generally the only solution is either to apply a
+
+200
+00:16:15,920 --> 00:16:21,660
+protective coating to use or to use another edge
+
+201
+00:16:21,660 --> 00:16:26,920
+of the steelأيوة another grades ال grades يعني في
+
+202
+00:16:26,920 --> 00:16:30,400
+هذا الحالة إيش بنحكي فيه ال type أو variations
+
+203
+00:16:30,400 --> 00:16:35,300
+مظبوط احنا عندنا بعض الأنواع اللي هي يمكن هذه
+
+204
+00:16:35,300 --> 00:16:41,600
+بتشوفوها اللي مين ساكنين قريب للبحر بشكل مباشر إيش
+
+205
+00:16:41,600 --> 00:16:45,120
+بتلاقي عندكوا كل إشي إيش بيصيرله بسرعة
+
+206
+00:16:46,690 --> 00:16:51,310
+كبيرة فلازم كل شي تعمليله يا أما بدك تدهني بشكل
+
+207
+00:16:51,310 --> 00:16:57,090
+دائم أو بدك تجيبي حديد مقلبة مظبوط المقلبة ايش
+
+208
+00:16:57,090 --> 00:17:05,430
+بنعمله بنحط طبقة من ال stainless steel حواليه طيب
+
+209
+00:17:05,430 --> 00:17:11,830
+هنا used ايش قولنا another grade of steel that is
+
+210
+00:17:11,830 --> 00:17:19,660
+resistant toto the rusting process او to corrosion
+
+211
+00:17:19,660 --> 00:17:25,820
+process او to oxidize process the most well-known
+
+212
+00:17:25,820 --> 00:17:30,880
+being ايش steel؟ stainless steel ماحنا قولنا هذا
+
+213
+00:17:30,880 --> 00:17:34,100
+انتوا خبرة فيها stainless steel which contains
+
+214
+00:17:34,100 --> 00:17:38,220
+significant quantity of ايش؟ and often nickel
+
+215
+00:17:38,220 --> 00:17:45,590
+chromium مظبوطعندها طبقة كبيرة بالـ alloy تبع كروم
+
+216
+00:17:45,590 --> 00:17:49,690
+و شوية نيكل there is however an alternative
+
+217
+00:17:49,690 --> 00:17:56,610
+solution so-called weathering needs weathering
+
+218
+00:17:56,610 --> 00:18:00,570
+steel ال weathering steel إيش هذا اللي هو ال steel
+
+219
+00:18:00,570 --> 00:18:04,970
+اللي بتعاوأ اللي يعني خلّيني أقول متأقلم مع الجو
+
+220
+00:18:04,970 --> 00:18:07,210
+كويس؟
+
+221
+00:18:08,200 --> 00:18:11,920
+is a special alloy suitable for outdoor use but
+
+222
+00:18:11,920 --> 00:18:14,720
+rather than being completely protected from
+
+223
+00:18:14,720 --> 00:18:18,540
+corrosion the surface of the steel is allowed to
+
+224
+00:18:18,540 --> 00:18:26,320
+go to go ايش rusty rusty ليش هذا ايش بتخلي انه
+
+225
+00:18:26,320 --> 00:18:31,400
+مسموح ان يصير طبقة من ال rust بس ايش اللي بيعمل ال
+
+226
+00:18:31,400 --> 00:18:37,700
+rust هذا هذا الطبقة hard تسمحش للي بعدهاالطبقات
+
+227
+00:18:37,700 --> 00:18:43,100
+الداخلية سيرلها أكسدها تاني once a layer of إيش
+
+228
+00:18:43,100 --> 00:18:49,680
+has formed on the surface a layer of إيش؟ of rust
+
+229
+00:18:49,680 --> 00:18:58,280
+أو أكسيد أو كروجل okay it stabilizes
+
+230
+00:18:58,280 --> 00:19:02,580
+and forms a hard protective layer إيش
+
+231
+00:19:02,580 --> 00:19:04,300
+stabilizable؟
+
+232
+00:19:07,650 --> 00:19:15,630
+ايش stable بتستقر .. هد بتستقر و بتشكل طبقة hard
+
+233
+00:19:15,630 --> 00:19:22,470
+اللي هي ايش صلبة this layer differs from ordinary
+
+234
+00:19:22,470 --> 00:19:28,050
+iron oxide as it does not continue to eat into the
+
+235
+00:19:28,050 --> 00:19:35,170
+metal هد بتبطلهاش تستمر تاكل في ال metal صوت صوت
+
+236
+00:19:35,170 --> 00:19:42,860
+صوتwhile not everyone may like the rusty look,
+
+237
+00:19:43,420 --> 00:19:46,420
+weathering steel has been widely used in
+
+238
+00:19:46,420 --> 00:19:50,940
+architectures, applications and outdoor sculptures
+
+239
+00:19:50,940 --> 00:19:57,120
+إيش يعني sculpture؟ شايفين هذا المنظر اللي قدامكم؟
+
+240
+00:19:57,120 --> 00:20:04,760
+اللي ع الصورة، الصورة، إيش هذا؟مجسم، مظبوط؟ اه ..
+
+241
+00:20:04,760 --> 00:20:11,020
+ايوة فهذا ال outdoor sculptures اللي هي المجسمات
+
+242
+00:20:11,020 --> 00:20:14,000
+اللي في الآخر معمولة من الحديد بيستخدموها في هذا
+
+243
+00:20:14,000 --> 00:20:17,700
+الشكل احنا في بلادنا مش كتير هذا بتشوفيه بس ببلاد
+
+244
+00:20:17,700 --> 00:20:24,220
+الأوروبا موجود بشكل كتير في كل مكان لو بتشوفيه حتى
+
+245
+00:20:24,220 --> 00:20:26,780
+الشكل المصضي هذا بتشوفيه طبيعي
+
+246
+00:20:31,460 --> 00:20:38,000
+طيب هيك بنبقى خلصنا chapter twelve الان يمكن من
+
+247
+00:20:38,000 --> 00:20:42,260
+الشغلات اللى بنطلع عليهم اول حاجة ال steel عندنا
+
+248
+00:20:42,260 --> 00:20:47,800
+نوعين منه صح عندنا ايش carbon steels و ايش
+
+249
+00:20:47,800 --> 00:20:52,080
+alloying steels ال carbon steel عندنا three grades
+
+250
+00:20:52,080 --> 00:21:00,890
+فيهم ايش هما mild و mediumوهاي هدولة عادة نسبة ال
+
+251
+00:21:00,890 --> 00:21:05,610
+carbon فيهم قداش منخفضة من point three percent لحد
+
+252
+00:21:05,610 --> 00:21:11,110
+ديت one point four الباقي كله ايش iron مافيش عندي
+
+253
+00:21:11,110 --> 00:21:17,490
+any other alloying materials بس carbon and iron ال
+
+254
+00:21:17,490 --> 00:21:22,270
+alloying steels الأنواع التانية بتختلف عن الأربع
+
+255
+00:21:22,270 --> 00:21:25,770
+ايش هم اللوهاد
+
+256
+00:21:25,770 --> 00:21:34,550
+ايش مميزتهانيني برسنت ايرن و تين برسنت ايش؟ ايوة و
+
+257
+00:21:34,550 --> 00:21:40,630
+هذه ايش الأنواع ال alloy اللي بنضيفهم؟ طيب النوع
+
+258
+00:21:40,630 --> 00:21:46,730
+التاني high string
+
+259
+00:21:46,730 --> 00:21:51,570
+ايش هذه؟ نسبة ال alloy قداشر؟ less than two
+
+260
+00:21:51,570 --> 00:21:57,270
+percentالان نوع التالت اللي هي ال stainless steel
+
+261
+00:21:57,270 --> 00:22:01,890
+ال stainless steel قد ايش الميزة تبعته؟ بنضيف ال
+
+262
+00:22:01,890 --> 00:22:06,030
+chromium و بنضيف ايش؟
+
+263
+00:22:06,030 --> 00:22:11,290
+nickels okay الان النوع الرابع ال tools او ال high
+
+264
+00:22:11,290 --> 00:22:17,150
+speed ايش؟ steel هذه اللي بنضيف ايش عندنا؟ ال
+
+265
+00:22:17,150 --> 00:22:21,810
+cobalt و ال ايش؟وال tungsten مظبوط هدول ال hard
+
+266
+00:22:21,810 --> 00:22:25,210
+عشان هم بيبقوا very hard و very tough فبنستخدمهم
+
+267
+00:22:25,210 --> 00:22:30,530
+لل cutting tools لما في حرارة درجة حرارة احتكاك
+
+268
+00:22:30,530 --> 00:22:34,430
+بتعمل درجة حرارة هدول اللي بتحمله درجات الحرارة
+
+269
+00:22:34,430 --> 00:22:34,910
+العالية
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/VwUFeAbFcZs_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/VwUFeAbFcZs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..006686bebd03498b267403456206fbdcffbfea33
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/VwUFeAbFcZs_raw.json
@@ -0,0 +1 @@
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schematic مخطط okay are used and everyday example is the map of a train network or a PCB عارفين ال printed circuit board هدولة بنسميهم schematic", "tokens": [3555, 47302, 3555, 11622, 1392, 309, 307, 4961, 281, 855, 264, 1715, 294, 257, 26335, 1254, 294, 341, 1389, 44739, 6316, 420, 321, 818, 309, 294, 2099, 44739, 44739, 3714, 9778, 9566, 9566, 1392, 366, 1143, 293, 7429, 1365, 307, 264, 4471, 295, 257, 3847, 3209, 420, 257, 42065, 6225, 9640, 5172, 9957, 2423, 13567, 9048, 3150, 8032, 3215, 12610, 3660, 44945, 38251, 1829, 16095, 44739], "avg_logprob": -0.2649253846994087, "compression_ratio": 1.3603603603603605, "no_speech_prob": 0.0, "words": [{"start": 358.67, "end": 359.55, "word": "بايبز", "probability": 0.54632568359375}, {"start": 359.55, "end": 360.43, "word": " okay", "probability": 0.062469482421875}, {"start": 360.43, "end": 360.77, "word": " it", "probability": 0.82470703125}, {"start": 360.77, "end": 361.01, "word": " is", "probability": 0.91357421875}, {"start": 361.01, 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sides of the machine or drawing 28, so one of these should show the front of the machine هنا إيش elevation هات تعبير جديد لما تطلعيه من الجنب There should be a section through the pipe showing the valve inside on drawing 56 section قولنا ال cross section", "tokens": [47943, 3357, 281, 341, 1329, 11, 456, 366, 7701, 763, 295, 439, 1451, 4881, 295, 264, 3479, 420, 6316, 7562, 11, 370, 472, 295, 613, 820, 855, 264, 1868, 295, 264, 3479, 34105, 11933, 1829, 8592, 25827, 8032, 9307, 37279, 3555, 13546, 10874, 16254, 3215, 5296, 15042, 6055, 9566, 1211, 3615, 1829, 3224, 9154, 25724, 1863, 3555, 821, 820, 312, 257, 3541, 807, 264, 11240, 4099, 264, 15294, 1854, 322, 6316, 19687, 3541, 12174, 12610, 8315, 2423, 3278, 3541], "avg_logprob": -0.3269531145691872, "compression_ratio": 1.4915254237288136, "no_speech_prob": 0.0, "words": [{"start": 489.69, "end": 490.29, "word": "According", "probability": 0.46785736083984375}, {"start": 490.29, "end": 490.53, "word": " to", "probability": 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"probability": 0.99501953125}, {"start": 1588.04, "end": 1588.54, "word": " التالي", "probability": 0.8946940104166666}, {"start": 1588.54, "end": 1589.44, "word": " انتوا", "probability": 0.8616536458333334}, {"start": 1589.44, "end": 1589.92, "word": " عادة", "probability": 0.9856770833333334}, {"start": 1589.92, "end": 1590.4, "word": " تخلينا", "probability": 0.8763427734375}, {"start": 1590.4, "end": 1590.62, "word": " نقول", "probability": 0.84423828125}, {"start": 1590.62, "end": 1590.92, "word": " good", "probability": 0.8720703125}, {"start": 1590.92, "end": 1591.44, "word": " technique", "probability": 0.9384765625}, {"start": 1591.44, "end": 1592.16, "word": " تعملوه", "probability": 0.88984375}, {"start": 1592.16, "end": 1592.88, "word": " للمادة", "probability": 0.96435546875}, {"start": 1592.88, "end": 1593.34, "word": " ما", "probability": 0.60498046875}, {"start": 1593.34, "end": 1593.72, "word": " تجيوش", "probability": 0.84228515625}, {"start": 1593.72, "end": 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"seek": 163734, "start": 1612.58, "end": 1637.34, "text": "بتغنيك عن انك تقرى فيهم كويس؟ good technique اول صبح وانت جاية طلع عليهم هذا بتغني عن اننا نحفظ لانه لما تحفظي هيصيرك cramp تعرف ايش ال cramp؟ لما تصير كمية معلومة جاية وانت المخ بطل يستوعب ال cramp في لغة الرياضة لما نيجي شد عضلي", "tokens": [3555, 2655, 17082, 22653, 4117, 18871, 16472, 4117, 6055, 4587, 2288, 7578, 8978, 16095, 9122, 45865, 3794, 22807, 665, 6532, 1975, 12610, 20328, 49628, 4032, 7649, 2655, 10874, 995, 10632, 23032, 1211, 3615, 25894, 16095, 23758, 39894, 17082, 22653, 18871, 16472, 8315, 8717, 5016, 5172, 19913, 5296, 7649, 3224, 5296, 15042, 6055, 5016, 5172, 19913, 1829, 8032, 1829, 9381, 13546, 4117, 941, 1215, 37279, 28480, 1975, 1829, 8592, 2423, 941, 1215, 22807, 5296, 15042, 6055, 9381, 13546, 9122, 2304, 10632, 20449, 1211, 20498, 3660, 10874, 995, 10632, 4032, 7649, 2655, 9673, 9778, 4724, 9566, 1211, 7251, 14851, 45367, 3555, 2423, 941, 1215, 8978, 5296, 17082, 3660, 2423, 16572, 46958, 3660, 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{"start": 1840.53, "end": 1841.77, "word": " المصادر", "probability": 0.9853515625}, {"start": 1841.77, "end": 1844.29, "word": " المصادر", "probability": 0.986083984375}, {"start": 1844.29, "end": 1848.69, "word": " المصاد", "probability": 0.9812825520833334}], "temperature": 1.0}, {"id": 71, "seek": 186253, "start": 1855.85, "end": 1862.53, "text": "pipe, valve, ايش ال valve؟ ميكنزم", "tokens": [79, 647, 68, 11, 15294, 11, 1975, 1829, 8592, 2423, 15294, 22807, 3714, 1829, 19452, 11622, 2304], "avg_logprob": -0.5616319311989678, "compression_ratio": 0.9574468085106383, "no_speech_prob": 0.0, "words": [{"start": 1855.85, "end": 1857.25, "word": "pipe,", "probability": 0.5564778645833334}, {"start": 1857.25, "end": 1858.25, "word": " valve,", "probability": 0.8828125}, {"start": 1858.37, "end": 1858.53, "word": " ايش", "probability": 0.7484537760416666}, {"start": 1858.53, "end": 1858.65, "word": " ال", "probability": 0.85546875}, {"start": 1858.65, "end": 1860.53, "word": " valve؟", "probability": 0.82958984375}, {"start": 1860.53, "end": 1862.53, "word": " ميكنزم", "probability": 0.6865234375}], "temperature": 1.0}, {"id": 72, "seek": 189813, "start": 1875.25, "end": 1898.13, "text": "components spaced out ايش يعني spaced out تشوف لو ما تكون حاجة مركبة و spaced out بنفكفكها بس بتفكفكها و بنوسعها يعني بنحط مسافات هي spaced out طيب visualize", "tokens": [21541, 40496, 43766, 484, 1975, 1829, 8592, 37495, 22653, 43766, 484, 6055, 8592, 38688, 45164, 19446, 6055, 30544, 11331, 26108, 3660, 3714, 31747, 49401, 4032, 43766, 484, 44945, 5172, 4117, 5172, 4117, 11296, 4724, 3794, 39894, 5172, 4117, 5172, 4117, 11296, 4032, 44945, 41779, 3615, 11296, 37495, 22653, 44945, 5016, 9566, 47524, 31845, 9307, 39896, 43766, 484, 23032, 1829, 3555, 23273], "avg_logprob": -0.17552923170789594, "compression_ratio": 1.5298013245033113, "no_speech_prob": 0.0, "words": [{"start": 1875.25, "end": 1876.21, "word": "components", "probability": 0.612060546875}, {"start": 1876.21, "end": 1876.89, "word": " spaced", "probability": 0.7880859375}, {"start": 1876.89, "end": 1877.33, "word": " out", "probability": 0.8916015625}, {"start": 1877.33, "end": 1877.89, "word": " ايش", "probability": 0.7027587890625}, {"start": 1877.89, "end": 1878.15, "word": " يعني", "probability": 0.937255859375}, {"start": 1878.15, "end": 1878.63, "word": " spaced", "probability": 0.9384765625}, {"start": 1878.63, "end": 1880.09, "word": " out", "probability": 0.93212890625}, {"start": 1880.09, "end": 1883.39, "word": " تشوف", "probability": 0.7887369791666666}, {"start": 1883.39, "end": 1883.55, "word": " لو", "probability": 0.471435546875}, {"start": 1883.55, "end": 1883.67, "word": " ما", "probability": 0.7412109375}, {"start": 1883.67, "end": 1883.95, "word": " تكون", "probability": 0.840087890625}, {"start": 1883.95, "end": 1884.31, "word": " حاجة", "probability": 0.9554036458333334}, {"start": 1884.31, "end": 1884.93, "word": " مركبة", "probability": 0.8719075520833334}, {"start": 1884.93, "end": 1885.37, "word": " و", "probability": 0.9423828125}, {"start": 1885.37, "end": 1885.75, "word": " spaced", "probability": 0.9248046875}, {"start": 1885.75, "end": 1886.17, "word": " out", "probability": 0.92041015625}, {"start": 1886.17, "end": 1887.39, "word": " بنفكفكها", "probability": 0.8783365885416666}, {"start": 1887.39, "end": 1888.17, "word": " بس", "probability": 0.918212890625}, {"start": 1888.17, "end": 1888.95, "word": " بتفكفكها", "probability": 0.9007568359375}, {"start": 1888.95, "end": 1889.17, "word": " و", "probability": 0.8115234375}, {"start": 1889.17, "end": 1890.01, "word": " بنوسعها", "probability": 0.934326171875}, {"start": 1890.01, "end": 1890.33, "word": " يعني", "probability": 0.91064453125}, {"start": 1890.33, "end": 1890.67, "word": " بنحط", "probability": 0.9650065104166666}, {"start": 1890.67, "end": 1891.19, "word": " مسافات", "probability": 0.9832356770833334}, {"start": 1891.19, "end": 1891.35, "word": " هي", "probability": 0.53369140625}, {"start": 1891.35, "end": 1891.77, "word": " spaced", "probability": 0.92138671875}, {"start": 1891.77, "end": 1892.41, "word": " out", "probability": 0.8974609375}, {"start": 1892.41, "end": 1894.21, "word": " طيب", "probability": 0.9669596354166666}, {"start": 1894.21, "end": 1898.13, "word": " visualize", "probability": 0.6826171875}], "temperature": 1.0}, {"id": 73, "seek": 192476, "start": 1899.36, "end": 1924.76, "text": "it's hard to visualize this essentially based on two dimensional elevation and suction it would be clearer if we had a three dimensional view as either an oblique projection or an isometric projection okay فيركوا أي تساؤل على هدول؟", "tokens": [270, 311, 1152, 281, 23273, 341, 4476, 2361, 322, 732, 18795, 25827, 293, 40431, 309, 576, 312, 26131, 498, 321, 632, 257, 1045, 18795, 1910, 382, 2139, 364, 23740, 1925, 22743, 420, 364, 307, 29470, 22743, 1392, 8978, 31747, 14407, 36632, 6055, 3794, 5718, 97, 1211, 15844, 8032, 3215, 12610, 22807], "avg_logprob": -0.33864183322741437, "compression_ratio": 1.3475935828877006, "no_speech_prob": 0.0, "words": [{"start": 1899.36, "end": 1899.68, "word": "it's", "probability": 0.5240478515625}, {"start": 1899.68, "end": 1899.9, "word": " hard", "probability": 0.8759765625}, {"start": 1899.9, "end": 1900.08, "word": " to", "probability": 0.98095703125}, {"start": 1900.08, "end": 1900.5, "word": " visualize", "probability": 0.2998046875}, {"start": 1900.5, "end": 1901.14, "word": " this", "probability": 0.84375}, {"start": 1901.14, "end": 1901.76, "word": " essentially", "probability": 0.2225341796875}, {"start": 1901.76, "end": 1902.82, "word": " based", "probability": 0.8486328125}, {"start": 1902.82, "end": 1903.18, "word": " on", "probability": 0.95751953125}, {"start": 1903.18, "end": 1903.46, "word": " two", "probability": 0.85791015625}, {"start": 1903.46, "end": 1904.08, "word": " dimensional", "probability": 0.386474609375}, {"start": 1904.08, "end": 1906.2, "word": " elevation", "probability": 0.9052734375}, {"start": 1906.2, "end": 1907.04, "word": " and", "probability": 0.96533203125}, {"start": 1907.04, "end": 1907.52, "word": " suction", "probability": 0.4169921875}, {"start": 1907.52, "end": 1908.1, "word": " it", "probability": 0.751953125}, {"start": 1908.1, "end": 1908.36, "word": " would", "probability": 0.90087890625}, {"start": 1908.36, "end": 1908.64, "word": " be", "probability": 0.94970703125}, {"start": 1908.64, "end": 1909.08, "word": " clearer", "probability": 0.779296875}, {"start": 1909.08, "end": 1909.64, "word": " if", "probability": 0.8134765625}, {"start": 1909.64, "end": 1910.4, "word": " we", "probability": 0.884765625}, {"start": 1910.4, "end": 1910.76, "word": " had", "probability": 0.76123046875}, {"start": 1910.76, "end": 1911.02, "word": " a", "probability": 0.53271484375}, {"start": 1911.02, "end": 1911.22, "word": " three", "probability": 0.865234375}, {"start": 1911.22, "end": 1911.92, "word": " dimensional", "probability": 0.55810546875}, {"start": 1911.92, "end": 1913.92, "word": " view", "probability": 0.67919921875}, {"start": 1913.92, "end": 1914.6, "word": " as", "probability": 0.6376953125}, {"start": 1914.6, "end": 1916.6, "word": " either", "probability": 0.86474609375}, {"start": 1916.6, "end": 1917.04, "word": " an", "probability": 0.78515625}, {"start": 1917.04, "end": 1918.02, "word": " oblique", "probability": 0.634033203125}, {"start": 1918.02, "end": 1919.02, "word": " projection", "probability": 0.9580078125}, {"start": 1919.02, "end": 1919.98, "word": " or", "probability": 0.9501953125}, {"start": 1919.98, "end": 1920.42, "word": " an", "probability": 0.85400390625}, {"start": 1920.42, "end": 1921.06, "word": " isometric", "probability": 0.95751953125}, {"start": 1921.06, "end": 1921.76, "word": " projection", "probability": 0.9736328125}, {"start": 1921.76, "end": 1922.36, "word": " okay", "probability": 0.24658203125}, {"start": 1922.36, "end": 1923.28, "word": " فيركوا", "probability": 0.5325520833333334}, {"start": 1923.28, "end": 1923.36, "word": " أي", "probability": 0.85205078125}, {"start": 1923.36, "end": 1923.98, "word": " تساؤل", "probability": 0.8634765625}, {"start": 1923.98, "end": 1924.2, "word": " على", "probability": 0.876953125}, {"start": 1924.2, "end": 1924.76, "word": " هدول؟", "probability": 0.9376220703125}], "temperature": 1.0}, {"id": 74, "seek": 193692, "start": 1926.38, "end": 1936.92, "text": "طيب احنا هيك بنبقى خلصنا بدر اليوم و ان شاء الله بنشوفكم محاضرة جاي بس لا تنسوش انه ال communication", "tokens": [9566, 1829, 3555, 1975, 5016, 8315, 39896, 4117, 44945, 3555, 4587, 7578, 16490, 1211, 9381, 8315, 47525, 2288, 45595, 20498, 4032, 16472, 13412, 16606, 21984, 44945, 8592, 38688, 24793, 3714, 5016, 46958, 25720, 10874, 47302, 4724, 3794, 20193, 6055, 1863, 3794, 2407, 8592, 16472, 3224, 2423, 6101], "avg_logprob": -0.14257812624176344, "compression_ratio": 1.302325581395349, "no_speech_prob": 0.0, "words": [{"start": 1926.38, "end": 1926.72, "word": "طيب", "probability": 0.9775390625}, {"start": 1926.72, "end": 1927.1, "word": " احنا", "probability": 0.9104817708333334}, {"start": 1927.1, "end": 1927.66, "word": " هيك", "probability": 0.962158203125}, {"start": 1927.66, "end": 1928.1, "word": " بنبقى", "probability": 0.78863525390625}, {"start": 1928.1, "end": 1928.62, "word": " خلصنا", "probability": 0.9388427734375}, {"start": 1928.62, "end": 1928.96, "word": " بدر", "probability": 0.8134765625}, {"start": 1928.96, "end": 1929.4, "word": " اليوم", "probability": 0.982666015625}, {"start": 1929.4, "end": 1931.84, "word": " و", "probability": 0.921875}, {"start": 1931.84, "end": 1932.08, "word": " ان", "probability": 0.64111328125}, {"start": 1932.08, "end": 1932.34, "word": " شاء", "probability": 0.987548828125}, {"start": 1932.34, "end": 1932.64, "word": " الله", "probability": 0.953125}, {"start": 1932.64, "end": 1933.34, "word": " بنشوفكم", "probability": 0.90625}, {"start": 1933.34, "end": 1933.9, "word": " محاضرة", "probability": 0.8292236328125}, {"start": 1933.9, "end": 1934.42, "word": " جاي", "probability": 0.8408203125}, {"start": 1934.42, "end": 1934.72, "word": " بس", "probability": 0.94091796875}, {"start": 1934.72, "end": 1934.82, "word": " لا", "probability": 0.3681640625}, {"start": 1934.82, "end": 1935.4, "word": " تنسوش", "probability": 0.99267578125}, {"start": 1935.4, "end": 1935.96, "word": " انه", "probability": 0.7548828125}, {"start": 1935.96, "end": 1936.18, "word": " ال", "probability": 0.7744140625}, {"start": 1936.18, "end": 1936.92, "word": " communication", "probability": 0.93994140625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1937.3105, "duration_after_vad": 1849.222499999996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/WBfXV9hslPg_postprocess.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/WBfXV9hslPg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0f1783790a68e549d8a4b9bef72fbae6f09ce4b6
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/WBfXV9hslPg_postprocess.srt
@@ -0,0 +1,1608 @@
+1
+00:00:20,920 --> 00:00:27,460
+طيب السلام عليكم اليوم سنقوم بمقعد تاري تري تاري
+
+2
+00:00:27,460 --> 00:00:29,620
+تري تاري تري تاري تري تري تري تري تري تري تري تري
+
+3
+00:00:29,620 --> 00:00:29,860
+تري تري تري تري تري تري تري تري تري تري تري تري
+
+4
+00:00:29,860 --> 00:00:30,060
+تري تري تري تري تري تري تري تري تري تري تري تري
+
+5
+00:00:30,060 --> 00:00:31,660
+تري تري تري تري تري تري تري تري تري تري تري تري
+
+6
+00:00:31,660 --> 00:00:32,240
+تري تري تري تري تري تري تري تري تري تري تري تري
+
+7
+00:00:32,240 --> 00:00:32,320
+تري تري تري تري تري تري تري تري تري تري تري تري
+
+8
+00:00:32,320 --> 00:00:42,240
+تري تري
+
+9
+00:00:42,240 --> 00:00:45,180
+ت
+
+10
+00:00:52,950 --> 00:00:57,790
+acceleration and motion if an object is at rest
+
+11
+00:00:57,790 --> 00:01:04,470
+not .. that meaning not moving يعني زي ال .. ال ..
+
+12
+00:01:04,470 --> 00:01:10,770
+okay and it's free to move not fixed an external
+
+13
+00:01:10,770 --> 00:01:16,910
+.. an external force a force from outside will
+
+14
+00:01:16,910 --> 00:01:22,410
+make the object accelerate يعنيش accelerate؟أيوة
+
+15
+00:01:22,410 --> 00:01:29,170
+لأنه بنعرف احنا في عندنا ال position بيجي بعده لو
+
+16
+00:01:29,170 --> 00:01:32,850
+أخدنا ال derivative تبعه اش بيحصل بيصير velocity
+
+17
+00:01:32,850 --> 00:01:36,470
+لو أخدنا ال derivative تبعت ال velocity بيصير
+
+18
+00:01:36,470 --> 00:01:41,130
+عندنا acceleration وهذا اللي هنتكلم عنه ان شاء
+
+19
+00:01:41,130 --> 00:01:43,810
+الله اليوم this means
+
+20
+00:01:47,380 --> 00:01:50,120
+Velocity of the object or the speed of its
+
+21
+00:01:50,120 --> 00:01:53,080
+movement in a given direction will increase
+
+22
+00:01:53,080 --> 00:01:58,160
+Velocity is measured in meters per second Position
+
+23
+00:01:58,160 --> 00:02:01,200
+is measured in meters Velocity is measured in
+
+24
+00:02:01,200 --> 00:02:04,160
+meters per second Acceleration is measured in
+
+25
+00:02:04,160 --> 00:02:07,040
+meters per second per second square
+
+26
+00:02:12,060 --> 00:02:19,300
+إذا إزالة السرعة تزال تزال تزال تزال تزال تزال
+
+27
+00:02:19,300 --> 00:02:24,080
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+28
+00:02:24,080 --> 00:02:24,820
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+29
+00:02:24,820 --> 00:02:28,900
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+30
+00:02:28,900 --> 00:02:29,960
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+31
+00:02:29,960 --> 00:02:41,120
+تزال تزال تزال تزال تزال تز
+
+32
+00:02:41,150 --> 00:02:46,130
+يعني meter per second per second The unit of
+
+33
+00:02:46,130 --> 00:02:48,870
+acceleration is therefore meter per second per
+
+34
+00:02:48,870 --> 00:02:52,570
+second stated as meter per second per second
+
+35
+00:02:52,570 --> 00:02:57,090
+squared وهذه كلها معلومات عامة لحتى الآن عندكم يا
+
+36
+00:02:57,090 --> 00:03:03,410
+طالبات الهندسة مرت عليكم في الفيزيا مرات عديدةIf
+
+37
+00:03:03,410 --> 00:03:08,070
+an object is in motion or moving and is subjected
+
+38
+00:03:08,070 --> 00:03:12,530
+to an opposing force that is when acting on it in
+
+39
+00:03:12,530 --> 00:03:16,790
+the opposite direction, the object will .. ده واحد
+
+40
+00:03:16,790 --> 00:03:22,370
+بيمشي و في حاجة بتعطيه مضادة، إيش بيصير فيه؟ بيصير
+
+41
+00:03:22,370 --> 00:03:27,070
+يتباطأ، كلمة تباطأ في الصراعيش بيسميها فيها
+
+42
+00:03:27,070 --> 00:03:28,370
+deceleration
+
+43
+00:03:30,380 --> 00:03:38,600
+acceleration تسارق تباطؤ تسارق تسارق
+
+44
+00:03:38,600 --> 00:03:48,820
+تسارق تسارق تسارق تسارق تسارق تسارق تسارق تسارق
+
+45
+00:03:48,820 --> 00:03:52,720
+تسارق تسارق تسارق تسارق تسارق تسارق تسارق تسارق
+
+46
+00:03:52,720 --> 00:03:58,120
+تسارق تسارق تسارق تسارق تسارق تسارق تسارق تسارق
+
+47
+00:03:58,120 --> 00:04:02,750
+تسارق تسارق تسارق تال linear إيش؟ خطي اللي عندي و
+
+48
+00:04:02,750 --> 00:04:10,510
+عادة مش بس خطي عملية التدرج فيها تبقى متناسبة، هذا
+
+49
+00:04:10,510 --> 00:04:16,180
+.. هذا اللي بيسموه خطيa car acceleration and
+
+50
+00:04:16,180 --> 00:04:19,160
+driving along a straight road is an example of
+
+51
+00:04:19,160 --> 00:04:23,120
+linear acceleration and linear motion في عندنا ال
+
+52
+00:04:23,120 --> 00:04:26,680
+linear motion اللي هو في اتجاه خطي في عندنا ال
+
+53
+00:04:26,680 --> 00:04:33,960
+circular motion اللي هو أيش دائري او circle من
+
+54
+00:04:33,960 --> 00:04:38,900
+حوالي .. هاي ال circular دائري اللي عندك و في non
+
+55
+00:04:38,900 --> 00:04:45,580
+-linear اللي هي غير خطيon air acceleration due to
+
+56
+00:04:45,580 --> 00:04:49,000
+gravity اللي أنا جيتلكوا المعنى هاي، الآن لو
+
+57
+00:04:49,000 --> 00:04:53,720
+رميتوا حجر إيش بيحصل فيه؟ هو طالع سرعت إيش بتصير
+
+58
+00:04:53,720 --> 00:04:54,260
+فيها؟
+
+59
+00:04:54,260 --> 00:05:04,340
+تطبططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططططط
+
+60
+00:05:05,840 --> 00:05:10,520
+is roughly 10 meters per second squared هي 9.81 زي
+
+61
+00:05:10,520 --> 00:05:14,780
+ما بتعرفوها تقريبا بتقول عنها 10 meters per second
+
+62
+00:05:14,780 --> 00:05:19,020
+squared in other words if an object is dropped and
+
+63
+00:05:19,020 --> 00:05:25,590
+lift to free fallسقوط الحر its velocity will
+
+64
+00:05:25,590 --> 00:05:31,250
+increase by 10 meter per second every second not
+
+65
+00:05:31,250 --> 00:05:35,530
+allowing for air resistance يعني هذه لو رميت حاجة
+
+66
+00:05:35,530 --> 00:05:39,470
+من ارتفاع معين او خليتها تسقط من ارتفاع معين ايش
+
+67
+00:05:39,470 --> 00:05:45,330
+هلاحظ فيها سرعتها تزداد 10 meter per second لكل
+
+68
+00:05:45,330 --> 00:05:52,260
+secondالان هذه طبعا إذا بدك تاخد في الحساب مقاومة
+
+69
+00:05:52,260 --> 00:05:58,340
+الهواء طبعا مش هتكون بهذه يعني بس لو أنا تجاهلت
+
+70
+00:05:58,340 --> 00:06:01,920
+مقاومة الهواء هذا المعنى اللي عندي إن سرعتها
+
+71
+00:06:01,920 --> 00:06:07,380
+بتزداد 10 meter per second لكل second بتيجي فيها
+
+72
+00:06:09,540 --> 00:06:12,920
+Acceleration and deceleration such as that
+
+73
+00:06:12,920 --> 00:06:17,140
+generated by aircraft and cars can be compared
+
+74
+00:06:17,140 --> 00:06:20,640
+with acceleration due to gravity الان الناس ايش
+
+75
+00:06:20,640 --> 00:06:25,220
+بيحكوا بدل ما انا احكي حاجات هاج بصير اقارن ال
+
+76
+00:06:25,220 --> 00:06:30,420
+acceleration او ال deceleration مقارة مع الجاذبية
+
+77
+00:06:30,420 --> 00:06:35,340
+الأرضية الجاذبية الأرضية قولنا حوالي 10 meter per
+
+78
+00:06:35,340 --> 00:06:42,010
+second square هاي بسميها one gأو one gravity force
+
+79
+00:06:42,010 --> 00:06:47,710
+او one g force فهذا صار ايه ماترك بقيس فيه
+
+80
+00:06:47,710 --> 00:06:51,410
+relative
+
+81
+00:06:51,410 --> 00:06:56,290
+measure is called g force g stands for gravity and
+
+82
+00:06:56,290 --> 00:06:59,530
+acceleration of 10 meters per second squared is
+
+83
+00:06:59,530 --> 00:07:01,970
+measured as one g
+
+84
+00:07:04,610 --> 00:07:12,350
+و 20 meter per second squared as 2G and so on يعني
+
+85
+00:07:12,350 --> 00:07:16,790
+هد بيصير لو عندى 100 meter per second squared هد
+
+86
+00:07:16,790 --> 00:07:23,930
+كداش بيصير 10G فانتوا هذا لأ لو كان عندى 32 meter
+
+87
+00:07:23,930 --> 00:07:32,240
+per second squared هد ايش بيسميها 3.2G forceفهذا
+
+88
+00:07:32,240 --> 00:07:37,220
+الـ measurement اللي عندنا اللي بسويها الان ال
+
+89
+00:07:37,220 --> 00:07:43,830
+inertia ايش ال inertia؟الـ inertia يعني ده ضربط ال
+
+90
+00:07:43,830 --> 00:07:49,870
+velocity بالإيش؟ بالmass لإنه لما أنا بده أجيب
+
+91
+00:07:49,870 --> 00:07:54,090
+حاجة كبيرة و أحركها مش ده حاجة صغيرة و أحركها، هذه
+
+92
+00:07:54,090 --> 00:07:57,970
+إلها force و هذه إلها force the greater the mass
+
+93
+00:07:57,970 --> 00:08:00,650
+of an object the greater the external force
+
+94
+00:08:00,650 --> 00:08:04,690
+required to cause it to accelerate or decelerate
+
+95
+00:08:04,690 --> 00:08:10,260
+يعني لو أنا جيبت حاجة كبيرة و بده أحركهامش زي حاجة
+
+96
+00:08:10,260 --> 00:08:14,940
+صغيرة و بده احركها هادئ او بده احركها بسرعة معينة
+
+97
+00:08:14,940 --> 00:08:19,120
+resistant to acceleration or deceleration due to
+
+98
+00:08:19,120 --> 00:08:22,820
+the mass of an object is called inertia ال inertia
+
+99
+00:08:22,820 --> 00:08:29,120
+اللي هي إيش الآن المقاومةالممانعة .. الممانعة ده
+
+100
+00:08:29,120 --> 00:08:34,380
+تعبير جديد مقاومة لما ن .. ده اللحظة بيسميها
+
+101
+00:08:34,380 --> 00:08:38,580
+الممانعة عشان نشروا تعليق عنها فالمقاومة اللي هي
+
+102
+00:08:38,580 --> 00:08:43,560
+إيش بيسميها اللي هي الإنرش مقاومة لل acceleration
+
+103
+00:08:43,560 --> 00:08:47,600
+أو or deceleration بيسميها المقاومة اللي عندي
+
+104
+00:08:51,040 --> 00:08:56,320
+بعرفش هنا في العربي ممرنش عليها دوة او مر الأخر
+
+105
+00:08:56,320 --> 00:09:02,700
+مرة أيام ثانوية و مش ذاكرهم بس resistance دايما
+
+106
+00:09:02,700 --> 00:09:09,340
+بيقول .. ب physicalityيبقى خلاص سموها اللي بتسموها
+
+107
+00:09:09,340 --> 00:09:16,080
+فيه زلم okay it's called inertia when an object is
+
+108
+00:09:16,080 --> 00:09:19,860
+in motion it's resistant to deceleration due to
+
+109
+00:09:19,860 --> 00:09:24,180
+inertia is often called momentum هذه مرت عليكم
+
+110
+00:09:24,180 --> 00:09:31,200
+مظبوط ايش بتسموها هذه momentum تحرر
+
+111
+00:09:33,970 --> 00:09:39,270
+خلاص اللي بيسموه .. انا
+
+112
+00:09:39,270 --> 00:09:44,630
+اتعودت عليها زي مهنة لما اندرست أول أسبوع ترجمت و
+
+113
+00:09:44,630 --> 00:09:50,660
+بعدها رميت الترجم و بديت أشغل بدون ترجمطيب simple
+
+114
+00:09:50,660 --> 00:09:54,760
+machines الان اتكلمنا عن ال motion بنتكلم الان عن
+
+115
+00:09:54,760 --> 00:09:58,560
+ال simple machines what we mean the word machine
+
+116
+00:09:58,560 --> 00:10:02,720
+generally referred to an assembly which has parts
+
+117
+00:10:02,720 --> 00:10:08,580
+that move يعني الماشيين دايما في حاجة جسم في أجزاء
+
+118
+00:10:08,580 --> 00:10:12,360
+تتحرك هذه الماشيين however a simple machine can be
+
+119
+00:10:12,360 --> 00:10:18,840
+very basic deviceالـ simple machine اللي هي جهاز
+
+120
+00:10:18,840 --> 00:10:23,480
+بسيط جدا a simple machine is something which
+
+121
+00:10:23,480 --> 00:10:27,020
+provides a mechanical advantage الآن ال mechanical
+
+122
+00:10:27,020 --> 00:10:31,380
+advantage إيش يعني يعني بيعطينا .. بيعطينا ميزة عن
+
+123
+00:10:31,380 --> 00:10:36,450
+الإيدمظبوط هاي mechanical advantage that is load
+
+124
+00:10:36,450 --> 00:10:40,870
+generated by the machine the force it puts out or
+
+125
+00:10:40,870 --> 00:10:45,050
+outputs is greater than efforts the force put in
+
+126
+00:10:45,050 --> 00:10:49,150
+or input required to generate the load يعني لو أنا
+
+127
+00:10:49,150 --> 00:10:55,510
+بده أجي أفك برغي بإيدي بقدرش لو جبت المفاك بعطيني
+
+128
+00:10:55,510 --> 00:11:00,890
+قوة أكتر مظبوطفهذه هي simple tool اللي هي بنسميها
+
+129
+00:11:00,890 --> 00:11:07,050
+دي machine ال .. يمكن spanner شفتوا انتوا قبل هيكا
+
+130
+00:11:07,050 --> 00:11:14,310
+اللي هي إيش؟ إيش سميناها بالعربي؟ المفتاح
+
+131
+00:11:15,760 --> 00:11:20,040
+مظبوط مفتاح ال .. هاي .. هاي هو مفتاح ال ..
+
+132
+00:11:20,040 --> 00:11:25,800
+البراغي أو مفتاح ال .. السمنات هدول، هاي سمناء،
+
+133
+00:11:25,800 --> 00:11:28,620
+برضه هذا simple machine زي ما هنشوف في ال example
+
+134
+00:11:28,620 --> 00:11:32,600
+هذا an example of simple machine is a lever ال
+
+135
+00:11:32,600 --> 00:11:42,300
+lever اللي إيش؟ which is used with a fulcrum a
+
+136
+00:11:42,300 --> 00:11:47,860
+point which act as a support الآن طلع عندىلو انا
+
+137
+00:11:47,860 --> 00:11:54,240
+.. اين جلب تبعي؟ انا
+
+138
+00:11:54,240 --> 00:12:06,260
+جيبت جلب معالي و ميبقى .. الان
+
+139
+00:12:06,260 --> 00:12:12,000
+هاذي رافعة لو انا حطيت حاجة هنا و بدها وزن هنا
+
+140
+00:12:12,000 --> 00:12:17,310
+بقدر ارفعها مصبوطهذا الان اللي بنحكي عنها هذي
+
+141
+00:12:17,310 --> 00:12:22,410
+بنسميها liver اللي هي الرافعة اللي أنا بضغط عليها
+
+142
+00:12:22,410 --> 00:12:26,190
+لأرفع عشي which is used with a fulcrum a point
+
+143
+00:12:26,190 --> 00:12:29,310
+which act as a support and allow the liver to
+
+144
+00:12:29,310 --> 00:12:34,970
+pivot الان هذه النقطة وين بحركها بتعطيني إيش؟
+
+145
+00:12:34,970 --> 00:12:39,370
+قداشي بده أرفعو هذا احنا بنستخدمهاش كتير يعني انها
+
+146
+00:12:39,370 --> 00:12:43,350
+.. بس لو بده أرفع حاجة بحطها على خشب و بدعس من
+
+147
+00:12:43,350 --> 00:12:48,650
+اتجاه المعاكس بترفحها لل .. للارتفاع اللي بديها،
+
+148
+00:12:48,650 --> 00:12:52,470
+هذا لو حاجة تقيلة بنستخدمها و بتزيه .. بتنزح ..
+
+149
+00:12:52,470 --> 00:12:57,150
+بتنزح .. هذا machine بسيطة جدا، بنزوقها لنوصلها
+
+150
+00:12:57,150 --> 00:13:04,810
+للنقطة اللي بدنا يعنيFulcrum هو موقع يعمل كمساعدة
+
+151
+00:13:04,810 --> 00:13:09,710
+ويسمح لشركة deliver تتحرك حول المساعدة إذا كانت
+
+152
+00:13:09,710 --> 00:13:13,970
+شركة deliver مواجهة فالمقارنة بين الهجوم و الـ
+
+153
+00:13:13,970 --> 00:13:18,630
+Fulcrum هي أكبر من المقارنة بين مواجهة و Fulcrum
+
+154
+00:13:18,630 --> 00:13:21,990
+هذه اللي بيسميها الـ Fulcrum اللي هي نقطة ال pivot
+
+155
+00:13:21,990 --> 00:13:26,930
+اللي عندي هذه الان لو هذه أجت هنا الهجوم اللي عندي
+
+156
+00:13:26,930 --> 00:13:33,070
+إيش بدي يكون؟أقل من .. يعني بدأ .. لو هذا حطيتها
+
+157
+00:13:33,070 --> 00:13:38,310
+هنا ال effort المطلوب هنا أعلى كتير من هذا فإيش
+
+158
+00:13:38,310 --> 00:13:43,410
+صار عندى؟ ال distance إلها مفعول مع ال effort اللي
+
+159
+00:13:43,410 --> 00:13:46,370
+تعطيني إياها، مظبوط ولا لأ؟ هذا خدناها برضه
+
+160
+00:13:46,370 --> 00:13:51,210
+بالفيزيا، صح؟ العزم، مظبوط؟ فهذه لسه ذاكرها من
+
+161
+00:13:51,210 --> 00:13:52,110
+أيام الثانوية
+
+162
+00:13:55,680 --> 00:13:59,000
+هنا if the lever is placed so that the distance
+
+163
+00:13:59,000 --> 00:14:01,680
+between the effort and the fulcrum is greater than
+
+164
+00:14:01,680 --> 00:14:03,960
+the distance between the load and the fulcrum, a
+
+165
+00:14:03,960 --> 00:14:07,980
+mechanical advantage is created فهنا إيش أنا اللي
+
+166
+00:14:07,980 --> 00:14:12,080
+بدي إياه؟ لو المسافة بين هنا و هنا أكبر من هذه و
+
+167
+00:14:12,080 --> 00:14:15,690
+هذهصار عندى mechanical advantage يعني صارت عندى
+
+168
+00:14:15,690 --> 00:14:21,770
+ميزة لإني أقدر أستخدمها أو بتخفف العبء المطلوب مني
+
+169
+00:14:21,770 --> 00:14:25,270
+لأشغل فيه in general language the turning force
+
+170
+00:14:25,270 --> 00:14:29,150
+generated by a lever is called leverage اللي هي
+
+171
+00:14:29,150 --> 00:14:32,970
+لازم in engineering a turning force is called a
+
+172
+00:14:32,970 --> 00:14:38,270
+turning moment or moment moments are calculated by
+
+173
+00:14:38,270 --> 00:14:43,310
+multiplyingthe distance from the fulcrum in meter
+
+174
+00:14:43,310 --> 00:14:46,990
+by the magnitude of force in newton اللي هي العزم
+
+175
+00:14:46,990 --> 00:14:52,290
+المسافة هذه ضرب قيمة ال force تعطينا ال moment
+
+176
+00:14:52,290 --> 00:14:56,570
+اللي عندنا أو ال turning moment اللي احنا سمناها
+
+177
+00:14:56,570 --> 00:15:00,410
+turning force اللي موجود they are measured in
+
+178
+00:15:00,410 --> 00:15:07,050
+newton meters الاهل اتكلمنا عنهم ايش لحد الآن نجي
+
+179
+00:15:07,050 --> 00:15:11,180
+نبدأ في الأول اتكلمنا عن ال accelerationو ال
+
+180
+00:15:11,180 --> 00:15:15,900
+deceleration صح؟ إيش اتكلمنا بعضها؟ اتكلمنا عن
+
+181
+00:15:15,900 --> 00:15:21,060
+الوحدات تبعتهم قلنا ال velocity الوحدة تبعتها إيش؟
+
+182
+00:15:22,050 --> 00:15:25,930
+meter per second و ال acceleration و ال
+
+183
+00:15:25,930 --> 00:15:30,230
+deceleration ايوة الان اتكلمنا عن ال inertia ال
+
+184
+00:15:30,230 --> 00:15:33,670
+inertia ايش عبارة عن ايش ال resistance لل
+
+185
+00:15:33,670 --> 00:15:37,870
+acceleration او ال deceleration و هذه الها علاقة
+
+186
+00:15:37,870 --> 00:15:42,590
+بمين بال mass مظبوط اتكلمنا اخر اشي هنا على ال
+
+187
+00:15:42,590 --> 00:15:46,350
+simple machines و ال simple machines قلنا بتعطينا
+
+188
+00:15:46,350 --> 00:15:52,110
+mechanical advantagesلنشتغل فيها فهي عادة نتكلم
+
+189
+00:15:52,110 --> 00:15:58,330
+منها بتعطينا leverage اللي هي ال leverage اللي هي
+
+190
+00:15:58,330 --> 00:16:03,310
+الميزة هذه ال engineering turning force is called
+
+191
+00:16:03,310 --> 00:16:06,850
+a moment اللي عندى ال turning force اللي عندى ال
+
+192
+00:16:06,850 --> 00:16:10,730
+moment are calculated by multiplying ال distance
+
+193
+00:16:11,660 --> 00:16:15,620
+multiplied by ال force اللي عندي وهي measured per
+
+194
+00:16:15,620 --> 00:16:21,960
+Newton متر اللي عادي واتكلمنا على ال gravity وكيف
+
+195
+00:16:21,960 --> 00:16:26,960
+احنا بنعمل measurement لل unit using ال 1G و ال 2G
+
+196
+00:16:26,960 --> 00:16:30,740
+و هذا اللي عادي هذا بشكل عام اللي اتكلمنا عنه الآن
+
+197
+00:16:30,740 --> 00:16:35,670
+نيجي نتطلع على ال exercises اللي موجودة عنديال
+
+198
+00:16:35,670 --> 00:16:38,610
+exercise بيسألكم please the article about the
+
+199
+00:16:38,610 --> 00:16:42,430
+Titanic taken from a popular science magazine
+
+200
+00:16:42,430 --> 00:16:47,570
+تعالوا اسمعتوا بالتايتانيك؟ ايش هي؟ سفينة .. سفينة
+
+201
+00:16:47,570 --> 00:16:49,190
+.. سفينة .. سفينة .. سفينة .. سفينة .. سفينة ..
+
+202
+00:16:49,190 --> 00:16:49,230
+سفينة .. سفينة .. سفينة .. سفينة .. سفينة .. سفينة
+
+203
+00:16:49,230 --> 00:16:50,110
+.. سفينة .. سفينة .. سفينة .. سفينة .. سفينة ..
+
+204
+00:16:50,110 --> 00:16:54,330
+سفينة .. سفينة .. سفينة .. سفينة .. سفينة .. سفينة
+
+205
+00:16:54,330 --> 00:16:55,390
+.. سفينة .. سفينة .. سفينة .. سفينة .. سفينة ..
+
+206
+00:16:55,390 --> 00:16:59,200
+.. سفينة .. سفينةضخمة جدا و قوية جدا و قالوا هذه
+
+207
+00:16:59,200 --> 00:17:03,600
+السفينة مش هت .. يعني هي مش .. مش هت .. هتبحر ال
+
+208
+00:17:03,600 --> 00:17:09,040
+.. ال .. الاطلس المحيط الأطلسي و تتحدى القدرات ال
+
+209
+00:17:09,040 --> 00:17:13,940
+.. ال .. القدرات الكون فهذه قالوا هذه السفينة مش
+
+210
+00:17:13,940 --> 00:17:18,860
+ممكن يحصللها أي حاجة هذه السفينة اللي عملت زي ذلك
+
+211
+00:17:18,860 --> 00:17:25,610
+انصدمت .. صدمت iceberg اللي هو جبل جليديواتكسرت
+
+212
+00:17:25,610 --> 00:17:33,030
+وغرقت ومات .. ومات فيها .. ومات
+
+213
+00:17:33,030 --> 00:17:41,990
+فيها يعني الف وخمسمية وسبعتاشر شخص الآن التحليل
+
+214
+00:17:41,990 --> 00:17:46,730
+تبعها بيحكي طيب خلينا نشوف إيش ال article بتكلم
+
+215
+00:17:46,730 --> 00:17:54,100
+عنهالأمر يتم إقتراحه بإن المسافر لينيار تيتانيك لن
+
+216
+00:17:54,100 --> 00:18:00,900
+يكون محطم بعد الاتفاق مع عصبار في عام 1912 إذا كان
+
+217
+00:18:00,900 --> 00:18:05,680
+محطم المحطم محطم ودمج فقط أمام السيارة
+
+218
+00:18:08,860 --> 00:18:15,000
+يعني ما بقترحوا انه لو السفينة ال Titanic اللي هي
+
+219
+00:18:15,000 --> 00:18:21,120
+الخط ال Titanic السفينة هذه لو انها اصطدمت بال
+
+220
+00:18:21,120 --> 00:18:27,560
+iceberg head on يعني بالمقدمة المباشرة كان انه
+
+221
+00:18:27,560 --> 00:18:34,760
+ممكن ما تغرقش ليش؟ طالعش التفسير اللي عندي as
+
+222
+00:18:34,760 --> 00:18:40,950
+historyas history tells حسب التاريخ the crew tried
+
+223
+00:18:40,950 --> 00:18:46,130
+to turn to avoid the iceberg يعني طاقم السفينة
+
+224
+00:18:46,130 --> 00:18:52,290
+حاول يلف السفينة و يبعدها عن جبل الجليد فانصدمت من
+
+225
+00:18:52,290 --> 00:18:52,950
+الجانب
+
+226
+00:18:57,680 --> 00:19:02,100
+and one thousand five hundred seventeen lives were
+
+227
+00:19:02,100 --> 00:19:05,880
+lost but how severe would a frontal impact have
+
+228
+00:19:05,880 --> 00:19:11,040
+been for the passengers يعني بيسأل طيب كيف لو كان
+
+229
+00:19:11,040 --> 00:19:17,720
+انه التصادم المباشرفي المقدمة تبعت السفينة مع ال
+
+230
+00:19:17,720 --> 00:19:22,160
+ice berg إيش تأثيرها على المسافرين the answer
+
+231
+00:19:22,160 --> 00:19:25,440
+depends on several questions إيش الأسئلة اللي
+
+232
+00:19:25,440 --> 00:19:29,840
+بنقولها the ship tried to slow while turning with
+
+233
+00:19:29,840 --> 00:19:37,980
+الآن السفينة حاولت تبطئ سرعتها و هي بتلف الآن with
+
+234
+00:19:37,980 --> 00:19:43,590
+إيش deceleration have been more effectivelinear
+
+235
+00:19:43,590 --> 00:19:49,570
+deceleration اللي هي linear خلال اللفة بطلك linear
+
+236
+00:19:49,570 --> 00:19:54,710
+have been more effective allowing the ship to more
+
+237
+00:19:54,710 --> 00:19:59,550
+rapidly decelerate احنا بتتكلم عن linear ال
+
+238
+00:19:59,550 --> 00:20:03,550
+deceleration فمعناته ايش؟ بدي ارتبط عنها ال
+
+239
+00:20:03,550 --> 00:20:08,030
+deceleration او decelerate more rapidly based on
+
+240
+00:20:08,030 --> 00:20:13,810
+this ايش of deceleration؟الان .. الان .. and
+
+241
+00:20:13,810 --> 00:20:16,930
+assuming the ship would not have .. would not have
+
+242
+00:20:16,930 --> 00:20:21,430
+stopped in time based on the rate of deceleration
+
+243
+00:20:21,430 --> 00:20:26,550
+يعني اللي هي what would have .. what would the
+
+244
+00:20:26,550 --> 00:20:30,350
+edge of the ship have been at that moment of the
+
+245
+00:20:30,350 --> 00:20:35,330
+impact الفلص يعني قديش بديكون الفلص يعني هنا حطينا
+
+246
+00:20:35,330 --> 00:20:38,610
+إيش linear
+
+247
+00:20:41,040 --> 00:20:46,740
+هنا حطينا دي سيلاريت دي
+
+248
+00:20:46,740 --> 00:20:57,620
+سيلاريت هنا حطينا ال rate هنا velocity of the ship
+
+249
+00:20:57,620 --> 00:21:02,480
+have been at the moment of impact what was the age
+
+250
+00:21:02,480 --> 00:21:07,340
+of the iceberg احنا قلنا في حاجة مع ال iceberg ايش
+
+251
+00:21:07,340 --> 00:21:10,400
+هي ال mass ال mass of the iceberg
+
+252
+00:21:13,730 --> 00:21:19,030
+calculate the appropriate number of kilograms of
+
+253
+00:21:19,030 --> 00:21:23,230
+the iceberg would allow the .. ايش .. ايش اللي
+
+254
+00:21:23,230 --> 00:21:33,130
+بيجي مع الmass و ال speed ال inertia inertia
+
+255
+00:21:33,130 --> 00:21:40,210
+inertia inertia طيب
+
+256
+00:21:40,210 --> 00:21:49,420
+of the iceberg haveسيكون مقارنة مع مدينة تيتانيك
+
+257
+00:21:49,420 --> 00:21:57,060
+وهذا سيسمح لإنبعاد الإنبعاد لإنبعاد الإنبعاد إلى
+
+258
+00:21:57,060 --> 00:21:57,620
+مدرج مهم
+
+259
+00:22:05,500 --> 00:22:11,880
+and so .. so observe some of the shock as it was
+
+260
+00:22:11,880 --> 00:22:16,440
+pushed forward يعني إيش بيحكي هذا؟ لو أحنا السفينة
+
+261
+00:22:16,440 --> 00:22:24,400
+صدمت في الجبل الجبل حسب قيمة الوزن تبعه هو هيتحرك
+
+262
+00:22:24,400 --> 00:22:30,100
+و هيتصارع في هذا فهذه هتعمل ال shock أخف من اللي
+
+263
+00:22:30,100 --> 00:22:34,960
+كانت عليه هذا اللي بنحكي فيه حسب
+
+264
+00:22:43,160 --> 00:22:47,400
+الان بالطبع السؤال الأعلى يعتمد على عدد غير معروف
+
+265
+00:22:47,400 --> 00:22:50,860
+غير معروف غير معروف غير معروف غير معروف غير معروف
+
+266
+00:22:50,860 --> 00:22:51,380
+غير معروف غير معروف غير معروف غير معروف غير معروف
+
+267
+00:22:51,380 --> 00:22:51,500
+غير معروف غير معروف غير معروف غير معروف غير معروف
+
+268
+00:22:51,500 --> 00:22:51,740
+غير معروف غير معروف غير معروف غير معروف غير معروف
+
+269
+00:22:51,740 --> 00:22:54,580
+غير معروف غير معروف غير معروف غير معروف غير معروف
+
+270
+00:22:54,580 --> 00:22:59,220
+غير معروف غير معروف غير معروف غير معروف غير معرو
+
+271
+00:22:59,240 --> 00:23:04,980
+that's seven هذا اللي بيقول خلينا نقول انه التصادم
+
+272
+00:23:04,980 --> 00:23:10,100
+حصل على سرعة سرعة خمسة وعشرين كيلومتر per an hour
+
+273
+00:23:10,100 --> 00:23:13,440
+هذه لما نحولها ل seconds ايش ممكن تصير that's
+
+274
+00:23:13,440 --> 00:23:21,130
+seven meter per second السرعةوالذي يسمح للمحطة
+
+275
+00:23:21,130 --> 00:23:27,670
+بملاحظة من المصدر التنقل والمحطة التنقل والمحطة
+
+276
+00:23:27,670 --> 00:23:29,610
+التنقل والمحطة التنقل والمحطة التنقل والمحطة
+
+277
+00:23:29,610 --> 00:23:33,390
+التنقل والمحطة التنقل والمحطة التنقل والمحطة
+
+278
+00:23:33,390 --> 00:23:34,250
+التنقل والمحطة التنقل والمحطة التنقل والمحطة
+
+279
+00:23:34,250 --> 00:23:34,430
+التنقل والمحطة التنقل والمحطة التنقل والمحطة
+
+280
+00:23:34,430 --> 00:23:36,250
+التنقل والمحطة التنقل والمحطة التنقل والمحطة
+
+281
+00:23:36,250 --> 00:23:41,290
+التنقل والمحطة التنقل والمحطة التنقل والمحطة
+
+282
+00:23:41,290 --> 00:23:47,210
+التنقل والمحطة التنقل والمحطة
+
+283
+00:23:47,210 --> 00:23:51,710
+التنقثوانى although it would probably have taken
+
+284
+00:23:51,710 --> 00:23:55,470
+longer this would have resulting in deceleration
+
+285
+00:23:55,470 --> 00:23:58,470
+of two point three ايش ال unit تبعت ال
+
+286
+00:23:58,470 --> 00:24:02,910
+deceleration نفسها meter per second square
+
+287
+00:24:02,910 --> 00:24:11,890
+expressed as in g قداش هاد in g ال two point three
+
+288
+00:24:11,890 --> 00:24:20,120
+قداش تلت نقسم على عشرة مظبوطas a g force that
+
+289
+00:24:20,120 --> 00:24:25,500
+gives 0.23 less than one third of deceleration
+
+290
+00:24:25,500 --> 00:24:29,780
+generated by a car breaking heavily يعني هذا بيقول
+
+291
+00:24:29,780 --> 00:24:34,020
+لو احنا ال assumption اللي عملناه زي هيكه هلاحظ
+
+292
+00:24:34,020 --> 00:24:41,640
+انه ال deceleration عندي تقريبا 0.23 g force يعني
+
+293
+00:24:41,640 --> 00:24:46,710
+2.3 هذه لو سيارة ماشيةوعملت breaking heavy ايش
+
+294
+00:24:46,710 --> 00:24:52,370
+بيصير للركاب اللي فيها؟ بيصدموا هيك بس بيموتوش
+
+295
+00:24:52,370 --> 00:24:57,510
+مظبوط هذا اللي بيحكوا فيها so the impact probably
+
+296
+00:24:57,510 --> 00:25:00,650
+wouldn't have caused too much of a shock to the
+
+297
+00:25:00,650 --> 00:25:04,350
+passengers whether or not the ship would have sunk
+
+298
+00:25:04,350 --> 00:25:08,390
+however is another story يعني هذا بيقول ان هذه
+
+299
+00:25:08,390 --> 00:25:14,050
+هتكون تقريبا تلت صدمة السيارة اللي بتوقف فجأةأو
+
+300
+00:25:14,050 --> 00:25:20,500
+بتضرب دركات فجأة وهذا ممكن كان انهالسفينة ماتغرقش
+
+301
+00:25:20,500 --> 00:25:25,260
+وهذا يمكن قصة تانية حسب الرواية تبعتهم هذا اللي
+
+302
+00:25:25,260 --> 00:25:30,340
+بنحك .. اللي بنحك فيه انه هذي بيتكلم على قصة ال
+
+303
+00:25:30,340 --> 00:25:35,360
+Titanic بس من منظور فيزيائي او منظور scientific
+
+304
+00:25:35,360 --> 00:25:38,540
+data
+
+305
+00:25:38,540 --> 00:25:43,000
+فاحنا هنا طلعنا عليها وفسرناها حسب الكتاب ببقول
+
+306
+00:25:43,000 --> 00:25:46,760
+انه ممكن ماكنتش تغرق لو احنا استخدمها بال term
+
+307
+00:25:46,760 --> 00:25:52,890
+اللي عندناطيب، الآن هذا شوفناه قبل هيك لما اتكلمنا
+
+308
+00:25:52,890 --> 00:25:56,570
+عن البراغي و ال tools ال screws و ال nuts هذا اللي
+
+309
+00:25:56,570 --> 00:26:00,270
+سمنها ال nuts هذا اللي سمنها ال spanner و قولنا
+
+310
+00:26:00,270 --> 00:26:04,690
+هذا ال spanner لما نجي لو انا بال ايه بداجة افكها
+
+311
+00:26:04,690 --> 00:26:09,610
+مش هعمل generation زي لو انا استخدمت دراع موجودة و
+
+312
+00:26:09,610 --> 00:26:15,110
+كل ما طولت الدراع كل ما ايش عملتنا هو عزم اكبر
+
+313
+00:26:15,110 --> 00:26:19,530
+الموجودةreplace the underlined word and expression
+
+314
+00:26:19,530 --> 00:26:24,050
+with alternative word and expression from a and b
+
+315
+00:26:24,050 --> 00:26:27,770
+اللي قدرنا اللي عندى ال first diagram below اللي
+
+316
+00:26:27,770 --> 00:26:33,610
+عندى below illustrates how a worker is able to
+
+317
+00:26:33,610 --> 00:26:39,010
+apply total force of fifty newtons to the corner
+
+318
+00:26:39,010 --> 00:26:43,790
+of a nut using just his fingers هذه اللي عندى بدى
+
+319
+00:26:43,790 --> 00:26:47,980
+يعمل خمسين نيوتن باستخدامالإيديان مش كل الناس
+
+320
+00:26:47,980 --> 00:26:55,200
+بتقدر تعملها صح؟ شو؟ لو أنت بدك تحزجي برغي سمونا
+
+321
+00:26:55,200 --> 00:27:00,580
+زي هيك زي هيك؟ ايوة اول لفات سهلة بعدين لما بداش
+
+322
+00:27:00,580 --> 00:27:05,340
+يحزج تظبطش احنا قدش .. قدش اللي أنت بندرناه؟ قدش
+
+323
+00:27:05,340 --> 00:27:08,820
+أكترش اللي أنت بندرناه؟ بعرفش تعتمد في ناس .. في
+
+324
+00:27:08,820 --> 00:27:14,670
+ناس بتحزج و بتقدريش تفكي من وراهمو في ناس سواء ..
+
+325
+00:27:14,670 --> 00:27:18,750
+بعرف في كان النجار كان بيحذق المصورة بيده و هات
+
+326
+00:27:18,750 --> 00:27:24,370
+اللي يفكها بس مش كل الناس زي هيكة في ناس بتقدرش
+
+327
+00:27:24,370 --> 00:27:31,270
+تفك حاجة كل شي طول موجود فهذه بتختلف حسب الأشخاص
+
+328
+00:27:31,270 --> 00:27:36,070
+الأشخاص اللي بتلاقيهم بيستغلوا مهنيين في ديهم أو
+
+329
+00:27:36,070 --> 00:27:40,390
+بيلعبوا حديث بتلاقيوا الجبدة تبعتهم جوية فبيقدر
+
+330
+00:27:40,390 --> 00:27:46,420
+يحذق الناس اللي زي حكيتكمخفيفة جدا فبتلاقيها هذه
+
+331
+00:27:46,420 --> 00:27:52,780
+مش كتير بتشتغل معاكم فالفوق الكلمة force إيه
+
+332
+00:27:52,780 --> 00:27:57,950
+شفناها مكتوبة عندنا في الكتاب effortsاذا لاحظناها
+
+333
+00:27:57,950 --> 00:28:01,950
+في .. في part تبع ال symbol machine كانت مستخدمين
+
+334
+00:28:01,950 --> 00:28:08,130
+ال word force effort وجنبها ال force generated of
+
+335
+00:28:08,130 --> 00:28:11,770
+fifty newtons in the corner of a nut using just
+
+336
+00:28:11,770 --> 00:28:17,450
+his finger the distance from the center of the nut
+
+337
+00:28:17,450 --> 00:28:22,810
+the points of the nuts the point around which the
+
+338
+00:28:22,810 --> 00:28:29,030
+nut turns ايش turns بيصير؟pivot ايش يعني pivot
+
+339
+00:28:29,030 --> 00:28:35,730
+بتلف بتركيز يعني هي turn النقطة اللي عندي هذه
+
+340
+00:28:35,730 --> 00:28:39,230
+بيصير فيها turn هذه بيسميها ال pivot لما أجي انا
+
+341
+00:28:39,230 --> 00:28:43,470
+أحط نقطة و أقول هذه اللي عندها بلف هيك هذه بسميها
+
+342
+00:28:43,470 --> 00:28:48,010
+النقطة إيش ال pivot point يعني لما أحط هذا عليها و
+
+343
+00:28:48,010 --> 00:28:51,530
+أقول هذه اللي عندي هذه صارت ال pivot point ال
+
+344
+00:28:51,530 --> 00:28:54,650
+pivot point اللي هي نقطة الرأس أو النقطة اللي فيها
+
+345
+00:28:54,650 --> 00:29:02,130
+التأثير الأقوىand the corner of the nuts is 10
+
+346
+00:29:02,130 --> 00:29:06,190
+millimeter يعني هذه المسافة اللي عندى طلعت عليها
+
+347
+00:29:06,190 --> 00:29:10,110
+من هالى هالى وين اليد 10 millimeter الان 10
+
+348
+00:29:10,110 --> 00:29:14,550
+millimeter ضارب fifty newtons قدرش بتعطينى ال 10
+
+349
+00:29:14,550 --> 00:29:19,770
+millimeter بتعطينى اللي هي بتتساوى في لغة ال meter
+
+350
+00:29:19,770 --> 00:29:22,830
+point o مظبوط
+
+351
+00:29:25,340 --> 00:29:32,100
+الان بدي احولها هذى تعطيني 50 ضارب 0.01 متر تعطيني
+
+352
+00:29:32,100 --> 00:29:36,640
+0.5 نيوتن متر اللي هي العزم اللي عندى او ال moment
+
+353
+00:29:36,640 --> 00:29:43,640
+الان لما انا بدي استخدم ال spanner اللي عندى and
+
+354
+00:29:43,640 --> 00:29:47,120
+the corner is thin the results in a force of
+
+355
+00:29:47,120 --> 00:29:53,600
+leverage of 0.5 نيوتن متر انا حكيت الكلمة تبعتها و
+
+356
+00:29:53,600 --> 00:30:00,140
+ايش هيسميهاالـ moment هذه سمنها okay this is
+
+357
+00:30:00,140 --> 00:30:05,900
+insufficient to tighten the nuts properly لأن هذه
+
+358
+00:30:05,900 --> 00:30:12,780
+مش جوية لإيش اعمل لأحزق السمونة هذه الان ال second
+
+359
+00:30:12,780 --> 00:30:18,560
+diagram show how a spanner can be used as a tool
+
+360
+00:30:18,560 --> 00:30:24,310
+to .. إيش هذه .. to provide .. إيش ال toolsimple
+
+361
+00:30:24,310 --> 00:30:30,670
+machine هذه عبارة عن اللي عندى simple machine to
+
+362
+00:30:30,670 --> 00:30:37,170
+provide a boost in force ايش هذه اللي
+
+363
+00:30:37,170 --> 00:30:42,730
+عملناها mechanical advantage هذا اللي سمناها نفس
+
+364
+00:30:42,730 --> 00:30:47,630
+الكلمة موجودة هناك mechanical advantage applying
+
+365
+00:30:47,630 --> 00:30:49,510
+the same 50 newton force
+
+366
+00:30:54,590 --> 00:30:58,610
+الان نطلع فيها applying 50 newton force to the end
+
+367
+00:30:58,610 --> 00:31:05,890
+of a 200 millimeter spanner which will act as a
+
+368
+00:31:05,890 --> 00:31:12,390
+turning tool ايش ال turning tool؟ liverهذه المسافة
+
+369
+00:31:12,390 --> 00:31:18,490
+تجعل 10 نيوتن متر فرصة
+
+370
+00:31:18,490 --> 00:31:25,370
+20 مرات أكتر و كافية لتحطم الناتز هذه
+
+371
+00:31:25,370 --> 00:31:30,290
+مقارنة
+
+372
+00:31:30,290 --> 00:31:38,540
+البيهات هذه 20 مراتالشغل بالإيد اللى عندى twenty
+
+373
+00:31:38,540 --> 00:31:41,880
+times greater and enough to tighten the nuts
+
+374
+00:31:41,880 --> 00:31:45,780
+وكافية لإنها تسوها وهذه بتلاحظوها كل ال simple
+
+375
+00:31:45,780 --> 00:31:51,000
+machine هذه بنستخدمها بالإيد بشكل مباشر إذا طلعنا
+
+376
+00:31:51,000 --> 00:31:56,220
+عليها فيها فال simple machine إيش بتعطينا من
+
+377
+00:31:56,220 --> 00:31:58,920
+الكلمات اللى بديك تطلع فيها ال mechanical
+
+378
+00:31:58,920 --> 00:32:06,690
+advantage يعني إيش؟boost in force الـ turning tool
+
+379
+00:32:06,690 --> 00:32:14,030
+اللي سمنها liver ال tool ال simple machine اللي
+
+380
+00:32:14,030 --> 00:32:20,170
+سمنها ال tool ال force of leveragemoment اللي عندى
+
+381
+00:32:20,170 --> 00:32:23,950
+ال force قلنا اللى هى ال effort اللى موجودة و ال
+
+382
+00:32:23,950 --> 00:32:28,730
+terms اللى هى ال ايش ال pivot اللى موجودات عندى
+
+383
+00:32:28,730 --> 00:32:33,810
+هدول الكلمات اللى مرن علينا في ال C الآن مر علينا
+
+384
+00:32:33,810 --> 00:32:41,800
+عدة شغلات بس خلّي نلخص هذا على السريعأما هي
+
+385
+00:32:41,800 --> 00:32:44,520
+الكلمات اللي بتمر عليكم عشان تبقوا داكرينها
+
+386
+00:32:44,520 --> 00:32:48,960
+اتكلموا انتوا روحين اتكلمنا على ال force وقلنا هي
+
+387
+00:32:48,960 --> 00:32:52,620
+عبارة عن ال effort اتكلمنا على ال velocity وقلنا
+
+388
+00:32:52,620 --> 00:32:56,700
+ال rate of velocity سمناه ايش acceleration او
+
+389
+00:32:56,700 --> 00:33:01,240
+deceleration الان
+
+390
+00:33:01,240 --> 00:33:06,040
+ال motion عادة في عندنا linear motion وفي عندنا
+
+391
+00:33:06,040 --> 00:33:13,050
+nonlinear او circular motionالان acceleration due
+
+392
+00:33:13,050 --> 00:33:18,690
+to gravity سمنها ايش؟ G force وقلنا هي بتسوى 10
+
+393
+00:33:18,690 --> 00:33:23,870
+متر per second square بتسوى 1 G force الان ال
+
+394
+00:33:23,870 --> 00:33:28,770
+inertia قلنا هي resistance to acceleration or
+
+395
+00:33:28,770 --> 00:33:35,020
+deceleration due to the mass of the objectال
+
+396
+00:33:35,020 --> 00:33:39,000
+simple machine اتكلمنا في ال simple machine ايش ال
+
+397
+00:33:39,000 --> 00:33:42,620
+tool اللي عندى ال tool هي عبارة عن simple machine
+
+398
+00:33:42,620 --> 00:33:47,880
+اتكلمنا فيه برضه على ال mechanical advantage ال
+
+399
+00:33:47,880 --> 00:33:56,820
+efforts و ال lever و ال moment كويس؟ هيك بنفجر
+
+400
+00:33:57,420 --> 00:34:01,360
+غطينا كل اللي بدنا يال مرة جاي بنتكلم على chapter
+
+401
+00:34:01,360 --> 00:34:07,020
+بس قبل ما أنسى حضرو حالكم عساس المجموعات هي في
+
+402
+00:34:07,020 --> 00:34:09,600
+quiz بدي أجيبكوا فيه عشان ندكرها
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/WBfXV9hslPg_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/WBfXV9hslPg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..81f2daffbfdd0030235f416ff0946d54037f7244
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/WBfXV9hslPg_raw.json
@@ -0,0 +1 @@
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هذا المعنى اللي عندي إن سرعتها بتزداد 10 meter per second لكل second بتيجي فيها", "tokens": [6027, 7649, 29538, 23032, 3555, 3615, 995, 11933, 15730, 47525, 4117, 6055, 47283, 3215, 8978, 21542, 3794, 16758, 3714, 4587, 995, 20498, 3660, 2423, 3224, 2407, 16606, 23032, 3555, 3615, 995, 37893, 8032, 2655, 30544, 39627, 24192, 37495, 22653, 4724, 3794, 45164, 41850, 6055, 7435, 40294, 1211, 2655, 3714, 4587, 995, 20498, 3660, 2423, 3224, 2407, 16606, 23758, 9673, 3615, 1863, 7578, 13672, 1829, 18871, 16254, 36145, 8608, 2288, 34268, 11296, 39894, 11622, 3215, 18513, 1266, 9255, 680, 1150, 5296, 28820, 1150, 39894, 1829, 7435, 1829, 8978, 11296], "avg_logprob": -0.1329880684949039, "compression_ratio": 1.638743455497382, "no_speech_prob": 0.0, "words": [{"start": 346.42, "end": 347.08, "word": "الان", "probability": 0.8681640625}, {"start": 347.08, "end": 347.58, "word": " هذه", "probability": 0.52685546875}, {"start": 347.58, "end": 348.42, "word": " طبعا", "probability": 0.9814453125}, 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"probability": 0.8790283203125}, {"start": 362.62, "end": 363.24, "word": " 10", "probability": 0.44677734375}, {"start": 363.24, "end": 363.64, "word": " meter", "probability": 0.580078125}, {"start": 363.64, "end": 364.22, "word": " per", "probability": 0.94873046875}, {"start": 364.22, "end": 364.76, "word": " second", "probability": 0.9326171875}, {"start": 364.76, "end": 365.8, "word": " لكل", "probability": 0.97802734375}, {"start": 365.8, "end": 366.34, "word": " second", "probability": 0.98583984375}, {"start": 366.34, "end": 367.08, "word": " بتيجي", "probability": 0.9234619140625}, {"start": 367.08, "end": 367.38, "word": " فيها", "probability": 0.978515625}], "temperature": 1.0}, {"id": 15, "seek": 39784, "start": 369.54, "end": 397.84, "text": "Acceleration and deceleration such as that generated by aircraft and cars can be compared with acceleration due to gravity الان الناس ايش بيحكوا بدل ما انا احكي حاجات هاج بصير اقارن ال acceleration او ال deceleration مقارة مع 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new file mode 100644
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أو بتنقطع لو شديت أحنا إيش قولنا في المنطقة اللي في النص اللي بيصير فيها بترفع لحد دي ما يصير إيش بتقطع لو شديته مغيطة في الآخر هتنقطع من النص اللي عندك in compression if it's stick it will crush or squash لو انت تعمليها إيش بدها تتطبق صح؟", "tokens": [686, 1251, 309, 486, 36877, 11933, 1829, 8592, 37495, 22653, 36877, 22807, 39894, 1863, 4117, 3794, 2288, 34051, 39894, 1863, 47432, 3615, 45164, 13412, 16254, 2655, 5551, 5016, 8315, 11933, 1829, 8592, 12174, 12610, 8315, 8978, 9673, 1863, 9566, 28671, 13672, 1829, 8978, 28239, 9381, 13672, 1829, 4724, 1829, 9381, 13546, 8978, 11296, 39894, 28480, 3615, 5296, 24401, 11778, 1829, 19446, 7251, 9381, 13546, 11933, 1829, 8592, 39894, 47432, 3615, 45164, 13412, 16254, 47395, 3714, 17082, 1829, 9566, 3660, 8978, 6024, 95, 34740, 8032, 2655, 1863, 47432, 3615, 9154, 28239, 9381, 13672, 1829, 43242, 4117, 294, 19355, 498, 309, 311, 2897, 309, 486, 10321, 420, 30725, 45164, 16472, 2655, 6055, 25957, 20292, 11296, 11933, 1829, 8592, 47525, 11296, 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"probability": 0.90234375}], "temperature": 1.0}, {"id": 61, "seek": 161389, "start": 1595.65, "end": 1613.89, "text": "أو thick بيصير لها crush الآن لما اتكلم على torsion إيش بيحصل لها؟ ممكن يصير لها fracture أو share اللي هي عندنا ال share بيصير لها إيش؟ كسر broken أو اللي هي هذه ملخص المحاضرة تبعتنا", "tokens": [10721, 2407, 5060, 4724, 1829, 9381, 13546, 5296, 11296, 10321, 6024, 48506, 5296, 15042, 1975, 2655, 4117, 19528, 15844, 3930, 82, 313, 11933, 1829, 8592, 4724, 1829, 5016, 36520, 5296, 11296, 22807, 3714, 43020, 7251, 9381, 13546, 5296, 11296, 36877, 34051, 2073, 13672, 1829, 39896, 43242, 8315, 2423, 2073, 4724, 1829, 9381, 13546, 5296, 11296, 11933, 1829, 8592, 22807, 9122, 3794, 2288, 5463, 34051, 13672, 1829, 39896, 29538, 3714, 1211, 9778, 9381, 9673, 5016, 46958, 25720, 6055, 3555, 34268, 8315], "avg_logprob": -0.19984567606890644, "compression_ratio": 1.6022099447513811, "no_speech_prob": 0.0, "words": [{"start": 1595.65, "end": 1595.99, "word": "أو", "probability": 0.778564453125}, {"start": 1595.99, "end": 1596.37, "word": " thick", "probability": 0.4482421875}, {"start": 1596.37, "end": 1596.81, "word": " بيصير", "probability": 0.9627685546875}, {"start": 1596.81, "end": 1597.15, "word": " لها", "probability": 0.767333984375}, {"start": 1597.15, "end": 1597.75, "word": " crush", "probability": 0.95068359375}, {"start": 1597.75, "end": 1598.81, "word": " الآن", "probability": 0.59423828125}, {"start": 1598.81, "end": 1599.01, "word": " لما", "probability": 0.958984375}, {"start": 1599.01, "end": 1599.49, "word": " اتكلم", "probability": 0.846435546875}, {"start": 1599.49, "end": 1599.87, "word": " على", "probability": 0.6865234375}, {"start": 1599.87, "end": 1600.77, "word": " torsion", "probability": 0.714599609375}, {"start": 1600.77, "end": 1600.99, "word": " إيش", "probability": 0.7405598958333334}, {"start": 1600.99, "end": 1601.39, "word": " بيحصل", "probability": 0.9862060546875}, {"start": 1601.39, "end": 1601.99, "word": " لها؟", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/ZbhGZWflaIQ_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/ZbhGZWflaIQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0901b834ef51e983c3c89377380db09eef1fcc8e
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/ZbhGZWflaIQ_raw.srt
@@ -0,0 +1,1220 @@
+1
+00:00:20,690 --> 00:00:26,470
+السلام عليكم اليوم سوف نتكلم عن قصة تاري وان تاري
+
+2
+00:00:26,470 --> 00:00:31,770
+وان تاري وان تتكلم عن قوات التنقل والخسارة ولكن
+
+3
+00:00:31,770 --> 00:00:37,690
+قبل أن نبدأ سوف نشاهد الفيديو لكي نفهم مصطلح
+
+4
+00:00:37,690 --> 00:00:44,190
+القوات وماذا يحدث عندما يحدث اتجارة هذه القوات
+
+5
+00:00:44,190 --> 00:00:50,090
+نسميها تنقل وعندما يحدث خسارة ما هي النتائج؟
+
+6
+00:00:54,330 --> 00:00:58,550
+this is the compression force اللي هو عملية الضغط
+
+7
+00:00:58,550 --> 00:01:06,350
+كويس إذا بتلاحظوا إيش بيحصل فيها اللي في النص بنفخ
+
+8
+00:01:06,350 --> 00:01:12,510
+هذه أو get crushed ال compression بيعمل ال
+
+9
+00:01:12,510 --> 00:01:17,650
+crushing اللي هي بتطبق الشغل tension اللي هي عايش
+
+10
+00:01:17,650 --> 00:01:23,330
+بنعمل bowling شدإيش اللي بيحصل هان؟ ت get thinner
+
+11
+00:01:23,330 --> 00:01:30,610
+this
+
+12
+00:01:30,610 --> 00:01:36,630
+is called bending إيش هي؟ إيش اللي بيحصل فوق؟
+
+13
+00:01:36,630 --> 00:01:40,110
+بيحصل هنا compression و تحت بيحصل إيش؟ stretching
+
+14
+00:01:40,110 --> 00:01:43,950
+يعني هنا .. هنا المنطقة بيحصل فيها إيش؟
+
+15
+00:01:43,950 --> 00:01:46,830
+compression هذه المنطقة اللي فوق اللي تحت بيحصل
+
+16
+00:01:46,830 --> 00:01:48,930
+فيها إيش؟ stretching تمغط
+
+17
+00:01:51,810 --> 00:01:56,990
+هذا الآن بيسميها Trojan force اللي هي إيش اللوي
+
+18
+00:01:56,990 --> 00:02:02,510
+تنستويست an object يعني إيش بيلف فيها في هذا ال
+
+19
+00:02:02,510 --> 00:02:05,630
+object إيش اللي بيحصل في هذا؟ هتلاحظيها بعض
+
+20
+00:02:05,630 --> 00:02:10,830
+المناطق هتصير ضعيفة هذا ممكن يحصل يعني كنتيجة إلها
+
+21
+00:02:10,830 --> 00:02:14,810
+بتنكسر هذا النوع التالت بيسميه share force share
+
+22
+00:02:14,810 --> 00:02:20,800
+force قوتين جايات كل واحدة مش متعامدات جانب بعضو
+
+23
+00:02:20,800 --> 00:02:24,220
+واحدة لفوق و واحدة ل .. هاذ ايش لما النتيجة انه
+
+24
+00:02:24,220 --> 00:02:31,200
+ممكن تنكسر Now
+
+25
+00:02:31,200 --> 00:02:32,840
+we gonna go into details
+
+26
+00:02:35,970 --> 00:02:38,950
+type of forces and deformation type of failures
+
+27
+00:02:38,950 --> 00:02:43,750
+then we gonna do couple of exercises now we have
+
+28
+00:02:43,750 --> 00:02:48,130
+non technical words technical words adjectives and
+
+29
+00:02:48,130 --> 00:02:53,830
+the meaning of them stretching اللي هو أيش شد اللي
+
+30
+00:02:53,830 --> 00:02:58,950
+بنسميها انا أيش technical tensionTensile stress
+
+31
+00:02:58,950 --> 00:03:02,690
+الobjective it will extend in length يعني الطول
+
+32
+00:03:02,690 --> 00:03:06,810
+تبحها إيش بيسوي بيها بازداد وهذه واضحة يعني المسك
+
+33
+00:03:06,810 --> 00:03:10,910
+المغيطة واسحبيها بتلاقيها إيش الطول تبحها زاد
+
+34
+00:03:10,910 --> 00:03:18,020
+squashing إيش هذه؟not غطخة أو بن .. زي ما بقول
+
+35
+00:03:18,020 --> 00:03:22,360
+بنحاول أن نزغر حجمها high squash compression
+
+36
+00:03:22,360 --> 00:03:27,300
+compressive stress it will compress اللي هي get
+
+37
+00:03:27,300 --> 00:03:33,600
+shorter اللي هي بتقصر بنقصر الحاجة bending ال non
+
+38
+00:03:33,600 --> 00:03:36,940
+technical ال technical bending bending stress it
+
+39
+00:03:36,940 --> 00:03:41,760
+will bend we can also say it will deflect or تلعن
+
+40
+00:03:41,760 --> 00:03:49,820
+الكلمة هاي deflect orflex deflect ايش يعني لأ بت
+
+41
+00:03:49,820 --> 00:03:54,440
+.. بت .. يعني لما تضغط عليها بتعمل ردة فعل
+
+42
+00:03:54,440 --> 00:04:03,000
+المعاكسة هي flex beams usually sag ايش sag؟ تنزل
+
+43
+00:04:03,000 --> 00:04:09,530
+لتحتيعني لو أنت عندك صورة أو حاجة وطولها طويل، إيش
+
+44
+00:04:09,530 --> 00:04:13,370
+هتلاحظ فيها؟ لو حطيتي حبل، أبسط شيء، شدتيه، إيش
+
+45
+00:04:13,370 --> 00:04:17,670
+هتلاقيه في النص؟ مش خط مستقيم، هتلاقي اللي في النص
+
+46
+00:04:17,670 --> 00:04:22,470
+دايما أوطة ولو بمليمترات عن باقي المنطقة، ليش هذه؟
+
+47
+00:04:22,470 --> 00:04:27,590
+في فعل قوة الجاذبية بتأثر فيه فبتنزله، فبنحكي إيش
+
+48
+00:04:27,590 --> 00:04:32,100
+هذه؟ Sag، الـ voltage عندكالتيار لما تجيسيه في
+
+49
+00:04:32,100 --> 00:04:36,160
+البيت لو أنت بعيد عن الـ Trans بتلاقيه أقل من قيمة
+
+50
+00:04:36,160 --> 00:04:42,340
+الـ 220 هذا بنسميه إيش؟ Sag اللي هو القيمة نزلت
+
+51
+00:04:44,160 --> 00:04:48,620
+deflecting downwards in some cases deflection on
+
+52
+00:04:48,620 --> 00:04:54,280
+the flexure is upward the beam hugs ال beam
+
+53
+00:04:54,280 --> 00:04:58,500
+بيسميها عملية هذه hugs لما يصير deflection upward
+
+54
+00:04:58,500 --> 00:05:03,070
+اللي عنديscissoring اللي هي المقاص، المقاص بيعمل
+
+55
+00:05:03,070 --> 00:05:07,390
+إيش؟ حاجتين، حاجة بتطلق من تحت، بتضغط لفوق، اللي
+
+56
+00:05:07,390 --> 00:05:11,230
+من فوق بتضغط لإيش؟ لتحت، التنتين بتلاقي في المقاص
+
+57
+00:05:11,230 --> 00:05:15,710
+مش متعمدان جن بعض، هذا اللي بيسميها share or
+
+58
+00:05:15,710 --> 00:05:19,430
+sharing و share stress it will deform very little
+
+59
+00:05:19,430 --> 00:05:25,930
+failing suddenly فجأة تنقطعtwisting اللى لفها
+
+60
+00:05:25,930 --> 00:05:30,710
+بيسميها torsion torque او torsional stress it will
+
+61
+00:05:30,710 --> 00:05:34,750
+twist بتلف اللى موجود عندى وهى الأشكال اللى عندى
+
+62
+00:05:34,750 --> 00:05:38,270
+هادى اللى شفتوها قبل شوية الفيديو هادى بنشد فيه
+
+63
+00:05:38,270 --> 00:05:42,990
+هنا بنعمل ضغط هنا بنعمل bending هنا بنعمل torsion
+
+64
+00:05:42,990 --> 00:05:48,090
+بنلف فيه هنا shear اللى هي حاجة لفوق و حاجة لتحت
+
+65
+00:05:49,820 --> 00:05:54,500
+Bending compromises two opposite stresses, tension
+
+66
+00:05:54,500 --> 00:05:58,620
+and compression. This is shown in the diagram of
+
+67
+00:05:58,620 --> 00:06:02,800
+assembly supported beam اللي عندها هذا الخط اللي
+
+68
+00:06:02,800 --> 00:06:06,750
+بيسمي هذا ال top و هذا ال bottomالـ top عندي
+
+69
+00:06:06,750 --> 00:06:12,370
+compression stress و ال bottom tensile stress اللي
+
+70
+00:06:12,370 --> 00:06:17,410
+هي هنا شد وهنا ضغط خط النص هذا بيسميه الـ neutral
+
+71
+00:06:17,410 --> 00:06:21,430
+axis مافيش عليه أي stress في المنطقة هذه اللي
+
+72
+00:06:21,430 --> 00:06:26,660
+بيسميها التعددبالنسبة للقوة البندقية، الجزء الأسفل
+
+73
+00:06:26,660 --> 00:06:30,880
+من الحرارة في حرارة والجزء الأعلى في مدفع المدفع
+
+74
+00:06:30,880 --> 00:06:34,020
+المدفع المدفع المدفع المدفع المدفع المدفع المدفع
+
+75
+00:06:34,020 --> 00:06:34,040
+المدفع المدفع المدفع المدفع المدفع المدفع المدفع
+
+76
+00:06:34,040 --> 00:06:36,340
+المدفع المدفع المدفع المدفع المدفع المدفع المدفع
+
+77
+00:06:36,340 --> 00:06:37,020
+المدفع المدفع المدفع المدفع المدفع المدفع المدفع
+
+78
+00:06:37,020 --> 00:06:37,600
+المدفع المدفع المدفع المدفع المدفع المدفع المدفع
+
+79
+00:06:37,600 --> 00:06:41,120
+المدفع المدفع المدفع المدفع المدفع المدفع المدفع
+
+80
+00:06:41,120 --> 00:06:41,200
+المدفع المدفع
+
+81
+00:06:52,730 --> 00:06:57,730
+الان هنا and progressively decreasing to zero at a
+
+82
+00:06:57,730 --> 00:07:01,610
+neutral zone اللي هي الخط الأكسس هذا اللي بيصير
+
+83
+00:07:01,610 --> 00:07:05,230
+فيه التعدد and imaginary line along the center of
+
+84
+00:07:05,230 --> 00:07:09,190
+the beam which is free from stress مافيش فيها أي
+
+85
+00:07:09,190 --> 00:07:14,050
+ضغط types of failure في عندى عدة أنواع من الفيليا
+
+86
+00:07:14,050 --> 00:07:17,270
+اللي هي الفشل لما نحصل ultimate failure of a
+
+87
+00:07:17,270 --> 00:07:20,150
+component or structure member depends on the type
+
+88
+00:07:20,150 --> 00:07:25,040
+of forceintention it will fracture إيش يعني
+
+89
+00:07:25,040 --> 00:07:30,420
+fracture؟ بتنكسر أو بتنقطع لو شديت أحنا إيش قولنا
+
+90
+00:07:30,420 --> 00:07:34,920
+في المنطقة اللي في النص اللي بيصير فيها بترفع لحد
+
+91
+00:07:34,920 --> 00:07:38,920
+دي ما يصير إيش بتقطع لو شديته مغيطة في الآخر
+
+92
+00:07:38,920 --> 00:07:43,800
+هتنقطع من النص اللي عندك in compression if it's
+
+93
+00:07:43,800 --> 00:07:47,900
+stick it will crush or squash لو انت تعمليها إيش
+
+94
+00:07:47,900 --> 00:07:53,760
+بدها تتطبق صح؟اللي عندي crush لما انت تعمل crush
+
+95
+00:07:53,760 --> 00:08:01,320
+لحاجة ايش بت .. بتعصريها يعني ايوه if it's slender
+
+96
+00:08:01,320 --> 00:08:07,380
+ايش يعني slender؟ شطرات لازم فيها slender بتبقى
+
+97
+00:08:07,380 --> 00:08:11,320
+طويلة و رفيعة هذا بنطبق على البنات دايما slender
+
+98
+00:08:11,320 --> 00:08:16,190
+girl بيحكوها زي هيك طويلة رفيعة فبدكوا تحفظوهلو حد
+
+99
+00:08:16,190 --> 00:08:19,610
+يتكلم عنكم تبقى عارفين عليه إيش بتتكلم ف slender
+
+100
+00:08:19,610 --> 00:08:24,110
+طويل ورفيع it will buckle bend out of shape إيش
+
+101
+00:08:24,110 --> 00:08:28,550
+بتتساوي فيها؟ لما تساويها إيش بيحصل فيها؟ لو طويلة
+
+102
+00:08:28,550 --> 00:08:32,730
+ورفيعة و بتضغط عليها إيش بيصير؟ مش بتكسر، بتنطج
+
+103
+00:08:32,730 --> 00:08:37,510
+هاي بتنطج و بتيجي على الجانب هذا اللي بنقول buckle
+
+104
+00:08:37,510 --> 00:08:41,990
+buckle يعني بتنطج و بتيجي يعني بيصير عندك حاجة في
+
+105
+00:08:41,990 --> 00:08:48,360
+النص جاية جربيها هذهin bending it will fracture
+
+106
+00:08:48,360 --> 00:08:54,240
+إيش بده يسوي ال fracture؟ تشجق تشجق منهم إيش
+
+107
+00:08:54,240 --> 00:09:00,480
+بتسوي؟ تحسي .. صار فيها تشققات ال fracture in the
+
+108
+00:09:00,480 --> 00:09:03,220
+side .. in the side of the component which is in
+
+109
+00:09:03,220 --> 00:09:06,900
+tension or crush on the side which is in
+
+110
+00:09:06,900 --> 00:09:10,500
+compression لو أنت عملتيها، ضغطي، تلاقي الشجق اللي
+
+111
+00:09:10,500 --> 00:09:14,200
+المضغوط عليها من تحت تبدأ تشجق الشجق اللي فوق إيش
+
+112
+00:09:14,200 --> 00:09:18,790
+بده يصير فيها؟بتحس إن فيه ضغط صار عليها تنعصر أو
+
+113
+00:09:18,790 --> 00:09:23,430
+تتجمع جانب بعض، يعني بتصير الطبق اللي فوق جربت
+
+114
+00:09:23,430 --> 00:09:27,870
+لبعض وصارت خميلة و اللي تحت فيه تشققات فيها اللي
+
+115
+00:09:27,870 --> 00:09:32,650
+عنديor fail due to the compression of both او
+
+116
+00:09:32,650 --> 00:09:38,630
+بتفشل ككلها and shear if it will shear or break in
+
+117
+00:09:38,630 --> 00:09:42,790
+to shear forces هذه ايش بتسوي بيصير عملية الكسر
+
+118
+00:09:42,790 --> 00:09:47,970
+and torsion it will fracture or shear يعني هذه
+
+119
+00:09:47,970 --> 00:09:53,390
+برضه هتلاقيها انكسرت بسهولة when vertical members
+
+120
+00:09:53,390 --> 00:09:59,370
+can no longer resist a load they either crush or
+
+121
+00:09:59,850 --> 00:10:04,070
+buckle لو جيبت حاجة عمودية لما أنا أشوف أنه
+
+122
+00:10:04,070 --> 00:10:08,230
+مابتقدرش تتحمل المقاومة إيش بيساوي فيها؟ يا إما
+
+123
+00:10:08,230 --> 00:10:14,930
+بتلتوي أو بتنطج يعني يا إما بيصير لها تكسير أو
+
+124
+00:10:14,930 --> 00:10:19,630
+تطبيق crush تطبيق بالظبط تتطبق على بعض يا إما إيش
+
+125
+00:10:19,630 --> 00:10:23,510
+بيصير فيها السلك زي هيك إيش بيحصله؟ بنتن زي هيك
+
+126
+00:10:23,510 --> 00:10:28,300
+شايفة هذه اللي بيسميها buckleتنتني الحاجة ال
+
+127
+00:10:28,300 --> 00:10:31,340
+slender بيصير لها تاني انت بتضغط زي هيك بتروح
+
+128
+00:10:31,340 --> 00:10:38,120
+تنتني ايوة اللي هي هذا اللي بنسميها ايش عملية ال
+
+129
+00:10:38,120 --> 00:10:42,120
+buckling الان
+
+130
+00:10:42,120 --> 00:10:46,880
+التمرين اللي هتكلم عليه من .. هذا انت خبرة فيها اه
+
+131
+00:10:46,880 --> 00:10:54,720
+حدا فيكوا اشتغل عليها طيب الان بنتdownward ايش
+
+132
+00:10:54,720 --> 00:10:58,360
+الكلمة اللي حكيناها ال voltage ايش بيحصل فيه لما
+
+133
+00:10:58,360 --> 00:11:04,220
+ننزل ايش كله بيصير كلمة sag فانت لما تنزل هاي
+
+134
+00:11:04,220 --> 00:11:10,220
+الحبل اللي بنشده لما ننزل لتحت بنسميه sag فهذا
+
+135
+00:11:10,220 --> 00:11:17,320
+بنحط كلمة sag طيب
+
+136
+00:11:17,320 --> 00:11:20,120
+a twisting force ايش هي
+
+137
+00:11:29,340 --> 00:11:35,200
+take a force without a breaking لأ
+
+138
+00:11:35,200 --> 00:11:42,360
+لان انا لما اضغط على هذه ايش بيصير في عندى انكسرت
+
+139
+00:11:42,360 --> 00:11:50,960
+هذه resist تقاوم resistance مقاوم أخدتها مظبوط؟الـ
+
+140
+00:11:50,960 --> 00:11:55,180
+Resistance مقاومة مرت عليكم بالكهربا أو في الفيزيا
+
+141
+00:11:55,180 --> 00:12:00,660
+ومرت عليكم بالتعبير العام في هذه الـ Palestinian
+
+142
+00:12:00,660 --> 00:12:04,720
+Resistance المقاومة الفلسطينية، مظبوط؟ فـ Resist
+
+143
+00:12:04,720 --> 00:12:15,340
+اللي عندك Increase
+
+144
+00:12:15,340 --> 00:12:21,670
+in length due totension لما انا اعمل increase انا
+
+145
+00:12:21,670 --> 00:12:29,570
+بسحب ايش بيصير expand هي stretch اه بس هذا ايش هو
+
+146
+00:12:29,570 --> 00:12:33,130
+قال increase in length عملية ال increase ايش
+
+147
+00:12:33,130 --> 00:12:39,710
+بنسميها expansion ف expand
+
+148
+00:12:39,710 --> 00:12:48,480
+ده تطلع هناك قاعد بعمل بكون كلمة في الجزء داlong
+
+149
+00:12:48,480 --> 00:12:57,100
+and thin likely إيش slender أيوة
+
+150
+00:12:57,100 --> 00:13:01,520
+هاي الكلمة هادة بتحفظوها على طول مش هتنسوها عشان
+
+151
+00:13:01,520 --> 00:13:05,680
+هي حكيتلك إيها عشان إيش تلزق في ال memory
+
+152
+00:13:05,680 --> 00:13:15,020
+scissoring force إيش هي shear إيش
+
+153
+00:13:15,020 --> 00:13:20,930
+الكلمة اللي صارت عندىالـ stress وهذا اللي لزجت
+
+154
+00:13:20,930 --> 00:13:29,470
+المعلومة الموجودة كويس؟ فالتمرين بيصحصحنا لهذه
+
+155
+00:13:29,470 --> 00:13:34,690
+الكلمات نجي للي بعده
+
+156
+00:13:34,690 --> 00:13:39,110
+الان what we need the question below which was
+
+157
+00:13:39,110 --> 00:13:46,790
+posted on a form ايش يعني form؟أنتوا شاطرين أيوة
+
+158
+00:13:46,790 --> 00:13:51,630
+ملتقة اللي هي انتوا بتطلع عليه في ال net الملتقيات
+
+159
+00:13:51,630 --> 00:13:55,710
+on a construction website contains a mistake about
+
+160
+00:13:55,710 --> 00:13:59,390
+technical fact can you find the mistake look at
+
+161
+00:13:59,390 --> 00:14:04,510
+اللي عندي I was under the impression that concrete
+
+162
+00:14:04,510 --> 00:14:08,530
+and steel parts were used together in reinforced
+
+163
+00:14:08,530 --> 00:14:13,270
+concrete يعني إيش هذه نيجي كلمة I was under the
+
+164
+00:14:13,270 --> 00:14:22,280
+impressionإيش يعني؟ أنا كنت بعتقد، بدنا إيش ناخد
+
+165
+00:14:22,280 --> 00:14:26,480
+ترجمة حرفية، إيش هقول؟ أنا كنت بعتقد، under the
+
+166
+00:14:26,480 --> 00:14:31,140
+impression يعني أنا كان في اعتقادي فهي انت بدك
+
+167
+00:14:31,140 --> 00:14:35,340
+تاخد المعنى مش الترجمة كلمة under the impression
+
+168
+00:14:35,340 --> 00:14:41,180
+أن أنا تحت الاعتقاد، لأ أنا بعتقدأو كان في اعتقادي
+
+169
+00:14:41,180 --> 00:14:48,320
+that concrete and steel الحديد والخرسانة were used
+
+170
+00:14:48,320 --> 00:14:51,800
+together يستخدموا مع بعض in reinforce concrete في
+
+171
+00:14:51,800 --> 00:14:55,000
+الحديد المسلح because concrete is good at
+
+172
+00:14:55,000 --> 00:15:00,160
+resisting compression اللي عندي إيش ال concrete
+
+173
+00:15:00,160 --> 00:15:06,770
+بقاوم ال إيش الضغطwhile إيش اللي عندي and poor at
+
+174
+00:15:06,770 --> 00:15:11,870
+resisting its tension الحديد البطون لو شدته بيجعب
+
+175
+00:15:11,870 --> 00:15:19,050
+بس لو ضغطه بيصير بيظلوا بقاوم whereas ال steel is
+
+176
+00:15:19,050 --> 00:15:24,830
+strong in tension الحديد لما أسحبه جوي بتحمل فاحنا
+
+177
+00:15:24,830 --> 00:15:31,430
+التمتين مع بعض بقاوم إيش ال bending forceI also
+
+178
+00:15:31,430 --> 00:15:36,630
+taught that the steel always went at the bottom of
+
+179
+00:15:36,630 --> 00:15:40,610
+the reinforced concrete beam يعني ده هو بقاهم، أنا
+
+180
+00:15:40,610 --> 00:15:45,390
+بعرف أنه عندي hand في السطح، إيش اللي بحصل؟ هنا في
+
+181
+00:15:45,390 --> 00:15:48,590
+عندي tension و هنا في عندي compression، صح؟
+
+182
+00:15:48,590 --> 00:15:54,330
+فالحديد بيبقى ال concrete فوق و الحديد تحت، فهو
+
+183
+00:15:54,330 --> 00:15:59,400
+هذا اللي بيحكي يعنيalways went at the bottom of a
+
+184
+00:15:59,400 --> 00:16:04,040
+RC reinforced beam because that's the part that's
+
+185
+00:16:04,040 --> 00:16:10,260
+in tension whereas the top of the beam is free
+
+186
+00:16:10,260 --> 00:16:18,300
+from stress يعني هنا مافيش فيه عندهضغط But if
+
+187
+00:16:18,300 --> 00:16:22,080
+that's the case when you see reinforcements being
+
+188
+00:16:22,080 --> 00:16:33,860
+fixed in the big RCB why are there bars both at
+
+189
+00:16:33,860 --> 00:16:37,500
+the bottom and the top؟يعني ليش أنا عنده إذا أنا
+
+190
+00:16:37,500 --> 00:16:43,570
+بشوفهم فوق ليش عنده في حديد فوق وحديد تحت؟إيش
+
+191
+00:16:43,570 --> 00:16:48,270
+الخطأ عندى؟
+
+192
+00:16:48,270 --> 00:16:53,870
+طلع عندى because that's the part in tension وين
+
+193
+00:16:53,870 --> 00:16:58,290
+هذا ال part اللي بنحكي عنه؟
+
+194
+00:16:58,290 --> 00:17:03,050
+I thought that the steel always went at the bottom
+
+195
+00:17:03,050 --> 00:17:05,950
+of the .. because that's the part in tension
+
+196
+00:17:05,950 --> 00:17:10,090
+whereas the top of the beam is free from stress
+
+197
+00:17:10,090 --> 00:17:18,430
+هذا صح؟الـ top إيش مش free في عنده إيش compression
+
+198
+00:17:18,430 --> 00:17:23,330
+مظبوط هذا اللي بنطلع عليها if the .. but if that
+
+199
+00:17:23,330 --> 00:17:25,930
+the case when you see the reinforcements being
+
+200
+00:17:25,930 --> 00:17:31,890
+forced in .. fixed in big RCBM why are there bars
+
+201
+00:17:31,890 --> 00:17:35,650
+at both the bottom and the top فاحنا هو ال .. ال
+
+202
+00:17:35,650 --> 00:17:41,190
+.. ال top مش free of إيش stress هذه المعلومة الخطأ
+
+203
+00:17:41,190 --> 00:17:41,950
+اللي عندي
+
+204
+00:17:46,140 --> 00:17:49,540
+طب هاي ال .. ال .. الكلمة اللي هي the top of the
+
+205
+00:17:49,540 --> 00:17:52,200
+beam is compression the part of the beam which is
+
+206
+00:17:52,200 --> 00:17:58,060
+free from stress is the neutral axis مش ال إيش ال
+
+207
+00:17:58,060 --> 00:18:01,740
+top of the .. يعني اللي عندي هان المنطقة اللي فيها
+
+208
+00:18:01,740 --> 00:18:06,260
+free stress اللي هي إيش الخط اللي هان ال neutral
+
+209
+00:18:06,260 --> 00:18:11,060
+هان عندي compression وهنا
+
+210
+00:18:11,060 --> 00:18:11,480
+tension
+
+211
+00:18:18,620 --> 00:18:23,100
+طيب، الأن نستخدم في ال exercise التالت اللي هي
+
+212
+00:18:23,100 --> 00:18:27,440
+إيش؟ الكلمات اللي موجودة وين؟ in the box يعني احنا
+
+213
+00:18:27,440 --> 00:18:30,900
+عادة بحطل فياهم مجموعة زي ما شفتوا في الامتحان
+
+214
+00:18:30,900 --> 00:18:35,680
+إيه؟ و بنقولك اختاروا منهم، مظبوط؟ ماعملناهاش هذه
+
+215
+00:18:35,680 --> 00:18:41,320
+عملها الدكتور فادي، قولنا لأ هذه صعبة نسويها
+
+216
+00:18:41,320 --> 00:18:48,060
+فحطينا multiple choice لكم، و هي أسهل هذههي اه بس
+
+217
+00:18:48,060 --> 00:18:53,740
+خياراتك بدل ما يكونوا تمانية او عشرة تختار زي هيكة
+
+218
+00:18:53,740 --> 00:19:00,880
+بنحطلك أقل منهم، مظبوط؟ او match بنعملكم، لأ ال
+
+219
+00:19:00,880 --> 00:19:05,880
+matching سهلة، هذا ما هي .. هذا اللي حطناها تمانية
+
+220
+00:19:05,880 --> 00:19:09,680
+hand وعقف تمانية hand بتصير تعملي matching، مظبوط؟
+
+221
+00:19:09,680 --> 00:19:14,700
+ايوة let me start by clarifying something، هذا ايش
+
+222
+00:19:14,700 --> 00:19:18,990
+بيحكي؟let me start by clarifying something يعني
+
+223
+00:19:18,990 --> 00:19:23,870
+إيش؟ بدي أبدأ بالتوضيح شيء when a beam is
+
+224
+00:19:23,870 --> 00:19:29,870
+subjected to إيش stress? bending stress إيش هو ال
+
+225
+00:19:29,870 --> 00:19:35,910
+bending؟ اللي هي عملية الضغط عليها من فوق مظبوط ال
+
+226
+00:19:35,910 --> 00:19:45,020
+forces bending stress وهي bending طيرناهاإيش عندى؟
+
+227
+00:19:45,020 --> 00:19:48,820
+the bottom part is generally in tension الجزء
+
+228
+00:19:48,820 --> 00:19:53,860
+السفلي إيش عنده؟ tension as
+
+229
+00:19:53,860 --> 00:19:57,200
+you rightly say but the top part is not free from
+
+230
+00:19:57,200 --> 00:20:01,180
+stress اللي قبل شوية اتكلمنا عليها as you suggest
+
+231
+00:20:01,180 --> 00:20:05,940
+it's in compression، مظبوط، هذا tension، هذا
+
+232
+00:20:05,940 --> 00:20:10,440
+bending، هاي واحد، compression وين اللي عندى، هاي
+
+233
+00:20:10,440 --> 00:20:12,620
+اتنين، سهل، هاد جانب بعض
+
+234
+00:20:15,480 --> 00:20:23,980
+الان only the horizontal central line of
+
+235
+00:20:23,980 --> 00:20:29,760
+the beam a zone called neutral axis
+
+236
+00:20:41,780 --> 00:20:45,480
+is not stressed it's also important to be clear
+
+237
+00:20:45,480 --> 00:20:49,660
+about the strengths of concrete and steel you're
+
+238
+00:20:49,660 --> 00:20:54,320
+right that concrete is poor at resisting tension
+
+239
+00:20:54,320 --> 00:21:01,040
+اللي حكينا ال shed إيش بظبطش فيه وهي tension هاي
+
+240
+00:21:01,040 --> 00:21:04,560
+أربعة كويس؟
+
+241
+00:21:06,110 --> 00:21:14,630
+stress as it's born to failure by إيش suddenly إيش
+
+242
+00:21:14,630 --> 00:21:22,010
+بيحصل لها fracture مظبوط وين fracture هيها to
+
+243
+00:21:22,010 --> 00:21:25,990
+fracturing ال
+
+244
+00:21:25,990 --> 00:21:29,730
+إيش tensile
+
+245
+00:21:29,730 --> 00:21:41,430
+tensile وين هي فوقأه طيب فوق تنصال خمسة fracturing
+
+246
+00:21:41,430 --> 00:21:48,490
+طيب it's also true that concrete is a good at
+
+247
+00:21:48,490 --> 00:21:54,730
+resisting stress compression أو compressive stress
+
+248
+00:21:54,730 --> 00:22:00,810
+اللي .. اللي هنا هذه الستة ال compression اللي هي
+
+249
+00:22:00,810 --> 00:22:05,680
+ال noun compressive اللي هي ال adjectiveولكن
+
+250
+00:22:05,680 --> 00:22:11,760
+الصناعة أقوى من المجلد ليس فقط في الـ intention
+
+251
+00:22:11,760 --> 00:22:18,680
+اللي هي السابعة اللي حطناها كما تستطيعين أن تشير
+
+252
+00:22:18,680 --> 00:22:25,160
+إليها، ولكن أيضًا عندما تكون محطمة،
+
+253
+00:22:25,160 --> 00:22:30,620
+فالصناعة عادة تمضي في أعضاء البرنامج في حالة تتسبب
+
+254
+00:22:30,620 --> 00:22:34,990
+بالبرنامج في مستوى عالي من المحطمةهو فيه مقاوم
+
+255
+00:22:34,990 --> 00:22:38,550
+برضه كويس في المقاومة أحيانا لما يكون عند ال .. ال
+
+256
+00:22:38,550 --> 00:22:41,550
+.. ال .. خلنا نقول compression عالي جدا ال
+
+257
+00:22:41,550 --> 00:22:45,950
+concrete لحاله مش كافي بنحط الحديد يعني زي المباني
+
+258
+00:22:45,950 --> 00:22:52,230
+عند السقوفة بتلاقي البطون الحديد موجود وين؟ أسفل و
+
+259
+00:22:52,230 --> 00:22:58,420
+فوق لأنه فيه ضغط كتير وكل ما زادت المسافةكل ما يش
+
+260
+00:22:58,420 --> 00:23:03,960
+كتر الحديد عشان يعمل الحماية اللي هيقدر يشيل ال
+
+261
+00:23:03,960 --> 00:23:08,100
+weight meaning that the concrete requires
+
+262
+00:23:08,100 --> 00:23:11,580
+reinforcing to prevent it from ايش and failing
+
+263
+00:23:11,580 --> 00:23:18,740
+crushing and failing ال crushing ايش؟اللي حكيناها
+
+264
+00:23:18,740 --> 00:23:24,200
+تطبيق another possible reason for a beam having
+
+265
+00:23:24,200 --> 00:23:29,000
+steel in the top is to take tension اللي هي ياخد
+
+266
+00:23:29,000 --> 00:23:31,740
+الضغط why would you get tension in the top of a
+
+267
+00:23:31,740 --> 00:23:37,540
+beam it's true that most beams want to ايش deflect
+
+268
+00:23:37,540 --> 00:23:43,680
+downward عادة ايش معظم مثلا السكف بيروح where
+
+269
+00:23:43,680 --> 00:23:53,730
+downward اللي هيdeflect اللي هي تسعة because
+
+270
+00:23:53,730 --> 00:23:59,050
+of gravity الوزن تبعها او الجاذبية ايش بتعمل تضغط
+
+271
+00:23:59,050 --> 00:24:06,050
+لوين؟ للأسفل because gravity causes them to ايش؟
+
+272
+00:24:06,050 --> 00:24:11,530
+ساج الكلمة اللي بتنزل انه ال gravity دايما بتنزل
+
+273
+00:24:11,530 --> 00:24:17,750
+لأسفل ساج هي عشرةهذا التعبير اذا بتطلع احنا
+
+274
+00:24:17,750 --> 00:24:21,410
+بنتساوى فيه في تعريف الاش ال bending force هذا
+
+275
+00:24:21,410 --> 00:24:26,830
+الموجود اذا بتطلع عليه putting only the bottom of
+
+276
+00:24:26,830 --> 00:24:30,290
+the beam in tension but in some structure there
+
+277
+00:24:30,290 --> 00:24:36,330
+are beams or part of the beams that want to ايش to
+
+278
+00:24:36,330 --> 00:24:36,790
+hug
+
+279
+00:24:43,260 --> 00:24:46,980
+الـ hug إيش .. خلّيني أحكيها إيش .. ال .. ال hug
+
+280
+00:24:46,980 --> 00:24:53,660
+إيش يعني بيعمل الآن لما الواحد بدي يدفع حده و بديش
+
+281
+00:24:53,660 --> 00:24:57,500
+أرجع إيش بأعمل؟
+
+282
+00:24:57,500 --> 00:25:01,920
+بتمسكه، مظبوط، و ال hug عملية المسك، الحضن هيك، لو
+
+283
+00:25:01,920 --> 00:25:06,080
+بتسكب فهو إيش الحديد؟ الهاي بدي يرفع له هاي،
+
+284
+00:25:06,080 --> 00:25:08,420
+فبتصير ردة الفعل معاكسة
+
+285
+00:25:10,450 --> 00:25:13,830
+أيوة بتصير هاي فهنا إيش بيقولك ها force into
+
+286
+00:25:13,830 --> 00:25:18,530
+upward deflection بيصير إيش الردة المعاكسة لفوق ال
+
+287
+00:25:18,530 --> 00:25:24,170
+deflection هاي فإيش اللي عندي يعني البطون لما تضغط
+
+288
+00:25:24,170 --> 00:25:28,550
+ع حاجة و تسيبيها إيش بيحصل ترتفع لفوق هذا اللي
+
+289
+00:25:28,550 --> 00:25:32,890
+بنحكي فيه فبتصير هاي فهي بتمسك فانت بتزعل زمبارك
+
+290
+00:25:32,890 --> 00:25:39,660
+تضغط تسيبيه بيروح في اتجاه المعاكسفهذا الـ high
+
+291
+00:25:39,660 --> 00:25:43,400
+فانتوا اللي بدنا نفهمه اليوم في إيش أولا ال type
+
+292
+00:25:43,400 --> 00:25:48,220
+of forces اللي اتكلمنا عنهم ال deformation إيش كل
+
+293
+00:25:48,220 --> 00:25:52,060
+واحدة النتيجة تبعتها يعني الشكل تبعها مثلا ال
+
+294
+00:25:52,060 --> 00:25:57,740
+tension بتول expand ال length ال compression إيش
+
+295
+00:25:57,740 --> 00:26:02,920
+بيحصل فيه shorten ال length الآن لما نتكلم على ال
+
+296
+00:26:02,920 --> 00:26:08,680
+shear إيش بيحصل فيهاأيوة بيصير انت ضغط في اتجاهين
+
+297
+00:26:08,680 --> 00:26:14,280
+ال torsion ايش بيعمل؟ بنلوي الآن بتلاحظوا ال
+
+298
+00:26:14,280 --> 00:26:19,920
+failure تبعها ال tension ايش بيصير فيها؟ بتشقق او
+
+299
+00:26:19,920 --> 00:26:26,500
+بتنقطع مظبوط ال compression تتطبق اللي عندي او
+
+300
+00:26:26,500 --> 00:26:30,740
+بتنثني اللي هي ايش buckle او اللي بيحصل ايش عندنا
+
+301
+00:26:30,740 --> 00:26:33,920
+اللي بنتكلم لو كانت slender بيصير buckle لو كانت
+
+302
+00:26:33,920 --> 00:26:39,870
+heavyأو thick بيصير لها crush الآن لما اتكلم على
+
+303
+00:26:39,870 --> 00:26:44,550
+torsion إيش بيحصل لها؟ ممكن يصير لها fracture أو
+
+304
+00:26:44,550 --> 00:26:49,490
+share اللي هي عندنا ال share بيصير لها إيش؟ كسر
+
+305
+00:26:49,490 --> 00:26:53,890
+broken أو اللي هي هذه ملخص المحاضرة تبعتنا
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/aUnYaOa2QUY.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/aUnYaOa2QUY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..493ced93307aa6f27b6bbe594420f95894d4305b
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/aUnYaOa2QUY.srt
@@ -0,0 +1,1719 @@
+1
+00:00:20,690 --> 00:00:26,890
+السلام عليكم اليوم سنتحدث عن القصة 27 القصة 27
+
+2
+00:00:26,890 --> 00:00:34,290
+تتحدث عن مقاطعات ميكانية اليوم سنتحدث عن مقاطعات
+
+3
+00:00:34,290 --> 00:00:40,730
+مقاطعات مقاطعات مقاطعات و مقاطعات مقاطعات مقاطعات
+
+4
+00:00:40,730 --> 00:00:44,090
+مقاطعات
+
+5
+00:00:44,090 --> 00:00:46,750
+مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات
+
+6
+00:00:46,750 --> 00:00:49,230
+مقاطعات مقاطعات مقاطعات مقاطعات مق هذا تعبير يمكن
+
+7
+00:00:49,230 --> 00:00:54,310
+عندكم ما سمعتوهوش سمعت الفجلة اللي 
+
+8
+00:00:54,310 --> 00:00:58,790
+بنحط فيها البرغي بتتحط بالحيط هذه بتسميها screw
+
+9
+00:00:58,790 --> 00:01:04,030
+anchors اللي هي الفجلة ال rivets اللي هي إيش
+
+10
+00:01:04,030 --> 00:01:09,850
+البرشومة البرشومة كل كهذه شفتوها بس أنتم شوية
+
+11
+00:01:09,850 --> 00:01:16,210
+شوفوا شبابيك الألمنيوم أو المطابق الألمنيوم بتتبطّ في
+
+12
+00:01:16,210 --> 00:01:22,750
+في إيش؟ مش في برغي، في حاجة ال needle هذه، هي هذه
+
+13
+00:01:22,750 --> 00:01:28,150
+اللي بنسميها ال rivet، كويس؟ الآن بعض الشغلات
+
+14
+00:01:28,150 --> 00:01:33,150
+الشناتي تبعتكم برضه بتتبطّ ب needle نوع ثاني،
+
+15
+00:01:33,150 --> 00:01:39,050
+بنسميها هذه flat و هذه إيش؟ بتبقى blind ال blind
+
+16
+00:01:39,050 --> 00:01:42,650
+اللي هي ال needle تبعت المطبخ أو تبعت اللي
+
+17
+00:01:42,650 --> 00:01:46,790
+بنستخدمها في المطبخ أو شبابيك الألمنيوم الآن في ال
+
+18
+00:01:46,790 --> 00:01:52,610
+needle الثانية من ما حش أنت تطلع فيها نشوف حاجة
+
+19
+00:01:52,610 --> 00:01:58,550
+معينة شايفة هذه اللي هنا؟ هذه برشومة هذه بنسميها
+
+20
+00:01:58,550 --> 00:02:03,290
+rivet شايفينها؟ rivet هذا النوع الثاني
+
+21
+00:02:10,440 --> 00:02:15,860
+الكاميرا اللي هان؟ البرجومة
+
+22
+00:02:15,860 --> 00:02:22,460
+اللي هان؟ بتبيع احنا الحين؟
+
+23
+00:02:22,460 --> 00:02:26,720
+طيب
+
+24
+00:02:26,720 --> 00:02:30,240
+screws .. screws have threaded على فكرة لمنزل
+
+25
+00:02:30,240 --> 00:02:36,280
+فيديوهاتعلى الموقع التابعي فيه تتكلم عن الأنواع
+
+26
+00:02:36,280 --> 00:02:39,240
+اللي بنحكي عنها ال screws و هذه الشغلات ال screws
+
+27
+00:02:39,240 --> 00:02:43,160
+have threaded shafts with heads الآن احنا بنلاحظ
+
+28
+00:02:43,160 --> 00:02:49,630
+إيش هي عبارة البرغي هو له يعني خلينا نقول يد أو
+
+29
+00:02:49,630 --> 00:02:53,930
+دراع الدراع حد إيش مسوي فيه مسنن treaded shaft
+
+30
+00:02:53,930 --> 00:02:58,910
+with heads وفيه له رأس الآن التصنيف اللي بتنعمل فيه
+
+31
+00:02:58,910 --> 00:03:03,850
+عدة أنواع بصنف البراغي حسب الرأس حسب مقطع الرأس
+
+32
+00:03:03,850 --> 00:03:09,810
+إيش معمول فيه و حسب ال tread اللي موجود فيه في بعض
+
+33
+00:03:09,810 --> 00:03:15,230
+البراغي بتصلح للحديد في بعض البراغي بتصلح للخشب في
+
+34
+00:03:15,230 --> 00:03:20,880
+براغي بتدخل بثقب يعني أنت بتبقى قزّقها لقزّق و
+
+35
+00:03:20,880 --> 00:03:24,240
+بتدخليها في القزّق في بعض البراغي يمكن تشوفوها في
+
+36
+00:03:24,240 --> 00:03:29,060
+المعادن أو في الألمنيوم هي اللي بتخزّق التقب يعني
+
+37
+00:03:29,060 --> 00:03:32,720
+ما لازم تخزّقي لها أي شيء كل اللي بدك تعمليه أنك تلف
+
+38
+00:03:32,720 --> 00:03:37,940
+فيها فهي بتفتح التقب لحالها وهذا هنتكلم عنها they
+
+39
+00:03:37,940 --> 00:03:44,320
+may be screwed into a pre-drilled hole الخزّق
+
+40
+00:03:44,320 --> 00:03:47,900
+أو الثقب المعمول له drilled for the screws to
+
+41
+00:03:47,900 --> 00:03:52,560
+enter self-tapping screws
+
+42
+00:03:56,910 --> 00:04:02,370
+يعني أنت لو لفيته turn .. يعني في اتجاه معين في ..
+
+43
+00:04:02,370 --> 00:04:06,450
+هو اللي بفتح الخزّق لحاله أو بيعمل الثقب لحاله و
+
+44
+00:04:06,450 --> 00:04:10,410
+هذا بتلاقيها دائماً بنستخدمها في مين الحديد مش
+
+45
+00:04:10,410 --> 00:04:14,570
+الجاسي، الحديد دائماً ال marine يعني زي الألمنيوم،
+
+46
+00:04:14,570 --> 00:04:19,950
+زي الصفائح الخفيفة، هذا اللي بنستخدم فيه الحديد
+
+47
+00:04:19,950 --> 00:04:23,950
+الجاسي طبعاً ما ينفعش هذا الشيء الخشب ما لازم، البرغ
+
+48
+00:04:23,950 --> 00:04:29,740
+لحاله بيضلّ داخلف self-tapping screws هي حطيناهم
+
+49
+00:04:29,740 --> 00:04:34,100
+بالإيش؟ بلون معين، هاي نكتبهم لأن لازمولنا كمان
+
+50
+00:04:34,100 --> 00:04:37,860
+شوية في التمرين الأول self-tapping
+
+51
+00:04:48,140 --> 00:04:53,420
+they do not require pre-drill holes they cut their
+
+52
+00:04:53,420 --> 00:04:58,140
+own holes as they screwed in لما نحنا نلفهم هم
+
+53
+00:04:58,140 --> 00:05:02,800
+بيعملوا ثقب تبعهم unlike bolts ال bolts بتعرفيش
+
+54
+00:05:02,800 --> 00:05:09,580
+إله سمونة أو إله مكان في الحديد بتلفيه فيه الدراجات
+
+55
+00:05:09,580 --> 00:05:13,780
+ليست مستخدمة لدراجات وليست مستخدمة لدراجات مستخدمة
+
+56
+00:05:13,780 --> 00:05:14,360
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+57
+00:05:14,360 --> 00:05:19,940
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+58
+00:05:19,940 --> 00:05:26,980
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+59
+00:05:26,980 --> 00:05:34,480
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+60
+00:05:34,480 --> 00:05:36,940
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+61
+00:05:36,940 --> 00:05:41,470
+لدراجات مستخدمة في مفك .. المفك هذا بدخل فيه
+
+62
+00:05:41,470 --> 00:05:46,510
+و أنواع حسب الرأس كيف معمول بتقولنا إيش نوع
+
+63
+00:05:46,510 --> 00:05:51,430
+المفك اللي بينفع معها Most screws hid are
+
+64
+00:05:51,430 --> 00:05:55,010
+designed to be screwed in using a screwdriver. The
+
+65
+00:05:55,010 --> 00:05:58,490
+most common types are slots hid screwed
+
+66
+00:06:01,950 --> 00:06:07,150
+head screws الآن ال slot head إيش فيه فيها فرزة
+
+67
+00:06:07,150 --> 00:06:11,230
+الفرزة بتبقى إيش في عندنا أنواع في فرزة بتلاقيها
+
+68
+00:06:11,230 --> 00:06:15,850
+cross في فرزة بتلاقيها خط مستقيم وفي فرزة بتلاقيها
+
+69
+00:06:15,850 --> 00:06:21,230
+على شكل نجمة الآن الفرزة ال slot head اللي هي
+
+70
+00:06:21,230 --> 00:06:26,010
+الفرزة تبعتنا إيش مستقيم and cross head screwed
+
+71
+00:06:33,520 --> 00:06:39,560
+الـ crosshead و هذه الشكل تبعهم هلاحظ هذه هي الـ
+
+72
+00:06:39,560 --> 00:06:44,300
+screwdriver هذا اللي هي هنا إذا صلحت هدي تطلع كيف
+
+73
+00:06:44,300 --> 00:06:49,340
+هنا الشكل اللي موجود تطلع هناك crosshead وهناك ال
+
+74
+00:06:49,340 --> 00:06:52,560
+starhead ال starhead ولا ال crosshead ولا ال
+
+75
+00:06:52,560 --> 00:06:57,420
+flathead بدك المفك الصح لتشتغل فيه لو ما عندكيش
+
+76
+00:06:57,420 --> 00:07:00,100
+المفك ما عندكيش المفك ما تقدريش تشتغل فيه في أنواع
+
+77
+00:07:00,100 --> 00:07:07,150
+ثانية small diameter bolts which can be used with
+
+78
+00:07:07,150 --> 00:07:10,950
+nuts or screwed into threaded holes are sometimes
+
+79
+00:07:10,950 --> 00:07:19,490
+called machine screws الآن
+
+80
+00:07:19,490 --> 00:07:23,290
+ال machine screws اللي هم إيش هم عبارة عن bolts بس
+
+81
+00:07:23,290 --> 00:07:26,490
+إيش اللي فارق بينه و بين اللي دلوقت هذا الحجم تبع
+
+82
+00:07:26,490 --> 00:07:31,460
+حقيقة صغير يعني زي ال boards بس حجمها وفي الها
+
+83
+00:07:31,460 --> 00:07:38,240
+سمونة بس حجمها إيش؟ صغير هذا الفرق بين ال machine
+
+84
+00:07:38,240 --> 00:07:43,020
+screws و ال bolts أو ال screws و بتشوفهم هدول
+
+85
+00:07:43,020 --> 00:07:47,440
+دائماً بتلاقيهم حجمها صغير و نوعها صغير و هدي بتتم
+
+86
+00:07:47,440 --> 00:07:51,400
+استخدامها bolts that hold components in a place by
+
+87
+00:07:51,400 --> 00:07:54,000
+pressing the end of the bolts against the
+
+88
+00:07:54,000 --> 00:07:56,600
+components in order to generate friction and
+
+89
+00:07:56,600 --> 00:08:01,240
+prevent sliding are called set screwed or grab
+
+90
+00:08:01,240 --> 00:08:02,040
+screws
+
+91
+00:08:12,750 --> 00:08:18,890
+grab screws الآن هاذي إيش بنعملهم هذول لما نضغط
+
+92
+00:08:18,890 --> 00:08:25,030
+حاجتين و نحط الحاجتين و نثبتّهم باستخدام هذا البرغي
+
+93
+00:08:25,030 --> 00:08:29,410
+بنسمي إيش هذا النوع grab أو set screws set يعني
+
+94
+00:08:29,410 --> 00:08:34,970
+تثبيت grab يعني إيش يعني التلزيج أو ال damage
+
+95
+00:08:34,970 --> 00:08:40,730
+الموجود هنا فعندي كم نوع اثنين أربعة خمس أنواع
+
+96
+00:08:40,730 --> 00:08:46,400
+الموجودة هنا screw anchors اللي حكينا عنهم هاد الاش
+
+97
+00:08:47,140 --> 00:08:54,740
+الفجلة اللي هي جزء بلاستيكي أحياناً بيبقى حتى مثل أو
+
+98
+00:08:54,740 --> 00:09:00,340
+هذا فبنحطها .. بنخزّق ثقب في الحيطة و بندخله هذا في
+
+99
+00:09:00,340 --> 00:09:03,500
+الحيطة و بعده بنلزّق هذا عادة كل البرويز اللي في
+
+100
+00:09:03,500 --> 00:09:08,300
+البيت بنعلقها باستخدام هذه الشغلات fasteners
+
+101
+00:09:08,300 --> 00:09:11,560
+designed to fix objects to walls وهذا عادة
+
+102
+00:09:11,560 --> 00:09:17,220
+بيستخدموها مع الحيطان أو بيسموها ال dry walls Okay
+
+103
+00:09:17,220 --> 00:09:22,420
+called screw anchors these fit into pre-drilled
+
+104
+00:09:22,420 --> 00:09:26,680
+holes عادة لما نسويها في ثقب جاهز بتدخليها في هذا
+
+105
+00:09:26,680 --> 00:09:31,700
+الثقب a simple screw anchor is a plastic tube
+
+106
+00:09:31,700 --> 00:09:36,180
+called a wall plug or plug اللي هي الحاجة البسيطة
+
+107
+00:09:36,180 --> 00:09:39,580
+اللي هي الفجلة البلاستيكية اللي بنحطها في الحيطة
+
+108
+00:09:39,580 --> 00:09:46,100
+هذه الآن لما ندخل البرغي إيش بيحصل لها؟ تفرد أو
+
+109
+00:09:46,100 --> 00:09:51,680
+expand فلما تفرد و expand بتصير إيش؟ الخروج إيش؟
+
+110
+00:09:51,680 --> 00:09:58,150
+أصعب مظبوط هذا الفكرة اللي هنا it is inserted in a
+
+111
+00:09:58,150 --> 00:10:02,350
+hole and a screw or bolt is then screwed into it
+
+112
+00:10:02,350 --> 00:10:07,110
+يعني بندخل ال bolt أو ال screw فيها as it enters
+
+113
+00:10:07,110 --> 00:10:10,410
+the plug the plug expand يعني ال diameter its
+
+114
+00:10:10,410 --> 00:10:14,610
+diameter increase this increases friction allowing
+
+115
+00:10:14,610 --> 00:10:18,290
+the plug to resist the pull out forces يعني هذا
+
+116
+00:10:18,290 --> 00:10:22,840
+لما ندخلها إيش بيصير فيها بيصير .. ساحبها مش سهل
+
+117
+00:10:22,840 --> 00:10:26,460
+يعني أصعب .. صعبة هذه طبعاً اللي بدي أسحبها زي ما
+
+118
+00:10:26,460 --> 00:10:31,420
+حكينا إيش بدي يسوي the forces which will cause it
+
+119
+00:10:31,420 --> 00:10:36,960
+to be pulled out of the hole if it were not firmly
+
+120
+00:10:36,960 --> 00:10:40,920
+anchored يعني عادة لو كان .. خليني بس أحكي بعض
+
+121
+00:10:40,920 --> 00:10:46,880
+الشغلات لو كان التقب أكبر إيش بيحصل؟ تدخل بس
+
+122
+00:10:46,880 --> 00:10:53,280
+بتلاقيها بت لاجلج تلعب لو كان صغير تدخليها بتطلعش
+
+123
+00:10:53,280 --> 00:10:58,680
+مظبوط و بتنكسر تنتني أو أنت لما تدخل البرغي البرغي
+
+124
+00:10:58,680 --> 00:11:03,300
+بتحسّس كأنه بيبطل يدخل بيوصل شوية و بعدين بيوقف هذه
+
+125
+00:11:03,300 --> 00:11:06,260
+من المشاكل اللي هنتكلم عليها في ال exercise إيش
+
+126
+00:11:06,260 --> 00:11:14,700
+اللي بيحصل هذه طيب إيش السؤال anchors اللي هي إيش
+
+127
+00:11:14,700 --> 00:11:18,300
+أنت ال anchor إيش قلنا عنها اللي هي الفجلة هذه
+
+128
+00:11:18,300 --> 00:11:24,490
+اللي هي اسمها screw anchor أو wall plug
+
+129
+00:11:24,490 --> 00:11:31,270
+نفس ال expression للاتنين الآن ال wall plugs في
+
+130
+00:11:31,270 --> 00:11:36,090
+بحاجة برضه ال anchors في حاجة ثانية ممكن شفتوها
+
+131
+00:11:36,090 --> 00:11:41,610
+أنتوا في اللي بده يتعلقوا حاجة في السقف إيش بنجيب
+
+132
+00:11:41,610 --> 00:11:44,890
+الفجلة
+
+133
+00:11:44,890 --> 00:11:45,450
+الحديد
+
+134
+00:11:48,600 --> 00:11:53,380
+أيوة إيش هذه بنحطها؟ هذه برضه بتحطيها بتسوي التقب
+
+135
+00:11:53,380 --> 00:11:58,420
+و بتدخليها بعدها لما تحزقيها بتصبح expansion برضه
+
+136
+00:11:58,420 --> 00:12:04,100
+نوع ثاني هي بتبقى برغي حديدة إطار يعني حديد وفيه
+
+137
+00:12:04,100 --> 00:12:08,380
+برغي وفيه برغي البرغي هذا مش زي البراغي العادية زي
+
+138
+00:12:08,380 --> 00:12:11,860
+ال what ال port فيه port يعني فأنت لما تدخليها
+
+139
+00:12:11,860 --> 00:12:15,580
+هناك بتصبح تحزقي فيها بتصبحها expansion بتصبح لما بدك
+
+140
+00:12:15,580 --> 00:12:20,430
+تسحبيها هذا بتتحمل الضغط يعني بتتحمل الوزن، بتتحمل
+
+141
+00:12:20,430 --> 00:12:26,310
+غير .. أصعب من هذا an expansion anchor is another
+
+142
+00:12:26,310 --> 00:12:29,970
+type of anchor it consists of a bolt fitted inside
+
+143
+00:12:29,970 --> 00:12:34,090
+a metal sleeve يعني هذا إيش بيقولوها؟ هذا اللي
+
+144
+00:12:34,090 --> 00:12:38,230
+بنحكي عنها النوع الثاني، اللي هي إيش؟ في عندها برغي
+
+145
+00:12:38,230 --> 00:12:42,110
+اللي سميناها bolt موجود sleeve اللي هي إيش؟ القم
+
+146
+00:12:43,090 --> 00:12:47,590
+فلما نتكلم عليكم إنها في لها حاجة زي غطاء خارجي
+
+147
+00:12:47,590 --> 00:12:51,690
+حديد الآن الغطاء الخارجي الحديد في هنا ال boat لما
+
+148
+00:12:51,690 --> 00:12:56,010
+الأقوى تحزق فيه إيش هادرستير بتوسع جوا بتدخل ضيقة و
+
+149
+00:12:56,010 --> 00:12:59,990
+بعدين بتتوسع برا و هنفرجيكم فيديو كمان شوية في هذه
+
+150
+00:12:59,990 --> 00:13:04,800
+الشغل عشان تشوفوا إياها The sleeves expand as the bolt
+
+151
+00:13:04,800 --> 00:13:08,720
+is tightened in the hole. هذي بتيجي زي ما أنا بحذق
+
+152
+00:13:08,720 --> 00:13:13,640
+في البرغي، إيش بيصير هذي؟ بتبقى ضيقة، بتصير تفتح،
+
+153
+00:13:13,640 --> 00:13:18,740
+تفتح إيش بتصير فيها؟ يعني الوسع الموجود هذي بتسكر
+
+154
+00:13:18,740 --> 00:13:23,630
+و بيصير الصعب تطلعيها in cases where pull-out
+
+155
+00:13:23,630 --> 00:13:28,550
+forces are very high chemical anchors can be used
+
+156
+00:13:28,550 --> 00:13:32,210
+الآن في بعض الحالات إيش بيصير عندي؟ بدي حاجة تتبت
+
+157
+00:13:32,210 --> 00:13:36,030
+كتير تتبت يعني فيها إيش؟ بحط chemical المادة
+
+158
+00:13:36,030 --> 00:13:39,590
+الكيميائية اللي هي بحطها بدخلها هناك و لما أحط ال
+
+159
+00:13:39,590 --> 00:13:44,390
+anchor ال anchor بلزق هذا إيش بيصير فيها؟ تلزقة
+
+160
+00:13:44,390 --> 00:13:47,970
+كتير بعد هذا permanent إلا أنا بحطه مش هاطلعه
+
+161
+00:13:47,970 --> 00:13:54,030
+بالمرة These are studs threaded bars into which
+
+162
+00:13:54,030 --> 00:13:59,330
+nuts can be screwed. The studs are set in. الآن هذا
+
+163
+00:13:59,330 --> 00:14:04,310
+إيش بأضيف المادة بيسموها أحيانا lucket المادة
+
+164
+00:14:04,310 --> 00:14:09,950
+الكيميائية بتضيفيها هناك لما أنت تحسكي تنفكش يعني زي
+
+165
+00:14:09,950 --> 00:14:14,930
+ما بقول زي الصمغ بتصير فأنت بتبطل تقدر تطلع زي
+
+166
+00:14:14,930 --> 00:14:20,030
+الصمغ الجامد مش صمغ بسيط that is held in the hole
+
+167
+00:14:20,030 --> 00:14:24,890
+by adhesive most chemical anchors are set in two
+
+168
+00:14:24,890 --> 00:14:29,330
+holes using a strong adhesive called epoxy resin
+
+169
+00:14:29,330 --> 00:14:33,710
+وهذه شفناها مرت علينا ال epoxy لما كنا بنتكلم عن ال
+
+170
+00:14:33,710 --> 00:14:35,290
+plastics
+
+171
+00:14:36,840 --> 00:14:42,200
+البالمرز كويسة اتكلمنا عنها epoxy resin اللي هي
+
+172
+00:14:42,200 --> 00:14:47,680
+هذه مادة لاصقة قوية فهيبقى نحطها هناك من حد ما
+
+173
+00:14:47,680 --> 00:14:55,950
+تحزقي خلاص تقدريش ترفعيها بعد هيك الآن ال rivets
+
+174
+00:14:55,950 --> 00:14:59,550
+اللي قولنا عنها البورشامة أو ال needle اللي بدكوا
+
+175
+00:14:59,550 --> 00:15:04,290
+تسموها في العامية rivets are permanent fasteners
+
+176
+00:15:04,290 --> 00:15:08,450
+أو fasteners إيش هنا؟ ليش permanent fasteners؟
+
+177
+00:15:08,450 --> 00:15:11,910
+لأنه ده حطيت .. استخدمت البورشامة بتقدر تفكيها
+
+178
+00:15:11,910 --> 00:15:16,370
+ثاني؟ إذا فكتيها إيش بتصير؟ تخرب، خلاص، بدك واحدة
+
+179
+00:15:16,370 --> 00:15:20,130
+بدالها، عشان هي كانت بنسميها غير الـscrewed،
+
+180
+00:15:20,130 --> 00:15:24,730
+الـscrewed بنطلعه و بنقدر نرجعه They cannot be
+
+181
+00:15:24,730 --> 00:15:29,070
+unscrewed، a solid rivet، solid هي consist of a
+
+182
+00:15:29,070 --> 00:15:33,470
+short solid shaft of metal with a head at one end
+
+183
+00:15:33,470 --> 00:15:37,070
+called the factory head الآن أنا لما أستخدم ال
+
+184
+00:15:37,070 --> 00:15:42,190
+rivet إيش فيها؟ لها رأس متى ما استخدمتها الرأس إيش
+
+185
+00:15:42,190 --> 00:15:47,930
+بيصير فيه؟ بنطعش، مظبوط؟ الآن قبل عملية الطعش
+
+186
+00:15:47,930 --> 00:15:53,510
+بنسميها إيش؟ factory head اللي هي رأس المصنع solid
+
+187
+00:15:53,510 --> 00:15:58,210
+هذه إيش؟ ال solid rivet ال solid rivet اللي هي لها
+
+188
+00:15:58,210 --> 00:16:02,450
+الرأس هنا the rivet is inserted through a pre
+
+189
+00:16:02,450 --> 00:16:05,450
+-drilled hole then a special tool is used to
+
+190
+00:16:05,450 --> 00:16:09,450
+deform إيش احنا بنعمل؟ بنقول deform، بتلاقيها في
+
+191
+00:16:09,450 --> 00:16:12,950
+الشنادي، في الصنادل، في كل الشغلات الجلدية بشكل
+
+192
+00:16:12,950 --> 00:16:16,410
+خاص، في الإكشاطات، كل هذه بيسغموها، متى ما انكبست
+
+193
+00:16:16,410 --> 00:16:23,530
+الراس خلاص بتصير إيش؟ Deformed Deformed يعني إيش؟
+
+194
+00:16:23,530 --> 00:16:28,110
+اتغير شكلها، اتشوّه شكلها، يعني نبطل الشكل الأصلي
+
+195
+00:16:28,110 --> 00:16:31,310
+اللي عندها، it changed the shape of the other end
+
+196
+00:16:31,310 --> 00:16:34,970
+of the rivet, flattening and widening it to form a
+
+197
+00:16:34,970 --> 00:16:38,850
+second head called the shop head. الآن لما نقبصها،
+
+198
+00:16:38,850 --> 00:16:41,990
+إيش بيصير عندي؟ في راس على الوجه هاد وشجة ثانية من
+
+199
+00:16:41,990 --> 00:16:47,510
+جوا، إيش بيصير؟ بتبقى أول داخلة يعني مالهاش راس على
+
+200
+00:16:47,510 --> 00:16:49,570
+الشجة الثانية، إيش بيصير لها؟ لما يصير لها
+
+201
+00:16:49,570 --> 00:16:52,870
+flattening بتصير راس الثانية، بتصير إيش؟ الحاجة
+
+202
+00:16:52,870 --> 00:16:56,910
+اللي في النص انحشرت بين شغلتين أكبر من الحجم، هذه
+
+203
+00:16:56,910 --> 00:17:01,130
+راس و هذه راس و هذه المنطقة اللي في النص إيش، لو
+
+204
+00:17:01,130 --> 00:17:04,630
+اتكلمنا عن راس بتبقى هذه مثلا بهذه الشكل، الأول
+
+205
+00:17:04,630 --> 00:17:09,980
+لما أكبسها هذه إيش بتصير فيها؟ expanse هذه اللي هان
+
+206
+00:17:09,980 --> 00:17:12,740
+بتروح على الجانب من هان وهذا الجانب من هان فبتصير
+
+207
+00:17:12,740 --> 00:17:17,940
+زي الشكل الرأسي هذه بنسميها ال factory head والشجة
+
+208
+00:17:17,940 --> 00:17:21,720
+الثانية اللي كانت مستقيمة بتصير إيش هذه بنسميها
+
+209
+00:17:21,720 --> 00:17:30,660
+الشاب head شاب إيش يعني مش الدكانة الشاب اللي هي
+
+210
+00:17:30,660 --> 00:17:36,020
+عادة بنقول عندها لما الواحد المشغل رأس المشغل الشاب
+
+211
+00:17:38,920 --> 00:17:43,300
+يعني انشغلت .. انشغلت الرأس الثاني انشغلت انعملت
+
+212
+00:17:43,300 --> 00:17:47,180
+أو انشغلت ف shop head solid rivets are widely used
+
+213
+00:17:47,180 --> 00:17:52,160
+in aircraft بتلاقيها مثلا في الطيارات كل الحاجات
+
+214
+00:17:52,160 --> 00:17:56,420
+اللي هناك مدقوقة دق في الصيارات بتشوفوها موجودة في
+
+215
+00:17:56,420 --> 00:18:00,840
+الفرش تبع الصيارات موجودة في أماكن كثيرة في
+
+216
+00:18:00,840 --> 00:18:05,540
+الشناتي في المواد الجلدية موجودة في الأواعي موجودة
+
+217
+00:18:06,390 --> 00:18:09,750
+يعني ممكن بتلاقوها هذه الزراير تبعت القواعي
+
+218
+00:18:09,750 --> 00:18:16,640
+بتشوفوا إيش؟ الكبس هدول كل هدول النوع هم rivets
+
+219
+00:18:16,640 --> 00:18:20,620
+solid rivets لأن إيش اللي بتصير تدخل هي في الأول
+
+220
+00:18:20,620 --> 00:18:25,280
+وبعدين بتكبس الرأس الرأس إيش بتتفلطح أو بتعمل زي
+
+221
+00:18:25,280 --> 00:18:29,840
+حاجة ثانية دائرة ثانية لهذا الدائرة الموجودة لما
+
+222
+00:18:29,840 --> 00:18:35,280
+بتفلطح هي بتمنع الهاي بتلاحظ إنه في حركة معينة
+
+223
+00:18:35,280 --> 00:18:40,290
+بتقدر تتحرك فيها خصوصا لبعض الأماكن بعضها لأبتتبت
+
+224
+00:18:40,290 --> 00:18:47,890
+تتبيت الحركة اللي بتتبت بنسميها هذه set ال blind
+
+225
+00:18:47,890 --> 00:18:55,250
+rivet احنا هذه سميناها solid هذه solid rivet
+
+226
+00:18:55,250 --> 00:19:00,150
+الثانية بنسميها blind وهذه كلكم شفتوها تبعات
+
+227
+00:19:00,150 --> 00:19:08,370
+الخزانات الألمنيوم ويلها جهاز معين فيها ريفيت أو
+
+228
+00:19:08,370 --> 00:19:12,210
+باب ريفيت are made from hollow tubes and are
+
+229
+00:19:12,210 --> 00:19:15,850
+fitted using a tool called rivet gun ال rivet gun
+
+230
+00:19:15,850 --> 00:19:19,530
+اللي هي إيش؟ الأداة اللي بي .. اللي بيعصوا فيها زي
+
+231
+00:19:19,530 --> 00:19:23,790
+الزرادية ويلها راس بيحطوا فيها ال .. البرشومة و
+
+232
+00:19:23,790 --> 00:19:26,730
+بدخلوها في ال .. في التاقم اللي موجود و بيعصه و
+
+233
+00:19:26,730 --> 00:19:32,230
+بتنكسر الدراعة الطويلة هذه و هاد بيصيرلها expansion
+
+234
+00:19:32,230 --> 00:19:35,390
+الراس اللي هنا بتنقل .. هاد شايف هاد الحفة؟ هاد
+
+235
+00:19:35,390 --> 00:19:39,270
+بتكبس بتصير الكبسة عليهم بتصير إيش؟ إنه خلاص
+
+236
+00:19:39,270 --> 00:19:44,190
+اتثبتت من الشكتين طلع عليهم موجودة لو في حاجة هان
+
+237
+00:19:44,190 --> 00:19:45,810
+جيبناها فارجيناكوا
+
+238
+00:19:48,130 --> 00:19:51,630
+blind rivets are not suitable for high strength
+
+239
+00:19:51,630 --> 00:19:57,150
+joints لو أنت لاحظتي أي حاجة بده يمكن .. كلكم
+
+240
+00:19:57,150 --> 00:19:59,950
+بتلاحظوها الأبواب الموجودة تبعات الحمامات و
+
+241
+00:19:59,950 --> 00:20:04,110
+المطابخ بيعملوها من إيش؟ الألمنيوم صح؟ الباب مع
+
+242
+00:20:04,110 --> 00:20:09,870
+الوقت إيش بيحصله؟ لأ بيحصله حاجة بتلاحظوا إيش
+
+243
+00:20:09,870 --> 00:20:15,600
+بيصير يكحد في الأرضية مظبوط؟ ليش؟ لأن هو النوع ال
+
+244
+00:20:15,600 --> 00:20:20,340
+joints تبعته مش مصممة إنه هذه تتحمل high strength
+
+245
+00:20:20,340 --> 00:20:22,880
+اللي هي و بعدين ما شاء الله اللي عندهم صغار و هو
+
+246
+00:20:22,880 --> 00:20:27,060
+طالع بضربه و هو داخل بضربه فإيش الشكل تبعه بيصير
+
+247
+00:20:27,060 --> 00:20:30,400
+.. بتخلخل .. بيصير يكحت في هذه لأن النوعية هذه
+
+248
+00:20:30,400 --> 00:20:35,920
+بتتبت كثير أشياء ل heavy duty يعني هذه الحاجات
+
+249
+00:20:35,920 --> 00:20:39,380
+خفيفة و بواب الخزانات بتلاقيهم بتظهر تابعة الحاجات
+
+250
+00:20:39,380 --> 00:20:45,180
+اللي زيكا ما فيش مشكلة فيها الآن احنا عملنا الخمس 
+
+251
+00:20:45,180 --> 00:20:48,660
+أنواع هنا في ال exercise الأول in this exercise
+
+252
+00:20:48,660 --> 00:20:51,820
+هاي ايش بيقولنا make words combination with screws
+
+253
+00:20:51,820 --> 00:20:55,680
+using words from a and b opposite then match the
+
+254
+00:20:55,680 --> 00:20:58,860
+combination with these with the description below
+
+255
+00:20:58,860 --> 00:21:02,600
+one description can be used twice اللي عندنا تطلع
+
+256
+00:21:02,600 --> 00:21:08,360
+اللي عندي هنا كام خيار هنا خمسة كام واحد هنا خمسة
+
+257
+00:21:08,360 --> 00:21:14,200
+ايش هذا screw is a tin bolt machine اللي عندي هذه
+
+258
+00:21:14,200 --> 00:21:19,840
+ال machine هي راحت مع مين؟ مع واحد لإنه يقولنا ال
+
+259
+00:21:19,840 --> 00:21:23,720
+bolts اللي هي بتختلف اللي إلها سمونا فهذا مافيش ال
+
+260
+00:21:23,720 --> 00:21:28,640
+.. ال .. البراغر فيها بنسميها machine bolts طيب a
+
+261
+00:21:28,640 --> 00:21:31,920
+screw does not require predrilling مين يقولنا اللي
+
+262
+00:21:31,920 --> 00:21:37,140
+بيعمل ال drill لحاله؟ بيعمل التقب self-tapping
+
+263
+00:21:49,010 --> 00:21:53,890
+سلات هد اللي هي الراس
+
+264
+00:21:53,890 --> 00:22:02,010
+زي هيك والثقب اللي فيها خط زي هيك الان screw fit
+
+265
+00:22:02,010 --> 00:22:08,450
+screwdriver with x shape profile at the end ال
+
+266
+00:22:08,450 --> 00:22:13,540
+cross اللي هي إيش هذه أربعة اللي بنتطلع عليها
+
+267
+00:22:19,160 --> 00:22:24,680
+الراس تبقى حزيها هذا على فكرة بنسميه slotted او
+
+268
+00:22:24,680 --> 00:22:29,960
+flatted screwdriver هذي بنسميها cross او phillips
+
+269
+00:22:29,960 --> 00:22:37,240
+اللي عندى المفاك phillips اللي مشهور هذا الشغل ال
+
+270
+00:22:37,240 --> 00:22:41,820
+fifth one ايش screws apply pressure at its end to
+
+271
+00:22:41,820 --> 00:22:47,340
+hold a component in place الست اللي عندى او grab
+
+272
+00:22:47,340 --> 00:22:51,160
+screw اللى هى هنا خمسة اللى هى بتتبت لو فى عندى
+
+273
+00:22:51,160 --> 00:22:57,460
+حاجة بتتبتها طيب الان complete the article from a
+
+274
+00:22:57,460 --> 00:23:00,580
+home improvement magazine using the words in the
+
+275
+00:23:00,580 --> 00:23:04,820
+box look at a and b opposite to help you الان
+
+276
+00:23:04,820 --> 00:23:09,300
+بتعرف ال home improvement magazine هدول ايش؟هذه
+
+277
+00:23:09,300 --> 00:23:14,900
+مجلة متخصصة في كيف تحسن بيتك يعني بتعطي أفكار انا
+
+278
+00:23:14,900 --> 00:23:20,020
+عند بيته قائم شجة اي حاجة فهذه بتعطي أفكار دايما
+
+279
+00:23:20,020 --> 00:23:24,520
+كيف نعمل improvement على الوضع الحالي كيف بده اظبط
+
+280
+00:23:24,520 --> 00:23:28,140
+الستير كيف بده اعمل redecoration لل living room
+
+281
+00:23:28,140 --> 00:23:33,880
+للكتشن لل bathroom لحاجة فهذه مجلة مشهورة في
+
+282
+00:23:33,880 --> 00:23:39,260
+أمريكااللي هو ممبرومان how not to use wall plug
+
+283
+00:23:39,260 --> 00:23:45,120
+العنوان تبعها كيف يعني ما نعملش ما نستخدمش الفجل
+
+284
+00:23:45,120 --> 00:23:49,640
+بالطريقة هذه you check the diameter of the hole
+
+285
+00:23:49,640 --> 00:23:53,880
+required then choose a drill bit one millimeter
+
+286
+00:23:53,880 --> 00:23:58,040
+narrower أول حاجة لما بدي أجي ل .. بدي أستخدم
+
+287
+00:23:58,040 --> 00:24:03,700
+الفجلة بدي أقول بالضاف حصحجم الفجلة هذه بعد هيك
+
+288
+00:24:03,700 --> 00:24:09,840
+اختار ريشة المجدح one millimeter smaller او
+
+289
+00:24:09,840 --> 00:24:16,840
+narrower ليش عشان انت لما تدخليهاوتدخل بالهاتف
+
+290
+00:24:16,840 --> 00:24:21,800
+وعادة لما انا بدي اقدح المجدح لحاله بوسع اكتر من
+
+291
+00:24:21,800 --> 00:24:26,040
+one millimeter لو انت عملتيها اكبر وهذا هتلاحظيه
+
+292
+00:24:26,040 --> 00:24:30,500
+هتلاقي هذي صارت loose بدك حاجة تانية تبتيها بتحطها
+
+293
+00:24:30,500 --> 00:24:37,940
+حواليها ورق clinics حاجات تانية عشان تكبر .. تسكر
+
+294
+00:24:37,940 --> 00:24:43,020
+هذا الفرق you've tried drilling the specified hole
+
+295
+00:24:43,020 --> 00:24:47,840
+size many many many times in the past and only for
+
+296
+00:24:47,840 --> 00:24:52,540
+it to be too big يعني هاي بيقولك انت حولتي مرات
+
+297
+00:24:52,540 --> 00:25:00,500
+عديدة لإنك تستخدمي تعملي تقب
+
+298
+00:25:00,500 --> 00:25:08,190
+مرات كبيرة only for it to be too big لإيش؟ تعمليها
+
+299
+00:25:08,190 --> 00:25:12,830
+لتشوفيها أنك لما تدخليها بتلاقيها كبيرة كتير طيب
+
+300
+00:25:12,830 --> 00:25:17,110
+الآن هيا احنا إيش أخدنا من هذه الأول واحدة قولنا
+
+301
+00:25:17,110 --> 00:25:22,290
+إيش؟ لسه أول واحدة هنا to pick the ash spinning in
+
+302
+00:25:22,290 --> 00:25:27,490
+the hole إيش اللي عندي بيدطلع؟ إيش اللي بيددخله في
+
+303
+00:25:27,490 --> 00:25:34,550
+ال .. في ال hole عادة في الثقب؟ ال plug مظبوط فانت
+
+304
+00:25:34,550 --> 00:25:38,130
+هنا انا حتى معلمك ايه عشان تشوف انت لو بتجري ايش
+
+305
+00:25:38,130 --> 00:25:46,170
+بيصير بتلاقي شغل مجواب على حالها فهنا only too big
+
+306
+00:25:46,170 --> 00:25:49,150
+leaving the plug هاي اللي عندنا ال plug شطبنا
+
+307
+00:25:49,150 --> 00:25:55,410
+عليها leaving the plug ايش؟ spinning in the hole
+
+308
+00:25:55,410 --> 00:25:59,290
+الآن ال plug لما يدخلها الفجلة العصر تبقى تابطة
+
+309
+00:25:59,290 --> 00:26:02,990
+إذا صارت تلف معناه لو حطيت ال screw إيش بدي يصير
+
+310
+00:26:02,990 --> 00:26:11,290
+فيه؟ بدي لف محة مش هيمسك مظبوط only to leave the
+
+311
+00:26:11,290 --> 00:26:15,470
+plug spinning in the hole when you try to tighten
+
+312
+00:26:15,470 --> 00:26:19,670
+دي إيش اللي أنا بدي أحاول أعمل tightening لمين؟ ال
+
+313
+00:26:19,670 --> 00:26:20,850
+screw مظبوط
+
+314
+00:26:24,320 --> 00:26:28,120
+انت قرر ان يكون افضل ان تقوم بتجارب فجلة اكبر لكي
+
+315
+00:26:28,120 --> 00:26:33,740
+تقوم بتجارب فجلة اكبر
+
+316
+00:26:35,280 --> 00:26:40,080
+يا إما بدي أجيب برغة أكبر إذا زبط يدخل وما زبطش
+
+317
+00:26:40,080 --> 00:26:44,680
+إيش بدي أعمل .. بدي أشوف حال تاني أو إيش بدي أسكر
+
+318
+00:26:44,680 --> 00:26:48,720
+الخزاج و أفتح واحد تاني الآن أنا من الناس .. يمكن
+
+319
+00:26:48,720 --> 00:26:52,780
+اتعلمت في أمريكا حاجة واحدة و أنا بدرس نطلع من بيت
+
+320
+00:26:52,780 --> 00:26:56,440
+لبيت إذا مخزق الحيطان بديك تسكر الخزاج .. الخزاج
+
+321
+00:26:56,440 --> 00:27:02,690
+هاد و تدهن و إلا أنت بتدفع بيسموها deposit فصاحب
+
+322
+00:27:02,690 --> 00:27:08,570
+العقار بصلح حاجة ببعتلك الفاتورة ف .. ف .. فأنا من
+
+323
+00:27:08,570 --> 00:27:12,310
+الطبيعي الآن حتى في بيتي بحب شخص أي خزق مالوش لزوم
+
+324
+00:27:12,310 --> 00:27:15,390
+فأي
+
+325
+00:27:15,390 --> 00:27:20,010
+حاجة .. هي التعود أنا تعودت إن هناك ده فيه أي خزق
+
+326
+00:27:20,010 --> 00:27:23,410
+في الحيطة مالوش لزوم بعملوش لإن في الآخر أنا اللي
+
+327
+00:27:23,410 --> 00:27:26,990
+بدي أصلحه أو بدي أدفع حاجة إيش تصليحه فاتعلمت عن
+
+328
+00:27:26,990 --> 00:27:31,890
+هذه الشغلة فش ثقب بحب أعمله إلا عند .. يمكن زوج
+
+329
+00:27:31,890 --> 00:27:34,770
+تفيد من الشغلات اللي بتنزعج فيها كل ما تقوللي حاجة
+
+330
+00:27:34,770 --> 00:27:39,870
+و اقولها لسه بتلزمش ليش؟ لأن خلاص هذه طبيعة تعودنا
+
+331
+00:27:39,870 --> 00:27:45,390
+عليه فهي اللي بنحكي فيه أنك أنت بدك تتعود عليه على
+
+332
+00:27:45,390 --> 00:27:52,270
+هذه بدك إيش؟ tight fit tight fit يعني إيش؟ يعني
+
+333
+00:27:52,270 --> 00:27:58,750
+لما .. يعني تركب حزقة هي tight fit الكلمة تركب حزق
+
+334
+00:28:01,040 --> 00:28:04,760
+اللي هي tight fit so you drill a smaller hole than
+
+335
+00:28:04,760 --> 00:28:08,480
+suggests then attempt to hammer it in .. to hammer
+
+336
+00:28:08,480 --> 00:28:12,960
+in the plug يعني أنت في الأول بتجيب خزك أصغر و
+
+337
+00:28:12,960 --> 00:28:18,620
+بتحاول تدخل الفجدة كيف بندخلها احنا؟ بندقها لجوا
+
+338
+00:28:18,620 --> 00:28:23,530
+صح؟مظبوط ولا لأ؟ و اللي بتطلع الصناعي اللي كويسين
+
+339
+00:28:23,530 --> 00:28:27,590
+إيش بيعملوا؟ بيحط .. لأ بيحط إيش ده ببوس عليها
+
+340
+00:28:27,590 --> 00:28:31,790
+البرغي هات بس بدخلوش كامل بيحط يده براسه و بدق على
+
+341
+00:28:31,790 --> 00:28:37,250
+البرغي فبتدخل .. إذا الحط هاد دخول بسهولة و يعني
+
+342
+00:28:37,250 --> 00:28:41,470
+بيسر معناته الشغل انعمل صح ما انعملش زيك معناته
+
+343
+00:28:41,470 --> 00:28:48,300
+الشغل ان عمل غلط it .. it .. لو كانت too tight أو
+
+344
+00:28:48,300 --> 00:28:53,980
+خلّيني أقول التقب الموجود هذا إيش نوعه ديق، إيش
+
+345
+00:28:53,980 --> 00:28:59,020
+بدي يصير؟ it bends sideways، بتنتني ع الجنب، ويمكن
+
+346
+00:28:59,020 --> 00:29:01,920
+كل هيتنا اللي حد فيكوا يسوي هذا الشغل أو شايفك
+
+347
+00:29:01,920 --> 00:29:08,520
+قدامه بلاحظ إنها بتميل ع الجنب الشكل تبعها هي
+
+348
+00:29:08,520 --> 00:29:13,800
+التقب مثلابتدخل الجزء الأولاني بعد هيش بتصير ..
+
+349
+00:29:13,800 --> 00:29:18,720
+هذه بتميل ع الجنب زي هيكة بتصير الرأس من هنا يعني
+
+350
+00:29:18,720 --> 00:29:23,100
+هذه جزئية إنتنت بدل ما هي عمود صارت ع الجنب وماشية
+
+351
+00:29:23,100 --> 00:29:28,160
+زي هيكة معناته هذه عليها السلام مش هتظبط فأسهل
+
+352
+00:29:28,160 --> 00:29:31,720
+حاجة اللي زي حكاتي بقص هنا و ب .. ده جزء اللي دخل
+
+353
+00:29:31,720 --> 00:29:33,920
+كويس بستقدمه و خلصنا
+
+354
+00:29:40,140 --> 00:29:45,740
+طبعا هاد انت بدك تحاوله مرة و مرة أسهل حاجة انوسع
+
+355
+00:29:45,740 --> 00:29:53,080
+الثقب شوية eventually you manage to get a plug
+
+356
+00:29:53,080 --> 00:29:59,960
+into the hole يعني بعد تكرار هتقدر تدخلي فجلة في
+
+357
+00:29:59,960 --> 00:30:02,420
+الثقب الموجود في الثقب
+
+358
+00:30:05,170 --> 00:30:08,370
+get a plug into the wall you insert the end of the
+
+359
+00:30:08,370 --> 00:30:12,650
+screw pick up your ايش and get to work الان انت
+
+360
+00:30:12,650 --> 00:30:16,110
+بدك تلحيني مسكت دخلتي الفجلة ايش بعد الفجلة بده
+
+361
+00:30:16,110 --> 00:30:22,010
+اعملك؟ بده امسك البرغي و امسك ال screw driver و
+
+362
+00:30:22,010 --> 00:30:26,250
+الف مظبوط فهنا ايش بتكون عندى you pick your ايش
+
+363
+00:30:26,250 --> 00:30:32,570
+screw driver اللي هى هنا طيب
+
+364
+00:30:32,570 --> 00:30:33,530
+هاي التلاتة
+
+365
+00:30:38,240 --> 00:30:44,240
+it is certainly in a tight fit and hard work and
+
+366
+00:30:44,240 --> 00:30:49,940
+as a screw goes in and the plug start to expand
+
+367
+00:30:49,940 --> 00:30:53,320
+احنا قولنا ايش الفجلة لما ندخل البرج ايش بيصيرلها
+
+368
+00:30:53,320 --> 00:30:57,260
+it expand start to expand
+
+369
+00:30:59,420 --> 00:31:03,280
+the going get harder by the time the screws
+
+370
+00:31:03,280 --> 00:31:07,180
+halfway in the screwdriver has slipped off the
+
+371
+00:31:07,180 --> 00:31:12,580
+screw so many times الان انا دخلت هذه بالعافية و
+
+372
+00:31:12,580 --> 00:31:19,840
+بديت ادخل في نص الطريق ايش بيصير ده هي حزقة بيصير
+
+373
+00:31:19,840 --> 00:31:29,940
+الراس تنهري كل ما احط المفك ألفهبفلت والراس بتصير
+
+374
+00:31:29,940 --> 00:31:34,880
+إيش بدل ما هي مثلا cross بتصير ال cross هذا يتأكل
+
+375
+00:31:34,880 --> 00:31:39,400
+هذه الجزئية بتصير تتأكل يعني هذه بتصير إيش شوية 
+
+376
+00:31:39,400 --> 00:31:42,440
+لما
+
+377
+00:31:42,440 --> 00:31:52,440
+في الآخر تبطل بتصير إيش فشي فشي ال cross هذا راحو
+
+378
+00:31:52,440 --> 00:31:55,620
+هذا اللي بتحكيله the screwdriver has slipped off
+
+379
+00:31:55,620 --> 00:32:03,020
+slipped off يعني إيش فلّت so many times that what
+
+380
+00:32:03,020 --> 00:32:08,040
+used to be إيش هنا إيش قلنا هناك cross head
+
+381
+00:32:08,040 --> 00:32:14,760
+الموجود كويس pattern on the screw إيش هاي on the
+
+382
+00:32:14,760 --> 00:32:18,540
+screw إيش هذه head مظبوط اللي هي
+
+383
+00:32:21,400 --> 00:32:25,660
+now more like a smooth round hole صار عنده شكله
+
+384
+00:32:25,660 --> 00:32:33,660
+إيش دائري وملس يعني المفك إيش بيساوي فيه بيركبش it
+
+385
+00:32:33,660 --> 00:32:40,780
+is impossible to screw in any further or unscrewed
+
+386
+00:32:40,780 --> 00:32:44,920
+فاحنا إيش لما نوصل لهك المرحلة بنبطل احنا قادرين
+
+387
+00:32:45,720 --> 00:32:50,320
+ندخلها ولا قدرين إيش نفكها لأن البرغي هذا إيش
+
+388
+00:32:50,320 --> 00:32:59,020
+بطل يشتغل So you take a pair of pliers إيش pliers؟
+
+389
+00:32:59,020 --> 00:33:04,500
+الزردية بتعرفوش الزردية؟ أيوة لأ بتعرفوها هدنش مش
+
+390
+00:33:04,500 --> 00:33:10,960
+كلكم بتعرفوها لو بسأل بناتي جيب الزردية بيجيبلي كل
+
+391
+00:33:10,960 --> 00:33:16,090
+حاجة إلا الزردية أخونا الصغير جيب الزرادية حافظت
+
+392
+00:33:16,090 --> 00:33:21,070
+وراح يجيبها الزرادية اللي هي الكماشة اللي هي شكلها
+
+393
+00:33:21,070 --> 00:33:31,350
+في cross head هنا الرأس وهنا الإيد أو 
+
+394
+00:33:31,350 --> 00:33:32,970
+بتلاقيها زي هيك أحيانا
+
+395
+00:33:37,400 --> 00:33:42,680
+وكلمة pair لأن هذا إيش هما اثنتين وملزقات في النص
+
+396
+00:33:42,680 --> 00:33:51,280
+فأنت لما تيجي تكمشيها أو تطلعيها فهذا ال pair of
+
+397
+00:33:51,280 --> 00:33:57,520
+pliers a pair of pliers grip the end of the screw
+
+398
+00:33:57,520 --> 00:34:01,680
+لأن أنت بتمسك الراس وإيش بعدها؟ an attempt to
+
+399
+00:34:01,680 --> 00:34:05,300
+drag the whole thing out of the wall بتحاول
+
+400
+00:34:05,300 --> 00:34:10,660
+تسحبيها برا الـ .. الـ .. الـ .. but إيش عندها؟ the
+
+401
+00:34:10,660 --> 00:34:17,920
+pull out force اللي عندها is beyond the power of
+
+402
+00:34:17,920 --> 00:34:24,660
+your now aching arms يعني هاد الأن إيدك وجعتك و
+
+403
+00:34:24,660 --> 00:34:30,040
+أنت إيش بتشدي الأن بتيجي تصحب إيدك تعبانة بتلاقيها
+
+404
+00:34:30,040 --> 00:34:35,500
+أكثر من قوة إيدك لأن إيدك من قوة إيدك التعبانة
+
+405
+00:34:35,500 --> 00:34:41,560
+aching arms اللي هي الإيد التعبانة أو الموجوعة the
+
+406
+00:34:41,560 --> 00:34:48,510
+screw might as well be إيش with باكسي ريزين set in
+
+407
+00:34:48,510 --> 00:34:53,730
+اللي هي تبتت هنا أخر واحدة اللي عندي فهذه بتحكي عن
+
+408
+00:34:53,730 --> 00:35:01,650
+تجربة إيش اللي بنعمل في هذا المجال لسه
+
+409
+00:35:01,650 --> 00:35:09,090
+الآن في عندي إيش ال match إيش
+
+410
+00:35:09,090 --> 00:35:16,920
+عندي هنا rivet gun اللي هي إيش هذه إيش قلنا عنها؟
+
+411
+00:35:16,920 --> 00:35:22,020
+اللي هي الأداة اللي احنا بنتبث فيها البرشومة فيه
+
+412
+00:35:22,020 --> 00:35:27,280
+سواء لفلات أو لصاليد أو لبلايد
+
+413
+00:35:30,860 --> 00:35:37,460
+الراس اللي هي اللي احنا بنشكلها بعد لما احنا نخلص
+
+414
+00:35:37,460 --> 00:35:40,900
+من البرشومة factory head اللي هي الشجة اللي
+
+415
+00:35:40,900 --> 00:35:45,820
+بتضلها أصلية ال solid rivet اللي هي ال flat هذا
+
+416
+00:35:45,820 --> 00:35:49,360
+ال blind rivet اللي هي ال إيش اللي طويلة زي ال
+
+417
+00:35:49,360 --> 00:35:53,300
+needle a type of fastener that is hollow مين هي
+
+418
+00:35:53,300 --> 00:36:00,770
+اللي هي إيش ال blind riveta type of fastener that
+
+419
+00:36:00,770 --> 00:36:08,330
+is not hollow solid اتول
+
+420
+00:36:08,330 --> 00:36:13,730
+used for installing a type of fastener اللي هي هذه
+
+421
+00:36:13,730 --> 00:36:18,690
+ال rivet gun the white part at the top of the
+
+422
+00:36:18,690 --> 00:36:23,930
+rivet present when the rivet is supplied اللي هي
+
+423
+00:36:23,930 --> 00:36:30,400
+إيش هذه اطلع على الكلمة، الكلمة بتقولك على طول، when
+
+424
+00:36:30,400 --> 00:36:33,780
+the rivet is supplied، لما أنت تجي من المصنع، يعني
+
+425
+00:36:33,780 --> 00:36:40,060
+إيش بتكون factory head، الآن the part of the
+
+426
+00:36:40,060 --> 00:36:43,400
+bottom of the rivet formed after the rivet is ..
+
+427
+00:36:43,400 --> 00:36:49,410
+اللي هي إيش؟ ال shop head على أي حال اللي بتطلع
+
+428
+00:36:49,410 --> 00:36:52,110
+عليه .. هاي ال video موجود على الصفحة تطلع عليه
+
+429
+00:36:52,110 --> 00:36:59,310
+بيعطيكوا فكرة عن اللي بنتكلم عنه، أي شيء بتطلع
+
+430
+00:36:59,310 --> 00:37:01,990
+عليه بتشوف الصورة سهل جدا تستوعبوه 
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/aUnYaOa2QUY_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/aUnYaOa2QUY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aaaeba810d1b4f60199e1894312f8a1ed30f1d4e
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/aUnYaOa2QUY_raw.srt
@@ -0,0 +1,1736 @@
+1
+00:00:20,690 --> 00:00:26,890
+السلام عليكم اليوم سنتحدث عن القصة 27 القصة 27
+
+2
+00:00:26,890 --> 00:00:34,290
+تتحدث عن مقاطعات ميكانية اليوم سنتحدث عن مقاطعات
+
+3
+00:00:34,290 --> 00:00:40,730
+مقاطعات مقاطعات مقاطعات و مقاطعات مقاطعات مقاطعات
+
+4
+00:00:40,730 --> 00:00:44,090
+مقاطعات
+
+5
+00:00:44,090 --> 00:00:46,750
+مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات
+
+6
+00:00:46,750 --> 00:00:46,750
+مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات
+
+7
+00:00:46,750 --> 00:00:46,750
+مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات
+
+8
+00:00:46,750 --> 00:00:46,750
+مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات مقاطعات
+
+9
+00:00:46,750 --> 00:00:49,230
+مقاطعات مقاطعات مقاطعات مقاطعات مقهذا تعبير يمكن
+
+10
+00:00:49,230 --> 00:00:54,310
+عندكم ماسمعتهوش سمعت الفجلة اللي
+
+11
+00:00:54,310 --> 00:00:58,790
+بنحط فيها البرغة بتتحط بالحيط هذه بتسميها screw
+
+12
+00:00:58,790 --> 00:01:04,030
+anchors اللي هي الفجلة ال rivets اللي هي ايش
+
+13
+00:01:04,030 --> 00:01:09,850
+البرشومة البرشومة كل كهذه شفتوها بس انتم شوية
+
+14
+00:01:09,850 --> 00:01:16,210
+شوفوا شبابيك الألمنيومأو المطابق الألمنيوم بتتبطوا
+
+15
+00:01:16,210 --> 00:01:22,750
+في إيش؟ مش في برغي، في حاجة ال needle هذه، هي هذه
+
+16
+00:01:22,750 --> 00:01:28,150
+اللي بنسميها ال rivet، كويس؟ الآن بعض الشغلات
+
+17
+00:01:28,150 --> 00:01:33,150
+الشناتي تبعتكم برضه بتتبط ب needle نوع تاني،
+
+18
+00:01:33,150 --> 00:01:39,050
+بنسميها هذه flat و هذه إيش؟ بتبقى blindال blind
+
+19
+00:01:39,050 --> 00:01:42,650
+اللي هي ال needle تبعت المطبخ أو تبعت اللي
+
+20
+00:01:42,650 --> 00:01:46,790
+بنستخدمها في المطبخ أو شبابيك الألمنيوم الآن في ال
+
+21
+00:01:46,790 --> 00:01:52,610
+needle التانية من ماحش انت تطلع فيها نشوف حاجة
+
+22
+00:01:52,610 --> 00:01:58,550
+معينة شايفة هذه اللي هنا؟ هذه برشومة هذه بنسميها
+
+23
+00:01:58,550 --> 00:02:03,290
+rivet شايفينها؟ rivet هذا النوع التاني
+
+24
+00:02:10,440 --> 00:02:15,860
+الكاميرا اللي هان؟ البرجومة
+
+25
+00:02:15,860 --> 00:02:22,460
+اللي هان؟ بتبيع احنا الحين؟
+
+26
+00:02:22,460 --> 00:02:26,720
+طيب
+
+27
+00:02:26,720 --> 00:02:30,240
+screws .. screws have threaded على فكرة لمنزل
+
+28
+00:02:30,240 --> 00:02:36,280
+فيديوهاتعلى الموقع التابعي فيه تتكلم عن الأنواع
+
+29
+00:02:36,280 --> 00:02:39,240
+اللي بنحكي عنها ال screws و هذه الشغلات ال screws
+
+30
+00:02:39,240 --> 00:02:43,160
+have threaded shafts with heads الآن احنا بنلاحظ
+
+31
+00:02:43,160 --> 00:02:49,630
+ايش هي عبارة البرغي هو لهيعني خلينا نقول ايد او
+
+32
+00:02:49,630 --> 00:02:53,930
+دراع الدراع حد ايش مسوا فيه مسنن treaded shaft
+
+33
+00:02:53,930 --> 00:02:58,910
+with heads وفيه له راس الان التصنيف اللي بتنعمل في
+
+34
+00:02:58,910 --> 00:03:03,850
+عدة أنواع بصنف البراغي حسب الراس حسب مقطع الراس
+
+35
+00:03:03,850 --> 00:03:09,810
+ايش معمول فيه وحسب ال tread اللي موجود فيه في بعض
+
+36
+00:03:09,810 --> 00:03:15,230
+البراغي بتصلح للحديد في بعض البراغي بتصلح للخشب في
+
+37
+00:03:15,230 --> 00:03:20,880
+براغيبتدخل بثقب يعني انت بتبقى قزقها لقزق و
+
+38
+00:03:20,880 --> 00:03:24,240
+بتدخليها في القزق في بعض البراغي يمكن تشوفوها في
+
+39
+00:03:24,240 --> 00:03:29,060
+المعادن او في الالمونيوم هي اللي بتخزق التقب يعني
+
+40
+00:03:29,060 --> 00:03:32,720
+مالزمش تخزقي لها اي شي كل اللي بدك تعمليه انك تلف
+
+41
+00:03:32,720 --> 00:03:37,940
+فيها فهي بتفتح التقب لحالها وهذا هنتكلم عنهاthey
+
+42
+00:03:37,940 --> 00:03:44,320
+may be screwed into a pre-drilled hole الخزج
+
+43
+00:03:44,320 --> 00:03:47,900
+أو الثقب المعمول لها drilled for the screws to
+
+44
+00:03:47,900 --> 00:03:52,560
+enter self-tapping screws
+
+45
+00:03:56,910 --> 00:04:02,370
+يعني انت لو لفتيه turn .. يعني في اتجاه معين في ..
+
+46
+00:04:02,370 --> 00:04:06,450
+هو اللي بفتح الخزق لحاله او بيعمل الثقب لحاله و
+
+47
+00:04:06,450 --> 00:04:10,410
+هذا بتلاقيها دايما بنستخدمها في مين الحديد مش
+
+48
+00:04:10,410 --> 00:04:14,570
+الجاسي، الحديد دايما ال marine يعني زي الألمنيوم،
+
+49
+00:04:14,570 --> 00:04:19,950
+زي الصفائح الخفيفة، هذا اللي بنستخدم فيها الحديد
+
+50
+00:04:19,950 --> 00:04:23,950
+الجاسي طبعا مانفعش هذا الشيء الخشب ملزمش، البرغ
+
+51
+00:04:23,950 --> 00:04:29,740
+لحاله بيضله داخلف self-tapping screws هي نحطتهم
+
+52
+00:04:29,740 --> 00:04:34,100
+بالإيش؟ بلون معين، هاي نكتبهم لإن بلزمولنا كمان
+
+53
+00:04:34,100 --> 00:04:37,860
+شوية في التمرين الأول self-tapping
+
+54
+00:04:48,140 --> 00:04:53,420
+they do not require pre-drill holes they cut their
+
+55
+00:04:53,420 --> 00:04:58,140
+own holes as they screwed in لما نحنا نلفهم هم
+
+56
+00:04:58,140 --> 00:05:02,800
+بيعملوا ثغب تبعهم unlike bolts ال bolts بتعرفيش
+
+57
+00:05:02,800 --> 00:05:09,580
+إله سمونه أو إله مكان في الحديد بتلفيه فيهالدراجات
+
+58
+00:05:09,580 --> 00:05:13,780
+ليست مستخدمة لدراجات وليست مستخدمة لدراجات مستخدمة
+
+59
+00:05:13,780 --> 00:05:14,360
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+60
+00:05:14,360 --> 00:05:19,940
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+61
+00:05:19,940 --> 00:05:26,980
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+62
+00:05:26,980 --> 00:05:34,480
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+63
+00:05:34,480 --> 00:05:36,940
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+64
+00:05:36,940 --> 00:05:36,940
+لدراجات مستخدمة لدراجات مستخدمة لدراجات مستخدمة
+
+65
+00:05:36,940 --> 00:05:41,470
+لدراجات مستخدمانه في مفاك .. المفاك هذا بدخل فيها
+
+66
+00:05:41,470 --> 00:05:46,510
+وانواع الحسب الراس كيف معمول بتقولنا ايش نوع
+
+67
+00:05:46,510 --> 00:05:51,430
+المفاك اللي بينفع معها Most screws hid are
+
+68
+00:05:51,430 --> 00:05:55,010
+designed to be screwed in using a screwdriver. The
+
+69
+00:05:55,010 --> 00:05:58,490
+most common types are slots hid screwed
+
+70
+00:06:01,950 --> 00:06:07,150
+head screws الان ال slot head ايش فيه فيها فرزة
+
+71
+00:06:07,150 --> 00:06:11,230
+الفرزة بتبقى ايش في عندنا انواع في فرزة بتلاقيها
+
+72
+00:06:11,230 --> 00:06:15,850
+cross في فرزة بتلاقيها خط مستقيم وفي فرزة بتلاقيها
+
+73
+00:06:15,850 --> 00:06:21,230
+على شكل نجمة الان الفرزة ال slot head اللي هي
+
+74
+00:06:21,230 --> 00:06:26,010
+الفرزة تبعتنا ايش مستقيم and cross head screwed
+
+75
+00:06:33,520 --> 00:06:39,560
+الـ crosshead وهذه الشكل تبعهم هلاحظ هذه هي الـ
+
+76
+00:06:39,560 --> 00:06:44,300
+screwdriver هذا اللي هي هنا إذا صلحت هدي تطلع كيف
+
+77
+00:06:44,300 --> 00:06:49,340
+هنا الشكل اللي موجود تطلع هناك crosshead وهناك ال
+
+78
+00:06:49,340 --> 00:06:52,560
+starhead ال starhead ولا ال crosshead ولا ال
+
+79
+00:06:52,560 --> 00:06:57,420
+flathead بدك المفاك الصح لتشتغل فيه لو ماعندكيش
+
+80
+00:06:57,420 --> 00:07:00,100
+المفاك ماعندكيش المفاك ماتقدريش تشتغل فيه في أنواع
+
+81
+00:07:00,100 --> 00:07:07,150
+تانيةsmall diameter bolts which can be used with
+
+82
+00:07:07,150 --> 00:07:10,950
+nuts or screwed into threaded holes are sometimes
+
+83
+00:07:10,950 --> 00:07:19,490
+called machine screws الان
+
+84
+00:07:19,490 --> 00:07:23,290
+ال machine screws اللي هم إيش هم عبارة عن bolts بس
+
+85
+00:07:23,290 --> 00:07:26,490
+إيش اللي فارق بينه و بين اللي دلوقت هذا الحجم تبع
+
+86
+00:07:26,490 --> 00:07:31,460
+حقيقة صغيريعني زي ال boards بس حجمها و في الها
+
+87
+00:07:31,460 --> 00:07:38,240
+سمونة بس حجمها إيش؟صغير هذا الفرق بين ال machine
+
+88
+00:07:38,240 --> 00:07:43,020
+screws و ال bolts أو ال screws و بتشوفهم هدولة
+
+89
+00:07:43,020 --> 00:07:47,440
+دايما بتلاقيهم حجمها صغير و نوعها صغير و هدى بتتم
+
+90
+00:07:47,440 --> 00:07:51,400
+استخدامها bolts that hold components in a place by
+
+91
+00:07:51,400 --> 00:07:54,000
+pressing the end of the bolts against the
+
+92
+00:07:54,000 --> 00:07:56,600
+components in order to generate friction and
+
+93
+00:07:56,600 --> 00:08:01,240
+prevent sliding are called set screwed or grab
+
+94
+00:08:01,240 --> 00:08:02,040
+screws
+
+95
+00:08:12,750 --> 00:08:18,890
+grab screws الان هاذي ايش بنعملهم هذوله لما نضغط
+
+96
+00:08:18,890 --> 00:08:25,030
+حاجتين و نحط الحاجتين و نتبتهم باستخدام هذا البرغي
+
+97
+00:08:25,030 --> 00:08:29,410
+بنسمي ايش هذا النوع grab او set screws set يعني
+
+98
+00:08:29,410 --> 00:08:34,970
+تثبيت grab يعني ايش يعني التلزيج او ال damage
+
+99
+00:08:34,970 --> 00:08:40,730
+الموجود هنا فعندي كام نوع اتنين اربع خمس انواع
+
+100
+00:08:40,730 --> 00:08:46,400
+الموجودة هناscrew anchors اللي حكينا عنهم هاد الاش
+
+101
+00:08:47,140 --> 00:08:54,740
+الفجل اللي هي جزء بلاستيكي أحيانا بيبقى حتى مثل أو
+
+102
+00:08:54,740 --> 00:09:00,340
+هذا فبنحطها .. بنخزق تقب في الحيطة و بندخله هذا في
+
+103
+00:09:00,340 --> 00:09:03,500
+الحيطة و بعده بنلزق هذا عادة كل البرويز اللي في
+
+104
+00:09:03,500 --> 00:09:08,300
+البيت بنعلقها باستخدام هذه الشغلات fasteners
+
+105
+00:09:08,300 --> 00:09:11,560
+designed to fix objects to walls وهذا عادة
+
+106
+00:09:11,560 --> 00:09:17,220
+بيستخدموها مع الحيطان أو بيسموها ال dry wallsOkay
+
+107
+00:09:17,220 --> 00:09:22,420
+called screw anchors these fit into pre-drilled
+
+108
+00:09:22,420 --> 00:09:26,680
+holes عادة لما نسويها في ثقب جاهز بتدخليها في هذا
+
+109
+00:09:26,680 --> 00:09:31,700
+الثقب a simple screw anchor is a plastic tube
+
+110
+00:09:31,700 --> 00:09:36,180
+calling a wall plug or plug اللي هي الحاجة البسيطة
+
+111
+00:09:36,180 --> 00:09:39,580
+اللي هي الفجلة البلاستيكية اللي بنحطها في الحيطة
+
+112
+00:09:39,580 --> 00:09:46,100
+هذه الآن لما ندخل البرج ايش بيحصل لها؟تفرد أو
+
+113
+00:09:46,100 --> 00:09:51,680
+expand فلما تفرد و expand بتصير ايش؟ الخروج هأيش؟
+
+114
+00:09:51,680 --> 00:09:58,150
+أصعبمظبوط هذا الفكرة اللي هنا it is inserted in a
+
+115
+00:09:58,150 --> 00:10:02,350
+hole and a screw or bolt is then screwed into it
+
+116
+00:10:02,350 --> 00:10:07,110
+يعني بندخل ال bolt أو ال screw فيها as it enters
+
+117
+00:10:07,110 --> 00:10:10,410
+the plug the plug expand يعني ال diameter its
+
+118
+00:10:10,410 --> 00:10:14,610
+diameter increase this increases friction allowing
+
+119
+00:10:14,610 --> 00:10:18,290
+the plug to resist the pull out forces يعني هذا
+
+120
+00:10:18,290 --> 00:10:22,840
+لما ندخلها إيش بيصير فيهابصير .. ساحبها مش سهل
+
+121
+00:10:22,840 --> 00:10:26,460
+يعني أصعب .. صعبة هذه طبعا اللي بدي أسحبها زي ما
+
+122
+00:10:26,460 --> 00:10:31,420
+حكينا إيش بدي يسوي the forces which will cause it
+
+123
+00:10:31,420 --> 00:10:36,960
+to be pulled out of the hole if it were not firmly
+
+124
+00:10:36,960 --> 00:10:40,920
+anchored يعني عادة لو كان .. خليني بس أحكي بعض
+
+125
+00:10:40,920 --> 00:10:46,880
+الشغلات لو كان التقب أكبر إيش بيحصل؟ تدخل بس
+
+126
+00:10:46,880 --> 00:10:53,280
+بتلاقيها بت لاجلج تلعب لو كان صغيرتدخلها بتطعش
+
+127
+00:10:53,280 --> 00:10:58,680
+مظبوط و بتنكسر تنتني او انت لما تدخل البرغة البرغة
+
+128
+00:10:58,680 --> 00:11:03,300
+بتحسس كفيه بيبطل يدخل بوصله شوية و بعدين بيوقف هذه
+
+129
+00:11:03,300 --> 00:11:06,260
+من المشاكل اللي هنتكلم عليها في ال exercise ايش
+
+130
+00:11:06,260 --> 00:11:14,700
+اللي بحصل هذه طيب ايش السؤال anchors اللي هي ايش
+
+131
+00:11:14,700 --> 00:11:18,300
+انت ال anchor ايش قلنا عنها اللي هي الفجلة هذه
+
+132
+00:11:18,300 --> 00:11:24,490
+اللي هيهي الاسم تبعها screw anchor أو wall plug
+
+133
+00:11:24,490 --> 00:11:31,270
+نفس ال expression لتنتين الان ال wall plugs في
+
+134
+00:11:31,270 --> 00:11:36,090
+بحاجة برضه ال anchors في حاجة تانية ممكن شفتوها
+
+135
+00:11:36,090 --> 00:11:41,610
+انتوا في اللي بدى يتعلقوا حاجة في السقف ايش بنجيب
+
+136
+00:11:41,610 --> 00:11:44,890
+الفجلة
+
+137
+00:11:44,890 --> 00:11:45,450
+الحديد
+
+138
+00:11:48,600 --> 00:11:53,380
+أيوة إيش هذه بنحطها؟ هذه برضه بتحطيها بتسوي التقب
+
+139
+00:11:53,380 --> 00:11:58,420
+و بتدخليها بعدها لما تحزقيها تصبح expansion برضه
+
+140
+00:11:58,420 --> 00:12:04,100
+نوع تاني هي بتبقى برغي حديدة إطار يعني حديد وفيه
+
+141
+00:12:04,100 --> 00:12:08,380
+برغي وفيه برغي البرغي هذا مش زي البراغ العادية زي
+
+142
+00:12:08,380 --> 00:12:11,860
+ال what ال port فيه port يعني فانت لما تدخليها
+
+143
+00:12:11,860 --> 00:12:15,580
+هناك تصبح تحزقي فيها تصبحها expansion تصبح لما بدك
+
+144
+00:12:15,580 --> 00:12:20,430
+تسحبيها هذا بتتحمل الضغطيعني بتتحمل الوزن، بتتحمل
+
+145
+00:12:20,430 --> 00:12:26,310
+غير .. أصعب من هذا an expansion anchor is another
+
+146
+00:12:26,310 --> 00:12:29,970
+type of anchor it consists of a bolt fitted inside
+
+147
+00:12:29,970 --> 00:12:34,090
+a metal sleeve يعني هذا إيش بيقولوها؟ هذا اللي
+
+148
+00:12:34,090 --> 00:12:38,230
+بنحكي عنها النوع التاني، اللي هي إيش؟ في عند برغة
+
+149
+00:12:38,230 --> 00:12:42,110
+اللي سمناها bolt موجود sleeve اللي هي إيش؟ القم
+
+150
+00:12:43,090 --> 00:12:47,590
+فلما نتكلم عليكم إنها في لها حاجة زي غطاء خارجي
+
+151
+00:12:47,590 --> 00:12:51,690
+حديد الآن الغطاء الخارجي الحديد في هنا ال boat لما
+
+152
+00:12:51,690 --> 00:12:56,010
+الأقوى دحزك فيه اش هادرستير بتوسع جوا تدخل ضيقة و
+
+153
+00:12:56,010 --> 00:12:59,990
+بعدين تتوسع برا و هنفرجيكم فيديو كمان شوية في هذه
+
+154
+00:12:59,990 --> 00:13:04,800
+الشغل عشان تشوفواهاThe sleeves expand as the bolt
+
+155
+00:13:04,800 --> 00:13:08,720
+is tightened in the hole. هذي بتيجي زي ما أنا بحذق
+
+156
+00:13:08,720 --> 00:13:13,640
+في البرغة، أيش بيصير هذي؟ بتبقى ضيقة، بتصير تفتح،
+
+157
+00:13:13,640 --> 00:13:18,740
+تفتح أيش بتصير فيها؟ يعني الوسع الموجود هذي بتسكر
+
+158
+00:13:18,740 --> 00:13:23,630
+و بيصير الصعب تطلعيهاin cases where pull-out
+
+159
+00:13:23,630 --> 00:13:28,550
+forces are very high chemical anchors can be used
+
+160
+00:13:28,550 --> 00:13:32,210
+الآن في بعض الحلات إيش بيصير عندى؟ بدي حاجة تتبت
+
+161
+00:13:32,210 --> 00:13:36,030
+كتير تتبت يعني فيها إيش؟ بحط chemical المادة
+
+162
+00:13:36,030 --> 00:13:39,590
+الكيميائية اللي هي بحطها بدخلها هناك و لما أحط ال
+
+163
+00:13:39,590 --> 00:13:44,390
+anchor ال anchor بلزق هذا إيش بيصير فيها؟ تلزقة
+
+164
+00:13:44,390 --> 00:13:47,970
+كتير بعد هذا permanent إلا أنا بحطه مش هاطلعه
+
+165
+00:13:47,970 --> 00:13:54,030
+بالمرةThese are studs threaded bars into which
+
+166
+00:13:54,030 --> 00:13:59,330
+nuts can be screwed. The studs are set in.الان هذا
+
+167
+00:13:59,330 --> 00:14:04,310
+ايش باضيف المادة بيسموها أحيانا lucket المادة
+
+168
+00:14:04,310 --> 00:14:09,950
+كيميائية بتضيفيها هناك لما انت تحسكي تنفكش يعني زي
+
+169
+00:14:09,950 --> 00:14:14,930
+ما بقول زي الصمغ بتصيرفانت بتبطل تقدر تطلع زي
+
+170
+00:14:14,930 --> 00:14:20,030
+الصمغ الجامد مش صمغ بسيط that is held in the hole
+
+171
+00:14:20,030 --> 00:14:24,890
+by adhesive most chemical anchors are set in two
+
+172
+00:14:24,890 --> 00:14:29,330
+holes using a strong adhesive called epoxy resin
+
+173
+00:14:29,330 --> 00:14:33,710
+وهذه شفناها مرت علينا ال epoxy لما كنا بنتكلم ع ال
+
+174
+00:14:33,710 --> 00:14:35,290
+plastics
+
+175
+00:14:36,840 --> 00:14:42,200
+البالمرز كويسة اتكلمنا عنها اباكسي ريزن اللي هي
+
+176
+00:14:42,200 --> 00:14:47,680
+هذه مادة لاصقة قوية فهيبقى نحطها هناك من حد ما
+
+177
+00:14:47,680 --> 00:14:55,950
+تحسقي خلاص تقدريش ترفعيها بعد هيكالان ال rivets
+
+178
+00:14:55,950 --> 00:14:59,550
+اللي قولنا عنها البورشامة أو ال needle اللي بدكوا
+
+179
+00:14:59,550 --> 00:15:04,290
+تسموها في العامية rivets are permanent fasteners
+
+180
+00:15:04,290 --> 00:15:08,450
+او fasteners ايش هنا؟ ليش permanent fasteners؟
+
+181
+00:15:08,450 --> 00:15:11,910
+لأنه ده حطيت .. استخدمت البورشامة بتقدر تفكيها
+
+182
+00:15:11,910 --> 00:15:16,370
+تاني؟إذا فكتيها إيش بتصير؟ تخرب، خلاص، بدك واحدة
+
+183
+00:15:16,370 --> 00:15:20,130
+بدالها، عشان هي كانت بنسميها غير الـscrewed،
+
+184
+00:15:20,130 --> 00:15:24,730
+الـscrewed بنطلعوه و بنقدر نرجعه They cannot be
+
+185
+00:15:24,730 --> 00:15:29,070
+unscrewed، a solid rivet، solid هي consist of a
+
+186
+00:15:29,070 --> 00:15:33,470
+short solid shaft of metal with a headat one end
+
+187
+00:15:33,470 --> 00:15:37,070
+called the factory head الان انا لما استخدم ال
+
+188
+00:15:37,070 --> 00:15:42,190
+rivet ايش فيها؟ لها رأس متى ما استخدمتها الرأس ايش
+
+189
+00:15:42,190 --> 00:15:47,930
+بيصير فيه؟ بنطعش، مظبوط؟ الان قبل عملية الطعش
+
+190
+00:15:47,930 --> 00:15:53,510
+بنسميها ايش؟ factory head اللي هي رأس المصنع solid
+
+191
+00:15:53,510 --> 00:15:58,210
+هذه ايش؟ ال solid rivet ال solid rivet اللي هي لها
+
+192
+00:15:58,210 --> 00:16:02,450
+الرأس هناthe rivet is inserted through a pre
+
+193
+00:16:02,450 --> 00:16:05,450
+-drilled hole then a special tool is used to
+
+194
+00:16:05,450 --> 00:16:09,450
+deform ايش احنا بنعمل؟ نقول deform، بتلاقيها في
+
+195
+00:16:09,450 --> 00:16:12,950
+الشنادي، في الصنادل، في كل الشغلات الجلدية بشكل
+
+196
+00:16:12,950 --> 00:16:16,410
+خاص، في الإكشاطات، كل هذه بيسغموها، ماتما انكبست
+
+197
+00:16:16,410 --> 00:16:23,530
+الراس خلاص بتصير ايش؟ DeformedDeformed يعني إيش؟
+
+198
+00:16:23,530 --> 00:16:28,110
+اتغير شكلها، اتشوّه شكلها، يعني نبطل الشكل الأصلي
+
+199
+00:16:28,110 --> 00:16:31,310
+اللي عندها، it changed the shape of the other end
+
+200
+00:16:31,310 --> 00:16:34,970
+of the rivet, flattening and widening it to form a
+
+201
+00:16:34,970 --> 00:16:38,850
+second hit called the sharp hit. الأن لما نقبصها،
+
+202
+00:16:38,850 --> 00:16:41,990
+إيش بيصير عندى؟ في راس على الوجه هاد وشجة تانية من
+
+203
+00:16:41,990 --> 00:16:47,510
+جوا، إيش بيصير؟ تبقى أول داخلةيعني مالهاش راس على
+
+204
+00:16:47,510 --> 00:16:49,570
+الشجة التانية، إيش بيصير لها؟ لما يصير لها
+
+205
+00:16:49,570 --> 00:16:52,870
+flattening بتصير راس التانية، بتصير إيش؟ الحاجة
+
+206
+00:16:52,870 --> 00:16:56,910
+اللي في النص انحشرت بين شغلتين أكبر من الحجم، هذه
+
+207
+00:16:56,910 --> 00:17:01,130
+راس و هذه راس و هذه المنطقة اللي في النص إيش، لو
+
+208
+00:17:01,130 --> 00:17:04,630
+اتكلمنا عن راس بتبقى هذه مثلا بهذه الشكل، الأول
+
+209
+00:17:04,630 --> 00:17:09,980
+لما أكبسها هذه إيش بتصير فيها؟expanse هذه اللي هان
+
+210
+00:17:09,980 --> 00:17:12,740
+بتروح على الجانب من هان وهذا الجانب من هان فبتصير
+
+211
+00:17:12,740 --> 00:17:17,940
+زي الشكل الرأسي هذه بنسميها ال factory head والشجة
+
+212
+00:17:17,940 --> 00:17:21,720
+التانية اللي كانت مستقيمة بتصير ايش هذه بنسميها
+
+213
+00:17:21,720 --> 00:17:30,660
+الشاب head شاب ايش يعني مش الدكانة الشاب اللي هي
+
+214
+00:17:30,660 --> 00:17:36,020
+عادة بنقول عنده لما الواحد المشغل رأس المشغل الشاب
+
+215
+00:17:38,920 --> 00:17:43,300
+يعني انشغلت .. انشغلت الرأس التاني انشغلت انعملت
+
+216
+00:17:43,300 --> 00:17:47,180
+او انشغلت ف shop head solid rivets are widely used
+
+217
+00:17:47,180 --> 00:17:52,160
+in aircraft تلاقيها مثلا في الطيارات كل الحاجات
+
+218
+00:17:52,160 --> 00:17:56,420
+اللي هناك مدقوقة دق في الصيارات بتشوفوها موجودة في
+
+219
+00:17:56,420 --> 00:18:00,840
+الفرش تبع الصيارات موجودة في أماكن كتيرة في
+
+220
+00:18:00,840 --> 00:18:05,540
+الشناتي في المواد الجلدية موجودة في الأواعي موجودة
+
+221
+00:18:06,390 --> 00:18:09,750
+يعني ممكن بتلاقوها هذه الزراير تبعت القواعي
+
+222
+00:18:09,750 --> 00:18:16,640
+بتشوفوا إيش؟ الكبس هدولكل هدولة النوع هم rivets
+
+223
+00:18:16,640 --> 00:18:20,620
+solid rivets لأن إيش اللي بتصير تدخل هي في الأول
+
+224
+00:18:20,620 --> 00:18:25,280
+وبعدين بتكبس الرأس الرأس إيش بتتفلطح أو بتعمل زي
+
+225
+00:18:25,280 --> 00:18:29,840
+حاجة تانية دائرة تانية لهذا الدائرة الموجودة لما
+
+226
+00:18:29,840 --> 00:18:35,280
+بتفلطح هي بتمنع الهاي بتلاحظ إنه في حركة معينة
+
+227
+00:18:35,280 --> 00:18:40,290
+بتقدر تتحرك فيها خصوص لبعض الأماكن بعضها لأبتتبت
+
+228
+00:18:40,290 --> 00:18:47,890
+تتبيت الحركة اللي بتتبت بنسميها هذه set ال blind
+
+229
+00:18:47,890 --> 00:18:55,250
+rivet احنا هذه سمناها solid هذه solid rivet
+
+230
+00:18:55,250 --> 00:19:00,150
+التانية بنسميها blind وهذه كلكم شفتوها تبعات
+
+231
+00:19:00,150 --> 00:19:08,370
+الخزانات الألمنيومويلها جهاز معين فيها ريفيت او
+
+232
+00:19:08,370 --> 00:19:12,210
+باب ريفيت are made from hollow tubes and are
+
+233
+00:19:12,210 --> 00:19:15,850
+fitted using a tool called rivet gun ال rivet gun
+
+234
+00:19:15,850 --> 00:19:19,530
+اللي هي إيش؟ الإيد اللي بي .. اللي بيعصوا فيها زي
+
+235
+00:19:19,530 --> 00:19:23,790
+الزرادية ويلها راس بيحطوا فيها ال .. البرشومة و
+
+236
+00:19:23,790 --> 00:19:26,730
+بدخلوها في ال .. في التاقم اللي موجود و بيعصه و
+
+237
+00:19:26,730 --> 00:19:32,230
+بتنكسر الدراعة الطويلة هذهو هاد بيصيرلها expansion
+
+238
+00:19:32,230 --> 00:19:35,390
+الراس اللي هنا بتنقل .. هاد شايف هاد الحفة؟ هاد
+
+239
+00:19:35,390 --> 00:19:39,270
+بتكبس بتصير الكبسة عليهم بتصير إيش؟ انه خلاص
+
+240
+00:19:39,270 --> 00:19:44,190
+اتثبتت من الشكتين طلع عليهم موجودة لو في حاجة هان
+
+241
+00:19:44,190 --> 00:19:45,810
+جيبناها فارجيناكوا
+
+242
+00:19:48,130 --> 00:19:51,630
+blind rivets are not suitable for high strength
+
+243
+00:19:51,630 --> 00:19:57,150
+joints لو انت لاحظتي اي حاجة بده يمكن .. كلكم
+
+244
+00:19:57,150 --> 00:19:59,950
+بتلاحظوها البواب الموجودات تبعات الحمامات و
+
+245
+00:19:59,950 --> 00:20:04,110
+المطابق بيعملوها من ايش؟ الالمنيوم صح؟ الباب مع
+
+246
+00:20:04,110 --> 00:20:09,870
+الوقت ايش بيحصله؟ لأ بيحصله حاجة بتلاحظوا ايش
+
+247
+00:20:09,870 --> 00:20:15,600
+بيصير يكحد في الأرضيةمصبوط؟ ليش؟ لأن هو النوع ال
+
+248
+00:20:15,600 --> 00:20:20,340
+joints تبعته مش مصممة إنه هذه تتحمل high strength
+
+249
+00:20:20,340 --> 00:20:22,880
+اللي هي و بعدين ما شاء الله اللي عندهم صغار و هو
+
+250
+00:20:22,880 --> 00:20:27,060
+طالع بضربه و هو داخل بضربه فإيش الشكل تبعه بيصير
+
+251
+00:20:27,060 --> 00:20:30,400
+.. بتخلخل .. بيصير يكحت في هذه لأن النوعية هذه
+
+252
+00:20:30,400 --> 00:20:35,920
+بتتبتشكثير اشياء ل heavy duty يعني هذه الحاجات
+
+253
+00:20:35,920 --> 00:20:39,380
+خفيفة و بواب الخازنات بتلاقيهم بتظهر تابعة الحاجات
+
+254
+00:20:39,380 --> 00:20:45,180
+اللي زيكا مافيش مشكلة فيهاالان احنا عملنا الخمس
+
+255
+00:20:45,180 --> 00:20:48,660
+أنواع هنا في ال exercise الأول in this exercise
+
+256
+00:20:48,660 --> 00:20:51,820
+هاي ايش بيقولنا make words combination with screws
+
+257
+00:20:51,820 --> 00:20:55,680
+using words from a and b opposite then match the
+
+258
+00:20:55,680 --> 00:20:58,860
+combination with these with the description below
+
+259
+00:20:58,860 --> 00:21:02,600
+one description can be used twice اللي عندنا تطلع
+
+260
+00:21:02,600 --> 00:21:08,360
+اللي عندي هنا كام خيار هنا خمسة كام واحد هنا خمسة
+
+261
+00:21:08,360 --> 00:21:14,200
+ايش هذا screw is a tin boltmachine اللي عندي هذه
+
+262
+00:21:14,200 --> 00:21:19,840
+ال machine هي راحت مع مين؟ مع واحد لإنه يقولنا ال
+
+263
+00:21:19,840 --> 00:21:23,720
+bolts اللي هي بتختلف اللي إلها سمونا فهذا مافيش ال
+
+264
+00:21:23,720 --> 00:21:28,640
+.. ال .. البراغر فيها بنسميها machine bolts طيب a
+
+265
+00:21:28,640 --> 00:21:31,920
+screw does not require predrilling مين يقولنا اللي
+
+266
+00:21:31,920 --> 00:21:37,140
+بيعمل ال drill لحاله؟ بيعمل التقب self-tapping
+
+267
+00:21:49,010 --> 00:21:53,890
+سلات هد اللي هي الراس
+
+268
+00:21:53,890 --> 00:22:02,010
+زي هيك والثقب اللي فيها خط زي هيك الان screw fit
+
+269
+00:22:02,010 --> 00:22:08,450
+screwdriver with x shape profile at the end ال
+
+270
+00:22:08,450 --> 00:22:13,540
+cross اللي هي إيشهذه أربعة اللي بنتطلع عليها
+
+271
+00:22:19,160 --> 00:22:24,680
+الراس تبقى حزيها هذا على فكرة بنسميه slotted او
+
+272
+00:22:24,680 --> 00:22:29,960
+flatted screwdriver هذي بنسميها cross او phillips
+
+273
+00:22:29,960 --> 00:22:37,240
+اللي عندى المفاك phillips اللي مشهور هذا الشغل ال
+
+274
+00:22:37,240 --> 00:22:41,820
+fifth one ايش screws apply pressure at its end to
+
+275
+00:22:41,820 --> 00:22:47,340
+hold a component in placeالست اللي عندى او grab
+
+276
+00:22:47,340 --> 00:22:51,160
+screw اللى هى هنا خمسة اللى هى بتتبت لو فى عندى
+
+277
+00:22:51,160 --> 00:22:57,460
+حاجة بتتبتها طيب الان complete the article from a
+
+278
+00:22:57,460 --> 00:23:00,580
+home improvement magazine using the words in the
+
+279
+00:23:00,580 --> 00:23:04,820
+box look at a and b opposite to help you الان
+
+280
+00:23:04,820 --> 00:23:09,300
+بتعرف ال home improvement magazine هدول ايش؟هذه
+
+281
+00:23:09,300 --> 00:23:14,900
+مجلة متخصصة في كيف تحسن بيتك يعني بتعطي أفكار انا
+
+282
+00:23:14,900 --> 00:23:20,020
+عند بيته قائم شجة اي حاجة فهذه بتعطي أفكار دايما
+
+283
+00:23:20,020 --> 00:23:24,520
+كيف نعمل improvement على الوضع الحالي كيف بده اظبط
+
+284
+00:23:24,520 --> 00:23:28,140
+الستير كيف بده اعمل redecoration لل living room
+
+285
+00:23:28,140 --> 00:23:33,880
+للكتشن لل bathroom لحاجة فهذه مجلة مشهورة في
+
+286
+00:23:33,880 --> 00:23:39,260
+أمريكااللي هو ممبرومان how not to use wall plug
+
+287
+00:23:39,260 --> 00:23:45,120
+العنوان تبعها كيف يعني ما نعملش ما نستخدمش الفجل
+
+288
+00:23:45,120 --> 00:23:49,640
+بالطريقة هذه you check the diameter of the hole
+
+289
+00:23:49,640 --> 00:23:53,880
+required then choose a drill bit one millimeter
+
+290
+00:23:53,880 --> 00:23:58,040
+narrower أول حاجة لما بدي أجي ل .. بدي أستخدم
+
+291
+00:23:58,040 --> 00:24:03,700
+الفجلة بدي أقول بالضاف حصحجم الفجلة هذه بعد هيك
+
+292
+00:24:03,700 --> 00:24:09,840
+اختار ريشة المجدح one millimeter smaller او
+
+293
+00:24:09,840 --> 00:24:16,840
+narrower ليش عشان انت لما تدخليهاوتدخل بالهاتف
+
+294
+00:24:16,840 --> 00:24:21,800
+وعادة لما انا بدي اقدح المجدح لحاله بوسع اكتر من
+
+295
+00:24:21,800 --> 00:24:26,040
+one millimeter لو انت عملتيها اكبر وهذا هتلاحظيه
+
+296
+00:24:26,040 --> 00:24:30,500
+هتلاقي هذي صارت loose بدك حاجة تانية تبتيها بتحطها
+
+297
+00:24:30,500 --> 00:24:37,940
+حواليها ورق clinics حاجات تانية عشان تكبر .. تسكر
+
+298
+00:24:37,940 --> 00:24:43,020
+هذا الفرقyou've tried drilling the specified hole
+
+299
+00:24:43,020 --> 00:24:47,840
+size many many many times in the past and only for
+
+300
+00:24:47,840 --> 00:24:52,540
+it to be too big يعني هاي بيقولك انت حولتي مرات
+
+301
+00:24:52,540 --> 00:25:00,500
+عديدة لإنك تستخدمي تعملي تقب
+
+302
+00:25:00,500 --> 00:25:08,190
+مرات كبيرة only for it to be too bigلإيش؟ تعمليها
+
+303
+00:25:08,190 --> 00:25:12,830
+لتشوفيها أنك لما تدخليها بتلاقيها كبيرة كتير طيب
+
+304
+00:25:12,830 --> 00:25:17,110
+الآن هيا احنا إيش أخدنا من هذه الأول واحدة قولنا
+
+305
+00:25:17,110 --> 00:25:22,290
+إيش؟ لسه أول واحدة هنا to pick the ash spinning in
+
+306
+00:25:22,290 --> 00:25:27,490
+the hole إيش اللي عندي بيدطلع؟ إيش اللي بيددخله في
+
+307
+00:25:27,490 --> 00:25:34,550
+ال .. في ال hole عادة في الثقب؟ ال plugمظبوط فانت
+
+308
+00:25:34,550 --> 00:25:38,130
+هنا انا حتى معلمك ايه عشان تشوف انت لو بتجري ايش
+
+309
+00:25:38,130 --> 00:25:46,170
+بيصير بتلاقي شغل مجواب على حالها فهنا only too big
+
+310
+00:25:46,170 --> 00:25:49,150
+leaving the plug هاي اللي عندنا ال plug شطبنا
+
+311
+00:25:49,150 --> 00:25:55,410
+عليها leaving the plug ايش؟spinning in the hole
+
+312
+00:25:55,410 --> 00:25:59,290
+الآن ال plug لما يدخلها الفجلة العصر تبقى تابطة
+
+313
+00:25:59,290 --> 00:26:02,990
+إذا صارت تلف معناه لو حطيت ال screw إيش بدي يصير
+
+314
+00:26:02,990 --> 00:26:11,290
+فيه؟ بدي لف محة مش هيمسك مظبوط only to leave the
+
+315
+00:26:11,290 --> 00:26:15,470
+plug spinning in the hole when you try to tighten
+
+316
+00:26:15,470 --> 00:26:19,670
+دي إيش اللي أنا بدي أحاول أعمل tightening لمين؟ ال
+
+317
+00:26:19,670 --> 00:26:20,850
+screw مظبوط
+
+318
+00:26:24,320 --> 00:26:28,120
+انت قرر ان يكون افضل ان تقوم بتجارب فجلة اكبر لكي
+
+319
+00:26:28,120 --> 00:26:33,740
+تقوم بتجارب فجلة اكبر
+
+320
+00:26:35,280 --> 00:26:40,080
+يا إما بدي أجيب برغة أكبر إذا زبط يدخل وما زبطش
+
+321
+00:26:40,080 --> 00:26:44,680
+إيش بدي أعمل .. بدي أشوف حال تاني أو إيش بدي أسكر
+
+322
+00:26:44,680 --> 00:26:48,720
+الخزاج و أفتح واحد تاني الآن أنا من الناس .. يمكن
+
+323
+00:26:48,720 --> 00:26:52,780
+اتعلمت في أمريكا حاجة واحدة و أنا بدرس نطلع من بيت
+
+324
+00:26:52,780 --> 00:26:56,440
+لبيت إذا مخزق الحيطان بديك تسكر الخزاج .. الخزاج
+
+325
+00:26:56,440 --> 00:27:02,690
+هاد و تدهن و إلا أنت بتدفع بيسموها depositفصاحب
+
+326
+00:27:02,690 --> 00:27:08,570
+العقار بصلح حاجة ببعتلك الفاتورة ف .. ف .. فأنا من
+
+327
+00:27:08,570 --> 00:27:12,310
+الطبيعي الآن حتى في بيتي بحب شخص أي خزق مالوش لزوم
+
+328
+00:27:12,310 --> 00:27:15,390
+فأي
+
+329
+00:27:15,390 --> 00:27:20,010
+حاجة .. هي التعود أنا تعودت إن هناك ده فيه أي خزق
+
+330
+00:27:20,010 --> 00:27:23,410
+في الحيطة مالوش لزوم بعملوش لإن في الآخر أنا اللي
+
+331
+00:27:23,410 --> 00:27:26,990
+بدي أصلحه أو بدي أدفع حاجة إيش تصليحه فاتعلمت عن
+
+332
+00:27:26,990 --> 00:27:31,890
+هذه الشغلة فش ثقب بحب أعملهإلا عند .. يمكن زوج
+
+333
+00:27:31,890 --> 00:27:34,770
+تفيد من الشغلات اللي بتنزعج فيها كل ما تقوللي حاجة
+
+334
+00:27:34,770 --> 00:27:39,870
+و اقولها لسه بتلزمش ليش؟ لأن خلاص هذه طبيعة تعودنا
+
+335
+00:27:39,870 --> 00:27:45,390
+عليه فهي اللي بنحكي فيه أنك أنت بدك تتعود عليه على
+
+336
+00:27:45,390 --> 00:27:52,270
+هذه بدك إيش؟ tight fit tight fit يعني إيش؟ يعني
+
+337
+00:27:52,270 --> 00:27:58,750
+لما .. يعني تركب حزقة هي tight fit الكلمة تركب حزق
+
+338
+00:28:01,040 --> 00:28:04,760
+اللي هي tight fit so you drill a smaller hole than
+
+339
+00:28:04,760 --> 00:28:08,480
+suggests then attempt to hammer it in .. to hammer
+
+340
+00:28:08,480 --> 00:28:12,960
+in the plug يعني أنت في الأول بتجيب خزك أصغر و
+
+341
+00:28:12,960 --> 00:28:18,620
+بتحاول تدخل الفجدة كيف بندخلها احنا؟ بندقها لجوا
+
+342
+00:28:18,620 --> 00:28:23,530
+صح؟مظبوط ولا لأ؟ و اللي بتطلع الصناعي اللي كويسين
+
+343
+00:28:23,530 --> 00:28:27,590
+إيش بيعملوا؟ بيحط .. لأ بيحط إيش ده ببوس عليها
+
+344
+00:28:27,590 --> 00:28:31,790
+البرغي هات بس بدخلوش كامل بيحط يده براسه و بدق على
+
+345
+00:28:31,790 --> 00:28:37,250
+البرغي فبتدخل .. إذا الحط هاد دخول بسهولة و يعني
+
+346
+00:28:37,250 --> 00:28:41,470
+بيسر معناته الشغل انعمل صح ما انعملش زيك معناته
+
+347
+00:28:41,470 --> 00:28:48,300
+الشغل ان عمل غلطit .. it .. لو كانت too tight أو
+
+348
+00:28:48,300 --> 00:28:53,980
+خلّيني أقول التقب الموجود هذا إيش نوعه ديق، إيش
+
+349
+00:28:53,980 --> 00:28:59,020
+بدي يصير؟ it bends sideways، بتنتني ع الجنب، ويمكن
+
+350
+00:28:59,020 --> 00:29:01,920
+كل هيتنا اللي حد فيكوا يسوي هذا الشغل أو شايفك
+
+351
+00:29:01,920 --> 00:29:08,520
+قدامه بلاحظ إنها بتميل ع الجنب الشكل تبعها هي
+
+352
+00:29:08,520 --> 00:29:13,800
+التقب مثلابتدخل الجزء الأولاني بعد هيش بتصير ..
+
+353
+00:29:13,800 --> 00:29:18,720
+هذه بتميل ع الجنب زي هيكة بتصير الرأس من هنا يعني
+
+354
+00:29:18,720 --> 00:29:23,100
+هذه جزئية إنتنت بدل ما هي عمود صارت ع الجنب وماشية
+
+355
+00:29:23,100 --> 00:29:28,160
+زي هيكة معناته هذه عليها السلام مش هتظبط فأسهل
+
+356
+00:29:28,160 --> 00:29:31,720
+حاجة اللي زي حكاتي بقص هنا و ب .. ده جزء اللي دخل
+
+357
+00:29:31,720 --> 00:29:33,920
+كويس بستقدمه و خلصنا
+
+358
+00:29:40,140 --> 00:29:45,740
+طبعا هاد انت بدك تحاوله مرة و مرة أسهل حاجة انوسع
+
+359
+00:29:45,740 --> 00:29:53,080
+الثقب شوية eventually you manage to get a plug
+
+360
+00:29:53,080 --> 00:29:59,960
+into the hole يعني بعد تكرار هتقدر تدخلي فجلة في
+
+361
+00:29:59,960 --> 00:30:02,420
+الثقب الموجود في الثقب
+
+362
+00:30:05,170 --> 00:30:08,370
+get a plug into the wall you insert the end of the
+
+363
+00:30:08,370 --> 00:30:12,650
+screw pick up your ايش and get to work الان انت
+
+364
+00:30:12,650 --> 00:30:16,110
+بدك تلحيني مسكت دخلتي الفجلة ايش بعد الفجلة بده
+
+365
+00:30:16,110 --> 00:30:22,010
+اعملك؟ بده امسك البرغي و امسك ال screw driver و
+
+366
+00:30:22,010 --> 00:30:26,250
+الف مظبوط فهنا ايش بتكون عندى you pick your ايش
+
+367
+00:30:26,250 --> 00:30:32,570
+screw driver اللي هى هنا طيب
+
+368
+00:30:32,570 --> 00:30:33,530
+هاي التلاتة
+
+369
+00:30:38,240 --> 00:30:44,240
+it is certainly in a tight fit and hard work and
+
+370
+00:30:44,240 --> 00:30:49,940
+as a screw goes in and the plug start to expand
+
+371
+00:30:49,940 --> 00:30:53,320
+احنا قولنا ايش الفجلة لما ندخل البرج ايش بيصيرلها
+
+372
+00:30:53,320 --> 00:30:57,260
+it expand start to expand
+
+373
+00:30:59,420 --> 00:31:03,280
+the going get harder by the time the screws
+
+374
+00:31:03,280 --> 00:31:07,180
+halfway in the screwdriver has slipped off the
+
+375
+00:31:07,180 --> 00:31:12,580
+screw so many times الان انا دخلت هذه بالعافية و
+
+376
+00:31:12,580 --> 00:31:19,840
+بديت ادخل في نص الطريق ايش بيصير ده هي حزقة بيصير
+
+377
+00:31:19,840 --> 00:31:29,940
+الراس تنهري كل ما احط المفك ألفهبفلت والراس بتصير
+
+378
+00:31:29,940 --> 00:31:34,880
+إيش بدل ما هي مثلا cross بتصير ال cross هذا يتأكل
+
+379
+00:31:34,880 --> 00:31:39,400
+هذه الجزئية بتصير تتأكل يعني هذه بتصير إيش شوية
+
+380
+00:31:39,400 --> 00:31:42,440
+لما
+
+381
+00:31:42,440 --> 00:31:52,440
+في الآخر تبطل بتصير إيش فشي فشي ال cross هذا راحو
+
+382
+00:31:52,440 --> 00:31:55,620
+هذا اللي بتحكيله the screwdriver has slipped off
+
+383
+00:31:55,620 --> 00:32:03,020
+slipped off يعني إيش فلّت so many times that what
+
+384
+00:32:03,020 --> 00:32:08,040
+used to be إيش هنا إيش قلنا هناك cross head
+
+385
+00:32:08,040 --> 00:32:14,760
+الموجود كويس pattern on the screw إيش هاي on the
+
+386
+00:32:14,760 --> 00:32:18,540
+screw إيش هذه head مظبوط اللي هي
+
+387
+00:32:21,400 --> 00:32:25,660
+now more like a smooth round hole صار عنده شكله
+
+388
+00:32:25,660 --> 00:32:33,660
+إيش دائري وملس يعني المفك إيش بيساوي فيه بيركبش it
+
+389
+00:32:33,660 --> 00:32:40,780
+is impossible to screw in any further or unscrewed
+
+390
+00:32:40,780 --> 00:32:44,920
+فاحنا إيش لما نوصل لهك المرحلة بنبطل احنا قادرين
+
+391
+00:32:45,720 --> 00:32:50,320
+اندخلها ولا قدرين إيش انفكها لإن البرغي هذا إيش
+
+392
+00:32:50,320 --> 00:32:59,020
+بطل يشتغل So you take a pair of pliers إيش pliers؟
+
+393
+00:32:59,020 --> 00:33:04,500
+الزردية بتعرفوش الزردية؟ أيوة لأ بتعرفوها هدنش مش
+
+394
+00:33:04,500 --> 00:33:10,960
+كلكم بتعرفوها لو بسأل بناتي جيب الزردية بيجيبلي كل
+
+395
+00:33:10,960 --> 00:33:16,090
+حاجة إلا الزرديةأخونا الصغير جيف الزرادية حافظت
+
+396
+00:33:16,090 --> 00:33:21,070
+وروح يجيبها الزرادية اللي هي الكماشة اللي هي شكلها
+
+397
+00:33:21,070 --> 00:33:31,350
+في cross head هنا الرأس وهنا الإيد أو
+
+398
+00:33:31,350 --> 00:33:32,970
+بتلاقيها زي هيك أحيانا
+
+399
+00:33:37,400 --> 00:33:42,680
+و كلمة pair لأن هذا ايش هما اتين و ملزقات في النص
+
+400
+00:33:42,680 --> 00:33:51,280
+فانت لما تيجي تكمشيها او تطلعيها فهذا ال pair of
+
+401
+00:33:51,280 --> 00:33:57,520
+pliersa pair of pliers grip the end of the screw
+
+402
+00:33:57,520 --> 00:34:01,680
+لان انت بتمسك الراس و إيش بعدها؟ an attempt to
+
+403
+00:34:01,680 --> 00:34:05,300
+drag the whole thing out of the wall بتحاول
+
+404
+00:34:05,300 --> 00:34:10,660
+تسحبيها برا ال .. ال .. ال .. but إيش عندها؟ the
+
+405
+00:34:10,660 --> 00:34:17,920
+pull out force اللي عندهاis beyond the power of
+
+406
+00:34:17,920 --> 00:34:24,660
+your now aching arms يعني هاد الأن إيدك وجعتك و
+
+407
+00:34:24,660 --> 00:34:30,040
+أنت إيش تشدّي الأن بتيجي تصحب إيدك تعبانة بتلاقيها
+
+408
+00:34:30,040 --> 00:34:35,500
+أكتر من قوة إيدك لأن إيدك من قوة إيدك التعبانة
+
+409
+00:34:35,500 --> 00:34:41,560
+aching arms اللي هي الإيد التعبانة أو الموجوعة the
+
+410
+00:34:41,560 --> 00:34:48,510
+screw might as well be إيش withباكسي ريزين set in
+
+411
+00:34:48,510 --> 00:34:53,730
+اللي هي تبتت هنا أخر واحدة اللي عندي فهذه بتحكي عن
+
+412
+00:34:53,730 --> 00:35:01,650
+تجربة إيش اللي بنعمل في هذا المجال لسه
+
+413
+00:35:01,650 --> 00:35:09,090
+الآن في عندي إيش ال match إيش
+
+414
+00:35:09,090 --> 00:35:16,920
+عندي هنا revet gun اللي هي إيش هذهأيش قلنا عنها؟
+
+415
+00:35:16,920 --> 00:35:22,020
+اللي هي الأداء اللي احنا بنتبث فيها البرشومة فيه
+
+416
+00:35:22,020 --> 00:35:27,280
+سواء لفلات أو لصاليد أو لبلايد
+
+417
+00:35:30,860 --> 00:35:37,460
+الراس اللي هي اللي احنا بنشكلها بعد لما احنا نخلص
+
+418
+00:35:37,460 --> 00:35:40,900
+من البرشومة factory head اللي هي الشجة اللي
+
+419
+00:35:40,900 --> 00:35:45,820
+بتضالها أصلية ال solid rivet اللي هي ال flat هذا
+
+420
+00:35:45,820 --> 00:35:49,360
+ال blind rivet اللي هي ال إيش اللي طويلة زي ال
+
+421
+00:35:49,360 --> 00:35:53,300
+needle a type of fastener that is hollow مين هي
+
+422
+00:35:53,300 --> 00:36:00,770
+اللي هي إيش ال blind riveta type of fastener that
+
+423
+00:36:00,770 --> 00:36:08,330
+is not hollow solid اتول
+
+424
+00:36:08,330 --> 00:36:13,730
+used for installing a type of fastener اللي هي هذه
+
+425
+00:36:13,730 --> 00:36:18,690
+ال rivet gun the white part at the top of the
+
+426
+00:36:18,690 --> 00:36:23,930
+rivet present when the rivet is supplied اللي هي
+
+427
+00:36:23,930 --> 00:36:30,400
+إيش هذهطلع على الكلمة، الكلمة بتقولك على طول، when
+
+428
+00:36:30,400 --> 00:36:33,780
+the revet is supplied، لما انتيجي من المصنع، يعني
+
+429
+00:36:33,780 --> 00:36:40,060
+ايش بتكون factory head، الان the part of the
+
+430
+00:36:40,060 --> 00:36:43,400
+bottom of the revet formed after the revet is ..
+
+431
+00:36:43,400 --> 00:36:49,410
+اللي هي ايش؟ ال shop headعلى اية حال اللي بتطلع
+
+432
+00:36:49,410 --> 00:36:52,110
+عليه .. هاي ال video موجود على الصفحة تطلع عليه
+
+433
+00:36:52,110 --> 00:36:59,310
+بيعطيكوا فكرة عن اللي بنتكلم عنه، أي اشي بتطلع
+
+434
+00:36:59,310 --> 00:37:01,990
+عليه بتشوف الصورة سهل جدا تستوعبوه
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/cm_F4Z_jq78.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/cm_F4Z_jq78.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e5c87fc369bc4de6865253b07a1609bfcf1809d7
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/cm_F4Z_jq78.srt
@@ -0,0 +1,1199 @@
+1
+00:00:23,690 --> 00:00:30,090
+دجيتال وورتا حلو حلو الحلو الحلو الحلو
+
+2
+00:00:31,390 --> 00:00:36,470
+اليوم سنتحدث عن القصة الـ 28، القصة الـ 28 تتحدث عن 
+
+3
+00:00:36,470 --> 00:00:42,050
+مجموعات غير ميكانية، يعني في الـ 27 و 26 تحدثنا عن
+
+4
+00:00:42,050 --> 00:00:47,650
+مجموعات ميكانية، تحدثنا عن مفاتيح ومفاتيح ومفاتيح
+
+5
+00:00:47,650 --> 00:00:53,380
+اليوم سنتحدث عن مجموعات غير ميكانية مع الـ non-
+
+6
+00:00:53,380 --> 00:00:56,700
+mechanical، نحن نتكلم عن الويلدنج ومشروع الهواء
+
+7
+00:00:56,700 --> 00:00:58,240
+ومشروع الهواء ومشروع الهواء ومشروع الهواء ومشروع 
+
+8
+00:00:58,240 --> 00:01:06,120
+الهواء ومشروع الهواء ومشروع الهواء ومشروع 
+
+9
+00:01:06,120 --> 00:01:10,060
+الهواء ومشروع الهواء ومشروع الهواء ومشروع الهواء
+
+10
+00:01:10,060 --> 00:01:13,400
+ومشروع الهواء ومشروع الهواء ومشروع الهواء ومشروع
+
+11
+00:01:13,400 --> 00:01:23,550
+الهواء ومشفانا لما أعمل joining لها بستخدم الحرارة
+
+12
+00:01:23,550 --> 00:01:29,250
+وعادة في مادة بنسميها filler تنزل في النص عندهم
+
+13
+00:01:29,770 --> 00:01:32,570
+The heat melts the edges of the components being
+
+14
+00:01:32,570 --> 00:01:35,670
+welded together and once the material becomes
+
+15
+00:01:35,670 --> 00:01:42,330
+molten, fusion occurs، يعني إيش بيصير؟ أنا بسيح
+
+16
+00:01:42,330 --> 00:01:46,430
+النقاط اللي بتلتقي هدول من الحرارة، فإيش بيصير؟
+
+17
+00:01:46,430 --> 00:01:53,620
+بيصير مادة سائلة، المادة السائلة هاي إيش بتعمل؟ بتُم
+
+18
+00:01:53,620 --> 00:01:59,180
+ربطها أو حامها مع بعض، الآن هذه لما في خلال هذا
+
+19
+00:01:59,180 --> 00:02:03,740
+اللي بيصير تلاحم fusion اللي هي إيش fusion تلاحم
+
+20
+00:02:03,740 --> 00:02:10,460
+يعني بالالتحام مع بعض، طيب when the joint fuses
+
+21
+00:02:10,460 --> 00:02:13,680
+material from each component is mixed together
+
+22
+00:02:13,680 --> 00:02:18,140
+joining to mix together, joining to form a solid
+
+23
+00:02:18,140 --> 00:02:23,600
+well، الآن لما هدول يسيحوا إيش بتسووا؟ بتدخلوا مع 
+
+24
+00:02:23,600 --> 00:02:30,740
+بعض، الآن اللي بتعمله، هذه المنطقة بيصير صلبة
+
+25
+00:02:30,740 --> 00:02:35,940
+metal is often welded, it is also possible to weld
+
+26
+00:02:35,940 --> 00:02:41,820
+plastic، عادة هذا للمواد المعدنية، الـ plastic 
+
+27
+00:02:41,820 --> 00:02:44,440
+أحيانًا بنعمله، بس مش كتير
+
+28
+00:02:48,950 --> 00:02:51,950
+Welding is usually used to join components of the
+
+29
+00:02:51,950 --> 00:02:55,570
+same base metals، نفس النوع عادة مع الحديده
+
+30
+00:02:55,570 --> 00:03:00,230
+بنستخدمه أكثر، أشهر مع الستيل Iron and steel بنعمل 
+
+31
+00:03:00,230 --> 00:03:07,090
+عملية الالتحام، نوع المعدن لما نعمل الـ joints
+
+32
+00:03:07,090 --> 00:03:11,190
+بنعملها من نفس نوع المعدن، هذه أشهر أساسية، that is
+
+33
+00:03:11,190 --> 00:03:13,670
+the metal the components are made of، it is
+
+34
+00:03:13,670 --> 00:03:18,110
+possible though more and more difficult to weld
+
+35
+00:03:18,110 --> 00:03:22,960
+certain dissimilar materials، يعني ممكن نعمل لحم
+
+36
+00:03:22,960 --> 00:03:29,300
+مواد مختلفة، مثلًا نحاس مع الـ steel أو نحاس مع الـ
+
+37
+00:03:29,300 --> 00:03:34,240
+brass أو مع الـ .. يعني مادة ثانية مختلفة، فممكن
+
+38
+00:03:34,240 --> 00:03:40,020
+عملها، بس هذه فيها شوية صعوبة، ليش؟ لأن معامل
+
+39
+00:03:40,020 --> 00:03:45,740
+التمدد تبعها والانكماش بيختلف، فهذه بيخليهم لما 
+
+40
+00:03:45,740 --> 00:03:50,920
+نيبردوا كل واحد يعني يبرد بدرجة بتختلف عن الثاني
+
+41
+00:03:50,920 --> 00:03:56,640
+وهذا بتعمل شوية تشقق وبتخلي الـ joints ضعيفة، for
+
+42
+00:03:56,640 --> 00:04:00,080
+example، copper can be welded to steel، often a
+
+43
+00:04:00,080 --> 00:04:03,420
+filler is added during the welding، عادة لما احنا
+
+44
+00:04:03,420 --> 00:04:07,320
+نستخدم حاجة مختلفة زي هيك بنحط مادة بنسميها اللي 
+
+45
+00:04:07,320 --> 00:04:12,020
+هي اللي بنصهرها بنسميها الـ filler، فليش؟ عشان هذه هي 
+
+46
+00:04:12,020 --> 00:04:16,380
+اللي تنصهر، اللي لها نفس معامل التمدد مش
+
+47
+00:04:16,380 --> 00:04:22,200
+التانيات اللي بنصهرهن، This is a new material of
+
+48
+00:04:22,200 --> 00:04:24,860
+the same type as the base metal which is melted
+
+49
+00:04:24,860 --> 00:04:29,860
+into the weld ball، هذه نفسها اللي بتتم عمل البحيرة
+
+50
+00:04:29,860 --> 00:04:35,520
+اللي بيسميها بحيرة المادة تبعت الحام، The molten
+
+51
+00:04:35,520 --> 00:04:39,820
+metal are the joints during the welding
+
+52
+00:04:43,260 --> 00:04:46,180
+Common gas and arc welding techniques، Shielded
+
+53
+00:04:46,180 --> 00:04:51,680
+metal arc welding اللي شفتها قبل شوية في الفقرة
+
+54
+00:04:51,680 --> 00:04:57,440
+one problem in welding is discontinuity اللي هي
+
+55
+00:04:57,440 --> 00:05:05,810
+إيش بيصير؟ أيوة بيصير إنه أيوة في حق في فراغات اللي
+
+56
+00:05:05,810 --> 00:05:10,110
+عندي، where joints are not completely solid، يعني هي
+
+57
+00:05:10,110 --> 00:05:16,470
+مش كلها مليانة، بتلاقي فراغات، أو هي، another problem
+
+58
+00:05:16,470 --> 00:05:20,410
+is residual stress، الـ residual stress إيش بيصير؟
+
+59
+00:05:20,410 --> 00:05:24,810
+ضغط على بعض المناطق، يعني أنا لما ألحم أحيانًا بعض
+
+60
+00:05:24,810 --> 00:05:28,110
+بلحم الـ joints بيصير جوية منطقة ثانية اللي فوقها
+
+61
+00:05:28,110 --> 00:05:33,810
+أو اللي جنبها بيصير إيش ضعيفة من تأثير الحرارة، هذه
+
+62
+00:05:33,810 --> 00:05:38,990
+القوة مثلًا، تنشأ محطمة حول الجمعات، وهذا المشكلة
+
+63
+00:05:38,990 --> 00:05:44,690
+تحدث بعد الـ welding بسبب التدخل في منطقة الـ welding
+
+64
+00:05:44,690 --> 00:05:51,000
+عادة ما يحدث هذا عملية الـ link mesh لما يصير تبرد
+
+65
+00:05:51,000 --> 00:05:54,580
+الحام هذه المادة الانصهار تبرد، إيش بتسوي؟ بتشد
+
+66
+00:05:54,580 --> 00:05:57,960
+حاجة، منطقة ثانية، بتصير المنطقة هذه عليها ضغط
+
+67
+00:05:57,960 --> 00:06:02,240
+ضعيفة، فممكن تنكسر بسهولة، ويمكن اللي بـ .. اللي
+
+68
+00:06:02,240 --> 00:06:05,000
+بلحم هو بشوف الناس اللي بتلحم بشوف في بعض المنطقة
+
+69
+00:06:05,000 --> 00:06:09,560
+هو لحم حاجة وبعد يومين حاجة ثانية فرضت، هذا بيبقى
+
+70
+00:06:09,560 --> 00:06:15,800
+اللي .. اللي بلحم إيش؟ إنه عملية الانصهار أضعف ..
+
+71
+00:06:15,800 --> 00:06:21,270
+أضعف منطقة ثانية من ورا هذه الشغلة، هذا المشكلة حصلت
+
+72
+00:06:21,270 --> 00:06:26,030
+بعد التبريد بسبب التوتر في منطقة التبريد أو
+
+73
+00:06:26,030 --> 00:06:32,010
+المنطقة المبردة، المنطقة التي كانت تبرّد البحر، It can
+
+74
+00:06:32,010 --> 00:06:36,250
+also occur in the heat affected zone، the material
+
+75
+00:06:36,250 --> 00:06:39,530
+close to the weld ball which is subject to high
+
+76
+00:06:39,530 --> 00:06:43,090
+temperature and was modified by the heat، المنطقة
+
+77
+00:06:43,090 --> 00:06:47,350
+اللي قريبة من منطقة الحرارة اللي انصهار حرارة 
+
+78
+00:06:47,350 --> 00:06:52,230
+عالية بتصير بتتأثر من درجة الحرارة الموجودة فبتصير
+
+79
+00:06:52,230 --> 00:06:57,440
+فيها ضعف لأن هي نفسها صارت انصهارت وصارت أضعف من
+
+80
+00:06:57,440 --> 00:07:00,840
+الوضع اللي كانت عليه، common gas and arc welding
+
+81
+00:07:00,840 --> 00:07:04,480
+technique، shielding metal، arc welding اللي هي
+
+82
+00:07:04,480 --> 00:07:09,200
+أول نوع من في الـ electrical اللي اتكلم عنه SMAW،
+
+83
+00:07:09,200 --> 00:07:12,000
+generally called arc welding or stick welding
+
+84
+00:07:12,000 --> 00:07:16,760
+involves striking an electrical arc between the
+
+85
+00:07:16,760 --> 00:07:21,820
+workpieces and electrode and electrical conductor
+
+86
+00:07:21,820 --> 00:07:28,790
+عادة بتلاحظ إيش بيفـ .. بيفسوي؟ بربط السالب في حديد
+
+87
+00:07:28,790 --> 00:07:33,070
+موجودة وهذاك اللي عنده هو الأنود الموجب اللي بيجي
+
+88
+00:07:33,070 --> 00:07:36,510
+لما يسويها ولازم يكون في عندك electricity عشان
+
+89
+00:07:36,510 --> 00:07:42,390
+تعمل الـ arc اللي هي الشرارة الموجودة، The
+
+90
+00:07:42,390 --> 00:07:45,410
+electrode consists of welding rod، a stick of
+
+91
+00:07:45,410 --> 00:07:49,190
+metal of the same type as the workpiece، عادة في
+
+92
+00:07:49,190 --> 00:07:53,180
+بعض الناس إيش بيجيبوا سلوك إذا لاحظتوا اللي بدونش
+
+93
+00:07:53,180 --> 00:07:57,640
+يستخدم .. الآن احنا في غزة السيوخ الحام مش موجودة،
+
+94
+00:07:57,640 --> 00:08:02,660
+إيش بيستخدموا؟ سلوك عادية من الـ steel، هدول بيجي
+
+95
+00:08:02,660 --> 00:08:08,860
+بيستخدموها ومنها بلحم لأن هذا إيش متوفرة، تلزمش
+
+96
+00:08:08,860 --> 00:08:12,480
+تعملها، فـ it's the same material اللي عندي which
+
+97
+00:08:12,480 --> 00:08:15,700
+provide the filler، the welding rod is therefore
+
+98
+00:08:15,700 --> 00:08:18,980
+consumable، يعني هذا الـ welding rod اللي هي العمود
+
+99
+00:08:18,980 --> 00:08:24,230
+اللي .. اللي احنا بنلحم فيه بتم استهلاكه، it is used
+
+100
+00:08:24,230 --> 00:08:28,410
+up، the rod is also coated with a material called
+
+101
+00:08:28,410 --> 00:08:33,990
+flux، الآن السيخ اللي بنشتريه هو مادة من نفس مادة
+
+102
+00:08:33,990 --> 00:08:40,250
+الحديد، الآن في حاجة أشبه هذا coated up مغلف بطبقة
+
+103
+00:08:40,250 --> 00:08:45,270
+من الـ flux، طبقة هاي، when heated this produces a
+
+104
+00:08:45,270 --> 00:08:53,310
+shielding gas، هذه بتعمل غاز، غاز لحماية أو بيغطي
+
+105
+00:08:53,310 --> 00:09:00,690
+shield اللي هي حاجة بتغطي أو بتحمي المادة المنصهرة
+
+106
+00:09:00,690 --> 00:09:06,280
+اللي حصلت، Which protects the molten metal from
+
+107
+00:09:06,280 --> 00:09:10,060
+oxygen. Without this gas, the hot metal would
+
+108
+00:09:10,060 --> 00:09:13,620
+combine with the oxygen in the air and this would
+
+109
+00:09:13,620 --> 00:09:14,820
+weaken the weld
+
+110
+00:09:23,100 --> 00:09:28,200
+المنطقة اللي لحموا فيها فبتلاقي هذه بتبدأ في منطقة
+
+111
+00:09:28,200 --> 00:09:32,000
+بتجيب الباب والباب بيبقى جايبها مقالفة حديد
+
+112
+00:09:32,000 --> 00:09:36,280
+مقالفة وكل شيء لما نلحم بهذه بتلاقي نقطة الحام هي
+
+113
+00:09:36,280 --> 00:09:40,860
+أضعف منطقة موجودة، فإيش بيعملوا بعدها الحداد الشاطر
+
+114
+00:09:40,860 --> 00:09:46,530
+بدهنها على طول عشان يعمل protective layer الموجودة
+
+115
+00:09:46,530 --> 00:09:50,810
+بس هي already اكسدت لأن أنت لما تعرضيها لحرارة
+
+116
+00:09:50,810 --> 00:09:54,630
+عالية الـ oxygen موجود في الجو على طول بأكسدها فهي
+
+117
+00:09:54,630 --> 00:10:01,670
+سيخ الحام هذا بحميها من عملية الـ accident هذه
+
+118
+00:10:01,670 --> 00:10:04,470
+الفيديوهات اللي فرجناها وأنا فرجناها صورة أحسن
+
+119
+00:10:04,470 --> 00:10:10,630
+منها، in gas welding heat comes لأن بيبقى الغاز اللي
+
+120
+00:10:10,630 --> 00:10:16,770
+بيسميها الحام
+
+121
+00:10:16,770 --> 00:10:20,330
+بالأكسجين، in gas welding heat comes from a torch
+
+122
+00:10:20,330 --> 00:10:26,860
+which burns oxyfuel اللي بيجي إيش؟ بتشعل اللي هي الـ
+
+123
+00:10:26,860 --> 00:10:31,800
+oxygen، a mixture of oxygen and a gas fuel، the gas
+
+124
+00:10:31,800 --> 00:10:35,380
+fuel burn much hotter in oxygen than it would be
+
+125
+00:10:35,380 --> 00:10:39,720
+in air، لما أنا أضيف الـ oxygen لها بتعطي درجة حرارة 
+
+126
+00:10:40,150 --> 00:10:45,350
+أعلى أو اشتعال أعلى the most common fuel is
+
+127
+00:10:45,350 --> 00:10:50,130
+acetylene called oxyacetylene which mixes with
+
+128
+00:10:50,130 --> 00:10:54,250
+oxygen welding rods provide filler but the flux is
+
+129
+00:10:54,250 --> 00:10:57,670
+not required as burning oxy fuel produces carbon
+
+130
+00:10:57,670 --> 00:11:02,410
+dioxide which acts as a shielding gas يعني هذه عادة 
+
+131
+00:11:02,410 --> 00:11:08,620
+في سيخبستخدمه اللي هو تقريباً مش حديد صلب هائل هان 
+
+132
+00:11:08,620 --> 00:11:12,920
+زي الخرسين أو الرصاص اللي بيستخدمه فهذا بيستخدمه 
+
+133
+00:11:12,920 --> 00:11:17,480
+إيش؟ ليعمل filler اللي هي يلحم فيه يعني هو المادة 
+
+134
+00:11:17,480 --> 00:11:22,100
+اللي بتسيح الآن لما تلاحظوا هان كان قبل قولنا مادة 
+
+135
+00:11:22,100 --> 00:11:26,540
+العازلة في ال oxygen هذه اللي بيصير production 
+
+136
+00:11:26,540 --> 00:11:30,540
+مادة ثانية أكسيد الكربون هي اللي بتعمل العزل 
+
+137
+00:11:30,540 --> 00:11:37,340
+the shielding المطلوب In gas metal arc welding often
+
+138
+00:11:37,340 --> 00:11:42,840
+called MIG welding, metal inert gas هاي ال MIG،
+
+139
+00:11:42,840 --> 00:11:47,150
+metal inert gas يعني أنا بدخل إيش؟ الـ metal
+
+140
+00:11:47,150 --> 00:11:50,410
+اللي هي المعدن an arc is struck between the
+
+141
+00:11:50,410 --> 00:11:53,170
+workpiece and the wire which is made of the same
+
+142
+00:11:53,170 --> 00:11:56,530
+metal as the base metal نفس نوع ال base الموجود
+
+143
+00:11:56,530 --> 00:12:00,130
+اللي عندي this wire acts as a consumable electrode
+
+144
+00:12:00,130 --> 00:12:04,310
+برضه هذه في ال MIG ال .. ال .. ال rod اللي بحطها 
+
+145
+00:12:04,310 --> 00:12:08,030
+هذه اللي هي ال filler is consumable يتم استهلاكها
+
+146
+00:12:09,270 --> 00:12:13,110
+supplying a filler a shield gas often argon is
+
+147
+00:12:13,110 --> 00:12:17,290
+blown onto the weld pool يعني بعد ما انتهوا فيه
+
+148
+00:12:17,290 --> 00:12:23,130
+غاز لازم يضيفه عشان يعمل الشيلنج وهذا عادة الشيلنج 
+
+149
+00:12:23,130 --> 00:12:31,350
+بنعمل من غاز الأرجون In gas tungsten arc welding
+
+150
+00:12:31,350 --> 00:12:35,550
+اللي بنسمي TIG, often called TIG welding, tungsten
+
+151
+00:12:35,550 --> 00:12:39,730
+inert gas and arc comes from an electrode made of
+
+152
+00:12:39,730 --> 00:12:44,190
+tungsten اللي عندي However, the tungsten is non
+
+153
+00:12:44,190 --> 00:12:50,010
+consumable، هذه هي رأس، عادة ال tungsten مش سهل 
+
+154
+00:12:50,010 --> 00:12:55,630
+تسيحه فعشان هي كهذا بيظلوا إيش؟ موجود، هو بيعمل ال
+
+155
+00:12:55,630 --> 00:13:00,090
+arc، it does not melt and it's not consumed as
+
+156
+00:13:00,090 --> 00:13:02,950
+filler during the welding process، a separate
+
+157
+00:13:02,950 --> 00:13:05,870
+welding rod is used to supply the filler، بيجي فيه
+
+158
+00:13:05,870 --> 00:13:13,880
+عندي سيخ ثاني هو اللي بنسيحه عشان يعمل اللحام أزمج
+
+159
+00:13:13,880 --> 00:13:17,420
+welding a shielding gas such as argon is applied
+
+160
+00:13:17,420 --> 00:13:21,280
+onto the weld يعني هذا في الغاز هو اللي بتتم
+
+161
+00:13:21,280 --> 00:13:29,590
+توجيهه نحو المادة عملية اللحام فبتعمل shield الآن
+
+162
+00:13:29,590 --> 00:13:32,130
+نجي نستخدم الكلمات التالية هنا base,
+
+163
+00:13:32,410 --> 00:13:36,130
+discontinuity, dissimilar, fuse, heat affected,
+
+164
+00:13:36,230 --> 00:13:40,170
+material, metal, residue, weld, molten, stress,
+
+165
+00:13:40,570 --> 00:13:46,110
+welded, pool, together وزود الآن ممكن نستخدم
+
+166
+00:13:46,110 --> 00:13:49,810
+الكلمة أكثر من مرة هنا it is possible for a
+
+167
+00:13:49,810 --> 00:13:53,850
+component made of different material to be لو احنا
+
+168
+00:13:53,850 --> 00:13:58,290
+استخدمنا مواد مختلفة، إيش ممكن نعمل لهم؟ welded
+
+169
+00:13:58,290 --> 00:14:01,830
+together ممكن احنا نلحمهم مع بعض for instance
+
+170
+00:14:01,830 --> 00:14:08,250
+steel can be welded to copper الحديد مع نحاس and
+
+171
+00:14:08,250 --> 00:14:15,670
+two brass حديد مع نحاس بيعمل ال brass however
+
+172
+00:14:15,670 --> 00:14:19,290
+it's much more difficult to weld component made of
+
+173
+00:14:19,290 --> 00:14:25,890
+two dissimilar materials يعني هاد ممكن احنا نعمل
+
+174
+00:14:25,890 --> 00:14:31,390
+إيش من مواد مختلفة أصعب من الهاد then it is to
+
+175
+00:14:31,390 --> 00:14:36,910
+weld those made of the same هذه الكلمات مرت علينا
+
+176
+00:14:36,910 --> 00:14:43,210
+قبل شوية base metal من نفس المعدن نفس قاعدة المعدن
+
+177
+00:14:43,210 --> 00:14:46,970
+while there is no difficulty in melting two
+
+178
+00:14:46,970 --> 00:14:51,170
+different metals and mixing them together in إيش؟ 
+
+179
+00:14:51,720 --> 00:14:56,080
+إيش احنا بنعمل فيهم؟ بنصهرهم molten state اللي هي
+
+180
+00:14:56,080 --> 00:14:59,660
+المنصهرة ال problem occur once the hot liquid
+
+181
+00:14:59,660 --> 00:15:04,860
+metal forming the ash start to cool إيش احنا قولنا
+
+182
+00:15:04,860 --> 00:15:10,720
+عنها بها؟ بحيرة المادة اللحام اللي هي whirl pool
+
+183
+00:15:10,720 --> 00:15:11,880
+بنسميها
+
+184
+00:15:13,760 --> 00:15:18,200
+as this process takes place two metals will not
+
+185
+00:15:18,200 --> 00:15:18,940
+necessarily
+
+186
+00:15:30,060 --> 00:15:36,160
+لما ينصهروا ويتلحموا مع بعض الآن احنا هنا بنقول as
+
+187
+00:15:36,160 --> 00:15:38,540
+this process takes place two metals will not
+
+188
+00:15:38,540 --> 00:15:42,940
+necessarily fuse properly يعني مش بالضرورة انه 
+
+189
+00:15:42,940 --> 00:15:46,960
+يلتحموا بشكل جيد مع بعض once the joint has cooled
+
+190
+00:15:46,960 --> 00:15:50,480
+this can result لو ما التحموش مع بعض إيش هتستعمل
+
+191
+00:15:50,480 --> 00:15:57,180
+ليه؟ discontinuity مظبوط هيصير end هنا such as
+
+192
+00:15:57,180 --> 00:16:03,780
+cracks at the heart of ده إيش؟ weld zone، يعني
+
+193
+00:16:03,780 --> 00:16:08,820
+هيصير عندي crack اللي هي تشقق في منطقة إيش؟ منطقة
+
+194
+00:16:08,820 --> 00:16:12,760
+اللحام weld zone .. zone اللي هي منطقة weld zone
+
+195
+00:16:12,760 --> 00:16:17,760
+منطقة اللحام In addition, as the metal contracts at
+
+196
+00:16:17,760 --> 00:16:20,180
+different rates due to different coefficients of
+
+197
+00:16:20,180 --> 00:16:25,340
+thermal expansion. Powerful إيش؟ لما هدولة اتنين
+
+198
+00:16:25,340 --> 00:16:29,800
+كل واحد، إيش بدي يحصل؟ كل واحدة تنكمش معامل يختلف
+
+199
+00:16:29,800 --> 00:16:34,400
+عن الثاني، إيش بدي يصير؟ Residual stress هيصير
+
+200
+00:16:34,400 --> 00:16:39,820
+عنده، ضغط لأنه انت لما تجيبي حاجتين وشوفي هذه تشد
+
+201
+00:16:39,820 --> 00:16:43,940
+وهذه تشد، إيش بدي يصير عندك؟ ضغط على المنطقة اللي
+
+202
+00:16:43,940 --> 00:16:47,260
+.. اللي في النص هذا اللي حصلت فهذا سميناها إيش؟
+
+203
+00:16:47,260 --> 00:16:51,260
+residual stress can build up not only in the
+
+204
+00:16:51,260 --> 00:16:54,680
+joints but also in the wider .. إيش؟ near the
+
+205
+00:16:54,680 --> 00:16:59,280
+joint heat affected area اللي هي كل المنطقة اللي 
+
+206
+00:16:59,280 --> 00:17:07,470
+اتعرضت للحرارة طيب هاي الهاد الآن بنعمل matching
+
+207
+00:17:07,470 --> 00:17:13,990
+between a and b الآن هذه الجزئية اللي هنا الآن كل
+
+208
+00:17:13,990 --> 00:17:17,230
+واحدة من هذه بحثنا طالعة shielded metal arc
+
+209
+00:17:17,230 --> 00:17:22,930
+welding uses shielded إيش بتستخدم تستخدم خلينا نقول
+
+210
+00:17:22,930 --> 00:17:30,590
+burning gas هي consumable electrode تستخدم هذه صح 
+
+211
+00:17:30,590 --> 00:17:35,710
+إيش كمان a non consumable لأ separate welding rod
+
+212
+00:17:35,710 --> 00:17:39,550
+لأ special coating on the welding rod which
+
+213
+00:17:39,550 --> 00:17:43,310
+produces shielded gas مظبوط مش هي اللي stick هذه
+
+214
+00:17:43,310 --> 00:17:49,110
+في حاجة ثانية تقريباً لأ separate gas supply لأ a
+
+215
+00:17:49,110 --> 00:17:55,350
+shielding gas لأ اللي هان gas فهذه تأخذ عندي B وE
+
+216
+00:17:57,050 --> 00:18:03,150
+كويس؟ نهجة gas welding uses إيش الجاز اللي هي تبعت
+
+217
+00:18:03,150 --> 00:18:08,910
+الأكسجيل؟ burning gas مظبوط consumable electrode
+
+218
+00:18:08,910 --> 00:18:14,150
+لأ non consumable electrode لأ separate welding rod
+
+219
+00:18:14,150 --> 00:18:17,590
+which is not an electrode مش فيه له عادة إيه
+
+220
+00:18:17,590 --> 00:18:24,070
+الحاجب المادة بصيحة فهذه مظبوطة إيه دي إيه special
+
+221
+00:18:24,070 --> 00:18:27,810
+coating on the welding rod which reduces لأ if
+
+222
+00:18:27,810 --> 00:18:32,960
+separate gas no shielding gas generated by burned
+
+223
+00:18:32,960 --> 00:18:38,080
+oxy fuel الاسم تبعها على طول بيقول لي oxy fuel a
+
+224
+00:18:38,080 --> 00:18:40,800
+gas whose purpose is to increase the temperature
+
+225
+00:18:40,800 --> 00:18:44,720
+of the welding process اللي هي الأكسجين مش
+
+226
+00:18:44,720 --> 00:18:48,700
+بيستخدموا الأكسجين، الأكسجين إيش غرضه؟ يزود درجة
+
+227
+00:18:48,700 --> 00:18:50,260
+الحرارة، فعندي هذه 
+
+228
+00:18:53,050 --> 00:18:59,870
+DGH كويس الآن gas metal arc welding uses ال arc
+
+229
+00:18:59,870 --> 00:19:04,450
+welding إيش using burning gas a consumable
+
+230
+00:19:04,450 --> 00:19:10,970
+electrode yes هذه a non consumable no a separate
+
+231
+00:19:10,970 --> 00:19:15,710
+welding rod لأ إيه a special coating in the
+
+232
+00:19:15,710 --> 00:19:21,290
+welding rod which producing a gas shield طيب 
+
+233
+00:19:21,620 --> 00:19:24,540
+separate gas supply blown into the weld as a
+
+234
+00:19:24,540 --> 00:19:28,540
+shielding gas صح هذه اللي هي قولنا غاز الأرجون
+
+235
+00:19:28,540 --> 00:19:32,440
+اللي بيستخدموه a shielding gas generated لأ a gas
+
+236
+00:19:32,440 --> 00:19:37,260
+whose purpose to increase لأ عندي يعني هذه B و F
+
+237
+00:19:38,890 --> 00:19:44,290
+Gas tungsten arc welding اللي هي TIG إيش بتستخدم؟
+
+238
+00:19:44,290 --> 00:19:48,990
+مش burning fuel ولا consumable بتستخدم إيش؟ non
+
+239
+00:19:48,990 --> 00:19:53,010
+consumable electrode طب بتستخدم separate welding
+
+240
+00:19:53,010 --> 00:20:02,130
+rod C وD يعني هدولة طيب special coating gas supply
+
+241
+00:20:02,130 --> 00:20:08,250
+separate gas supply blown into yes يعني C D و F
+
+242
+00:20:09,460 --> 00:20:13,520
+هدولة الثلاثة اللي بتتم استخدامها الفيديو الأصلي
+
+243
+00:20:13,520 --> 00:20:19,140
+ركزلكوا يعني بعض الأمور لأن كل هذا اتحدث عنها إيش
+
+244
+00:20:19,140 --> 00:20:25,540
+بنعمل طيب آخر حاجة بدنا نعمل matching إيش هذا
+
+245
+00:20:25,540 --> 00:20:29,520
+بتعني فيها اللي في ال A إيش يقابلها ال flux إيش ال
+
+246
+00:20:29,520 --> 00:20:35,840
+flux هل هو burning gas consumable
+
+247
+00:20:35,840 --> 00:20:41,000
+electrode a non consumable electrode, separate
+
+248
+00:20:41,000 --> 00:20:44,880
+welding, a special coating on the welding rod
+
+249
+00:20:44,880 --> 00:20:49,600
+which producing a shielding gas مظبوط؟ اللي هو
+
+250
+00:20:49,600 --> 00:20:55,120
+بيعملي هذه المادة بتبقى موجودة على ال .. خلّيني 
+
+251
+00:20:55,120 --> 00:20:59,540
+أقول أصبع الحام اللي هي بتعملي الغاز اللي بيعمل 
+
+252
+00:20:59,540 --> 00:21:06,620
+shielding للموجود فهي إيه؟ طب argon إيش هي بتعمل؟ 
+
+253
+00:21:06,620 --> 00:21:10,540
+separate gas supply blown onto اللي هي F اللي هو
+
+254
+00:21:10,540 --> 00:21:13,840
+غاز الارغون اللي هو بيجي بعد الهيليوم في العائلة
+
+255
+00:21:13,840 --> 00:21:20,300
+تبعته هدا ذاكرين؟ هيدروجين هيليوم ارغون طيب الآن
+
+256
+00:21:20,300 --> 00:21:27,380
+عندي ال tungsten إيش هو؟ non consumable ال oxygen
+
+257
+00:21:27,380 --> 00:21:34,330
+اللي هو إيش عبارة؟ burn ال gas مظبوط والا لأ؟ لأ مش 
+
+258
+00:21:34,330 --> 00:21:38,170
+ال burning gas هو separate هو اللي بيعمل الجاز هو
+
+259
+00:21:38,170 --> 00:21:42,490
+purpose to increase the temperature H طيب الآن
+
+260
+00:21:42,490 --> 00:21:47,730
+tungsten non consumable electrode ال acetylene
+
+261
+00:21:47,730 --> 00:21:51,430
+اللي هي إيش ال burning gas اللي هو الغاز اللي بيتم
+
+262
+00:21:51,430 --> 00:21:56,930
+حرقه في عملية اللحم بالغاز carbon dioxide إيش
+
+263
+00:21:56,930 --> 00:22:01,970
+بيعملناه؟ Shielding gas generated
+
+264
+00:22:01,970 --> 00:22:06,430
+by burning oxy-fuel اللي هي المادة اللي عندنا،
+
+265
+00:22:06,430 --> 00:22:11,090
+الآن إيش احنا بنطلع؟ شفنا يعني ليهم عملية الحام،
+
+266
+00:22:11,090 --> 00:22:16,870
+هي قولنا هي non-mechanical joint بتعمل، طلعنا على
+
+267
+00:22:16,870 --> 00:22:22,590
+الأنواع الخامسة، إيش قولنا أول واحدة؟ في نوع اللي
+
+268
+00:22:22,590 --> 00:22:26,910
+هي الـ oxy fuel welding ال oxy fuel اللي بنستخدم
+
+269
+00:22:26,910 --> 00:22:31,150
+مادة ال oxygen to increase the temperature و ال
+
+270
+00:22:31,150 --> 00:22:35,290
+acetylene as a burning gas وبطلع عندنا ال shield
+
+271
+00:22:35,290 --> 00:22:41,290
+هو عبارة عن إيش؟ عن الـ shield اللي يعطينا أقصد
+
+272
+00:22:41,290 --> 00:22:44,850
+carbon dioxide المادة اللي بتعملنا shielding
+
+273
+00:22:44,850 --> 00:22:49,930
+لعملية اللحم النوع التاني اللي سمنها stick welding
+
+274
+00:22:49,930 --> 00:22:53,750
+اللي هي stick arc welding اللي عندى سيخ الحديد
+
+275
+00:22:53,750 --> 00:22:58,330
+اللي مغلف بمادة flux أو بغلف مادة المادة هي لما
+
+276
+00:22:58,330 --> 00:23:03,960
+يسيح بتعمل protection للموجود عندى، بس بالزمن إيش؟
+
+277
+00:23:03,960 --> 00:23:07,600
+ال stick هادى، و لو ماعملتش ب stick المادة اللى
+
+278
+00:23:07,600 --> 00:23:11,340
+بلحمهم هدول عادة من نفس النوع بتصير علها عملية
+
+279
+00:23:11,340 --> 00:23:15,660
+أكسدة ده بتصير ضعيفة الآن إيش اتكلمنا عن النوع
+
+280
+00:23:15,660 --> 00:23:19,300
+التالت اللي هي الـ mig أو ال flux الـ mig و ال flux
+
+281
+00:23:19,300 --> 00:23:23,460
+هذه بتلزم عند ال electrode بين صهر و في عندى بتنزل
+
+282
+00:23:23,460 --> 00:23:27,660
+المادة اللي هي بتعمل عازلة و عادة بتعمل generation
+
+283
+00:23:27,660 --> 00:23:31,440
+للغاز اللي بعزل اللي هو عادة يا اما ارغون يا اما
+
+284
+00:23:31,440 --> 00:23:37,390
+ارغون plus carbon dioxide الـ TIG اللي بنستخدمه
+
+285
+00:23:37,390 --> 00:23:43,210
+تنجستين تنجستين هذا هو non consumable بسيحش فيه
+
+286
+00:23:43,210 --> 00:23:46,430
+مادة ال filler اللي بنحطها و عادة بنعمل في
+
+287
+00:23:46,430 --> 00:23:51,250
+separate channel بنعمل الغاز اللي بنضخ عليه اللي
+
+288
+00:23:51,250 --> 00:23:55,550
+هو غاز ال argon في هذا المجلد الآن عملية ال
+
+289
+00:23:55,550 --> 00:24:03,810
+welding بتحصل لو أنا في مشكلتين بتحصل فيها عادة لو
+
+290
+00:24:03,810 --> 00:24:06,650
+أنا المواد اللي .. اللي .. اللي أنا بلحن فيها مش
+
+291
+00:24:06,650 --> 00:24:10,910
+من نفس النوع إيش بيصير لكل واحدة معامل باختلاق two
+
+292
+00:24:10,910 --> 00:24:16,230
+different material إيش اللي بيحصل عندك؟ و في معاملة
+
+293
+00:24:16,230 --> 00:24:22,950
+التمدد أحياناً تحصل فيه discontinuity، وهذا سيجعل
+
+294
+00:24:22,950 --> 00:24:26,990
+الوضع 
+
+295
+00:24:26,990 --> 00:24:33,250
+أضعف عملية الهام و الحاجة التانية اللي ممكن تحصل
+
+296
+00:24:33,250 --> 00:24:41,010
+برضه أن الـ heat effected zone بتعمل أن تضعف، ت
+
+297
+00:24:41,010 --> 00:24:45,410
+weaken ال area surrounding عملية الولدة، هذا مختصر
+
+298
+00:24:45,410 --> 00:24:49,390
+المحاضرة، تتفرجوا على الفيديو الموجود، بيدكركم
+
+299
+00:24:49,390 --> 00:24:55,330
+بمعظم هذه العبارات الموجودة، كويس هيك؟ يعطيكوا
+
+300
+00:24:55,330 --> 00:24:55,790
+العافية 
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/h4Be7E6BT60.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/h4Be7E6BT60.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6d58062a23eac58484893ac6bd014a1a04d2d346
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/h4Be7E6BT60.srt
@@ -0,0 +1,1509 @@
+1
+00:00:20,770 --> 00:00:26,170
+السلام عليكم اليوم سوف نتكلم عن حلقة 11 حلقة 11
+
+2
+00:00:26,170 --> 00:00:31,990
+تتكلم عن نوعات المواد المواد المواد المواد المواد
+
+3
+00:00:31,990 --> 00:00:33,190
+المواد المواد المواد المواد المواد المواد المواد
+
+4
+00:00:33,190 --> 00:00:33,570
+المواد المواد المواد المواد المواد المواد المواد
+
+5
+00:00:33,570 --> 00:00:34,550
+المواد المواد المواد المواد المواد المواد المواد
+
+6
+00:00:34,550 --> 00:00:34,810
+المواد المواد المواد المواد المواد المواد المواد
+
+7
+00:00:34,810 --> 00:00:35,090
+المواد المواد المواد المواد المواد المواد المواد
+
+8
+00:00:35,090 --> 00:00:35,190
+المواد المواد المواد المواد المواد المواد المواد
+
+9
+00:00:35,190 --> 00:00:36,910
+المواد المواد المواد المواد المواد المواد المواد
+
+10
+00:00:36,910 --> 00:00:45,530
+المواد المواد المواد المواد
+
+11
+00:00:46,890 --> 00:00:52,770
+أيوة examples of non-metallic materials are carbon
+
+12
+00:00:52,770 --> 00:00:57,170
+and silicon and 
+
+13
+00:00:57,170 --> 00:01:01,450
+iron is such a widely used material. Metals can be
+
+14
+00:01:01,450 --> 00:01:07,150
+divided into two. The metals, ferrous metals, those
+
+15
+00:01:07,150 --> 00:01:12,780
+that contain iron. يعني إيش بنسميها هاي اللي هو
+
+16
+00:01:12,780 --> 00:01:17,600
+المعادن التي تحتوي على حديد بنسميها ferrous. Non-
+
+17
+00:01:17,600 --> 00:01:22,560
+-ferrous metals, those that do not contain iron.
+
+18
+00:01:22,560 --> 00:01:29,620
+النوع الثاني with regard to... now we're gonna talk
+
+19
+00:01:29,620 --> 00:01:34,560
+about elements, compounds and mixtures. ثلاثة هذه
+
+20
+00:01:34,560 --> 00:01:40,650
+elements العناصر, compounds مركبات, and mixtures الخليط.
+
+21
+00:01:40,650 --> 00:01:45,370
+With regard to the chemical composition of material
+
+22
+00:01:45,370 --> 00:01:49,410
+the chemicals they contain and how the chemicals
+
+23
+00:01:49,410 --> 00:01:53,510
+are combined. يعني ال composition اللي هي التكوينة 
+
+24
+00:01:53,510 --> 00:01:59,420
+three main categories can be used. Elements are pure 
+
+25
+00:01:59,420 --> 00:02:03,860
+materials in their most basic form. They cannot be
+
+26
+00:02:03,860 --> 00:02:07,680
+broken down into different constituents or
+
+27
+00:02:07,680 --> 00:02:10,860
+ingredients. يعني هدول العناصر اللي بنقدرش إن
+
+28
+00:02:10,860 --> 00:02:16,740
+نفصلهم أو بنقدرش إن... يعني هدولها pure فيش... يعني
+
+29
+00:02:16,740 --> 00:02:21,640
+فيش إمكانية إنه نفصلهم لجزئيات أخرى أو عناصر أخرى،
+
+30
+00:02:21,640 --> 00:02:27,260
+فبيسميها العناصر و constituent أو ingredients اللي 
+
+31
+00:02:27,260 --> 00:02:32,800
+هي التركيبات أو المكونات، كويس؟ Examples of
+
+32
+00:02:32,800 --> 00:02:36,160
+elements widely used in engineering materials are
+
+33
+00:02:36,160 --> 00:02:42,610
+iron, carbon, aluminium. Compounds consist of two or
+
+34
+00:02:42,610 --> 00:02:45,990
+more elements that are chemically bound. المفروض
+
+35
+00:02:45,990 --> 00:02:53,410
+مركبات إيش؟ اتنين أو أكثر؟ chemically bound إيش
+
+36
+00:02:53,410 --> 00:03:00,650
+يعني؟ التركيبة أو اللي احنا بنقول يتحدوا مع بعض
+
+37
+00:03:00,650 --> 00:03:06,110
+بطريقة كيميائية. يعني إيش الاتحاد الكيميائي؟ يعني بدك
+
+38
+00:03:06,110 --> 00:03:10,170
+تفصليهم، بدك تفصليهم كيميائيا، يعني بدك عملية
+
+39
+00:03:10,170 --> 00:03:13,430
+كيميائية لفصلهم. That is combined by a chemical
+
+40
+00:03:13,430 --> 00:03:19,560
+reaction. And everyday example is water. الميه عبارة
+
+41
+00:03:19,560 --> 00:03:24,460
+عن إيش؟ Oxygen and Hydrogen، مظبوط. الآن هدول اللي
+
+42
+00:03:24,460 --> 00:03:28,360
+هفصلهم بيدعمل عملية كيميائية، ما بينفصلوش لحالهم،
+
+43
+00:03:28,360 --> 00:03:32,040
+ما بيجيش يقول هاي ال hydrogen لحاله، هزلهم و هاي ال
+
+44
+00:03:32,040 --> 00:03:37,960
+oxygen لحاله، which is a compound of hydrogen and
+
+45
+00:03:37,960 --> 00:03:44,220
+oxygen. Mixtures consist of two or more elements or
+
+46
+00:03:44,220 --> 00:03:49,220
+compounds which are mixed together but which
+
+47
+00:03:49,220 --> 00:03:53,620
+are not chemically bound. هدولة خلطناهم مع بعض بس
+
+48
+00:03:53,620 --> 00:03:58,600
+ما اتحدوش مع بعض. يعني كل واحد لحاله. In engineering
+
+49
+00:03:58,600 --> 00:04:05,940
+common examples are alloys. إيش يعني؟ طلع التفسير
+
+50
+00:04:05,940 --> 00:04:12,620
+تبعهم. Metal which have other metals and/or non-
+
+51
+00:04:12,620 --> 00:04:18,040
+-metals mixed together. يعني حاطينا حاجة عليهم الآن.
+
+52
+00:04:18,040 --> 00:04:24,020
+A common example is steel. Steel إيش هو؟ which is
+
+53
+00:04:24,020 --> 00:04:30,220
+an iron-carbon alloy. الآن ال steel قوي صح؟ إيش 
+
+54
+00:04:30,220 --> 00:04:36,610
+السر القوة فيه؟ إنه حاطينا عليه شوية carbon. الآن
+
+55
+00:04:36,610 --> 00:04:41,330
+خدنا نشوف عليها and can include other alloying
+
+56
+00:04:41,330 --> 00:04:46,250
+metals which are added to alloys in small
+
+57
+00:04:46,250 --> 00:04:50,130
+quantities. إيش هذه ال alloys بنحط؟ الحاجات اللي
+
+58
+00:04:50,130 --> 00:04:55,050
+بنحطها، بنحطها in small quantities. يعني ما بنحطش
+
+59
+00:04:55,050 --> 00:04:59,090
+خلطة جد بعض أو حاجة زي ذلك. عادة اللي بنحط حاجة
+
+60
+00:04:59,090 --> 00:05:04,270
+خفيفة. الأمثلة المستخدمة بشكل عام في المواد
+
+61
+00:05:04,270 --> 00:05:08,990
+التنجستينية هي كروم و منجنيز و تنجستن.
+
+62
+00:05:23,800 --> 00:05:30,060
+مجلة هندسية تتكلم على مادة تحت الميكروسكوب. مادة تحت
+
+63
+00:05:30,060 --> 00:05:32,700
+الميكروسكوب. مادة تحت الميكروسكوب. مادة تحت الميكروسكوب.
+
+64
+00:05:32,700 --> 00:05:32,880
+مادة تحت الميكروسكوب. مادة تحت الميكروسكوب. مادة تحت
+
+65
+00:05:32,880 --> 00:05:34,000
+الميكروسكوب. مادة تحت الميكروسكوب. مادة تحت الميكروسكوب.
+
+66
+00:05:34,000 --> 00:05:34,240
+مادة تحت الميكروسكوب. مادة تحت الميكروسكوب. مادة تحت
+
+67
+00:05:34,240 --> 00:05:35,800
+الميكروسكوب. مادة تحت الميكروسكوب. مادة تحت الميكروسكوب.
+
+68
+00:05:35,800 --> 00:05:39,700
+مادة تحت الميكروسكوب. مادة تحت الميكروسكوب. مادة تحت
+
+69
+00:05:39,700 --> 00:05:52,600
+الميكروسكوب. مادة تحت الميكروسكوب. الغلاف تبعها مش حديد. الجسم
+
+70
+00:05:52,600 --> 00:06:00,720
+تبعها... ليش؟ أخف في نفس الوقت قوية. عرفتوا؟ فهذه
+
+71
+00:06:00,720 --> 00:06:05,060
+ال formula الجديدة خففت الوزن عشان السيارة تصير
+
+72
+00:06:05,060 --> 00:06:11,300
+تمشي بكفاءة أعلى و سرعة أعلى. فالأجسام هذه بتبقى
+
+73
+00:06:11,300 --> 00:06:17,050
+قوية كتير. ال aerospace اللي هي أجسام الطيارات. الـ
+
+74
+00:06:17,050 --> 00:06:21,110
+Formula 1 اللي هي سيارات السباق. سيارات السباق بدنا
+
+75
+00:06:21,110 --> 00:06:28,290
+نياهم إيش؟ سريعة جدا و قوية في نفس الواجهة. But
+
+76
+00:06:28,290 --> 00:06:32,410
+although we think of composites as a high-tech and
+
+77
+00:06:32,410 --> 00:06:36,330
+highly expensive. دائما نتكلم عنها إن هذه تكنولوجيا
+
+78
+00:06:36,330 --> 00:06:41,960
+متطورة و غالية. طلعش بحكي that's not always true. هذا
+
+79
+00:06:41,960 --> 00:06:47,340
+مش الحقيقة اللي دائمة. The earliest example of
+
+80
+00:06:47,340 --> 00:06:51,060
+composite materials were bricks made from mud and
+
+81
+00:06:51,060 --> 00:06:55,700
+straw. يمكن ما حدش فيكوا شافن هذه الشغلات زمان
+
+82
+00:06:55,700 --> 00:07:00,470
+البيوت اللي عندنا في غزة كانوا مش حتى في مناطق
+
+83
+00:07:00,470 --> 00:07:05,150
+تانية. كان في بعض البيوت بيعملوهم من إيش؟ من طينة
+
+84
+00:07:05,150 --> 00:07:09,530
+تعرف ال... مش التبن. تعرف التبن. بعض منكم سمع فيه
+
+85
+00:07:09,530 --> 00:07:14,730
+تبن اللي بيتعموه للإيش؟ للغنم و البقر و هدول اللي
+
+86
+00:07:14,730 --> 00:07:19,330
+هو من الشعير لما ن... أو الجمح لما نحصده. ناخد احنا
+
+87
+00:07:19,330 --> 00:07:22,950
+الشعير و الجمح و الباقي بيعملوا منه تبن. الآن في
+
+88
+00:07:22,950 --> 00:07:30,230
+بعض الحاجات بتظل. يعني في مكينة الدرس هذه بتبقى جامدة
+
+89
+00:07:30,230 --> 00:07:39,010
+هذا بيسموه إيش؟ القشر. هذي تقولك تكنولوجيا معظمكم
+
+90
+00:07:39,010 --> 00:07:43,270
+ما شفوه. مش هذا إيش بيسووا فيه؟ بيخلطوه مع الطينة.
+
+91
+00:07:43,270 --> 00:07:47,430
+الحين لو عملوا جوالب قبل ال cement هذا. ويمكن في
+
+92
+00:07:47,430 --> 00:07:53,330
+بعض البيوت اللي بعد حرب 2008 اللي عملتها الوزارة
+
+93
+00:07:53,330 --> 00:07:59,520
+كانت عملها من الطين. سمعتوا فيها فرن الطينة. فإيش
+
+94
+00:07:59,520 --> 00:08:06,260
+بيعملوا في هذه حاجة. مادة بتظل من... لما يدرسوا
+
+95
+00:08:06,260 --> 00:08:10,880
+الجمح أو الشعير بتظل هدول... الحيوانات بتاكلهاش و
+
+96
+00:08:10,880 --> 00:08:14,520
+مالهاش لزوم. يا بيحرقوها يا إيش كانوا بيستخدموها
+
+97
+00:08:14,520 --> 00:08:18,900
+بيخلطوها مع الطين و بيعملوا منها جوالب من الطين و
+
+98
+00:08:18,900 --> 00:08:23,410
+بيبني البيوت من هذه الجوالب. فهذه... هذه اللي
+
+99
+00:08:23,410 --> 00:08:28,210
+بيسموها إيش؟ هو سماها mud اللي هو طين و straw اللي
+
+100
+00:08:28,210 --> 00:08:34,230
+هو القشر اللي بيسموه. هذا اللي هو بقايا الاش... مش
+
+101
+00:08:34,230 --> 00:08:40,380
+الحيوانات. بقايا بقايا عملية الدرس اللي بتحصل اللي
+
+102
+00:08:40,380 --> 00:08:45,540
+هو بيبقى التبن بتعرفوه. ناعم إذا حد شافه القشر
+
+103
+00:08:45,540 --> 00:08:50,700
+بتلاقيه كبير و دفش. فهو... حتى الحيوانات صعبة تاكله.
+
+104
+00:08:50,700 --> 00:08:56,880
+فهذا بيستخدموه في هذه الشغلات. أنا زمان هذه شفتها
+
+105
+00:08:56,880 --> 00:08:59,960
+حتى مش... يعني بتضحكوا انتوا. هذا شفتها في أمريكا هذه
+
+106
+00:08:59,960 --> 00:09:05,310
+ال... البيوت بيعتبروها حاجة كبيرة. فعراي واحد صحابي
+
+107
+00:09:05,310 --> 00:09:10,070
+السعوديين. روحنا على مطعم فمعمول من هيكة. فطلع فوق
+
+108
+00:09:10,070 --> 00:09:13,890
+لجي الخشب و لجي هيك. و قول انا ما صدقت اطلع من هذه
+
+109
+00:09:13,890 --> 00:09:16,330
+الشغلات. جايين نرجع فيها. يلا قوم.
+
+110
+00:09:20,230 --> 00:09:25,410
+فهي من الحاجات الموجودة قديمة كثير هذه. فهي
+
+111
+00:09:25,410 --> 00:09:29,410
+صراعتيا موجودة في بعض المناطق. ويمكن زي ما حلق احكت
+
+112
+00:09:29,410 --> 00:09:34,970
+لصمتكم. الفرن الطيني معمول من هذه الشغلة. لأن ليش
+
+113
+00:09:34,970 --> 00:09:40,850
+بتلاقيه يكون جامد و يتحمل. Or to use the correct
+
+114
+00:09:40,850 --> 00:09:44,950
+composite term for strong reinforcement. الآن في
+
+115
+00:09:44,950 --> 00:09:50,980
+لغة مدعوم بالإيش؟ بالقشر. هو الحلمش احنا بنقول
+
+116
+00:09:50,980 --> 00:09:57,080
+concrete, reinforced concrete. الحديد المسلح. فهذا
+
+117
+00:09:57,080 --> 00:10:02,610
+إيش؟ ال straw المسلح. لم يقص المسلح. Okay, the
+
+118
+00:10:02,610 --> 00:10:05,950
+structure network that reinforces the material
+
+119
+00:10:05,950 --> 00:10:11,630
+inside. And the mud matrix of the material
+
+120
+00:10:11,630 --> 00:10:16,790
+surrounding the reinforcement. هذا بنحط كأنه شيء
+
+121
+00:10:16,790 --> 00:10:24,040
+يعني بيقوي. و الخارج بنحط إيش؟ حتى بتلاحظوها انت
+
+122
+00:10:24,040 --> 00:10:28,700
+ما شوفتهوش هذه. ليش بقولكوا هدول زمان يمكن اختفت لأن
+
+123
+00:10:28,700 --> 00:10:34,900
+ال cement حل محل كل هذه الشغلات. بس في 2008 عملوا
+
+124
+00:10:34,900 --> 00:10:39,460
+بيوت من هذه الشغلة. بيوت لناس سكنت فيها. و ده
+
+125
+00:10:39,460 --> 00:10:44,560
+بتلاحظوا يمكن حاجة معينة تضحكوا فيها فيها. الآن حد 
+
+126
+00:10:44,560 --> 00:10:47,380
+فيكوا رأى على البيوت الأثرية في غزة؟
+
+127
+00:10:50,750 --> 00:10:55,770
+بتلاحظوا فيه جواس في البيت الجواس بتفكروا من إيش 
+
+128
+00:10:55,770 --> 00:11:03,090
+معمولة؟ من مواد .. من مواد بسيطة جدا ليش؟ لأنها 
+
+129
+00:11:03,090 --> 00:11:08,210
+بتقدر تتمسك مع بعضها إذا لاحظته لو حطيت كمية سمنت،
+
+130
+00:11:08,210 --> 00:11:13,170
+السمنت إيش بيصيرله؟ بيشجج بسرعة بس هدولة الشغلات
+
+131
+00:11:13,170 --> 00:11:19,250
+بيشججينش فبتلاقيه معمولة بنفس طريقة عمل الفخار
+
+132
+00:11:20,360 --> 00:11:24,580
+الفخار بتقدر تعمليه بهذه الطريقة فالفخار إيش هو 
+
+133
+00:11:24,580 --> 00:11:30,160
+عبارة عن إيش مضطينة فنفس الطريقة يعني الطرق
+
+134
+00:11:30,160 --> 00:11:36,440
+البدائية بتعمل منها حاجات مش بسيطة و أنتم هندسة
+
+135
+00:11:36,440 --> 00:11:40,720
+الحين يعني تفكروا إيش البسيط و إيش المعقد و إيش كل 
+
+136
+00:11:40,720 --> 00:11:45,130
+شيء these terms explain what composite material is
+
+137
+00:11:45,130 --> 00:11:49,670
+a matrix with reinforcement material عادة بتصفطه 
+
+138
+00:11:49,670 --> 00:11:55,710
+بشكل متناسق عشان يساوي فهو على شكل إيش ال matrix؟
+
+139
+00:11:55,710 --> 00:12:00,530
+مصفوفة okay of reinforcing material ال reinforce
+
+140
+00:12:00,530 --> 00:12:03,990
+إيش مدعم؟ كويس؟
+
+141
+00:12:06,850 --> 00:12:11,270
+ومثلاً مثلًا فيبر غلاس مسمى بشكل صحيح Glass
+
+142
+00:12:11,270 --> 00:12:17,110
+Reinforced Plastic الفيبر غلاس هو فيه زجاج وفيه 
+
+143
+00:12:17,110 --> 00:12:22,990
+بلاستيك الزجاج بدعم مقلوط مع البلاستيك فبيعمل مادة 
+
+144
+00:12:22,990 --> 00:12:28,030
+قوية أقوى من الميزات 
+
+145
+00:12:28,030 --> 00:12:31,690
+أحسن من البلاستيك أقوى منه وفي نفس الوقت مش 
+
+146
+00:12:31,690 --> 00:12:33,410
+breakable زي ال glass
+
+147
+00:12:36,370 --> 00:12:41,050
+which has a plastic matrix reinforced with glass
+
+148
+00:12:41,050 --> 00:12:46,930
+fibers فبدل ما نحط الجزل نحط شرائح زجاج في النص
+
+149
+00:12:46,930 --> 00:12:53,790
+طيب الآن هذه الشغلات هنجي نتكلم على بعض التمارين
+
+150
+00:12:53,790 --> 00:12:58,050
+هنا في نفس الوقت التمارين هي examples يعني هنا
+
+151
+00:12:58,050 --> 00:13:02,990
+complete the sentences .. the sentences using the 
+
+152
+00:13:02,990 --> 00:13:07,810
+words in the box طيب إيش هم اللي عندي؟ metal و non
+
+153
+00:13:07,810 --> 00:13:11,050
+-metal, metallic, non-metallic, ferrous, non
+
+154
+00:13:11,050 --> 00:13:13,810
+-ferrous هدول الشغلات اللي كانت في ال slide ال
+
+155
+00:13:13,810 --> 00:13:21,050
+إيش؟ الأولى ال إيه؟ carbon is non-metallic طيب
+
+156
+00:13:21,050 --> 00:13:26,630
+copper is .. لأ هي metal أه بس إيش نوع ال metal؟
+
+157
+00:13:28,290 --> 00:13:32,570
+ferrous ولا non-ferrous؟ ferrous إيش معناته؟ في 
+
+158
+00:13:32,570 --> 00:13:39,630
+حديد، الحاس في حديد، يبغى non-ferrous aluminum is
+
+159
+00:13:39,630 --> 00:13:46,470
+a common .. هو متل ولا non-metal؟ common metal
+
+160
+00:13:46,470 --> 00:13:51,570
+طيب، steel is widely used .. إيش متل؟ ال steel إيش
+
+161
+00:13:51,570 --> 00:13:57,390
+بتكون من؟ ferrous لأنه في حديد although it is used
+
+162
+00:13:57,390 --> 00:14:03,270
+in steel, carbon is non-metallic aluminum is
+
+163
+00:14:03,270 --> 00:14:09,190
+relatively lightweight for a metallic material
+
+164
+00:14:09,190 --> 00:14:16,690
+metallic لأن objective هذه ال objective بتاخد ايش 
+
+165
+00:14:16,690 --> 00:14:23,430
+الصفة بتاخد metallic ال noun متى معدن و معدني
+
+166
+00:14:24,420 --> 00:14:29,220
+المعدن بيبقى اسم والمعدني صفة وظبط عشان هي كما
+
+167
+00:14:29,220 --> 00:14:34,520
+بنحط واحد
+
+168
+00:14:34,520 --> 00:14:40,400
+واربعة طيب
+
+169
+00:14:40,400 --> 00:14:46,760
+هنا carbon is metal هنا هناك ايش؟ metallic هنا non
+
+170
+00:14:46,760 --> 00:14:54,030
+-metal و هناك ايش؟ non-metallic هنا أخد اسم وهناك 
+
+171
+00:14:54,030 --> 00:14:58,270
+أخد الصفة هنجي لسه في ال slide الأخير على 
+
+172
+00:14:58,270 --> 00:15:05,290
+reinforcement طيب decide whether the sentences 
+
+173
+00:15:05,290 --> 00:15:08,390
+below are true or false and correct the false
+
+174
+00:15:08,390 --> 00:15:12,930
+sentences the elements that make up a compound are 
+
+175
+00:15:12,930 --> 00:15:18,090
+chemically bound لأن ال compound ايش قلنا two or 
+
+176
+00:15:18,090 --> 00:15:22,650
+more metallic or non-metallic material compound
+
+177
+00:15:22,650 --> 00:15:28,290
+ايش او or chemically bound يعني اتحدوا مع بعض 
+
+178
+00:15:28,290 --> 00:15:34,170
+كيميائيا فهذا صح true Alloys are chemical
+
+179
+00:15:34,170 --> 00:15:38,450
+compounds that are frequently used in engineering
+
+180
+00:15:43,630 --> 00:15:50,950
+chemical compounds ولا mixtures؟ أيوة، مظبوط؟ طيب،
+
+181
+00:15:50,950 --> 00:15:54,770
+يبقى هذه false Alloys can contain both metallic
+
+182
+00:15:54,770 --> 00:16:01,040
+and non-metallic constituents true مظبوط ال carbon
+
+183
+00:16:01,040 --> 00:16:06,520
+و ال iron ال carbon nonmetal و ال iron metal فهذه 
+
+184
+00:16:06,520 --> 00:16:12,620
+true sentence in an alloy an alloying metal is the
+
+185
+00:16:12,620 --> 00:16:17,760
+biggest constituent by percentage false هي small
+
+186
+00:16:17,760 --> 00:16:22,900
+quantities نستخدم مظبوط طيب steel is a metallic
+
+187
+00:16:22,900 --> 00:16:29,920
+element false ولا true الستيل .. ستيل إيش؟ قولنا
+
+188
+00:16:29,920 --> 00:16:35,240
+عبارة عن إيش؟ alloy مظبوط؟ مظبوط؟ يبقى هذه false
+
+189
+00:16:35,240 --> 00:16:43,140
+complete
+
+190
+00:16:43,140 --> 00:16:49,380
+the extract about concrete and steel using
+
+191
+00:16:49,380 --> 00:16:52,900
+suitable form of the word reinforce الآن نمسك ال
+
+192
+00:16:52,900 --> 00:16:57,360
+word reinforce و نستخدمها إيش يعني reinforce؟
+
+193
+00:16:57,360 --> 00:17:05,800
+قولنا يسلح أو يدعم، كويس؟ الآن نتكلم عن ال
+
+194
+00:17:05,800 --> 00:17:11,800
+concrete، إيش ال concrete قلنا؟ لأ البتون أو
+
+195
+00:17:11,800 --> 00:17:18,460
+الخرسانة، بالعربية الفصحى الخرسانة كويس بالعامية 
+
+196
+00:17:18,460 --> 00:17:23,800
+البتون، بصبوح؟ طيب إيش concrete is one of the most
+
+197
+00:17:23,800 --> 00:17:28,100
+widely used construction .. construction material؟
+
+198
+00:17:28,100 --> 00:17:32,240
+إيش بنسميه؟ الخرسانة الإيش؟ المسلحة، هيبقى إيش بده 
+
+199
+00:17:32,240 --> 00:17:37,420
+يكون عندنا؟ reinforced concrete أخذنا من الـ
+
+200
+00:17:37,420 --> 00:17:43,070
+reinforced حطينا إيه؟ حطينا D لها فصارت reinforced
+
+201
+00:17:43,070 --> 00:17:48,470
+concrete اللي عندي الخرسانة المسلحة and when we
+
+202
+00:17:48,470 --> 00:17:52,690
+take for granted however using steel part to ..
+
+203
+00:17:52,690 --> 00:17:59,230
+إيش بيجي بعد to؟ فعل reinforce concrete structure
+
+204
+00:17:59,230 --> 00:18:03,730
+located outdoor is only possible thanks to the
+
+205
+00:18:03,730 --> 00:18:07,270
+fortune coincidence concrete and steel have
+
+206
+00:18:07,270 --> 00:18:09,730
+practically the same coefficient of thermal
+
+207
+00:18:09,730 --> 00:18:15,090
+expansion الآن لما نقول concrete structure located
+
+208
+00:18:15,090 --> 00:18:19,810
+outdoor اللي هي الخرسانة المسلحة اللي في الخارج is
+
+209
+00:18:19,810 --> 00:18:25,410
+only possible .. is only possible to the fortune
+
+210
+00:18:25,410 --> 00:18:30,810
+coincidence إيش يعني fortune coincidence؟
+
+211
+00:18:30,810 --> 00:18:33,850
+هي
+
+212
+00:18:33,850 --> 00:18:41,950
+coincidence صدفة و fortune لأ الحظ يعني ل .. ل ..
+
+213
+00:18:41,950 --> 00:18:49,650
+تقولي إيش؟ للحظ السعيد يعني، كويس؟ أنه .. يعني هنا
+
+214
+00:18:49,650 --> 00:18:56,270
+لاحظنا الحظ، هذا اللي بنقولها، يعني لما نقول يعني
+
+215
+00:18:56,270 --> 00:19:02,000
+..الترجمة تبعتها مش حرفية بدك تكوني بس المرادف
+
+216
+00:19:02,000 --> 00:19:08,500
+لها لاحظنا الحظ أنه إيش concrete and steel البتون
+
+217
+00:19:08,500 --> 00:19:15,220
+والحديد اللي هم نفس معامل هنا إيش هنا the same
+
+218
+00:19:15,220 --> 00:19:19,340
+coefficient of thermal expansion نفس معامل التمدد 
+
+219
+00:19:19,340 --> 00:19:23,060
+الحراري يعني اتنين اللي هم نفس الدرجة من التمدد
+
+220
+00:19:23,060 --> 00:19:29,420
+الحراري بيتمددوا بنفس الدرجة طيب in other words as
+
+221
+00:19:29,420 --> 00:19:33,280
+atmospheric temperature varies the concrete and
+
+222
+00:19:33,280 --> 00:19:38,220
+steel إيش؟ ال steel إيش؟ reinforcement أو 
+
+223
+00:19:38,220 --> 00:19:42,360
+reinforcing expand and contract at the same rate
+
+224
+00:19:42,360 --> 00:19:49,960
+يعني اتنين بيتمددوا وبينكمشوا بنفس المعدل allowed
+
+225
+00:19:49,960 --> 00:19:55,900
+uniform movement فبتلاحظ الحركة بتكون إيش؟ متجانسة
+
+226
+00:19:56,370 --> 00:20:00,990
+يعني نفس درجة الانكماش ونفس درجة التمدد التمدد
+
+227
+00:20:00,990 --> 00:20:06,850
+بيتمددوا مع بعض وبينكمشوا بنفس الدرجة using a
+
+228
+00:20:06,850 --> 00:20:10,750
+reinforced material with .. reinforced زي أول
+
+229
+00:20:10,750 --> 00:20:14,470
+واحدة material with a different coefficient of
+
+230
+00:20:14,470 --> 00:20:19,110
+expansion would not be feasible يعني إيش feasible؟
+
+231
+00:20:19,110 --> 00:20:21,310
+ممكن
+
+232
+00:20:23,080 --> 00:20:30,000
+يعني هي .. هي ما .. هي مش .. مش مار إيه؟ يعني ممكن
+
+233
+00:20:30,000 --> 00:20:36,820
+أو محتمل، أيوة فهي هان .. هان بنقول feasible،
+
+234
+00:20:36,820 --> 00:20:44,660
+feasible solution يعني في حل ممكن كويس for example
+
+235
+00:20:44,660 --> 00:20:48,800
+aluminum reinforced concrete أو aluminum
+
+236
+00:20:48,800 --> 00:20:54,540
+reinforcement concrete would quickly disintegrate
+
+237
+00:20:54,540 --> 00:20:59,100
+يعني لو أنا جيت حطيت بدل الحديد aluminum إيش 
+
+238
+00:20:59,100 --> 00:21:02,840
+هيحصل؟
+
+239
+00:21:02,840 --> 00:21:09,820
+يعني إيش يعني disintegrate بتشوفي
+
+240
+00:21:09,820 --> 00:21:15,530
+لما تحطي حاجة واتفكك يعني ممكن حاجتين مع بعض و
+
+241
+00:21:15,530 --> 00:21:19,550
+تلاقي واحدة صارت تشجيج والتفكيك بيصير الحدث
+
+242
+00:21:19,550 --> 00:21:24,550
+الحدث نفس الشيء أنه مع معدل التمدد هتلاحظ
+
+243
+00:21:24,550 --> 00:21:30,250
+disintegrate هتتفكك الحدث
+
+244
+00:21:30,250 --> 00:21:37,410
+اللي عندنا في الحدث طيب، الآن read the text below
+
+245
+00:21:37,410 --> 00:21:41,410
+and find two elements بدنا إيش؟ two elements من
+
+246
+00:21:41,410 --> 00:21:46,050
+هنا، two compounds, one alloy and one composite
+
+247
+00:21:46,920 --> 00:21:50,480
+كويس من ال text يعني هنا بدنا نعمل .. نعب الجدول
+
+248
+00:21:50,480 --> 00:21:54,820
+هذا في ال element بده اتنين في ال combined بده 
+
+249
+00:21:54,820 --> 00:21:58,040
+اتنين في ال alloy one و في ال composite واحد الآن 
+
+250
+00:21:58,040 --> 00:22:02,260
+كل كلمة متعرف عليها بنمر عليها هنقول إيش هذي 
+
+251
+00:22:02,260 --> 00:22:06,180
+generally the steel used in the reinforced
+
+252
+00:22:06,180 --> 00:22:11,820
+concrete ايش .. ال steel ايش نوعه element ولا 
+
+253
+00:22:11,820 --> 00:22:20,740
+alloyالاستيل بتكون من ايش؟ iron and carbon فبيجي
+
+254
+00:22:20,740 --> 00:22:25,940
+ايش؟ تحت ال .. ال alloy الموجود هنا steel طيب
+
+255
+00:22:25,940 --> 00:22:32,780
+reinforced concrete ايش بيجي؟ composite لأن اتنين
+
+256
+00:22:32,780 --> 00:22:37,020
+هدولة أجزاء تحت ال composite will have previously
+
+257
+00:22:37,020 --> 00:22:41,860
+been exposed to water and to the oxygen in the
+
+258
+00:22:41,860 --> 00:22:47,770
+air يعني هدولة ايش يعني exposed؟ تعرضوا لـ explode
+
+259
+00:22:47,770 --> 00:22:56,910
+هذيك فجأة expose يتعرض expose to water and oxygen
+
+260
+00:22:56,910 --> 00:23:01,190
+اللي هي الميه و ال oxygen ايش بده يحصل as a result
+
+261
+00:23:01,190 --> 00:23:05,650
+it will usually partly corroded ايش يعني corroded؟
+
+262
+00:23:08,460 --> 00:23:13,420
+ايش بيحصل لما ن .. خلينا نتطلع عليها ال .. ال ..
+
+263
+00:23:13,420 --> 00:23:20,540
+أيوة بيصير له ايش؟ شوية يعني تآكل .. تآكل بتلاحظوا
+
+264
+00:23:20,540 --> 00:23:26,220
+لو طلعت على بطون قديم بتلاقي ايه شكله؟ فيه تآكل
+
+265
+00:23:26,220 --> 00:23:30,560
+فيه، مبين، مظبوط و هذا اللي بنقول corroded being
+
+266
+00:23:30,560 --> 00:23:36,140
+covered with a layer of iron oxide rust ايش يعني
+
+267
+00:23:36,140 --> 00:23:41,820
+iron oxide؟ صدق و ال iron oxide ايش هذه عبارة عن
+
+268
+00:23:41,820 --> 00:23:48,900
+ايش؟ هذا ال compound اللي هو ال rust هذا ال rust
+
+269
+00:23:48,900 --> 00:23:55,060
+الصدق الآن من ال oxygen بيجي تحت أي خانة؟ تحت ال
+
+270
+00:23:55,060 --> 00:24:01,620
+element هنا و ال water بيجي تحت ال compound أيوة ال
+
+271
+00:24:01,620 --> 00:24:05,660
+Now however once the steel is inside the hardened
+
+272
+00:24:05,660 --> 00:24:10,400
+concrete اللي هي ال ايش .. اللي .. اللي .. يعني
+
+273
+00:24:10,400 --> 00:24:13,400
+اللي .. لما تحط البطون بيه ايش بتبقى في الأول؟
+
+274
+00:24:16,560 --> 00:24:20,760
+الخرسانة في أولها ايش بتبقى؟ سائلة تقريبا يعني
+
+275
+00:24:20,760 --> 00:24:24,840
+بتبقى سائلة، الآن مع الوقت ايش بيحصللها؟ بتجمد، ف
+
+276
+00:24:24,840 --> 00:24:30,360
+hardened concrete اللي هي خرسانة جامدة يعني it
+
+277
+00:24:30,360 --> 00:24:33,780
+will be protected from air and water which prevent
+
+278
+00:24:33,780 --> 00:24:39,260
+further rusting يعني لما نحط الحديد و نحطه جوا هذا
+
+279
+00:24:39,260 --> 00:24:44,440
+جوا الخرسانة، هذا بيشكل غلاف بتحميه من عملية ايش
+
+280
+00:24:44,440 --> 00:24:53,140
+الصدأ ذلك، الاسمنت في الكامكس لا يتفاعل عضوًا مع 
+
+281
+00:24:53,140 --> 00:24:59,460
+الحرارة في الكامكس، حرارة، حرارة، حرارة، حرارة،
+
+282
+00:24:59,460 --> 00:25:00,180
+حرارة، حرارة، حرارة، حرارة، حرارة، حرارة، حرارة،
+
+283
+00:25:00,180 --> 00:25:02,660
+حرارة، حرارة، حرارة، حرارة، حرارة، حرارة، حرارة،
+
+284
+00:25:02,660 --> 00:25:04,000
+حرارة، حرارة، حرارة، حرارة، حرارة، حرارة، حرارة،
+
+285
+00:25:04,000 --> 00:25:09,340
+حرارة، حرارة، حرارة،
+
+286
+00:25:09,340 --> 00:25:14,680
+حرارة، حرارة،
+
+287
+00:25:14,680 --> 00:25:23,160
+هدولة بشكل عام اللي احنا اتعرضنا لهم طيب نرجع
+
+288
+00:25:23,160 --> 00:25:30,540
+تاني لـ اللي ال paragraph و ال words اللي عندنا طيب
+
+289
+00:25:30,540 --> 00:25:36,300
+مين بدها تقرأ تتطوع بدنا وجوه جديدة تنسوش ان في
+
+290
+00:25:36,300 --> 00:25:42,020
+حاجة واحدة في خمس علامات عن اللي بيشاركوا طيب مين
+
+291
+00:25:42,020 --> 00:25:49,300
+مشاركتش قبل هيك اجدد شاركت انت اجدد طيب تنتين هاي
+
+292
+00:25:49,300 --> 00:25:52,640
+واحد اتنين تلاتة اربعة في اربع slides من عندك ابدي
+
+293
+00:25:52,640 --> 00:25:59,220
+بس عارفه باسمك طيب بس صوت اعلى بدنا صوت هندسة
+
+294
+00:25:59,220 --> 00:26:15,940
+اتفضلي اه المهندسات معروفات شخصية جوية اتفضلي ايه
+
+295
+00:26:16,020 --> 00:26:25,100
+examples of materials are iron, Fe and copper, Cu
+
+296
+00:26:25,100 --> 00:26:28,060
+and fundamental examples of fundamentals
+
+297
+00:26:28,060 --> 00:26:37,520
+materials are pipeline and plastic, silicon and
+
+298
+00:26:37,520 --> 00:26:41,540
+silicon as iron is such a widely used material
+
+299
+00:26:41,930 --> 00:26:44,670
+البرنامج يمكن أن يتم مقاطعها إلى البرنامج الهجومي
+
+300
+00:26:44,670 --> 00:26:48,450
+والبرنامج غير هجومي البرنامج الهجومية تحتوي على
+
+301
+00:26:48,450 --> 00:26:52,710
+نفو 10 ايران والبرنامج غير هجومية تحتوي على نفو 10
+
+302
+00:26:52,710 --> 00:26:57,340
+ايران طيب ال words اللي عندنا metals و non-metal
+
+303
+00:26:57,340 --> 00:27:02,140
+هدولة nouns زي ما حكينا ال adjective metallic و
+
+304
+00:27:02,140 --> 00:27:06,240
+non-metallic الحاجتين التانيات ferrous و non
+
+305
+00:27:06,240 --> 00:27:11,240
+-ferrous هدولة اللي في ال slide هذه و زي ما بتعرف
+
+306
+00:27:11,240 --> 00:27:16,220
+ال metal اللي هو معدني non-metal اللي هو مش معدني
+
+307
+00:27:16,220 --> 00:27:21,870
+ال ferrous ..اللي هي المعادن التي تحتوي على حديد
+
+308
+00:27:21,870 --> 00:27:27,250
+nonferrous التي لا تحتوي على حديد طيب اللي جنبك
+
+309
+00:27:27,250 --> 00:27:40,530
+الحين تفضلي الاسم طيب تفضلي الاسم
+
+310
+00:27:40,530 --> 00:27:42,650
+الاسم الاسم الاسم الاسم الاسم الاسم الاسم الاسم
+
+311
+00:27:42,650 --> 00:27:43,990
+الاسم الاسم الاسم الاسم الاسم الاسم الاسم الاسم
+
+312
+00:27:43,990 --> 00:27:46,890
+الاسم الاسم الاسم الاسم الاسم الاسم الاسم الاسم
+
+313
+00:27:46,890 --> 00:27:48,170
+الاسم الاسم الاسم الاسم الاسم الاسم الاسم الاسم ال
+
+314
+00:28:06,190 --> 00:28:12,550
+categories constituent ingredients
+
+315
+00:28:15,080 --> 00:28:20,440
+العمال المستخدمة في التصميم هي أيرو كاربون و ترينو
+
+316
+00:28:20,440 --> 00:28:26,200
+تحتوي على أكثر من أكثر من أكثر من أكثر من أكثر من
+
+317
+00:28:26,200 --> 00:28:26,540
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+318
+00:28:26,540 --> 00:28:28,740
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+319
+00:28:28,740 --> 00:28:30,060
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+320
+00:28:30,060 --> 00:28:30,660
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+321
+00:28:30,660 --> 00:28:34,240
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+322
+00:28:34,240 --> 00:28:43,790
+أكثر من أكثر من أكثر من أكثرOkay شكرا الان اللي
+
+323
+00:28:43,790 --> 00:28:49,250
+عندنا هنا elements و compounds الان ال compounds
+
+324
+00:28:49,250 --> 00:28:54,170
+chemically bound ال elements they can't be broken
+
+325
+00:28:54,170 --> 00:28:58,210
+into ingredients or constituents they are pure
+
+326
+00:28:58,210 --> 00:29:05,090
+فهذه الكلمات الموجودة بشكل مفصل طيب اللي منكوا
+
+327
+00:29:05,090 --> 00:29:09,110
+قدامي تفضلي الاسم
+
+328
+00:29:11,100 --> 00:29:30,700
+طيب وعدي صوتك شوية أعلى ال noise
+
+329
+00:29:40,400 --> 00:29:43,640
+المثال الثاني هو البرتقال البرتقال البرتقال
+
+330
+00:29:43,640 --> 00:29:46,000
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+331
+00:29:46,000 --> 00:29:47,500
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+332
+00:29:47,500 --> 00:29:48,880
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+333
+00:29:48,880 --> 00:29:49,060
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+334
+00:29:49,060 --> 00:29:49,820
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+335
+00:29:49,820 --> 00:29:50,440
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+336
+00:29:50,440 --> 00:29:51,060
+البرتقال البرتقال البرتقال البرتقال البرتقال
+
+337
+00:29:51,060 --> 00:29:55,680
+البرتقال البرتقال البرتقال البرتقال البرتقال البر
+
+338
+00:29:56,110 --> 00:30:00,710
+اسم ال quantities they insert to the main metal in
+
+339
+00:30:00,710 --> 00:30:05,530
+samples for widely used alloying metals are
+
+340
+00:30:05,530 --> 00:30:13,270
+chromium and manganese and this one is titanium
+
+341
+00:30:16,510 --> 00:30:21,990
+طيب هنا ال mixture و ال alloy هدول أهم جزئيتين ال
+
+342
+00:30:21,990 --> 00:30:26,670
+alloy بنعرف أن هم metallic و non-metallic material
+
+343
+00:30:26,670 --> 00:30:34,630
+added to metallic materials in small
+
+344
+00:30:34,630 --> 00:30:41,170
+quantities الآن هذا بشكل مباشر الموجود عندنا طيب
+
+345
+00:30:41,170 --> 00:30:41,930
+اللي بعدها
+
+346
+00:30:44,520 --> 00:30:51,180
+مين اللي قلناها الهاد؟ أيوة تفضلي الاسم سمعيهم عشان
+
+347
+00:30:51,180 --> 00:30:56,240
+الكل يعرف و أنا اعرف سمية ايش؟ نصر الله تفضلي يا
+
+348
+00:30:56,240 --> 00:30:56,680
+سمية
+
+349
+00:31:00,550 --> 00:31:04,590
+ميكروفوسكوز وموارد الموارد عندما تفكر في مثال
+
+350
+00:31:04,590 --> 00:31:08,370
+موارد موارد موارد موارد موارد موارد موارد موارد
+
+351
+00:31:08,370 --> 00:31:09,930
+موارد موارد موارد موارد موارد موارد موارد موارد
+
+352
+00:31:09,930 --> 00:31:11,790
+موارد موارد موارد موارد موارد موارد موارد موارد
+
+353
+00:31:11,790 --> 00:31:12,690
+موارد موارد موارد موارد موارد موارد موارد موارد
+
+354
+00:31:12,690 --> 00:31:14,550
+موارد موارد موارد موارد موارد موارد موارد موارد
+
+355
+00:31:14,550 --> 00:31:14,590
+موارد موارد موارد موارد موارد موارد موارد موارد
+
+356
+00:31:14,590 --> 00:31:30,330
+موارد مو
+
+357
+00:31:32,030 --> 00:31:39,370
+أو استخدام كلمات صحيحة من خلال عبارة عن عبارة عن
+
+358
+00:31:39,370 --> 00:31:40,050
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+359
+00:31:40,050 --> 00:31:43,770
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+360
+00:31:43,770 --> 00:31:45,870
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+361
+00:31:45,870 --> 00:31:46,650
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+362
+00:31:46,650 --> 00:31:46,690
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+363
+00:31:46,690 --> 00:31:46,710
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+364
+00:31:46,710 --> 00:31:52,450
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+365
+00:31:52,450 --> 00:31:56,820
+عن طيب هنا الـ composites و الـ composites زي ما
+
+366
+00:31:56,820 --> 00:32:01,040
+حكينا بيجيب ال word reinforce أو reinforcement
+
+367
+00:32:01,040 --> 00:32:08,980
+فهذولة يعني هي الهدف منها عملية تدعيم طيب آخر
+
+368
+00:32:08,980 --> 00:32:14,770
+slide اتفضلي please translate what comes in material
+
+369
+00:32:14,770 --> 00:32:18,270
+is a matrix with reinforcing material inside it a
+
+370
+00:32:18,270 --> 00:32:21,050
+modern everyday example is fabric glass correctly
+
+371
+00:32:21,050 --> 00:32:26,130
+called reinforced plastic GRD which has a plastic
+
+372
+00:32:26,130 --> 00:32:30,030
+matrix reinforced with glass fibers okay بنشكركم
+
+373
+00:32:30,030 --> 00:32:33,630
+جميعا على هذا التفاعل وهو انا زي ما حكيت ال
+
+374
+00:32:33,630 --> 00:32:39,170
+reinforcement هي العنصر و الكلمات المشتقة منها
+
+375
+00:32:39,170 --> 00:32:42,380
+اتعودوا عليها يوم السبت عندكم
+
+Okay, please provide the Arabic/English lecture transcript you would like me to review and correct. I will ensure that I:
+
+* **Focus on typos and grammatical errors only.**
+* **Preserve the original text dialect and grammar.**
+* **Maintain the original meaning and style.**
+* **Output the corrected transcript ONLY in the same format as the input.** 
+* **Keep the text in its original language (no translation).** 
+
+I'm ready when you are!  
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/h4Be7E6BT60_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/h4Be7E6BT60_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a09c5443fd4035a6f73884ab4c3917d171e0457e
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/h4Be7E6BT60_raw.json
@@ -0,0 +1 @@
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"probability": 0.618896484375}, {"start": 1914.44, "end": 1915.16, "word": " composites", "probability": 0.71630859375}, {"start": 1915.16, "end": 1915.82, "word": " و", "probability": 0.57763671875}, {"start": 1915.82, "end": 1915.96, "word": " الـ", "probability": 0.645263671875}, {"start": 1915.96, "end": 1916.48, "word": " composites", "probability": 0.831298828125}, {"start": 1916.48, "end": 1916.7, "word": " زي", "probability": 0.936767578125}, {"start": 1916.7, "end": 1916.82, "word": " ما", "probability": 0.96630859375}, {"start": 1916.82, "end": 1917.22, "word": " حكينا", "probability": 0.986083984375}, {"start": 1917.22, "end": 1918.1, "word": " بيجمح", "probability": 0.841796875}, {"start": 1918.1, "end": 1918.32, "word": " ال", "probability": 0.8720703125}, {"start": 1918.32, "end": 1918.66, "word": " word", "probability": 0.9228515625}, {"start": 1918.66, "end": 1919.5, "word": " reinforce", "probability": 0.72216796875}, {"start": 1919.5, "end": 1920.22, "word": " أو", "probability": 0.6142578125}, {"start": 1920.22, "end": 1921.04, "word": " reinforcement", "probability": 0.96728515625}, {"start": 1921.04, "end": 1923.18, "word": " فهدولة", "probability": 0.88212890625}, {"start": 1923.18, "end": 1923.64, "word": " يعني", "probability": 0.6683349609375}, {"start": 1923.64, "end": 1923.88, "word": " هي", "probability": 0.5029296875}, {"start": 1923.88, "end": 1924.54, "word": " الهدف", "probability": 0.9068603515625}, {"start": 1924.54, "end": 1924.82, "word": " منها", "probability": 0.992431640625}, {"start": 1924.82, "end": 1925.4, "word": " عملية", "probability": 0.974609375}, {"start": 1925.4, "end": 1926.04, "word": " تدعيم", "probability": 0.9144287109375}, {"start": 1926.04, "end": 1928.62, "word": " طيب", "probability": 0.9296875}, {"start": 1928.62, "end": 1928.98, "word": " أخر", "probability": 0.7197265625}, {"start": 1928.98, "end": 1929.6, "word": " slide", "probability": 0.96923828125}, {"start": 1929.6, "end": 1930.72, "word": " اتفضل", "probability": 0.7843017578125}], "temperature": 1.0}, {"id": 80, "seek": 196007, "start": 1932.03, "end": 1960.07, "text": "please translate what comes in material is a matrix with reinforcing material inside it a modern everyday example is fabric glass correctly called reinforced plastic GRD which has a plastic matrix reinforced with glass fibers okay بنشكركم جميعا على هذا التفاعل وهو انا زي ما حكيت ال reinforcement هي العنصر والكلمات المشتقة منها اتعودوا عليها", "tokens": [40764, 13799, 437, 1487, 294, 2527, 307, 257, 8141, 365, 48262, 2527, 1854, 309, 257, 4363, 7429, 1365, 307, 7253, 4276, 8944, 1219, 31365, 5900, 10903, 35, 597, 575, 257, 5900, 8141, 31365, 365, 4276, 25252, 1392, 44945, 8592, 37983, 24793, 10874, 2304, 40228, 995, 15844, 23758, 16712, 5172, 995, 30241, 37037, 2407, 1975, 8315, 30767, 1829, 19446, 11331, 4117, 36081, 2423, 29280, 39896, 18863, 1863, 9381, 2288, 16070, 4117, 19528, 9307, 9673, 8592, 2655, 28671, 9154, 11296, 1975, 2655, 3615, 23328, 14407, 25894, 11296], "avg_logprob": -0.28106832573580187, "compression_ratio": 1.5629629629629629, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1932.03, "end": 1932.35, "word": "please", "probability": 0.35595703125}, {"start": 1932.35, "end": 1932.69, "word": " translate", "probability": 0.5234375}, {"start": 1932.69, "end": 1933.51, "word": " what", "probability": 0.75048828125}, {"start": 1933.51, "end": 1933.91, "word": " comes", "probability": 0.6455078125}, {"start": 1933.91, "end": 1934.23, "word": " in", "probability": 0.68798828125}, {"start": 1934.23, "end": 1934.77, "word": " material", "probability": 0.4345703125}, {"start": 1934.77, "end": 1935.11, "word": " is", "probability": 0.5322265625}, {"start": 1935.11, "end": 1935.29, "word": " a", "probability": 0.90478515625}, {"start": 1935.29, "end": 1935.73, "word": " matrix", "probability": 0.79638671875}, {"start": 1935.73, "end": 1936.05, "word": " with", "probability": 0.80224609375}, {"start": 1936.05, "end": 1936.47, "word": " reinforcing", "probability": 0.82373046875}, {"start": 1936.47, "end": 1937.27, "word": " material", "probability": 0.8232421875}, {"start": 1937.27, "end": 1937.63, "word": " inside", "probability": 0.92041015625}, {"start": 1937.63, "end": 1938.03, "word": " it", "probability": 0.92626953125}, {"start": 1938.03, "end": 1938.27, "word": " a", "probability": 0.51318359375}, {"start": 1938.27, "end": 1938.63, "word": " modern", "probability": 0.9072265625}, {"start": 1938.63, "end": 1938.97, "word": " everyday", "probability": 0.75732421875}, {"start": 1938.97, "end": 1939.51, "word": " example", "probability": 0.96240234375}, {"start": 1939.51, "end": 1939.81, "word": " is", "probability": 0.94482421875}, {"start": 1939.81, "end": 1940.23, "word": " fabric", "probability": 0.202392578125}, {"start": 1940.23, "end": 1940.61, "word": " glass", "probability": 0.6904296875}, {"start": 1940.61, "end": 1941.05, "word": " correctly", "probability": 0.131591796875}, {"start": 1941.05, "end": 1941.49, "word": " called", "probability": 0.88916015625}, {"start": 1941.49, "end": 1942.53, "word": " reinforced", "probability": 0.58740234375}, {"start": 1942.53, "end": 1943.35, "word": " plastic", "probability": 0.86767578125}, {"start": 1943.35, "end": 1944.77, "word": " GRD", "probability": 0.593994140625}, {"start": 1944.77, "end": 1945.41, "word": " which", "probability": 0.89306640625}, {"start": 1945.41, "end": 1945.69, "word": " has", "probability": 0.92578125}, {"start": 1945.69, "end": 1945.83, "word": " a", "probability": 0.6064453125}, {"start": 1945.83, "end": 1946.13, "word": " plastic", "probability": 0.6044921875}, {"start": 1946.13, "end": 1946.65, "word": " matrix", "probability": 0.94482421875}, {"start": 1946.65, "end": 1947.05, "word": " reinforced", "probability": 0.6962890625}, {"start": 1947.05, "end": 1947.43, "word": " with", "probability": 0.865234375}, {"start": 1947.43, "end": 1947.83, "word": " glass", "probability": 0.50341796875}, {"start": 1947.83, "end": 1948.19, "word": " fibers", "probability": 0.55078125}, {"start": 1948.19, "end": 1949.21, "word": " okay", "probability": 0.319091796875}, {"start": 1949.21, "end": 1950.03, "word": " بنشكركم", "probability": 0.954833984375}, {"start": 1950.03, "end": 1950.75, "word": " جميعا", "probability": 0.8958740234375}, {"start": 1950.75, "end": 1951.23, "word": " على", "probability": 0.96826171875}, {"start": 1951.23, "end": 1951.67, "word": " هذا", "probability": 0.94287109375}, {"start": 1951.67, "end": 1952.35, "word": " التفاعل", "probability": 0.9488525390625}, {"start": 1952.35, "end": 1952.61, "word": " وهو", "probability": 0.3841552734375}, {"start": 1952.61, "end": 1952.79, "word": " انا", "probability": 0.760986328125}, {"start": 1952.79, "end": 1952.97, "word": " زي", "probability": 0.889892578125}, {"start": 1952.97, "end": 1953.09, "word": " ما", "probability": 0.95556640625}, {"start": 1953.09, "end": 1953.47, "word": " حكيت", "probability": 0.9817708333333334}, {"start": 1953.47, "end": 1953.63, "word": " ال", "probability": 0.425048828125}, {"start": 1953.63, "end": 1954.85, "word": " reinforcement", "probability": 0.9501953125}, {"start": 1954.85, "end": 1955.91, "word": " هي", "probability": 0.9052734375}, {"start": 1955.91, "end": 1957.11, "word": " العنصر", "probability": 0.974365234375}, {"start": 1957.11, "end": 1958.29, "word": " والكلمات", "probability": 0.78326416015625}, {"start": 1958.29, "end": 1958.89, "word": " المشتقة", "probability": 0.8602294921875}, {"start": 1958.89, "end": 1959.17, "word": " منها", "probability": 0.988525390625}, {"start": 1959.17, "end": 1959.75, "word": " اتعودوا", "probability": 0.903515625}, {"start": 1959.75, "end": 1960.07, "word": " عليها", "probability": 0.89501953125}], "temperature": 1.0}, {"id": 81, "seek": 196238, "start": 1960.7, "end": 1962.38, "text": "يوم السبت عندكم", "tokens": [1829, 20498, 21136, 3555, 2655, 43242, 24793], "avg_logprob": -0.08929443359375, "compression_ratio": 0.717948717948718, "no_speech_prob": 0.0, "words": [{"start": 1960.7, "end": 1961.24, "word": "يوم", "probability": 0.92724609375}, {"start": 1961.24, "end": 1961.76, "word": " السبت", "probability": 0.9251302083333334}, {"start": 1961.76, "end": 1962.38, "word": " عندكم", "probability": 0.982421875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1962.62025, "duration_after_vad": 1869.259999999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/hX5CWpY7Tbg_postprocess.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/hX5CWpY7Tbg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..743c2a96e67d3e6c7ee409363c66d3203f84f9d1
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/hX5CWpY7Tbg_postprocess.srt
@@ -0,0 +1,1600 @@
+1
+00:00:20,810 --> 00:00:26,970
+السلام عليكم اليوم سنغطي الحلقة الثالاثة، الحلقة
+
+2
+00:00:26,970 --> 00:00:30,850
+الثالاثة تتكلم عن نانفيراس متاليا، يعني ايش
+
+3
+00:00:30,850 --> 00:00:40,870
+نانفيراس متاليا؟ هاد من اللي فات، متاليا
+
+4
+00:00:40,870 --> 00:00:42,050
+with no iron
+
+5
+00:00:45,150 --> 00:00:49,050
+ووبسايت الـ common nonferrous engineering metals.
+
+6
+00:00:49,170 --> 00:00:53,630
+These websites extracts look at the engineering
+
+7
+00:00:53,630 --> 00:00:56,710
+application of some nonferrous metals that is
+
+8
+00:00:56,710 --> 00:01:01,890
+metal that do not contain iron الان هذه جاي من
+
+9
+00:01:01,890 --> 00:01:09,890
+مقتطفة من صفحات وبسايت فيها بتتكلم على ال metals
+
+10
+00:01:09,890 --> 00:01:10,890
+with no iron
+
+11
+00:01:13,600 --> 00:01:19,920
+alluminium is widely used often in alloy form إيش
+
+12
+00:01:19,920 --> 00:01:25,900
+يعني الألمنيوم بيستخدم بشكل كبير في الغالب in the
+
+13
+00:01:25,900 --> 00:01:32,760
+form of alloy an example is chromium دورال ..
+
+14
+00:01:32,760 --> 00:01:39,920
+دورالوميومان دورال .. دورالو
+
+15
+00:01:40,880 --> 00:01:47,820
+من ديورالومن ديورالومن ديورالومن ديورالومن
+
+16
+00:01:47,820 --> 00:01:47,960
+ديورالومن ديورالومن ديورالومن ديورالومن ديورالومن
+
+17
+00:01:47,960 --> 00:01:51,180
+ديورالومن ديورالومن ديورالومن ديورالومن ديورالومن
+
+18
+00:01:51,180 --> 00:01:55,600
+ديورالومن ديورالومن ديورالومن ديورالومن ديورالومن
+
+19
+00:01:55,600 --> 00:02:05,420
+ديورالومن ديورالومن ديورالومن
+
+20
+00:02:05,420 --> 00:02:08,140
+د
+
+21
+00:02:09,280 --> 00:02:20,000
+والذي يحتوي أيضا على الكبار 4.4 وميجنيسيوم 1.5
+
+22
+00:02:20,000 --> 00:02:23,060
+أولو
+
+23
+00:02:23,060 --> 00:02:29,300
+يومينيوم يمكن أيضا أن يكون مدفعا مع تيتانيوم
+
+24
+00:02:29,300 --> 00:02:31,920
+لتصنيع مصاريف قوي جدا
+
+25
+00:02:35,670 --> 00:02:40,530
+القبرة موظفة إلكترونية ممتازة التي تجعلها أفضل
+
+26
+00:02:40,530 --> 00:02:45,190
+لإستخدامها في قطع إلكترونية دكتورية
+
+27
+00:02:45,190 --> 00:02:50,010
+جيدة أيضًا تجعلها مناسبة لقبرة قبرة مستخدمة كثيرًا
+
+28
+00:02:50,010 --> 00:02:56,450
+في المجرمات وخصوصًا مجرم قبرة وهو قبرة وزنك وقبرة
+
+29
+00:02:56,450 --> 00:03:02,060
+برونز وقبرة تنand sometimes lead الان يجي نتطلع
+
+30
+00:03:02,060 --> 00:03:07,420
+على ال cover cover اللي هو أيش نعتبره انحاس انحاس
+
+31
+00:03:07,420 --> 00:03:11,420
+is an electrical conductor تطلع سلوك الكهربا اللي
+
+32
+00:03:11,420 --> 00:03:17,080
+في البيت كلها مصنوعة من أيش؟ من انحاس الان في حاجة
+
+33
+00:03:17,080 --> 00:03:20,840
+مش موجود بتشوفوها عندنا بس قليل حد فيكوا تطلع
+
+34
+00:03:20,840 --> 00:03:26,690
+عندهم خط غاز في البيتالغاز، انبوبة الغاز، مش
+
+35
+00:03:26,690 --> 00:03:30,650
+البربيش الجرة، إذا في في البيوت بعضهم، حاطط خط غاز
+
+36
+00:03:30,650 --> 00:03:37,190
+خط الغاز من إيش مصنوع؟ انحاس ومغلف، ده لاحظته هذا
+
+37
+00:03:37,190 --> 00:03:40,830
+إيش .. إيش بيقولك good؟ ductability، also make it
+
+38
+00:03:40,830 --> 00:03:44,090
+suitable ال duct اللي هي إيش؟ التغليفة تبعته
+
+39
+00:03:44,090 --> 00:03:49,190
+فبتخليه إيش؟ حاجة مناسبة للاستخدام في المواصير،
+
+40
+00:03:49,190 --> 00:03:54,560
+هذي بيستخدموها عادة في مواصير الميهاللي هي بتستخدم
+
+41
+00:03:54,560 --> 00:03:58,480
+للتدفئة الآن في بعض البيوت برا بيعملوا central
+
+42
+00:03:58,480 --> 00:04:01,820
+heating اللي هي تدفئة المركزية التدفئة المركزية
+
+43
+00:04:01,820 --> 00:04:06,380
+إيش بيعملوا فيها؟ ميه حامية و بيدخلوها على قنابيب
+
+44
+00:04:06,380 --> 00:04:11,060
+و بيلفوها حوالين البيت فهذا الميه الحامية بتطلع
+
+45
+00:04:11,060 --> 00:04:15,580
+حرارة بتدفئ البيت فهذه المواثير المعمولة منها
+
+46
+00:04:15,580 --> 00:04:22,200
+بتبقى مصنوعة من ال copper انحاسOkay. Copper is
+
+47
+00:04:22,200 --> 00:04:27,560
+widely used in alloys notably brass. إيش ال brass؟
+
+48
+00:04:27,560 --> 00:04:34,280
+أيوة في .. في ممكن هذه ماتشوفوهوش كتير، في صواني
+
+49
+00:04:34,280 --> 00:04:40,720
+الزمان أو الأوان النحاسيةبيعملولها طبقة بيغلفوها
+
+50
+00:04:40,720 --> 00:04:44,560
+من ال brass الموجود هنا ال bronze اللي هو إيش
+
+51
+00:04:44,560 --> 00:04:46,860
+اللون ال bronze هذا اللي بتشوفوه أو الحاجات
+
+52
+00:04:46,860 --> 00:04:53,320
+البرونزية cover and tin و بعض الأحيان إيش lead
+
+53
+00:04:53,320 --> 00:05:08,130
+كويسة؟ ال tin ..لأ لأ مش تنهار الان في عدة معادن
+
+54
+00:05:08,130 --> 00:05:14,890
+إيش بنعمل فيهم في مادة بيشتغلوا فيها تبعين زمان
+
+55
+00:05:14,890 --> 00:05:20,190
+الحددين الحددين ما هي .. كل الشغلات اختفت هذه
+
+56
+00:05:20,190 --> 00:05:24,370
+الحدد كان .. كان بيستخدم ال oxygen في عنده مكوه
+
+57
+00:05:24,370 --> 00:05:32,330
+صغير فهي الجسديرأيوة الجسدير بلحم فيه الحداد
+
+58
+00:05:32,330 --> 00:05:36,430
+والعين بلحم فيه تبعين الكهربا اللي بتخص في الكهربا
+
+59
+00:05:36,430 --> 00:05:42,250
+لما بنعمل هذا بيجيب الجسدير والهالي هذه ال lead
+
+60
+00:05:42,250 --> 00:05:49,930
+اللي هي .. هذه مادة في الغالب سامة كويس لو وجدت في
+
+61
+00:05:49,930 --> 00:05:54,590
+.. في .. في الميه في غيره هدم المواد السامة بس هذه
+
+62
+00:05:54,590 --> 00:06:00,460
+بتعطي صلابة لل ..لها كلمة بس أنا بدورش على المعاني
+
+63
+00:06:00,460 --> 00:06:04,580
+العربي ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+64
+00:06:04,580 --> 00:06:04,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+65
+00:06:04,920 --> 00:06:05,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+66
+00:06:05,220 --> 00:06:05,580
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+67
+00:06:05,580 --> 00:06:09,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+68
+00:06:09,160 --> 00:06:09,280
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+69
+00:06:09,280 --> 00:06:18,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+70
+00:06:18,800 --> 00:06:19,200
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+71
+00:06:19,200 --> 00:06:19,980
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+72
+00:06:19,980 --> 00:06:20,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+73
+00:06:20,440 --> 00:06:20,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+74
+00:06:20,520 --> 00:06:20,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+75
+00:06:20,840 --> 00:06:27,540
+.. ال .. الالفضة is طالع عليه precious .. precious
+
+76
+00:06:27,540 --> 00:06:33,980
+metal ايش يعني precious؟ من المعادن الثمينةa
+
+77
+00:06:33,980 --> 00:06:37,500
+reference to its high cost يعني دايما تكلفة ..
+
+78
+00:06:37,500 --> 00:06:42,960
+دايما الدهب و الفضة مشهورين بالإيش؟ بال .. التكلفة
+
+79
+00:06:42,960 --> 00:06:46,520
+الغالية it is a better electrical conductor than
+
+80
+00:06:46,520 --> 00:06:50,440
+any other material هي أحسن إشي لنستخدمه في الكهربا
+
+81
+00:06:50,440 --> 00:06:54,320
+بس كام واحد بيستخدم حاجات من الفضة في الكهربا؟
+
+82
+00:06:54,950 --> 00:06:58,730
+الجليل لأنه سعر .. او الدهب لأن سعرهم غالي ماحدش
+
+83
+00:06:58,730 --> 00:07:03,170
+بيستخدمهم، so often .. it's often used for
+
+84
+00:07:03,170 --> 00:07:05,930
+electronic connections
+
+85
+00:07:07,660 --> 00:07:11,260
+في الهاتف الان another precious metal ايش هو ال
+
+86
+00:07:11,260 --> 00:07:14,620
+gold is also an excellent conductor بس بتشوف عشان
+
+87
+00:07:14,620 --> 00:07:19,760
+حد بيستخدم ال gold لأي توصيلة كهربائية and is
+
+88
+00:07:19,760 --> 00:07:24,540
+highly .. now is highly corrosion resistance الدهب
+
+89
+00:07:24,540 --> 00:07:31,180
+شفت عمر الدهب بتاكل؟ بتاكلش انحاس بصدي كل شيء الا
+
+90
+00:07:31,180 --> 00:07:37,420
+ايش الدهب فهو حاجة يعني زي ما بيقولها اكتر منو
+
+91
+00:07:37,420 --> 00:07:42,740
+الفضل هدول متاكلنش بس ماحدش بيستخدمهم لإن precious
+
+92
+00:07:42,740 --> 00:07:48,940
+metals تمانهم غالي في حاجة بنسميها plating with
+
+93
+00:07:48,940 --> 00:07:54,240
+non-ferrous metals إيش يعني plating؟
+
+94
+00:07:54,240 --> 00:07:57,740
+تصفيح أو زي ما بيقولوا إحنا إيش لما بنعمل حاجة،
+
+95
+00:07:57,740 --> 00:08:04,020
+بنغلفها، بندهنها، صح؟أو plating أو إيش بنرسب عليها
+
+96
+00:08:04,020 --> 00:08:09,200
+حاجات يعني بن .. ايوة بنمنع عملية التأكل أو الصدر
+
+97
+00:08:09,200 --> 00:08:13,240
+nonferrous metal can be used to protect steel from
+
+98
+00:08:13,240 --> 00:08:18,260
+corrosion by plating it احنا عادة لو نجيبنا للحديد
+
+99
+00:08:18,260 --> 00:08:22,260
+و بدنا نخلوه مايتأكلش إيش بدنا نسوي؟ بدنا نغلفه
+
+100
+00:08:23,410 --> 00:08:27,750
+الان that is covering it with a layer of non-metal
+
+101
+00:08:27,750 --> 00:08:33,450
+بدنا نغلفه بطبقة مش .. metal زي الآن طلع إن احنا
+
+102
+00:08:33,450 --> 00:08:38,130
+في البيت إيش بنسوي؟ لا الحديد بندهنه، مظبوط؟ هذه
+
+103
+00:08:38,130 --> 00:08:42,050
+plating، الآن هذا جزء من عملية ال plating، الآن
+
+104
+00:08:42,050 --> 00:08:47,630
+اللي بنتكلم عليه an example is galvanization ..
+
+105
+00:08:47,630 --> 00:08:52,170
+galvanizing بتعرف الجالفنة؟ لو بنقول حديد م galvan
+
+106
+00:08:52,980 --> 00:08:58,840
+هو إيش؟ لأ ال .. ال galvanization أنت زي الجلتان
+
+107
+00:08:58,840 --> 00:09:03,460
+عاملية بس إيش أنت بتغطيه بطبقة تانية، الآن هذه
+
+108
+00:09:03,460 --> 00:09:07,560
+عملية ال galvanization ممكن تكون manual إنه أنا
+
+109
+00:09:07,560 --> 00:09:12,620
+باجي للشغل و بحطها مثلا بجيب عندي بركة أو شيء و ب
+
+110
+00:09:12,620 --> 00:09:16,260
+.. و بغطها فيها و بطلحها تنشف، هذه الطريقة
+
+111
+00:09:16,260 --> 00:09:21,590
+البدائية جدامظبوط يمكن حتى ناس كتير بتكلمه لما بدك
+
+112
+00:09:21,590 --> 00:09:26,630
+تسوي في دهان البواب ده بتطلع فيه دهان بواب بتلاقيه
+
+113
+00:09:26,630 --> 00:09:31,850
+بلمعة وفيه دهان عادي مظبوط أبو لمعة اسأل النجار
+
+114
+00:09:31,850 --> 00:09:36,170
+بيقولك مات .. ماتستخدموهوش لأنه لو انضرب أي إشي
+
+115
+00:09:36,170 --> 00:09:40,750
+فيه صعب هذا بيسموه صب الدهان بالصب بييجي بيكب و
+
+116
+00:09:40,750 --> 00:09:45,130
+بقعد يسوي فيه فهذا بيسوي طبقة عازة بس لما بدك
+
+117
+00:09:45,130 --> 00:09:51,100
+تستعمليه صيانةصعبة جدا، فال galvanization عملية زي
+
+118
+00:09:51,100 --> 00:09:55,720
+هيك، يا بدك تصبي على حاجة، يا إما إيش، بدك تحطيها
+
+119
+00:09:55,720 --> 00:10:00,320
+في شيء، تغرقيه و تطلعيه ال steel can be .. طلع على
+
+120
+00:10:00,320 --> 00:10:03,900
+اللي عندي هان ال steel can be hot dip galvanized
+
+121
+00:10:03,900 --> 00:10:09,300
+يعني باجي لشغلة ساخنة و بساحة و بنزله فيها و
+
+122
+00:10:09,300 --> 00:10:13,260
+بطلعه، كويس؟ يعني أنا لما بدي أعمل عملية ال
+
+123
+00:10:13,260 --> 00:10:18,620
+galvanization، بدي تكون الشغلة سخنةby placing in
+
+124
+00:10:18,620 --> 00:10:24,380
+molten zinc الآن ال molten اللي هو ال liquid ال
+
+125
+00:10:24,380 --> 00:10:29,560
+zinc سائح و انا بدخله فيه سائل السائل ليش بديكون
+
+126
+00:10:29,560 --> 00:10:33,820
+ال zinc مادة صلبة لما بدي سايحه يعني بديكون ساخن و
+
+127
+00:10:33,820 --> 00:10:39,020
+بدي نزل هذا فيه و اطلعه it can also be electro
+
+128
+00:10:39,020 --> 00:10:43,580
+galvanized و هذه الطرق الحديثة التكنولوجية electro
+
+129
+00:10:43,580 --> 00:10:48,620
+يعني عن طريق ال إيش الكهرباالان which is the type
+
+130
+00:10:48,620 --> 00:10:52,160
+of electroplating الـ electroplating هاي شايفين
+
+131
+00:10:52,160 --> 00:10:55,900
+اللي عندي هاي عندي ال metal being used for plating
+
+132
+00:10:55,900 --> 00:11:00,280
+الزنك بنحطها هنا على ايش الموجب ال positive
+
+133
+00:11:00,280 --> 00:11:05,780
+terminal هذه بنسميها ال anode positive terminal
+
+134
+00:11:05,780 --> 00:11:10,580
+الاسم تبعها ايش؟ anode دخلتوه بالثانوية مظبوط وهذه
+
+135
+00:11:10,580 --> 00:11:15,000
+كاتود بنحط ال steel component that being plated
+
+136
+00:11:15,000 --> 00:11:20,220
+بنحطها في الكاتودهنا ال .. الحاجة اللي بنحطها
+
+137
+00:11:20,220 --> 00:11:25,740
+تانية اللي هي المادة الموصل بنسميها electrolyte
+
+138
+00:11:25,740 --> 00:11:30,780
+اللي هي ايش؟ المادة الموصل لأ ال electrolyte اللي
+
+139
+00:11:30,780 --> 00:11:34,140
+هي المادة اللي بنحطها هنا الموصل هنا المادة اللي
+
+140
+00:11:34,140 --> 00:11:39,680
+بدي ارسب منها او بدي ادهن منها خليني اقول هنا ال
+
+141
+00:11:39,680 --> 00:11:45,480
+item اللي انا بدي اعمله galvanizationهنا المادة
+
+142
+00:11:45,480 --> 00:11:49,760
+الموصلة بنسميها الـ electrolyte اللي عندى وهنا ال
+
+143
+00:11:49,760 --> 00:11:54,360
+terminal ال electricity which electroplating with
+
+144
+00:11:54,360 --> 00:11:57,500
+this technique the steel components is placed in a
+
+145
+00:11:57,500 --> 00:12:01,880
+liquid often an acid عادة ال liquid هذا بيبقى حمض
+
+146
+00:12:01,880 --> 00:12:06,880
+okay called the electrolyte and connected to the
+
+147
+00:12:06,880 --> 00:12:11,410
+negative terminalof the electrical supply to
+
+148
+00:12:11,410 --> 00:12:16,330
+become the cathode، the negative side، الكاتود
+
+149
+00:12:16,330 --> 00:12:23,390
+وهذه مرة تعالى كنت .. ما حكيت؟
+
+150
+00:12:26,500 --> 00:12:31,460
+مع هذه التقنية التجارب الصناعة موضعة في ميزة عادة
+
+151
+00:12:31,460 --> 00:12:35,520
+في ميزة مسمى إلكتروليت ومتصلة بالمقاطع
+
+152
+00:12:35,520 --> 00:12:39,740
+الإلكتريكالية لتصبح الميزة الكاتويد اللي هو الـ
+
+153
+00:12:39,740 --> 00:12:43,660
+negative pipe مجزرة من الزنك موضعة أيضًا في الميزة
+
+154
+00:12:43,660 --> 00:12:48,950
+الإلكتريكالية ومتصلة بالمقاطع المفضلةهي اللي عندى
+
+155
+00:12:48,950 --> 00:12:51,910
+ال positive terminal of the supply this then
+
+156
+00:12:51,910 --> 00:12:55,450
+becomes the anode or the positive side an electric
+
+157
+00:12:55,450 --> 00:12:59,630
+current then flows between the pieces of metal
+
+158
+00:12:59,630 --> 00:13:02,930
+through the electrolyte this causes a chemical
+
+159
+00:13:02,930 --> 00:13:08,170
+reaction هذا اللي بحصل عندىElectric current causes
+
+160
+00:13:08,170 --> 00:13:12,350
+a chemical reaction which deposits zinc on the
+
+161
+00:13:12,350 --> 00:13:14,830
+cathode depleting the components يعني إيش اللي
+
+162
+00:13:14,830 --> 00:13:20,530
+بيصير عنده؟ الذنك بيروح من ال .. ال anode يعني هذه
+
+163
+00:13:20,530 --> 00:13:24,870
+ال .. الايونات تبعت الذنك تعرفوا الايون إيش؟ هو
+
+164
+00:13:24,870 --> 00:13:28,170
+الايون
+
+165
+00:13:28,170 --> 00:13:33,330
+اللي هي الضرر لما سواء ال positive بتفقد ال
+
+166
+00:13:33,330 --> 00:13:38,100
+electrode و ال negativeأيوة، الآن هذه اللي عندى ال
+
+167
+00:13:38,100 --> 00:13:42,140
+terminal إيش هي؟ negative لو عندى positive ion إيش
+
+168
+00:13:42,140 --> 00:13:46,580
+بدى يروح؟ بدى get attracted لل negative فهذا اللي
+
+169
+00:13:46,580 --> 00:13:51,380
+بيحصل عندي عرفتوا إيش اللي بيحصل؟ فهي بيحصل إنه
+
+170
+00:13:51,380 --> 00:13:57,420
+هذا عملية كيميائية فيزيائية اللي بتحصل إنه هنا ال
+
+171
+00:13:57,420 --> 00:14:01,380
+positive ion تبعت ال zinc بتروح على ال cathode و
+
+172
+00:14:01,380 --> 00:14:06,380
+بتلزق في اللي موجود عندى فبتعملى طبقةاللي هي طبقة
+
+173
+00:14:06,380 --> 00:14:11,600
+الوقاية اللي احنا بنتكلم فيها a related process
+
+174
+00:14:11,600 --> 00:14:16,980
+called anodizing is used to protect aluminum the
+
+175
+00:14:16,980 --> 00:14:20,760
+components to be anodized is connected to the
+
+176
+00:14:20,760 --> 00:14:24,460
+positive terminal هاي نفس الشغلة اللي عندى هنا بس
+
+177
+00:14:24,460 --> 00:14:28,820
+هنا عملناها ايش anodizing لأن اللي بنعمله هذا لمين
+
+178
+00:14:28,820 --> 00:14:34,290
+للالمونيوم اللي عندى الموجود فيه هناطلع عندى ايش
+
+179
+00:14:34,290 --> 00:14:38,730
+الفرق هنا اللى حطناها ايش ال aluminum components
+
+180
+00:14:38,730 --> 00:14:42,490
+هنا ال cathode اللى اللى موجود عندى هنا ال bathing
+
+181
+00:14:42,490 --> 00:14:48,420
+containing ال electro lightis connected to the
+
+182
+00:14:48,420 --> 00:14:51,780
+positive terminal to become the anode and placed
+
+183
+00:14:51,780 --> 00:14:55,380
+in the electrolyte with a cathode and electricity
+
+184
+00:14:55,380 --> 00:14:59,660
+flow through the aluminum aluminum oxide is
+
+185
+00:14:59,660 --> 00:15:02,520
+deposited on the anode هذا ايش اللي احنا بتتذكره
+
+186
+00:15:02,520 --> 00:15:06,520
+محاضرة فادة ايش اتكلمنا قولنا ال aluminum oxide
+
+187
+00:15:06,520 --> 00:15:12,620
+مادة هي هي شبيهة بال rust ال rust اللي هو الصدى
+
+188
+00:15:12,620 --> 00:15:18,050
+فالصدى ال aluminumvery hard وبتعمل طبقة protective
+
+189
+00:15:18,050 --> 00:15:23,550
+فهي هذه يعني اللي بتحمي الطبقات اللي بعتها فالغرض
+
+190
+00:15:23,550 --> 00:15:27,990
+من هذه العملية انه ندخل صدر ألمنيوم على الألمنيوم
+
+191
+00:15:27,990 --> 00:15:32,330
+عشان نحميه عشان هي كده بنسميها anodizing اللي هي
+
+192
+00:15:32,330 --> 00:15:35,270
+.. ال .. ال .. الاسم تبعها اختلف عن اللي قبل ما
+
+193
+00:15:35,270 --> 00:15:39,190
+يكون اكسيد الألمنيوم يا عزيزي هو بيكون مادة هي هي
+
+194
+00:15:39,190 --> 00:15:46,230
+ألمنيوم أكسيد أكسيد الألمنيومهو صدق، بس صدق ..
+
+195
+00:15:46,230 --> 00:15:50,490
+المحاضرة الفاتحة تقول صدق الألمنيوم بيحمي الطبقة،
+
+196
+00:15:50,490 --> 00:15:53,990
+بيعملش .. بيخليش يتخلل الطبقات اللي منها و تحت،
+
+197
+00:15:53,990 --> 00:15:59,000
+بينما صدق الحديد إيش بيصير؟ هو بيجشربجشر و بيصير
+
+198
+00:15:59,000 --> 00:16:02,960
+الطبقات اللي تحته تصدوا و تجشر لما ايش تدوب
+
+199
+00:16:02,960 --> 00:16:07,300
+الحديدة فالالمونيوم لأ بيعمل hard cover و بنعمل ..
+
+200
+00:16:07,300 --> 00:16:11,500
+اذا لاحظته لما اتكلمنا على اخر عملية في عملية ال
+
+201
+00:16:11,500 --> 00:16:16,740
+culture ايش قلنا عملنا؟ دخلنا صدا بس الصدا هذا
+
+202
+00:16:16,740 --> 00:16:23,280
+بيشتغل زي الالمونيومفبيعطيني الشكل تبع اللي هاي بس
+
+203
+00:16:23,280 --> 00:16:27,040
+ايش بدوبش هاي وهذا بيستخدموها حتى في المناطق اللي
+
+204
+00:16:27,040 --> 00:16:32,020
+جريبة من البحر لأن البحر بتعرفوا رطوبة عالية و
+
+205
+00:16:32,020 --> 00:16:36,820
+التأكل بيخرب كل إشي فهذه بيعملوها في هذه العملية
+
+206
+00:16:36,820 --> 00:16:41,540
+and this is harder than aluminium metal it
+
+207
+00:16:41,540 --> 00:16:47,060
+provides a protection زي ما لاحظته هذهأقوى من
+
+208
+00:16:47,060 --> 00:16:53,280
+الالمنيوم وعشان هيك بتعمل protection الادنان ي
+
+209
+00:16:53,280 --> 00:16:57,480
+make the correct sentences using one from .. one
+
+210
+00:16:57,480 --> 00:17:00,320
+part from each column look at the opposite الادنان
+
+211
+00:17:00,320 --> 00:17:05,220
+تطلع عليه، تطلع عندي هنا دور الالمنيوم، إيش عندي؟
+
+212
+00:17:05,220 --> 00:17:08,940
+is an aluminum alloy that are contained ..
+
+213
+00:17:08,940 --> 00:17:15,080
+contains copper and magnesiumالان تواصلي بس مش فى
+
+214
+00:17:15,080 --> 00:17:19,960
+شجة واحدة فى شجتين الان titanium ايش بتيجي معها
+
+215
+00:17:19,960 --> 00:17:23,180
+can be mixed with copper while it resists
+
+216
+00:17:23,180 --> 00:17:27,580
+corrosion better than the other metal brushes, has
+
+217
+00:17:27,580 --> 00:17:30,580
+a high strength to weight ratio and is often
+
+218
+00:17:30,580 --> 00:17:31,460
+alloyed with
+
+219
+00:17:36,200 --> 00:17:40,280
+with aluminium اللي عندى اللي هان ولا with bronze
+
+220
+00:17:40,280 --> 00:17:44,900
+ولا brass ولا silver فش لل إيش ال aluminium الان
+
+221
+00:17:44,900 --> 00:17:50,180
+zinc إيش بتعملى can be mixed with copper to make
+
+222
+00:17:50,180 --> 00:17:57,420
+ال zinc مع ال copper إيش بيعملى brass مظبوط الآن
+
+223
+00:17:57,420 --> 00:18:01,860
+copper can be mixed with tin and lead to produce
+
+224
+00:18:01,860 --> 00:18:08,340
+meanالبرونز البرونز ايش بياخد قولنا tin and lead
+
+225
+00:18:08,340 --> 00:18:15,400
+طيب gold resist corrosion better than other
+
+226
+00:18:15,400 --> 00:18:21,400
+precious metals silver اللي عندك طبعا افضل اشي ال
+
+227
+00:18:21,400 --> 00:18:25,260
+gold في هذه المجال بس الطريقة اللي بدك تحفظيهم في
+
+228
+00:18:25,260 --> 00:18:30,520
+هذه ايش هي الان البرونز ايش التكوينة تبعتهاللي هو
+
+229
+00:18:30,520 --> 00:18:35,300
+ايش قولنا؟ Tin and lead البراس بتكون من أيش؟
+
+230
+00:18:35,300 --> 00:18:41,380
+Copper and zinc الان التيتانيوم مع الالمونيوم
+
+231
+00:18:41,380 --> 00:18:46,240
+بيعملولي ايش؟ بيعملوا .. بيعملوا .. بيعملوا
+
+232
+00:18:46,240 --> 00:18:50,140
+strength .. strong material الان ال brushes metals
+
+233
+00:18:50,140 --> 00:18:55,960
+عبارة عن ايش؟الجولد والسلفر والجولد the best
+
+234
+00:18:55,960 --> 00:18:59,540
+conductor او ال .. ال best يعني خلينا نقول
+
+235
+00:18:59,540 --> 00:19:07,960
+resistance for corrosion اللي عندى طيب الأن metals
+
+236
+00:19:07,960 --> 00:19:12,460
+ايش اللي بدنا نقول عن انواع ال metals؟ في سؤال
+
+237
+00:19:12,460 --> 00:19:13,100
+عندك؟
+
+238
+00:19:15,750 --> 00:19:19,430
+السؤال الأول هو complete the word group below
+
+239
+00:19:19,430 --> 00:19:24,050
+using the names of the metals in 13 one بدنا الـ
+
+240
+00:19:24,050 --> 00:19:28,550
+metal elements فلنحطهم هنا alloys و precious مرضو
+
+241
+00:19:28,550 --> 00:19:35,410
+.. مرضو .. هاي .. هاي بدنا ال metal alloys
+
+242
+00:19:35,410 --> 00:19:41,290
+و بدنا precious metals
+
+243
+00:19:43,560 --> 00:19:49,980
+نجي نطلع على السؤال اللي قبله الان نجي نطلع
+
+244
+00:19:49,980 --> 00:20:00,920
+تيتانيوم ايش هذا؟ متر، زنك، كابر، gold يعني هذه
+
+245
+00:20:00,920 --> 00:20:07,580
+بنحطها .. خلّينا نقول a, b, c، نصنفهم هذه هذه
+
+246
+00:20:07,580 --> 00:20:22,010
+بتيجي تحت ايش؟ a, a, a, cهذه C A و C هى طيب هده A
+
+247
+00:20:22,010 --> 00:20:34,810
+و C Press B Aluminium Prunes Magnesium A دلها
+
+248
+00:20:34,810 --> 00:20:44,510
+درالهم B طيب اش في عنده دل حاجةفي aluminum موجودة
+
+249
+00:20:44,510 --> 00:20:51,250
+هنخلصنا هيك هذه lead و zinc هنا هى ايه؟ هى ايه؟
+
+250
+00:20:51,250 --> 00:20:54,570
+كويس؟
+
+251
+00:20:54,570 --> 00:20:59,890
+اللى هى هذه زى ما حكينا nonferrous اللى بنطلع
+
+252
+00:20:59,890 --> 00:21:04,990
+عليها nonferrous metals اللى موجودة عندى في هذه
+
+253
+00:21:04,990 --> 00:21:10,070
+الآن اللى عندى ال alloysاللي عندى B و الـ C اللي
+
+254
+00:21:10,070 --> 00:21:13,790
+عندى ال precious metals و ال precious metals
+
+255
+00:21:13,790 --> 00:21:21,510
+سمناهم اللي هنا موجودين ال gold و ال silver طيب
+
+256
+00:21:21,510 --> 00:21:33,730
+التالت طيب
+
+257
+00:21:33,730 --> 00:21:40,150
+metal elements هاي اللي هناComplete the checklist
+
+258
+00:21:40,150 --> 00:21:44,830
+list for Electroplating using the words in the box
+
+259
+00:21:44,830 --> 00:21:49,190
+اللي عندى في عندى Anode, Cathode, Electrolyte,
+
+260
+00:21:49,330 --> 00:21:53,710
+Electroplating, Galvanizing, Negative, Plated,
+
+261
+00:21:54,130 --> 00:21:59,610
+Positive Check that there is sufficient ايش in the
+
+262
+00:21:59,610 --> 00:22:04,930
+path to completely cover the components الان انا
+
+263
+00:22:04,930 --> 00:22:09,510
+لما بدى احط اي حاجةو بدي أعملها plating ايش اول
+
+264
+00:22:09,510 --> 00:22:14,570
+شرط انها بتغطي المادة هذه ال acid اللي بدي أحطه
+
+265
+00:22:14,570 --> 00:22:19,530
+بدي أغطي الادش بناه ايش هذا سمناه ال electrolyte
+
+266
+00:22:19,530 --> 00:22:24,470
+يعني هاي واحد، كويس؟ there is sufficient
+
+267
+00:22:24,470 --> 00:22:28,290
+electrolyte اللي عندي in order to ensure that the
+
+268
+00:22:28,290 --> 00:22:32,510
+component will subsequently be ايش over its entire
+
+269
+00:22:32,510 --> 00:22:33,030
+surface
+
+270
+00:22:38,120 --> 00:22:43,580
+to be plated over its entirety يعني هذا اللي
+
+271
+00:22:43,580 --> 00:22:50,640
+بتحطيه عشان يتغطى كاملا لازم يكون هو في مهد مغطيه
+
+272
+00:22:50,640 --> 00:22:55,500
+الاسد مغطيه في هذا المجال ensure that the
+
+273
+00:22:55,500 --> 00:23:02,260
+component is connected to the negative terminal
+
+274
+00:23:05,600 --> 00:23:15,320
+هي وين هنا؟ تلاتة of the electrical supply during
+
+275
+00:23:15,320 --> 00:23:22,500
+the إيش؟ electroplating، هاي four process the
+
+276
+00:23:22,500 --> 00:23:28,740
+component should function as negative بدروح معاه
+
+277
+00:23:28,740 --> 00:23:34,440
+إيش؟ كاتود، اللي هو هاي خمسة أين راحنا فيها؟ هاي
+
+278
+00:23:34,440 --> 00:23:40,600
+خمسةاكتشف ان المسلح يتم استخدامه للوصول للأمثلة
+
+279
+00:23:40,600 --> 00:23:49,000
+زنك 4 هو مرتبط
+
+280
+00:23:49,000 --> 00:23:53,340
+بالـ positive
+
+281
+00:23:57,360 --> 00:24:01,460
+Terminal of the electrical supply during the
+
+282
+00:24:01,460 --> 00:24:05,280
+process it should be functioned as a node التي هي
+
+283
+00:24:05,280 --> 00:24:11,180
+التمانية ولمّا تحط زي هيك شاف التكنيكات على رغم
+
+284
+00:24:11,180 --> 00:24:15,820
+بساطته انا بلاحظ في عندكم في أحيان بتحط السخنة
+
+285
+00:24:15,820 --> 00:24:20,280
+دلّك عودي إيدك أنا بحاول أعودكم أعمل زي هيك عشان
+
+286
+00:24:20,280 --> 00:24:20,800
+أنتوا
+
+287
+00:24:23,570 --> 00:24:30,530
+تعملوا copying لها ال process اللي بدك تتطلع عليها
+
+288
+00:24:30,530 --> 00:24:35,110
+احنا ايش عندنا اهم اشيها اتكلمنا عن ال process of
+
+289
+00:24:35,110 --> 00:24:39,210
+electroplating ال electroplating تتطلب يكون عندي
+
+290
+00:24:39,210 --> 00:24:43,810
+electrolyte اللي هو ال acid ال electrolyte ال acid
+
+291
+00:24:43,810 --> 00:24:47,590
+مش احنا هاي ال electroplating هاي اللي .. اللي ها
+
+292
+00:24:47,590 --> 00:24:53,090
+في عنديحاجة هنا و هنا .. خلّيني أقول هنا الكاتود
+
+293
+00:24:53,090 --> 00:24:59,930
+وهنا ال إيش؟ anode هذه موصلة مع ال positive
+
+294
+00:24:59,930 --> 00:25:04,690
+terminal وهذه موصلة مع ال negative terminal الآن
+
+295
+00:25:04,690 --> 00:25:09,910
+هذا السائل اللي عنده إيش سمنها؟ اللي هو acid ما هو
+
+296
+00:25:09,910 --> 00:25:15,710
+هذا الإسم اللي هتشوفوه كلمة acid إيش هو ال acid؟هو
+
+297
+00:25:15,710 --> 00:25:19,710
+عبارة عن ال electrolyte ال electrolyte اللي عندي
+
+298
+00:25:19,710 --> 00:25:27,530
+ها هنا اللي .. اللي بدي أحط ال إيش هنا بدي
+
+299
+00:25:27,530 --> 00:25:33,890
+أحط مثلا ال iron اللي عندي هنا، مظبوط؟ هنا بدي أحط
+
+300
+00:25:33,890 --> 00:25:39,150
+ال إيش؟ ال zinc اللي هو المادة اللي هتعمل لـ
+
+301
+00:25:39,150 --> 00:25:43,310
+galvanization هتعمل
+
+302
+00:25:48,230 --> 00:25:51,970
+Galvanizing هتعمل ليه؟ هاي لما تروح من هنا ايون
+
+303
+00:25:51,970 --> 00:25:56,130
+هتروح من هان لهان يعني هان بدي يطلع عندى positive
+
+304
+00:25:56,130 --> 00:26:03,430
+ايون هيدلوا ماشي لهان الان
+
+305
+00:26:03,430 --> 00:26:07,670
+هيترسب ال positive ions على مين؟ على ال service
+
+306
+00:26:07,670 --> 00:26:12,080
+اللى موجود عندى هانلما نترسب على ال service بيصير
+
+307
+00:26:12,080 --> 00:26:16,480
+لها عملية اللي هي ال galvanization أو ال galvanة
+
+308
+00:26:16,480 --> 00:26:23,360
+اللي بيسميها بال .. بالعامية عندنا أه كويس؟ الآن
+
+309
+00:26:23,360 --> 00:26:28,660
+من الشغلات اللي طلعنا عليهم إيش هما؟ أولا كلمة ال
+
+310
+00:26:28,660 --> 00:26:31,880
+nonferrous metals هذه صارت من الشغلات اللي احنا
+
+311
+00:26:31,880 --> 00:26:36,940
+لازم نعتبرها ان عرفت إيش ال nonferrous metals؟
+
+312
+00:26:38,300 --> 00:26:42,940
+metals that do not contain iron الferrous metals
+
+313
+00:26:42,940 --> 00:26:50,020
+اللي هى ايش؟ اللي هى .. metals that contain iron
+
+314
+00:26:50,020 --> 00:27:00,760
+الان عملية ال .. ال plating اللي هى عملية ال ايش؟
+
+315
+00:27:00,760 --> 00:27:07,610
+هى .. هى لو قلت a process toخلّيني أقول لو في عندي
+
+316
+00:27:07,610 --> 00:27:14,510
+a process to fight or resist corrosion إيش بنسميها
+
+317
+00:27:14,510 --> 00:27:19,530
+الـplating a process to resist or to fight
+
+318
+00:27:19,530 --> 00:27:24,310
+corrosion هي عملية الـplating زي عملية الطلاقة هي
+
+319
+00:27:24,310 --> 00:27:31,710
+كويسة بس بدل ما نطلب بوية بنطلب إيش؟ معادن اللي هي
+
+320
+00:27:31,710 --> 00:27:33,830
+nonferrous metals
+
+321
+00:27:45,650 --> 00:28:04,350
+طيب نرجع تاني نشوف
+
+322
+00:28:04,350 --> 00:28:07,570
+حد يقرأ، ماحدش بده
+
+323
+00:28:30,350 --> 00:28:44,910
+دورة لوميوم دورة لوميوم دورة لوميوممن من دورة لومن
+
+324
+00:28:44,910 --> 00:28:50,050
+دورة لومن دورة لومن دورة لومن دورة لومن دورة لومن
+
+325
+00:28:50,050 --> 00:28:50,770
+دورة لومن دورة لومن دورة لومن دورة لومن دورة لومن
+
+326
+00:28:50,770 --> 00:28:51,110
+دورة لومن دورة لومن دورة لومن دورة لومن دورة لومن
+
+327
+00:28:51,110 --> 00:28:51,910
+دورة لومن دورة لومن دورة لومن دورة لومن دورة لومن
+
+328
+00:28:51,910 --> 00:28:57,850
+دورة لومن دورة لومن دورة لومن دورة لومن دورة لومن
+
+329
+00:28:57,850 --> 00:29:01,870
+دورة لومن
+
+330
+00:29:05,550 --> 00:29:09,550
+يعني خلينا نقول أقوى من الألمنيوم لأن الألمنيوم
+
+331
+00:29:09,550 --> 00:29:15,290
+بدي حد منكم مسك الألمنيوم خفيف بس ضعيف يعني لو جيت
+
+332
+00:29:15,290 --> 00:29:18,770
+انت بدك تتعذيب انت عايز لحاله طب هل هذا ممكن نعمل
+
+333
+00:29:18,770 --> 00:29:23,910
+منه للطائرات ولا غيره؟ لأن الطيارة بتعرف تتعرض
+
+334
+00:29:23,910 --> 00:29:30,620
+لظروف صعبة أولا ضغط جوةال .. ال .. الموجودة الحاجة
+
+335
+00:29:30,620 --> 00:29:36,320
+التانية برضه في ال .. الطوارق أحيانا بدها تنزل ..
+
+336
+00:29:36,320 --> 00:29:39,500
+لأ أحيانا في الطوارق بتنزل crash landing يمكن
+
+337
+00:29:39,500 --> 00:29:43,880
+نتكلم عن ال crash landing إيش أنها بتيجي بتنزل في
+
+338
+00:29:43,880 --> 00:29:46,580
+ظروف طبيعية .. غير مش طبيعية يعني بتيجي الطيارة
+
+339
+00:29:46,580 --> 00:29:50,940
+بدل ما تنزل طبيعي بتنزل .. هي تزحف على الجسم
+
+340
+00:29:50,940 --> 00:29:56,620
+بتستخدم جسمها للحماية فده لو كان ضعيف بتطبق على
+
+341
+00:29:56,620 --> 00:30:02,500
+اللي فيه، مظبوط؟فهو عشان هي كإيش بتتكلم نتكلم عنه
+
+342
+00:30:02,500 --> 00:30:09,900
+هادي مادة صلبة very strong light weight هي قوية
+
+343
+00:30:09,900 --> 00:30:15,190
+جدا وخفيفة جداyou can allow use in aircraft
+
+344
+00:30:15,190 --> 00:30:20,870
+manufacturing which also contain carbon 1.1% and
+
+345
+00:30:20,870 --> 00:30:26,970
+magnesium 1.5% and you can also be allowed with
+
+346
+00:30:26,970 --> 00:30:31,230
+titanium to produce natural light which you don't
+
+347
+00:30:37,990 --> 00:30:43,290
+which makes it ideal for you in electric wires
+
+348
+00:30:43,290 --> 00:30:47,870
+goes back .. back to the tree and also makes it
+
+349
+00:30:47,870 --> 00:30:52,290
+suitable for bio cover is biodegradable in alloys
+
+350
+00:30:52,290 --> 00:30:58,130
+and not in wood and clay and brass is copper and
+
+351
+00:30:58,130 --> 00:31:02,810
+zinc and bronze copper and tin and silicon and
+
+352
+00:31:02,810 --> 00:31:05,950
+zinc this bio is precious, precious
+
+353
+00:31:23,020 --> 00:31:28,100
+Okay السطر البعد اللي هو بس بيكمل الصفحة اللي هو
+
+354
+00:31:28,100 --> 00:31:32,440
+بتكلم على ال gold is also an excellent conductor
+
+355
+00:31:32,440 --> 00:31:37,720
+طيب مين هتتكلم على ال plating تقرا؟ فضلا
+
+356
+00:31:54,270 --> 00:32:03,750
+Galvanization Galvanizing Galvanize
+
+357
+00:32:03,750 --> 00:32:11,050
+By placing it in molten liquidممكن أيضًا أن يكون
+
+358
+00:32:11,050 --> 00:32:16,210
+الهجوم الهجوم الهجوم الهجوم الهجوم الهجوم الهجوم
+
+359
+00:32:16,210 --> 00:32:20,190
+الهجوم الهجوم الهجوم الهجوم الهجوم الهجوم الهجوم
+
+360
+00:32:20,190 --> 00:32:36,290
+الهجوم الهجوم الهجوم الهجوم الهجوم الهجوم الهجوم
+
+361
+00:32:41,690 --> 00:32:46,890
+طيب مين بدها تكمل التانية؟
+
+362
+00:32:46,890 --> 00:32:52,210
+بدها تشوف ترفع القلم بقى. في حدا هنا بدها كانت؟
+
+363
+00:32:52,210 --> 00:32:54,310
+طيب تفضل
+
+364
+00:33:06,440 --> 00:33:14,920
+والكتره كانت تبقى موجودة في مجموعه وكانت موجودة في
+
+365
+00:33:14,920 --> 00:33:22,900
+مجموعه وكانت موجودة في مجموعه وكانت موجودة في
+
+366
+00:33:22,900 --> 00:33:24,420
+مجموعه وكانت موجودة في مجموعه
+
+367
+00:33:39,610 --> 00:33:46,890
+deposit يعني ايش deposit؟ لما تروح تحط دفعة في
+
+368
+00:33:46,890 --> 00:33:53,870
+البنك ايش بتعمليه؟ ايداع ال deposit عملية الايداع
+
+369
+00:33:55,310 --> 00:33:59,350
+هي .. هي
+
+370
+00:33:59,350 --> 00:34:06,790
+عشان الكلمات برضه ضالها مركزها دوبوزيت اي داع فهي
+
+371
+00:34:06,790 --> 00:34:12,030
+دوبوزيت انت ها إيش بتعمل which deposit zinc on the
+
+372
+00:34:12,030 --> 00:34:17,510
+cathode لما إيش دوبوزيت بتحط بتدع الذنك على ال ..
+
+373
+00:34:17,510 --> 00:34:19,370
+ال cathode اللي عندي
+
+374
+00:34:25,520 --> 00:34:30,580
+أش حكينا بالهندسة في كلمات كتير أحيانا بتيجي تتطلع
+
+375
+00:34:30,580 --> 00:34:36,610
+عليها إلها معانا بتختلف عن معنى الحقيقيالان احنا
+
+376
+00:34:36,610 --> 00:34:41,010
+كهندسة زي ما حكيت بنحب دايما لو بنتكلم ماحدش يفهم
+
+377
+00:34:41,010 --> 00:34:48,590
+علينا اللي الهندسة هذه من الشغلات اللي بتلاحظيها ف
+
+378
+00:34:48,590 --> 00:34:52,590
+.. فهذه من الشغلات ال coding بنحب نعمل coding
+
+379
+00:34:52,590 --> 00:34:56,910
+لشغلات كتيرة فبتلاقي من ضمن الشغلات اللي بتحصل ان
+
+380
+00:34:56,910 --> 00:35:01,510
+بعض الكلمات بتعني لنا شي بتعني للناس تاني حاجة
+
+381
+00:35:01,510 --> 00:35:07,970
+تانيةرأي واحد طيب لأ لأ لأ ال process called
+
+382
+00:35:07,970 --> 00:35:11,670
+anodizing is used to protect aluminium component
+
+383
+00:35:11,670 --> 00:35:14,550
+to be anodized is connected to the positive
+
+384
+00:35:14,550 --> 00:35:19,250
+tetanus to become to become the anode and placed
+
+385
+00:35:19,250 --> 00:35:23,230
+in an electrolyte with a cathode as interesting
+
+386
+00:35:23,230 --> 00:35:28,590
+glass full of aluminium oxide is deposited on the
+
+387
+00:35:28,590 --> 00:35:34,860
+anode as this is harder than aluminium metalال
+
+388
+00:35:34,860 --> 00:35:39,240
+protections الدرس هذا من الدروس السهلة، هذا
+
+389
+00:35:39,240 --> 00:35:45,680
+لاحظته؟ يعني بتحفظوه بسرعة؟
+
+390
+00:35:45,680 --> 00:35:50,820
+يعني مالاحظوش أنه سهل؟
+
+391
+00:35:50,820 --> 00:36:00,640
+طيب بالنسبة لنا هي ..هنوزعلكم الموجود هاي بتاخد ال
+
+392
+00:36:00,640 --> 00:36:05,580
+.. ال .. هاي في سؤال .. السؤال بالنسبة لل .. هذا A
+
+393
+00:36:05,580 --> 00:36:11,120
+و B في السؤال A في واحدة فيكم مش كاتبة اسمها مين
+
+394
+00:36:11,120 --> 00:36:18,380
+هي؟ مش هقول قداش جايبة جايبة
+
+395
+00:36:18,380 --> 00:36:24,060
+عشرة كلكم تكونوا إياها طيب السؤال عادة في السؤال
+
+396
+00:36:24,060 --> 00:36:28,890
+اتنينال answer الموجود مش موجود هنا، بس أنا طلعت
+
+397
+00:36:28,890 --> 00:36:34,050
+عليه، لقيت الغالبية العظمى ماخدين ال choice دي،
+
+398
+00:36:34,050 --> 00:36:37,030
+ليش هو بتكلم؟ the dimension measured from the line
+
+399
+00:36:37,030 --> 00:36:40,050
+down the middle of the ship، هذه سمنها إيش؟ ال
+
+400
+00:36:40,050 --> 00:36:41,330
+central line
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/hX5CWpY7Tbg_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/hX5CWpY7Tbg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..405a3b1a103e937d6865b519e5a999b7d2ba2f5f
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/hX5CWpY7Tbg_raw.json
@@ -0,0 +1 @@
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"end": 843.3, "word": " موجود", "probability": 0.9599609375}, {"start": 843.3, "end": 843.44, "word": " عندى", "probability": 0.809326171875}, {"start": 843.44, "end": 844.16, "word": " فبتعملى", "probability": 0.754736328125}, {"start": 844.16, "end": 844.72, "word": " طبقة", "probability": 0.955078125}], "temperature": 1.0}, {"id": 34, "seek": 87292, "start": 845.42, "end": 872.92, "text": "اللي هي طبقة الوقاية اللي احنا بنتكلم فيها a related process called anodizing is used to protect aluminum the components to be anodized is connected to the positive terminal هاي نفس الشغلة اللي عندى هنا بس هنا عملناها ايش anodizing لأن اللي بنعمله هذا لمين للالمونيوم اللي عندى الموجود فيه هنا", "tokens": [6027, 20292, 39896, 23032, 3555, 28671, 2423, 30543, 995, 10632, 13672, 1829, 1975, 5016, 8315, 44945, 2655, 4117, 19528, 8978, 11296, 257, 4077, 1399, 1219, 364, 378, 3319, 307, 1143, 281, 2371, 15656, 264, 6677, 281, 312, 364, 378, 1602, 307, 4582, 281, 264, 3353, 14709, 8032, 47302, 8717, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/qefHJ9wNvBE_postprocess.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/qefHJ9wNvBE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..35f760ef9782f33bba0202adbabf9317f2c2529a
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/qefHJ9wNvBE_postprocess.srt
@@ -0,0 +1,2184 @@
+1
+00:00:21,280 --> 00:00:26,720
+طيب السلام عليكم اليوم سنقوم بمقاطع الحلقة السادسة
+
+2
+00:00:26,720 --> 00:00:33,100
+حلقة السادسة تتكلم عن أقراص ديمينيائية لديها
+
+3
+00:00:33,100 --> 00:00:36,680
+أثنان حلقات حلقة السادسة أثنان تتكلم عن أقراص و
+
+4
+00:00:36,680 --> 00:00:44,940
+تلرانس أيش يعني أقراص أقراص أقراص
+
+5
+00:00:44,940 --> 00:00:47,000
+يعني تلرانس
+
+6
+00:00:48,970 --> 00:00:53,310
+variations accepted variation الآن لو روحت ل ..
+
+7
+00:00:53,310 --> 00:00:58,070
+خلّيني أحكيها بأي حاجة، بدي تصنع أي إشي فيه لكل
+
+8
+00:00:58,070 --> 00:01:03,690
+إشي مقادير، صح؟ لو بدي أصنع plastic، بدي أعمل أي
+
+9
+00:01:03,690 --> 00:01:08,070
+حاجة، على الرغم إن في مقادير بجيسها بالظبط، إلا إن
+
+10
+00:01:08,070 --> 00:01:11,870
+في عندي variation بتبقى مختلفة، يعني ال accuracy
+
+11
+00:01:11,870 --> 00:01:17,510
+لقداشيعني في عادة حتى الميزان لو بدى وزن عليه مش
+
+12
+00:01:17,510 --> 00:01:21,810
+كل إشي exact بعطيك إياها بيعطي شوية variation الآن
+
+13
+00:01:21,810 --> 00:01:25,150
+هذه ال variation إذا هي within the acceptable
+
+14
+00:01:25,150 --> 00:01:32,350
+range يعني هي في الحدود المقبولةفهي تعد .. يعني
+
+15
+00:01:32,350 --> 00:01:35,850
+بيسميها .. هنتكلم عنها في حاجة بيسميها in
+
+16
+00:01:35,850 --> 00:01:39,630
+tolerance .. within tolerance بيسموها لو كانت برا
+
+17
+00:01:39,630 --> 00:01:44,210
+هذا ال range بيسموها outside tolerance برا ال ..
+
+18
+00:01:44,210 --> 00:01:48,870
+ال .. يعني الاختلاف اللي مش مسموح فاحنا بتتكلم في
+
+19
+00:01:48,870 --> 00:01:52,770
+ال tolerance ال tolerance اللي هو قداش الاختلافit
+
+20
+00:01:52,770 --> 00:01:55,450
+is impossible to produce components with
+
+21
+00:01:55,450 --> 00:02:01,230
+dimensions that are absolutely precise يعني هذا
+
+22
+00:02:01,230 --> 00:02:09,760
+صعب نعمل ننتج أي حاجة بالظبط بدقة تماماwith sizes
+
+23
+00:02:09,760 --> 00:02:15,000
+يعني mean and precise with sizes exactly the same
+
+24
+00:02:15,000 --> 00:02:18,880
+as those specified in the design يعني عادة لما
+
+25
+00:02:18,880 --> 00:02:23,560
+تيجي تتكلمي الآن نتكلم خلينا نقول حاجات صغيرة جدا
+
+26
+00:02:23,560 --> 00:02:27,140
+نتكلم في ال millimeter within قداش من millimeter
+
+27
+00:02:27,140 --> 00:02:32,500
+تعريفات في تعريفات هتمر علينا كمان شوية حاجة
+
+28
+00:02:32,500 --> 00:02:36,560
+بنسميها tight toleranceوحاجة بنسميها loose
+
+29
+00:02:36,560 --> 00:02:40,500
+tolerance الـ tied اللي هو إيش؟ الديق يعني
+
+30
+00:02:40,500 --> 00:02:47,440
+tolerance يعني ديق كتير أو ال tolerance محدود جدا
+
+31
+00:02:47,440 --> 00:02:52,800
+وفي tolerance شويه في مجال بحبح بحبح يعني this is
+
+32
+00:02:52,800 --> 00:02:57,140
+because all production processes are imprecise to
+
+33
+00:02:57,140 --> 00:03:02,180
+a certain extent لأن في الغالب معظم عمليات الإنتاج
+
+34
+00:03:03,240 --> 00:03:10,660
+مش دقيقة يعني بدرجة الكمال، في حاجة تختلف، حتى
+
+35
+00:03:10,660 --> 00:03:14,760
+ربنا لما خلقنا كل شيء فيه اختلاف بيننا وبين بعض،
+
+36
+00:03:14,760 --> 00:03:19,480
+لما تيجي تطلع مثلا twin sister، لو تنتين، خوات
+
+37
+00:03:19,480 --> 00:03:24,740
+أجنتوقة، دلوقت دقيقة هتلاقي اختلافات، فهذه الآن
+
+38
+00:03:24,740 --> 00:03:30,890
+لما تيجي لخوات التانية هتلاقي اختلاف اكترالأن
+
+39
+00:03:30,890 --> 00:03:34,210
+بيتكلم، Therefore, the sizes of several components
+
+40
+00:03:34,210 --> 00:03:38,070
+produced from the same design will vary or differ,
+
+41
+00:03:38,470 --> 00:03:41,630
+although the variations may only be a few
+
+42
+00:03:41,630 --> 00:03:46,670
+hundredths of a millimeter, sizes will not be one
+
+43
+00:03:46,670 --> 00:03:50,750
+hundred percent accurate or exact compared with
+
+44
+00:03:50,750 --> 00:03:55,360
+the designيعني حتى لما نجي اتلاحظ باللحظة احيان
+
+45
+00:03:55,360 --> 00:04:00,560
+الاختلافات جداش اجزاء صغيرة من ال millimeter بس
+
+46
+00:04:00,560 --> 00:04:04,700
+هذا بيظله انه مش كامل مية في المية حسب ال design
+
+47
+00:04:04,700 --> 00:04:09,220
+في اختلافات مختلفة because engineers know the
+
+48
+00:04:09,220 --> 00:04:13,580
+accuracy cannot be perfect لأن المهندسين بعرفوا ان
+
+49
+00:04:13,580 --> 00:04:18,660
+الدقة مش كاملةالتعريف التعريف التعريف التعريف
+
+50
+00:04:18,660 --> 00:04:24,020
+التعريف التعريف التعريف التعريف التعريف
+
+51
+00:04:24,020 --> 00:04:27,480
+التعريف
+
+52
+00:04:27,480 --> 00:04:32,460
+التعريف التعريف التعريف التعريف التعريف التعريف
+
+53
+00:04:32,460 --> 00:04:33,060
+التعريف التعريف التعريف التعريف التعريف التعريف
+
+54
+00:04:33,060 --> 00:04:37,140
+التعريف التعريف التعريف التعريف التعريف التعريف
+
+55
+00:04:37,140 --> 00:04:38,080
+التعريف التعريف التعريف التعريف التعريف التعريف
+
+56
+00:04:38,080 --> 00:04:38,100
+التعريف التعريف التعريف التعريف التعريف التعريف
+
+57
+00:04:38,100 --> 00:04:41,280
+التعريف
+
+58
+00:04:41,280 --> 00:04:46,700
+التعريف التعريف التعري
+
+59
+00:04:47,550 --> 00:04:52,450
+حجم محدد مثلا خلّيني أعطيكم بعض الأمثلة الآن في
+
+60
+00:04:52,450 --> 00:04:56,870
+قطع الإلكتروينات الـ resistors مرت عليكم الـ
+
+61
+00:04:56,870 --> 00:05:00,090
+resistor فيها tolerance عالي الـ typical اللي
+
+62
+00:05:00,090 --> 00:05:03,090
+بنشتريها يعني ممكن تشتري هذا فيه عندي 10%
+
+63
+00:05:03,090 --> 00:05:07,390
+tolerance لما أشتري حاجة بتساوي يعني بديها one
+
+64
+00:05:07,390 --> 00:05:13,610
+kilo ohmممكن يلاقيها 900 Ohm و ممكن يلاقيها 1100
+
+65
+00:05:13,610 --> 00:05:17,770
+Ohm الـ 1100 Ohm و الـ 900 هدول acceptable الـ L
+
+66
+00:05:17,770 --> 00:05:21,810
+لو روحي شوية بيسموها ال military specification ال
+
+67
+00:05:21,810 --> 00:05:24,890
+military specification بتعطيني قداش 2% range
+
+68
+00:05:24,890 --> 00:05:32,530
+فالمسموح فيه من ال 1000 ينزل قداش 20يعني من تسعمية
+
+69
+00:05:32,530 --> 00:05:37,870
+بيصير من تسعمية و تمانين إلى الف و عشرين، الآن هذا
+
+70
+00:05:37,870 --> 00:05:41,850
+ال tolerance التكلفة تبعته غالية كتير، انه ايش أنا
+
+71
+00:05:41,850 --> 00:05:45,910
+عملت tie tolerance، يعني هذا صار ال tolerance عندي
+
+72
+00:05:45,910 --> 00:05:50,950
+مش فيه بحبة، حديق على الآخرفهذا اللي بنتكلم عنه
+
+73
+00:05:50,950 --> 00:05:54,290
+Instead of giving one precise size, sellers
+
+74
+00:05:54,290 --> 00:05:58,510
+specified a range of acceptable sizes or an
+
+75
+00:05:58,510 --> 00:06:01,610
+allowed amount of variation. This is often given
+
+76
+00:06:01,610 --> 00:06:06,110
+as a deviation or differences from a precise size
+
+77
+00:06:06,110 --> 00:06:10,510
+الان كلمة deviation إيش معناتها؟ هذه كلمة ال
+
+78
+00:06:10,510 --> 00:06:17,010
+difference Deviate from تختلف عن كويس؟
+
+79
+00:06:19,960 --> 00:06:28,080
+الرسم على الجانب يظهر شفت بمعدل 88 ميلي متر انتظر
+
+80
+00:06:28,080 --> 00:06:37,940
+هنا الشفت درع يتحرك الشفت 88
+
+81
+00:06:37,940 --> 00:06:49,650
+ميلي متر بلاس او مايناس.05 يعني هذا ال 88 ال point
+
+82
+00:06:49,650 --> 00:06:55,910
+eight eight millimeter مسموح فيه قداشربزيادة سفر
+
+83
+00:06:55,910 --> 00:07:00,990
+خمسة أو بنقصان سفر خمسة plus or minus that
+
+84
+00:07:00,990 --> 00:07:08,450
+therefore the diameters of 87.95 millimeter and 88
+
+85
+00:07:08,450 --> 00:07:14,070
+.05 millimeter which are slightly inaccurate are
+
+86
+00:07:14,070 --> 00:07:18,230
+still permissible يعني ايش permissible allowed او
+
+87
+00:07:18,230 --> 00:07:24,160
+مقبولacceptable هاي ال permissible اللي عندي فهي
+
+88
+00:07:24,160 --> 00:07:28,500
+ايش طالما هي في هذا بين ال range هدوء هذا وهذا فهو
+
+89
+00:07:28,500 --> 00:07:32,020
+مقبول لو طلعت برا ال range بالزيادة عن هذه صارت
+
+90
+00:07:32,020 --> 00:07:39,140
+مثلا 88.06 او صارت عندي 87.94 صارت out of the
+
+91
+00:07:39,140 --> 00:07:44,060
+range فصارت ايش مش مقبولنا permissible as they are
+
+92
+00:07:44,060 --> 00:07:49,390
+within tolerance طلع الكلمة الاشwithin tolerance
+
+93
+00:07:49,390 --> 00:07:56,450
+يعني حسب ال tolerance المقبول acceptable tolerance
+
+94
+00:07:57,850 --> 00:08:07,170
+However, the diameters of 87.94 mm or 88.06 mm are
+
+95
+00:08:07,170 --> 00:08:08,450
+not permissible
+
+96
+00:08:29,590 --> 00:08:33,150
+when the permissible deviations in size is very
+
+97
+00:08:33,150 --> 00:08:37,270
+small we say it is a tight tolerance شايفة كلمة
+
+98
+00:08:37,270 --> 00:08:42,350
+tight tolerance؟ لما الواحد يلبسحاجة، جاكيت أو اشي
+
+99
+00:08:42,350 --> 00:08:45,890
+بتلاقيها ديجة كتير، في أحيان بعض الشغلات within
+
+100
+00:08:45,890 --> 00:08:50,790
+tolerance، مظبوط في شغلات بتلتبس ديجة وفي شغلات
+
+101
+00:08:50,790 --> 00:08:54,610
+بتلتبس واسعة، الآن ال tight tolerance الشغل اللي
+
+102
+00:08:54,610 --> 00:08:59,130
+بتحسيه يدق جاية بس على الجد، هذا بتقول أيش؟ tight
+
+103
+00:08:59,130 --> 00:09:04,450
+toleranceor closed tolerance هاي في عندى كلمتين
+
+104
+00:09:04,450 --> 00:09:08,690
+tight tolerance و closed tolerance هي نفس المعنى a
+
+105
+00:09:08,690 --> 00:09:12,050
+large permissible deviation is a loose tolerance
+
+106
+00:09:12,050 --> 00:09:15,670
+اللوس الاش الواسع احيانا انت بتروح تشتري حاجة
+
+107
+00:09:15,670 --> 00:09:21,520
+تلاقيها واسعة بس مقبولةمظبوط في size لو جبتيه أكبر
+
+108
+00:09:21,520 --> 00:09:26,500
+بركبش بتقولي هذا way too much الحين بنسميها too
+
+109
+00:09:26,500 --> 00:09:30,940
+much play يعني بلعب كتير بتلاقي هذا كل تعبير اللي
+
+110
+00:09:30,940 --> 00:09:34,500
+في العربة أيوة
+
+111
+00:09:35,200 --> 00:09:39,800
+الحاجة الأدق زي هيك أحيانا بجيب حاجة ال range فيها
+
+112
+00:09:39,800 --> 00:09:44,700
+فيش يعني المجال مثلا زي ما حكيت ال .. ال error
+
+113
+00:09:44,700 --> 00:09:47,540
+تبعه ضيق صغير مثلا لو جبت ال ال military
+
+114
+00:09:47,540 --> 00:09:50,220
+specification في ال registers قداش ال percentage
+
+115
+00:09:50,220 --> 00:09:56,720
+تبعتنا قولنا 2%كويس 2% type tolerance مش ميعطي
+
+116
+00:09:56,720 --> 00:10:02,120
+مجال أما لو أروح على ال 10% و 20% اللي هي ال
+
+117
+00:10:02,120 --> 00:10:05,280
+commercial هذا ال tolerance loose tolerance معطيني
+
+118
+00:10:05,280 --> 00:10:08,880
+مجال أكبر بكتير أسوأ فيه طبعا ال loose tolerance
+
+119
+00:10:08,880 --> 00:10:14,120
+دايما بيبقىأرخص من الـ tight tolerance طلع عندي
+
+120
+00:10:14,120 --> 00:10:18,040
+هنا machining a metal components لأن لو أنا بداش
+
+121
+00:10:18,040 --> 00:10:23,100
+تسغل على metal components ال metal components to a
+
+122
+00:10:23,100 --> 00:10:26,860
+tolerance of plus or minus point one millimeter is
+
+123
+00:10:26,860 --> 00:10:30,440
+relatively easy to doيعني لو كان بدى انا اشتغل على
+
+124
+00:10:30,440 --> 00:10:33,720
+اشي حديد و اقول بدى عندى ال range تبع ال error
+
+125
+00:10:33,720 --> 00:10:38,100
+point one millimeter ال point one millimeter نوعا
+
+126
+00:10:38,100 --> 00:10:42,830
+ما سهل في ال machines انه احققهit's easy to do so
+
+127
+00:10:42,830 --> 00:10:47,030
+it is a lost tolerance but a tolerance of just
+
+128
+00:10:47,030 --> 00:10:50,530
+plus or minus point oh one شوف قداش ال point oh
+
+129
+00:10:50,530 --> 00:10:54,930
+one يعني لو جيت انا على ال kilo قلت بدي اطلع فيها
+
+130
+00:10:54,930 --> 00:10:58,710
+gram مع ال range gram او اكتر بقدر اجهزها
+
+131
+00:10:58,710 --> 00:11:02,550
+بالموازين ال digital بس لو قلت point oh one gram
+
+132
+00:11:02,550 --> 00:11:07,050
+على ال kiloفي الموازين العادية بتبقى اياش صعبة
+
+133
+00:11:07,050 --> 00:11:12,290
+موازين الدهب بيجيبوه يعني نوعا ما أدق كتير فهذا
+
+134
+00:11:12,290 --> 00:11:15,350
+اللي بتتكلم عليه فهذا بيسمي ال point one
+
+135
+00:11:15,350 --> 00:11:20,050
+millimeter is a tight tolerance in metal working
+
+136
+00:11:20,050 --> 00:11:25,050
+طلع عندي في ال cement a concrete structure لو جيت
+
+137
+00:11:25,050 --> 00:11:31,080
+انا لصبط بطون السطح عادة يمكن كل هيتكو بتشوفوافي
+
+138
+00:11:31,080 --> 00:11:33,960
+الشتوية اللي فاتت أخر كم من يوم إذا حدا فيكوا طلع
+
+139
+00:11:33,960 --> 00:11:39,820
+على السطح إيش بيلاقي فيه ميه بتبرق، مظبوط؟ ليش؟
+
+140
+00:11:39,820 --> 00:11:43,680
+لأنه طالع حد بنفسره plus or minus ten millimeters
+
+141
+00:11:43,680 --> 00:11:49,000
+is a loose tolerance لو إنت جيت طلعت يعني الصنطي
+
+142
+00:11:50,060 --> 00:11:53,660
+سهل جدا انك اتحقق لو قلت بدى السطح يكون في حدود
+
+143
+00:11:53,660 --> 00:11:58,000
+سانتي الاختلاف تبعه بتلاقيه سهل يتحقق هذا الانش
+
+144
+00:11:58,000 --> 00:12:02,720
+اللي مش سهل but plus or minus one millimeter is
+
+145
+00:12:02,720 --> 00:12:06,320
+tight لو انا بدي احقق بس الاختلاف بينه يعني
+
+146
+00:12:06,320 --> 00:12:10,140
+بتلاقيش ولا نقطة مية one centimeter هذا بتلاقيها
+
+147
+00:12:10,140 --> 00:12:13,910
+أصعب ليش؟because it's difficult to place with
+
+148
+00:12:13,910 --> 00:12:18,050
+concrete accurately لأن انت لما بدك تفرد ال
+
+149
+00:12:18,050 --> 00:12:23,710
+concrete اللي هي البطون هو يعني خليني أقول سائل
+
+150
+00:12:23,710 --> 00:12:28,630
+صعبة تتحكمي فيها عشان هيك بتلاقوا إيش الاختلافات
+
+151
+00:12:28,630 --> 00:12:32,110
+هالأهل لو هذه بدي أعملها على السطح كل هذه بتلاقيها
+
+152
+00:12:32,110 --> 00:12:36,750
+مقبولة بس لو أنا بدي أعملها أرضية مصنعة تتحرك فيه
+
+153
+00:12:36,750 --> 00:12:43,040
+السيارات والرافعات وزي هيك بظبطشلأنها تحتاج لـ
+
+154
+00:12:43,040 --> 00:12:47,100
+Tight Tolerance لأنها تخاف أنه يحصل أي شيء تقع
+
+155
+00:12:47,100 --> 00:12:52,020
+تتنزل .. يعني مثل مطبات ماشية فهذا السبب بتلاقيها
+
+156
+00:12:52,020 --> 00:12:56,180
+الـ Tolerance تبعها بيبقى Very Tight Tolerance
+
+157
+00:12:56,180 --> 00:13:00,160
+مقارنة بالتانية ففهمنا إيش المعنى اللي مرن عليناها
+
+158
+00:13:00,160 --> 00:13:06,440
+الـ Loose Tolerance إيش معناته؟ الدقة مش عالية الـ
+
+159
+00:13:06,440 --> 00:13:09,020
+Tight Tolerance الدقة أعلى
+
+160
+00:13:16,350 --> 00:13:19,990
+طيب الحاجة التانية اللي بنتكلم عليها ال fit انا
+
+161
+00:13:19,990 --> 00:13:24,450
+لما بدي اركب حاجة عادة هذه بتشوفوها كتير لما بدي
+
+162
+00:13:24,450 --> 00:13:29,510
+ادخل برغي في حاجة و مش ضابطة او بدي الزر بده ادخله
+
+163
+00:13:29,510 --> 00:13:33,770
+في شي مش ضابط او القلب او ال pin او اي حاجة بنتكلم
+
+164
+00:13:33,770 --> 00:13:37,850
+في لغة الهندسة بنقابلها كتير when one component go
+
+165
+00:13:37,850 --> 00:13:43,030
+through another لما بدنا ادخليعني جزء أو حاجة في
+
+166
+00:13:43,030 --> 00:13:48,130
+التانية، إيش بنحصل هان؟ Such as a shaft or a bolt
+
+167
+00:13:48,130 --> 00:13:51,150
+going through a hole، إيش ال bolt؟ shaft قولنا
+
+168
+00:13:51,150 --> 00:13:56,410
+ضراع اللي هي الإيد اللي بتحرك فيها يعني جسم، الآن
+
+169
+00:13:56,410 --> 00:13:59,630
+ال bolt اللي هو البرغي، بتعرفوا في عندنا برغي، في
+
+170
+00:13:59,630 --> 00:14:02,550
+screw وفي ال bolt، إيش الفرق بينهم؟
+
+171
+00:14:08,470 --> 00:14:11,450
+ال part بتشوف الحاجة المثننة ليه اللي هسمونها
+
+172
+00:14:11,450 --> 00:14:17,310
+بسموها part وفي mechanical هنجيناها في أنواع كتير
+
+173
+00:14:17,310 --> 00:14:20,490
+كيف بنسمي إيش هد وإيش هد وإيش هدي في ال mechanical
+
+174
+00:14:20,490 --> 00:14:23,670
+ف ال part اللي هي سمونها هذا عادة بدها تدخل بدها
+
+175
+00:14:23,670 --> 00:14:27,670
+تكون على الجد لأنه لو كانت إيش مش على الجد إيش
+
+176
+00:14:27,670 --> 00:14:32,350
+بتصيرلأ إذا كانت كبيرة بتدخلش و إذا كانت صغيرة
+
+177
+00:14:32,350 --> 00:14:36,010
+بيصير فيها إيش؟ بيلعب بينما البرغي ال screw اللي
+
+178
+00:14:36,010 --> 00:14:41,050
+بنتكلم عنه هذا بيدخل للخشب أو بيعمل التسكيرة أكتر
+
+179
+00:14:41,050 --> 00:14:44,290
+going through a hole the two must fit together
+
+180
+00:14:44,290 --> 00:14:48,150
+their sizes and shape must match يعني fit together
+
+181
+00:14:48,150 --> 00:14:53,710
+or .. fit together إيش معناته؟ بدي اتناسب مع بعض،
+
+182
+00:14:53,710 --> 00:15:00,020
+كويس؟the key question is how tightly or loosely
+
+183
+00:15:00,020 --> 00:15:04,480
+should they fit together؟ tightly شوفت إيش؟ جداش
+
+184
+00:15:04,480 --> 00:15:10,740
+يعني زي ممكن كلمة loose جداش في وسع و جداش هو راكب
+
+185
+00:15:10,740 --> 00:15:16,540
+بيسموه بإحكام tight اللي هو إيش بإحكام و loose
+
+186
+00:15:16,540 --> 00:15:22,380
+اللي هو واسع أو رخو الرخاوة ال loose هاي و الإحكام
+
+187
+00:15:22,380 --> 00:15:28,850
+اللي هي إيش ال tightshould they fit together there
+
+188
+00:15:28,850 --> 00:15:32,330
+are two main types of fit في عندى نوعين a
+
+189
+00:15:32,330 --> 00:15:36,450
+clearance fit وفي عندى النوع التانى هنشوفه في ال
+
+190
+00:15:36,450 --> 00:15:40,170
+slide التانى ال clearance fit ايش بتقول allows a
+
+191
+00:15:40,170 --> 00:15:43,790
+component to slide or turn freely by leaving
+
+192
+00:15:43,790 --> 00:15:47,110
+clearance or a gap between itself and the side of
+
+193
+00:15:47,110 --> 00:15:52,850
+the wall يعني هاد بتدخل بسلاسة وفي وسع فيهاهي إيش
+
+194
+00:15:52,850 --> 00:15:56,190
+بنقول؟ إيش فيه? clearance. إيش ال clearance؟ أنت
+
+195
+00:15:56,190 --> 00:16:01,670
+لما تيجي تدخلي تحت عادة مثلا لو بتلاقي في الشوارع
+
+196
+00:16:01,670 --> 00:16:06,550
+برابيحطين ارتفعته في مثلا جسور وغيره، على الجسر
+
+197
+00:16:06,550 --> 00:16:10,350
+بيقول ال clearance قداش الارتفاع تبع السيارة اللي
+
+198
+00:16:10,350 --> 00:16:14,610
+بتمرك تحتها أو أي فهيكة اللي بتمرك تحتها، نفس
+
+199
+00:16:14,610 --> 00:16:18,810
+الشيء لل people، فال clearance اللي طولها أطول
+
+200
+00:16:18,810 --> 00:16:22,790
+بتعطيه warning إنه لو أنت جيت بدك تدخل هتضرب في
+
+201
+00:16:22,790 --> 00:16:27,030
+هدها، فجسور الموجودة في العالم كلها عندنا مافيش
+
+202
+00:16:27,030 --> 00:16:32,960
+هالمشكلةكان جسر او اتنين الموجودين في غزة .. فمش
+
+203
+00:16:32,960 --> 00:16:38,620
+.. لأ مش جسر هذا .. الجسر الاشي بتتذكره كان على
+
+204
+00:16:38,620 --> 00:16:43,730
+مدخل المغازيكان في جسر ع الشارع هذا الان بيحطوا
+
+205
+00:16:43,730 --> 00:16:47,130
+الارتفاع تبعه بيبقى الاصل مكتوب عليه قداش الارتفاع
+
+206
+00:16:47,130 --> 00:16:51,330
+للسيارات اللي هتمرق من تحته فعادة بيحطوا هذه
+
+207
+00:16:51,330 --> 00:16:56,050
+الشغلات عساس اي حد اكتر من هيكه هو عنده warning ان
+
+208
+00:16:56,050 --> 00:17:01,270
+ان انت لو مرقت وضربت انت ضربت لانك ماقريتش الإشارة
+
+209
+00:17:01,270 --> 00:17:05,090
+فهذا ال clearance فال clearance اللي هي قداش
+
+210
+00:17:05,090 --> 00:17:10,100
+المجال اللي عنديفال clearance او ال gap ال gap ايش
+
+211
+00:17:10,100 --> 00:17:14,540
+هو برضه وسعه هي هذا between itself and the sides
+
+212
+00:17:14,540 --> 00:17:18,520
+of the hole هدول قديش موجود this distance must be
+
+213
+00:17:18,520 --> 00:17:23,240
+quite precise يعني هذه المسافة بدها تكون دقيقة if
+
+214
+00:17:23,240 --> 00:17:27,380
+there is insufficient clearance لو في عندي صار ايش
+
+215
+00:17:27,380 --> 00:17:31,930
+المساحة مش كافية هذهif the gap is too small the
+
+216
+00:17:31,930 --> 00:17:35,070
+components will fit too tightly احيانا انت بدك
+
+217
+00:17:35,070 --> 00:17:41,030
+الشغلة تبغي ايش فيها بحبحة لو هي كانت اجت و .. و
+
+218
+00:17:41,030 --> 00:17:46,170
+اجت يعني خلينا نقول شوية حزجة if the gap is too
+
+219
+00:17:46,170 --> 00:17:49,710
+small the component will fit too tightly as a
+
+220
+00:17:49,710 --> 00:17:53,230
+result the component will bend الان لما يكون عندى
+
+221
+00:17:53,230 --> 00:17:56,890
+tight gap ايش بده يصير للكمبونس بده اخليها تنتني
+
+222
+00:17:56,890 --> 00:18:02,740
+bendلما تدخل حاجة في خصوص البراغة بتلاقي البرغة
+
+223
+00:18:02,740 --> 00:18:08,440
+انتنا على طول او صارله تجويس لان انت قاعد تفرضيه
+
+224
+00:18:08,440 --> 00:18:14,620
+على منطقة مش تساهوش okay as a result the component
+
+225
+00:18:14,620 --> 00:18:20,720
+will not be able to slide or turn freely انت اللي
+
+226
+00:18:20,720 --> 00:18:24,200
+بدك في البوابة اللي بتتحرك دايما او اي اش بتتحرك
+
+227
+00:18:24,200 --> 00:18:30,260
+بدك اياه تبقى انبح بح شوية ليش؟عشان يقدر يحرك بدون
+
+228
+00:18:30,260 --> 00:18:34,960
+مقاومة، الآن لو كانت tight هتلاقيها مجرد الحركة
+
+229
+00:18:34,960 --> 00:18:39,660
+فيها هيصير bend و بعد ال bend هيصير تنكسر it will
+
+230
+00:18:39,660 --> 00:18:44,400
+breakin other words there will not be enough play
+
+231
+00:18:44,400 --> 00:18:50,280
+شايفة كلمة ال play مش هتلعب كلمة اللعب احنا حتى
+
+232
+00:18:50,280 --> 00:18:53,780
+بنقولها في العامية عندنا بدي يكون شوية مجال للعب
+
+233
+00:18:53,780 --> 00:18:57,960
+في هذا المجال however if there is too much
+
+234
+00:18:57,960 --> 00:19:01,340
+clearance there will be too much play هتلاقي رخوة
+
+235
+00:19:01,340 --> 00:19:04,600
+كتير too much play رخوة كتير بلعب زيادة عن اللازم
+
+236
+00:19:04,600 --> 00:19:08,160
+يعني بطلع و بنزل أحيان بتلاقيه وهذا بتلاقيه حتى
+
+237
+00:19:08,160 --> 00:19:11,570
+يمكن كل هيتكم بتشوفوها في البوابة عندكمأحيانا
+
+238
+00:19:11,570 --> 00:19:13,830
+بتلاقي الباب بحزق الزيادة على اللازم و أحيانا
+
+239
+00:19:13,830 --> 00:19:18,670
+بتلاقي ايش بفتح لحاله و بخلق لحاله بتسويها فهذه
+
+240
+00:19:18,670 --> 00:19:22,510
+بتشوفوها and the component will be able to move
+
+241
+00:19:22,510 --> 00:19:27,130
+too much تتحرك كتير و هذه برضه بتسبب أنها بتنكسر
+
+242
+00:19:27,130 --> 00:19:32,790
+لأن مع ال .. ال .. هذه بتحصل يعني الآن النوع الأول
+
+243
+00:19:32,790 --> 00:19:37,770
+إيش سمناه clearance fit كويس؟ النوع التاني إيش
+
+244
+00:19:37,770 --> 00:19:43,640
+بنسميه interface fitinterference fit ال
+
+245
+00:19:43,640 --> 00:19:46,980
+interference fit وفي عندي ال clearance fit ال
+
+246
+00:19:46,980 --> 00:19:52,560
+interference fit هد ايش معناته؟ tight fit it is
+
+247
+00:19:52,560 --> 00:19:56,300
+very tight fit which does not allow a component to
+
+248
+00:19:56,300 --> 00:20:01,000
+move freely inside a hole يعني هد الجزء اللي بدخل
+
+249
+00:20:01,000 --> 00:20:05,240
+بتحركش زي ما تقول ايش اتمصمر سامعين كلمة لو تمصمر
+
+250
+00:20:05,240 --> 00:20:10,820
+حاجة بتلاقيها ايش؟ملزقة تلزيج فيش مجال انها تفرط
+
+251
+00:20:10,820 --> 00:20:14,580
+يعني طلعوا كيف هاد بالتم this type of thing can be
+
+252
+00:20:14,580 --> 00:20:17,180
+achieved by forcing the components into the whole
+
+253
+00:20:17,180 --> 00:20:23,780
+يعني هاد مينعملها لما ندخل الحاجة بالقوة force it
+
+254
+00:20:25,650 --> 00:20:29,310
+الخيار هو أن المثل حول الحفرة يمكن أن يكون مقفل
+
+255
+00:20:29,310 --> 00:20:30,870
+لكي يتوسع
+
+256
+00:20:46,860 --> 00:20:50,420
+after a sufficient expansion, the component is
+
+257
+00:20:50,420 --> 00:20:53,320
+placed in the hole, the metal then cools and
+
+258
+00:20:53,320 --> 00:20:57,560
+contracts بيصيرش انها بتبرد وبقاش بتساوي بتنكمش
+
+259
+00:20:57,560 --> 00:21:01,240
+contract decrease in the size due to cooling, the
+
+260
+00:21:01,240 --> 00:21:04,460
+contraction results in a tight fit, an example of
+
+261
+00:21:04,460 --> 00:21:09,180
+interference fit is a train wheel fitted on the
+
+262
+00:21:09,180 --> 00:21:15,300
+axle طلع انت العجل تبع القطار لما نيجي يمشي بيمشي
+
+263
+00:21:15,300 --> 00:21:20,450
+على ايش؟ع سكة، الآن لو هذا فيه شوية رخاوة، إيش
+
+264
+00:21:20,450 --> 00:21:26,670
+بيحصل فيه؟ السكة بتلاحظ انتظام، فيش فيها مطابات،
+
+265
+00:21:26,670 --> 00:21:32,510
+فيش حاجة، بينما طلعت السيارة كيف؟ في مطابات
+
+266
+00:21:32,510 --> 00:21:37,550
+فبتلاقيها بتتحرك أكتر يعني في عندك ..في عندك
+
+267
+00:21:37,550 --> 00:21:41,510
+suspension wheels بتلاحظيها هنا في suspension على
+
+268
+00:21:41,510 --> 00:21:45,370
+ال wheel اللي هي إيش هذه ال .. ال snippers اللي
+
+269
+00:21:45,370 --> 00:21:49,630
+بيسموه بالعامية أو إذا طلعت عليه بتلاقيه زي ال ..
+
+270
+00:21:49,630 --> 00:21:55,090
+الزنبرك موجود هذا للمطبات عشان يطلع وينزل بتلاقيش
+
+271
+00:21:55,090 --> 00:22:00,310
+العجل ملزق تلزيجبتلاقي فيه رخاوة، بتطلع و بنزل حسب
+
+272
+00:22:00,310 --> 00:22:07,370
+المطاب هذي، بينما في القطار السكة تابتة، مافيش سكة
+
+273
+00:22:07,370 --> 00:22:12,330
+بتطلعش ولا بتنزل، فبتلاقي إيش؟ العجل تبع القطار
+
+274
+00:22:12,330 --> 00:22:17,610
+تابت بالظبط، يعني مابتحركش، فهذا عطوه فت اللي
+
+275
+00:22:17,610 --> 00:22:21,590
+عندنا، اللي هو استخدم معاه interference، فتلة
+
+276
+00:22:21,590 --> 00:22:25,930
+يدخلهالكتير بتلاقي من الشغلات اللي انت بدك إياها
+
+277
+00:22:25,930 --> 00:22:29,450
+بدك إيش حركة بالمرة فيها نستخدم ال interference
+
+278
+00:22:29,450 --> 00:22:34,130
+فيها اللي بدي حركة فيها بستخدم ال إيش ال clearance
+
+279
+00:22:34,130 --> 00:22:39,310
+fit فاحنا أهم إيش إيش عندنا الكلمتين في ال fit ال
+
+280
+00:22:39,310 --> 00:22:44,510
+interference fit و ال إيش؟ أيوة و ال clearance fit
+
+281
+00:22:44,510 --> 00:22:49,070
+هدولة اللي عندناالان نيجي نطلع على ال exercises
+
+282
+00:22:49,070 --> 00:22:52,970
+ايش بنتكلم هنا find words and expressions with
+
+283
+00:22:52,970 --> 00:22:55,670
+similar meanings to the words and expressions
+
+284
+00:22:55,670 --> 00:22:59,730
+below sometimes there is more than one possible
+
+285
+00:22:59,730 --> 00:23:06,730
+answer الان نيجي نطلع ايش معناه exact accurate
+
+286
+00:23:06,730 --> 00:23:18,880
+او precise مظبوط نفس الشي صح؟differ vary okay
+
+287
+00:23:18,880 --> 00:23:24,560
+exactness حكيتها
+
+288
+00:23:24,560 --> 00:23:29,780
+بس اعمليها now ال
+
+289
+00:23:29,780 --> 00:23:37,200
+exactness ايش precision او accuracy precision or
+
+290
+00:23:37,200 --> 00:23:47,160
+accuracy not exact and precise orinaccurate or
+
+291
+00:23:47,160 --> 00:23:54,120
+loose deviation between maximum and minimum الان
+
+292
+00:23:54,120 --> 00:23:57,360
+range في عند ال deviation اللي هي إيش ال deviation
+
+293
+00:23:57,360 --> 00:24:02,420
+ال differences okay فهي deviation between ال
+
+294
+00:24:02,420 --> 00:24:05,380
+maximum و ال minimum و هذا بيسميه range
+
+295
+00:24:05,380 --> 00:24:10,500
+unacceptable deviation within
+
+296
+00:24:13,320 --> 00:24:18,940
+tolerance مظبوط within tolerance unacceptable
+
+297
+00:24:18,940 --> 00:24:24,900
+deviation outside tolerance little deviations
+
+298
+00:24:24,900 --> 00:24:33,080
+allowed tight طيب الان large deviations allowed
+
+299
+00:24:33,080 --> 00:24:40,020
+loose الكلمات هي سهلة يعني طيب match the related
+
+300
+00:24:40,020 --> 00:24:46,410
+sentencesit bends مين ال bend؟
+
+301
+00:24:46,410 --> 00:24:50,870
+الحاجات اللي بندخلها بالجوا ومافيش فيها fit مظبوط
+
+302
+00:24:50,870 --> 00:24:55,250
+مين فيهم تيجي بيه ال part won't be able to turn
+
+303
+00:24:55,250 --> 00:25:00,760
+freely enough in the hole so it will bendلما نيجي
+
+304
+00:25:00,760 --> 00:25:04,560
+لهذا .. علشان أقول .. ال .. ال .. البرغي اللي عنده
+
+305
+00:25:04,560 --> 00:25:10,080
+مش هيتحرك بحرية في ال .. ال .. ال .. يعني ال .. ال
+
+306
+00:25:10,080 --> 00:25:12,680
+.. ال hole اللي موجود له، إيش بدي يصيرله؟ بيصيرله
+
+307
+00:25:12,680 --> 00:25:18,460
+بنتعج It will contract .. إيش هذا اللي بيصير ..
+
+308
+00:25:18,460 --> 00:25:25,740
+إيش يعني contract؟ تنكمش .. متنكمش ليش؟لأنها بتبرد
+
+309
+00:25:25,740 --> 00:25:30,540
+فيه حاجة بظبط the hole will be widened أي واحدة
+
+310
+00:25:30,540 --> 00:25:36,860
+دويل will be fit هان ولا .. the shaft will shorten
+
+311
+00:25:36,860 --> 00:25:42,620
+and narrow slightly as it cools it cools ف it will
+
+312
+00:25:42,620 --> 00:25:46,460
+expand ال expand دي يصير من إيش؟ من الحرارة وين
+
+313
+00:25:46,460 --> 00:25:53,420
+الحرارة؟هي high temperature widen with the high
+
+314
+00:25:53,420 --> 00:25:58,340
+temperature يبقى هذا will expand there will be too
+
+315
+00:25:58,340 --> 00:26:04,120
+much play too much play قولنا لإيش؟ لما يكون .. في
+
+316
+00:26:04,120 --> 00:26:10,000
+رخوة كتير لما يكون الحجم كبير مظبوط؟ مين فيهم
+
+317
+00:26:10,000 --> 00:26:14,520
+الحجم الكبير؟see the whole one fit tightly enough
+
+318
+00:26:14,520 --> 00:26:19,860
+كلمة tightly enough معناته ايش؟ في وسع كتير
+
+319
+00:26:19,860 --> 00:26:24,280
+tightly enough هذا ايش يعني؟ هاي بدكوا تفكروا فيها
+
+320
+00:26:24,280 --> 00:26:29,780
+كلمة انه في .. ايوة في وسع يعني كتير هذا هي يعني
+
+321
+00:26:29,780 --> 00:26:35,380
+مش حزق بالدرجة الكافية فمعناته وسع it needs a
+
+322
+00:26:35,380 --> 00:26:38,820
+clearance fit مين فيهم؟
+
+323
+00:26:43,290 --> 00:26:50,210
+the bolt will have to turn in the hole اي طيب it
+
+324
+00:26:50,210 --> 00:26:55,150
+needs an interference fit دي the wheel will have
+
+325
+00:26:55,150 --> 00:27:00,970
+to fit very tightly on the axle فبتلاحظوا الكلمات
+
+326
+00:27:00,970 --> 00:27:05,390
+يعني هذه من الشغلات اللي هتمر عليكم كتير بس احنا
+
+327
+00:27:05,390 --> 00:27:08,470
+بنحاول انا هوقف
+
+328
+00:27:12,860 --> 00:27:17,860
+طيب complete the article about engine blue
+
+329
+00:27:17,860 --> 00:27:21,740
+printing using the words in the box ايش يعني blue
+
+330
+00:27:21,740 --> 00:27:26,000
+printing blue
+
+331
+00:27:26,000 --> 00:27:33,200
+printing هو
+
+332
+00:27:33,200 --> 00:27:36,880
+الآن complete the article about engine ايش engine
+
+333
+00:27:36,880 --> 00:27:41,320
+المحرك blue printing using the words in the box
+
+334
+00:27:42,490 --> 00:27:47,790
+الان خليني اعطيكوا فكرة، الان مثلا من الشغلات اللي
+
+335
+00:27:47,790 --> 00:27:51,630
+بيعملوها هنا في الصباقات ايش، بيقولوا احنا هاي
+
+336
+00:27:51,630 --> 00:27:56,530
+المواصفات تبعتنا تبعت ال .. ال .. ال motor تبع
+
+337
+00:27:56,530 --> 00:28:01,050
+السيارة، الان الأصل بنفعش حد يجيب motor أقوى من
+
+338
+00:28:01,050 --> 00:28:05,400
+التاني بكتير و يجي سابق فيهلازم .. فهو بيصير إيش؟
+
+339
+00:28:05,400 --> 00:28:09,440
+بيصير إن هو عنده advantage فإيش لازم يحصل؟ إن كلهم
+
+340
+00:28:09,440 --> 00:28:13,420
+يبقوا نفس القوة، نفس المواصفات، الآن نفس المواصفات
+
+341
+00:28:13,420 --> 00:28:18,080
+إذا أنا روحت وصنعت حاجة، كويس؟ الآن احنا قلنا في
+
+342
+00:28:18,080 --> 00:28:22,580
+عندنا variance أو tolerance accepted tolerance ال
+
+343
+00:28:22,580 --> 00:28:25,260
+accepted tolerance معناته بقدر أعمل matching
+
+344
+00:28:25,260 --> 00:28:29,790
+للشغلات مثلا الشجة اليمين بتهتأخد نفسالـ Tolerance
+
+345
+00:28:29,790 --> 00:28:33,470
+تبع الشمال يعني لو هذه في عندى زيادة ملي أنا بدى
+
+346
+00:28:33,470 --> 00:28:38,930
+اعمل زيادة ملي عشان يعمل matching فهذا acceptable
+
+347
+00:28:38,930 --> 00:28:42,810
+الان ال blue printing بيجي بيطلع على ال variation
+
+348
+00:28:42,810 --> 00:28:46,570
+و هو بيكون within ال variation هذه او within the
+
+349
+00:28:46,570 --> 00:28:50,890
+tolerance بس في نفس الوقت بيحاول ياخد advantage ال
+
+350
+00:28:50,890 --> 00:28:53,830
+advantage هذا لما تيجي ال blue printing بيجي انا
+
+351
+00:28:54,270 --> 00:28:57,930
+بدي أستخدم ال matching كل حاجة بدي أعملها matching
+
+352
+00:28:57,930 --> 00:29:03,310
+to the best of my design يعني لصالحي أنا بدي أاخد
+
+353
+00:29:03,310 --> 00:29:08,550
+زي ما أقول بدي أزوج لآخر حاجة مسموح فيها فهذا يمكن
+
+354
+00:29:08,550 --> 00:29:13,310
+في كلمة بيحكوها عند ال competition دايما الناس
+
+355
+00:29:13,310 --> 00:29:16,670
+اللي بتنافس على حاجة if you if you haven't tried
+
+356
+00:29:16,670 --> 00:29:20,630
+to cheat you're not doing enoughيعني انت .. انت
+
+357
+00:29:20,630 --> 00:29:24,950
+بدك تربح، تكسب في الصباقات، لازم توصل لحفة ..
+
+358
+00:29:24,950 --> 00:29:29,570
+المنطقة اللي بيسموها حفة الغش .. حفة الغش الاش ..
+
+359
+00:29:29,570 --> 00:29:33,270
+انت كتوصل .. انت بدك .. يعني تزوج لآخر نفس موجود
+
+360
+00:29:33,270 --> 00:29:37,110
+مسموح .. مسموح فيه، انت مادخلتش على حارة الاش ..
+
+361
+00:29:37,110 --> 00:29:44,060
+الغش، بس في نفس الوقتمات فهو اللي بيحكوها يعني هذا
+
+362
+00:29:44,060 --> 00:29:46,220
+في ال .. في ال America sport بيقولها if you
+
+363
+00:29:46,220 --> 00:29:49,160
+haven't tried to cheat if you haven't tried to
+
+364
+00:29:49,160 --> 00:29:54,150
+cheat you're not trying enoughانك to win يعني فهو
+
+365
+00:29:54,150 --> 00:30:00,150
+لازم توصل لهذه النقطة اللي بيسموها ال grey area ال
+
+366
+00:30:00,150 --> 00:30:04,330
+grey area انت لساته مسموح مش مادخلتشه الممنوع بس
+
+367
+00:30:04,330 --> 00:30:09,050
+ماحدش بحسبك عليه يعني مثلا ع سبيل المثال السرعة
+
+368
+00:30:09,050 --> 00:30:14,170
+وانت ماشي في ذاك fixed مثلا بيقولوا السرعة على
+
+369
+00:30:14,170 --> 00:30:18,530
+الخط السريع 75 كيلو 75 ميل بالساعة اللي هي تقريبا
+
+370
+00:30:18,530 --> 00:30:24,280
+تسعين .. مية وعشرين كيلوالـ 120 كيلو هات .. إذا
+
+371
+00:30:24,280 --> 00:30:27,180
+أنت ماشي مسافة طويلة، يعني خلينا نقول بدك تمشي
+
+372
+00:30:27,180 --> 00:30:32,180
+سبعمية لألف ميل، صعب تظلك محافظ عليها، يعني تقول
+
+373
+00:30:32,180 --> 00:30:37,740
+أنا في الدمشي إيش، نظامي، فغالبا الشرط بيوقفش
+
+374
+00:30:37,740 --> 00:30:42,440
+طالما و أنت within five miles، يعني خمسة .. خمسة
+
+375
+00:30:42,440 --> 00:30:46,400
+ميل أكتر من الخمس سبعين طالما أنت في حدود التمانين
+
+376
+00:30:46,400 --> 00:30:51,430
+أو أقلبتوقفش فبتلاقي أنت شايف الشرطة بتضلك ماشي
+
+377
+00:30:51,430 --> 00:30:55,550
+على التسعة أو سبعين مش بتنزل إلى الخمس السبعين
+
+378
+00:30:55,550 --> 00:30:59,510
+بتمسك عليها فماحدش بوقف فالمسافات اللي مش فيها
+
+379
+00:30:59,510 --> 00:31:04,130
+حاجة تمشي بزيادة طبعا إذا أنت ماشي قدام الشرطة زي
+
+380
+00:31:04,130 --> 00:31:08,210
+هيك فهو .. هذه من الشغلات اللي بتطلع عليها مثلا
+
+381
+00:31:08,210 --> 00:31:11,650
+اللي بتلاحظوها في ال .. في ال .. في ال .. هات
+
+382
+00:31:11,650 --> 00:31:17,490
+بتشوفوها كتير الإشارة الصفرة إيش معناتها؟استعيد ..
+
+383
+00:31:17,490 --> 00:31:22,850
+استعيد للوقوف او لل .. اه .. الآن كتير من الناس
+
+384
+00:31:22,850 --> 00:31:27,090
+اللي بيفعل إشارة شطافرة تظل معدي، مظبوط؟ هذا
+
+385
+00:31:27,090 --> 00:31:30,290
+trying .. انتوا مش .. مافيش قانون يقولوا مات ..
+
+386
+00:31:30,290 --> 00:31:33,850
+ماتعديش، بس في نفس الوقت إيش؟ تسووا، انتوا
+
+387
+00:31:33,850 --> 00:31:38,190
+بامتحاناتكم، إيش بتسووا؟ بنقولكم ماتعملوش،
+
+388
+00:31:38,190 --> 00:31:42,510
+ماتطلعوش علي جافكم، ماتعملوش، كام واحدة بتلزم؟
+
+389
+00:31:45,910 --> 00:31:50,970
+فهذه بتظهر في الحدود اللي بنحكي فيها يعني فطالما
+
+390
+00:31:50,970 --> 00:31:54,510
+انت ماعملتيش حركة يمكن بتلاحظوا هذه في الامتحانات
+
+391
+00:31:54,510 --> 00:31:59,810
+حركة كتيرة ماحدش بيسويلك محضرغش محضرغش وقتين بيصير
+
+392
+00:31:59,810 --> 00:32:04,810
+لما الاشي واضح جدا مظبوط في الأغلب بنجاومكم من
+
+393
+00:32:04,810 --> 00:32:09,570
+مكان للتاني بنعمل خطوات قبل ما نوصل لمحضرغش طيب
+
+394
+00:32:09,570 --> 00:32:14,680
+نيجيف blue printing for performance يعني ايش بده
+
+395
+00:32:14,680 --> 00:32:20,240
+اعمل الخطوات اللي بده امشي عليها الانتظامية لعملها
+
+396
+00:32:20,240 --> 00:32:24,800
+the advantage of racing in a kart class with ..
+
+397
+00:32:25,960 --> 00:32:30,560
+خليني تانية هندسة انتوا بس the advantage of racing
+
+398
+00:32:30,560 --> 00:32:34,300
+in a kart class with standard engine specs seems
+
+399
+00:32:34,300 --> 00:32:38,840
+obvious يعني لما انا بدأ ادخل في سباق سيارات
+
+400
+00:32:38,840 --> 00:32:45,020
+فالمعروف انه الحجم الماتور او الماتور بدي يكون حسب
+
+401
+00:32:45,020 --> 00:32:49,800
+المواصفات المعطاع لنا واضحeveryone has the same
+
+402
+00:32:49,800 --> 00:32:53,100
+power so it's driving talent that makes the
+
+403
+00:32:53,100 --> 00:32:58,180
+difference كل واحد عنده نفس قوة ال mature فمهارات
+
+404
+00:32:58,180 --> 00:33:05,620
+السواقة هي اللي هتحدد من الفائز but things are not
+
+405
+00:33:05,620 --> 00:33:09,580
+.. aren't quite that simple بس الأمور مش بهذه
+
+406
+00:33:09,580 --> 00:33:14,800
+السهولة هكذا no two standard engines are identical
+
+407
+00:33:14,800 --> 00:33:21,330
+مش هتلاقي matureينبنفس يعني identical بظبط نفس
+
+408
+00:33:21,330 --> 00:33:27,910
+المواصفات اللي عندى there will always be a slight
+
+409
+00:33:27,910 --> 00:33:30,810
+ish in the size of the engine ايش بدنا ناخد
+
+410
+00:33:30,810 --> 00:33:36,870
+variations في عندى دايما اختلاف بوجود الكلمة هي
+
+411
+00:33:36,870 --> 00:33:40,930
+عشان قبل ما نسوي و نشطف عليها عشان تعرف ايش اللي
+
+412
+00:33:40,930 --> 00:33:46,860
+راح طيبSince they are manufacturers not to
+
+413
+00:33:46,860 --> 00:33:52,460
+perfectly .. إيش؟ The dimensions .. dimensions Not
+
+414
+00:33:52,460 --> 00:33:58,400
+to perfectly precise dimension مش يعني هم مابيش
+
+415
+00:33:58,400 --> 00:34:03,540
+بالضقة .. اللي هي But to specified tolerances
+
+416
+00:34:03,540 --> 00:34:06,940
+كويس؟
+
+417
+00:34:06,940 --> 00:34:10,160
+اللي هي ان هاي ال variation و ال precise و ال
+
+418
+00:34:10,160 --> 00:34:12,080
+tolerance إيش؟ راحوا
+
+419
+00:34:15,460 --> 00:34:22,580
+أنا حطيت التاني هنا وينها اوبس
+
+420
+00:34:22,580 --> 00:34:42,560
+هذا اللي عملت على اللي عندي طيب
+
+421
+00:34:44,060 --> 00:34:47,980
+الان انتوا عندكوا الكلمات خلينا نتكلم although
+
+422
+00:34:47,980 --> 00:34:53,240
+these differences may only be إيش؟ plus or minus a
+
+423
+00:34:53,240 --> 00:34:56,820
+few hundredths of a millimeter they will
+
+424
+00:34:56,820 --> 00:35:01,660
+nevertheless result in a slight performance gap
+
+425
+00:35:01,660 --> 00:35:06,360
+between any two engines على الرغم من أنه هتلاحظي
+
+426
+00:35:06,360 --> 00:35:11,740
+الحاجات أجزاء من الmillimeter الإختلافات إلا إنها
+
+427
+00:35:11,740 --> 00:35:19,860
+هتعطيشوية advantage في ال performance اللى عندنا
+
+428
+00:35:19,860 --> 00:35:23,760
+فيه عندنا حيكون فيه شوية gap بين الأداء طبعت كل
+
+429
+00:35:23,760 --> 00:35:29,400
+واحدة فيهم one way one way around this one way
+
+430
+00:35:29,400 --> 00:35:33,300
+around this problem if you have the cash is to
+
+431
+00:35:33,300 --> 00:35:38,630
+have your engine blueprinted احدى الشغلاتاللي احنا
+
+432
+00:35:38,630 --> 00:35:43,410
+بنتكلم فيها بعد هيك ايش انه لو انت ماعندك الفلوس
+
+433
+00:35:43,410 --> 00:35:47,890
+انت بتروحي بتجيبي بتعملي ال blueprint اللي هي
+
+434
+00:35:47,890 --> 00:35:51,790
+بتعمليه حسب المواصفات اللي انت بدكيها بالظبط اللي
+
+435
+00:35:51,790 --> 00:35:57,450
+هي ال process is perfectly legal as the sizes of
+
+436
+00:35:57,450 --> 00:36:03,620
+all parts remain withinthe tolerances طبعا هذه
+
+437
+00:36:03,620 --> 00:36:07,480
+قانونية مية في المية طالما انت within the
+
+438
+00:36:07,480 --> 00:36:12,200
+tolerances الموجودة that are ايش for the standard
+
+439
+00:36:12,200 --> 00:36:21,540
+ايش الكلمة نسينا ايش الكلمات هي سبعة خلينا نشوف
+
+440
+00:36:21,540 --> 00:36:25,820
+هنا احنا خلصنا plus و minus و ال range و ال
+
+441
+00:36:25,820 --> 00:36:30,460
+variationو ال .. و ال precision و ال terrace دل
+
+442
+00:36:30,460 --> 00:36:37,300
+عندنا إيش permissible permissible و دل عندنا fit و
+
+443
+00:36:37,300 --> 00:36:40,920
+clearances مظبوط orange
+
+444
+00:36:42,680 --> 00:36:46,600
+الـ tolerances that are permissible for the
+
+445
+00:36:46,600 --> 00:36:50,600
+standard engine specifications however by
+
+446
+00:36:50,600 --> 00:36:54,380
+carefully matching pairs or groups of parts that
+
+447
+00:36:54,380 --> 00:36:58,040
+are all in either the lower or the upper half of
+
+448
+00:36:58,040 --> 00:37:02,580
+the tolerance الـ Ad طالع عنده إيش بنعمل في ال
+
+449
+00:37:02,580 --> 00:37:07,320
+blue printing أنا بعمل طالما عنده بدي maximum باخد
+
+450
+00:37:07,320 --> 00:37:12,300
+ال upper partفي ال tolerance أقصى درجة بدي أقل
+
+451
+00:37:12,300 --> 00:37:16,640
+باخد ال lower bound اللي هي أقل اشي مسموح فيه فانا
+
+452
+00:37:16,640 --> 00:37:20,040
+بعمل matching فهي طالما انا within the range
+
+453
+00:37:20,040 --> 00:37:24,380
+tolerance range a blueprinted engine is built to
+
+454
+00:37:24,380 --> 00:37:28,760
+ايش؟ ت fit together very precisely thanks to
+
+455
+00:37:28,760 --> 00:37:32,630
+almost perfect clearanceclearance between moving
+
+456
+00:37:32,630 --> 00:37:37,610
+parts الان علشان اللي بنعمل هنا فيهم انا باجي بعمل
+
+457
+00:37:37,610 --> 00:37:41,490
+matching يعني انا لما بدي اجيب في عندي يمين و في
+
+458
+00:37:41,490 --> 00:37:45,970
+عندي شجة شمال باجي بعمل matching انا بدي اكبر عجل
+
+459
+00:37:45,970 --> 00:37:51,130
+باخد قداش المسموح فيه بعمله على اكبر عجل بالظبط
+
+460
+00:37:51,130 --> 00:37:58,000
+الان بدي خلينا نقول اصغر weight اقل weightبنزل ال
+
+461
+00:37:58,000 --> 00:38:01,300
+weight على الحد الأدنى عشان تبقى تعطيني سرعة أكتر
+
+462
+00:38:01,300 --> 00:38:06,020
+كل ما قل الوزن كل ما زادت الكفاءة فهو هذا اللي
+
+463
+00:38:06,020 --> 00:38:13,200
+بعمل فيه في هذا المجال طيب الأن نرجع نقرا هدول
+
+464
+00:38:13,200 --> 00:38:17,820
+عشان نعيد لأ
+
+465
+00:38:17,820 --> 00:38:21,760
+كويس هذه بدنا نقراها اليوم عشان برضه تلزج الكلمات
+
+466
+00:38:21,760 --> 00:38:24,200
+مين تتطوع اتفضل
+
+467
+00:38:27,350 --> 00:38:36,290
+بتقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+468
+00:38:36,290 --> 00:38:39,870
+تقدر
+
+469
+00:38:39,870 --> 00:38:47,170
+تقدر
+
+470
+00:38:47,170 --> 00:38:54,290
+تقدر تقدر تقدر تقدر
+
+471
+00:38:54,290 --> 00:38:54,390
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+472
+00:38:54,390 --> 00:38:54,510
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+473
+00:38:54,510 --> 00:39:00,620
+تقدر تالتصميم، لأن المهندسين عرفوا أن الوضع لا
+
+474
+00:39:00,620 --> 00:39:04,180
+يمكن أن يكون ممتاز، في التصميم، يعتمدوا على
+
+475
+00:39:04,180 --> 00:39:12,220
+توليرات مستحيلة وتغييرات وقصة، بإمكانهم أن يكونوا
+
+476
+00:39:12,220 --> 00:39:15,740
+مستحيلين أن يكونوا مستحيلين أن يكونوا مستحيلين أن
+
+477
+00:39:15,740 --> 00:39:17,080
+يكونوا مستحيلين أن يكونوا مستحيلين أن يكونوا
+
+478
+00:39:17,080 --> 00:39:19,680
+مستحيلين أن يكونوا مستحيلين أن يكونوا مستحيلين أن
+
+479
+00:39:19,680 --> 00:39:19,860
+يكونوا مستحيلين أن يكونوا مستحيلين أن يكونوا
+
+480
+00:39:19,860 --> 00:39:20,380
+يكونوا مستحيلين أن يكونوا مستحيلين أن يكونوا
+
+481
+00:39:20,380 --> 00:39:25,500
+مستحيلين أن يكونوا مستحيلين أن
+
+482
+00:39:26,090 --> 00:39:35,690
+طيب اتطلع الكلمات اللي عندى هنا precise exact
+
+483
+00:39:35,690 --> 00:39:42,050
+accurate هدولة
+
+484
+00:39:42,050 --> 00:39:47,470
+كلها تهم نفس المعنى precision exactness او
+
+485
+00:39:47,470 --> 00:39:53,710
+accuracy نفس الشغلة الان very different
+
+486
+00:39:58,160 --> 00:40:03,960
+deviate هدول كلهم نفس المعنى ال variation ال
+
+487
+00:40:03,960 --> 00:40:07,720
+differences و ال deviation و ال tolerance بيجوا
+
+488
+00:40:07,720 --> 00:40:12,840
+نفس الشغلة اللي عندي يعني لما تشوفوهم هدول هتلاقوا
+
+489
+00:40:12,840 --> 00:40:17,800
+نفس الشغلات اللي بنتكلم عليها الأهل لما نتكلم عنده
+
+490
+00:40:17,800 --> 00:40:23,620
+هدولة لخصوا الكلمات اللي موجودين عندنا كلنا بدور
+
+491
+00:40:23,620 --> 00:40:29,520
+الحل معنيينهذا الموجود سواء الآن بنطلع على ال
+
+492
+00:40:29,520 --> 00:40:33,700
+nouns و ال adjectives لكل هدول الموجودين طيب ال
+
+493
+00:40:33,700 --> 00:40:39,380
+slide التانية مين تقراها؟ فضل ال drawing below
+
+494
+00:40:39,380 --> 00:40:44,320
+shows a shaft with a specified diameter of 88 mm
+
+495
+00:40:44,320 --> 00:40:50,400
+plus or minus 0.05 mm this means the diameter may
+
+496
+00:40:50,400 --> 00:40:57,010
+be 8.5مليمتر على الجانب الأخر لهذه الصميمة، لذلك
+
+497
+00:40:57,010 --> 00:41:06,410
+ديامتر 87.95 مليمتر و 88.5.05 مليمتر، وهي قليلاً
+
+498
+00:41:06,410 --> 00:41:11,370
+غير صحيحة ومسموحة للعمل في المستشفى، وهي داخل
+
+499
+00:41:11,370 --> 00:41:19,650
+توليرانت، ولكن ديامتر 87.94 مليمتر أو 88.06
+
+500
+00:41:19,650 --> 00:41:25,640
+مليمتر، ليس مسموحطيب، الآن نتكلم على الـ Tolerance
+
+501
+00:41:25,640 --> 00:41:30,480
+الـ Tolerance عندي plus or minus certain
+
+502
+00:41:30,480 --> 00:41:36,720
+percentage كويس؟ or number؟ الآن عندي نوعين هنا
+
+503
+00:41:36,720 --> 00:41:41,020
+acceptable و
+
+504
+00:41:41,020 --> 00:41:47,980
+إيش؟ unacceptable الـ acceptable بنسميه
+
+505
+00:41:47,980 --> 00:41:48,680
+permissible
+
+506
+00:41:53,330 --> 00:42:03,190
+وهنا بنسمي .. ده بده تطلع عليه Unpermissible هذا
+
+507
+00:42:03,190 --> 00:42:13,230
+بنسمي Within Tolerance وهنا Outside Tolerance
+
+508
+00:42:13,230 --> 00:42:18,990
+هدولة ملخص هذا ال slide
+
+509
+00:42:21,780 --> 00:42:28,900
+طيب نشوف اللي بعدها مين بدها .. تفضّال يا تسنييب
+
+510
+00:42:28,900 --> 00:42:34,120
+نحن
+
+511
+00:42:34,120 --> 00:42:43,700
+نقول إنه نوع من كلمات أو كلمات مفقودة كلمة مفقودة
+
+512
+00:42:43,700 --> 00:42:44,880
+مثلا
+
+513
+00:42:48,460 --> 00:42:53,560
+المكينيك يعطي ميزة تتعامل مع طرق اكتر من اكتر من
+
+514
+00:42:53,560 --> 00:42:58,400
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+515
+00:42:58,400 --> 00:43:06,840
+اكتر من اكتر من اكتر من اكتر من اكتر
+
+516
+00:43:06,840 --> 00:43:07,340
+من اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+517
+00:43:07,340 --> 00:43:09,120
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+518
+00:43:09,120 --> 00:43:09,660
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+519
+00:43:09,660 --> 00:43:09,680
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+520
+00:43:09,680 --> 00:43:16,680
+اكتر من اكتر من اكتر من
+
+521
+00:43:16,680 --> 00:43:17,320
+اكت
+
+522
+00:43:27,800 --> 00:43:31,860
+هنا عندنا نوعين لـ Acceptive Tolerance ايش هما
+
+523
+00:43:31,860 --> 00:43:40,340
+Tight و Loose الـ Tight Tolerance بنلاحظ الدقة
+
+524
+00:43:40,340 --> 00:43:46,270
+عالية الـ Loose Tolerance الدقة مش هالالعلو
+
+525
+00:43:46,270 --> 00:43:52,910
+الموجود الان ال fit .. مين بي .. اتفضل .. مضال
+
+526
+00:43:52,910 --> 00:44:00,790
+عدنا .. اتفضل
+
+527
+00:44:00,790 --> 00:44:03,450
+.. مضال عدنا .. اتفضل .. مضال عدنا .. اتفضل ..
+
+528
+00:44:03,450 --> 00:44:05,270
+مضال عدنا .. اتفضل .. مضال عدنا .. اتفضل .. مضال
+
+529
+00:44:05,270 --> 00:44:05,530
+عدنا .. مضال عدنا .. مضال عدنا .. مضال عدنا ..
+
+530
+00:44:05,530 --> 00:44:07,270
+مضال عدنا .. مضال عدنا .. مضال عدنا .. مضال عدنا
+
+531
+00:44:07,270 --> 00:44:09,010
+عدنا .. مضال عدنا .. مضال عدنا .. مضال عدنا ..
+
+532
+00:44:09,010 --> 00:44:11,370
+مضال عدنا .. مضال عدنا .. مضال عدنا .. مضال عدنا
+
+533
+00:44:19,930 --> 00:44:24,730
+Gap between itself and the side of the wall, this
+
+534
+00:44:24,730 --> 00:44:27,870
+distance must be quite precise if there is a gap
+
+535
+00:44:29,620 --> 00:44:40,340
+انسفشانت انسفشانت انسفشانت انسفشانت
+
+536
+00:44:40,340 --> 00:44:40,360
+انسفشانت انسفشانت انسفشانت انسفشانت انسفشانت
+
+537
+00:44:40,360 --> 00:44:40,620
+انسفشانت انسفشانت انسفشانت انسفشانت انسفشانت
+
+538
+00:44:40,620 --> 00:44:41,700
+انسفشانت انسفشانت انسفشانت انسفشانت انسفشانت
+
+539
+00:44:41,700 --> 00:44:46,060
+انسفشانت انسفشانت انسفشانت انسفشانت انسفشانت
+
+540
+00:44:46,060 --> 00:44:54,220
+انسفشانت انسفشانت
+
+541
+00:44:54,220 --> 00:44:57,820
+انسفشانت
+
+542
+00:44:57,820 --> 00:45:04,250
+انسطيب، آخر واحدة، مين بدها؟ تفضل
+
+543
+00:45:45,530 --> 00:45:50,590
+الان عندي نوعين من ال fit clearance fit و
+
+544
+00:45:50,590 --> 00:45:53,850
+interference fit ال clearance fit في عندي loose
+
+545
+00:45:53,850 --> 00:45:58,070
+بيبقى في وسع اللي هنا ال interference fit بيبقى
+
+546
+00:45:58,070 --> 00:46:04,690
+tight هذا ملخصالمحاضرة اللي عندنا، يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/riuyYD8BWPA_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/riuyYD8BWPA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6feff3fcceb0fe9db9d4ffe7437d950225edce31
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/riuyYD8BWPA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5031, "start": 20.87, "end": 50.31, "text": "اليوم هنتكلم السلام عليكم اليوم هنتكلم على chapter 10 chapter 10 talks about measurable parameters يعني ال parameters القابل للقياس supply, demand and capacity ايش يعني supply؟ ايوة هي المداد او المتوفر في السوق او المنتج", "tokens": [6027, 1829, 20498, 8032, 29399, 4117, 19528, 21136, 37440, 25894, 24793, 45595, 20498, 8032, 29399, 4117, 19528, 15844, 7187, 1266, 7187, 1266, 6686, 466, 43615, 9834, 37495, 22653, 2423, 9834, 25062, 16758, 1211, 24976, 4587, 25528, 3794, 5847, 11, 4733, 293, 6042, 1975, 1829, 8592, 37495, 22653, 5847, 22807, 1975, 1829, 2407, 3660, 39896, 9673, 3215, 18513, 1975, 2407, 9673, 2655, 38688, 2288, 8978, 21136, 30543, 1975, 2407, 9673, 29399, 7435], "avg_logprob": -0.1672092028376129, "compression_ratio": 1.6358974358974359, "no_speech_prob": 0.0, "words": [{"start": 20.87, "end": 21.33, "word": "اليوم", "probability": 0.96337890625}, {"start": 21.33, "end": 22.03, "word": " 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0.978271484375}, {"start": 88.52, "end": 89.02, "word": " interest", "probability": 0.64208984375}, {"start": 89.02, "end": 89.18, "word": " في", "probability": 0.8408203125}, {"start": 89.18, "end": 89.4, "word": " هذا", "probability": 0.939453125}, {"start": 89.4, "end": 89.94, "word": " الموضوع", "probability": 0.9979248046875}, {"start": 89.94, "end": 91.04, "word": " calculating", "probability": 0.767578125}, {"start": 91.04, "end": 91.42, "word": " the", "probability": 0.85888671875}, {"start": 91.42, "end": 91.94, "word": " capacity", "probability": 0.85302734375}, {"start": 91.94, "end": 92.14, "word": " of", "probability": 0.96044921875}, {"start": 92.14, "end": 92.36, "word": " an", "probability": 0.59228515625}, {"start": 92.36, "end": 92.9, "word": " electricity", "probability": 0.93994140625}, {"start": 92.9, "end": 93.58, "word": " grid", "probability": 0.93603515625}, {"start": 93.58, "end": 94.46, "word": " يعني", "probability": 0.93505859375}, {"start": 94.46, "end": 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"end": 101.37, "word": "نحسب", "probability": 0.8056640625}, {"start": 101.37, "end": 101.95, "word": " قدرة", "probability": 0.9637044270833334}, {"start": 101.95, "end": 102.49, "word": " شبكة", "probability": 0.991455078125}, {"start": 102.49, "end": 103.25, "word": " الكهربا", "probability": 0.95458984375}, {"start": 103.25, "end": 104.09, "word": " capacity", "probability": 0.1436767578125}, {"start": 104.09, "end": 104.63, "word": " of", "probability": 0.9326171875}, {"start": 104.63, "end": 105.63, "word": " electricity", "probability": 0.91845703125}, {"start": 105.63, "end": 106.73, "word": " grid", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 5, "seek": 13800, "start": 109.48, "end": 138.0, "text": "أو كمية الكهربا التي يتوفرها للمستخدمين قد تبدو بسيطة، ممكن تكون بسيطة، ايش بيللاحظ؟ فقط اضافة كمية الكهربا التي تتوفرها للمستخدمين في مدى وقت معين لتحفظ كمية الكهربا التي تتخذ من المستخدمين", "tokens": [10721, 2407, 9122, 2304, 10632, 33251, 3224, 25513, 995, 38392, 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هذا بيسموها off peak hour فعندنا ال peak hour و ال off peak hour طيب in other words consumption does not stay the same at the same level all the time فال consumption بيضلوش بنفس المستوى طول الوقت", "tokens": [6027, 995, 14851, 3224, 15040, 4117, 2423, 10651, 1773, 6024, 48506, 5551, 4587, 1211, 8717, 35457, 3660, 44713, 3224, 15040, 4117, 4032, 38149, 11933, 1829, 8592, 22807, 8978, 13672, 26895, 4032, 2423, 8315, 3794, 8717, 995, 32640, 3660, 23758, 4724, 1829, 38251, 2407, 11296, 766, 10651, 1773, 6156, 3615, 41260, 8315, 2423, 10651, 1773, 4032, 2423, 766, 10651, 1773, 23032, 1829, 3555, 294, 661, 2283, 12126, 775, 406, 1754, 264, 912, 412, 264, 912, 1496, 439, 264, 565, 6156, 6027, 12126, 4724, 1829, 11242, 1211, 2407, 8592, 44945, 36178, 9673, 14851, 2407, 7578, 23032, 12610, 2423, 30543, 2655], "avg_logprob": -0.14638573443046723, "compression_ratio": 1.6578947368421053, "no_speech_prob": 0.0, "words": [{"start": 296.61, "end": 297.49, "word": "الاستهلاك", "probability": 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0.49298095703125}, {"start": 1218.82, "end": 1219.22, "word": " لاتيجي", "probability": 0.76416015625}, {"start": 1219.22, "end": 1219.68, "word": " تتطلع", "probability": 0.81044921875}, {"start": 1219.68, "end": 1220.0, "word": " اصلا", "probability": 0.8037109375}, {"start": 1220.0, "end": 1220.18, "word": " ال", "probability": 0.8857421875}, {"start": 1220.18, "end": 1220.68, "word": " mature", "probability": 0.7763671875}, {"start": 1220.68, "end": 1224.26, "word": " الصافي", "probability": 0.8133951822916666}, {"start": 1224.26, "end": 1224.6, "word": " تبعه", "probability": 0.7899169921875}, {"start": 1224.6, "end": 1225.38, "word": " قداشة،", "probability": 0.63037109375}, {"start": 1225.38, "end": 1225.68, "word": " لا", "probability": 0.69677734375}, {"start": 1225.68, "end": 1226.38, "word": " يتجاوز", "probability": 0.9571940104166666}, {"start": 1226.38, "end": 1226.84, "word": " اربعين", "probability": 0.8602294921875}, {"start": 1226.84, "end": 1226.96, "word": " في", 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"temperature": 1.0}, {"id": 72, "seek": 184061, "start": 1829.75, "end": 1840.61, "text": "و جميع انبوت و اخر انبوت مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد", "tokens": [2407, 10874, 2304, 40228, 16472, 3555, 35473, 4032, 1975, 34740, 16472, 3555, 35473, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215, 3714, 7435, 2288, 3215], "avg_logprob": -0.6460597787214362, "compression_ratio": 2.169811320754717, "no_speech_prob": 0.0, "words": [{"start": 1829.75, "end": 1830.27, "word": "و", "probability": 0.60546875}, {"start": 1830.27, "end": 1830.73, "word": " جميع", "probability": 0.6806640625}, {"start": 1830.73, "end": 1832.33, "word": " انبوت", "probability": 0.55078125}, {"start": 1832.33, "end": 1832.43, "word": " و", "probability": 0.169189453125}, {"start": 1832.43, "end": 1832.81, "word": " اخر", "probability": 0.284423828125}, {"start": 1832.81, "end": 1833.05, 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{"id": 74, "seek": 187960, "start": 1861.68, "end": 1879.6, "text": "الـ four هدولة في عندى اتنين كل اتنين مع بعض واحد بياخد .. بطلع حرارة والتانى بيستغلوا هذه الحرارة ليعمل generation بشوية دعم طبعا fuel .. شوية fuel بيعمل generation تانى وبيعطيني full capacity اللى عندى هذه", "tokens": [6027, 39184, 1451, 8032, 3215, 12610, 3660, 8978, 43242, 7578, 1975, 2655, 1863, 9957, 28242, 1975, 2655, 1863, 9957, 20449, 45030, 11242, 36764, 24401, 4724, 1829, 47283, 3215, 4386, 4724, 9566, 1211, 3615, 11331, 2288, 9640, 3660, 16070, 2655, 7649, 7578, 4724, 1829, 14851, 17082, 1211, 14407, 29538, 21542, 2288, 9640, 3660, 32239, 25957, 1211, 5125, 4724, 8592, 2407, 10632, 11778, 25957, 23032, 3555, 3615, 995, 6616, 4386, 13412, 2407, 10632, 6616, 4724, 1829, 25957, 1211, 5125, 6055, 7649, 7578, 4032, 21292, 3615, 9566, 1829, 22653, 1577, 6042, 13672, 7578, 43242, 7578, 29538], "avg_logprob": -0.18251330072575428, "compression_ratio": 1.65, "no_speech_prob": 0.0, "words": [{"start": 1861.68, 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Sarah plus heat and it can't all be recycled", "tokens": [6027, 39184, 3738, 483, 30674, 4724, 40228, 9566, 1829, 22653, 5847, 2423, 5847, 8032, 47302, 4724, 40228, 9566, 1829, 22653, 4386, 20449, 14739, 44713, 17082, 1211, 2655, 27188, 995, 4587, 9566, 4724, 40228, 9566, 1829, 22653, 7148, 1185, 2171, 456, 307, 43495, 49429, 9519, 1804, 4386, 9519, 1804, 3738, 293, 309, 393, 380, 439, 312, 30674], "avg_logprob": -0.35142543023092704, "compression_ratio": 1.4502923976608186, "no_speech_prob": 0.0, "words": [{"start": 1906.96, "end": 1907.26, "word": "الـ", "probability": 0.4443359375}, {"start": 1907.26, "end": 1907.58, "word": " heat", "probability": 0.63623046875}, {"start": 1907.58, "end": 1908.32, "word": " get", "probability": 0.387451171875}, {"start": 1908.32, "end": 1909.18, "word": " recycled", "probability": 0.82568359375}, {"start": 1909.18, "end": 1909.88, "word": " بيعطيني", "probability": 0.6966796875}, {"start": 1909.88, "end": 1910.46, "word": " supply", "probability": 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" production", "probability": 0.9697265625}, {"start": 2162.96, "end": 2164.1, "word": " نسميها", "probability": 0.80029296875}, {"start": 2164.1, "end": 2164.38, "word": " ال", "probability": 0.501953125}, {"start": 2164.38, "end": 2165.06, "word": " net", "probability": 0.845703125}, {"start": 2165.06, "end": 2165.7, "word": " أو", "probability": 0.454345703125}, {"start": 2165.7, "end": 2165.86, "word": " ال", "probability": 0.9443359375}, {"start": 2165.86, "end": 2166.16, "word": " gain", "probability": 0.9169921875}, {"start": 2166.16, "end": 2168.16, "word": " ال", "probability": 0.400390625}, {"start": 2168.16, "end": 2168.92, "word": " surplus", "probability": 0.95751953125}, {"start": 2168.92, "end": 2171.34, "word": " اللي", "probability": 0.975830078125}, {"start": 2171.34, "end": 2171.54, "word": " هي", "probability": 0.9248046875}, {"start": 2171.54, "end": 2171.9, "word": " كده", "probability": 0.6460367838541666}, {"start": 2171.9, "end": 2172.1, "word": " إيش", "probability": 0.8644205729166666}, {"start": 2172.1, "end": 2172.98, "word": " ال", "probability": 0.888671875}, {"start": 2172.98, "end": 2173.5, "word": " amount", "probability": 0.97412109375}, {"start": 2173.5, "end": 2174.0, "word": " that", "probability": 0.93505859375}, {"start": 2174.0, "end": 2174.84, "word": " exceeds", "probability": 0.953125}], "temperature": 1.0}, {"id": 86, "seek": 219744, "start": 2175.52, "end": 2197.44, "text": "consumption بنسميه surplus الآن في عندي .. إذا بلاحظ في عندي .. إيش العكس تبع surplus shortage shortage اللي هي ال opposite ل surplus اللي هي أنا في عندي عجز بنسميه shortage", "tokens": [21190, 449, 1695, 44945, 38251, 1829, 3224, 31019, 6024, 48506, 8978, 18871, 16254, 4386, 11933, 15730, 4724, 15040, 5016, 19913, 8978, 18871, 16254, 4386, 11933, 1829, 8592, 18863, 4117, 3794, 6055, 3555, 3615, 31019, 24708, 24708, 13672, 1829, 39896, 2423, 6182, 5296, 31019, 13672, 1829, 39896, 41850, 8978, 18871, 16254, 6225, 7435, 11622, 44945, 38251, 1829, 3224, 24708], "avg_logprob": -0.2176906784712258, "compression_ratio": 1.625, "no_speech_prob": 0.0, "words": [{"start": 2175.52, "end": 2176.36, "word": "consumption", "probability": 0.8313802083333334}, {"start": 2176.36, "end": 2176.88, "word": " بنسميه", "probability": 0.70166015625}, {"start": 2176.88, "end": 2177.32, "word": " surplus", "probability": 0.6103515625}, {"start": 2177.32, "end": 2178.52, "word": " الآن", "probability": 0.53070068359375}, {"start": 2178.52, "end": 2178.7, "word": " في", "probability": 0.88623046875}, {"start": 2178.7, "end": 2179.8, "word": " عندي", "probability": 0.83935546875}, {"start": 2179.8, "end": 2180.66, "word": " ..", "probability": 0.336669921875}, {"start": 2180.66, "end": 2181.9, "word": " إذا", "probability": 0.7127685546875}, {"start": 2181.9, "end": 2182.36, "word": " بلاحظ", "probability": 0.72894287109375}, {"start": 2182.36, "end": 2182.54, "word": " في", "probability": 0.90380859375}, {"start": 2182.54, "end": 2182.96, "word": " عندي", "probability": 0.951904296875}, {"start": 2182.96, "end": 2183.84, "word": " ..", "probability": 0.76708984375}, {"start": 2183.84, "end": 2184.62, "word": " إيش", "probability": 0.8800455729166666}, {"start": 2184.62, "end": 2185.08, "word": " العكس", "probability": 0.9879557291666666}, {"start": 2185.08, "end": 2185.3, "word": " تبع", "probability": 0.8226725260416666}, {"start": 2185.3, "end": 2186.06, "word": " surplus", "probability": 0.97314453125}, {"start": 2186.06, "end": 2187.2, "word": " shortage", "probability": 0.83642578125}, {"start": 2187.2, "end": 2189.98, "word": " shortage", "probability": 0.94482421875}, {"start": 2189.98, "end": 2190.3, "word": " اللي", "probability": 0.977294921875}, {"start": 2190.3, "end": 2190.5, "word": " هي", "probability": 0.86328125}, {"start": 2190.5, "end": 2190.62, "word": " ال", "probability": 0.83154296875}, {"start": 2190.62, "end": 2191.14, "word": " opposite", "probability": 0.95556640625}, {"start": 2191.14, "end": 2191.4, "word": " ل", "probability": 0.96044921875}, {"start": 2191.4, "end": 2191.9, "word": " surplus", "probability": 0.978515625}, {"start": 2191.9, "end": 2192.66, "word": " اللي", "probability": 0.98291015625}, {"start": 2192.66, "end": 2192.86, "word": " هي", "probability": 0.7412109375}, {"start": 2192.86, "end": 2193.3, "word": " أنا", "probability": 0.8115234375}, {"start": 2193.3, "end": 2193.82, "word": " في", "probability": 0.810546875}, {"start": 2193.82, "end": 2194.14, "word": " عندي", "probability": 0.966796875}, {"start": 2194.14, "end": 2194.9, "word": " عجز", "probability": 0.9716796875}, {"start": 2194.9, "end": 2197.04, "word": " بنسميه", "probability": 0.9395751953125}, {"start": 2197.04, "end": 2197.44, "word": " shortage", "probability": 0.984375}], "temperature": 1.0}, {"id": 87, "seek": 220976, "start": 2199.06, "end": 2209.76, "text": "surplus اللي هو الفائض وال shortage اللي هو العاجز في ال system لما أنا فيه عندي طلب أكتر من المعروض بنسميه shortage", "tokens": [36054, 18954, 13672, 1829, 31439, 27188, 16373, 11242, 16070, 24708, 13672, 1829, 31439, 18863, 26108, 11622, 8978, 2423, 1185, 5296, 15042, 41850, 8978, 3224, 18871, 16254, 23032, 46152, 5551, 4117, 2655, 2288, 9154, 9673, 3615, 32887, 11242, 44945, 38251, 1829, 3224, 24708], "avg_logprob": -0.24073401024175245, "compression_ratio": 1.368421052631579, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2199.06, "end": 2199.64, "word": "surplus", "probability": 0.544647216796875}, {"start": 2199.64, "end": 2199.84, "word": " اللي", "probability": 0.678955078125}, {"start": 2199.84, "end": 2200.0, "word": " هو", "probability": 0.9873046875}, {"start": 2200.0, "end": 2200.58, "word": " الفائض", "probability": 0.9319661458333334}, {"start": 2200.58, "end": 2200.84, "word": " وال", "probability": 0.5478515625}, {"start": 2200.84, "end": 2201.86, "word": " shortage", "probability": 0.833984375}, {"start": 2201.86, "end": 2202.26, "word": " اللي", "probability": 0.9794921875}, {"start": 2202.26, "end": 2202.46, "word": " هو", "probability": 0.921875}, {"start": 2202.46, "end": 2203.6, "word": " العاجز", "probability": 0.6722005208333334}, {"start": 2203.6, "end": 2203.72, "word": " في", "probability": 0.96826171875}, {"start": 2203.72, "end": 2203.82, "word": " ال", "probability": 0.91845703125}, {"start": 2203.82, "end": 2204.16, "word": " system", "probability": 0.96728515625}, {"start": 2204.16, "end": 2204.44, "word": " لما", "probability": 0.817626953125}, {"start": 2204.44, "end": 2204.68, "word": " أنا", "probability": 0.47998046875}, {"start": 2204.68, "end": 2204.88, "word": " فيه", "probability": 0.69140625}, {"start": 2204.88, "end": 2205.1, "word": " عندي", "probability": 0.6837158203125}, {"start": 2205.1, "end": 2205.54, "word": " طلب", "probability": 0.99560546875}, {"start": 2205.54, "end": 2206.8, "word": " أكتر", "probability": 0.9339599609375}, {"start": 2206.8, "end": 2207.02, "word": " من", "probability": 0.99267578125}, {"start": 2207.02, "end": 2207.78, "word": " المعروض", "probability": 0.958251953125}, {"start": 2207.78, "end": 2209.46, "word": " بنسميه", "probability": 0.8902587890625}, {"start": 2209.46, "end": 2209.76, "word": " shortage", "probability": 0.97900390625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2209.843125, "duration_after_vad": 2095.7362499999936}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/s751BsBTw4U.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/s751BsBTw4U.srt
new file mode 100644
index 0000000000000000000000000000000000000000..440e0a61cea258dafef84900c0d8c8ec22683c32
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/s751BsBTw4U.srt
@@ -0,0 +1,1647 @@
+1
+00:00:20,940 --> 00:00:28,680
+السلام عليكم اليوم سنتحدث عن قصة 41 قصة 41 تتحدث
+
+2
+00:00:28,680 --> 00:00:34,940
+عن الترانزميشن مع الترانزميشن نعني تتبع جيارات ..
+
+3
+00:00:34,940 --> 00:00:39,360
+جيارات .. جيارات .. جيارات .. جيارات .. جيارات
+
+4
+00:00:39,360 --> 00:00:43,620
+يعني هتكلم على الجيارة اللي هو .. إيش بنسميه 
+
+5
+00:00:43,620 --> 00:00:52,160
+بالعربي؟ لأ لأ خلاص كلكم عارفين إيش بيبنانيأيوة ف
+
+6
+00:00:52,160 --> 00:00:57,960
+.. الجير
+
+7
+00:00:57,960 --> 00:01:03,280
+اللي هو بيحول من يعني هنتكلم عنه اللي بيعملنا يعني
+
+8
+00:01:03,280 --> 00:01:07,510
+بيخففال mechanical effort أو بيعطينا mechanical
+
+9
+00:01:07,510 --> 00:01:12,090
+advantage يعني بيعطينا ميزة في العمل أو بيخفف 
+
+10
+00:01:12,090 --> 00:01:18,550
+بيعطينا قدرات أكثر لنرفع شيء أو نحرك شيء بدرجة أو
+
+11
+00:01:18,550 --> 00:01:25,200
+نغير في الصراعات لشيء معين فنيجي نطلع عليه كلكم
+
+12
+00:01:25,200 --> 00:01:29,540
+بتعرفوا هذه موجودة في البسكليتات أحيانا بتقولي
+
+13
+00:01:29,540 --> 00:01:32,700
+ليش؟ وين موجود؟ بتلاقيه موجود في البسكليت، موجود
+
+14
+00:01:32,700 --> 00:01:36,500
+في السيارة، موجود في حاجات كثيرة، في الغسالة، في
+
+15
+00:01:36,500 --> 00:01:41,880
+كل شيء موجود إيش بنعمل؟ في عندي حاجة بتلف بسرعة،
+
+16
+00:01:41,880 --> 00:01:51,390
+بتحرك شيء أكبر، سرعة هذا أخف، لأن عدد الأسنان تبعه
+
+17
+00:01:51,390 --> 00:01:57,150
+أو عدد الأسنان اللي فيه أكثر، فإيش اللي بيحصل فيه؟
+
+18
+00:01:57,150 --> 00:02:02,150
+هذا بولد عزم أكبر أو بياخد مجهود أقل هذا من
+
+19
+00:02:02,150 --> 00:02:05,590
+الموجود اللي .. اللي هنا، يعني لو جيت حد كل كرة
+
+20
+00:02:05,590 --> 00:02:09,560
+كبتلبوا سكالتات وانتوا صغار، أقل شيء لو جيتوا كان ال
+
+21
+00:02:09,560 --> 00:02:14,420
+.. اللفة اللي بدك تسويها صغيرة، بدك تضلك تلف أكثر، 
+
+22
+00:02:14,420 --> 00:02:18,880
+فهتاخدك مجهود أكبر، بينما لو كانت اللفة كبيرة، كل
+
+23
+00:02:18,880 --> 00:02:22,840
+ما زادت بتلاقيها أسهل، الآن في .. في الجبال الناس
+
+24
+00:02:22,840 --> 00:02:26,660
+اللي بتطلع بس .. على ال .. البسكليت ع الجبل لو جيت
+
+25
+00:02:26,660 --> 00:02:31,980
+لبسكليت عادي، ما بيقدروش يطلعوهلأنه بدها مجهود كبير
+
+26
+00:02:31,980 --> 00:02:35,180
+وبدها السرعة فإيش بيسووا النسب بيلعبوا فيه هنا
+
+27
+00:02:35,180 --> 00:02:40,720
+عشان السرعة انه ما تاخدش المجهود العالي هذا بنسميه
+
+28
+00:02:40,720 --> 00:02:46,460
+driver هذا بنسميه ال follower هذا بيبقى عندي shaft
+
+29
+00:02:46,460 --> 00:02:53,780
+اللي هي دراع الآن هذه بنسميها tooth الأسنان
+
+30
+00:02:53,780 --> 00:03:01,840
+الموجودة عندي gear wheel اللي هو العجل or gears are
+
+31
+00:03:01,840 --> 00:03:07,700
+wheels with teeth or cogs ال cogs هم نفسهم مسمى ال
+
+32
+00:03:07,700 --> 00:03:10,920
+إيش الأسنان بس هذا بتبقى ال .. ال .. ال .. الاسم
+
+33
+00:03:10,920 --> 00:03:19,700
+مخصص لمين؟ لل gear wheels هم أسنان العجل
+
+34
+00:03:19,700 --> 00:03:24,480
+اللي بلب فيها the teeth interlock interlock يعني
+
+35
+00:03:24,480 --> 00:03:28,500
+إيش مشبكين في بعض fit together يعني بتشوف كل واحد
+
+36
+00:03:28,500 --> 00:03:34,020
+كل سن راكب مع السن الثاني with those of the other
+
+37
+00:03:34,020 --> 00:03:38,600
+gear wheel when one gear wheel revolves لما واحد
+
+38
+00:03:38,600 --> 00:03:44,540
+بلف إيش الثاني the other revolves with it عجلة
+
+39
+00:03:44,540 --> 00:03:51,330
+بتلف الثانية لازم تلف معها الآن في الغالب إيش
+
+40
+00:03:51,330 --> 00:03:55,750
+بيصير؟ واحدة بتلف clockwise والتانية بتبقى counter
+
+41
+00:03:55,750 --> 00:04:01,450
+clockwise يعني بيلفوا اثنين في اتجاهين مختلفين as
+
+42
+00:04:01,450 --> 00:04:05,370
+they rotate mesh together ال mesh اللي هي إيش
+
+43
+00:04:05,370 --> 00:04:09,670
+بيركبوا مع بعض gears are normally fitted to shafts
+
+44
+00:04:09,670 --> 00:04:15,030
+عادة تبقى فيه دراع مربوطة مع ال gear الموجودة عشان
+
+45
+00:04:15,030 --> 00:04:21,250
+هي اللي بتعمل الحركة they transmit rotary motion
+
+46
+00:04:21,250 --> 00:04:25,970
+from one shaft to another that is they transmit
+
+47
+00:04:25,970 --> 00:04:31,130
+drive يعني هم عادة الحركة الدائرية بيمجلوها من
+
+48
+00:04:31,130 --> 00:04:38,410
+مكان أو من جزء لجزء ثاني وهذا واضح أن مثلا أنا لما
+
+49
+00:04:38,410 --> 00:04:43,750
+نبدل على البسكليت تبدلت الحركة بتنتقل من وين؟ من
+
+50
+00:04:43,750 --> 00:04:48,150
+عندي للعجل اللي وراي فبيصير يعمل لي الدفع الدفع
+
+51
+00:04:48,150 --> 00:04:52,430
+اللي سميناها إيش؟ drive transmit ال drive اللي هي
+
+52
+00:04:52,430 --> 00:04:59,850
+قوة الدافعة ال drive usually supplied by an engine
+
+53
+00:04:59,850 --> 00:05:05,190
+or a motor causes a shaft to revolve عادة أنا لما
+
+54
+00:05:05,190 --> 00:05:11,370
+بدي أعملها يا إما بدي أكون موتور يا إما إيش مولد
+
+55
+00:05:11,370 --> 00:05:15,610
+اللي بيعملها المشبوك مع ال دراع اللي بيعمل الحركة
+
+56
+00:05:17,550 --> 00:05:22,210
+reverb اللي هي إيش تلف a shaft connected directly
+
+57
+00:05:22,210 --> 00:05:26,950
+to an engine or a motor is called a drive shaft or
+
+58
+00:05:26,950 --> 00:05:31,350
+as an input shaft drive المشبوخ مع الموتور أو ال
+
+59
+00:05:31,350 --> 00:05:34,910
+engine إيش بنسميه؟ يا إما drive shaft نسبة
+
+60
+00:05:34,910 --> 00:05:39,530
+لل driver أو input shaft لأن هو اللي بدخل عنده
+
+61
+00:05:39,530 --> 00:05:45,260
+الحركة الآن في عندي هيكون عندي output shaft كمان
+
+62
+00:05:45,260 --> 00:05:49,980
+فال input اللي هو اللي إيش اللي بتدخل منه الحركة
+
+63
+00:05:49,980 --> 00:05:55,720
+الآن
+
+64
+00:05:55,720 --> 00:05:59,480
+تطلع عنده إيش القطع هي ال follower هي driver وهي
+
+65
+00:05:59,480 --> 00:06:04,590
+ال follower إيش حطينا في النص idler ال idler إيش
+
+66
+00:06:04,590 --> 00:06:10,210
+بيعمل ليه طلع هذا الاتجاه إيش هنا معاكس هنا معاكس
+
+67
+00:06:10,210 --> 00:06:16,610
+اثنين صاروا إيش نفس الاتجاه فهو بوحد لي الاتجاه هاي
+
+68
+00:06:16,610 --> 00:06:23,470
+ال idler اللي عندي a
+
+69
+00:06:23,470 --> 00:06:28,940
+gear wheel on a drive shaft is called a driver اللي
+
+70
+00:06:28,940 --> 00:06:33,400
+هو هنا وشفتوا أنتو هناك the second gear wheel
+
+71
+00:06:33,400 --> 00:06:35,900
+which meshes with the driver is called the
+
+72
+00:06:35,900 --> 00:06:40,380
+follower the driver drives the follower عادة ال
+
+73
+00:06:40,380 --> 00:06:44,310
+follower بتبع مين؟ ال driver ال driver هو اللي
+
+74
+00:06:44,310 --> 00:06:47,430
+بتحرك an assembly of several shafts and gear
+
+75
+00:06:47,430 --> 00:06:51,890
+wheels is called gear train or transmission system
+
+76
+00:06:51,890 --> 00:06:57,130
+الآن ال transmission ده بتطلع عنده السيارة ال
+
+77
+00:06:57,130 --> 00:07:02,670
+automatic إيش بيسموها automatic إيش؟ transmission
+
+78
+00:07:02,670 --> 00:07:07,930
+حتى لما بدك تحط الزيت بقى بيسموه transmission oil
+
+79
+00:07:07,930 --> 00:07:15,520
+بينما ال manual بيسموه gearbox oil ال transmission
+
+80
+00:07:15,520 --> 00:07:19,920
+هي كلمة لما يكون عندك gearbox فيه أكثر من نسبة
+
+81
+00:07:19,920 --> 00:07:26,860
+بنسميه يعني أنت عادة كل خلينا gear له نسبة ratio
+
+82
+00:07:26,860 --> 00:07:31,040
+من هالجد لهالجد بيحول لما يكون عندي خيارات كثيرة
+
+83
+00:07:31,040 --> 00:07:34,240
+وأنا بحول من واحد للثاني هذا بيسميه transmission
+
+84
+00:07:34,240 --> 00:07:37,400
+box transmission
+
+85
+00:07:41,780 --> 00:07:45,540
+هي نفس المسمى بس ال transmission إيش فيه؟ فيه عندي
+
+86
+00:07:45,540 --> 00:07:50,080
+أكثر من gear system كويس؟
+
+87
+00:07:50,080 --> 00:07:59,800
+يعني لما يكون عندي أحيانًا بيبقى عندي خيارات لأ
+
+88
+00:07:59,800 --> 00:08:06,420
+مش بالضرورة فيها نفس ال system اللي موجود هناك بس
+
+89
+00:08:06,420 --> 00:08:10,860
+إيش هديك؟ حاجة بتتحرك يدويًا وحاجة بتتحرك
+
+90
+00:08:10,860 --> 00:08:16,270
+automatically وحسب الأنواع الموجودة عندك أنت بتحسش
+
+91
+00:08:16,270 --> 00:08:20,710
+فيها بس إذا أنت براكبة سيارة بتحس السيارة لما تنقل
+
+92
+00:08:20,710 --> 00:08:26,070
+ال gear بتبقى خفيفة الحركة بس بتحس أن في نغلة حصلت
+
+93
+00:08:26,070 --> 00:08:30,030
+بس هذا بتحصل automatic بينما في ال manual إيش
+
+94
+00:08:30,030 --> 00:08:35,610
+بتعمله السواك بنقل لحاله فأنت بتحس الحركة هو اللي
+
+95
+00:08:35,610 --> 00:08:39,350
+بقرر وقت إيش ينقل هداك هي بتقرر السيارة بتقرر
+
+96
+00:08:39,350 --> 00:08:41,010
+لحالها وقت إيش تنقل
+
+97
+00:08:43,810 --> 00:08:47,750
+فعندي several طلع عندي هنا إيش بنقول هنا an
+
+98
+00:08:47,750 --> 00:08:51,790
+assembly of several shafts and gear wheels يعني
+
+99
+00:08:51,790 --> 00:08:55,890
+عندي مجموعة من الشافت ومجموعة من ال gear wheel
+
+100
+00:08:55,890 --> 00:08:59,470
+اللي هي العجال تبعات ال gear لهذا السبب سمنها إيش
+
+101
+00:08:59,470 --> 00:09:07,070
+gear train train or transmission system it begins
+
+102
+00:09:07,070 --> 00:09:11,370
+with an input shaft and ends with an output shaft
+
+103
+00:09:11,370 --> 00:09:15,490
+في عندي حاجة بتطلع منها هي اللي بتزود shaft دراعها
+
+104
+00:09:15,490 --> 00:09:18,450
+هي اللي بتبدأ الحركة في دراعها في الآخر هي اللي
+
+105
+00:09:18,450 --> 00:09:22,370
+بنتي عندها اللي هي الحركة ال output shaft اللي هي
+
+106
+00:09:22,370 --> 00:09:26,470
+الشافت اللي بينتهي عنده خط النهاية ال input shaft
+
+107
+00:09:26,470 --> 00:09:29,930
+مشبوك مع ال motor أو ال engine وهو اللي ببدأ عنده
+
+108
+00:09:29,930 --> 00:09:35,260
+ال generation للحركة النظام قد يحتوي على أسنان
+
+109
+00:09:35,260 --> 00:09:42,020
+idler أو أسنان idler هذه تغيير اتجاه اتجاه اتجاه
+
+110
+00:09:42,020 --> 00:09:42,300
+اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه
+
+111
+00:09:42,300 --> 00:09:46,460
+اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه
+
+112
+00:09:46,460 --> 00:09:49,140
+اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه
+
+113
+00:09:49,140 --> 00:09:49,360
+اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه
+
+114
+00:09:49,360 --> 00:09:50,960
+اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه اتجاه
+
+115
+00:09:50,960 --> 00:09:54,620
+اتجاه اتجاه اتجاه اتجاه 
+
+116
+00:09:57,980 --> 00:10:02,600
+الآن نتكلم على ال gear ratio إيش ال gear ratio؟ زي
+
+117
+00:10:02,600 --> 00:10:09,060
+ما بتعرفوا أنتو الحركة عادة بستخدم ال gear يا إما
+
+118
+00:10:09,060 --> 00:10:14,680
+لأزود عدد اللفات يا إما لما أقللها gears can
+
+119
+00:10:14,680 --> 00:10:17,920
+provide a mechanical advantage ذاكرين هدف ال
+
+120
+00:10:17,920 --> 00:10:22,520
+chapter إيش؟ هاي ال chapter عندي 33 ال mechanical
+
+121
+00:10:22,520 --> 00:10:27,560
+advantage بتعطيني ميزة ميكانيكية بأبدل جهد أقل
+
+122
+00:10:29,080 --> 00:10:33,900
+باستخدام gear ratio مختلف باستخدام gear ratio مختلف
+
+123
+00:10:33,900 --> 00:10:42,120
+باستخدام gear ratio مختلف باستخدام gear ratio مختلف
+
+124
+00:10:42,120 --> 00:10:46,060
+باستخدام gear ratio مختلف باستخدام gear ratio مختلف
+
+125
+00:10:46,060 --> 00:10:47,120
+باستخدام gear ratio مختلف باستخدام gear ratio مختلف 
+
+126
+00:10:47,120 --> 00:10:50,140
+باستخدام جير ريشيو مختلف باستخدام جير ريشيو مختلف
+
+127
+00:10:50,140 --> 00:10:53,900
+باستخدام جير ريشيو مختلف باستخدام جير ريشيو مختلف
+
+128
+00:10:53,900 --> 00:10:56,940
+باستخدام جير ريشيو مختلف باستخدام جير ريشيو مختلف
+
+129
+00:10:57,130 --> 00:11:05,210
+مرة واحدة مرة
+
+130
+00:11:05,210 --> 00:11:08,350
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+131
+00:11:08,350 --> 00:11:09,050
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+132
+00:11:09,050 --> 00:11:09,130
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+133
+00:11:09,130 --> 00:11:09,190
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+134
+00:11:09,190 --> 00:11:09,650
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+135
+00:11:09,650 --> 00:11:10,390
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+136
+00:11:10,390 --> 00:11:15,150
+واحدة مرة واحدة مرة واحدة مرة واحدة مرة واحدة مرة
+
+137
+00:11:15,150 --> 00:11:26,890
+واحدة مرة واحدة مرة واحدة مرة
+
+138
+00:11:26,890 --> 00:11:32,800
+واحدة  لأ بتسميها run ال run اللي هي إيش لفة run per
+
+139
+00:11:32,800 --> 00:11:40,140
+minute rpm the output speed of the follower will 
+
+140
+00:11:40,140 --> 00:11:47,140
+be one thousand rpm run per minute runs per minute
+
+141
+00:11:47,140 --> 00:11:50,700
+هي يعني دورة
+
+142
+00:11:55,900 --> 00:12:01,440
+في بعض الأجهزة تستخدم جرس جهاز لإعطاء عدد مختلف من
+
+143
+00:12:01,440 --> 00:12:05,890
+عدد الجهاز جزء من جزء من جزء من جزء من جزء من جزء
+
+144
+00:12:05,890 --> 00:12:07,090
+من جزء من جزء من جزء من جزء من جزء من جزء من جزء
+
+145
+00:12:07,090 --> 00:12:08,750
+من جزء من جزء من جزء من جزء من جزء من جزء من جزء
+
+146
+00:12:08,750 --> 00:12:14,850
+من جزء من جزء من جزء من جزء من جزء من جزء من جزء
+
+147
+00:12:14,850 --> 00:12:22,450
+من جزء من جزء من جزء من جزء من جزء من جزء من جزء
+
+148
+00:12:22,450 --> 00:12:30,290
+من جزء من عدد اللفات اللي عندي إذا بتلاحظوا دائماً
+
+149
+00:12:30,290 --> 00:12:33,850
+يعني حاجتين بتشوفوها في السيارات ممكن بتلاحظوها
+
+150
+00:12:33,850 --> 00:12:39,030
+لما الواحد يمشي على منطقة رملية إيش بيعمل ال gear
+
+151
+00:12:39,030 --> 00:12:44,610
+بيبقى واطي لما حد بدي يمشي على جبال ال gear بيبقى
+
+152
+00:12:44,610 --> 00:12:49,490
+واطي يعني بدي عزم أكثر فهذا .. الآن لما أروح على
+
+153
+00:12:49,490 --> 00:12:56,770
+خط سريع أو في طريق سريع فاضي فيها وقفات بحط الـ gear
+
+154
+00:12:56,770 --> 00:13:01,830
+العالي في الشوارع بتلاقيهم ماشيين بسرعة على second 
+
+155
+00:13:01,830 --> 00:13:05,670
+gear أو بالكثير أو third gear بالكثير بينما في
+
+156
+00:13:05,670 --> 00:13:09,370
+الخط السريع بروح لل gear الخامس ليش؟ اللي هو أعلى
+
+157
+00:13:09,370 --> 00:13:14,550
+gear في السيارة لأن في عندك حاجتين أولاً الحركة
+
+158
+00:13:14,550 --> 00:13:21,320
+بتبقى smooth فبتاخدش طاقة عالية فبت .. فهذا السبب 
+
+159
+00:13:21,320 --> 00:13:25,640
+الرئيسي أنك .. يعني السيارة بتتطلبش عزم كثير عشان
+
+160
+00:13:25,640 --> 00:13:29,180
+تتحرك بينما لو طالع جبل ب .. ب .. بنفعش أطلع على
+
+161
+00:13:29,180 --> 00:13:33,600
+غير خامس إلا إذا كان الجبل خط سريع والسيارة نظيفة
+
+162
+00:13:33,600 --> 00:13:40,360
+فهذا اللي بتساوي فيه، طيب this may be a manual
+
+163
+00:13:42,200 --> 00:13:45,300
+gearbox where gears are changed by a person الـ
+
+164
+00:13:45,300 --> 00:13:49,600
+manual اللي هو إيش التغيير بيه المستخدم هو اللي
+
+165
+00:13:49,600 --> 00:13:53,200
+بيغير or automatic gearbox which automatically
+
+166
+00:13:53,200 --> 00:13:57,500
+select a higher gear or lower gear as needed الآن 
+
+167
+00:13:57,500 --> 00:14:02,340
+بالـ automatic بتحسيش في التغيير في حاجة واحدة هي
+
+168
+00:14:02,340 --> 00:14:05,780
+لحالها بتغير يعني وأنت راكب السيارة لو أنت بتسوقي
+
+169
+00:14:05,780 --> 00:14:09,400
+وهذا معظم الستات بحبوا أن هذا النوع من السيارات
+
+170
+00:14:09,400 --> 00:14:13,480
+بتلاقيها مركزة على ال brake والـ إيش والبنزين هذول
+
+171
+00:14:13,480 --> 00:14:18,740
+حاجتين اللي بدهم ال gear كيف تحطه وكيف تشغل ما تش
+
+172
+00:14:18,740 --> 00:14:23,220
+سويش هذا الناس اللي بتقل حركتهم في المدن ودائماً
+
+173
+00:14:23,220 --> 00:14:26,680
+إيديهم على التليفونات وغيره برضه بحبوا ال
+
+174
+00:14:26,680 --> 00:14:30,890
+automatic لأن هذا بتتيح لهم مجال أكثر يتحركوا في
+
+175
+00:14:30,890 --> 00:14:35,630
+السيارة إلا المخ اللي ما تتحركش مركز على شغل واحدة
+
+176
+00:14:35,630 --> 00:14:40,110
+هي
+
+177
+00:14:40,110 --> 00:14:45,770
+يعني يمكن حاجتين بتلاحظيها يعني هدف العام اللي 
+
+178
+00:14:45,770 --> 00:14:51,050
+سايق سيارة وهو بتكلم زي وزي اللي شاربله حاجة هو
+
+179
+00:14:51,050 --> 00:14:57,240
+مش في الطريق ونفس الشيء دائماً حتى طلعوا على الأجهزة
+
+180
+00:14:57,240 --> 00:15:01,220
+الموجودة يمكن هذه ما لهاش داخل بالموضوع تبعنا طلعوا 
+
+181
+00:15:01,220 --> 00:15:07,580
+الأجهزة اللي فيها heavy machines اللي فيها قص وقطع
+
+182
+00:15:07,580 --> 00:15:11,560
+وحاجة بتعرفيش بيخلوا الواحد يستخدم إيديه ورجليه
+
+183
+00:15:11,560 --> 00:15:17,300
+الأربعة ليش؟ عشان هذا ما يفكرش لو الأربعة مش محطوطين
+
+184
+00:15:17,300 --> 00:15:21,200
+في المواقع اللي هو بدي أحطهم، الماشينا بتشتغلش من
+
+185
+00:15:21,200 --> 00:15:25,480
+قدر ما اتقطع أصابع عقدين الناس فهذا صارت safety
+
+186
+00:15:25,480 --> 00:15:31,000
+procedure أنه بدي أستخدم كل إشي بتحرك أحط في مكانه
+
+187
+00:15:31,000 --> 00:15:36,800
+عشان أنقص اللي موجود، اللي هايطيب، الآن هنتكلم على
+
+188
+00:15:36,800 --> 00:15:41,420
+عدة .. عدة أنواع من الـ gear هذا بنسميه spare gear
+
+189
+00:15:41,420 --> 00:15:48,700
+إيش هو؟ طلعوا الإسنان كيف شكلهم هذه عبارة عن اثنان
+
+190
+00:15:48,700 --> 00:15:54,320
+بتتحرك كل واحد بتتعامل مع الحفل الموجود عندي هان
+
+191
+00:15:54,320 --> 00:15:58,940
+ال spare gear are the simplest gears the teeth run
+
+192
+00:15:58,940 --> 00:16:02,580
+straight across the wheel هاي ال wheel straight
+
+193
+00:16:02,580 --> 00:16:06,520
+across على طول عبر ال wheel فهي بتحرك ال wheel
+
+194
+00:16:06,520 --> 00:16:12,260
+بسهولة هذا سمينهم إيش spare gear وأنا حاططهم واحدة
+
+195
+00:16:12,260 --> 00:16:18,500
+واحدة عشان تشوفوهم الثاني بنسميه helical gear طلع
+
+196
+00:16:18,500 --> 00:16:25,660
+هدول الشكل تبعهم كيف؟ على شكل curved helical gears
+
+197
+00:16:25,660 --> 00:16:32,000
+have curved teeth الإسنان إيش شكلهم؟ curved so
+
+198
+00:16:32,000 --> 00:16:35,920
+that they mesh together more smoothly هذه الحركة
+
+199
+00:16:35,920 --> 00:16:41,060
+بتلاقيها ناعمة عادة السيارات بيستخدموا هذا النوع من
+
+200
+00:16:41,060 --> 00:16:45,640
+الـ gear الحركة إيش بنسميها ناعمة؟ هذه سميناها إيش؟
+
+201
+00:16:45,640 --> 00:16:50,020
+helical gears هذه إيش؟ spare وهذه إيش؟ straight
+
+202
+00:16:50,020 --> 00:16:58,940
+طيب إيش في غيرهم؟ bevel gear allowed drive to be
+
+203
+00:16:58,940 --> 00:17:02,900
+transmitted through an angle of 90 degrees طلع
+
+204
+00:17:02,900 --> 00:17:08,180
+الزاوية اللي عندي 90 درجة الموجودة فهذه سميناها
+
+205
+00:17:08,180 --> 00:17:14,740
+bevel gear النوع
+
+206
+00:17:14,740 --> 00:17:22,560
+الرابع crown gear and crown gear and pinion هذا
+
+207
+00:17:22,560 --> 00:17:26,300
+اللي هو طلع عندي الأسنان كيف هدي هدي بتلف الدائرة
+
+208
+00:17:26,300 --> 00:17:30,640
+وهدي بتلف بشكل الدائرة اللي عندي يعني crown gear
+
+209
+00:17:30,640 --> 00:17:34,100
+transmit drive through ninety degree often to a
+
+210
+00:17:34,100 --> 00:17:38,660
+smaller gear called pinion هدي اللي عندي smaller و
+
+211
+00:17:38,660 --> 00:17:45,820
+هدي إيش bigger فهده بتعطيني ال people بتعطيني إيش
+
+212
+00:17:46,750 --> 00:17:51,150
+زاوية تسعين درجة بس مش فيها smaller gear يعني هذه
+
+213
+00:17:51,150 --> 00:17:56,350
+.. هنا إيش اللي عندي؟ crown gear هات زي التاج شكله
+
+214
+00:17:56,350 --> 00:18:00,750
+إذا بطلها crown إيش معناته تاج؟ وهذا سموه pinion
+
+215
+00:18:00,750 --> 00:18:05,130
+اللي عندي pinion اللي هو ال gear فهي ال crown gear
+
+216
+00:18:05,130 --> 00:18:09,890
+اللي هو عبارة transmitting through ninety degrees
+
+217
+00:18:09,890 --> 00:18:16,580
+بس إيش to smaller gear called pinion النوع الأخير
+
+218
+00:18:16,580 --> 00:18:22,260
+اللي بنسميه worm gear الشكل هذا زي إيش؟ زي الدودة
+
+219
+00:18:22,260 --> 00:18:27,960
+worm معناها إيش؟ دودة فهي الشكل تبعه زي الدودة
+
+220
+00:18:27,960 --> 00:18:32,240
+worm gear transmit drive through an angle they
+
+221
+00:18:32,240 --> 00:18:37,200
+allow a low output speed relative to the input
+
+222
+00:18:37,200 --> 00:18:41,340
+speed يعني هذا اللي عند ال speed هذا low lower
+
+223
+00:18:41,340 --> 00:18:49,500
+مقارنة بالدائرة اللي عندي they can provide a
+
+224
+00:18:49,500 --> 00:18:52,740
+one-way drive as a worm can drive a gear but a
+
+225
+00:18:52,740 --> 00:18:56,740
+gear cannot drive a worm يعني هذا إيش؟ هذا اللي
+
+226
+00:18:56,740 --> 00:19:00,560
+بيعمل drive لمين؟ لل worm بس ال worm بيعملش drive
+
+227
+00:19:00,560 --> 00:19:06,400
+لمين؟ لل gear فهذا بنسميه one-way one-way drive
+
+228
+00:19:06,400 --> 00:19:11,850
+وشكله زي الدودة والدودة بتمشي كيف؟ حركتها؟ بطيئة
+
+229
+00:19:11,850 --> 00:19:19,350
+هذا .. هذا ال .. ال .. الكلمة اللي جاية منها الآن
+
+230
+00:19:19,350 --> 00:19:22,430
+أنا بدأت أعمل إيش هنا change four words in the text
+
+231
+00:19:22,430 --> 00:19:26,170
+below to make it correct اللي عندي، بدأت أصلح
+
+232
+00:19:26,170 --> 00:19:30,450
+الكلمات هنا بس خليني قبل ما نمشي هناك نرجع شوية
+
+233
+00:19:30,450 --> 00:19:34,630
+نتكلم
+
+234
+00:19:34,630 --> 00:19:41,630
+.. بس نذكر في الشغلات المهمة عندي عشان تبقوا معنا
+
+235
+00:19:41,630 --> 00:19:46,090
+مركزين الآن
+
+236
+00:19:46,090 --> 00:19:49,930
+اللي عندي في البداية في عندي driver وفي عندي
+
+237
+00:19:49,930 --> 00:19:54,430
+follower ال driver هو اللي بيحرك اللي بيجي عنده ال
+
+238
+00:19:54,430 --> 00:19:59,510
+input ال input shaft الـ follower اللي بنتهي عنده
+
+239
+00:19:59,510 --> 00:20:05,410
+ال output shaft ال driver و ال follower عادة they
+
+240
+00:20:05,410 --> 00:20:09,050
+.. أيوة they move in opposite .. opposite
+
+241
+00:20:09,050 --> 00:20:15,170
+direction ال
+
+242
+00:20:15,170 --> 00:20:19,030
+three components اللي عندي ال follower و ال shaft
+
+243
+00:20:19,030 --> 00:20:23,350
+و ال إيش و ال driver اللي عندي
+
+244
+00:20:27,060 --> 00:20:32,380
+ال idler إيش بيعمل ليه؟ change .. change of the
+
+245
+00:20:32,380 --> 00:20:37,680
+motion direction يعني لو حد رايحة clockwise بيعمل
+
+246
+00:20:37,680 --> 00:20:41,160
+يعني خلينا ال driver follower going different
+
+247
+00:20:41,160 --> 00:20:44,600
+direction or opposite direction لما نحط idler في
+
+248
+00:20:44,600 --> 00:20:47,100
+النص بيعملهم the same direction
+
+249
+00:20:53,610 --> 00:20:58,270
+الـ transmission system أو gear train عبارة عن
+
+250
+00:20:58,270 --> 00:21:03,670
+إيش؟ a system or assembly of several shafts and 
+
+251
+00:21:03,670 --> 00:21:08,770
+several gear wheels في عندي يعني مجموعة من الـ
+
+252
+00:21:08,770 --> 00:21:12,410
+wheels ومجموعة من الشافات فهذا بنسميه transmission
+
+253
+00:21:12,410 --> 00:21:14,610
+system أو gear train
+
+254
+00:21:17,440 --> 00:21:23,820
+الـ ratio عادة تعطينا ميكانيكال advantage لما 
+
+255
+00:21:23,820 --> 00:21:29,300
+نستخدمها لأن شفتوا example ل 3 to 1 و ال input
+
+256
+00:21:29,300 --> 00:21:33,280
+speed اللي عندي وفي output speed إيش بدخل للـ
+
+257
+00:21:33,280 --> 00:21:36,960
+system وإيش بيطلع للـ system حسب ال ratio الموجودة
+
+258
+00:21:36,960 --> 00:21:37,580
+عندي 
+
+259
+00:21:40,440 --> 00:21:47,720
+الـ gearbox والـ gear selection بتعمل
+
+260
+00:21:47,720 --> 00:21:54,020
+تغيير أو تشيفت للجهاز اللي عندي الـ manual gearbox
+
+261
+00:21:54,020 --> 00:21:59,640
+اللي هو بتعمل تغيير للجهاز بيحصل من شخص للاستخدام
+
+262
+00:21:59,640 --> 00:22:05,000
+الترانزميشن أو automatic gearbox اللي بيحصل عندي
+
+263
+00:22:05,000 --> 00:22:10,800
+تغيير from higher gear or lower gear automatically
+
+264
+00:22:10,800 --> 00:22:16,920
+يعني بدون استخدام الإنسان التلاتة أنواع عند الـ
+
+265
+00:22:16,920 --> 00:22:21,500
+spur gear اللي هو إيش بيعمل simplest هذا الـ
+
+266
+00:22:21,500 --> 00:22:27,580
+teeth run straight across the wheel هذا بشكل مباشر
+
+267
+00:22:27,580 --> 00:22:32,720
+ال helical في عندك curved teeth وهذا الحركة بيصير
+
+268
+00:22:32,720 --> 00:22:33,760
+إيش smoothly
+
+269
+00:22:36,800 --> 00:22:41,000
+الـ bevel gear هذه في عندي بتعطيني 90 degrees اللي
+
+270
+00:22:41,000 --> 00:22:47,460
+عندي وهذي إيش ال vertical الـ .. الآن ال crown
+
+271
+00:22:47,460 --> 00:22:54,420
+الشكل تبعه زي إيش الـ تاج وعندي عادة pinion الـ
+
+272
+00:22:54,420 --> 00:22:58,700
+pinion هذا الحجم تبعه عدد الـ .. يعني بتبقى أصغر من
+
+273
+00:22:58,700 --> 00:23:04,610
+ال crown وبعطيني 90 degrees في نفس الوجه الـ worm
+
+274
+00:23:04,610 --> 00:23:10,650
+gear في عندي حاجة زي الـ worm هذه بتعطيني برضه هذه
+
+275
+00:23:10,650 --> 00:23:15,950
+90 degrees إذا بتلاحظوا في عندي one way drive و
+
+276
+00:23:15,950 --> 00:23:19,510
+عادة ال speed اللي عندي ال output speed بتبقى
+
+277
+00:23:19,510 --> 00:23:26,610
+lower than ال input speed اللي عندي 90 degrees إذا 
+
+278
+00:23:26,610 --> 00:23:32,090
+بتلاحظوا هذه بتتطلع عليها إيش بنسميه في الخط .. في الـ
+
+279
+00:23:32,090 --> 00:23:37,670
+.. في الدائرة لما نيجي عليها خط تماثل؟ آه .. آه
+
+280
+00:23:37,670 --> 00:23:42,190
+عمودي على الدائرة بتلاقيها طيب الآن بدنا نتطلع على
+
+281
+00:23:42,190 --> 00:23:45,350
+الكلمات الغريبة ونتطلع عليها an engine is
+
+282
+00:23:45,350 --> 00:23:50,510
+connected to a driveshaft يعني الموتور شبكناه مع
+
+283
+00:23:50,510 --> 00:23:56,440
+مين؟ مع الـ driveshaft الموجود هنا fitted to this output
+
+284
+00:23:56,440 --> 00:24:01,440
+shaft ولا إيش؟ input قولنا أي إيش بنشبك مع الموتور
+
+285
+00:24:01,440 --> 00:24:07,200
+بنسمي إيش؟ أو ال engine input shaft is a gear
+
+286
+00:24:07,200 --> 00:24:14,040
+wheel called the idler ولا إيش هذه؟ إيش بنشبك الآن
+
+287
+00:24:14,040 --> 00:24:15,300
+عند هاي الموتور؟
+
+288
+00:24:23,570 --> 00:24:31,670
+شبكنا معاه shaft هذا سمينا input shaft كويس اللي
+
+289
+00:24:31,670 --> 00:24:38,370
+هنا المشبوك معاه بنشبك عليه driver ولا follower
+
+290
+00:24:38,370 --> 00:24:45,770
+ولا idler هنا بنشبك معاه driver كويس
+
+291
+00:24:45,770 --> 00:24:52,170
+as this gear wheel turn it drives another gear
+
+292
+00:24:52,170 --> 00:24:56,610
+wheel alongside it's called إيش ال follower اللي
+
+293
+00:24:56,610 --> 00:25:03,330
+بي .. بي .. بي .. ده حاطيت هنا عندي هذا سميتها
+
+294
+00:25:03,330 --> 00:25:09,310
+التاني اللي بدي انشبك عليه هذا
+
+295
+00:25:09,310 --> 00:25:15,230
+سميناه ال follower which
+
+296
+00:25:15,230 --> 00:25:20,680
+fit to an input shaft ولا إيش هذه؟ هذه اللي عندي بدي
+
+297
+00:25:20,680 --> 00:25:26,700
+أطلع عليه ال output shaft اللي عندي يعني ال output
+
+298
+00:25:26,700 --> 00:25:33,880
+بيجي مع مين؟ مع ال follower وال input بيجي مع الـ
+
+299
+00:25:33,880 --> 00:25:43,420
+driver هذا المختصر اللي احنا بنتكلم عنه الأجوبة
+
+300
+00:25:43,420 --> 00:25:51,470
+الآن complete the text اللي عندي هي عندي سيارة وهاد
+
+301
+00:25:51,470 --> 00:25:56,430
+السيارة موجود فيها إيش the case is IIH BOMA CVX
+
+302
+00:25:56,430 --> 00:25:59,910
+TRACTOR is equipped with continuously variable
+
+303
+00:25:59,910 --> 00:26:05,290
+transmission الأدنى نكمل حسب الكلمات المطلوبة
+
+304
+00:26:05,290 --> 00:26:09,690
+gearbox allow the driver of the vehicle إيش هذا الـ
+
+305
+00:26:09,690 --> 00:26:13,070
+.. إيش .. إيش الأنواع اللي بيخلي ال driver يتحكم
+
+306
+00:26:13,070 --> 00:26:19,270
+فيها manual gearbox allow the driver of the vehicle
+
+307
+00:26:19,270 --> 00:26:24,390
+to .. إيش gear؟ بده يعمل shift اللي هو بده يغير
+
+308
+00:26:24,390 --> 00:26:29,550
+يعني shift it change shift gear as required if
+
+309
+00:26:29,550 --> 00:26:37,270
+gear is selected إيش هذه؟ if .. اتطلع .. اتطلع
+
+310
+00:26:37,270 --> 00:26:40,430
+عليها if إيش gear is selected the speed of the
+
+311
+00:26:40,430 --> 00:26:44,410
+output shaft will increase relatively higher الآن
+
+312
+00:26:44,410 --> 00:26:49,630
+هذه من الكلمات المختارة هذا الـ select the speed of
+
+313
+00:26:49,630 --> 00:26:52,450
+the output shaft will increase relative to the
+
+314
+00:26:52,450 --> 00:26:57,090
+input shaft for a given engine speed in a typical
+
+315
+00:26:57,090 --> 00:27:01,790
+automatic gearbox الآن هان اتكلمنا على مين؟ على الـ
+
+316
+00:27:01,790 --> 00:27:05,290
+manual ال manual الشخص اللي بيعمل اللي عنده in
+
+317
+00:27:05,290 --> 00:27:10,460
+automatic gearbox however the gear إيش system is
+
+318
+00:27:10,460 --> 00:27:14,140
+automated؟ إيش اللي بيصير automated؟ عملية
+
+319
+00:27:14,140 --> 00:27:18,620
+الاختيار، الاختيار إيش سمينه هنا؟ selection الـ
+
+320
+00:27:18,620 --> 00:27:21,940
+selection اللي هي الكلمة اللي هنا is automated
+
+321
+00:27:21,940 --> 00:27:25,940
+requiring no action by the driver يعني السواق
+
+322
+00:27:25,940 --> 00:27:29,260
+بيعملش أي حاجة in addition most automatic
+
+323
+00:27:29,260 --> 00:27:34,060
+transmission system use so-called planetary gears
+
+324
+00:27:34,060 --> 00:27:37,720
+in basic terms these allow the transmission to
+
+325
+00:27:37,720 --> 00:27:42,640
+remain connected at all time unlike manual gearbox
+
+326
+00:27:42,640 --> 00:27:49,370
+الآن في الـ .. في الـ automated الـ Gear إيش بيحصل؟
+
+327
+00:27:49,370 --> 00:27:52,270
+في الـ Manual Gear ممكن السواق يفك الـ Gear يعني
+
+328
+00:27:52,270 --> 00:27:55,910
+لو واحد نزل نزلة إيش بيعمل؟ السواقين غزة كلهم
+
+329
+00:27:55,910 --> 00:27:59,350
+بيستخدموها عشان يوفروا بنزين بيفك الـ Gear
+
+330
+00:27:59,350 --> 00:28:04,170
+فالسيارة بتضالها ماشية حسب الجاذبية وقوة الدفع
+
+331
+00:28:04,170 --> 00:28:07,650
+اللي فيها لحد ما توصل بيشتغل بيشتبك الـ Gear
+
+332
+00:28:07,650 --> 00:28:12,390
+وبيعمل في الـ Automatic السيارة بتفكش Gear بتضالها
+
+333
+00:28:12,390 --> 00:28:17,090
+ماشية بنفس الـ Gear اللي موجود عليها فهذا .. إيه؟
+
+334
+00:28:18,640 --> 00:28:21,800
+في عندهم حاجة بيعملوها بس هاي خطرة إيش بيحطها
+
+335
+00:28:21,800 --> 00:28:29,240
+بيحطها على ال neutral ال neutral بيفك ال gear ماهي
+
+336
+00:28:29,240 --> 00:28:33,600
+هاد أنت بدك تسير تفكر يعني زي حد مهود بسرعة وفجأة
+
+337
+00:28:33,600 --> 00:28:38,320
+بدك تشبكه بحاجة فهد بتصير شوية shock لل gear
+
+338
+00:28:38,320 --> 00:28:42,580
+system تبع السيارة غير عن ال manual ال manual ..
+
+339
+00:28:42,580 --> 00:28:47,420
+السيارة مصممة إنها تغير gear حسب السواق ففي الـ
+
+340
+00:28:47,420 --> 00:28:51,600
+automatic هي مصممة إنها لحالها تبقى، فهذا اللي
+
+341
+00:28:51,600 --> 00:28:55,600
+بنحكي فيها In addition, most transmission systems
+
+342
+00:28:55,600 --> 00:28:59,400
+use so-called planetary gears in basic terms.
+
+343
+00:28:59,740 --> 00:29:02,380
+These allow the transmission to remain connected
+
+344
+00:29:02,380 --> 00:29:06,840
+at all times بتلاحظوا هذا بيبقى مشبوك في كل الوقت
+
+345
+00:29:09,280 --> 00:29:15,120
+يوم الخميس كان الشباب عندنا راحوا روحوا ل شاروم بارك
+
+346
+00:29:15,120 --> 00:29:19,040
+شباب القسم الكهرباء فراحوا هناك بتعرفوا تشوفوا الـ
+
+347
+00:29:19,040 --> 00:29:23,240
+discovery اللي البنات بيحبنها والشباب بيحبوها
+
+348
+00:29:23,240 --> 00:29:28,540
+فهذه إيش بتلاحظ موجودة فيها موجود فوق في عندك
+
+349
+00:29:28,540 --> 00:29:33,980
+أربعة gearbox الاربعة gearbox هدول مشبكين على طول
+
+350
+00:29:34,590 --> 00:29:39,350
+يعني ماشي لما تطلع هي بتبقى مشبوكة وبعدين لما
+
+351
+00:29:39,350 --> 00:29:44,170
+تنزل بتفلط لأ هي صح بتستخدموها وهي بتفلط as an
+
+352
+00:29:44,170 --> 00:29:49,450
+engine بتولد كهرباء وهي طالعة بتسير تسهلك الكهرباء
+
+353
+00:29:49,450 --> 00:29:54,710
+بس هذه بتعطيكي فكرة كيف الشغل اللي هنا بيشغل شايفة
+
+354
+00:29:54,710 --> 00:29:59,150
+الوزن تبعهم؟ قد إيش هذه؟ بتعرفوا قد إيش هذا الوزن
+
+355
+00:29:59,150 --> 00:30:08,030
+تبعها؟ تقريباً 16 قنطار الوزن العمود طبعاً فأنت لما
+
+356
+00:30:08,030 --> 00:30:14,010
+تحركي هذا بدك قوة كبيرة لتقدر تعمل حركة لهذا هذا
+
+357
+00:30:14,010 --> 00:30:20,930
+بتاخد تقريباً حسب مجالون ل 200 أمبير لما بدهم تبدأ
+
+358
+00:30:20,930 --> 00:30:28,170
+تشتغل فقوة كبيرة جداً عشان أنت .. آه
+
+359
+00:30:34,240 --> 00:30:41,040
+طيب آه طيب I like manual gearbox in which pair of
+
+360
+00:30:41,040 --> 00:30:45,420
+each gear are momentarily disconnected each time a
+
+361
+00:30:45,420 --> 00:30:51,500
+shift is made إيش هذا بنقول؟ طيب helical اللي هي
+
+362
+00:30:51,500 --> 00:30:54,960
+إيش اللي عندي اللي هي النوع المستخدم في الـ .. مش
+
+363
+00:30:54,960 --> 00:30:59,200
+حاكينها لكوا في البداية في السيارات القواعد هي
+
+364
+00:30:59,200 --> 00:31:03,060
+خلصنا هذه خلصنا ال automatic وخلصنا ال higher و
+
+365
+00:31:03,060 --> 00:31:10,140
+ال manual وال selection وال shift أعتقد shift آه
+
+366
+00:31:10,140 --> 00:31:14,660
+و الـ .. ال wheel خلصناها هو مش ذاكر القواعد
+
+367
+00:31:14,660 --> 00:31:20,340
+للترسيم المستمر مختلف تماماً لكلا ال manual والـ
+
+368
+00:31:20,340 --> 00:31:24,120
+automatic system بدل من أن يكون هناك عدد محدد من
+
+369
+00:31:24,120 --> 00:31:33,080
+جهاز مختلف ويلز هاجتناها each with different number
+
+370
+00:31:33,080 --> 00:31:37,360
+of teeth CVT uses a special mechanism to
+
+371
+00:31:37,360 --> 00:31:41,080
+continuously and progressively adjust the gear
+
+372
+00:31:41,080 --> 00:31:47,160
+ratio between the input and output shaft
+
+373
+00:31:50,130 --> 00:31:53,530
+وهنا الـ shafts Therefore, as the vehicle
+
+374
+00:31:53,530 --> 00:31:57,310
+accelerates or decelerates, continual adjustments
+
+375
+00:31:57,310 --> 00:32:01,690
+are made to the transmission automatically. This 
+
+376
+00:32:01,690 --> 00:32:05,750
+allows the engine to be maintained at a constant
+
+377
+00:32:05,750 --> 00:32:10,710
+speed for optimal power and fuel efficiency while
+
+378
+00:32:10,710 --> 00:32:15,710
+the system is able to continuously drive to the
+
+379
+00:32:15,710 --> 00:32:23,080
+vehicle's wheels, transmit drive اللي عندي، فهيك هذه
+
+380
+00:32:23,080 --> 00:32:28,040
+العشر كلمات المختلفة استخدمناهم، الآن بشكل عام
+
+381
+00:32:28,040 --> 00:32:31,600
+بتقولي طب أنا عندي كلمات كتيرة صارت كيف بتسوي؟ إذا 
+
+382
+00:32:31,600 --> 00:32:35,980
+أنت فهمت الفكرة الأساسية تبعت الهندسة، إيش عندي؟ في
+
+383
+00:32:35,980 --> 00:32:40,860
+عندي driver وفي عندي follower إذا بدي أحط حاجة في
+
+384
+00:32:40,860 --> 00:32:44,900
+النص بسميها idler هذه إلها shaft وهذه إلها shaft
+
+385
+00:32:44,900 --> 00:32:50,300
+عادة بعمل transmit the drive عندي من ال driver لمن؟
+
+386
+00:32:50,300 --> 00:32:55,420
+لل follower الآن لما أطلع فيه عندي ال ratio ال
+
+387
+00:32:55,420 --> 00:33:00,780
+gear ratio هي اللي بتحدد لي هل أنا بستخدم higher
+
+388
+00:33:00,780 --> 00:33:05,460
+gear ولا lower gear، ظل في كلمات مختلفة ما
+
+389
+00:33:05,460 --> 00:33:10,300
+استخدمناها عشان هذا كل اللي عملناها لخصناها في كم
+
+390
+00:33:10,300 --> 00:33:15,260
+من كلمة، طيب أخر واحدة بتقول لي إيش أنواع ال gear
+
+391
+00:33:15,260 --> 00:33:19,780
+اللي أنا مستخدمهم، طلع هنا هنا gears are used to
+
+392
+00:33:19,780 --> 00:33:22,540
+transmit drive through the angle، مين اللي
+
+393
+00:33:22,540 --> 00:33:30,440
+بيستخدمه؟ في ثلاثة أنواع صح؟ إيش هما؟ bevel و worm و
+
+394
+00:33:30,440 --> 00:33:37,800
+crown، طلع عليهم هذه الثلاثة موجودين، طيب gears run
+
+395
+00:33:37,800 --> 00:33:42,880
+more quietly than spur gears، مين هم الهلكل اللي
+
+396
+00:33:42,880 --> 00:33:47,320
+بيستخدموه في السيارات مظبوط؟
+
+397
+00:33:47,320 --> 00:33:51,100
+gears can generally only transmit drive in one
+
+398
+00:33:51,100 --> 00:33:56,780
+direction، مين اللي بيعمل؟ ال worm اللي هي الشكل تبعه
+
+399
+00:33:56,780 --> 00:34:01,150
+هذا، طيب gears allow drivers and followers to
+
+400
+00:34:01,150 --> 00:34:05,570
+revolve in the same direction؟ ال idler اللي هو
+
+401
+00:34:05,570 --> 00:34:11,570
+بيعمل اللي موجود هنا، هدول صعبات؟ هذه الأسئلة هادرة
+
+402
+00:34:11,570 --> 00:34:15,810
+أنت بتبقى مركزة اليوم وأنت مروحة إيش بتسوي؟
+
+403
+00:34:15,810 --> 00:34:22,450
+راجعيه بتشبك معاك وبتبقى ماشية كويس، اتفضلي
+
+404
+00:34:28,120 --> 00:34:34,360
+الاثنين ال quiz بس عشان ما تنسوش، مش الاثنين هذا
+
+405
+00:34:34,360 --> 00:34:40,560
+الاثنين الجاي، الاثنين هذا ما في إجازة ستة وعشرين و
+
+406
+00:34:40,560 --> 00:34:44,340
+سبعة وعشرين وثمانية وعشرين عشان أجهزهم هدول
+
+407
+00:34:44,340 --> 00:34:49,080
+كويسين
+
+408
+00:34:49,080 --> 00:34:55,050
+هيك؟ فاليوم اتكلمنا على ال transmission system على ال
+
+409
+00:34:55,050 --> 00:35:00,670
+gear system اللي عندنا، اتكلمنا عن مكوناته ال
+
+410
+00:35:00,670 --> 00:35:07,630
+components of the system، اتكلمنا على ال driver و
+
+411
+00:35:07,630 --> 00:35:13,710
+ال follower و ال idler و ال ratio و
+
+412
+00:35:13,710 --> 00:35:19,510
+ال types of gears اللي غطيناهم، يعطيكم العافية 
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/s751BsBTw4U_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/s751BsBTw4U_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e128440eac1ae49efcd1691cb788247ae5af4c29
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/s751BsBTw4U_raw.json
@@ -0,0 +1 @@
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892.91, "text": "لأن هذا بتتيح لهم مجال أكتر يتحركوا في السيارة إلا المخ اللي ماتتحركش مركز على شغل واحدة هي يعني يمكن حاجتين بتلاحظيها يعني هدف العام اللي سايق سيارة و هو بتكلم زي و زي اللي شاربله حاجة هو مش في الطريق", "tokens": [1211, 33456, 23758, 39894, 31371, 5016, 5296, 16095, 3714, 7435, 6027, 5551, 4117, 2655, 2288, 7251, 2655, 5016, 31747, 14407, 8978, 21136, 1829, 9640, 3660, 11933, 15040, 9673, 9778, 13672, 1829, 3714, 9307, 2655, 5016, 31747, 8592, 3714, 31747, 11622, 15844, 13412, 17082, 1211, 36764, 24401, 3660, 39896, 37495, 22653, 7251, 43020, 11331, 26108, 2655, 9957, 39894, 15040, 5016, 19913, 1829, 11296, 37495, 22653, 8032, 3215, 5172, 18863, 10943, 13672, 1829, 8608, 47302, 4587, 8608, 1829, 9640, 3660, 4032, 31439, 39894, 4117, 19528, 30767, 1829, 4032, 30767, 1829, 13672, 1829, 13412, 9640, 3555, 43761, 11331, 26108, 3660, 31439, 37893, 8978, 41950, 16572, 4587], "avg_logprob": -0.1512920678808139, "compression_ratio": 1.846938775510204, "no_speech_prob": 0.0, 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{"start": 872.73, "end": 873.43, "word": " ماتتحركش", "probability": 0.8469645182291666}, {"start": 873.43, "end": 874.73, "word": " مركز", "probability": 0.6983235677083334}, {"start": 874.73, "end": 874.83, "word": " على", "probability": 0.49951171875}, {"start": 874.83, "end": 875.17, "word": " شغل", "probability": 0.8748372395833334}, {"start": 875.17, "end": 875.63, "word": " واحدة", "probability": 0.98583984375}, {"start": 875.63, "end": 880.11, "word": " هي", "probability": 0.477783203125}, {"start": 880.11, "end": 881.03, "word": " يعني", "probability": 0.840576171875}, {"start": 881.03, "end": 881.41, "word": " يمكن", "probability": 0.7471923828125}, {"start": 881.41, "end": 881.89, "word": " حاجتين", "probability": 0.9404296875}, {"start": 881.89, "end": 882.71, "word": " بتلاحظيها", "probability": 0.8593343098958334}, {"start": 882.71, "end": 883.93, "word": " يعني", "probability": 0.741455078125}, {"start": 883.93, "end": 884.29, "word": " هدف", "probability": 0.923828125}, 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"text": "طيب، الآن هنتكلم على عدة .. عدة أنواع من الـ gear هذا بنسميه spare gear إيش هو؟ طلعوا الإسنان كيف شكلهم", "tokens": [9566, 1829, 3555, 12399, 6024, 48506, 8032, 29399, 4117, 19528, 15844, 6225, 41891, 4386, 6225, 41891, 14739, 14407, 3615, 9154, 2423, 39184, 7394, 23758, 44945, 38251, 1829, 3224, 13798, 7394, 11933, 1829, 8592, 31439, 22807, 23032, 1211, 3615, 14407, 33688, 3794, 1863, 7649, 9122, 33911, 13412, 28820, 16095], "avg_logprob": -0.2109375, "compression_ratio": 1.2761194029850746, "no_speech_prob": 0.0, "words": [{"start": 935.28, "end": 935.72, "word": "طيب،", "probability": 0.84503173828125}, {"start": 935.72, "end": 936.0, "word": " الآن", "probability": 0.753662109375}, {"start": 936.0, "end": 936.58, "word": " هنتكلم", "probability": 0.933837890625}, {"start": 936.58, "end": 936.8, "word": " على", "probability": 0.4443359375}, {"start": 936.8, "end": 937.06, "word": " عدة", "probability": 0.79345703125}, {"start": 937.06, "end": 937.18, "word": " ..", 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2655, 7649, 1829, 44945, 38251, 1829, 3224, 801, 804, 7394, 23032, 1211, 3615, 8032, 3215, 12610, 25124, 28820, 6055, 3555, 3615, 16095, 9122, 33911, 22807, 15844, 13412, 28820, 24991, 801, 804, 20915, 362, 24991, 7798, 33688, 3794, 1863, 7649, 11933, 1829, 8592, 13412, 28820, 16095, 22807, 24991, 370, 300, 436, 17407, 1214, 544, 19565, 23758, 21542, 31747, 3660, 39894, 15040, 38436, 11296, 8717, 25957, 3660], "avg_logprob": -0.18913246580024265, "compression_ratio": 1.427807486631016, "no_speech_prob": 0.0, "words": [{"start": 975.22, "end": 975.84, "word": "التاني", "probability": 0.8958740234375}, {"start": 975.84, "end": 976.62, "word": " بنسميه", "probability": 0.93701171875}, {"start": 976.62, "end": 977.34, "word": " helical", "probability": 0.876708984375}, {"start": 977.34, "end": 978.08, "word": " gear", "probability": 0.72314453125}, {"start": 978.08, "end": 978.5, "word": " طلع", "probability": 0.740234375}, {"start": 978.5, "end": 978.76, "word": " هدول", "probability": 0.9300130208333334}, {"start": 978.76, "end": 979.16, "word": " الشكل", "probability": 0.908447265625}, {"start": 979.16, "end": 979.66, "word": " تبعهم", "probability": 0.8516845703125}, {"start": 979.66, "end": 981.78, "word": " كيف؟", "probability": 0.9033203125}, {"start": 981.78, "end": 983.26, "word": " على", "probability": 0.488525390625}, {"start": 983.26, "end": 983.66, "word": " شكل", "probability": 0.88623046875}, {"start": 983.66, "end": 984.08, "word": " curved", "probability": 0.52392578125}, {"start": 984.08, "end": 985.18, "word": " helical", "probability": 0.888916015625}, {"start": 985.18, "end": 985.66, "word": " gears", "probability": 0.91015625}, {"start": 985.66, "end": 986.32, "word": " have", "probability": 0.90234375}, {"start": 986.32, "end": 986.86, "word": " curved", "probability": 0.94091796875}, {"start": 986.86, "end": 987.42, "word": " teeth", "probability": 0.94140625}, {"start": 987.42, "end": 988.54, "word": " الإسنان", "probability": 0.647247314453125}, {"start": 988.54, "end": 988.84, "word": " إيش", "probability": 0.8929036458333334}, {"start": 988.84, "end": 989.7, "word": " شكلهم؟", "probability": 0.9000244140625}, {"start": 989.7, "end": 990.9, "word": " curved", "probability": 0.83251953125}, {"start": 990.9, "end": 992.0, "word": " so", "probability": 0.438232421875}, {"start": 992.0, "end": 992.44, "word": " that", "probability": 0.89208984375}, {"start": 992.44, "end": 993.14, "word": " they", "probability": 0.77294921875}, {"start": 993.14, "end": 993.5, "word": " mesh", "probability": 0.904296875}, {"start": 993.5, "end": 994.06, "word": " together", "probability": 0.84130859375}, {"start": 994.06, "end": 994.56, "word": " more", "probability": 0.916015625}, {"start": 994.56, "end": 995.12, "word": " smoothly", "probability": 0.865234375}, {"start": 995.12, "end": 995.44, "word": " هذا", "probability": 0.30029296875}, {"start": 995.44, "end": 995.92, "word": " الحركة", "probability": 0.9855143229166666}, {"start": 995.92, "end": 996.5, "word": " بتلاقيها", "probability": 0.9444580078125}, {"start": 996.5, "end": 997.02, "word": " نعمة", "probability": 0.9064127604166666}], "temperature": 1.0}, {"id": 43, "seek": 101478, "start": 998.42, "end": 1014.78, "text": "عادة السيارات بيستخدموك هذا النوع من الـ gear الحركة إيش بنسميها نعمة؟ هذه سمنها إيش؟ helical gears هذه إيش؟ spare وهذه إيش؟ straight طيب إيش في غيرهم؟", "tokens": [3615, 18513, 3660, 21136, 1829, 9640, 9307, 4724, 1829, 14851, 9778, 40448, 2407, 4117, 23758, 28239, 45367, 9154, 2423, 39184, 7394, 21542, 31747, 3660, 11933, 1829, 8592, 44945, 38251, 1829, 11296, 8717, 25957, 3660, 22807, 29538, 8608, 27842, 11296, 11933, 1829, 8592, 22807, 801, 804, 20915, 29538, 11933, 1829, 8592, 22807, 13798, 37037, 24192, 11933, 1829, 8592, 22807, 2997, 23032, 1829, 3555, 11933, 1829, 8592, 8978, 32771, 13546, 16095, 22807], "avg_logprob": -0.1867297522618737, "compression_ratio": 1.5153374233128833, "no_speech_prob": 0.0, "words": 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"probability": 0.9698893229166666}, {"start": 1012.28, "end": 1013.92, "word": " إيش", "probability": 0.9059244791666666}, {"start": 1013.92, "end": 1014.06, "word": " في", "probability": 0.96240234375}, {"start": 1014.06, "end": 1014.78, "word": " غيرهم؟", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 44, "seek": 103776, "start": 1015.38, "end": 1037.76, "text": "bevel gear allowed drive to be transmitted through an angle of 90 degrees طلع الزاوية اللي عندي 90 درجة الموجودة فهذه سمناها bevel gear النوع الرابع crown gear", "tokens": [650, 779, 7394, 4350, 3332, 281, 312, 25355, 807, 364, 5802, 295, 4289, 5310, 23032, 1211, 3615, 6024, 110, 995, 2407, 10632, 13672, 1829, 18871, 16254, 4289, 11778, 47341, 3660, 9673, 29245, 23328, 3660, 6156, 3224, 24192, 8608, 2304, 8315, 11296, 312, 779, 7394, 28239, 45367, 34892, 16758, 3615, 11841, 7394], "avg_logprob": -0.3485576934539355, "compression_ratio": 1.320754716981132, "no_speech_prob": 0.0, "words": [{"start": 1015.38, 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"end": 1034.74, "word": " النوع", "probability": 0.92431640625}, {"start": 1034.74, "end": 1036.34, "word": " الرابع", "probability": 0.9832356770833334}, {"start": 1036.34, "end": 1037.02, "word": " crown", "probability": 0.583984375}, {"start": 1037.02, "end": 1037.76, "word": " gear", "probability": 0.90576171875}], "temperature": 1.0}, {"id": 45, "seek": 106582, "start": 1038.18, "end": 1065.82, "text": "and crown gear and bunion هذا اللي هو طلع عندى الأسنان كيف هدى هدى بتلف الدائرة و هدى بتلف بشكل الدائرة اللى عندى يعنى crown gear transmit drive through ninety degree often to a smaller gear called bunion هدى اللى عندى smaller و هدى ايش bigger فهدك بتعطينى ال people بتعطينى ايش", "tokens": [474, 11841, 7394, 293, 6702, 313, 23758, 13672, 1829, 31439, 23032, 1211, 3615, 43242, 7578, 16247, 3794, 1863, 7649, 9122, 33911, 8032, 3215, 7578, 8032, 3215, 7578, 39894, 46538, 32748, 16373, 25720, 4032, 8032, 3215, 7578, 39894, 46538, 4724, 8592, 28820, 32748, 16373, 25720, 13672, 7578, 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"probability": 0.9736328125}, {"start": 1047.18, "end": 1047.98, "word": " بشكل", "probability": 0.92578125}, {"start": 1047.98, "end": 1048.84, "word": " الدائرة", "probability": 0.9900716145833334}, {"start": 1048.84, "end": 1048.98, "word": " اللى", "probability": 0.90185546875}, {"start": 1048.98, "end": 1049.3, "word": " عندى", "probability": 0.8212890625}, {"start": 1049.3, "end": 1049.5, "word": " يعنى", "probability": 0.6259765625}, {"start": 1049.5, "end": 1050.28, "word": " crown", "probability": 0.385986328125}, {"start": 1050.28, "end": 1050.64, "word": " gear", "probability": 0.95263671875}, {"start": 1050.64, "end": 1051.28, "word": " transmit", "probability": 0.7001953125}, {"start": 1051.28, "end": 1051.82, "word": " drive", "probability": 0.7119140625}, {"start": 1051.82, "end": 1052.14, "word": " through", "probability": 0.7412109375}, {"start": 1052.14, "end": 1052.48, "word": " ninety", "probability": 0.580078125}, {"start": 1052.48, "end": 1052.92, "word": " degree", "probability": 0.80908203125}, {"start": 1052.92, "end": 1053.36, "word": " often", "probability": 0.57470703125}, {"start": 1053.36, "end": 1053.7, "word": " to", "probability": 0.95166015625}, {"start": 1053.7, "end": 1054.1, "word": " a", "probability": 0.94873046875}, {"start": 1054.1, "end": 1054.56, "word": " smaller", "probability": 0.85205078125}, {"start": 1054.56, "end": 1054.92, "word": " gear", "probability": 0.95849609375}, {"start": 1054.92, "end": 1055.46, "word": " called", "probability": 0.89404296875}, {"start": 1055.46, "end": 1056.3, "word": " bunion", "probability": 0.9599609375}, {"start": 1056.3, "end": 1056.88, "word": " هدى", "probability": 0.7521158854166666}, {"start": 1056.88, "end": 1057.02, "word": " اللى", "probability": 0.89111328125}, {"start": 1057.02, "end": 1057.54, "word": " عندى", "probability": 0.93310546875}, {"start": 1057.54, "end": 1058.28, "word": " smaller", "probability": 0.83056640625}, {"start": 1058.28, "end": 1058.66, "word": " 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crown إيش معناته تاج؟ وهذا سموه pinion اللي عندى pinion اللي هو ال gear فهي ال crown gear اللي هو عبارة transmitting through ninety degrees بس إيش to smaller gear called pinion", "tokens": [11622, 995, 2407, 10632, 6055, 3794, 3615, 9957, 11778, 47341, 3660, 4724, 3794, 37893, 8978, 11296, 4356, 7394, 37495, 22653, 29538, 4386, 34105, 11933, 1829, 8592, 13672, 1829, 43242, 7578, 22807, 11841, 7394, 8032, 9307, 30767, 1829, 16712, 26108, 13412, 28820, 3224, 11933, 15730, 4724, 9566, 1211, 11296, 11841, 11933, 1829, 8592, 20449, 8315, 47395, 6055, 26108, 22807, 37037, 15730, 8608, 2304, 2407, 3224, 5447, 313, 13672, 1829, 43242, 7578, 5447, 313, 13672, 1829, 31439, 2423, 7394, 6156, 3224, 1829, 2423, 11841, 7394, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 7715, 2414, 807, 25063, 5310, 4724, 3794, 11933, 1829, 8592, 281, 4356, 7394, 1219, 5447, 313], "avg_logprob": -0.1893983694994561, "compression_ratio": 1.7196652719665273, "no_speech_prob": 0.0, "words": [{"start": 1066.75, "end": 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كويس اتفضلي", "tokens": [9566, 1829, 3555, 20915, 2089, 11590, 293, 13071, 281, 16908, 303, 294, 264, 912, 3513, 22807, 2423, 4496, 1918, 13672, 1829, 31439, 4724, 1829, 25957, 1211, 13672, 1829, 3714, 29245, 23328, 34105, 8032, 3215, 12610, 20328, 3615, 3555, 9307, 22807, 29538, 16247, 3794, 19986, 37977, 8032, 18513, 25720, 14739, 2655, 39894, 3555, 4587, 7578, 3714, 31747, 11622, 3660, 45595, 20498, 4032, 14739, 2655, 3714, 32887, 5016, 3660, 11933, 1829, 8592, 39894, 3794, 45865, 22807, 12602, 26108, 3615, 1829, 3224, 39894, 8592, 3555, 4117, 20449, 995, 4117, 4032, 39894, 3555, 4587, 7578, 3714, 33599, 10632, 9122, 45865, 3794, 1975, 2655, 5172, 11242, 20292], "avg_logprob": -0.2371055799201854, "compression_ratio": 1.5391304347826087, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2037.65, "end": 2038.07, "word": "طيب", "probability": 0.8821614583333334}, {"start": 2038.07, "end": 2038.77, "word": " gears", "probability": 0.56201171875}, {"start": 2038.77, "end": 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"text": "فاليوم اتكلمنا ع ال transmission system ع ال gear system اللي عندنا اتكلمنا من المكوناته ال components of the system اتكلمنا على ال driver و ال follower و ال idler و ال ratio و ال types of gears اللي غطيناهم يعطيكوا العافية", "tokens": [5172, 6027, 1829, 20498, 1975, 2655, 4117, 19528, 8315, 6225, 2423, 11574, 1185, 6225, 2423, 7394, 1185, 13672, 1829, 43242, 8315, 1975, 2655, 4117, 19528, 8315, 9154, 9673, 4117, 2407, 8315, 47395, 2423, 6677, 295, 264, 1185, 1975, 2655, 4117, 19528, 8315, 15844, 2423, 6787, 4032, 2423, 35413, 4032, 2423, 4496, 1918, 4032, 2423, 8509, 4032, 2423, 3467, 295, 20915, 13672, 1829, 32771, 9566, 1829, 8315, 16095, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.19161183583109, "compression_ratio": 1.7777777777777777, "no_speech_prob": 0.0, "words": [{"start": 2090.41, "end": 2090.97, "word": "فاليوم", "probability": 0.9183349609375}, {"start": 2090.97, "end": 2091.67, "word": " اتكلمنا", "probability": 0.918359375}, {"start": 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diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/x5vJt_R3Q6A_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/x5vJt_R3Q6A_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3009652fe463f63f4c6b935a17b886e58b60ab88
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+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/x5vJt_R3Q6A_raw.json
@@ -0,0 +1 @@
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1035.65, "word": " تعمل", "probability": 0.9788411458333334}, {"start": 1035.65, "end": 1036.17, "word": " presentation", "probability": 0.900390625}, {"start": 1036.17, "end": 1036.73, "word": " هاي", "probability": 0.659912109375}, {"start": 1036.73, "end": 1037.29, "word": " بدك", "probability": 0.6787109375}, {"start": 1037.29, "end": 1038.93, "word": " تتدربي", "probability": 0.8876953125}], "temperature": 1.0}, {"id": 40, "seek": 106256, "start": 1040.34, "end": 1062.56, "text": "حاجات .. حاجات كتيرة و عناس كتيرة و هنقولكوا إيش تعملوا التدريب في شغلات بنقولكوا اعملوا هذه و ماتعملوش هذه طيب who are your audience؟ بدك تحدّي دي مين هم و الله هدولة عندي طالبات سنة أولى، هيجيلي مثلا دكاترة، هيجيلي غيره، بدك تعرف مين هم", "tokens": [5016, 26108, 9307, 4386, 11331, 26108, 9307, 9122, 2655, 48923, 4032, 18871, 32277, 9122, 2655, 48923, 4032, 8032, 1863, 39648, 4117, 14407, 11933, 1829, 8592, 6055, 25957, 1211, 14407, 16712, 3215, 16572, 3555, 8978, 13412, 17082, 1211, 9307, 44945, 39648, 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1041.6, "end": 1041.68, "word": " و", "probability": 0.7412109375}, {"start": 1041.68, "end": 1042.02, "word": " عناس", "probability": 0.846435546875}, {"start": 1042.02, "end": 1042.42, "word": " كتيرة", "probability": 0.8929036458333334}, {"start": 1042.42, "end": 1042.56, "word": " و", "probability": 0.513671875}, {"start": 1042.56, "end": 1043.0, "word": " هنقولكوا", "probability": 0.88720703125}, {"start": 1043.0, "end": 1043.16, "word": " إيش", "probability": 0.8779296875}, {"start": 1043.16, "end": 1043.58, "word": " تعملوا", "probability": 0.9866943359375}, {"start": 1043.58, "end": 1044.06, "word": " التدريب", "probability": 0.9715576171875}, {"start": 1044.06, "end": 1045.36, "word": " في", "probability": 0.357666015625}, {"start": 1045.36, "end": 1045.88, "word": " شغلات", "probability": 0.9764404296875}, {"start": 1045.88, "end": 1046.32, "word": " بنقولكوا", "probability": 0.9630126953125}, {"start": 1046.32, "end": 1046.8, "word": " اعملوا", "probability": 0.914306640625}, {"start": 1046.8, "end": 1047.16, "word": " هذه", "probability": 0.332275390625}, {"start": 1047.16, "end": 1047.46, "word": " و", "probability": 0.994140625}, {"start": 1047.46, "end": 1048.26, "word": " ماتعملوش", "probability": 0.9014485677083334}, {"start": 1048.26, "end": 1048.86, "word": " هذه", "probability": 0.85205078125}, {"start": 1048.86, "end": 1049.94, "word": " طيب", "probability": 0.94287109375}, {"start": 1049.94, "end": 1051.4, "word": " who", "probability": 0.69921875}, {"start": 1051.4, "end": 1051.8, "word": " are", "probability": 0.96240234375}, {"start": 1051.8, "end": 1052.36, "word": " your", "probability": 0.94482421875}, {"start": 1052.36, "end": 1053.86, "word": " audience؟", "probability": 0.77880859375}, {"start": 1053.86, "end": 1054.14, "word": " بدك", "probability": 0.8720703125}, {"start": 1054.14, "end": 1054.56, "word": " تحدّي", "probability": 0.785888671875}, {"start": 1054.56, "end": 1054.7, "word": " دي", "probability": 0.929931640625}, {"start": 1054.7, "end": 1054.86, "word": " مين", "probability": 0.98974609375}, {"start": 1054.86, "end": 1055.14, "word": " هم", "probability": 0.968505859375}, {"start": 1055.14, "end": 1055.92, "word": " و", "probability": 0.308837890625}, {"start": 1055.92, "end": 1056.14, "word": " الله", "probability": 0.9697265625}, {"start": 1056.14, "end": 1056.64, "word": " هدولة", "probability": 0.8529052734375}, {"start": 1056.64, "end": 1056.94, "word": " عندي", "probability": 0.93701171875}, {"start": 1056.94, "end": 1057.46, "word": " طالبات", "probability": 0.990966796875}, {"start": 1057.46, "end": 1057.78, "word": " سنة", "probability": 0.95849609375}, {"start": 1057.78, "end": 1058.5, "word": " أولى،", "probability": 0.82464599609375}, {"start": 1058.5, "end": 1058.98, "word": " هيجيلي", "probability": 0.7325439453125}, {"start": 1058.98, "end": 1059.3, "word": " مثلا", "probability": 0.986328125}, {"start": 1059.3, "end": 1060.1, "word": " دكاترة،", "probability": 0.95576171875}, {"start": 1060.1, "end": 1060.54, "word": " هيجيلي", "probability": 0.952392578125}, {"start": 1060.54, "end": 1061.18, "word": " غيره،", "probability": 0.87060546875}, {"start": 1061.18, "end": 1061.46, "word": " بدك", "probability": 0.9658203125}, {"start": 1061.46, "end": 1061.84, "word": " تعرف", "probability": 0.97705078125}, {"start": 1061.84, "end": 1062.22, "word": " مين", "probability": 0.986328125}, {"start": 1062.22, "end": 1062.56, "word": " هم", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 41, "seek": 107620, "start": 1063.28, "end": 1076.2, "text": "what do they know they have in common؟ يعني إيش عندهم حاجة مشتركة؟ في إيش مشترك بين الجمهور ولا مافيش؟ why will they be there؟ ليش هم جايين؟", "tokens": [5479, 360, 436, 458, 436, 362, 294, 2689, 22807, 37495, 22653, 11933, 1829, 8592, 43242, 16095, 11331, 26108, 3660, 37893, 2655, 31747, 3660, 22807, 8978, 11933, 1829, 8592, 37893, 2655, 31747, 49374, 25724, 2304, 3224, 13063, 49429, 19446, 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إيش", "probability": 0.85498046875}, {"start": 1066.44, "end": 1066.74, "word": " عندهم", "probability": 0.966064453125}, {"start": 1066.74, "end": 1067.08, "word": " حاجة", "probability": 0.9957682291666666}, {"start": 1067.08, "end": 1068.22, "word": " مشتركة؟", "probability": 0.94560546875}, {"start": 1068.22, "end": 1068.36, "word": " في", "probability": 0.66845703125}, {"start": 1068.36, "end": 1068.54, "word": " إيش", "probability": 0.7351888020833334}, {"start": 1068.54, "end": 1069.08, "word": " مشترك", "probability": 0.9583333333333334}, {"start": 1069.08, "end": 1069.36, "word": " بين", "probability": 0.91064453125}, {"start": 1069.36, "end": 1069.92, "word": " الجمهور", "probability": 0.9530029296875}, {"start": 1069.92, "end": 1070.14, "word": " ولا", "probability": 0.6611328125}, {"start": 1070.14, "end": 1072.02, "word": " مافيش؟", "probability": 0.95263671875}, {"start": 1072.02, "end": 1072.6, "word": " why", "probability": 0.8271484375}, {"start": 1072.6, "end": 1072.9, "word": " will", "probability": 0.89794921875}, {"start": 1072.9, "end": 1073.14, "word": " they", "probability": 0.93896484375}, {"start": 1073.14, "end": 1073.54, "word": " be", "probability": 0.96923828125}, {"start": 1073.54, "end": 1074.86, "word": " there؟", "probability": 0.845703125}, {"start": 1074.86, "end": 1075.08, "word": " ليش", "probability": 0.972412109375}, {"start": 1075.08, "end": 1075.24, "word": " هم", "probability": 0.96044921875}, {"start": 1075.24, "end": 1076.2, "word": " جايين؟", "probability": 0.8526611328125}], "temperature": 1.0}, {"id": 42, "seek": 110026, "start": 1077.32, "end": 1100.26, "text": "هذه جاوبة عامة بديك تحطيها لزي كنت سهلة هذه how much do they already know about my subject؟ في عندهم خلفية عن الموضوع ولا لا؟ و عندهم كده حجم هذا الخلفية؟ how much do they want to know؟ برضه هذه مهمة، كده هم حابين يعرفوا؟ وهذه بدك تسويها", "tokens": [3224, 24192, 10874, 995, 37746, 3660, 6225, 10943, 3660, 4724, 16254, 4117, 6055, 5016, 9566, 1829, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/x5vJt_R3Q6A_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/x5vJt_R3Q6A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5c2357b615c35477826c9c74cc2c5235572ed9d1
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/x5vJt_R3Q6A_raw.srt
@@ -0,0 +1,1924 @@
+1
+00:00:20,690 --> 00:00:29,870
+السلام عليكم اليوم سنتحدث عن مهارات التقديم كيف
+
+2
+00:00:29,870 --> 00:00:37,970
+تجهز مهارتك بوربوينت وكيف تسيطر على وقتك وكيف تقوم
+
+3
+00:00:37,970 --> 00:00:44,110
+بتقديم مهارة يعني كيف بدك تحضر الشرايح تبعاتك، كيف
+
+4
+00:00:44,110 --> 00:00:52,100
+بدك تحضر حالك للمهارة، إيش تعمل وإيش ماتعمليشكيف
+
+5
+00:00:52,100 --> 00:00:56,680
+بدك .. يعني تقطل ال presentation، أيش مطلوب منك؟
+
+6
+00:00:56,680 --> 00:01:00,700
+أحيانا كتير من الناس اللي بتيجي بتحكي قدام .. حتى
+
+7
+00:01:00,700 --> 00:01:07,340
+ولو انهم زمايلكم بتبقى فيه شوية nervous، مظبوط؟ و
+
+8
+00:01:07,340 --> 00:01:11,060
+شوية هيك متوتر .. توتر موجود في الجو، الأن احنا
+
+9
+00:01:11,060 --> 00:01:15,640
+بنساعدكم، بنعلمكم كيف تتقلبوا على هذه الأجواء، من
+
+10
+00:01:15,640 --> 00:01:20,540
+الشغلات اللي هنتكلم عنهاoutlines اللي هي هذه slide
+
+11
+00:01:20,540 --> 00:01:25,360
+structure كيف احنا بدنا نجهز slides fonts, colors,
+
+12
+00:01:25,540 --> 00:01:28,600
+background, graphs هدول اللي هم دخل بال structure
+
+13
+00:01:28,600 --> 00:01:32,760
+لإن أحيان تيجي بتطلع على شغلة تعبان عليها كلشي
+
+14
+00:01:32,760 --> 00:01:37,360
+وماحدش شايفها أو الألوان بتخلي عيني الواحد زاقه
+
+15
+00:01:37,360 --> 00:01:42,520
+منك فبدنا نفع هذا طبعا مافيش داعي في عصر الكمبيوتر
+
+16
+00:01:42,520 --> 00:01:46,990
+الحديث إنه يقول في عندك أخطاء إملائيةكويس؟ ال
+
+17
+00:01:46,990 --> 00:01:51,750
+conclusion كيف بتسوي الأسئلة؟ الحاجات كتير لو حد
+
+18
+00:01:51,750 --> 00:01:58,510
+سأل سؤال بتكون الدنيا أو أنت بتفجأش .. ممكن ..
+
+19
+00:01:58,510 --> 00:02:04,990
+التحضرات prepare for your presentation كيف تسوي؟
+
+20
+00:02:04,990 --> 00:02:11,480
+حاجة مهمة دايما اعرف مين جمهوركليش؟ تلت ارباع
+
+21
+00:02:11,480 --> 00:02:14,940
+الشغلاء ده انا عرفت مين جمهوري بعرف كيف بدي أتعامل
+
+22
+00:02:14,940 --> 00:02:21,760
+معاه، إيش أعطيه، كيف بدي أفتتح الموضوع تبعي أو ال
+
+23
+00:02:21,760 --> 00:02:22,440
+presentation
+
+24
+00:02:26,140 --> 00:02:29,660
+بدك تتمرن على ال presentation إيش خطوات التمرين؟
+
+25
+00:02:29,660 --> 00:02:33,480
+إيش اللي تعمليه و ماتعملهوش؟ كيف بدك تدير الوقت في
+
+26
+00:02:33,480 --> 00:02:37,780
+ال presentation؟ كيف بدك تجفى؟ إيش تلبسي؟ كيف نغمط
+
+27
+00:02:37,780 --> 00:02:42,860
+صوتك؟ العينين تبعاتك كيف يطلعن؟ لأن أحيان بتجفى
+
+28
+00:02:42,860 --> 00:02:50,980
+شايفة كل اللي قدامك مش شايفة ولا حدا طيب
+
+29
+00:02:55,520 --> 00:03:00,280
+عادة في ال presentation شغلة واحدة دايما بتحب
+
+30
+00:03:00,280 --> 00:03:06,460
+تكررها، إيش هي؟ في البداية بتفكريهم علشان تتكلمي،
+
+31
+00:03:06,460 --> 00:03:10,060
+خلال ال presentation بتبقى دايما تتكريهم انت علشان
+
+32
+00:03:10,060 --> 00:03:16,130
+بتتكلمي، و أخر ال presentation انت علشان تتكلميفي
+
+33
+00:03:16,130 --> 00:03:20,590
+العشر دقايق انا بضل ايش؟ بضل في البداية هيني
+
+34
+00:03:20,590 --> 00:03:24,090
+بقولكوا ايش، هنتكلم على هات، خلال ال presentation
+
+35
+00:03:24,090 --> 00:03:27,390
+بقولكوا اتكلمنا على واحد، اتنين، ثلاثة، في آخرها
+
+36
+00:03:27,390 --> 00:03:31,690
+بقولوا اليوم اتكلمنا على هيكا، فبظل الشغلة بتعلق
+
+37
+00:03:31,690 --> 00:03:37,990
+عن اللي جاعدينها، موجودين في هذا الشغل طيب الوقت
+
+38
+00:03:37,990 --> 00:03:43,220
+كافي، هات هنتكلم عليهففي واحدة منهم هتكون ايش
+
+39
+00:03:43,220 --> 00:03:46,160
+outline زي ما شفتوه قلنا هنتكلم على واحد اتنين
+
+40
+00:03:46,160 --> 00:03:50,620
+تلاتة لازم تعملوا slide زي هيك وفي slide الأولانية
+
+41
+00:03:50,620 --> 00:03:54,840
+اللي فيها العنوان وفيها اساميكم بتكون موجودة الان
+
+42
+00:03:54,840 --> 00:03:57,720
+follow the order of your outline for the rest of
+
+43
+00:03:57,720 --> 00:04:00,320
+the presentation لو انت حطيت النقاط اللي بدك
+
+44
+00:04:00,320 --> 00:04:05,880
+تغطيها امشي حسب محطتيه مش تصير جامبك مرة هنا و مرة
+
+45
+00:04:05,880 --> 00:04:10,400
+هنا و هكذاonly place main points in the outline
+
+46
+00:04:10,400 --> 00:04:15,660
+slide عادة ما تخليش انواع النقاط اللي بدك تغطيها
+
+47
+00:04:15,660 --> 00:04:21,260
+هذا القدر كلمة
+
+48
+00:04:21,260 --> 00:04:26,060
+كلمتين في الكتير تلت كلمات حوالين اربعة حاجة خفيفة
+
+49
+00:04:26,060 --> 00:04:31,640
+تقدر تحكي عنها هذه ال outline بدها تكون زي ذلك او
+
+50
+00:04:31,640 --> 00:04:35,260
+المحتوى ال contents ال outline بدها تكون خفيفة
+
+51
+00:04:35,260 --> 00:04:42,850
+الكلمات اللي فيها خفيفةو سهل النظر إليها slide
+
+52
+00:04:42,850 --> 00:04:47,910
+structure عادة يعني
+
+53
+00:04:47,910 --> 00:04:52,810
+أنا عندي عشر دقائق كام slides بتعمل بيمر عليكم بعض
+
+54
+00:04:52,810 --> 00:04:57,150
+المدرسين اللي حاجش يجلب slides مظبوط؟ انتوا لسه
+
+55
+00:04:57,150 --> 00:05:01,030
+أبقوا جداد ماشوفتوش بس اللي لهم فترة بيشوف المدرس
+
+56
+00:05:01,030 --> 00:05:05,890
+شغال يجلب slides فبيبطل حدا معاه هذه من الشغلات
+
+57
+00:05:05,890 --> 00:05:11,730
+الاشاللي ماحدش بيحبها انا هايدل غطيت فيه الله هادل
+
+58
+00:05:11,730 --> 00:05:15,930
+تروح على حالكه هادل لأ بتلاقيه بنخب اللي قدام و
+
+59
+00:05:15,930 --> 00:05:20,350
+اللي قدام بيصير طيب بس خلصنا هذا مش هو البيت
+
+60
+00:05:20,350 --> 00:05:25,650
+القصير فانت عدد ال slides دايما بدك حوالين تلاتين
+
+61
+00:05:25,650 --> 00:05:31,430
+تانية لدقيقة لكل slide بتحس بحسابك زي هي طيب write
+
+62
+00:05:31,430 --> 00:05:36,190
+in points form ما تكتبيش جملة كاملة عادة تطلع نقطة
+
+63
+00:05:36,190 --> 00:05:41,080
+موجودة على ال slidesاربع على خمس نقاط الفونت بيبقى
+
+64
+00:05:41,080 --> 00:05:46,820
+كبير واضح و النقاط معدودة في هذه ما تستخدميش
+
+65
+00:05:46,820 --> 00:05:51,560
+الكلمات الكتيرة wordiness الكلمات الكتيرة و لو
+
+66
+00:05:51,560 --> 00:05:56,700
+بتشوف ال slide مليانة الناس زي هيكها هذه بتعجبكم؟
+
+67
+00:05:56,700 --> 00:06:01,680
+هذه ولا اللي قبل؟ الحد بتشوف هاي اللي خمض عنك
+
+68
+00:06:04,290 --> 00:06:08,450
+أنا قاعد بفرجيكوا examples ال example هذا ماحدش
+
+69
+00:06:08,450 --> 00:06:12,670
+بيحبه، صح؟ ال example اللي قبله، تحسوا حالكم
+
+70
+00:06:12,670 --> 00:06:17,390
+مرتحين، أنتوا قادرين تشوفوا إيش اللي هي طيب، issue
+
+71
+00:06:17,390 --> 00:06:24,990
+كمان، في ناس بتحب تبين سطر سطر، تبعين الترم يعملوك
+
+72
+00:06:24,990 --> 00:06:29,850
+هذه الشغلة، حتى قبل بيصلاع السطر و بعده بيعملك
+
+73
+00:06:29,850 --> 00:06:34,150
+اللي بعده اللي بعده، احنا الهندسة بنزهجأنا بحكيكوا
+
+74
+00:06:34,150 --> 00:06:38,070
+تجربتنا كهندسة بحبش شوف ال slide camera، مصبوط ام
+
+75
+00:06:38,070 --> 00:06:42,420
+لا؟أهل الترمية أنا بقولكوا .. أهل الترمية بيحطوا
+
+76
+00:06:42,420 --> 00:06:47,080
+.. أنا بحب أطلع على كل شي بعدين .. أشوف اللي قدامي
+
+77
+00:06:47,080 --> 00:06:51,600
+بيعطينا النقار .. ماحبش يدقق عليه في القطارة ..
+
+78
+00:06:51,600 --> 00:06:54,640
+تبعين الترمية بيحبوا القطارة .. انت حرين .. ايش
+
+79
+00:06:54,640 --> 00:06:57,540
+اللي بتختاروه حسب الجمهور .. إذا جمهورك هندسة ..
+
+80
+00:06:57,540 --> 00:07:02,180
+بيظبطش .. بيسحقوا .. إذا جمهورك برا .. ماشي الحال
+
+81
+00:07:02,180 --> 00:07:02,720
+في هذه ..
+
+82
+00:07:06,190 --> 00:07:10,830
+هو بيقولك إيش مش هخل الجمهور يجرى لجدام طب أنا
+
+83
+00:07:10,830 --> 00:07:16,630
+الهندسة هم بيحبوا يجروا جدام طيب
+
+84
+00:07:16,630 --> 00:07:25,130
+ال bad structure do not use distraction animation
+
+85
+00:07:25,130 --> 00:07:29,010
+أحيانا انت بتحطه بس بده حاجات احيانا بتحط
+
+86
+00:07:29,010 --> 00:07:35,140
+animation بزعج أحيانايعني go overboard with
+
+87
+00:07:35,140 --> 00:07:39,020
+animation بدي ادخل هذه عندى وماهارا وشايفها وانا
+
+88
+00:07:39,020 --> 00:07:45,220
+كويس فيها بدي احطها بالعافية زبطت ولا مزبطتش؟ be
+
+89
+00:07:45,220 --> 00:07:49,140
+consistent with animation that you use يعني إذا
+
+90
+00:07:49,140 --> 00:07:53,600
+انت حطيت حاجة ماتدركيش تنوعي فيها خليكي ماشية في
+
+91
+00:07:53,600 --> 00:07:58,640
+style معين، مظبوط؟ الناس بتحب يكون لك style،
+
+92
+00:07:58,640 --> 00:08:05,070
+ماتنوعيش فيه كثيرالان انا بحط حاجات حركة في ال ..
+
+93
+00:08:05,070 --> 00:08:09,350
+في ال slide سابع عادي أحيانا انت بتلاحظوا في ناس
+
+94
+00:08:09,350 --> 00:08:12,690
+في .. اول .. اول متطلع ال slide الأحرف بيجي نهجر
+
+95
+00:08:12,690 --> 00:08:16,730
+زي هيك الجمعة أحيان طايرة أحيان بيسوي .. هذه ال
+
+96
+00:08:16,730 --> 00:08:19,990
+animation أحيانا بتحبهاش احنا تخلي على نمط واحد
+
+97
+00:08:19,990 --> 00:08:24,090
+ايوة .. لما حدت دخلي .. دخلي نمط واحد مش كل مرة
+
+98
+00:08:24,090 --> 00:08:28,910
+تسويالي حركة شكلت انا
+
+99
+00:08:28,910 --> 00:08:34,550
+بحبش ال animation ده بتلاحظواالـ fonts at least 18
+
+100
+00:08:34,550 --> 00:08:37,470
+points اللي بديك الناس اللي قاعدين في آخر القاعة
+
+101
+00:08:37,470 --> 00:08:45,230
+يقدر يجروا مش صغير بده مدور ل degree use different
+
+102
+00:08:45,230 --> 00:08:48,450
+font sizes for main points and secondary points
+
+103
+00:08:48,450 --> 00:08:52,550
+انت بتلاحظي هو بجهزلكيه لما تحطي secondary point
+
+104
+00:08:52,550 --> 00:09:01,030
+بصغر ال font شويه عن الموجودعادة ما تحطيش يعني
+
+105
+00:09:01,030 --> 00:09:05,970
+خطوط ماحدش بعرف يقراها، أحيانا الخط شكله حلو و
+
+106
+00:09:05,970 --> 00:09:13,110
+بتحطيله أحيانا من ضلال و حاجات زي هيك، shades، بس
+
+107
+00:09:13,110 --> 00:09:17,130
+أحيانا ماعرفش نقراها يعني اللي قاعديني، فانت خليه
+
+108
+00:09:17,130 --> 00:09:23,320
+مقروق و الخط الناس اللي متعودة عليهbad font size
+
+109
+00:09:23,320 --> 00:09:27,880
+شبيه ال .. هذا ايه؟ حجم صغير، هذا ايه؟ capital
+
+110
+00:09:27,880 --> 00:09:36,560
+capital مزعج bold مزعج فانت بدك حاجة تريح النظر
+
+111
+00:09:36,560 --> 00:09:43,080
+للي قدامك good colors ما تلونيش زيادة على اللازم
+
+112
+00:09:43,080 --> 00:09:52,000
+عادة الخلفية بيضةعالون أزرق أو أسود كويس بتصير ..
+
+113
+00:09:52,000 --> 00:09:55,960
+بتصير خلفطيط و انت هتشوفي إيش الموجود هنا فدايما
+
+114
+00:09:55,960 --> 00:10:00,040
+خلّي تطلع عليه و ماتطلعيش على ألوان ال computer
+
+115
+00:10:00,040 --> 00:10:03,220
+شاشة ال computer لأن أحيان .. ألوان شاشة ال
+
+116
+00:10:03,220 --> 00:10:07,260
+computer إيش بتسويه؟ أحيان misguide you يعني إيش
+
+117
+00:10:07,260 --> 00:10:11,740
+بتسويه؟ بتغرر فيكي لما تيجي تعرض بتشوفيها مختلفة
+
+118
+00:10:11,740 --> 00:10:17,370
+تمامالأن الكفاءة تبع الشاشة ال LCD مش كفاءة شاشة
+
+119
+00:10:17,370 --> 00:10:24,670
+ال computer، بدك تفهم هذه الشغلة طلع الألوار، إيش
+
+120
+00:10:24,670 --> 00:10:30,490
+هذه؟ أنا بستخدم ألوان كتير، بس حد .. حد مبسوط
+
+121
+00:10:30,490 --> 00:10:33,850
+عليها؟
+
+122
+00:10:40,800 --> 00:10:48,960
+فالألوان لما تبقى مش منتظبة بتحس في إزعاج فيها هنا
+
+123
+00:10:48,960 --> 00:10:52,400
+ال good use background such as this مثلا هذه ال
+
+124
+00:10:52,400 --> 00:10:56,800
+background الموجودة كويسة هذه مافيش فيها أي يعني
+
+125
+00:10:56,800 --> 00:11:01,000
+dark على light, light على dark بظبط طلع هذه
+
+126
+00:11:06,070 --> 00:11:10,790
+هذه النقطة أنه أحيانا أنت بتشوفيها مبسوط عليها و
+
+127
+00:11:10,790 --> 00:11:15,450
+حاطيتلك صورة خلفية صورة أو شعار أو غيره بس على
+
+128
+00:11:15,450 --> 00:11:20,110
+رأيك بتجيب الحوار للي قاعدين فمعناته هذه مش مناسبة
+
+129
+00:11:20,110 --> 00:11:23,890
+بتبقى هي
+
+130
+00:11:23,890 --> 00:11:26,150
+صوات، شايفين؟
+
+131
+00:11:29,850 --> 00:11:34,550
+أحيانا انا مبسوط عليه بتلاقيه بس عند جمهور تبقى
+
+132
+00:11:34,550 --> 00:11:39,570
+يقول إيش هذا قاعد بيسوي طيب
+
+133
+00:11:39,570 --> 00:11:44,610
+ال graph .. use graph rather than chart or word ..
+
+134
+00:11:44,610 --> 00:11:50,890
+words أو equation عادة ال graphs الصور أسهل الناس
+
+135
+00:11:50,890 --> 00:11:56,070
+اللي ساعدها من ده تحطي معادلة أو تحطي إيش جدول
+
+136
+00:11:56,070 --> 00:12:02,150
+ليش؟الإنسان بترتاح للصورة أكتر من بترتاح للأرقام
+
+137
+00:12:02,150 --> 00:12:07,550
+فهذه .. يعني هذه عندي pad جدول .. طب مين بتطلع
+
+138
+00:12:07,550 --> 00:12:11,130
+عليه؟ محدش هيطلع .. طب يلا أقلب .. هذه على طول
+
+139
+00:12:11,130 --> 00:12:17,590
+بتشوف ايش .. بتشوف أيش بتعني .. بس تطلع على هذه ..
+
+140
+00:12:17,590 --> 00:12:25,770
+حفظ حطلنا هدولة .. صارت أيش العملية بتتحول .. طيب
+
+141
+00:12:27,160 --> 00:12:30,900
+minor, a great line, unnecessary, full to small,
+
+142
+00:12:31,000 --> 00:12:34,420
+colors illogic or illogical, title is missing,
+
+143
+00:12:34,540 --> 00:12:39,540
+shading is distraction هذ عيب ليش الرسم اللي قبل
+
+144
+00:12:39,540 --> 00:12:44,140
+طيب spelling عندك الكمبيوتر بصليح لك كل الأخطاء
+
+145
+00:12:44,140 --> 00:12:49,840
+استخدم هذه الإمكانية أي إش بتلاقي عليه أحمر تحته
+
+146
+00:12:49,840 --> 00:12:55,460
+أحمر ماتخليهاش تروح عندكفي النهاية لو ما نيجي
+
+147
+00:12:55,460 --> 00:13:00,440
+نتكلم على كيف بدنا نعمل ال powerpoint خليكي ماشية
+
+148
+00:13:00,440 --> 00:13:07,300
+simple تكون مرئية الألوان بتعكس أنه لو الأحرف
+
+149
+00:13:07,300 --> 00:13:12,560
+بألوان فاتحة الخلفية بتبقى غامقة الأحرف بألوان
+
+150
+00:13:12,560 --> 00:13:17,680
+غامقة الخلفية بتبقى فاتحة اعمل تناسق للألوان هذا
+
+151
+00:13:17,680 --> 00:13:24,240
+اللي بنحكي في هذا المجال طيب لو أنا خلصتال
+
+152
+00:13:24,240 --> 00:13:35,120
+presentation أو خلال ال presentation حد بيسأل عادة
+
+153
+00:13:35,120 --> 00:13:41,720
+أسهل حاجة انت شوف السؤال، لو السؤال بتقدر تجاوزيه
+
+154
+00:13:41,720 --> 00:13:46,080
+بتقول .. بتعيد السؤال عشان الكل يسمع و يقول السؤال
+
+155
+00:13:46,080 --> 00:13:49,920
+كالتالي و الإجابة زي هذهالكيشة تجاوزيك بتقولي
+
+156
+00:13:49,920 --> 00:13:53,860
+بتخليه لآخر حاجة وبعدين بقعد أنا وياكم بنناقش
+
+157
+00:13:53,860 --> 00:13:57,920
+السؤال هذه
+
+158
+00:13:57,920 --> 00:14:01,660
+.. احنا بقولكوا استقانية هذه عشان .. إيش هي؟ لو
+
+159
+00:14:01,660 --> 00:14:06,020
+الجمهور اللي عندك ضاله بدي يزعج و بدي يسأل الناس
+
+160
+00:14:06,020 --> 00:14:10,140
+بتنزعج منه و بتنزعج منك بينما لو انت قعدت تجالج
+
+161
+00:14:10,140 --> 00:14:14,820
+معاه الناس بتنزعج منك أكتر من الشخص اللي في
+
+162
+00:14:14,820 --> 00:14:20,810
+الجمهور موجودفانت دايما خليكي متزنه و ما تنزعجيش
+
+163
+00:14:20,810 --> 00:14:27,910
+من الأسئلة هذه الوصيلة اللي نسمح بها الان طب انا
+
+164
+00:14:27,910 --> 00:14:32,550
+كيف بتحضر حالك ل presentation اول خطوة بنقول اعرفي
+
+165
+00:14:32,550 --> 00:14:37,590
+مين جمهورك عندى تلت أنواع من الجمهور ايش هم جمهور
+
+166
+00:14:37,590 --> 00:14:42,150
+عام معلوماته عن الموضوع عامة يعني مش متخصص بيه
+
+167
+00:14:42,150 --> 00:14:45,430
+جمهور متخصص لما انا اجي اتكلم في حارة المهندسين عن
+
+168
+00:14:45,430 --> 00:14:50,250
+موضوع أندسيإنهم معلومة معاهم، لما أجي أروح في
+
+169
+00:14:50,250 --> 00:14:53,470
+الشارع أتكلم عن موضوع هندسة، أبيض يولد حاجبه،
+
+170
+00:14:53,470 --> 00:14:57,830
+مظبوط؟ فكلمة أبيض هذه أنا بتعطيهم معلومات عامة
+
+171
+00:14:57,830 --> 00:15:02,750
+كتيرة، في الهندسة بتتعطي خلفية معينة، لما أجي
+
+172
+00:15:02,750 --> 00:15:07,830
+لجمهور خبير، بجيش أكون أشرح لهم كل بسيط، هم كل هذا
+
+173
+00:15:07,830 --> 00:15:12,510
+عارفينهفبقول بدي أروح أوصل ليش؟ للنقاط الرئيسية
+
+174
+00:15:12,510 --> 00:15:15,370
+اللي هي في Solve التخصص الو و أنا أشرح فيها ف ال
+
+175
+00:15:15,370 --> 00:15:20,370
+structure تبع ال presentation تبعتي بختلف لما أنا
+
+176
+00:15:20,370 --> 00:15:24,490
+أتكلم على ناس عامة جدا بيسميها lay audience أو
+
+177
+00:15:24,490 --> 00:15:28,370
+أتكلم على technical audience أو very specific
+
+178
+00:15:28,370 --> 00:15:33,070
+technical audience اللي هم هدول الناس المتخصصينشكل
+
+179
+00:15:33,070 --> 00:15:38,270
+المحاضرة كده بده أعمل في العقل العمومي كل هذا يمكن
+
+180
+00:15:38,270 --> 00:15:42,970
+80% من ال representation بيعطيها في العموميات 20%
+
+181
+00:15:42,970 --> 00:15:47,830
+اللي هي الحاجة المتخصة اللي فيها تخص الناس يعني لأ
+
+182
+00:15:47,830 --> 00:15:55,050
+في ال technical general technical حوالين 60% ل 50%
+
+183
+00:15:55,050 --> 00:15:58,870
+في العموميات و العكس تبقى في التخصيات في ال very
+
+184
+00:15:58,870 --> 00:16:05,320
+technical80% في صلبة التخصص اللي بعطيه في الحاجات
+
+185
+00:16:05,320 --> 00:16:09,820
+اللي هي very technical الآن من الشغلات اللي بتاخد
+
+186
+00:16:09,820 --> 00:16:13,000
+طريقها القاعة و الأجهزة الحاسوب اللي انت
+
+187
+00:16:13,000 --> 00:16:18,420
+بتستخدميها ماتجيش متفاجأة تقول ولا القاعة بيشتغل
+
+188
+00:16:18,420 --> 00:16:23,620
+بيشتغل الجهاز ال flash تبقى شغال ولا لأبدك تبقى
+
+189
+00:16:23,620 --> 00:16:28,700
+جاى .. جاى قبل و مجرب الأجهزة اللي عندك و تعرفي كل
+
+190
+00:16:28,700 --> 00:16:32,100
+حاجة فيها إضاءة كل حاجة بدك تعرفيها عن المكان اللي
+
+191
+00:16:32,100 --> 00:16:35,580
+بدك تعملي ال presentation فيها و بتيجي بتقف هان و
+
+192
+00:16:35,580 --> 00:16:40,220
+بتمشي و بتطلع أيش موجود كل حاجة عساس انت البيئة
+
+193
+00:16:40,220 --> 00:16:43,440
+اللي بدك تعملي فيها ال presentation انت familiar
+
+194
+00:16:43,440 --> 00:16:50,440
+معها افتح الكل بقى بشأن الكلام الآن ال opening كيف
+
+195
+00:16:50,440 --> 00:16:57,370
+تبدأ؟هذه من الشغلات المهمة جدا لأن كيف اتدبدأ يا
+
+196
+00:16:57,370 --> 00:17:01,990
+إما بنسي الجمهور تبعي يبقى مشتاق ويبقى يسمع ليه يا
+
+197
+00:17:01,990 --> 00:17:12,390
+إما الجمهور هتبتسي يفكر و وقتش يخلص من الشغلات
+
+198
+00:17:12,390 --> 00:17:16,730
+اللي مهمة جدا قبل ما تيجي تعمل presentation هاي
+
+199
+00:17:16,730 --> 00:17:18,930
+بدك تتدربي
+
+200
+00:17:20,340 --> 00:17:23,160
+حاجات .. حاجات كتيرة و عناس كتيرة و هنقولكوا إيش
+
+201
+00:17:23,160 --> 00:17:27,460
+تعملوا التدريب في شغلات بنقولكوا اعملوا هذه و
+
+202
+00:17:27,460 --> 00:17:34,560
+ماتعملوش هذه طيب who are your audience؟ بدك تحدّي
+
+203
+00:17:34,560 --> 00:17:38,500
+دي مين هم و الله هدولة عندي طالبات سنة أولى،
+
+204
+00:17:38,500 --> 00:17:42,560
+هيجيلي مثلا دكاترة، هيجيلي غيره، بدك تعرف مين هم
+
+205
+00:17:43,280 --> 00:17:46,440
+what do they know they have in common؟ يعني إيش
+
+206
+00:17:46,440 --> 00:17:50,140
+عندهم حاجة مشتركة؟ في إيش مشترك بين الجمهور ولا
+
+207
+00:17:50,140 --> 00:17:57,640
+مافيش؟ why will they be there؟ ليش هم جايين؟هذه
+
+208
+00:17:57,640 --> 00:18:01,780
+جاوبة عامة بديك تحطيها لزي كنت سهلة هذه how much
+
+209
+00:18:01,780 --> 00:18:05,500
+do they already know about my subject؟ في عندهم
+
+210
+00:18:05,500 --> 00:18:09,120
+خلفية عن الموضوع ولا لا؟ و عندهم كده حجم هذا
+
+211
+00:18:09,120 --> 00:18:13,620
+الخلفية؟ how much do they want to know؟ برضه هذه
+
+212
+00:18:13,620 --> 00:18:22,140
+مهمة، كده هم حابين يعرفوا؟ وهذه بدك تسويهاwhat is
+
+213
+00:18:22,140 --> 00:18:25,920
+their level of understanding؟ كدهش مستواهم؟ هل هم
+
+214
+00:18:25,920 --> 00:18:30,220
+بيقدروا يفهموا الشغلات ال technical كتير ولا بس
+
+215
+00:18:30,220 --> 00:18:35,460
+يدوبوا على السطح؟what is their attitude؟ هل هم
+
+216
+00:18:35,460 --> 00:18:43,240
+جمهور صديق؟ هل هم hostile؟ معادي؟ هل هم .. مش
+
+217
+00:18:43,240 --> 00:18:48,600
+فارقة عندهم؟ وانت بدك تعرفي هد .. هد .. صنفيهم هد
+
+218
+00:18:48,600 --> 00:18:53,340
+الجمهور ما هو الجمهور ال hostile معادي على طول بس
+
+219
+00:18:53,340 --> 00:18:58,620
+بده نكشف وفي عليهالجمهور الصديق بتحبلك كل إشي و
+
+220
+00:18:58,620 --> 00:19:03,260
+بتقعد تطلع عليك و بيبتسم الجمهور اللي مش فارق عنده
+
+221
+00:19:03,260 --> 00:19:07,940
+قاعد كل واحدة بحها جوالها و قاعدة بتلعب فيه مثلكي
+
+222
+00:19:07,940 --> 00:19:15,600
+و احنا بقول كل إشي بيعمل هو ال opening .. your
+
+223
+00:19:15,600 --> 00:19:18,980
+opening is the most important part of the speech
+
+224
+00:19:18,980 --> 00:19:21,720
+it should catch the interest of your audience
+
+225
+00:19:21,720 --> 00:19:25,890
+stimulate their ..their curiosity and impress them
+
+226
+00:19:25,890 --> 00:19:31,470
+عادة يمكن .. ماعرفش فيكوا حد بتفرج على ناس بيجي
+
+227
+00:19:31,470 --> 00:19:35,970
+يتكلموا، بيعملوا press conference، بيجي يعطي كلمة،
+
+228
+00:19:35,970 --> 00:19:40,490
+يعطي مقابلة، في كتير من الناس يمكن الأمر كان ملوك
+
+229
+00:19:40,490 --> 00:19:45,690
+التدريب، يعني مافيش اشي عفوي، كل اشي بتدربوا عليه،
+
+230
+00:19:45,690 --> 00:19:49,530
+فأول مايجي يتكلم بقي نقطة، الحين النقطة إيش بتسوي
+
+231
+00:19:49,530 --> 00:19:54,740
+في جبوره تبعه؟ بتخليهم مرتاحةيعني لما تيجي .. لما
+
+232
+00:19:54,740 --> 00:19:59,600
+تدرس تيجي بعطيك نقطة من أول محاضرة بت .. بترخخ هيك
+
+233
+00:19:59,600 --> 00:20:04,240
+و بتفضح .. يعني بتحس حالك في جو مألوم أحيانا في
+
+234
+00:20:04,240 --> 00:20:08,500
+ناس بتيجي مثلا بتعطيك بيت شعر، في ناس بتعطيك حديث
+
+235
+00:20:08,500 --> 00:20:13,500
+شريف، في ناس بتعطيك آية قرآنية، في ناس بتستشهد في
+
+236
+00:20:13,500 --> 00:20:18,200
+قولة حدا مشهور، في ناس بتيجي بتعطي قصة صغيرة هيك
+
+237
+00:20:18,200 --> 00:20:22,900
+بس أو موعدة أو عبرةفهذه الشغلات إيش اللي انت
+
+238
+00:20:22,900 --> 00:20:29,060
+بتعمليها؟ هي في ناس تطرع عليك عدة تساؤلات، أسئلة
+
+239
+00:20:29,060 --> 00:20:34,040
+تشوف يمكن فصل قاسم لما نيجي في الاتجاه المعاكس أول
+
+240
+00:20:34,040 --> 00:20:38,820
+ما بيبدأ في إيش فهناك كبشة أسئلة، هذه كلها طرق
+
+241
+00:20:38,820 --> 00:20:45,680
+لكيف أنت تجد بالجمهور تبعك فكل واحد بدي .. بدي شوف
+
+242
+00:20:45,680 --> 00:20:51,040
+إيش اتناسب شخصيتهإيش اللي بتناسب شخصيتك، بتعمليها،
+
+243
+00:20:51,040 --> 00:20:55,040
+إيش بتحس حالك مرتاحة فيها، بتعمليها، في ناس بتيجي
+
+244
+00:20:55,040 --> 00:20:59,060
+بتعرض فيديو صغير، مثلا بتعمل presentation من
+
+245
+00:20:59,060 --> 00:21:03,220
+دقيقة، دقيقة و نصف، دبل بقى أبدأ سواء، فهذه بعمل
+
+246
+00:21:03,220 --> 00:21:08,100
+curiosity، يعني ب .. بس يعني بخل الجمهور يصير
+
+247
+00:21:08,100 --> 00:21:11,980
+مشتاق أن يعرف إيش فيه ورا هذه الشيء
+
+248
+00:21:18,620 --> 00:21:22,080
+ال quotation هذه حكيناها في stalker event
+
+249
+00:21:22,080 --> 00:21:26,920
+reference from literature طيب
+
+250
+00:21:26,920 --> 00:21:31,800
+بدك إيش تجربي ال presentation؟ يمكن أصعب اشي
+
+251
+00:21:31,800 --> 00:21:37,290
+التدريب لل presentation، ليش؟ أول حاجة تبقىيعني
+
+252
+00:21:37,290 --> 00:21:41,530
+شوية هيكة متوترة، يمكن أنتوا البنات أشدع من الشباب
+
+253
+00:21:41,530 --> 00:21:45,370
+في حاجة واحدة إيه؟ تحاضير، تحاضرة كويسة، أنا بنتي
+
+254
+00:21:45,370 --> 00:21:49,270
+في صف أول، اليوم عندها إداعة من المبروحي، ما سكتنا
+
+255
+00:21:49,270 --> 00:21:54,150
+ما اسكتها لها، لأ تمعت اللي بتدجى، هاد اللي بتدجو
+
+256
+00:21:54,150 --> 00:21:59,780
+فيها هاد المطرفون وماسكة قاعدة بتجربكل من البارحة
+
+257
+00:21:59,780 --> 00:22:02,740
+لليوم هم بتجربوا تطلع الصوت و تسمعوا، بقول ما شاء
+
+258
+00:22:02,740 --> 00:22:09,060
+الله عليهم، الفنات مرتبين، الولاد أنا جاهز، الابن
+
+259
+00:22:09,060 --> 00:22:14,820
+بيه زيك، انا بقولك أنا جاهز على طوليعني فكر حاله
+
+260
+00:22:14,820 --> 00:22:19,520
+هو يعني عنده القدرة يسويها، لأ التدريب مهم جدا
+
+261
+00:22:19,520 --> 00:22:22,920
+جدا، اول ما تبدأ تتدرب في ال presentation ايقف
+
+262
+00:22:22,920 --> 00:22:27,820
+قدام المرايا، ايقف
+
+263
+00:22:27,820 --> 00:22:32,560
+قدام المرايا وجربي، بعد هيك اجيب اخواتك و جمعيهم
+
+264
+00:22:33,810 --> 00:22:38,890
+تحبت حلوة بسكوتة بالهال بتجيب .. بتجيب الهال قبل
+
+265
+00:22:38,890 --> 00:22:42,250
+ما تصل الهال بتجيب زميلاتك في قاعة من القاعات و
+
+266
+00:22:42,250 --> 00:22:47,330
+بتجرب عليهم لإن مافيش شيء زي بعد إيش تجرب الهال
+
+267
+00:22:47,330 --> 00:22:51,510
+أحيانا تقف في قاعة زي هيكا و زي ما حكيت بتشوفيش حد
+
+268
+00:22:51,510 --> 00:22:56,270
+انا بتذكر أول مرة عملت presentation كنت بدي أشرح
+
+269
+00:22:56,270 --> 00:23:00,810
+موضوعفإيه شجعه؟ جابونا كلهم دكاترة جامعة غير
+
+270
+00:23:00,810 --> 00:23:05,010
+التربية قاعدوا وقالولي اتبع اي موضوع بدأت تشرحه
+
+271
+00:23:05,010 --> 00:23:08,930
+وقعدت على اللوح وقعدت اشرحه انا مبسوط احالي قاعد
+
+272
+00:23:08,930 --> 00:23:13,710
+بشرحه كويس الحين واحد من المدرس قاعد واقف بشوح في
+
+273
+00:23:13,710 --> 00:23:18,290
+إيديه وهاي وانا مش عايزطبعا .. مستغربة، طبيعي هذا،
+
+274
+00:23:18,290 --> 00:23:22,470
+انك انت تبكي في القاعة ومش شايفها اللي قدامك لأنك
+
+275
+00:23:22,470 --> 00:23:26,290
+انت مركز على إيش .. على موضوعيك، مش مركز على مين
+
+276
+00:23:26,290 --> 00:23:31,050
+عجبهم، فاجب يقولي بعد ما خلصت .. طبعا مصورة، بيجي
+
+277
+00:23:31,050 --> 00:23:34,530
+يقولي أنا رفعت إيدي ومسويش ماريسو .. ماجوابتنيش،
+
+278
+00:23:34,530 --> 00:23:38,380
+مش ماشوفتش إيش، فانت بتقعد ها يوميفجانك و هو واقف
+
+279
+00:23:38,380 --> 00:23:43,980
+بيشوّح فبعدها تنتبهي لحاجة واحدة انك ال eye
+
+280
+00:23:43,980 --> 00:23:48,340
+contact مهم هذا خلال المحاقر خلال و انت بتعمل يعني
+
+281
+00:23:48,340 --> 00:23:54,120
+بدك تطلعي تشوفين حدا friend face في الشجة هذه واسع
+
+282
+00:23:54,120 --> 00:24:01,470
+صاحباتك كل واحدة في ..فتطلع عليه على الجهد، طلع في
+
+283
+00:24:01,470 --> 00:24:05,250
+النصر، طلع وراه، طلع في كل اتجاهك، فانت لما تطلع
+
+284
+00:24:05,250 --> 00:24:10,570
+كل واحد بيحسك ماذا؟ انك بتتكلمي معاه، فارق كبير
+
+285
+00:24:10,570 --> 00:24:15,190
+لما انت تتكلمي وكل يحس انك قاعدة بتعطي المحاضرة أو
+
+286
+00:24:15,190 --> 00:24:20,590
+بتعطي .. بتعمل تقديم لهم عند انك بتعطي لحالك، في
+
+287
+00:24:20,590 --> 00:24:25,410
+ناس مضالها تطلع زي هيك و مالها استخدم حاجة، مظبوط؟
+
+288
+00:24:26,060 --> 00:24:29,660
+ففي الآخر هو مبسوطين على حالهم بتلاقيهم مالهم مش
+
+289
+00:24:29,660 --> 00:24:33,780
+داخل بيه إيش القاعة و في ناس بتبطلع في السطح و
+
+290
+00:24:33,780 --> 00:24:40,720
+بتبطلع تتكلم ف ال eye contact مهم، إيش بتعطينا ال
+
+291
+00:24:40,720 --> 00:24:44,740
+eye contact؟ أنا كمدرس على طول بتطلع على طلابي
+
+292
+00:24:44,740 --> 00:24:50,990
+بعرف هم وينبعرفهم هم معي، هم مستوعبين، مش
+
+293
+00:24:50,990 --> 00:24:55,090
+مستوعبين، ال feedback، الحركات تبع الجسم بتعرفي هل
+
+294
+00:24:55,090 --> 00:25:00,170
+هم فاهمين و لا مش فاهمين، هل هم معي و لا لأ، انت
+
+295
+00:25:00,170 --> 00:25:03,710
+في ال eye contact، كل هذه المعلومات بتجيلك، انا
+
+296
+00:25:03,710 --> 00:25:07,810
+ماشي بسرعة و لا ماشي بطيء، هذه بتاخديها بشكل كامل،
+
+297
+00:25:07,810 --> 00:25:12,960
+من النظر للموجودkeep body movement quiet، في ناس
+
+298
+00:25:12,960 --> 00:25:17,000
+بتلاقيها إيديها و .. و .. و .. وخبط و .. و .. و ..
+
+299
+00:25:17,000 --> 00:25:18,380
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+300
+00:25:18,380 --> 00:25:18,640
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+301
+00:25:18,640 --> 00:25:18,840
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+302
+00:25:18,840 --> 00:25:19,060
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+303
+00:25:19,060 --> 00:25:19,060
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+304
+00:25:19,060 --> 00:25:21,740
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+305
+00:25:21,740 --> 00:25:22,020
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+306
+00:25:22,020 --> 00:25:22,020
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+307
+00:25:22,020 --> 00:25:25,020
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+308
+00:25:25,020 --> 00:25:30,680
+و .. و .. و .. و .. و .. و ..
+
+309
+00:25:38,780 --> 00:25:42,900
+بس هذا فدايما خليكي ايش طبيعي احيانا في ناس
+
+310
+00:25:42,900 --> 00:25:46,120
+بتلاقوها ان يمكن اكتر من المدرسين قاعد باعد خطوات
+
+311
+00:25:46,120 --> 00:25:50,940
+رايك انك تنقص الناس و واحد، اثنين، تلاتين و اتنين
+
+312
+00:25:50,940 --> 00:25:51,560
+و اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+313
+00:25:51,560 --> 00:25:52,100
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+314
+00:25:52,100 --> 00:25:53,140
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+315
+00:25:53,140 --> 00:25:54,240
+اتنين و اتنين و اتنين و اتنين و اتنين و اتنين و
+
+316
+00:25:54,240 --> 00:25:59,120
+اتنين و اتنين و اتنين و اتنين
+
+317
+00:26:06,150 --> 00:26:09,530
+maintain appropriate voice value بعض الناس بيبقى
+
+318
+00:26:09,530 --> 00:26:13,890
+بتتكلم شويه شويه بتسمعوا فيه حاجة، ليش بتسمعوا
+
+319
+00:26:13,890 --> 00:26:17,510
+بمبسطين؟ لو حد بتتكلم بيقول هو مش طالع، لو حد
+
+320
+00:26:17,510 --> 00:26:20,630
+بتتكلم هو مش طالع، لو حد بتتكلم هو مش طالع، لو حد
+
+321
+00:26:20,630 --> 00:26:25,580
+بتتكلم هو مش طالعإنك أنت .. أنت هندسة، الهندسة
+
+322
+00:26:25,580 --> 00:26:32,600
+تتكلمش في عزها، المهندسة صوت مسموع، فلازم إيش
+
+323
+00:26:32,600 --> 00:26:37,700
+الصوت يبقى مسموع، بعدين مابتدركيش ماسية وما نتعذب،
+
+324
+00:26:37,700 --> 00:26:42,840
+يعني إيش؟ على نغمة واحدة، أحيان بيبقوا واطوا معاهم
+
+325
+00:26:42,840 --> 00:26:49,060
+الناس، اللي هو يضلوا باشيرفهذه من الشغلات اللي بدك
+
+326
+00:26:49,060 --> 00:26:55,020
+تطلعي عليها الصوت لازم يظله متناسب الناس بتسمعه
+
+327
+00:26:55,020 --> 00:27:00,800
+الكل بيبقى في نفس الاتجاه الآن انتوا يا البنات هذه
+
+328
+00:27:00,800 --> 00:27:08,860
+مهم avoid wearing ايش ملابس مثيرة يعنيفي الجامعة
+
+329
+00:27:08,860 --> 00:27:12,000
+الإستامية .. في الجامعة الإستامية خلّيني أقول
+
+330
+00:27:12,000 --> 00:27:19,020
+مربطين فين؟ ليش؟ أفضل يا عزيزي احنا اختارنا ..
+
+331
+00:27:19,020 --> 00:27:21,260
+احنا اختارنا ال .. ال .. ال .. ال .. ال .. ال ..
+
+332
+00:27:21,260 --> 00:27:21,760
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+333
+00:27:21,760 --> 00:27:22,560
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+334
+00:27:22,560 --> 00:27:22,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+335
+00:27:22,840 --> 00:27:23,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+336
+00:27:23,080 --> 00:27:24,040
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+337
+00:27:24,040 --> 00:27:25,580
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+338
+00:27:25,580 --> 00:27:25,580
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+339
+00:27:25,580 --> 00:27:25,580
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+340
+00:27:25,580 --> 00:27:28,900
+ال .. ال .. ال .. ال .. ال .. ال ..
+
+341
+00:27:28,900 --> 00:27:32,300
+ال
+
+342
+00:27:32,300 --> 00:27:36,460
+.. ال .. ال
+
+343
+00:27:37,810 --> 00:27:42,050
+هذا ما هو .. احنا بنحكي عنه، هذا مش لازم تلبسيه
+
+344
+00:27:42,050 --> 00:27:44,770
+لما تروح تقطي ال presentation ده يا دكتور اللي قعد
+
+345
+00:27:44,770 --> 00:27:50,950
+روح أنا نفسي طيب
+
+346
+00:27:50,950 --> 00:27:54,710
+فأي حاجة .. أي حاجة بتخلي الجمهور .. بس خليكم
+
+347
+00:27:54,710 --> 00:27:57,770
+معاها .. أي حاجة بتخلي الجمهور هو متبهي على انت
+
+348
+00:27:57,770 --> 00:28:03,870
+إيش لابسها مش انت إيش بتحكيشليها لأن في ناس بتيجي
+
+349
+00:28:03,870 --> 00:28:06,630
+.. انت لما تيجي إيش بنتقده؟ هم ب .. بشوفوا ..
+
+350
+00:28:06,630 --> 00:28:10,050
+خسوقة .. بقول لبنات، بشوف كيش إيش بتحكي، بشوف إيش
+
+351
+00:28:10,050 --> 00:28:15,990
+لابسه و إيش بساوي حالك طيب، هي professional، هذا
+
+352
+00:28:15,990 --> 00:28:21,970
+اللي بنحكي فيه maintain a constant rate of speech،
+
+353
+00:28:21,970 --> 00:28:26,590
+في ناس بتتكلم بسرعة هائلةبتبلع الكلام .. بتبلع
+
+354
+00:28:26,590 --> 00:28:30,570
+الكلام و البنات عندهم طلاقة ما شاء الله في صورة
+
+355
+00:28:30,570 --> 00:28:37,190
+الكلام يعني ماتعديش عليهم كذلك بتتكلموا فهذه بتخلي
+
+356
+00:28:37,190 --> 00:28:41,530
+الناس شوية تسوى و أحيانا اللي بتكلم photo اكفية
+
+357
+00:28:41,530 --> 00:28:47,470
+برضه بمل منه الجمهور تبعه يمكن .. بعرفش لحدة فيكوا
+
+358
+00:28:47,470 --> 00:28:52,720
+شاف محاضرات لحدة ب .. هم دي ..هندى .. هندى
+
+359
+00:28:52,720 --> 00:28:59,900
+بيشرحلسه .. كيف بتحسه؟ لا الهند .. لا اللغة سريعة
+
+360
+00:28:59,900 --> 00:29:05,460
+بس الشرح تبعه بطيق يعني لو انت بدك تتفرج على موضوع
+
+361
+00:29:05,460 --> 00:29:09,060
+احنا بنشرحه بتلاقي اللي بنشرحه بمحاضرة بدهم تلتة
+
+362
+00:29:09,060 --> 00:29:14,080
+اربعة محاضرات ليشرحوه فبيزهجوا منه يعني انت .. انت
+
+363
+00:29:14,080 --> 00:29:16,680
+لو تيجي مخدة عندنا بدك تحضر ايه بتزهجي؟
+
+364
+00:29:22,840 --> 00:29:26,280
+won't be able to duplicate the real audience
+
+365
+00:29:26,280 --> 00:29:29,620
+stress زي ما حكيتها لما تيجي في قدام ال audience
+
+366
+00:29:29,620 --> 00:29:34,680
+دايما في صعوبة أحيان .. أحيان لما تتوترش لازم
+
+367
+00:29:34,680 --> 00:29:39,020
+تعملش طلع علي رجليكي كيف يدهم بيجيكوا، أمريكيش
+
+368
+00:29:39,020 --> 00:29:43,980
+تيجي في وقف غلط، رجليكي خليهم فتحس زي هيك الوزل
+
+369
+00:29:43,980 --> 00:29:47,680
+تبعك موزز على وين؟ على التنتين، على رجليكي التنتين
+
+370
+00:29:48,480 --> 00:29:52,600
+و اخوك يا عزيزي لو انت شوفت حالك متوتر اصحى بنفس
+
+371
+00:29:52,600 --> 00:29:56,200
+هذه
+
+372
+00:29:56,200 --> 00:30:01,700
+.. هذه بتريحك هذه من ال techniques اللي دايما
+
+373
+00:30:01,700 --> 00:30:05,920
+بنحكيها ف .. لو إيديك شوفتيهم يعني هاتحط إيديك على
+
+374
+00:30:05,920 --> 00:30:09,940
+الطاولة اللي قدامك فهدول من الشغلات اللي إيش
+
+375
+00:30:09,940 --> 00:30:14,480
+بتخليك .. بتخليك شوية مش مبين التوتر عليه بتخفي
+
+376
+00:30:14,480 --> 00:30:19,810
+التوتر خليني أقول أو بتخفي فيهبيفحص يوقف ورا طاولة
+
+377
+00:30:19,810 --> 00:30:26,690
+عشان
+
+378
+00:30:26,690 --> 00:30:29,390
+يشوف رجليه إذا بيروش روح بعمل .. يعني لازم يرفع ..
+
+379
+00:30:29,390 --> 00:30:33,690
+الهدف في ال presentation أن ما تفرجيش ولا نقطة ضعف
+
+380
+00:30:33,690 --> 00:30:37,930
+إليك، لو أنت حاسس حالك زيك الوقف هادر أحسن بيشوف
+
+381
+00:30:37,930 --> 00:30:42,640
+رجليكطيب احنا بتروح .. طيب احنا بتروح .. طيب احنا
+
+382
+00:30:42,640 --> 00:30:42,640
+بتروح .. طيب احنا بتروح .. طيب احنا بتروح .. طيب
+
+383
+00:30:42,640 --> 00:30:43,560
+احنا بتروح .. طيب احنا بتروح .. طيب احنا بتروح ..
+
+384
+00:30:43,560 --> 00:30:44,800
+طيب احنا بتروح .. طيب احنا بتروح .. طيب احنا بتروح
+
+385
+00:30:44,800 --> 00:30:45,160
+.. طيب احنا بتروح .. طيب احنا بتروح .. طيب احنا
+
+386
+00:30:45,160 --> 00:30:45,540
+بتروح .. طيب احنا بتروح .. طيب احنا بتروح .. طيب
+
+387
+00:30:45,540 --> 00:30:51,520
+احنا بتروح .. طيب احنا بتروح .. طيب احنا بتروح ..
+
+388
+00:30:51,520 --> 00:30:58,120
+طيب احنا بتروح .. طيب احنا
+
+389
+00:30:58,120 --> 00:31:07,180
+بتروح .. طيب احنا بتروح .. طيب اطيب use body
+
+390
+00:31:07,180 --> 00:31:10,620
+language effective, relax, gesture, eye contact,
+
+391
+00:31:10,960 --> 00:31:15,120
+don't play with pen or pointer, don't block visual
+
+392
+00:31:15,120 --> 00:31:19,140
+aids أحيان بتلاقيهم إيه؟ وهذا كثير بتحسيها وقت
+
+393
+00:31:19,140 --> 00:31:25,110
+قدام ال LCD والتانين مش حاجة اللي ورالازم تقول ان
+
+394
+00:31:25,110 --> 00:31:28,090
+انت بعيد شوية، فانت بدك تكون aware of your
+
+395
+00:31:28,090 --> 00:31:32,030
+position انت وين واقفة، هذه من الشغلات اللي لازم ت
+
+396
+00:31:32,030 --> 00:31:37,050
+.. التمرين بعودك ع هيك، انا بقولك التمرين بخفف كل
+
+397
+00:31:37,050 --> 00:31:42,750
+هذه الشغلات do test your computer and practice the
+
+398
+00:31:42,750 --> 00:31:45,330
+slideshow before the audience او عشان، في ناس
+
+399
+00:31:45,330 --> 00:31:50,660
+بتيجي بتبقى تعرض، بتشوفيهم بتطلعواصحيح هذا الكلام؟
+
+400
+00:31:50,660 --> 00:31:54,940
+و الله لا كأنهم أول مرة شايفين الاش .. الكلام اللي
+
+401
+00:31:54,940 --> 00:31:58,060
+بدهم يحكوه و بعدين خليني أشوف إيش الكلمة هذه مش
+
+402
+00:31:58,060 --> 00:32:03,420
+باينة فهذه مبينة إنهم جايين و إيش مش متحضرين إذا
+
+403
+00:32:03,420 --> 00:32:08,060
+إنت مش حاطة مجهود للناس اللي على جبالك بيصير مافيش
+
+404
+00:32:08,060 --> 00:32:14,020
+أدهم رغبة يسمعولك بيقولك حد أدنى أنت بدك تحط مجهود
+
+405
+00:32:14,020 --> 00:32:19,900
+تتحضر حالك إلنا عشان نقدر نسمعلكالـ check ahead of
+
+406
+00:32:19,900 --> 00:32:23,460
+time for the proper room lighting and for any
+
+407
+00:32:23,460 --> 00:32:25,120
+glare from windows
+
+408
+00:32:34,630 --> 00:32:38,870
+يعني عشان انت قاعديش عارف اقول .. فكل هذه الشغلات
+
+409
+00:32:38,870 --> 00:32:43,050
+بتعرفيها لما تروح على هذه do make everyone in the
+
+410
+00:32:43,050 --> 00:32:47,350
+audience can see and hear you clearly يعني لما
+
+411
+00:32:47,350 --> 00:32:50,890
+تيجي و أنت تقعد قبل هذه تقعد حد في مقفلة تقول
+
+412
+00:32:50,890 --> 00:32:54,730
+الصوت مسموح ولا لأ حتى ممكن انت تسأل او قبل ما
+
+413
+00:32:54,730 --> 00:32:58,250
+تتكلم صوتي مسموح يا جماعة ولا لأ انت مش مسموح
+
+414
+00:32:58,250 --> 00:33:02,910
+بترفعيه شوية بس ماتتكلميش بهذه كل واحد بده يشوفي و
+
+415
+00:33:02,910 --> 00:33:07,610
+يسمعكdo memorize your speech يعني ما تحفظهاش كلمة
+
+416
+00:33:07,610 --> 00:33:12,390
+بكلمة بس ما تجيش متفاجأة بالكلمات اللي قدامك يعني
+
+417
+00:33:12,390 --> 00:33:17,310
+انت بدك أجلش تتذكري او يعني عندك القدرة لما تشوفي
+
+418
+00:33:17,310 --> 00:33:23,070
+حاجة تتذكريها بس مش تيجي انت ماعندكيش خلفية او
+
+419
+00:33:23,070 --> 00:33:27,390
+ماعندكيش فكرة علي إيش أنت بتحكي do use visuals,
+
+420
+00:33:27,750 --> 00:33:34,230
+charts, graphs, tables, photo هدولة دايما بتريحما
+
+421
+00:33:34,230 --> 00:33:38,130
+تخليهاش كلها هي، يمكن احنا الكتاب اللي فيه صورة،
+
+422
+00:33:38,130 --> 00:33:42,950
+بنحب نقراها، الكتاب اللي فيه ولا صورة ولا حاجة،
+
+423
+00:33:42,950 --> 00:33:48,850
+بنحبهوش Do speak to your audience, do not speak to
+
+424
+00:33:48,850 --> 00:33:53,250
+the screen، يعني ما تجيش تقف زي هيك و تبقى .. انت
+
+425
+00:33:53,250 --> 00:33:57,250
+بتتكلم مع الشاشة مش مع ال audience يعني ال
+
+426
+00:33:57,250 --> 00:34:00,630
+audience زي ما حكيت، بدك تتكلمي، بدك توزع نظراتك
+
+427
+00:34:00,630 --> 00:34:05,580
+على القاعة كلهاتخلى الكل انه يحس انه انت قاعدة
+
+428
+00:34:05,580 --> 00:34:11,360
+تعمل محاضرة لهم وهذه ما تاخدش مجهود بس بدها تمرين
+
+429
+00:34:11,360 --> 00:34:25,300
+عادة
+
+430
+00:34:25,300 --> 00:34:30,060
+من الشغلات برضه كويسة ترقيم ال slidesليش؟ لو حد
+
+431
+00:34:30,060 --> 00:34:33,040
+بتسأل سؤال أو في حاجة مش واضحة بيقول والله في ال
+
+432
+00:34:33,040 --> 00:34:37,740
+slide الرقم هالجد فانت دايما من الشغلات اللي احنا
+
+433
+00:34:37,740 --> 00:34:44,160
+نطلع عليها time management ماحدش بيحب المتحدث فيه
+
+434
+00:34:44,160 --> 00:34:48,420
+وقت أكتر من وقته يعني انتش تطلع المدرس لو بيعطيكوا
+
+435
+00:34:48,420 --> 00:34:54,120
+أيش ما بيعطيكوا بعد الخمسين دقيقة بتتكروا نفس
+
+436
+00:34:54,120 --> 00:34:59,120
+الشيءعند ال presentation يعني انت عندك عشر دقايق
+
+437
+00:34:59,120 --> 00:35:04,520
+معك عشر دقايق بالكتير بالكتير بتزيدي جداش دقيقة
+
+438
+00:35:04,520 --> 00:35:10,900
+لنص دقيقة فده المسموح فيه ال egg برضه التخلصي بدري
+
+439
+00:35:10,900 --> 00:35:14,640
+مش مربوبة في بتلاقي بتعطيهم عشر دقايق تلت دقايق
+
+440
+00:35:14,640 --> 00:35:19,400
+اللي هم مخلصينه فانا دلوقت مش صعب اشتغل حتى الوقت
+
+441
+00:35:19,400 --> 00:35:24,460
+اللي بتتخلص فيهفي حدود دقيقتين اقل من العشر دقائق
+
+442
+00:35:24,460 --> 00:35:28,520
+مثلا اللي عندكم ال video animation او اي حاجة
+
+443
+00:35:28,520 --> 00:35:34,390
+دقيقة دقيقة و نص هذا الحدود المسموح فيهاStand
+
+444
+00:35:34,390 --> 00:35:38,090
+straight up, legs spread, hands in the podium اللي
+
+445
+00:35:38,090 --> 00:35:40,970
+هي الطاولة اللي قدامك Take deep breath with
+
+446
+00:35:40,970 --> 00:35:44,970
+nervous Formal clothing, no flashy or colorful
+
+447
+00:35:44,970 --> 00:35:48,570
+clothes, no jewelry Speak up with a clear voice
+
+448
+00:35:48,570 --> 00:35:53,830
+الآن انتوا عندكوا فريق من تلاتة لاربع طالبان حاجة
+
+449
+00:35:53,830 --> 00:35:58,670
+مهمة دايما بتشوف انتوا في الصدقاء الجري في عندهم
+
+450
+00:35:58,670 --> 00:36:02,930
+الفريق اللي من أربعة بيسموها relayالآن إيش بيبقى
+
+451
+00:36:02,930 --> 00:36:08,350
+فيه كل واحدة اللي بتجري؟ البطان هذا العصاية لازم
+
+452
+00:36:08,350 --> 00:36:12,450
+يسلموها لك تانية شايفين كده الدقة هات؟ لو انت
+
+453
+00:36:12,450 --> 00:36:18,290
+جريتي بدون .. بدون ما تسلمي هذهتعد ايش؟ فشلت في
+
+454
+00:36:18,290 --> 00:36:23,390
+التسليم فتخسر نفس الشي عملية التسليم من واحدة
+
+455
+00:36:23,390 --> 00:36:27,590
+لتالية يعني في بداية ال presentation بدك تقولي ايش
+
+456
+00:36:27,590 --> 00:36:31,670
+انا المجموع الفريق تبعي هتكون من فلانة و فلانة و
+
+457
+00:36:31,670 --> 00:36:36,230
+فلانة و المتحدث هتقول اسمه لما تخلص بتقول انا
+
+458
+00:36:36,230 --> 00:36:41,800
+بشكركم لستماعكم و الان هتيجي زميلتي فلانةاتكمل،
+
+459
+00:36:41,800 --> 00:36:45,700
+فلانا لما تيجي تسلم بتقول أنا بشكر زميلتك اللي
+
+460
+00:36:45,700 --> 00:36:50,220
+جابلي بتقول اسمها و هي بتكمل .. و هي بتكمل، انت
+
+461
+00:36:50,220 --> 00:36:54,760
+الآن عملت introduction لزميلتك و في نفس الوقت
+
+462
+00:36:54,760 --> 00:36:58,820
+زميلتك أجت شكرتك باسمك، فال .. اللي جاعدين حفظوا
+
+463
+00:36:58,820 --> 00:37:03,510
+اسمك و اسمهاهذا الهدف منها، يعني أنت بتأكدي على
+
+464
+00:37:03,510 --> 00:37:07,170
+هذا، و بعدين بتصير .. هي بتصير زي عملية الفرطان
+
+465
+00:37:07,170 --> 00:37:10,230
+هذا اللي هي العصير اللي بيبتم تسليمها، فانت صار
+
+466
+00:37:10,230 --> 00:37:15,070
+استلام و تسليم في العملية، فصارت إيش؟ متابعات
+
+467
+00:37:15,070 --> 00:37:18,170
+فعلا، فهذه من الشغلات اللي كويسة دايما، good
+
+468
+00:37:18,170 --> 00:37:21,830
+technique لما يكون عندك أكتر منها، ماتعملوش زي
+
+469
+00:37:21,830 --> 00:37:25,870
+مدعين الأخبار، و هذا عندكم تحصل، إيش؟كل واحدة
+
+470
+00:37:25,870 --> 00:37:28,270
+بتيجي بتحكي لها كلمتين و بتيجي ازملتها، بعدها
+
+471
+00:37:28,270 --> 00:37:31,950
+بتيجي .. فاش يهدفش و مصبوطش التقنيق، خداعة الأخبار
+
+472
+00:37:31,950 --> 00:37:35,530
+تقنيق تبعها مش مرغوب في ال professional
+
+473
+00:37:35,530 --> 00:37:39,370
+presentation، يعني لما بدك تحكي، أنت بتحكي كل اللي
+
+474
+00:37:39,370 --> 00:37:42,330
+عندك و بتيجي اللي بعدها بالكتير، اللي في الأول و
+
+475
+00:37:42,330 --> 00:37:45,760
+اللي في الآخر ممكن يكون شخص واحداللي هو ال opening
+
+476
+00:37:45,760 --> 00:37:51,060
+و ال end لإنه مهم جدا في آخر ال .. يعني ال ..
+
+477
+00:37:51,060 --> 00:37:55,960
+العرض تبعك بتفتأكدي إيش اللي عملتيه لا تنسوش هذا
+
+478
+00:37:55,960 --> 00:37:59,340
+لإن احنا حكينا في الأول في نقطة في الآخر بتقولوا
+
+479
+00:37:59,340 --> 00:38:02,200
+والله اليوم شرحنا واحد اتنين تلات و قطين النقاط
+
+480
+00:38:02,200 --> 00:38:06,340
+التالية و إذا عندكم أي استفسارات احنا جاهزين و
+
+481
+00:38:06,340 --> 00:38:07,280
+شكرا لحسن
+
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/zXajBMb03h0_raw.json b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/zXajBMb03h0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..47bd201c22060cd8002470bf7362fd898fd0ffd7
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/zXajBMb03h0_raw.json
@@ -0,0 +1 @@
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25724, 2304, 3615, 10632, 25724, 16254, 46007, 8978, 45030, 11242, 16247, 3555, 14407, 3555, 39894, 15040, 38436, 23758, 4724, 1829, 3555, 9957, 31439, 4724, 9566, 1211, 3615, 34051, 44945, 11622, 1211, 37495, 22653, 8032, 3215, 12610, 4724, 1829, 8592, 2655, 17082, 1211, 14407, 15844, 2423, 4386, 15844, 2423, 393, 401, 1389, 1975, 2407, 2423, 7936, 25724, 16254, 3215, 9122, 45865, 3794, 39896, 4117, 39896, 25961, 2655, 4724, 1829, 3555, 17082, 7578, 7251, 9778, 1211, 9381, 8315, 7187], "avg_logprob": -0.377477146503402, "compression_ratio": 1.5913978494623655, "no_speech_prob": 0.0, "words": [{"start": 1273.2, "end": 1274.0, "word": "المواتير", "probability": 0.7098388671875}, {"start": 1274.0, "end": 1274.48, "word": " الجمعية", "probability": 0.72955322265625}, {"start": 1274.48, "end": 1275.14, "word": " الجديمة", "probability": 0.78515625}, {"start": 1275.14, "end": 1275.86, "word": " في", "probability": 0.8828125}, {"start": 1275.86, "end": 1276.14, "word": " بعض", "probability": 0.98046875}, {"start": 1276.14, "end": 1276.5, "word": " الأبواب", "probability": 0.62286376953125}, {"start": 1276.5, "end": 1276.9, "word": " بتلاقي", "probability": 0.7919921875}, {"start": 1276.9, "end": 1277.16, "word": " هذا", "probability": 0.607421875}, {"start": 1277.16, "end": 1277.7, "word": " بيبين", "probability": 0.71356201171875}, {"start": 1277.7, "end": 1278.26, "word": " هو", "probability": 0.5185546875}, {"start": 1278.26, "end": 1278.62, "word": " بطلع", "probability": 0.8876953125}, {"start": 1278.62, "end": 1278.7, "word": " أو", "probability": 0.54833984375}, {"start": 1278.7, "end": 1279.14, "word": " بنزل", "probability": 0.8787434895833334}, {"start": 1279.14, "end": 1279.96, "word": " يعني", "probability": 0.575927734375}, {"start": 1279.96, "end": 1280.28, "word": " هدول", "probability": 0.8898111979166666}, {"start": 1280.28, "end": 1280.86, "word": " بيشتغلوا", "probability": 0.9229910714285714}, {"start": 1280.86, "end": 1282.52, "word": " على", "probability": 0.57080078125}, {"start": 1282.52, "end": 1282.68, "word": " ال", "probability": 0.76123046875}, {"start": 1282.68, "end": 1282.68, "word": " ..", "probability": 0.0966796875}, {"start": 1282.68, "end": 1283.4, "word": " على", "probability": 0.447998046875}, {"start": 1283.4, "end": 1284.22, "word": " ال", "probability": 0.94921875}, {"start": 1284.22, "end": 1284.68, "word": " canol", "probability": 0.23687744140625}, {"start": 1284.68, "end": 1285.14, "word": " case", "probability": 0.0716552734375}, {"start": 1285.14, "end": 1286.18, "word": " او", "probability": 0.7103271484375}, {"start": 1286.18, "end": 1286.46, "word": " ال", "probability": 0.90771484375}, {"start": 1286.46, "end": 1286.76, "word": " solar", "probability": 0.87841796875}, {"start": 1286.76, "end": 1287.74, "word": " الجديد", "probability": 0.9609375}, {"start": 1287.74, "end": 1291.92, "word": " كويس", "probability": 0.9088541666666666}, {"start": 1291.92, "end": 1292.4, "word": " هيك", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/zXajBMb03h0_raw.srt b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/zXajBMb03h0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3652a644bdb38482120dd1fde17689c882236e64
--- /dev/null
+++ b/PL9fwy3NUQKwYzxItuFJ3u0l52cGGpeZEW/zXajBMb03h0_raw.srt
@@ -0,0 +1,1020 @@
+1
+00:00:20,690 --> 00:00:26,430
+السلام عليكم سنتحدث في الفيديو 40 عن موالدات
+
+2
+00:00:26,430 --> 00:00:34,850
+ومحركات موالدات ومحركات
+
+3
+00:00:34,850 --> 00:00:41,830
+موالدات
+
+4
+00:00:41,830 --> 00:00:42,670
+ومحركات
+
+5
+00:00:46,300 --> 00:00:50,860
+Types and functions of engines and motors and the
+
+6
+00:00:50,860 --> 00:00:54,580
+term engine usually refers to petrol engines,
+
+7
+00:00:54,720 --> 00:00:59,340
+diesel engines and jet engines عندنا three types
+
+8
+00:00:59,340 --> 00:01:07,570
+of engines ايش هما petrol و diesel و jetالأن in
+
+9
+00:01:07,570 --> 00:01:12,510
+engineering motor usually means electric motor but
+
+10
+00:01:12,510 --> 00:01:16,450
+in general language motor can also refer to petrol
+
+11
+00:01:16,450 --> 00:01:20,830
+and diesel engines الموتور عندنا في العامية هو
+
+12
+00:01:20,830 --> 00:01:26,070
+توليد وتحريك مظبوط هو موتور كل شي اسمه موتور هذا
+
+13
+00:01:26,070 --> 00:01:30,250
+اللي بنحكيه بس in engineering معناته electric
+
+14
+00:01:30,250 --> 00:01:37,200
+motor المحرك الكهربائيEngines and motors power or
+
+15
+00:01:37,200 --> 00:01:40,540
+drive machines by generating rotary motions
+
+16
+00:01:40,540 --> 00:01:46,820
+الانجين والموتورات ايش بيعملولي؟ بيولدوا قوة اللي
+
+17
+00:01:46,820 --> 00:01:54,060
+بتحرك .. بتحرك ايش؟ ال machines اللي عنده بشكل ..
+
+18
+00:01:54,060 --> 00:01:59,490
+يعني حركة دائريةfor example to drive wheels in jet
+
+19
+00:01:59,490 --> 00:02:04,350
+engine compressors and turbines rotate to generate
+
+20
+00:02:04,350 --> 00:02:09,650
+thrust اللي عندي إيش بالjet engine ال compressors
+
+21
+00:02:09,650 --> 00:02:16,790
+اللي بتغطوه بالترباين اللي عندي اللي هي المولدات
+
+22
+00:02:16,790 --> 00:02:20,310
+rotate to generate thrust اللي هي إيش بنسميه trust
+
+23
+00:02:20,310 --> 00:02:24,110
+دافع
+
+24
+00:02:26,560 --> 00:02:33,920
+Bushing force produced by forcing air from the
+
+25
+00:02:33,920 --> 00:02:37,400
+back of the engine at high velocity فهي بتعمل ..
+
+26
+00:02:37,400 --> 00:02:43,440
+الهواء اللي بيطلع المضغوط هو اللي بيحرك الموجودة
+
+27
+00:02:43,440 --> 00:02:50,040
+السرعةAn engine produce a couple rotate force
+
+28
+00:02:50,040 --> 00:02:54,640
+القوة
+
+29
+00:02:54,640 --> 00:02:59,640
+محركة بشكل دائري The moving parts of the machine
+
+30
+00:02:59,640 --> 00:03:05,260
+it is driving will produce resistance الأجزاء
+
+31
+00:03:05,260 --> 00:03:11,260
+الجهاز أو الماشين اللي بتتحرك تعمل مقاومةdue to
+
+32
+00:03:11,260 --> 00:03:14,240
+friction and other forces اللي هي المقاومة
+
+33
+00:03:14,240 --> 00:03:19,360
+للاحتكاك والقوة الأخرى as a result torque اللي هي
+
+34
+00:03:19,360 --> 00:03:23,910
+twisting forceTorque is exerted on the output
+
+35
+00:03:23,910 --> 00:03:25,390
+shaft of the engine
+
+36
+00:03:53,580 --> 00:03:58,340
+القوة اللي .. خلينا نقول .. ايوة القوة اللي هي
+
+37
+00:03:58,340 --> 00:04:04,410
+الدائرية اللي بولدها ال .. ال .. ال maturethe rate
+
+38
+00:04:04,410 --> 00:04:08,190
+of which an engine can work to exert torque is the
+
+39
+00:04:08,190 --> 00:04:11,790
+power of the engine وهذا بتلاقوه موجود على كل محرك
+
+40
+00:04:11,790 --> 00:04:18,550
+إحصان إحصانين تسمعوا فيه هذه بتلاقوها مكتوبة عليه
+
+41
+00:04:18,550 --> 00:04:23,270
+measured in watt الوات اللي هي ال rating أحيان
+
+42
+00:04:23,270 --> 00:04:28,030
+بتلاقوه مكتوب بالإحصان والإحصان عادة قديش بيعتبروه
+
+43
+00:04:33,630 --> 00:04:40,350
+لأ الإحصان العام تقريبا كيلو بس الإحصان اللي هو
+
+44
+00:04:40,350 --> 00:04:46,450
+بيبقى أقل من هيك حوالي تسعمية و حاجة بس هي هذا
+
+45
+00:04:46,450 --> 00:04:51,370
+اللي بتكلموه althoughEngineers normally calculate
+
+46
+00:04:51,370 --> 00:04:53,930
+engine power in watts. The power of a vehicle
+
+47
+00:04:53,930 --> 00:04:57,890
+engine is often given in brake horse power.
+
+48
+00:05:01,330 --> 00:05:04,970
+This is the power of an engine's output shaft
+
+49
+00:05:04,970 --> 00:05:09,130
+measured in horsepower حسب قوة الحصان قوة الحصان
+
+50
+00:05:09,130 --> 00:05:11,290
+قوة الحصان قوة الحصان قوة الحصان قوة الحصان قوة
+
+51
+00:05:11,290 --> 00:05:13,330
+الحصان قوة الحصان قوة الحصان قوة الحصان قوة الحصان
+
+52
+00:05:13,330 --> 00:05:16,110
+قوة الحصان قوة الحصان قوة الحصان قوة الحصان قوة
+
+53
+00:05:16,110 --> 00:05:16,310
+الحصان قوة الحصان قوة الحصان قوة الحصان قوة الحصان
+
+54
+00:05:16,310 --> 00:05:16,310
+قوة الحصان قوة الحصان قوة الحصان قوة الحصان قوة
+
+55
+00:05:16,310 --> 00:05:16,310
+الحصان قوة الحصان قوة الحصان قوة الحصان قوة الحصان
+
+56
+00:05:16,310 --> 00:05:16,430
+قوة الحصان قوة الحص
+
+57
+00:05:19,680 --> 00:05:23,660
+الـ internal combustion engine petrol و الديزل يجب
+
+58
+00:05:23,660 --> 00:05:29,840
+أن يفهمكوا أيش الفرق بين ماتور البنزين و ماتور
+
+59
+00:05:29,840 --> 00:05:37,180
+الديزل ال solar إذا بتلاحظوا ماتور المواتير ال
+
+60
+00:05:37,180 --> 00:05:40,860
+solar زمان أيام أزمة ال solar عندنا اتشغلت على
+
+61
+00:05:40,860 --> 00:05:47,750
+إيش؟ لأ مش على الغاز، على الزيتلأن الزيت بنحرج
+
+62
+00:05:47,750 --> 00:05:52,430
+فممكن تنشغل عليه أي مادة محترقة بتنشغل فهذا بدي
+
+63
+00:05:52,430 --> 00:05:57,010
+أحكيلكم كيف الفرق this means they are driven by
+
+64
+00:05:57,010 --> 00:06:01,010
+combustion اللي هي عملية الاحتراق burning of fuel
+
+65
+00:06:01,010 --> 00:06:04,950
+in enclosed sealed spaces called combustion
+
+66
+00:06:04,950 --> 00:06:11,050
+chambers يعني هذه بتتم عملية الاحتراق في خلينا
+
+67
+00:06:11,050 --> 00:06:17,890
+نقول chamber اللي هي زيحلقة او فرن الاحتراق in
+
+68
+00:06:17,890 --> 00:06:20,870
+petrol and diesel engine the combustion chambers
+
+69
+00:06:20,870 --> 00:06:25,890
+are cylinders surrounding by a cylinder block هي
+
+70
+00:06:25,890 --> 00:06:33,230
+عبارة عن أسطوانات محيطة بإيش بعوازل للأسطوانات and
+
+71
+00:06:33,230 --> 00:06:36,690
+closed at the top by a cylinder head ومسكرة من فوق
+
+72
+00:06:36,690 --> 00:06:42,880
+براس لهذا السيلندرeach cylinder contain ايش؟ a
+
+73
+00:06:42,880 --> 00:06:50,660
+piston عارفين ايش ال piston؟ طيب الان في عندى انا
+
+74
+00:06:50,660 --> 00:06:58,120
+ايش اللى بتحرك عندى هاد بتطلع عليه هاي
+
+75
+00:06:58,120 --> 00:07:02,900
+الصوانة مكبس هو بيسموه بالعربي بس برضه مش هجيبلكوا
+
+76
+00:07:02,900 --> 00:07:08,770
+حاجة هاد بتحرك يا اما لفوق يا اما لتحتفحركته هادى
+
+77
+00:07:08,770 --> 00:07:12,910
+بتتبنى يقدر اتحرك لتحت مثلا لو في عندى غاز هان او
+
+78
+00:07:12,910 --> 00:07:17,290
+اي حاجة و بيكبس عليه فهو الاسم تبعه بالعربي مكبس
+
+79
+00:07:17,290 --> 00:07:22,230
+بس مش حايم يسويه بس المعروف بيسموه بستون في
+
+80
+00:07:22,230 --> 00:07:23,270
+العالمية عندنا
+
+81
+00:07:27,390 --> 00:07:32,710
+مكبس بالعربية فصحى بالعامية اسمه باستون اسألى أي
+
+82
+00:07:32,710 --> 00:07:37,490
+حد بيقولك السيارة مثلا فيها كام باستون سيارات
+
+83
+00:07:37,490 --> 00:07:41,870
+العادية في غزة غالبا المش مستهلكة للبنزين عادة
+
+84
+00:07:41,870 --> 00:07:46,690
+فيها أربعة باستون سيارات في أمريكا بتلاقيها بحب
+
+85
+00:07:46,690 --> 00:07:51,270
+القوة بتلاقي فيها كام باستون تمانية بس هي بتسحب
+
+86
+00:07:51,270 --> 00:07:56,750
+بنزين كتير مقارنة بالاربعةطيب في هذا ال contain
+
+87
+00:07:56,750 --> 00:07:59,370
+each cylinder contain a piston the number of
+
+88
+00:07:59,370 --> 00:08:02,710
+piston cylinder in the engine vary engine in a
+
+89
+00:08:02,710 --> 00:08:06,930
+small motorcycle have only one piston الموتور ساكل
+
+90
+00:08:06,930 --> 00:08:11,940
+او المكان الصغير فيها دايما باستون واحدده بتتطلع
+
+91
+00:08:11,940 --> 00:08:17,840
+على مثلا المكينة اللي بتشتغل لحالها بتقص الحشيش،
+
+92
+00:08:17,840 --> 00:08:23,300
+هذه فيها بستون واحد المكاين اللي خلينا نقول ال
+
+93
+00:08:23,300 --> 00:08:29,960
+motorcycles فيها دايما بستون واحد معظم الحاجات
+
+94
+00:08:29,960 --> 00:08:33,440
+الصغيرة فيها بستون واحد الآن لما نيجي في بعض
+
+95
+00:08:33,440 --> 00:08:38,550
+السيارات الحجمها صغير بتلاقي فيها تلاتةالغالب
+
+96
+00:08:38,550 --> 00:08:43,890
+عندنا في غزة فيه أربعة اقليل بتشوفي ستة تمانية
+
+97
+00:08:43,890 --> 00:08:47,070
+معناته دي بتسحب بنزين عليها اللي بنحكيها بنشوف
+
+98
+00:08:47,070 --> 00:08:51,430
+عداد البنزين بتتحرك وانت بتسوقي فيها فهذه بس ايش
+
+99
+00:08:51,430 --> 00:08:55,630
+السيارة بتلاقيها كبيرة ومريحة وفيها كل ال option ف
+
+100
+00:08:55,630 --> 00:09:00,670
+.. فبدها بلد ما البنزين فيها مش غالي في أوروبا و
+
+101
+00:09:00,670 --> 00:09:05,520
+بلادنا بتلاقيهم اقلال هدولطيب while sport car
+
+102
+00:09:05,520 --> 00:09:10,320
+engines may have twelve الآن الفراريو جماعتها اللي
+
+103
+00:09:10,320 --> 00:09:14,480
+هي سيارات السباق بدهم ايش قوة كبيرة و سرعة كبيرة
+
+104
+00:09:14,480 --> 00:09:21,320
+فبتلاقي عدد ال pistons بزيد ففيها اتناشر
+
+105
+00:09:21,320 --> 00:09:25,320
+fuel is supplies to each cylinder from a tank in
+
+106
+00:09:25,320 --> 00:09:29,780
+most enginesthe flow of fuel is generated by a
+
+107
+00:09:29,780 --> 00:09:32,660
+pump which is .. which forces it at a high
+
+108
+00:09:32,660 --> 00:09:36,560
+pressure إذا بتلاحظوا في حاجة بيسموها ال fuel pump
+
+109
+00:09:36,560 --> 00:09:39,720
+وموجودة هذا في السيارات لما جيبنا البنزين المصري
+
+110
+00:09:39,720 --> 00:09:43,340
+عرفنا أنها موجودة لإيش؟ لأنها كانت تخرب و تسكن
+
+111
+00:09:43,340 --> 00:09:47,180
+بسرعة فكان بدها تصنيح دايما فعرفنا وين هي وين
+
+112
+00:09:47,180 --> 00:09:50,920
+محلها بتلاقيها هذه جنب ال tank بعد ال tank بالظبط
+
+113
+00:09:50,920 --> 00:09:54,700
+تحت .. إذا بتلاحظوا حد فيكوا في الكرسي الخالفي تحت
+
+114
+00:09:54,700 --> 00:09:58,990
+الكرسي الخالفي في السياراتعرفناها أيام هذيك الأيام
+
+115
+00:09:58,990 --> 00:10:04,510
+allowing it to mix هي إيش بنقول forces it at a
+
+116
+00:10:04,510 --> 00:10:08,270
+high pressure true fuel injection السيارات الحديثة
+
+117
+00:10:08,270 --> 00:10:13,450
+كلها تفيها إيش؟ fuel injection اللي هي إيش؟ بتضخ
+
+118
+00:10:13,450 --> 00:10:19,780
+يعني inject بتعمل اللي هي ضخ ال fuelأو تنظيم ضغط
+
+119
+00:10:19,780 --> 00:10:24,440
+الفيول، these vaporize the fuel allowing it to mix
+
+120
+00:10:24,440 --> 00:10:29,440
+with air، إيش بيصير لها؟ بتحوله لغاز وبتخليه إيش؟
+
+121
+00:10:29,440 --> 00:10:34,530
+يختلط مع الهواءUsing this mixture of fuel and air,
+
+122
+00:10:34,650 --> 00:10:39,110
+most engines function as four-stroke engines هذا
+
+123
+00:10:39,110 --> 00:10:42,430
+من .. هنتفسر أيش ال four-stroke engine فمعظم
+
+124
+00:10:42,430 --> 00:10:46,470
+المواتير المولدة .. المواتير بتشتغل على four
+
+125
+00:10:46,470 --> 00:10:50,510
+-stroke engine this mean they work on a cycle of
+
+126
+00:10:50,510 --> 00:10:56,970
+four stages عندهم الcycle من أربعة مراحلor for a
+
+127
+00:10:56,970 --> 00:11:00,670
+stroke a stroke is an upward or downward movement
+
+128
+00:11:00,670 --> 00:11:04,230
+of a piston يا إما بنروح في ال upward يا إما بنروح
+
+129
+00:11:04,230 --> 00:11:08,050
+في ال downward أول واحدة بنسميها induction or
+
+130
+00:11:08,050 --> 00:11:12,310
+intake تاني واحدة بنسميها اللي هي الادخال تاني
+
+131
+00:11:12,310 --> 00:11:16,030
+واحدة ال compression الضغط تالت واحدة power or
+
+132
+00:11:16,030 --> 00:11:19,490
+ignition اللي هي الشعلة الاشتعال خامس واحدة ال
+
+133
+00:11:19,490 --> 00:11:23,130
+exhaust اللي هي المخرج وهي هنفسر كل واحدة فيهم
+
+134
+00:11:23,130 --> 00:11:28,250
+بشكل مفصلinduction or intake the intake valve open
+
+135
+00:11:28,250 --> 00:11:32,450
+the mixture enter the cylinder through a port in
+
+136
+00:11:32,450 --> 00:11:36,410
+the cylinder head while the piston moves downward
+
+137
+00:11:36,410 --> 00:11:39,530
+يعني أول حاجة بدخل تدخل عند الفيول و ال piston
+
+138
+00:11:39,530 --> 00:11:44,390
+بنزل في اتجاه downward الاتجاه السفلي ال
+
+139
+00:11:44,390 --> 00:11:49,810
+compression the intake valve closes اللي هي الصمام
+
+140
+00:11:49,810 --> 00:11:55,240
+اللي بدخل او الشبر اللي بدخل بسكرthe piston moves
+
+141
+00:11:55,240 --> 00:11:58,220
+upward compressing the mixture الآن دخل عندى
+
+142
+00:11:58,220 --> 00:12:02,440
+الفيول الحين ال piston كان أسفل فبدي ارجع لفوق ايش
+
+143
+00:12:02,440 --> 00:12:08,080
+هيسوي هيضغط على الغاز و الفيول اللى موجود عندى
+
+144
+00:12:08,080 --> 00:12:12,960
+الهوى و الفيول فبعمل compression power or ignition
+
+145
+00:12:12,960 --> 00:12:17,460
+the spark plug اللى بيسموها هنا البوجية حد سمع
+
+146
+00:12:17,460 --> 00:12:23,450
+فيهاهو اللي بتطلع الشرارة هذه البوجية موجودة فوق
+
+147
+00:12:23,450 --> 00:12:30,650
+وشكلها بيبقى زي .. يعني راسها شكل خزفي تحت حديد و
+
+148
+00:12:30,650 --> 00:12:36,190
+فوق راس حديد و بتنشبك في هذه فهدولة اللي شافوهم في
+
+149
+00:12:36,190 --> 00:12:43,110
+غزة اسمها البوجية في ال English اسمها spark plug
+
+150
+00:12:46,700 --> 00:12:51,960
+بدروسج أسبارك لإن إيش بتطلع تطلع شرارة which
+
+151
+00:12:51,960 --> 00:12:55,980
+ignites or lights the mixture on the ignition the
+
+152
+00:12:55,980 --> 00:12:59,720
+mixture explode generating a sudden pressure which
+
+153
+00:12:59,720 --> 00:13:03,900
+forces the piston down فإيش بيصير فيه هذه بيصير
+
+154
+00:13:03,900 --> 00:13:08,120
+اشتعال و بيصير explosion مع الضغط إيش بدي يحصل ال
+
+155
+00:13:08,120 --> 00:13:12,760
+piston اللي كان فوق هينزل تحتال exhaust اللي هي
+
+156
+00:13:12,760 --> 00:13:17,700
+المخرج او ال muffler او بحيات بيسموها اللي بيطلع
+
+157
+00:13:17,700 --> 00:13:21,980
+حرارة ال exhaust valves open and the piston moves
+
+158
+00:13:21,980 --> 00:13:25,760
+upward فبيفتح ال exhaust اللي عنده و ال piston
+
+159
+00:13:25,760 --> 00:13:30,960
+بيصير يطلع لفوق forcing the exhaust gases those
+
+160
+00:13:30,960 --> 00:13:35,210
+produced during the combustion اللي همخلال عملية
+
+161
+00:13:35,210 --> 00:13:38,450
+الاشتعال اللى تمها out of the cylinder via the
+
+162
+00:13:38,450 --> 00:13:42,850
+exhaust port the exhaust valve then closes and the
+
+163
+00:13:42,850 --> 00:13:48,030
+cycle begins again فهو اول حاجة ايش بنسوي بدخل عند
+
+164
+00:13:48,030 --> 00:13:52,750
+ال intake او ال induction بدخل ال fuel على شكل
+
+165
+00:13:52,750 --> 00:13:57,570
+vapor اللى هو mixed with gas الان ال piston عندى
+
+166
+00:13:57,570 --> 00:14:02,630
+في هذا اللحظة ايش بيصيرله بنزلالان الـ intake
+
+167
+00:14:02,630 --> 00:14:09,850
+valve بيسكر بيغطي اللي عند
+
+168
+00:14:09,850 --> 00:14:15,210
+ال piston بيصير move upward بيغطي ال gas واللي ها
+
+169
+00:14:15,210 --> 00:14:19,450
+الان نتيجة الضغط ايش بيصير عنده ال spark plug
+
+170
+00:14:19,450 --> 00:14:24,150
+بتعمل ignition او شرارة spark فا ايش بيصير بيصير
+
+171
+00:14:24,150 --> 00:14:27,910
+عملية احتراق عملية الاحتراق ال combustion هاد او
+
+172
+00:14:27,910 --> 00:14:33,520
+ال ignition بتولد gasesالغازات هاذي ايش بتعمل؟
+
+173
+00:14:33,520 --> 00:14:36,840
+بتضغط على ال piston، ال piston بنزل down، الآن
+
+174
+00:14:36,840 --> 00:14:40,260
+بفتح عشان يعمل release لهذه الغازات، مين بيسميه؟
+
+175
+00:14:40,260 --> 00:14:44,660
+ال exhaust، ال exhaust valve، صمام اللي هي هاذي،
+
+176
+00:14:44,660 --> 00:14:48,080
+فبطلع منه الغازات، فال piston برجع لفوق، و بترجع
+
+177
+00:14:48,080 --> 00:14:50,360
+العملية من أول و جديد
+
+178
+00:14:53,380 --> 00:14:56,780
+الان عندي complete the text about diesel engine
+
+179
+00:14:56,780 --> 00:15:00,460
+using the words from A and B diesel engine differ
+
+180
+00:15:00,460 --> 00:15:05,820
+from مين؟ petrol ال petrol هو في أوروبا بيسموه
+
+181
+00:15:05,820 --> 00:15:11,640
+petrol في أمريكا بيسموه gas البنزين هذا في
+
+182
+00:15:11,640 --> 00:15:15,980
+اختلافين gas engine in one key respect they are
+
+183
+00:15:15,980 --> 00:15:21,210
+not fitted with ايش؟إيش الحاجة؟ عمركوا .. حد فيكوا
+
+184
+00:15:21,210 --> 00:15:26,550
+تطلع على ال motor لسيارات الديزل، فيش spark plugs
+
+185
+00:15:26,550 --> 00:15:30,730
+فيهم، بينما spark plugs في سيارات ال إيه؟ البنزين،
+
+186
+00:15:30,730 --> 00:15:35,350
+شباب يعني جزء منهم بيعرف أكتر منكوا، في هذا
+
+187
+00:15:35,350 --> 00:15:41,900
+المعلومة، هذه الخبيرة تبعتكمطيب هنا with a spark
+
+188
+00:15:41,900 --> 00:15:46,160
+plug in each cylinder to ignite the fuel this is
+
+189
+00:15:46,160 --> 00:15:50,640
+because when ايش of the diesel and air ايش هذه ال
+
+190
+00:15:50,640 --> 00:15:53,720
+mixture الحاجة المشتركة ماحزمة تشوفوا diesel and
+
+191
+00:15:53,720 --> 00:15:58,820
+air هذا ال mixture is compressed inside a hot ايش
+
+192
+00:15:58,820 --> 00:16:06,580
+سمنها الجزء هذا ال chamber
+
+193
+00:16:09,260 --> 00:16:13,780
+إيش سامناها combustion chamber it will explode
+
+194
+00:16:13,780 --> 00:16:18,180
+spontaneously without the need for a spark to
+
+195
+00:16:18,180 --> 00:16:26,120
+provide إيش إيش بتعمل هذه ignition مظبوط بيصير إيه
+
+196
+00:16:26,120 --> 00:16:31,420
+لما الآن دق ال combustion chamber إيش بيحصل له لما
+
+197
+00:16:31,420 --> 00:16:36,260
+الغاز ينضغط و تجيله ignition إيش بيحصل بتشتعل
+
+198
+00:16:38,510 --> 00:16:42,930
+السيارات الديزلية يجب أن تعمل بطريقة تمنع الديزل
+
+199
+00:16:42,930 --> 00:16:47,150
+من الانفجار قبل أن يكون السيارة على أعلى السليندر
+
+200
+00:16:47,150 --> 00:16:51,190
+لإيقاف هذا، يأخذ السيارة فقط الهواء خلال مرحلة إيش
+
+201
+00:16:51,190 --> 00:17:00,470
+السيكل الأول مرحلة إيش هي الاندوكشن لذلك خلال
+
+202
+00:17:00,470 --> 00:17:06,130
+مرحلة إيش فقط الهواء و لا .. خلال مرحلة إيش .. أي
+
+203
+00:17:06,130 --> 00:17:12,430
+مرحلة فقط الهواء و لا ..طيب ال ignition stage only
+
+204
+00:17:12,430 --> 00:17:16,650
+air and not an air fuel mixture is pressurized
+
+205
+00:17:16,650 --> 00:17:20,490
+يعني هد .. ال compression مظبوط ال compression
+
+206
+00:17:20,490 --> 00:17:24,430
+لإنه during ال first stage سمنها ال induction ال
+
+207
+00:17:24,430 --> 00:17:27,830
+second stage سمنها .. أو ال intake ال second stage
+
+208
+00:17:27,830 --> 00:17:33,090
+سمنها ال compressionis pressurized it's only at
+
+209
+00:17:33,090 --> 00:17:35,750
+that last instance when the fuel compression has
+
+210
+00:17:35,750 --> 00:17:40,090
+occurred and that the ash above each cylinder
+
+211
+00:17:40,090 --> 00:17:43,130
+forces vaporized diesel into the combustion
+
+212
+00:17:43,130 --> 00:17:49,330
+chamber ايش اللي بيعمل ال fuel ال fuel above تتجيش
+
+213
+00:17:49,330 --> 00:17:56,320
+ايش اللي بيجيالـ fuel injector الـ fuel injector
+
+214
+00:17:56,320 --> 00:17:59,720
+above each cylinder forces the vaporized diesel
+
+215
+00:17:59,720 --> 00:18:06,780
+into the combustion chamber where it ignites طيب
+
+216
+00:18:06,780 --> 00:18:12,020
+diesel engine operates at lower speed than petrol
+
+217
+00:18:12,020 --> 00:18:17,700
+engines عادة أتلاحظوا ال speed أقل و عشان هيك هي
+
+218
+00:18:17,700 --> 00:18:23,580
+سيارات الديزل more efficientبتلاقي معظم السيارات
+
+219
+00:18:23,580 --> 00:18:31,780
+بيحاولوا يحاولوا لديزل ليش؟لأن الليتر تبعهم بيعطيه
+
+220
+00:18:31,780 --> 00:18:35,880
+كفاءة أعلى بيعطيه mileage أعلى فبتوفر أكتر من
+
+221
+00:18:35,880 --> 00:18:39,540
+البنزين لأن هذا lower speed than petrol engines
+
+222
+00:18:39,540 --> 00:18:42,040
+making them less suitable for high speed
+
+223
+00:18:42,040 --> 00:18:46,340
+applications عادة السيارات اللي بدها قوة أو بدها
+
+224
+00:18:46,340 --> 00:18:50,960
+سرعة السيارات السابقة بتستخدم مش ايش أو الطيارات
+
+225
+00:18:50,960 --> 00:18:55,320
+بتستخدم مش diesel بينما ال heavy machines بتستخدم
+
+226
+00:18:55,320 --> 00:19:02,380
+مش dieselhowever they are more able to power
+
+227
+00:19:02,380 --> 00:19:07,380
+heavy vehicle as they can produce greater amount
+
+228
+00:19:07,380 --> 00:19:13,900
+of torque than petrol engine ايش ال torque؟ عزم
+
+229
+00:19:13,900 --> 00:19:21,780
+طيب الرسمة الجاية هذي بتعرفكم على اللي يعرفه ايش
+
+230
+00:19:21,780 --> 00:19:28,360
+كل جزء من موجود عندههذا بنسميه ال camp shaft اللي
+
+231
+00:19:28,360 --> 00:19:32,460
+عندي هذا ال camp هاي ال mixture اللي هو عندي قولنا
+
+232
+00:19:32,460 --> 00:19:38,380
+إيش ال mixture air and gas اللي عندي هذا اللي عندي
+
+233
+00:19:38,380 --> 00:19:43,380
+إيش بنسميه هذا هذا عندي valve ال intake اللي هو
+
+234
+00:19:43,380 --> 00:19:48,420
+اللي بدخل هذا لما ننزل بدخل الموجود عندي هذا اللي
+
+235
+00:19:48,420 --> 00:19:53,480
+سمناه إيش ال chamberاللي ايش combustion chamber
+
+236
+00:19:53,480 --> 00:20:00,100
+اللي عندى اتنين تلاتة ايش سمناها هذه سيلندر اللي
+
+237
+00:20:00,100 --> 00:20:06,740
+موجودة عندى اربعةإيش هذه؟ شايفين الشكل تبعها؟ هذه
+
+238
+00:20:06,740 --> 00:20:09,480
+ال spark plug عشان اللي بتعرفش تعرف إيش الشكل
+
+239
+00:20:09,480 --> 00:20:14,900
+تبعها، هاي ال spark plug الشكل تبعها، هنا حديد،
+
+240
+00:20:14,900 --> 00:20:19,280
+هذه المنطقة اللي لونها على بياض هي هذه الخزافة،
+
+241
+00:20:19,280 --> 00:20:23,780
+وهنا الشعلة بتطلع من وين؟ من تحت من هذا، لو
+
+242
+00:20:23,780 --> 00:20:28,140
+فتحتوها وشفتوها بتلاقوها من الشعلة القربانة فيهم
+
+243
+00:20:28,140 --> 00:20:33,740
+لونها عسوانفبتعرف أنها بطلت تطلع الشعلة لأن هذه
+
+244
+00:20:33,740 --> 00:20:37,720
+لازم تكون مش ع سواد يعني مش مصدية عشان تطلع شعلة
+
+245
+00:20:37,720 --> 00:20:44,160
+خمسة هنا إيش بنسميها؟ هاي ال spring .. ال valve
+
+246
+00:20:44,160 --> 00:20:48,760
+spring هنا إيش؟ exhaust valve لأن هذا اللي بطلع
+
+247
+00:20:48,760 --> 00:20:55,310
+ليه؟ ال exhaust هنا six إيش بنسميها؟cylinder head
+
+248
+00:20:55,310 --> 00:20:59,730
+هذا cooling water اللي عندها هذا التمانية شايفينه
+
+249
+00:20:59,730 --> 00:21:07,270
+ال piston شايفين كيف شكله فالمكبس هذا لما يطلع فوق
+
+250
+00:21:07,270 --> 00:21:11,970
+او ينزل تحت هو اللي بتحرك هذا بتلاقوه يمكن لو حدا
+
+251
+00:21:11,970 --> 00:21:16,500
+فيكوا شافالمواتير الجمعية الجديمة في بعض الأبواب
+
+252
+00:21:16,500 --> 00:21:20,280
+بتلاقي هذا بيبين هو بطلع أو بنزل يعني هدول
+
+253
+00:21:20,280 --> 00:21:26,760
+بيشتغلوا على ال .. على ال canol case او ال solar
+
+254
+00:21:26,760 --> 00:21:31,920
+الجديد كويس
+
+255
+00:21:31,920 --> 00:21:34,680
+هيك هي كانت بيبغى يخلصنا chapter
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9ee5e4245c06a1112be8f0ad6cfbc519b4a9a8f3
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_postprocess.srt
@@ -0,0 +1,3708 @@
+1
+00:00:04,910 --> 00:00:08,190
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,190 --> 00:00:12,270
+والصلاة والسلام على سيد المرسلين سيدنا محمد على
+
+3
+00:00:12,270 --> 00:00:18,470
+آله وصحبه أجمعين هذه هي المحاضرة رقم 22 في مساق
+
+4
+00:00:18,470 --> 00:00:23,930
+تحليل حقيقة نيل لطلاب وطالبات الجامعة الإسلاميةقسم
+
+5
+00:00:23,930 --> 00:00:29,530
+الرياضيات في كلية العلوم عنوان المحاضرة اليوم
+
+6
+00:00:29,530 --> 00:00:32,850
+هنكمل chapter تمانية هيكون في عندي اللي هو
+
+7
+00:00:32,850 --> 00:00:37,130
+applications على اللي هي تمانية اللي هي واحد و
+
+8
+00:00:37,130 --> 00:00:41,630
+تمانية اتنين المحاضرة اليوم اللي هي هنحكي عن the
+
+9
+00:00:41,630 --> 00:00:46,730
+exponential and the logarithmic functions هنحكي عن
+
+10
+00:00:46,730 --> 00:00:51,830
+اللي هو دالة ال E to the X ودالة ال Lin أو دالة ال
+
+11
+00:00:51,830 --> 00:00:57,660
+logالان هنثبت اللي هو من خلال .. في البداية هنحكي
+
+12
+00:00:57,660 --> 00:01:03,280
+عن اللي هو ال exponential function أو هنثبت اللي
+
+13
+00:01:03,280 --> 00:01:05,740
+هو وجود ال exponential function
+
+14
+00:01:09,490 --> 00:01:13,630
+احنا استخدمناها قبل هيك مجرد أمثلة بعيدا عن اللي
+
+15
+00:01:13,630 --> 00:01:18,730
+هو انه اللي هي مفترضنا انه معلومات موجودة مسبقا
+
+16
+00:01:18,730 --> 00:01:22,170
+ولا تناقض اللي هو انه نثبتها اليوم لإنه اثباتها
+
+17
+00:01:22,170 --> 00:01:25,410
+اليوم لا يعتمد على اللي حكيناه سابقا بما يخص
+
+18
+00:01:25,410 --> 00:01:29,350
+بأمثلة اللي ذكرت فيها ال exponential الان ال
+
+19
+00:01:29,350 --> 00:01:34,310
+exponential function بدنا نثبت وجودها ايش اللي
+
+20
+00:01:34,310 --> 00:01:38,820
+بنقوله نشوف عبر ال theorem 8 3 1 theoremبقول there
+
+21
+00:01:38,820 --> 00:01:44,060
+exists a function U دلّة E من R ل R إذا في عندنا
+
+22
+00:01:44,060 --> 00:01:49,680
+دلّة اسمها E من R ل R such that الـ E prime of X
+
+23
+00:01:49,680 --> 00:01:55,280
+لها بساول EX لكل X element in Rإتنين E of Zero
+
+24
+00:01:55,280 --> 00:01:58,820
+بساوي إيش واحد يعني الآن النظرية دي بتقولي إنه
+
+25
+00:01:58,820 --> 00:02:02,920
+يوجد عندنا دالة domainها كل ال R و rangeها بروح
+
+26
+00:02:02,920 --> 00:02:10,220
+بصوب في ال R هذه الدالة تحقق شرطين اللي هي E prime
+
+27
+00:02:10,220 --> 00:02:14,500
+of X بساوي E of X و E of Zero بساوي إيش واحدالان
+
+28
+00:02:14,500 --> 00:02:19,920
+نجي اللي هو بدنا نثبت وجود هذه الدالة ايه التي
+
+29
+00:02:19,920 --> 00:02:25,380
+تحقق اللي هو الخواص اللي عندنا المذكورة فيه اللي
+
+30
+00:02:25,380 --> 00:02:29,960
+هي نظريا الان خلينا عشان نروح باتجاه اثبات وجود
+
+31
+00:02:29,960 --> 00:02:34,080
+هذه الدالة خلينا ناخد we inductively define a
+
+32
+00:02:34,080 --> 00:02:37,900
+sequence of continuous functions as follows بدي
+
+33
+00:02:37,900 --> 00:02:43,590
+الآن اعرف اللي هو sequence of functionsالأولى
+
+34
+00:02:43,590 --> 00:02:48,790
+اسمها E1 of X بتساوي واحد زائد X طبعا هذه الدالة
+
+35
+00:02:48,790 --> 00:02:52,790
+موجودة E1 of X بتساوي واحد زائد X هي دالة خطية
+
+36
+00:02:52,790 --> 00:02:58,590
+الآن بدي أعرف ال E2 ال E2 of X بساوي ال
+
+37
+00:02:58,590 --> 00:03:04,170
+integration واحد زائد ال integration من سفر لعند X
+
+38
+00:03:04,170 --> 00:03:13,140
+اللي هو E1 of X D أو E1 of T DTإذاً الـ E2 بدي
+
+39
+00:03:13,140 --> 00:03:17,960
+أجيبها من مين؟ من الـ E1 طبعاً بتيجي الـ E والـ E2
+
+40
+00:03:17,960 --> 00:03:23,500
+اللي هي عبارة عن واحد زائد هذه واحد زائد T اللي هو
+
+41
+00:03:23,500 --> 00:03:27,730
+تفاضلها زي ما انتوا عارفين تكملها اللي هي Tزائد
+
+42
+00:03:27,730 --> 00:03:32,910
+اللي هي T تربيع على اتنين من صفر لعند X ويسوا واحد
+
+43
+00:03:32,910 --> 00:03:38,490
+زائد X زائد X على X تربيع على اتنين هذه الدالة من
+
+44
+00:03:38,490 --> 00:03:45,020
+هي E2 of X E3 of Xبتعرفها بنفس الأسلوب بالساوي 1
+
+45
+00:03:45,020 --> 00:03:49,840
+زائد الـ integration من 0 ل X لدالة اللي وجدتها
+
+46
+00:03:49,840 --> 00:03:56,140
+قبلها اللي هي E2 of T DT بضل أسائي ساير في التعريف
+
+47
+00:03:56,140 --> 00:04:03,760
+بقول in general بتعرف ال E N زائد 1 of Xبساوة الـ
+
+48
+00:04:03,760 --> 00:04:11,420
+1 زي ال integration من 0 ل X EN of T DT إذن الآن
+
+49
+00:04:11,420 --> 00:04:16,020
+عرفت اللي هي ال E1 of X بساوة 1 زي X ومنها عرفت
+
+50
+00:04:16,020 --> 00:04:21,840
+اللي هي E2 وE2 عرفت منها E3 وE3 عرفت منها E4 وهكذا
+
+51
+00:04:21,840 --> 00:04:26,120
+ال EN زي ال 1 of X هتساوة 1 زي ال integration من 0
+
+52
+00:04:26,120 --> 00:04:31,440
+ل X لل EN اللي جاب الها ديof D D T لكل N element
+
+53
+00:04:31,440 --> 00:04:36,720
+in N و لكل X element in M in R نيجي الآن نطلع على
+
+54
+00:04:36,720 --> 00:04:40,920
+الملاحظات اللي بدنا نحكيها عشان نستخدمها الان 1
+
+55
+00:04:40,920 --> 00:04:46,840
+زائد X دالة متصلة مش متصلة أصلا بس هي أصلا قابلة
+
+56
+00:04:46,840 --> 00:04:51,900
+للتفاضل أيضا اللي هي differentiable الان بناء عليه
+
+57
+00:04:51,900 --> 00:05:00,140
+مدام ال E1 is continuous هتكون اللي هي E2E2 هي
+
+58
+00:05:00,140 --> 00:05:03,940
+الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 الـ E1
+
+59
+00:05:03,940 --> 00:05:04,180
+هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 الـ
+
+60
+00:05:04,180 --> 00:05:07,840
+E1 هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1
+
+61
+00:05:07,840 --> 00:05:11,080
+الـ E1 هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ
+
+62
+00:05:11,080 --> 00:05:12,820
+E1 الـ E1 هي الانتجراش للـ E1 الـ E1 هي الانتجراش
+
+63
+00:05:12,820 --> 00:05:14,980
+للـ E1 الـ E1 هي الانتجراش للـ E1 الـ E1 هي
+
+64
+00:05:14,980 --> 00:05:18,980
+الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 الـ E1
+
+65
+00:05:18,980 --> 00:05:22,820
+هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 ال
+
+66
+00:05:25,750 --> 00:05:27,270
+الآن F.E.L
+
+67
+00:05:31,050 --> 00:05:34,950
+in on R then it is integrable over any bounded
+
+68
+00:05:34,950 --> 00:05:39,590
+interval زي ما قلنا مدام هذا continuous اللي هي E
+
+69
+00:05:39,590 --> 00:05:45,210
+اللي هي 2 continuous ومن هنا هتطلع E 3 continuous
+
+70
+00:05:45,210 --> 00:05:49,530
+وE 4 continuous إذا صارت هذي دايما continuous وده
+
+71
+00:05:49,530 --> 00:05:53,170
+continuous وده integration exist و by fundamental
+
+72
+00:05:53,170 --> 00:05:57,250
+theorem هذا ال integration كله على بعض can be
+
+73
+00:05:57,250 --> 00:06:01,160
+differentiatedوهتكون الهو ايش is differentiable
+
+74
+00:06:01,160 --> 00:06:05,520
+ومنه so EN زائد واحد is well defined by the above
+
+75
+00:06:05,520 --> 00:06:09,300
+formula moreover زي ما قلت it is from fundamental
+
+76
+00:06:09,300 --> 00:06:12,400
+theorem of calculus ال second form اللي هي سبعة
+
+77
+00:06:12,400 --> 00:06:15,920
+تلاتة خمسة هيكون عند ال EN زائد واحد is
+
+78
+00:06:15,920 --> 00:06:19,280
+differentiable ومش هيك وتفاضل هذه زي ما احنا
+
+79
+00:06:19,280 --> 00:06:24,540
+عارفين بساوي بنشيل ال integration طبعا التفاضل بلغ
+
+80
+00:06:24,540 --> 00:06:29,220
+ال integrationبصير en of x فبصير عندي ال en زائد
+
+81
+00:06:29,220 --> 00:06:34,240
+واحد prime of x موجودة ويساوي en x for all n
+
+82
+00:06:34,240 --> 00:06:37,720
+element in N إذن الآن عملنا sequence ال sequence
+
+83
+00:06:37,720 --> 00:06:40,580
+هذه طلعت sequence of differentiable functions و ال
+
+84
+00:06:40,580 --> 00:06:43,860
+derivative لل en زائد واحد prime هي بترجع لمين
+
+85
+00:06:43,860 --> 00:06:50,320
+بتيجي اللي هي ال en of xطيب الان هذا كله و ده
+
+86
+00:06:50,320 --> 00:06:53,900
+خليني اسميها تلاتة و خليني نحضر حالنا نصل للي بدنا
+
+87
+00:06:53,900 --> 00:06:59,500
+ياجولكم وين هنصل في الآخر هوصلكم انه اللي هو ال
+
+88
+00:06:59,500 --> 00:07:05,400
+limit لهذه ال sequence او لهذه ال sequence هي ال E
+
+89
+00:07:05,400 --> 00:07:12,300
+of X اللي انا بثبت وجودهاوستكون اللي هي بتحقق
+
+90
+00:07:12,300 --> 00:07:16,440
+الشروط اللي حكيناها خلّينا نشوف ما لاستعجلش نشوف
+
+91
+00:07:16,440 --> 00:07:19,900
+إيش اللي بدنا نصلله إذا اللي عملناه كوّننا
+
+92
+00:07:19,900 --> 00:07:23,380
+sequence sequence زي ما قلنا اللي هي ال sequence
+
+93
+00:07:23,380 --> 00:07:28,160
+بدأت عشان يبقى لكم الذاكرين E1 of X بساوي واحد
+
+94
+00:07:28,160 --> 00:07:34,760
+زائد X E and زائد واحد of X بساوي الانتجرأت واحد
+
+95
+00:07:35,450 --> 00:07:39,790
+بسوء واحدة زي الـ integration من صفر لعدد X E N of
+
+96
+00:07:39,790 --> 00:07:47,450
+T DT خلّين هذولة أمامنا طبعاً N element in N عندي
+
+97
+00:07:47,450 --> 00:07:54,630
+و X أي element وين in Rطيب إذا الان سار عندي اللي
+
+98
+00:07:54,630 --> 00:07:58,430
+هو ال .. ده اللي هذي is differential لان بقوللي
+
+99
+00:07:58,430 --> 00:08:03,230
+انه ابن الدعي ويمكن لو حد شاف قبل بشوية ما وصلنا ل
+
+100
+00:08:03,230 --> 00:08:08,450
+E2 E2 كانت عبارة عن واحد زي دكستر بيه على اتنين
+
+101
+00:08:08,450 --> 00:08:13,070
+اللي هو اللي هي اتنين factorialلو كملنا هيكون E N
+
+102
+00:08:13,070 --> 00:08:16,910
+of X بتساوي 1 زياد X على 1 factorial X تربيه على 2
+
+103
+00:08:16,910 --> 00:08:21,170
+factorial زياد X وصف N على 100 على N factorial لكل
+
+104
+00:08:21,170 --> 00:08:25,750
+X element in R هذه الـ N صحيحة اللي هي لكل N
+
+105
+00:08:25,750 --> 00:08:31,470
+element in R اللي هو طبعا اثباتها سهل نثبتها by
+
+106
+00:08:31,470 --> 00:08:36,010
+induction خلينا نشوف كيفنا نثبت أربعة by induction
+
+107
+00:08:58,380 --> 00:09:01,020
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+108
+00:09:01,020 --> 00:09:04,640
+أربعة
+
+109
+00:09:04,640 --> 00:09:06,540
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+110
+00:09:06,540 --> 00:09:06,720
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+111
+00:09:06,720 --> 00:09:06,900
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+112
+00:09:06,900 --> 00:09:08,610
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أfour is
+
+113
+00:09:08,610 --> 00:09:16,450
+a true four and بتساوي كتابة يعني صار عند الالالـ
+
+114
+00:09:16,450 --> 00:09:23,550
+E K of X بتساوي 1 زائد X على 1 factorial زائد X
+
+115
+00:09:23,550 --> 00:09:29,170
+تربيع على 2 factorial زائد X أُس K على K factorial
+
+116
+00:09:29,170 --> 00:09:33,890
+هذا لما نفرض إن اللي هي .. اللي هي الأربعة is true
+
+117
+00:09:33,890 --> 00:09:39,150
+for N بتساوي K بدنا نثبت إن E K زائد 1 هتطلع اللي
+
+118
+00:09:39,150 --> 00:09:43,870
+هي هذهزائد x أس k على k زائد واحد فيكتوريا اللي
+
+119
+00:09:43,870 --> 00:09:48,790
+على ال net بتطلع أربعة صحيحة for k زائد واحد ده
+
+120
+00:09:48,790 --> 00:09:56,070
+نحسب خلّينا نحسب الآن E k زائد واحد of x حسب اللي
+
+121
+00:09:56,070 --> 00:10:01,370
+احنا مفترضينه أو معرفين ال sequence على أساسه E k
+
+122
+00:10:01,370 --> 00:10:04,830
+زائد واحد of x أيش بتساوي واحد زائد ال integration
+
+123
+00:10:04,830 --> 00:10:14,410
+من صفر ل X E k of T DTمظبوط؟ طيب الان بدي اعوض عن
+
+124
+00:10:14,410 --> 00:10:20,030
+E K of T احنا مفترضينها صحيحة ل K اذا E K of X
+
+125
+00:10:20,030 --> 00:10:24,230
+هيها اذا باجي بعوض بيصير Y ساوي واحد زائد ال
+
+126
+00:10:24,230 --> 00:10:29,250
+integration من صفر ل X E K of T اللي هي واحد زائد
+
+127
+00:10:29,250 --> 00:10:33,170
+T زائد T تربيع طبعا واحد فيكتوريال اللي هي واحد
+
+128
+00:10:33,170 --> 00:10:40,080
+على اتنين فيكتوريال زائد لما أصل X أو T أس Kعلى K
+
+129
+00:10:40,080 --> 00:10:46,520
+فكتوريال الكل إشماله DT لأن اللي هي أكيد وضحت
+
+130
+00:10:46,520 --> 00:10:49,660
+الصورة بدل الفاضل نطلع قيمة التفاصيل الكامل و نطلع
+
+131
+00:10:49,660 --> 00:10:54,360
+قيمة التكامل و يساوي واحد هيوزايد ما هو جاعد زاد
+
+132
+00:10:54,360 --> 00:11:00,520
+هذا ال integration اللي هو عبارة عن Tزائد T تربيع
+
+133
+00:11:00,520 --> 00:11:06,140
+على 2 في 1 يعني 2 factorial زائد T تكعيب على 3 في
+
+134
+00:11:06,140 --> 00:11:10,920
+2 factorial يعني 3 factorial زائد لما أصل لآخر 1 T
+
+135
+00:11:10,920 --> 00:11:15,640
+أُس K زائد 1 على K زائد 1 في K factorial هي K زائد
+
+136
+00:11:15,640 --> 00:11:22,230
+1 لكل factorial هذا الكلام من 0 لمين؟لعند X واضحة
+
+137
+00:11:22,230 --> 00:11:26,550
+الصورة ويساوي عبارة عن لما اعوض من 0 ل X بيصير 1
+
+138
+00:11:26,550 --> 00:11:32,090
+زائد X زائد X تربيع على 2 factorial لما أصل لأخر
+
+139
+00:11:32,090 --> 00:11:38,210
+واحد X K زائد 1 على K زائد 1فاكتوريال إذا فعلاً
+
+140
+00:11:38,210 --> 00:11:42,110
+طلعت عندي a k زائد واحد بساوي هذا المقدار يعني
+
+141
+00:11:42,110 --> 00:11:46,450
+بمعنى آخر أربعة طلعت ال true for n بتساوي k زائد
+
+142
+00:11:46,450 --> 00:11:51,830
+واحد إذا من كل هذا ال induction بنكون أثبتنا أن e
+
+143
+00:11:51,830 --> 00:11:56,430
+n of x بساوي هذا الكلام لكل x element in R لكل n
+
+144
+00:11:56,430 --> 00:12:00,630
+element in Nإذاً هذه صورة اللي هي الـEN of X صورة
+
+145
+00:12:00,630 --> 00:12:05,150
+غير الصورة اللي عرفناها فوق استنتجناها منها الآن
+
+146
+00:12:05,150 --> 00:12:11,770
+خلّينا نروح باتجاه إثبات إنه ال limit للـEN هذه أو
+
+147
+00:12:11,770 --> 00:12:17,910
+الـEK أو الـEN أو اللي هي is uniformly convergent
+
+148
+00:12:18,680 --> 00:12:23,900
+to some function هذه الـ some function هي اللي
+
+149
+00:12:23,900 --> 00:12:29,120
+بتدعي انها هتكون ال exponential طيب اللي بنسميها
+
+150
+00:12:29,120 --> 00:12:32,840
+exponential بعد شوية اللي هي بتحقق شرطين اللي
+
+151
+00:12:32,840 --> 00:12:35,400
+حكينا عنهم لسه احنا بنعرف ال exponential احنا
+
+152
+00:12:35,400 --> 00:12:38,340
+بنعرف الدالة هذه لكن لأن معلوماتنا عارفين من اول
+
+153
+00:12:38,340 --> 00:12:43,000
+ال exponentialالان احنا الدالة هذه اللى هنثبت
+
+154
+00:12:43,000 --> 00:12:46,540
+وجودها اليوم هي اللى بعد شوية بعد ما نثبت ال
+
+155
+00:12:46,540 --> 00:12:50,880
+uniqueness لها بنسميها ال exponential زي ما هنشوف
+
+156
+00:12:50,880 --> 00:12:56,620
+بعد شوية الان اذا ال sequence اللى عندى هذه
+
+157
+00:12:56,620 --> 00:13:05,300
+هيوضعها الان قلنا E Nof X هذه المعادلة التانية هي
+
+158
+00:13:05,300 --> 00:13:11,560
+واحد زائد X زائد X تربيع على اتنين factorial زائد
+
+159
+00:13:11,560 --> 00:13:15,600
+X أُس N على N factorial وهذا الشكل طبعا أنتوا مش
+
+160
+00:13:15,600 --> 00:13:20,240
+غريب عليكم بتعرفوه الآن خليني أخد الان let A أكبر
+
+161
+00:13:20,240 --> 00:13:24,120
+من سفر بيه given افترض ان A اني اللي هو real
+
+162
+00:13:24,120 --> 00:13:28,660
+number أكبر من مين من سفر باخده arbitrarily لكن
+
+163
+00:13:28,660 --> 00:13:33,470
+خليني نحكي عن A محددةالان if absolute value of X
+
+164
+00:13:33,470 --> 00:13:37,910
+أصغر أو تساوي A يعني بتحكي الحديث هان على ال Xات
+
+165
+00:13:37,910 --> 00:13:43,590
+اللي في ال R اللي من عند ناقص A لعند مين ال A يعني
+
+166
+00:13:43,590 --> 00:13:48,610
+ال absolute value لهن هذولة أصغر أو تساوي ال A
+
+167
+00:13:48,610 --> 00:13:52,390
+يعني في الفترة المغلقة اللي أمامي اللي بين ناقص ال
+
+168
+00:13:52,390 --> 00:13:58,870
+A و ال A بتتحدث شوف الآن احسبلي Em of X ناقص En of
+
+169
+00:13:58,870 --> 00:14:03,750
+Xو يساوي و بدنا نفترض لكم ان الان ايه شمالها اكبر
+
+170
+00:14:03,750 --> 00:14:07,910
+من الان و الان اكبر من اتنين ايه اتنين ايه مكتوب
+
+171
+00:14:07,910 --> 00:14:10,850
+اتنين ايه لغرض الحسابات اللي جيت منشوفها بنفع
+
+172
+00:14:10,850 --> 00:14:13,270
+تلاتة ايه، بنفع اربعة ايه، بنفع خمسة ايه، بنفع ستة
+
+173
+00:14:13,270 --> 00:14:16,550
+ايه، بنفع كله بنفع هذا الكلام على اساس انك ماينفعش
+
+174
+00:14:16,550 --> 00:14:19,550
+اقول نص ايه او تلت ايه او ربع ايه لأنها مش هتقد
+
+175
+00:14:19,550 --> 00:14:23,910
+الغرض اللي بدي انالأن مين اخترت أنا اخترت اللي هو
+
+176
+00:14:23,910 --> 00:14:29,650
+الأمات والأنات اللي أكبر منين من اتنين في الـA
+
+177
+00:14:29,650 --> 00:14:34,390
+اللي هي قيبة مين الـA اللي هي نص الفترة اللي عندي
+
+178
+00:14:34,390 --> 00:14:39,210
+أو طول نص الفترة طيب، احسبلي ايه M of X ناقص Y of
+
+179
+00:14:39,210 --> 00:14:44,360
+X؟E M of X اللي هي عبارة عن واحد زائد X زائد X
+
+180
+00:14:44,360 --> 00:14:49,360
+تربيع و هجابل في الطريق من ال X M لأنه M أكبر X
+
+181
+00:14:49,360 --> 00:14:52,720
+تربيع على M فكتوريال زائد X M زائد واحد على M زائد
+
+182
+00:14:52,720 --> 00:14:57,280
+واحد فكتوريال لما أصل الأخر واحدة من X أُس M على M
+
+183
+00:14:57,280 --> 00:15:03,400
+فكتوريال يعني الآن هذي هيكون زي هيك لما أصل طبعا X
+
+184
+00:15:03,400 --> 00:15:10,500
+M زائد واحد على Mزائد واحد factorial زائد لمّا أصل
+
+185
+00:15:10,500 --> 00:15:15,760
+لعند X أُس M على M factorial هذه مين هي هذه عبارة
+
+186
+00:15:15,760 --> 00:15:24,220
+عن ال EM يعني ال EM هتساوي اللي هي E of XE N of X
+
+187
+00:15:24,220 --> 00:15:30,020
+زائد المتبقي هذا الان حاصل طرح الاتنتين هيكون
+
+188
+00:15:30,020 --> 00:15:33,480
+عبارة عن لإن المفترض ال M أكبر من L زي ما قلنا
+
+189
+00:15:33,480 --> 00:15:37,700
+حاصل طرح اللي هيكون اللي هو المتبقي هذا X N زائد
+
+190
+00:15:37,700 --> 00:15:40,840
+واحد على N زائد واحد فيكتوريال لما أصل ل X M على M
+
+191
+00:15:40,840 --> 00:15:46,240
+إيش فيكتوريال ماشي الحال إذا الأن أوصلنا لحاصل طرح
+
+192
+00:15:46,240 --> 00:15:51,340
+دولة بساوي هذا المقدر نيجي نكمل الأن عندي
+
+193
+00:15:53,560 --> 00:15:58,460
+عند ال absolute value لل X أصغر من 100 من A
+
+194
+00:16:10,590 --> 00:16:17,130
+زائد absolute value زائد xn زائد اتنين على n زائد
+
+195
+00:16:17,130 --> 00:16:22,710
+اتنين factorial زائد لما أصل لأخر واحد x أسم م على
+
+196
+00:16:22,710 --> 00:16:28,150
+m factorial ماشي الحال طيب الآن ان ان كل x من
+
+197
+00:16:28,150 --> 00:16:31,270
+هدولة ال absolute value هي أصغر يساوي منين ايه إذا
+
+198
+00:16:31,270 --> 00:16:36,650
+صار هذا المقدار أصغر أو يساوي هذا المقدار اللي هنا
+
+199
+00:16:36,650 --> 00:16:45,550
+أصغر أو يساوي Mزائد واحد على N آسف A أُس N زائد
+
+200
+00:16:45,550 --> 00:16:49,970
+واحد لأن ال absolute value X أصغر تساوي A إذا X N
+
+201
+00:16:49,970 --> 00:16:54,510
+زائد واحد أصغر أو ساوي ال A أُس N زائد واحد على N
+
+202
+00:16:54,510 --> 00:17:00,870
+زائد واحد factorial زائد التاني اللي هو A N زائد
+
+203
+00:17:00,870 --> 00:17:07,130
+اتنينعلى n زائد 2 factorial زائد لما أصل لآخر واحد
+
+204
+00:17:07,130 --> 00:17:14,870
+اللي هو عبارة عن a أس m على m factorial ماشي الحال
+
+205
+00:17:14,870 --> 00:17:21,080
+طيبالان خليني اخد من هدولة ال a n زائد واحد على ال
+
+206
+00:17:21,080 --> 00:17:24,480
+n زائد واحد factorial عامل مشترك قبل ما اصلح هذه
+
+207
+00:17:24,480 --> 00:17:28,520
+الخطوة لسه اه خليني اخد عامل مشترك بيصير عندي a n
+
+208
+00:17:28,520 --> 00:17:33,180
+زائد واحد على n زائد واحد factorial فاش اللي بيضل
+
+209
+00:17:33,180 --> 00:17:39,420
+هنا فيه اللي بيضل هنا واحد زائد هنا بيضل a على n
+
+210
+00:17:39,420 --> 00:17:46,280
+زائد اتنين اكيد زائد اللي بعدها a تربيع على nزائد
+
+211
+00:17:46,280 --> 00:17:52,160
+اتنين فان زائد تلاتة زائد لما أصل لآخر واحد مين
+
+212
+00:17:52,160 --> 00:17:57,080
+آخر واحد بشيل منه ان زائد واحد بيصير a أس ام ناقص
+
+213
+00:17:57,080 --> 00:18:03,000
+ان ناقص واحد على اللي بيضل من ان زائد اتنين مضروب
+
+214
+00:18:03,000 --> 00:18:09,250
+لعند ان ام ناقص ان ناقص واحد هذول الأنماشي الحال
+
+215
+00:18:09,250 --> 00:18:13,470
+هذا أخد تمين يا جماعة ماعليش دخل الكلام مع بعضه بس
+
+216
+00:18:13,470 --> 00:18:18,130
+أكيد أنتوا مستوعبين إيش بقول طلعت ال a n زائد واحد
+
+217
+00:18:18,130 --> 00:18:21,090
+على n زائد واحد في كتوريا العام المشترك طلع عندي
+
+218
+00:18:21,090 --> 00:18:26,550
+هذا المقدار الان عندي أكيد ال n زائد اتنين أكبر من
+
+219
+00:18:26,550 --> 00:18:32,050
+مين من ال end فمقلوبه أصغرأه فبصير عندى اللى هو
+
+220
+00:18:32,050 --> 00:18:38,050
+عندى اللى هى هذا المقدار a n على l زائد 2 أصغر أو
+
+221
+00:18:38,050 --> 00:18:42,170
+شاوي a على n و اللى بعده a تربيع أصغر أو شاوي ا ا
+
+222
+00:18:42,170 --> 00:18:44,370
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+223
+00:18:44,370 --> 00:18:44,410
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+224
+00:18:44,410 --> 00:18:45,090
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+225
+00:18:45,090 --> 00:18:46,010
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+226
+00:18:46,010 --> 00:18:47,730
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+227
+00:18:47,730 --> 00:18:48,010
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+228
+00:18:51,320 --> 00:18:55,380
+أكبر من أنه وهذه أكبر من أنه فمقلوبهم بيصير هذا
+
+229
+00:18:55,380 --> 00:19:00,980
+المقدار أصغر اللي هو أو يساوي المقدار اللي بعده
+
+230
+00:19:00,980 --> 00:19:07,730
+بيصير عندى هذا المقدارأصغر أو يساوي هذا زي ما هو و
+
+231
+00:19:07,730 --> 00:19:13,670
+هذه واحد هذه a على n لأنها هتكون أكبر a تربيع على
+
+232
+00:19:13,670 --> 00:19:19,170
+n تربيع ان تربيع هتكبر لما أصل ل a m minus n نقص
+
+233
+00:19:19,170 --> 00:19:25,420
+واحد على m minus n نقص واحد لأن هنا دولة عددهمن
+
+234
+00:19:25,420 --> 00:19:30,200
+نقص واحد من الانز هيكون ان طبعا استبدالت كل واحدة
+
+235
+00:19:30,200 --> 00:19:34,400
+بان فهيطلع بالشكل هذا وبتظل ال inequality صحيحة
+
+236
+00:19:34,400 --> 00:19:38,540
+خلصنا من هذا طيب دعونا نشوف كيف أضبح لكم هذا دعونا
+
+237
+00:19:38,540 --> 00:19:48,770
+نخلص منه نجي الآن اللي هو نرجعانكمل الحسبة هذا
+
+238
+00:19:48,770 --> 00:19:57,670
+الان المقدار عندى اللى هو المقدار هذا هيه اتطلعوا
+
+239
+00:19:57,670 --> 00:20:06,710
+عندى ال a ال a على n ايش انا ماخد ال n ماخد ال n
+
+240
+00:20:06,710 --> 00:20:12,930
+اكبر من مين من اتنين a يعني ال a اصغر من n على مين
+
+241
+00:20:13,680 --> 00:20:21,900
+على اتنين مظبوط ال A أصغر من N على اتنين واضحة جسم
+
+242
+00:20:21,900 --> 00:20:25,660
+ال N على اتنين و N على اتنين صارت N على اتنين أكبر
+
+243
+00:20:25,660 --> 00:20:29,940
+من مين من ايه بدي استخدمها الآن هذه ال N بصير أصغر
+
+244
+00:20:29,940 --> 00:20:34,020
+أو يساوي هذا المقدار بصير أصغر أو يساوي هذا بحكي
+
+245
+00:20:34,020 --> 00:20:39,590
+عن هذا بصير أصغر أو يساوي اللي هو Aأُس ان زائد
+
+246
+00:20:39,590 --> 00:20:45,410
+واحد على ان زائد واحد الكل فكتوريال فيه اللي هو
+
+247
+00:20:45,410 --> 00:20:56,830
+واحد زائد ا على ان زائد ا تربية على ان تربية زائد
+
+248
+00:20:56,830 --> 00:21:06,530
+ا اللي هو ا تكعيب على ان تكعيبزائد مش بتصل لهذا
+
+249
+00:21:06,530 --> 00:21:11,670
+زائد و بتظل ماشيها يشمالها إلى ما لا نهاية يعني
+
+250
+00:21:11,670 --> 00:21:17,110
+بتضيف عليها a على n أس ام ناقص n a على n أس ام
+
+251
+00:21:17,110 --> 00:21:20,290
+ناقص n زائد واحد وهكذا تظلها إلى ما لا نهاية يعني
+
+252
+00:21:20,290 --> 00:21:23,850
+بتحولها لمين ل infinite series طيب احنا قلنا ال a
+
+253
+00:21:23,850 --> 00:21:28,670
+أصغر من n على 2يعني ال a n على n أصغر من مين؟ من
+
+254
+00:21:28,670 --> 00:21:32,930
+نص عرفته الأن إيش بدأ أسأل صار عندي هذا المقدار
+
+255
+00:21:32,930 --> 00:21:39,310
+أصغر أو يساوي a أس n زائد واحد على n زائد واحد لكل
+
+256
+00:21:39,310 --> 00:21:45,690
+factorial مضروب في مين؟ اللي هو واحد زائد نص زائد
+
+257
+00:21:45,690 --> 00:21:50,670
+نص تربيع أه لأن a على n أصغر من مين يا جماعة؟ من
+
+258
+00:21:50,670 --> 00:21:57,850
+نص زائدتربيع زاد نص تتعيد زاد الآخرين لأن هذه صارت
+
+259
+00:21:57,850 --> 00:22:02,470
+عبارة عن geometric series مجموحها هذه بتساوي مجموح
+
+260
+00:22:02,470 --> 00:22:07,050
+هذه عبارة عن واحد على واحد ناقصه اللي هو نص وهي
+
+261
+00:22:07,050 --> 00:22:12,730
+ساوي جداش اتنينماشي إذا هذا المقدار اللي هو صار
+
+262
+00:22:12,730 --> 00:22:16,510
+عبارة عن اتنين في هذا المقدار اللي هو وصلنا له
+
+263
+00:22:16,510 --> 00:22:20,650
+أصغر أو يساوي a n زائد واحد على n زائد واحد
+
+264
+00:22:20,650 --> 00:22:23,890
+فيكتوريا مضروب في مين؟ في اتنين يعني حسابات هذه
+
+265
+00:22:23,890 --> 00:22:28,770
+طيب إذا صار عندي الآن هاي اللي بدي أصله و اللي
+
+266
+00:22:28,770 --> 00:22:31,630
+كاتبه باختصار هو لإنه بيعتبر ان الباقية حساباتي
+
+267
+00:22:31,630 --> 00:22:36,950
+بتعرفوا تحسبوها em-n of x of x أصغر أو يساوي هذا
+
+268
+00:22:36,950 --> 00:22:43,450
+المقدار على مين؟ على اتنينالان شوف ما يليه الان as
+
+269
+00:22:43,450 --> 00:22:49,590
+n goes to infinity هذا المقدار هذا المقدار as n
+
+270
+00:22:49,590 --> 00:22:54,230
+goes to infinity ال limit بتروح للصفر لأن a n زائد
+
+271
+00:22:54,230 --> 00:22:57,110
+واحد على n زائد واحد كل factorial as n goes to
+
+272
+00:22:57,110 --> 00:23:01,190
+infinity ايش بده يروح للصفر يعني بمعنى اخر مدام
+
+273
+00:23:01,190 --> 00:23:04,430
+بده يروح للصفر طبعا وذا كبرت الان بتكبر مين برضه
+
+274
+00:23:04,430 --> 00:23:07,850
+مباشرة ام لأن ام اكبر منها اذا four
+
+275
+00:23:10,880 --> 00:23:19,800
+for large ن و أم we get
+
+276
+00:23:23,490 --> 00:23:31,050
+E M of X ناقص E N of X اللي هي أصغر أو يساوي من
+
+277
+00:23:31,050 --> 00:23:38,070
+هذه هذه أصلا for large N as N goes to infinity هذا
+
+278
+00:23:38,070 --> 00:23:43,470
+المقدار بيصير أصغر من أي ي في الدنيا اللي هي بيصير
+
+279
+00:23:43,470 --> 00:23:49,330
+أصغر من مين من ي أو أصغر أو يساوي ي as N و M
+
+280
+00:23:49,330 --> 00:23:54,630
+become very very largeماشي الحال لإنه ال limit لل
+
+281
+00:23:54,630 --> 00:23:59,110
+a n على n فكتوره ليش بيساوي بيساوي سفر إذا صار
+
+282
+00:23:59,110 --> 00:24:05,950
+عندي الآن اللي هي E m of X E n of X أصغر وشوى Y
+
+283
+00:24:05,950 --> 00:24:15,250
+لكل X وين موجودة في الفترة A ماقص A أو A ماشي
+
+284
+00:24:15,250 --> 00:24:23,160
+الحال الآن بناء عليهالان لكل X بغض النظر على ال X
+
+285
+00:24:23,160 --> 00:24:28,000
+اللي هو بيكون عندي أنه I'm very large وبيعطيني هذا
+
+286
+00:24:28,000 --> 00:24:32,560
+أصغر وسوء من إبسلون وهذه اللي سميناها Cauchy's
+
+287
+00:24:32,560 --> 00:24:37,470
+criterion for uniformاللي هو convergence في ال ..
+
+288
+00:24:37,470 --> 00:24:43,590
+اللي هو section 81 بناء عليها بطلع عندى E and اللي
+
+289
+00:24:43,590 --> 00:24:47,090
+هو converges uniformly to some function مش
+
+290
+00:24:47,090 --> 00:24:51,410
+عارفينها اللي هي .. اللي هي converges uniformly on
+
+291
+00:24:51,410 --> 00:24:59,770
+mean سالب a أو a باشي الحالة الالالآن عندي it
+
+292
+00:24:59,770 --> 00:25:02,610
+follows the sequence a and a converge uniformly on
+
+293
+00:25:02,610 --> 00:25:07,210
+the interval ناقص a و a where a أكبر من 0 لكن a
+
+294
+00:25:07,210 --> 00:25:11,670
+أكبر من 0 was a شمالها arbitrarily يعني اللي وصلنا
+
+295
+00:25:11,670 --> 00:25:18,110
+له ما ياليا يا جماعة اللي وصلنا له أنهعندي اللي هي
+
+296
+00:25:18,110 --> 00:25:23,210
+الـ sequence هذه لو جيت أخدت for every a element
+
+297
+00:25:23,210 --> 00:25:27,130
+in R و a أكبر من سفر لو وصلنا له اللي كانت a
+
+298
+00:25:27,130 --> 00:25:32,130
+arbitrarily وجدنا أنه هيكون عند الـ EL converges
+
+299
+00:25:32,130 --> 00:25:39,550
+uniformly on ماقص a و مين و a ماشي الحال طيب بناء
+
+300
+00:25:39,550 --> 00:25:48,200
+عليه لو أنت جيت أخدت خد الآن letX element in R، أي
+
+301
+00:25:48,200 --> 00:25:53,540
+X element in R، مدام X في R، إذا أكيد الـ X عشر،
+
+302
+00:25:53,540 --> 00:25:59,250
+عشرين، تلاتين، مليون، ممكن ما تكون،بقدر ألاقي A
+
+303
+00:25:59,250 --> 00:26:05,890
+بحيث أن X تنتمي إلى الفترة من ناقص A لعند مين لعند
+
+304
+00:26:05,890 --> 00:26:11,590
+إيه يعني مثلا ال X لجيتها 100 باخد ال A 110 بصير
+
+305
+00:26:11,590 --> 00:26:17,850
+ال X بين اللي هي ناقص 110 و100 إيش ما تيجي X بلاقي
+
+306
+00:26:17,850 --> 00:26:24,470
+لها Aإذا there exists a such that x element in a
+
+307
+00:26:24,470 --> 00:26:31,410
+minus a أكبر من صفر طبعا minus a ومين أو a أكيد طب
+
+308
+00:26:31,410 --> 00:26:34,390
+ما هو احنا قد أثبتنا انه لكل a element in R
+
+309
+00:26:38,870 --> 00:26:44,730
+Converge uniformly للـ A اللي لاجناها هذه On ناقص
+
+310
+00:26:44,730 --> 00:26:49,690
+A و A لهذه الـ A يعني بمعنى معناه مادام Converge
+
+311
+00:26:49,690 --> 00:26:55,030
+uniformly لإذا E N of Xاللي هو converges point
+
+312
+00:26:55,030 --> 00:26:58,250
+-wise to some function عند مين؟ عند الـ X اللي
+
+313
+00:26:58,250 --> 00:27:03,670
+أخدتها هانا هذه إذا الأن for any X element in R
+
+314
+00:27:03,670 --> 00:27:11,450
+for any X element in R هنلاقي E N of X convergesما
+
+315
+00:27:11,450 --> 00:27:15,250
+دام ال E N of X is convergent for every X element
+
+316
+00:27:15,250 --> 00:27:22,230
+in R إذا صارت عندي limit ال E N of X as N goes to
+
+317
+00:27:22,230 --> 00:27:27,830
+infinity exists for every X element in R ما دام
+
+318
+00:27:27,830 --> 00:27:34,210
+exist حسب اللي قلناها إذا الآن شرعت لتعريف الدالة
+
+319
+00:27:34,210 --> 00:27:40,600
+التالية الآن أنا بقول إنه احنا صار عندنااللي هو
+
+320
+00:27:40,600 --> 00:27:47,760
+مشروع ان نقول we define E من R لR by limit E N of
+
+321
+00:27:47,760 --> 00:27:53,940
+X اللي هي موجودة سميتها إيش اسمها E of X for X
+
+322
+00:27:53,940 --> 00:28:00,760
+element of Rوجود اللي هو دالة اسمها E أنا سميتها E
+
+323
+00:28:00,760 --> 00:28:06,400
+من R لعند R بحيث ان E of X هي limit ال E أنه VIX
+
+324
+00:28:06,400 --> 00:28:11,480
+اللي أثبتت وجوده بدي أثبتلك الأن أن E of X هذه هي
+
+325
+00:28:11,480 --> 00:28:16,120
+الدالة المبتغة اللي بتحقق الشروط اللي طلبها في
+
+326
+00:28:16,120 --> 00:28:21,740
+النظرية نشوف كيف طيب صلوا على النبي عليه الصلاة
+
+327
+00:28:21,740 --> 00:28:22,160
+والسلام
+
+328
+00:28:35,970 --> 00:28:39,830
+الان عندى ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+329
+00:28:39,830 --> 00:28:39,910
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+330
+00:28:39,910 --> 00:28:39,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+331
+00:28:39,970 --> 00:28:40,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+332
+00:28:40,290 --> 00:28:42,410
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+333
+00:28:42,410 --> 00:28:42,810
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+334
+00:28:42,810 --> 00:28:44,810
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+335
+00:28:44,810 --> 00:28:49,770
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+336
+00:28:49,770 --> 00:28:51,450
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+337
+00:28:51,450 --> 00:28:51,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+338
+00:28:51,610 --> 00:28:52,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+339
+00:28:52,610 --> 00:28:55,710
+.. ال ..
+
+340
+00:29:00,330 --> 00:29:06,370
+converge such that x element ناقص a أو a كلها هذه
+
+341
+00:29:06,370 --> 00:29:12,330
+الـen converged uniformly الان لمن؟ للـe معايا
+
+342
+00:29:12,330 --> 00:29:19,190
+converged uniformly للـe for every أو on ناقص a أو
+
+343
+00:29:19,190 --> 00:29:23,010
+a لأنه سمناها إيش اللي هي ال limit بتروحلها اسمها
+
+344
+00:29:23,010 --> 00:29:27,670
+إيه الآن en اتفجنا إنه أثبتناها إنها إيش معالها
+
+345
+00:29:28,810 --> 00:29:34,050
+continuous مادام continuous و en اللي هو طبعا
+
+346
+00:29:34,050 --> 00:29:36,330
+continuous مش بس على ناقص a و a continuous وين
+
+347
+00:29:36,330 --> 00:29:39,690
+مكان احنا الآن هنحكي عن ناقص a و a continuous صارت
+
+348
+00:29:39,690 --> 00:29:42,910
+ال en continuous sequence converts uniformly to e
+
+349
+00:29:42,910 --> 00:29:48,110
+على ناقص a و a إذا صارت ال e هذه حسب نظريتنا هتكون
+
+350
+00:29:48,110 --> 00:29:53,560
+continuous نظرية الأولىفي سيكشن 8 اللي هو 2 هتكون
+
+351
+00:29:53,560 --> 00:29:57,800
+الـ E is continuous على ناقص A و A قولنا if E N is
+
+352
+00:29:57,800 --> 00:30:00,200
+a sequence of continuous functions that converge
+
+353
+00:30:00,200 --> 00:30:03,200
+uniformly to some function then this function or
+
+354
+00:30:03,200 --> 00:30:06,880
+some function is continuous on ناقص A و Eإذا صارت
+
+355
+00:30:06,880 --> 00:30:10,200
+ال E continuous على نقص A و A يعني ال E continuous
+
+356
+00:30:10,200 --> 00:30:14,520
+عند من؟ عند ال X و since X was arbitrary in R then
+
+357
+00:30:14,520 --> 00:30:21,180
+E هتكون is continuous على كل ال R إذا صارت عندي E
+
+358
+00:30:21,180 --> 00:30:26,560
+is continuous at any X element in R الآن لو جينا
+
+359
+00:30:26,560 --> 00:30:31,600
+حسبنا ال E N of 0 و E 1 of 0 و E 1 of 0 أشو
+
+360
+00:30:31,600 --> 00:30:39,410
+بالساوية؟ هي واحدE اللي هو N زائد واحد of Zero
+
+361
+00:30:39,410 --> 00:30:45,630
+اللي هو بساوي من سفر لسفر هيطلع سفر وهذا واحد يعني
+
+362
+00:30:45,630 --> 00:30:52,470
+دايما ال E N of Zero هتطلع إيش؟ Zero مدام E N of
+
+363
+00:30:52,470 --> 00:31:00,670
+Zero Zero وبما أنه E is continuous إذن limit ال Eن
+
+364
+00:31:00,670 --> 00:31:05,930
+of zero as n goes to infinity بسوء اللي هو E of
+
+365
+00:31:05,930 --> 00:31:10,990
+zero أو E of X أسف E of X as n goes to infinity
+
+366
+00:31:10,990 --> 00:31:18,450
+بسوء E of X وبما أنه اللي هواللي هي ال ال ال ال ال
+
+367
+00:31:18,450 --> 00:31:20,590
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+368
+00:31:20,590 --> 00:31:21,370
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+369
+00:31:21,370 --> 00:31:22,190
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+370
+00:31:22,190 --> 00:31:25,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+371
+00:31:25,670 --> 00:31:30,470
+ال ال ال ال ال ال ال ال ال ال
+
+372
+00:31:30,470 --> 00:31:32,430
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+373
+00:31:32,430 --> 00:31:32,790
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+374
+00:31:32,790 --> 00:31:32,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+375
+00:31:32,950 --> 00:31:35,550
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+376
+00:31:35,550 --> 00:31:39,680
+ال الأنا كنت بخلطها أنا بقول E n of 0 بساوي 1
+
+377
+00:31:39,680 --> 00:31:43,540
+limit E n of X بساوي E of X وال E is continuous
+
+378
+00:31:43,540 --> 00:31:48,900
+إذا الحيكون ال E of 0 هذه هتساوي إيش؟ هيساوي 1
+
+379
+00:31:48,900 --> 00:31:53,800
+لأنه limit E n of 0 point twice بساوي E of 0 اللي
+
+380
+00:31:53,800 --> 00:31:58,580
+هي 0الان e n of zero بتساوي واحد for all and infim
+
+381
+00:31:58,580 --> 00:32:04,940
+therefore e of zero بتساوي واحد لإن اللي هي e
+
+382
+00:32:04,940 --> 00:32:11,240
+نفسها is continuous إذا حصلنا على اللي هو الجزء
+
+383
+00:32:11,240 --> 00:32:16,080
+الأول أذكركم في الظاهرية على اللي هو المطلوب أو
+
+384
+00:32:16,080 --> 00:32:20,770
+الخاصية الأولىالخاصية الأولى هى الخاصية الأولى هى
+
+385
+00:32:20,770 --> 00:32:25,430
+عندى أثبتنا .. التانى أسف أثبتنا E اللى هى E of
+
+386
+00:32:25,430 --> 00:32:29,370
+Zero بالساوية واحدة بدى أثبتلك الأن E prime of X
+
+387
+00:32:29,370 --> 00:32:34,750
+هتساوي E of X عشان أثبتها بدنا نذكركم في نظرية
+
+388
+00:32:34,750 --> 00:32:45,750
+أخدناها المرة الماضية اللى هى بتقول ما يليه أذكركم
+
+389
+00:32:45,750 --> 00:32:51,350
+يا جماعةبالنظرية اللي بستخدمها كانت ان عندي لو في
+
+390
+00:32:51,350 --> 00:32:56,330
+عندي fn sequence of functions و هذه fn ال
+
+391
+00:32:56,330 --> 00:33:00,050
+differentiable لأن fn برايم بتروح ل g uniformly
+
+392
+00:33:00,050 --> 00:33:08,330
+ماشي on some interval on some j وكان عندي fn of x
+
+393
+00:33:08,330 --> 00:33:11,050
+not converge
+
+394
+00:33:12,940 --> 00:33:21,240
+converts to f of x not مثلا on j اه for x not
+
+395
+00:33:21,240 --> 00:33:31,300
+element in j then بقول لي اللي هو ال f هذه f prime
+
+396
+00:33:31,300 --> 00:33:39,230
+existsو FN converts uniformly to this F او FN
+
+397
+00:33:39,230 --> 00:33:46,950
+converts uniformly to this F and F' هي مين هي الـ
+
+398
+00:33:46,950 --> 00:33:50,370
+G هذا حكيناه المرة الماضية طيب، بدأ استخدمها الآن
+
+399
+00:33:50,370 --> 00:33:54,510
+شوف عنده، ان شوف عنده الـ N أثبتنا او الـ N
+
+400
+00:33:54,510 --> 00:33:57,110
+interval لاقصية و ايه؟ we have the uniform
+
+401
+00:33:57,110 --> 00:34:02,350
+convergence of the sequence EN اللي هو هتكون EN
+
+402
+00:34:04,720 --> 00:34:12,400
+converge uniformly ماشي الحالة of you of me of
+
+403
+00:34:12,400 --> 00:34:15,900
+تلاتة اللي هو تلاتة اللي حكيناها قبل بشوية خليني
+
+404
+00:34:15,900 --> 00:34:21,540
+بس نذكركم فيها اللي هي تلاتة هي عندي اللي هي تلاتة
+
+405
+00:34:21,840 --> 00:34:25,980
+عندي الان conversion formally to some function E
+
+406
+00:34:25,980 --> 00:34:30,140
+سمناها الان بناء عليه بدلا من الان زائد واحد هي
+
+407
+00:34:30,140 --> 00:34:34,820
+سافسة الان إذا صارت الان زائد واحد prime برضه
+
+408
+00:34:34,820 --> 00:34:38,140
+conversion هادي هادي أصلا conversion formally to
+
+409
+00:34:38,140 --> 00:34:46,280
+مين؟ to ال E اللي عندي الان وضحت الصورة الان صارت
+
+410
+00:34:46,280 --> 00:34:53,410
+الصورة واضحة الان اللي حصلنا انهانتبه عليا، on any
+
+411
+00:34:53,410 --> 00:34:56,010
+interval ناقص a و a, we have the inferred
+
+412
+00:34:56,010 --> 00:35:01,170
+convergence of E n وفي ضوء اللي هو تلاتة, we also
+
+413
+00:35:01,170 --> 00:35:04,290
+have the inferred convergence E n prime of the
+
+414
+00:35:04,290 --> 00:35:08,350
+derivatives الآن من ال theorem 8.2.3 اللي حكيتها
+
+415
+00:35:08,350 --> 00:35:13,700
+هنا، مدام F n prime converges ل Gماشي الحال و ال
+
+416
+00:35:13,700 --> 00:35:17,160
+.. او ال Fn X0 بتروح ل F of X0 for X0 اللي بتنجح
+
+417
+00:35:17,160 --> 00:35:21,880
+اللي هو اكتر من النقطة و اصلا على اساس عرفنا ان Fn
+
+418
+00:35:21,880 --> 00:35:27,420
+of X بالساوي اللي هو مين E of X بتروح لمين لل E of
+
+419
+00:35:27,420 --> 00:35:31,780
+X اذا اكيد هذه متحققة كمان بالنسبة لمين لل E N
+
+420
+00:35:31,780 --> 00:35:36,760
+صارت هذه متحققة و هذه متحققة من التحقق هذههذه يا
+
+421
+00:35:36,760 --> 00:35:42,140
+عزيزي التحقق هذه إذا إذا هيكون عنده ال F N بتروح
+
+422
+00:35:42,140 --> 00:35:46,020
+لل F اللي هي ال E N بتروح لل E صنادر أثبتناها بس
+
+423
+00:35:46,020 --> 00:35:51,720
+إيش المهم أنه ال F prime لهذه اللي بتروحلها هذه
+
+424
+00:35:51,720 --> 00:35:57,080
+اللي هي ال E prime هي مين اللي هي اللي بتروحلها ال
+
+425
+00:35:57,080 --> 00:36:02,340
+E N ال F ال F N prime عند ال E N زائد واحد prime
+
+426
+00:36:02,340 --> 00:36:03,260
+بتروح لل E
+
+427
+00:36:06,460 --> 00:36:13,560
+إذا من نظرية إيان ستذهب إلى الـ E برضه وليس كذلك
+
+428
+00:36:13,560 --> 00:36:20,250
+الـ E' لهذههي هذه يعني بمعنى آخر E N زي دول برايم
+
+429
+00:36:20,250 --> 00:36:25,830
+برايم limitها ال E برايم زي ما هي مين ال E يعني
+
+430
+00:36:25,830 --> 00:36:29,950
+مدام الان limitها هي ال E و هي نفسها limitها من
+
+431
+00:36:29,950 --> 00:36:33,370
+النظرية اللي بنستنتجها E برايم إذا صارت ال E هي
+
+432
+00:36:33,370 --> 00:36:38,610
+مين ال E برايم أو بطريقة أخرى limit ال E N برايم
+
+433
+00:36:38,610 --> 00:36:43,440
+حسب النظرية بتساوي ال E برايمومن جهة أخرى limit en
+
+434
+00:36:43,440 --> 00:36:50,500
+براي هو نفسه limit en نفسهاو limit en اللي هي طبعا
+
+435
+00:36:50,500 --> 00:36:53,280
+انا مسميها n و n نقص واحد احنا مسميينها n و n زاد
+
+436
+00:36:53,280 --> 00:36:57,740
+واحد طبيعي en برايم هي limit من limit en نقص واحد
+
+437
+00:36:57,740 --> 00:37:02,620
+لحالها لأن هذه بتساوي هذه و هذه اصلا limit احنا
+
+438
+00:37:02,620 --> 00:37:07,140
+اثبتنا ايش بساوي ال E اذا صارت عند ال E برايم هي
+
+439
+00:37:07,140 --> 00:37:10,720
+ايش بتساوي ال E يعني هذه ال E برايم استنتاجا من
+
+440
+00:37:10,720 --> 00:37:16,260
+النظريةو هذه اللي هو من اللي أثبتنا في البداية و
+
+441
+00:37:16,260 --> 00:37:19,800
+أيضا نقدر نستخدم .. لسه نتجه من النظرية لكن أحنا
+
+442
+00:37:19,800 --> 00:37:25,540
+أثبتنا فيها قبل ما نستعمل المظلةطيب هذا الكلام
+
+443
+00:37:25,540 --> 00:37:30,680
+صحيح وين لكل x وين موجودة في ناقص a و a لكن a احنا
+
+444
+00:37:30,680 --> 00:37:35,600
+أخدناها أجمالها arbitrary يعني الآن بيصير عندي
+
+445
+00:37:35,600 --> 00:37:40,740
+اللي هو لكل x بلقي لواحدة زي هيك بتحقق الكلام هذا
+
+446
+00:37:40,740 --> 00:37:44,560
+الآن فبصير عندي a prime of x بسوية of x لكل x
+
+447
+00:37:44,560 --> 00:37:50,720
+element in R وهيك بيكون احنا أثبتنا وجود اللي هو
+
+448
+00:37:50,720 --> 00:37:58,390
+ال E of Xأثبتنا وجود دالة أثبتنا
+
+449
+00:37:58,390 --> 00:38:06,100
+وجود دالة سمناها E of Xهذه الدالة بتحقق شرطين اللي
+
+450
+00:38:06,100 --> 00:38:11,900
+هو E prime of X بساوي E of X وبتحقق الشرط التاني E
+
+451
+00:38:11,900 --> 00:38:20,680
+of 0 بساوي 1 السؤال الآن هل في غيرها؟ هل في غيرها
+
+452
+00:38:20,680 --> 00:38:25,860
+ولا لأ؟ طبعا لحظة الحظ أنه لا يوجد دالة غير هذه
+
+453
+00:38:25,860 --> 00:38:31,140
+الدالة اللي بتحقق هذا الكلامبس قبل ما نثبت الـ
+
+454
+00:38:31,140 --> 00:38:35,740
+uniqueness خلّينا ناخد بعض النتائج بشكل سريع و
+
+455
+00:38:35,740 --> 00:38:39,900
+نتائج سهلة و اللي هي ان شاء الله متاخدش وقتها
+
+456
+00:38:39,900 --> 00:38:43,040
+شوفوا يا جماعة صلوا على النبي عليه الصلاة والسلام
+
+457
+00:38:43,040 --> 00:38:48,080
+الـ function E has a derivative of every order and
+
+458
+00:38:48,080 --> 00:38:51,260
+E N of X بيساوي E of X for all N element in N و X
+
+459
+00:38:51,260 --> 00:38:54,480
+element in Rيعني الآن لو فضلناها كمان مرة و مرتين
+
+460
+00:38:54,480 --> 00:38:56,980
+و تلاتة و أربعة هتطلع أيش نفس الدالة طبعا هذا
+
+461
+00:38:56,980 --> 00:39:00,360
+الكلام سهل و by induction زي ما انتوا عارفين أول
+
+462
+00:39:00,360 --> 00:39:03,120
+حاجة ماثبتها فوران بالساوية واحد فوران بالساوية
+
+463
+00:39:03,120 --> 00:39:06,480
+واحد ماحنا أثبتنا E prime of X أيش بالساوية E of X
+
+464
+00:39:06,480 --> 00:39:11,070
+إذا هذه is true فوران بالساوية واحدطيب لان افترض
+
+465
+00:39:11,070 --> 00:39:15,510
+انها هذه صحيحة في القرآن بيساوي K بيصير E K of X
+
+466
+00:39:15,510 --> 00:39:20,010
+بيساوي E of X لما ان اتبتها ل K زائد واحد طيب ل K
+
+467
+00:39:20,010 --> 00:39:23,870
+زائد واحد خد A K زائد واحد of X ايش هذه؟ هذه اللي
+
+468
+00:39:23,870 --> 00:39:30,840
+هي A K of X الكل اشمالها إبراهيمالان a k of x
+
+469
+00:39:30,840 --> 00:39:33,540
+فرضناها ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+470
+00:39:33,540 --> 00:39:33,940
+بالساوية ايه بالساوية ايه بالساوية ايه بالساوية
+
+471
+00:39:33,940 --> 00:39:34,880
+ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+472
+00:39:34,880 --> 00:39:35,180
+ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+473
+00:39:35,180 --> 00:39:37,200
+بالساوية ايه بالساوية ايه بالساوية ايه بالساوية
+
+474
+00:39:37,200 --> 00:39:43,180
+ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+475
+00:39:43,180 --> 00:39:54,500
+بالساوية ايه بالساوية ايه بالسا
+
+476
+00:39:55,640 --> 00:40:01,620
+وضلك فاضل إلى ما لا نهاية حيظل تطلع نفس الدالة نجي
+
+477
+00:40:01,620 --> 00:40:07,340
+الآن لـ Corollary أو الخاصية اللي بعدها لهذه
+
+478
+00:40:07,340 --> 00:40:15,040
+الدالة هذه الدالة Fx أكبر من 0 بقولك دايماً حيكون
+
+479
+00:40:15,040 --> 00:40:21,280
+الواحد زائد X strictly أصغر من مين من E of X من E
+
+480
+00:40:21,280 --> 00:40:32,910
+of X ان انعندي اللي هي أربعة أربعة عشان تشوف أيش
+
+481
+00:40:32,910 --> 00:40:40,550
+أربعة الأربعة اللي هي ال E prime of X أظن هيك كنا
+
+482
+00:40:40,550 --> 00:40:51,590
+حاكين ال E الناس في ال E of X عندي
+
+483
+00:40:51,590 --> 00:40:53,390
+E
+
+484
+00:40:55,380 --> 00:41:03,750
+انا of Xأقبى أو أصغر strictly من E N زائد واحد of
+
+485
+00:41:03,750 --> 00:41:09,850
+X لكل X أكبر من مين من صفر ليه؟ لأن هذه هيزيد
+
+486
+00:41:09,850 --> 00:41:12,630
+عليها term اللي هو X أسوان زائد واحد على N زائد
+
+487
+00:41:12,630 --> 00:41:15,630
+واحد فكتوريا وهذا ال term الاكساتي اللي أكبر من
+
+488
+00:41:15,630 --> 00:41:19,810
+صفر أشماله اللي هو مودة إذا صارت ال sequence اللي
+
+489
+00:41:19,810 --> 00:41:25,010
+عندي يا جماعة هذه عبارة عن strictly increasing
+
+490
+00:41:25,680 --> 00:41:29,120
+sequence strictly increasing sequence بناءً عليه
+
+491
+00:41:29,120 --> 00:41:36,240
+هيكون عند E1 of X أصغر strictly من E2 of X وهذا
+
+492
+00:41:36,240 --> 00:41:42,020
+أصغر strictly من E N of X لكل N أكبر أو يساوي
+
+493
+00:41:42,020 --> 00:41:51,440
+تلاتة وال X أشمالها أكبر من سفر ماشي الحال طيب E1
+
+494
+00:41:51,440 --> 00:42:02,170
+of X مين هي؟ واحد زاد Xوهذا أصغر من E2 of X وهذا
+
+495
+00:42:02,170 --> 00:42:08,170
+أصغر من E N of X إذا نخد ال limit لكل الجهات as N
+
+496
+00:42:08,170 --> 00:42:10,670
+goes to infinity وهذا independent of N وهذا
+
+497
+00:42:10,670 --> 00:42:15,590
+independent of N إذا سيصبح أصغر أو يساوي limit E N
+
+498
+00:42:15,590 --> 00:42:20,430
+of X as N goes to infinityو limit E n of X as n
+
+499
+00:42:20,430 --> 00:42:25,350
+goes to infinity هو عبارة عن مين قلنا عنه E of X
+
+500
+00:42:25,350 --> 00:42:31,350
+إذا صارت 1 زائد X strictly أصغر من E of X أو E of
+
+501
+00:42:31,350 --> 00:42:39,850
+X أكبر strictly من 1 زائد Xطيب نيجي اللي هو نثبت
+
+502
+00:42:39,850 --> 00:42:45,310
+الـ uniqueness للدالة اللي أثبتنا وجودها الآن إذا
+
+503
+00:42:45,310 --> 00:42:51,290
+أثبتنا وجود دالة سميناها E of X هذه الدالة تحقق
+
+504
+00:42:51,290 --> 00:43:01,390
+الشرطين اللي قلناهن اللي هو E of E primeof X بساوي
+
+505
+00:43:01,390 --> 00:43:07,430
+E of X لكل X element in R الشرط الأول والشرط
+
+506
+00:43:07,430 --> 00:43:14,350
+التاني اللي هو E of Zero بتساوي إياش واحد الآن هذه
+
+507
+00:43:14,350 --> 00:43:17,390
+الشرط ده اللي أكبرنا وجودها لنتبت إنها إياش وحيدة
+
+508
+00:43:17,700 --> 00:43:22,860
+الأن الـ function E من R لـ R that satisfies I and
+
+509
+00:43:22,860 --> 00:43:29,200
+I I هكذا of theorem 8.3.1 is unique إذا ما لها هذه
+
+510
+00:43:29,200 --> 00:43:32,940
+الدالة وحيدة ونشوف كيف نثبت وحيدة طبعا انتوا
+
+511
+00:43:32,940 --> 00:43:36,140
+عارفين ال .. الاستراتيجية تثبت انها وحيدة ونفترض
+
+512
+00:43:36,140 --> 00:43:39,340
+ان في دالتين وفي الآخر يا بنسأل لتناقض أو بنسأل
+
+513
+00:43:39,340 --> 00:43:43,260
+لإن الدالتين إشمالهم متساويتين خلينا نشوف
+
+514
+00:43:47,010 --> 00:43:52,110
+لأن let E1 and E2 be two functions on R ماشي الحال
+
+515
+00:43:52,110 --> 00:43:59,470
+E1 وE2 عبارة عن دالتين من R لR تحقيقان البرو بارتز
+
+516
+00:43:59,470 --> 00:44:03,010
+I and I I of T والمتمنى هو تلاتة واحد اللي كتبه ان
+
+517
+00:44:03,010 --> 00:44:08,700
+انا على الجنب هناكالان و خلّينا نسمي E1-E2 يتساوي
+
+518
+00:44:08,700 --> 00:44:14,840
+F رايحكم باتجاهة F يتساوي 0 إذا أثبتنا F يتساوي 0
+
+519
+00:44:14,840 --> 00:44:21,630
+إذا سيصبح E1 يتساوي E2 يكون خلصناطيب then فضلي هذه
+
+520
+00:44:21,630 --> 00:44:24,510
+.. فضلي هذه لأن هذا قبل التفاضل و هذا قبل التفاضل
+
+521
+00:44:24,510 --> 00:44:27,350
+إذا F prime of X بيساوي E1 prime of X ناقص E2
+
+522
+00:44:27,350 --> 00:44:32,230
+prime of X E1 prime of X إيش هتساوي اللي هو نفسها
+
+523
+00:44:32,230 --> 00:44:35,730
+لأن مفترضين احنا و E2 prime of X برضه هتساوي نفسها
+
+524
+00:44:35,730 --> 00:44:39,770
+إذا E1 ناقص E2 يعني مين بيساوي F يعني صارت F prime
+
+525
+00:44:39,770 --> 00:44:44,610
+تبعتنا مين هي بيساوي F of X لكل X element المين
+
+526
+00:44:44,610 --> 00:44:50,090
+إنا احسب اللي دي إيش يا جماعة احسب لولي F في صفرأف
+
+527
+00:44:50,090 --> 00:44:53,350
+اف صفر بيساوي ا واحد اف صفر ناقص اتنين اف صفر ا
+
+528
+00:44:53,350 --> 00:44:56,710
+واحد اف صفر واحد و اتنين اف صفر برضه اش بتساوي
+
+529
+00:44:56,710 --> 00:44:59,510
+واحد لإن مفترضين ا واحد و اتنين بتحفق اللي هي
+
+530
+00:44:59,510 --> 00:45:02,970
+الشطن الأمامنا إذا بيساوي واحد ناقص واحد و اي ساوي
+
+531
+00:45:02,970 --> 00:45:04,350
+اش صفر
+
+532
+00:45:07,320 --> 00:45:13,380
+by induction f double prime هتساوي f نفسها f
+
+533
+00:45:13,380 --> 00:45:18,060
+triple بتساوي f نفسها fn of x بيساوي f of x وعملت
+
+534
+00:45:18,060 --> 00:45:21,920
+قبل بشوية واحدة زيها إذا by induction fn of x
+
+535
+00:45:21,920 --> 00:45:28,280
+بيساوي f of x لكل x element in R إذا حققت الآن f
+
+536
+00:45:28,280 --> 00:45:34,500
+of 0 بيساوي 0 و fn of x بيساوي مين؟ f of x شوف
+
+537
+00:45:34,500 --> 00:45:42,870
+الآنأذا صار عندي F of Zero بساوي Zero أو F
+
+538
+00:46:10,090 --> 00:46:17,830
+بساوة 0طب ايش علاقتنا ابوها الجيت بتشوف عشان بدنا
+
+539
+00:46:17,830 --> 00:46:20,690
+نطبق اللي هو taylor's theorem تبعت ال derivative
+
+540
+00:46:20,690 --> 00:46:25,930
+نص اللي اللي بدنا يعني برهان حلو let x element in
+
+541
+00:46:25,930 --> 00:46:29,550
+R be arbitrary أخدنا إذا x element in R arbitrary
+
+542
+00:46:29,550 --> 00:46:33,810
+x اللي يعني let I x be the closed interval with
+
+543
+00:46:33,810 --> 00:46:40,760
+end point 0x يعني I xهناخدها بتساوي 0 و X أو اللي
+
+544
+00:46:40,760 --> 00:46:47,080
+هي X و 0 على .. على اللي هو اللي هي حسب X اللي هي
+
+545
+00:46:47,080 --> 00:46:51,980
+سالبة أو مجبة إذا أخدنا ال I X عبارة عن اللي هي ال
+
+546
+00:46:51,980 --> 00:46:56,600
+closed interval اللي within point 0 X الآن F is
+
+547
+00:46:56,600 --> 00:47:01,020
+continuous on I Xعلى الـ closed interval مدام
+
+548
+00:47:01,020 --> 00:47:03,320
+continuous على closed interval and function that
+
+549
+00:47:03,320 --> 00:47:06,460
+is continuous على closed interval then it is
+
+550
+00:47:06,460 --> 00:47:09,200
+bounded on this interval يعني بمعنى أخر there
+
+551
+00:47:09,200 --> 00:47:12,880
+exist k بحيث أن absolute value of f of t أصغر أو
+
+552
+00:47:12,880 --> 00:47:17,960
+يساوي k for all t element in I X يعني f is bounded
+
+553
+00:47:17,960 --> 00:47:23,580
+on this intervalالان بدنا نطبق if we apply
+
+554
+00:47:23,580 --> 00:47:27,540
+taylor's theorem 6 4 1 to F بدنا نطبقها على
+
+555
+00:47:27,540 --> 00:47:31,800
+النقطتين النقطة الأولى اللى هى ال X X و X naught 0
+
+556
+00:47:31,800 --> 00:47:35,640
+يعني بنطبقها على مين اللى هى X X اللى هى طبعا
+
+557
+00:47:35,640 --> 00:47:41,370
+انتوا متذكرين F of Xأف of X تيلر سيوريم there
+
+558
+00:47:41,370 --> 00:47:46,370
+exists C in اللي هي ال interval مثلا X not و X
+
+559
+00:47:46,370 --> 00:47:52,690
+such that F of X بيساوي اللي هو F of X not زائد F
+
+560
+00:47:52,690 --> 00:47:58,490
+prime of X not على واحد factorial في X minus X not
+
+561
+00:47:58,490 --> 00:48:05,910
+زائد زائد Fn of x0 على n factorial في x minus x0
+
+562
+00:48:05,910 --> 00:48:11,610
+الكلوس n زائد ال remainder اللي هو fn زائد واحد of
+
+563
+00:48:11,610 --> 00:48:15,730
+اللي هي ال c اللي لاجيناها there exists c اللي هي
+
+564
+00:48:15,730 --> 00:48:19,170
+of c طبعا ال c هنا هتعتمد على ال n اللي احنا
+
+565
+00:48:19,170 --> 00:48:24,850
+اختارناها واشتغلنا عليها هو مسميها cn على اللي هو
+
+566
+00:48:24,850 --> 00:48:28,670
+n زائد واحد factorial في x
+
+567
+00:48:33,180 --> 00:48:37,920
+الـ N هو
+
+568
+00:48:37,920 --> 00:48:42,580
+ما خدها لعند مين بدل ما هو remainder N زائد واحد
+
+569
+00:48:42,580 --> 00:48:45,880
+نسميه remainder N نفس الشيء مافيش مشكلة احنا
+
+570
+00:48:45,880 --> 00:48:51,880
+كملناها يعني بدل ما اشتغل على N زي ما اشتغل على N
+
+571
+00:48:51,880 --> 00:48:54,460
+زائد واحد اشتغل على ال N هو اما هي ال Taylor's
+
+572
+00:48:54,460 --> 00:48:59,460
+theorem طيب المهم انتبهوا عن ديلنبن Taylor's
+
+573
+00:48:59,460 --> 00:49:03,580
+theorem على ال interval Ix اللي X0 بيساوي 0
+
+574
+00:49:03,580 --> 00:49:08,040
+وخلّينا نستخدم Fk of 0 اللي كتبتها هناك اللي هو
+
+575
+00:49:08,040 --> 00:49:12,020
+هتساوي Fk of 0 هتساوي 0 دايما اللي هو و لكل k
+
+576
+00:49:12,020 --> 00:49:15,740
+element n it follows thatfor each n unlimited on
+
+577
+00:49:15,740 --> 00:49:20,000
+there exist a point cn unlimited on x هذه اللي هي
+
+578
+00:49:20,000 --> 00:49:23,920
+ال cn بتعتمد على مين على n يعني الأن لو أخدت ببدل
+
+579
+00:49:23,920 --> 00:49:28,860
+اللي هنا على اللي هي on بتساوي مثلا اتنين أخد on
+
+580
+00:49:28,860 --> 00:49:31,660
+بتساوي تلتة أخد بتساوي on بتساوي أربعة ده هتختلف
+
+581
+00:49:31,660 --> 00:49:35,740
+من ال cn اللي بنلاقيها such that f of x بيساوي f
+
+582
+00:49:35,740 --> 00:49:39,420
+of zero زيد f prime of zero على واحد factorial في
+
+583
+00:49:39,420 --> 00:49:44,390
+xطبعاً نقص صفر X هتظلها زائد FN نقص واحد لأن نقص
+
+584
+00:49:44,390 --> 00:49:47,630
+واحد factorial في X minus X note اللي هي صفر طبعاً
+
+585
+00:49:47,630 --> 00:49:52,830
+هتصير X نقص واحد زائد FN of CN على N factorial X
+
+586
+00:49:52,830 --> 00:49:56,530
+أثن يعني هنا ناخد ال remainder اللي هو RN مش RN
+
+587
+00:49:56,530 --> 00:50:01,410
+زائد واحد زي ما نعمله طبعاً ماتفرجشبتزيده و بتشتغل
+
+588
+00:50:01,410 --> 00:50:04,910
+عليه نفس الاشي الان بس ال cn اللي بتختلف من n زائد
+
+589
+00:50:04,910 --> 00:50:07,650
+واحد بصير cn زائد واحد مثلا لأنه حاجة تانية ممكن
+
+590
+00:50:07,650 --> 00:50:11,290
+تيجي غير ال cn اللي لاجيناها حسب النظرية و يساوي
+
+591
+00:50:11,290 --> 00:50:16,350
+لأن كل هدول التاريج زي شمال هي الصفار لإنه fk of
+
+592
+00:50:16,350 --> 00:50:21,290
+00 إذا هذا سفر وهذا سفر طبعا هذا عند مين محسب عند
+
+593
+00:50:21,290 --> 00:50:25,800
+السفر وهذا عند السفر إلى آخرهإذا كل هذول هيكون
+
+594
+00:50:25,800 --> 00:50:30,700
+الصفار هيظل عندى بس القيمة هذه ايش القيمة هذه اللي
+
+595
+00:50:30,700 --> 00:50:35,320
+هي fn of cn طبيعي هتكون f of min of cn لأنه احنا
+
+596
+00:50:35,320 --> 00:50:41,070
+عرفنا انه ال derivative f primeأف دابل برايم أف
+
+597
+00:50:41,070 --> 00:50:45,710
+تريبل كل نياش بيساوي الأف إذا حيكون أف of CN على N
+
+598
+00:50:45,710 --> 00:50:50,710
+فيكتوريال في X أُس N إذا وصلنا له الآن أنه بعد ما
+
+599
+00:50:50,710 --> 00:50:57,170
+طبقنا Taylor's theorem طلع عندي الآن F of X هذه
+
+600
+00:50:57,170 --> 00:51:04,710
+اللي بنصبه إلى أن نثبتها بتساوي صفر طلعت عندي F of
+
+601
+00:51:04,710 --> 00:51:10,230
+X بيساوي F of CN على N فيكتوريال في X أُس Nالان خد
+
+602
+00:51:10,230 --> 00:51:14,510
+لل absolute value لها absolute value لل F of X
+
+603
+00:51:14,510 --> 00:51:20,090
+هيصير اصغر او يساوي ال absolute value او بيساوي
+
+604
+00:51:20,090 --> 00:51:26,870
+بالظبط absolute value F of C N فال absolute value
+
+605
+00:51:27,400 --> 00:51:33,440
+للـ X أُس N على N فكتوريال، مظبوط؟ لكن F of C N
+
+606
+00:51:33,440 --> 00:51:37,200
+هذه is .. الـ F is bounded على الفترة اللي لجيناها
+
+607
+00:51:37,200 --> 00:51:40,180
+اللي هي الفترة اليمين اللي قلت عنها اللي هي الـ I
+
+608
+00:51:40,180 --> 00:51:44,380
+X مدان bounded قلنا هذه أصغر أو يساوي الـ K إذا
+
+609
+00:51:44,380 --> 00:51:47,380
+هذه بيصير أصغر أو يساوي الـ K في ال absolute value
+
+610
+00:51:47,380 --> 00:51:52,750
+X أس N على N فكتوريال نيجي الآنهذه as n goes to
+
+611
+00:51:52,750 --> 00:51:56,770
+infinity هذه independent of n هذه أكبره يساوي سفر
+
+612
+00:51:56,770 --> 00:51:59,430
+و أصغره يساوي هذه as n goes to infinity هذه بتروح
+
+613
+00:51:59,430 --> 00:52:05,590
+للسفر إذا هذه بتروح أشمالها بدها تصير f of x تساوي
+
+614
+00:52:05,590 --> 00:52:11,230
+السفر ومنه ال E1 بتساوي ال E2 لأن f بتساوي E1 ناقص
+
+615
+00:52:11,230 --> 00:52:17,350
+Eإتنين وهو المطلوب وهذا الكلام صحيح لكل X element
+
+616
+00:52:17,350 --> 00:52:25,050
+in R لأن X اللي أخدناها arbitrary element in R هيك
+
+617
+00:52:25,050 --> 00:52:31,990
+بنكون أثبتنا وجود ال E واحد ال E التي تحقق الشرطين
+
+618
+00:52:31,990 --> 00:52:38,590
+اللي عندنا وفي نفس الوقت أثبتنا أن هذه الدالة اللي
+
+619
+00:52:38,590 --> 00:52:46,680
+بتحقق الشرطينهي دالة وحيدةمدام الدالة واحدة إذن
+
+620
+00:52:46,680 --> 00:52:53,280
+الآن يعني شرّعنا إنه نعطيها اسم إنه نقدر نعرف
+
+621
+00:52:53,280 --> 00:52:59,200
+الدالة اللي بتحقق هذول الشرطين إنها اسمها كذا the
+
+622
+00:52:59,200 --> 00:53:02,660
+unique definition ثمانية تلاتة خمسة the unique
+
+623
+00:53:02,660 --> 00:53:06,140
+function E من R لR such that E prime of X في سوء E
+
+624
+00:53:06,140 --> 00:53:10,120
+of X for all X elements in R وتحقق ال E زيرو
+
+625
+00:53:10,120 --> 00:53:15,190
+بالسوء واحد موجودةووحيدة إذا بحق اللي أقول is
+
+626
+00:53:15,190 --> 00:53:18,450
+called the exponential function وهي الـ
+
+627
+00:53:18,450 --> 00:53:22,350
+exponential اللي أنتوا مبسوطين عليها و بتستخدموها
+
+628
+00:53:22,350 --> 00:53:27,530
+أثبتنا الآن من خلال اللي هو اللي هي الترتيب اللي
+
+629
+00:53:27,530 --> 00:53:31,690
+رتبناه في المادة differentiability integrability و
+
+630
+00:53:31,690 --> 00:53:36,350
+بعدين اللي هو sequences of functions وصلنا إلى
+
+631
+00:53:36,350 --> 00:53:41,190
+اللي هو ال exponential هذه function existsالتي
+
+632
+00:53:41,190 --> 00:53:43,850
+سمناها الـ Exponential Function
+
+633
+00:53:48,710 --> 00:53:53,850
+بدنا نسمي الـ E of واحد قيمة الدالة القيمة الدالة
+
+634
+00:53:53,850 --> 00:53:58,650
+الـ E هذه عند الواحد بدنا نسميها E E و هذا اللي
+
+635
+00:53:58,650 --> 00:54:04,410
+بنسميه Ehlers number و احنا يعني بعد هيك هيصير
+
+636
+00:54:04,410 --> 00:54:09,410
+عندي اللي هو الرمز E of X ان هو ال exponential X
+
+637
+00:54:09,410 --> 00:54:15,710
+او أسهلنا في الاستخدام ال E of X ايش هتساويالـ E X
+
+638
+00:54:15,710 --> 00:54:21,530
+هذا الـ E واحد قيمة الدالة عند مين عند اللي هو
+
+639
+00:54:21,530 --> 00:54:26,750
+الرقم واحد سمناها E ماشي الحالة الان E of X
+
+640
+00:54:26,750 --> 00:54:32,610
+بالساوي E to the X هذه عبارة عن اللي هي الدالة E
+
+641
+00:54:32,610 --> 00:54:37,550
+of X بالساوي X notation لها لكن بعد شوية هنلاقي ال
+
+642
+00:54:37,550 --> 00:54:42,310
+notation consistent of اللي هو مع مين مع اللي هو
+
+643
+00:54:42,310 --> 00:54:47,480
+ال exponentيعني هيصير الـ E to the exponent X هو
+
+644
+00:54:47,480 --> 00:54:51,960
+عبارة عن بالظبط اللي هو قيمة الـ E of X لأن الـ E
+
+645
+00:54:51,960 --> 00:54:54,620
+of X بيساوي E to the X و ال E of واحد بيساوي E
+
+646
+00:54:54,620 --> 00:54:59,440
+واحد بيصير عندي E لما أرفحها للقوة X يطلع قيمتها
+
+647
+00:54:59,440 --> 00:55:05,840
+هي عبارة عن اللي هي قيمة دل E of X حسب اللي احنا
+
+648
+00:55:05,840 --> 00:55:11,550
+معرفينه هنايعني من الإحسابات ومن تعريفنا للدالة
+
+649
+00:55:11,550 --> 00:55:23,070
+هيكون فيه consistent it is consistent في الحالتين
+
+650
+00:55:23,070 --> 00:55:28,990
+طيبنجي الآن لما الكلام هذا ال number E can be
+
+651
+00:55:28,990 --> 00:55:32,570
+obtained as a limit and thereby approximated in
+
+652
+00:55:32,570 --> 00:55:36,410
+several different ways طبيعا احنا مادام عنده اللي
+
+653
+00:55:36,410 --> 00:55:42,990
+هو عبارة عن limit لل E N of Xاللي هي بتطلع عندى
+
+654
+00:55:42,990 --> 00:55:47,450
+limit عند ال .. ال .. ال .. ال end of واحد لأنها
+
+655
+00:55:47,450 --> 00:55:52,130
+continuous بصير عندى مدام limit إذا بصير أقدر أقرب
+
+656
+00:55:52,130 --> 00:55:56,490
+هذه القيمة اللي هي و نحصل على قيمة تقريبية بال E و
+
+657
+00:55:56,490 --> 00:56:00,010
+هذا مش شغلنا شغل تبعين اللي هو numerical analysis
+
+658
+00:56:00,010 --> 00:56:05,530
+أو الناس اللي بدأت .. اللي هي تشتغل في التقريب أو
+
+659
+00:56:05,530 --> 00:56:09,270
+مش شغل نهاني يعني بصديإلى أن الـ use of notation E
+
+660
+00:56:09,270 --> 00:56:15,050
+و X of E X زي ما قلنا كله تمام تمام consistent إلى
+
+661
+00:56:15,050 --> 00:56:19,910
+أن يجي اللي هو لبعض الخواص الأخرى لهذه اللي هي
+
+662
+00:56:19,910 --> 00:56:24,130
+الدالة إلى أن الـ exponential function satisfies
+
+663
+00:56:24,130 --> 00:56:26,150
+the following properties
+
+664
+00:56:32,620 --> 00:56:35,960
+أول حاجة أن الـ E of X لا تساوي سفر لكل X element
+
+665
+00:56:35,960 --> 00:56:40,140
+in R هي أول حاجة أن هذه الدالة دايما لا تساوي سفر
+
+666
+00:56:40,140 --> 00:56:45,980
+طبعا شغالة على R E of X زي Y بسوء E of X في E of Y
+
+667
+00:56:45,980 --> 00:56:50,880
+for all X element .. Y element in R الآن E of R
+
+668
+00:56:50,880 --> 00:56:56,080
+هنا اللي هي E of R قيمة الـ function هذه هتطلع لنا
+
+669
+00:56:56,080 --> 00:57:00,260
+بالظبطهي عبارة عن الـ E اللي قلنا عنها الرقم اللي
+
+670
+00:57:00,260 --> 00:57:06,000
+قبل و شوية لما نرفع للقوة R فبصير الان consistency
+
+671
+00:57:06,000 --> 00:57:11,440
+between the definition of the exponential and the
+
+672
+00:57:11,440 --> 00:57:15,700
+exponent of E to the power R بس هذي الـ R إيش اللي
+
+673
+00:57:15,700 --> 00:57:21,880
+من الين؟ NQ لان ماشي الحالة ده نشوف نبرهن اللي هو
+
+674
+00:57:21,880 --> 00:57:27,390
+الأولى by contradictionبدي افترض انه في عندي E of
+
+675
+00:57:27,390 --> 00:57:31,930
+α for some α element in R والـ E of α ايش تساوي
+
+676
+00:57:31,930 --> 00:57:35,870
+تساوي سفر ونوصل لcontradiction لان suppose that
+
+677
+00:57:35,870 --> 00:57:39,550
+there exists α element in R such that E of α ايش
+
+678
+00:57:39,550 --> 00:57:44,750
+بساوي بساوي سفرالآن and let G α be the closed
+
+679
+00:57:44,750 --> 00:57:49,710
+interval with endpoints mean α و 0 يعني الـ G of α
+
+680
+00:57:49,710 --> 00:57:54,230
+زي اللي فوق يا بساوي اللي هو 0 ألفة أو ألف و زيره
+
+681
+00:57:54,230 --> 00:57:59,440
+حسب قيمة الألف موجبة أو سالبة طيبالان زي ما قلت
+
+682
+00:57:59,440 --> 00:58:02,480
+قبل بشوية بما ان E is continuous on a closed
+
+683
+00:58:02,480 --> 00:58:07,700
+interval Iα او Jα اللي هو مسميها then there exist
+
+684
+00:58:07,700 --> 00:58:10,280
+case such that اللي هو ال absolute value E of D
+
+685
+00:58:10,280 --> 00:58:16,030
+أصفر سوى K لكل T element in Gالأن مشابه للي قبل دي
+
+686
+00:58:16,030 --> 00:58:19,930
+ربالكم الان بدنا نستخدم mean taylor theorem اللي
+
+687
+00:58:19,930 --> 00:58:24,890
+هو على اللي هي ال function اللي عندي هذه اللي هو
+
+688
+00:58:24,890 --> 00:58:29,310
+بس في مين الآن في ال end points ألف ومين ألف وصفر
+
+689
+00:58:29,310 --> 00:58:32,610
+اذا there exist cn element in dn such that مسرع
+
+690
+00:58:32,610 --> 00:58:35,950
+لإنه قاعد بعيد نفس البرهان اللي قبله شوية such
+
+691
+00:58:35,950 --> 00:58:42,200
+that اللي هو E of صفربطبق عند e of 0 بساوي e of
+
+692
+00:58:42,200 --> 00:58:44,340
+alpha زائد e prime of alpha على واحد factorial في
+
+693
+00:58:44,340 --> 00:58:47,280
+ناقص alpha اللي هي zero ناقص alpha زائد e n ناقص
+
+694
+00:58:47,280 --> 00:58:50,780
+واحد على ناقص واحد factorial alpha ناقص alpha أُس
+
+695
+00:58:50,780 --> 00:58:54,160
+n ناقص واحد لما أصل لعند ال remainder e n of alpha
+
+696
+00:58:54,160 --> 00:59:00,060
+على n factorial في ناقص alpha أُس n الآن اخلق هذه
+
+697
+00:59:00,060 --> 00:59:05,770
+مش e alpha هذه الـCnهذه الـ C أنا مخربط بصيحة الله
+
+698
+00:59:05,770 --> 00:59:11,430
+ماشي الحالة الان E of Zero طبيعي ايش يساوي واحد
+
+699
+00:59:11,430 --> 00:59:14,510
+ماحنا عارفين ان خلاص عرضناها الدالة هذه E of Zero
+
+700
+00:59:14,510 --> 00:59:17,630
+بتساوي واحد اتساوي واحد يساوي E of Zero و يساوي
+
+701
+00:59:20,060 --> 00:59:23,400
+الأن E of Alpha فرضناها إيش بالساوية سفر هيك
+
+702
+00:59:23,400 --> 00:59:28,280
+مفترضينها E prime of Alpha اللي هي نفس E of Alpha
+
+703
+00:59:28,280 --> 00:59:32,880
+إذا سفر برضه وهذا نفس الشيء إذا كلنا دول أصفر مع
+
+704
+00:59:32,880 --> 00:59:36,100
+دمين الأخيرة إذا هتساوي E of Cn على N factorial
+
+705
+00:59:36,100 --> 00:59:42,340
+ناقص Alpha أسعى وزي ما قلنا إنه احنا الآن هذا
+
+706
+00:59:42,340 --> 00:59:48,390
+المقدار عندي صار .. نوضح لكم هذهنشوف كيف نصل لـ
+
+707
+00:59:48,390 --> 00:59:53,770
+contradiction هال gate صار عند مايا ليه يا جماعة
+
+708
+00:59:53,770 --> 00:59:57,190
+صارت عند الواحد هذه اللي بيساوي E to the zero
+
+709
+00:59:57,190 --> 01:00:03,630
+بيساوي E to the zero اللي هي أصغر أو يساوي ال
+
+710
+01:00:03,630 --> 01:00:07,510
+absolute value لهذه بيساويها بعد إنه أصغر أو يساوي
+
+711
+01:00:07,510 --> 01:00:14,420
+بيساوي ال absolute value E of CL على N factorialفي
+
+712
+01:00:14,420 --> 01:00:22,320
+absolute value ناقص Alpha أُس N و هذه زي ما قلنا E
+
+713
+01:00:22,320 --> 01:00:25,880
+of C N إيش ما اللي قلنا قبل بشوية هذه أصغر أوي و
+
+714
+01:00:25,880 --> 01:00:32,960
+ساوي K إذا K على N factorial في ناقص Alpha أُس N
+
+715
+01:00:32,960 --> 01:00:38,710
+ماشي الآن هذا المقدارas n goes to infinity بيروح
+
+716
+01:00:38,710 --> 01:00:42,910
+لـ0 هذا independent of n و هذا independent of n
+
+717
+01:00:42,910 --> 01:00:48,650
+صار عندى الان هذا الان هي الواحد أصغر أو يساوي
+
+718
+01:00:48,650 --> 01:00:53,390
+اللي هو هذا المقدار خد ال limit as n goes to
+
+719
+01:00:53,390 --> 01:00:57,430
+infinity بيصير الواحد أصغر أو يساوي سفر و هذا إيش
+
+720
+01:00:57,430 --> 01:01:03,250
+ماله contradictionإذا صار في عندي الفرضية الأولى
+
+721
+01:01:03,250 --> 01:01:07,770
+خاطئة إذا there is no such Alpha اللي هو بتكون
+
+722
+01:01:07,770 --> 01:01:10,530
+عندها ال K of Alpha بتساوي سفر إذا ال K of Alpha
+
+723
+01:01:10,530 --> 01:01:16,090
+بتساوي أكبر لا تساوي سفر دائما إذا صار عندي اللي
+
+724
+01:01:16,090 --> 01:01:22,150
+هو قيمة اللي هي E to the X لا تساوي سفر أبدا نيجي
+
+725
+01:01:22,150 --> 01:01:29,110
+الآن إن بدنا نثبت أنهنثبت الخاصية اللي بعدها اللي
+
+726
+01:01:29,110 --> 01:01:38,430
+هي عبارة عن E of X زائد Y بساوة E of X في E of Y
+
+727
+01:01:38,430 --> 01:01:42,670
+لكل X و Y element in R هذه الخاصية اللي بدنا
+
+728
+01:01:42,670 --> 01:01:48,410
+نثبتها شوف طريقته حلوة في الإثبات بيقول ليه نفترض
+
+729
+01:01:48,410 --> 01:01:53,030
+Y fixed arbitrary لكن ليهاش fixed بنحكي عن Y محددة
+
+730
+01:01:53,030 --> 01:01:59,760
+arbitrary لكن نحكي عن Y محددةالان مادام Y اللي هي
+
+731
+01:01:59,760 --> 01:02:05,240
+ال E of Y أكيد يشملها لا تساوي سفر اتفجنا عليها
+
+732
+01:02:05,240 --> 01:02:11,520
+الان عرفلي الان function G من R لR عرفها كيف؟G of
+
+733
+01:02:11,520 --> 01:02:15,720
+X المتغير X الان Y اللي هي عبارة عن اشي Fix ثابت
+
+734
+01:02:15,720 --> 01:02:19,080
+بحكي عنه لكن كان arbitrary اللي هي G of X بيساوي E
+
+735
+01:02:19,080 --> 01:02:24,420
+of X زائد Y على E of Y for X element in R أخدنا
+
+736
+01:02:24,420 --> 01:02:30,060
+هذه الدالة الآن شوف هذه الدالة اعمله G prime لها G
+
+737
+01:02:30,060 --> 01:02:33,920
+prime of X بالفضل بالنسبالي XY ثابتة اللي هي بيصير
+
+738
+01:02:33,920 --> 01:02:38,280
+هذه E prime of X زائد Y على E of Y عدد ما لاش
+
+739
+01:02:38,280 --> 01:02:43,080
+علاقة فيه Y ساويالـ E' هي نفس مين؟ الـ E of X زي Y
+
+740
+01:02:43,080 --> 01:02:48,720
+على E of Y ماشي؟ طيب، الآن صار هذا الـ E X زي Y
+
+741
+01:02:48,720 --> 01:02:53,280
+على E of Y هو مين؟ رجع G إذا رجعت إن الـ G' مش
+
+742
+01:02:53,280 --> 01:03:01,770
+بيساوي الـ G الآن andأحسب لي g of 0 بساوية e of 0
+
+743
+01:03:01,770 --> 01:03:06,070
+زائد y على e of y يعني بساوية واحدة إذا الدالة
+
+744
+01:03:06,070 --> 01:03:11,050
+اللي عرفناها هذه g of x طلعت لي g prime لها نفسها
+
+745
+01:03:11,050 --> 01:03:15,310
+وطلعت لي g of 0 واحدة وعلمة قبل قليل عمال بيقول
+
+746
+01:03:15,310 --> 01:03:18,610
+مافيش لغير واحدة في الدنيا بتهبها الخاصيتين اللي
+
+747
+01:03:18,610 --> 01:03:23,190
+هي مين ال E of X إذا هذه غصب عننا لازم تطلع مين ال
+
+748
+01:03:23,190 --> 01:03:27,080
+E of X because of the uniqueness of Eإذا صحيح أنا
+
+749
+01:03:27,080 --> 01:03:31,000
+عندي E of X بساوي E X Z Y على E E of Y يعني E X Z
+
+750
+01:03:31,000 --> 01:03:37,940
+Y بساوي E of Y في ال E of X و هو المطلوب طيب نيجي
+
+751
+01:03:37,940 --> 01:03:46,800
+الآن نثبت اللي بعدها اللي هي بدنا نثبت E of R
+
+752
+01:03:46,800 --> 01:03:54,870
+بساوي E to the RR المنتنين LQ اللي هو rational
+
+753
+01:03:54,870 --> 01:04:00,870
+number طيب جماعة فيكم تصل على النبي عليه الصلاة
+
+754
+01:04:00,870 --> 01:04:09,370
+والسلام لنشوف كيف نيجي
+
+755
+01:04:09,370 --> 01:04:14,690
+البرهن اللي هو الجزء الثالث أو هذا جزء من النظرية
+
+756
+01:04:14,690 --> 01:04:18,830
+أول
+
+757
+01:04:18,830 --> 01:04:24,560
+حاجةهذه صحيحة لكل أنهي المتنانة كيف؟ by induction
+
+758
+01:04:24,560 --> 01:04:53,330
+E of X بساوي E of Xأكيد أكيد أكيد أكيد أكيد
+
+759
+01:04:53,330 --> 01:04:56,270
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+760
+01:04:56,270 --> 01:04:56,330
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+761
+01:04:56,330 --> 01:04:57,110
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+762
+01:04:57,110 --> 01:05:00,170
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+763
+01:05:00,170 --> 01:05:02,740
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكE
+
+764
+01:05:02,740 --> 01:05:08,660
+of K في X زائد X ويساوي من الخاصية اللي احنا لسه
+
+765
+01:05:08,660 --> 01:05:12,880
+ماخلصنهاش هذه بساوي E للأول زايد في E للتاني اللي
+
+766
+01:05:12,880 --> 01:05:17,960
+هي E للأول اللي هو KX في E للتاني اللي هي EX
+
+767
+01:05:17,960 --> 01:05:22,780
+ويساوي EKX اللي هو E of X أُس K لأنه فرضينا أنا
+
+768
+01:05:22,780 --> 01:05:31,260
+صحيحة اللي هي K بيصير عندي E of X أُس K في E of Xو
+
+769
+01:05:31,260 --> 01:05:39,800
+يساوي E of X الكل أُس K زائد واحد إذا صارت
+
+770
+01:05:39,800 --> 01:05:49,580
+هذه is true for all N element in N طيب .. الآن شوف
+
+771
+01:05:49,580 --> 01:05:53,920
+ما يليه نلاحظ ما يليه
+
+772
+01:06:02,460 --> 01:06:06,080
+Lit x بتساوي ايش؟ واحدة على ان ناخد الـ x ايش
+
+773
+01:06:06,080 --> 01:06:10,540
+بتساوي واحدة على ان؟ بتصير هذا E of واحد لأن ان في
+
+774
+01:06:10,540 --> 01:06:13,840
+واحدة على ان واحد ال E of واحد رمزناها من رمز ايش
+
+775
+01:06:13,840 --> 01:06:17,940
+يا جماعة؟ E وهذا اللي بدأ اصليه هذا رمزناها من رمز
+
+776
+01:06:17,940 --> 01:06:22,420
+E وال E عبارة عن رقم ال E of واحد هي قيمة الدالة
+
+777
+01:06:22,420 --> 01:06:28,100
+اللي تبعتنا عند اللي هي الواحد سمينها Eالان E of N
+
+778
+01:06:28,100 --> 01:06:33,380
+في 1 على N تساوي اللي هي عبارة عن ال X هذه اللي هي
+
+779
+01:06:33,380 --> 01:06:40,720
+عبارة عن 1 على N E of 1 على N الكل اسمه أُس N يعني
+
+780
+01:06:40,720 --> 01:06:48,380
+الآن عندي هذه ال X E N X بساوي E X أُس N X مين 1
+
+781
+01:06:48,380 --> 01:06:53,210
+على N E of 1 على N أُس Nإذا صار عندى الآن هي هذا
+
+782
+01:06:53,210 --> 01:06:59,010
+القيمة بساوية هذا إذا بمعنى آخر E of واحدة الان
+
+783
+01:06:59,010 --> 01:07:05,830
+بساوية E العدد أس واحد على N هذا الان E of واحدة
+
+784
+01:07:05,830 --> 01:07:14,050
+الان بساوية E أس واحد على N الآن من جهة أخرى لو
+
+785
+01:07:14,050 --> 01:07:23,700
+جيت E أس minus Mهتساوي واحد على E أُس M خد
+
+786
+01:07:23,700 --> 01:07:26,760
+ال
+
+787
+01:07:26,760 --> 01:07:33,460
+E of M ناقص M اللي هي بيساوي E of Zero اللي هي
+
+788
+01:07:33,460 --> 01:07:41,020
+بيساوي واحد صح وإيه ساوي E of Mفي E of ناقص M حسب
+
+789
+01:07:41,020 --> 01:07:45,900
+الخاصية اللي هي زائد ناقص M هذه X وهذه ال Y E
+
+790
+01:07:45,900 --> 01:07:49,760
+الأولى في E التانية الان صار عندى هذا المقدار
+
+791
+01:07:49,760 --> 01:07:57,600
+بساوي واحد يعني إذا E of ناقص M بساوي بنجل هدهان
+
+792
+01:07:57,600 --> 01:08:03,260
+واحد على E of M إذا صارت عندى E of ناقص M بساوي
+
+793
+01:08:03,260 --> 01:08:09,360
+واحد على E of M وال E of M ال E of Mمن فوق E of M
+
+794
+01:08:09,360 --> 01:08:14,280
+هذا X بواحد يعني بيساوي E of واحد أُس M يعني عبارة
+
+795
+01:08:14,280 --> 01:08:19,500
+عن E أُس M وهي فوق إيش واحد الآن هذه اللي هو عدد
+
+796
+01:08:19,500 --> 01:08:23,800
+عادي اللي هو E مرفوع للأُس M اللي هو نفسه E to the
+
+797
+01:08:23,800 --> 01:08:27,360
+minus M لأن هذه معلومة قديمة لذا انصار عندي الآن E
+
+798
+01:08:27,360 --> 01:08:34,820
+of minus M بيساوي E أُس ماقص M وال E أُس واحد على
+
+799
+01:08:34,820 --> 01:08:43,460
+N بيساوي Eأُس واحد على N نجي
+
+800
+01:08:43,460 --> 01:08:46,780
+الآن احنا غايتنا مين؟ E of R الـ R إيش اللي نقدر
+
+801
+01:08:46,780 --> 01:08:50,640
+نكتبها؟ الـ R في الـ Q إذا الـ R بتنكتب على صورة M
+
+802
+01:08:50,640 --> 01:08:54,780
+على N إذا نخد R في اللي نمتني Q إذا there exists M
+
+803
+01:08:54,780 --> 01:08:58,820
+و N اي واحدة في زد واحدة في N صحيح ده؟ R بتساوي M
+
+804
+01:08:58,820 --> 01:09:03,320
+على N بتثبتلك إن E of M على N بساوي E to the M على
+
+805
+01:09:03,320 --> 01:09:12,580
+N شوف كيفE of M على N ايش هيساوي E أُس واحدة ل N
+
+806
+01:09:12,580 --> 01:09:21,400
+الكل A شماله أُس M أُس M E of واحدة ل N أُس M مين
+
+807
+01:09:21,400 --> 01:09:28,870
+اللي شرعلي اللي هوعندي اللي هي E-M و هي سالبة طلعت
+
+808
+01:09:28,870 --> 01:09:33,870
+E أص مينس M و اللي شرعلي E و واحدة ل N و N مودبة
+
+809
+01:09:33,870 --> 01:09:41,130
+هي E أص واحد على N فبصير عندي الأن E أص M على N أص
+
+810
+01:09:41,130 --> 01:09:45,970
+M على N بساوي E أص واحد على N هذه اللي جوا الكل
+
+811
+01:09:45,970 --> 01:09:53,650
+أسمين الكل أص M ماشي الحال هو يساوي E
+
+812
+01:09:58,010 --> 01:10:03,730
+هذه شرعات لإي و واحدة الان كل اس ام وهذا عدد عادي
+
+813
+01:10:03,730 --> 01:10:08,730
+الان وهذا عدد عادية بيصير اي أس ام عالميا على ان و
+
+814
+01:10:08,730 --> 01:10:14,850
+هذه بيكون عندي اي أس اي او ام على ان بساوي اللي هو
+
+815
+01:10:14,850 --> 01:10:18,870
+عبارة عن اي أس ام على ان و ام على ان was our
+
+816
+01:10:18,870 --> 01:10:21,710
+arbitral rational number اذا صار عندي اي أس ار
+
+817
+01:10:21,710 --> 01:10:24,210
+بساوي اي أس ار
+
+818
+01:10:29,400 --> 01:10:35,160
+نجي الآن للنظرية اللي هي تمانية تلاتة سبعة اللي هي
+
+819
+01:10:35,160 --> 01:10:39,980
+النظرية الأخيرة في اللي هي الحديث عن اللي هو ال
+
+820
+01:10:39,980 --> 01:10:45,260
+exponential function و بعدها طبعا بنحكي عن اللي هو
+
+821
+01:10:45,260 --> 01:10:48,060
+ال logarithmic function بس خلينا الآن نحكي عالميا
+
+822
+01:10:48,060 --> 01:10:54,340
+انكمل نظريتنا على ال exponential function بنشوف
+
+823
+01:10:55,540 --> 01:11:00,240
+الأن بقولي الـ exponential function E is strictly
+
+824
+01:11:00,240 --> 01:11:04,840
+increasing on R يعني الـ derivative إلها أكبر من
+
+825
+01:11:04,840 --> 01:11:11,460
+سفر ماشي؟ and this range اللي هو Y المتنرسج ده Y
+
+826
+01:11:11,460 --> 01:11:16,720
+أكبر من سفر يعني الـ E هتكون بالظبط ده اللي من R
+
+827
+01:11:16,720 --> 01:11:24,080
+بتصب إلى R positive إلى R positive يعني عبارة عن
+
+828
+01:11:24,080 --> 01:11:31,370
+Zeroومالة نهاية هي التي هي range دالة range دالة
+
+829
+01:11:31,370 --> 01:11:34,610
+هذه هي من سفر إلى مالة نهاية لأن كتابة على سورة
+
+830
+01:11:34,610 --> 01:11:40,210
+function is on to طيب مش هيك limit E of X لما X
+
+831
+01:11:40,210 --> 01:11:43,470
+تروح لسالب مالة نهاية بتساوي سفر and limit E of X
+
+832
+01:11:43,470 --> 01:11:47,110
+لما X تروح لمالة نهاية ايش بتساوي؟ بتساوي مالة
+
+833
+01:11:47,110 --> 01:11:55,670
+نهايةيعني الدالة هذه في حالة ال ال E of X اللي
+
+834
+01:11:55,670 --> 01:11:59,070
+احنا سميناها ال X exponential لل X هذه الدالة هذه
+
+835
+01:11:59,070 --> 01:12:03,130
+الدالة زي ما انتوا عارفين لما X تروح إلى سالب ماله
+
+836
+01:12:03,130 --> 01:12:06,830
+نهاية هذا هيروح للسفر ال E of X هتروح للسفر و لما
+
+837
+01:12:06,830 --> 01:12:10,890
+ال X تروح لماله نهاية ال E of X هتروح إيش إلى ماله
+
+838
+01:12:10,890 --> 01:12:14,810
+نهاية نشوف أول شي بالنسبة لمن؟ لل range
+
+839
+01:12:19,570 --> 01:12:24,250
+الان we know that E of 0 بيساوي Eاش واحد اكبر من
+
+840
+01:12:24,250 --> 01:12:29,770
+Eاش من سفر اكيد،ظبط ولا لا؟ and E of X ده بيساوي
+
+841
+01:12:29,770 --> 01:12:36,390
+سفر for X element in R صار عندى الان هاي دالة E of
+
+842
+01:12:36,390 --> 01:12:38,650
+0 إلها واحد،ماشي؟
+
+843
+01:12:40,360 --> 01:12:46,000
+أو E of X مش سفر يعني إيه شمالها لا تقطع محور
+
+844
+01:12:46,000 --> 01:12:51,910
+السينات إطلاقااللي E of X نفسها و 0 من سفرها الأن
+
+845
+01:12:51,910 --> 01:12:57,110
+أنا بقول مستحيل تكون في إيها قيم سالبة يعني مستحيل
+
+846
+01:12:57,110 --> 01:13:02,030
+نلاقي E of X naught اللي هي أصغر من 0 ليش؟ لأنه لو
+
+847
+01:13:02,030 --> 01:13:05,990
+لجينا E of X naught سالبة لو هالجيت عندنا X naught
+
+848
+01:13:05,990 --> 01:13:09,910
+و هيها قيمتها E of X naught اللي هو سالبة يعني
+
+849
+01:13:09,910 --> 01:13:16,460
+هتكون تحتطب ما هي الدالة متصلة مدام متصلة إذا غصب
+
+850
+01:13:16,460 --> 01:13:20,940
+عنها هتيجي تقطع اللي هو ما هتيجي منها لها هتقطع
+
+851
+01:13:20,940 --> 01:13:24,760
+محور السينات إذا هتصير سفر وهذا Contradiction من
+
+852
+01:13:24,760 --> 01:13:28,380
+أين الكلام هذا؟ By Bolzano Intermediate Value
+
+853
+01:13:28,380 --> 01:13:32,760
+Theorem بما أنه احنا في عندنا X0 فرضناها ال E of
+
+854
+01:13:32,760 --> 01:13:39,260
+X0 أصغر من سفر وفي عندي اللي هي E of Zero بساوي
+
+855
+01:13:39,260 --> 01:13:40,980
+واحد اللي هي
+
+856
+01:13:44,440 --> 01:13:48,620
+أه لو فرضنا ان في اكس نوت اكس نوت تكون اللي هو
+
+857
+01:13:48,620 --> 01:13:56,300
+سالبة اكس نوت اصغر من سفر فعندي E of X naught اصغر
+
+858
+01:13:56,300 --> 01:14:05,740
+من سفر وعندي اللي هو في اللي هو E of X بساوي
+
+859
+01:14:05,740 --> 01:14:14,470
+واحد اه وهادي اكبر من سفرأه وفرضنا وجود هذه وفرضنا
+
+860
+01:14:14,470 --> 01:14:18,810
+وجود هذه اذا by intermediate value theorem غصبن
+
+861
+01:14:18,810 --> 01:14:23,650
+عنها there exists c element الفترة اللي احنا بنحكي
+
+862
+01:14:23,650 --> 01:14:28,510
+عنها R such that f of هذه الـ c اللي هي E of C
+
+863
+01:14:28,510 --> 01:14:33,330
+بتساول كمية اللي بينين اللي هي اسمها سفر وهذا
+
+864
+01:14:33,330 --> 01:14:41,860
+contradictionبالتالي بيحقق البلزان انها مستمرة على
+
+865
+01:14:41,860 --> 01:14:47,060
+اي انتقال مغلق على كل أرض لانها بيحقق البلزان انها
+
+866
+01:14:47,060 --> 01:14:47,260
+مستمرة على اي انتقال مغلق على كل أرض لانها بيحقق
+
+867
+01:14:47,260 --> 01:14:47,280
+البلزان انها مستمرة على اي انتقال مغلق على كل أرض
+
+868
+01:14:47,280 --> 01:14:47,700
+لانها بيحقق البلزان انها مستمرة على اي انتقال مغلق
+
+869
+01:14:47,700 --> 01:14:48,880
+على كل أرض لانها بيحقق البلزان انها مستمرة على اي
+
+870
+01:14:48,880 --> 01:14:49,100
+انتقال مغلق على كل أرض لانها بيحقق البلزان انها
+
+871
+01:14:49,100 --> 01:14:51,280
+مستمرة على اي انتقال مغلق على كل أرض لانها بيحقق
+
+872
+01:14:51,280 --> 01:14:54,390
+البلزان انها مستمرة على اي انتقمن سفر طيب مدام ال
+
+873
+01:14:54,390 --> 01:14:57,010
+E of X أكبر من سفر و احنا بنعرف ان ال E prime of X
+
+874
+01:14:57,010 --> 01:15:00,690
+بيتساوي E of X اذا صارت ال E prime أكبر من مين من
+
+875
+01:15:00,690 --> 01:15:04,890
+سفر كل X element ال R ومن ثم هذا معناته ان E is
+
+876
+01:15:04,890 --> 01:15:10,450
+strictly increasing on R اذا اللي هو المطلوب الأول
+
+877
+01:15:10,450 --> 01:15:15,810
+أثبتناه ان E is strictly increasing on R طيب
+
+878
+01:15:24,230 --> 01:15:30,250
+عندي اتنين strictly increasing ال function مظبوط
+
+879
+01:15:30,250 --> 01:15:41,510
+يعني اتنين اصغر من مين من اياش من ال E ليش لأن
+
+880
+01:15:41,510 --> 01:15:53,730
+عندي الواحد E واحد او E of Xقلنا أصغر strictly ولا
+
+881
+01:15:53,730 --> 01:15:57,890
+أكبر strictly من واحد زاد X صح؟ هذه الكورولا
+
+882
+01:15:57,890 --> 01:16:02,810
+remained تمانية تلاتة تلاتة اثبتناها إذا صار عند E
+
+883
+01:16:02,810 --> 01:16:08,050
+of واحدأكبر strictly من واحد زائد وا أكبر strictly
+
+884
+01:16:08,050 --> 01:16:13,970
+من واحد زائد واحد وال E of واحد مين هو E أس واحد
+
+885
+01:16:13,970 --> 01:16:17,390
+مش هيك اتفاجنا يعني هذا إياش اتنين يعني ال E أكبر
+
+886
+01:16:17,390 --> 01:16:22,450
+strictly من مين من الاتنين اتفاجنا طيب اتفاجنا إذا
+
+887
+01:16:22,450 --> 01:16:26,410
+صار عند ال E of اتنين أكبر strictly ال E أكبر من
+
+888
+01:16:26,410 --> 01:16:29,950
+مين من اتنين خلينا نبدأ عليها هذه ال E أكبر من
+
+889
+01:16:29,950 --> 01:16:41,000
+إياش من اتنينالان اكيد عنده ال E of R اللي بيسوي E
+
+890
+01:16:41,000 --> 01:16:48,440
+R او E N خليني اقول E N اكبر من اتنين هتكون اصغر
+
+891
+01:16:48,440 --> 01:16:53,700
+اللي هي اكبر من اتنين أُس N الان as N goes to
+
+892
+01:16:53,700 --> 01:16:57,680
+infinity اذا
+
+893
+01:16:57,680 --> 01:17:04,230
+اكيد هذه هتروح لمين لإنفينيتيوالـ E نفسها اللي هي
+
+894
+01:17:04,230 --> 01:17:08,750
+is strictly increasing is strictly increasing إذا
+
+895
+01:17:08,750 --> 01:17:12,370
+ال E of X تبعتها برضه هتروح لمين ل Infinity لما X
+
+896
+01:17:12,370 --> 01:17:18,650
+تروح إلى وين إلى مالة نهاية ليش لأن لكل L في X
+
+897
+01:17:18,650 --> 01:17:24,670
+أكبر منهابحيث انه اللي هو تصير E of X اللي هي
+
+898
+01:17:24,670 --> 01:17:30,110
+بيساوي E to the X أكبر من E to the N لكل N في X
+
+899
+01:17:30,110 --> 01:17:33,850
+أكبر منها بتصير E of X أكبر منها لأنها strictly
+
+900
+01:17:33,850 --> 01:17:37,710
+increasing فلان لما تروح هذه إلى مالة نهاية الكبار
+
+901
+01:17:37,710 --> 01:17:41,170
+تبعتها وهذه طبعا أكبر دايما موجودة هذا هتروح إلى
+
+902
+01:17:41,170 --> 01:17:45,540
+أين برضه إلى مالة نهاية يعني limit ال E of Xلما X
+
+903
+01:17:45,540 --> 01:17:48,980
+تروح إلى مالة نهاية بتساوي مالة نهاية وقلكم اللي
+
+904
+01:17:48,980 --> 01:17:54,040
+هو لو تجربته اللي هو تثبته أنه بما أنه limit E of
+
+905
+01:17:54,040 --> 01:17:58,840
+N بتروح إلى مالة نهاية by اللي هي limit definition
+
+906
+01:17:58,840 --> 01:18:03,020
+إذا limit E of X لما X تروح إلى مالة نهاية بتساوي
+
+907
+01:18:03,020 --> 01:18:08,080
+مالة نهاية الآن similarly for mean for اللي هو
+
+908
+01:18:08,080 --> 01:18:11,120
+limit
+
+909
+01:18:12,620 --> 01:18:16,560
+الـ E of X لما X تروح لسالب ملا نهاية هذه الان
+
+910
+01:18:16,560 --> 01:18:22,840
+بيصير اتنين أو minus N أكبر من E أو minus N ماشي
+
+911
+01:18:22,840 --> 01:18:28,000
+الحال الان ال limit لهذه as N goes to infinity
+
+912
+01:18:28,000 --> 01:18:31,940
+أكبر أو ساوي ال limit لهذه as N goes to infinity
+
+913
+01:18:31,940 --> 01:18:33,420
+الان
+
+914
+01:18:35,300 --> 01:18:40,100
+هذه اش مالها بيساوي سفر وهذه اوتوماتيك هيساوي ايش؟
+
+915
+01:18:40,100 --> 01:18:44,840
+هيساوي سفر الان as N goes to infinity يعني ال E to
+
+916
+01:18:44,840 --> 01:18:49,720
+the minus N بتروح للسفر من وين؟من اليمين، مظبوط أو
+
+917
+01:18:49,720 --> 01:18:53,060
+تروح للـ Zero، مظبوط لأن at E minus N تروح لما
+
+918
+01:18:53,060 --> 01:18:57,440
+لنهاية As N goes to infinity E to the minus N تروح
+
+919
+01:18:57,440 --> 01:19:03,460
+لإنفينيتي لأن as X بتروح إلى سالب ما لنهاية ال E
+
+920
+01:19:03,460 --> 01:19:07,560
+to the minus X برضه هتروح إلى وين؟ إلى السفر يعني
+
+921
+01:19:07,560 --> 01:19:11,220
+ال E to the X نفسها لما ناخد ال limit لما X تروح
+
+922
+01:19:11,220 --> 01:19:14,580
+بدل ما لنهاية تروح إلى مين؟ سالب ما لنهاية برضه
+
+923
+01:19:14,580 --> 01:19:20,200
+هتساوي إيش؟ السفرإذا صار عندى limit E ضو X لما X
+
+924
+01:19:20,200 --> 01:19:23,560
+تروح السلمة لها يابسة أو سفر و بعتمد على اللى هو
+
+925
+01:19:23,560 --> 01:19:26,780
+الجهتين على ال strictly increasing تبع ال E و
+
+926
+01:19:26,780 --> 01:19:30,580
+التفاصيل اللى هى ال definition بتظهر عندكم أنا
+
+927
+01:19:30,580 --> 01:19:34,220
+مافصلتاش لإنه هو إيه هذا القائم
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a01d5dd629de031a23b14cbea0e12552fb084a37
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2PcqkFMSAOE_raw.srt
@@ -0,0 +1,3764 @@
+1
+00:00:04,910 --> 00:00:08,190
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,190 --> 00:00:12,270
+والصلاة والسلام على سيد المرسلين سيدنا محمد على
+
+3
+00:00:12,270 --> 00:00:18,470
+آله وصحبه أجمعين هذه هي المحاضرة رقم 22 في مساق
+
+4
+00:00:18,470 --> 00:00:23,930
+تحليل حقيقة نيل لطلاب وطالبات الجامعة الإسلاميةقسم
+
+5
+00:00:23,930 --> 00:00:29,530
+الرياضيات في كلية العلوم عنوان المحاضرة اليوم
+
+6
+00:00:29,530 --> 00:00:32,850
+هنكمل chapter تمانية هيكون في عندي اللي هو
+
+7
+00:00:32,850 --> 00:00:37,130
+applications على اللي هي تمانية اللي هي واحد و
+
+8
+00:00:37,130 --> 00:00:41,630
+تمانية اتنين المحاضرة اليوم اللي هي هنحكي عن the
+
+9
+00:00:41,630 --> 00:00:46,730
+exponential and the logarithmic functions هنحكي عن
+
+10
+00:00:46,730 --> 00:00:51,830
+اللي هو دالة ال E to the X ودالة ال Lin أو دالة ال
+
+11
+00:00:51,830 --> 00:00:57,660
+logالان هنثبت اللي هو من خلال .. في البداية هنحكي
+
+12
+00:00:57,660 --> 00:01:03,280
+عن اللي هو ال exponential function أو هنثبت اللي
+
+13
+00:01:03,280 --> 00:01:05,740
+هو وجود ال exponential function
+
+14
+00:01:09,490 --> 00:01:13,630
+احنا استخدمناها قبل هيك مجرد أمثلة بعيدا عن اللي
+
+15
+00:01:13,630 --> 00:01:18,730
+هو انه اللي هي مفترضنا انه معلومات موجودة مسبقا
+
+16
+00:01:18,730 --> 00:01:22,170
+ولا تناقض اللي هو انه نثبتها اليوم لإنه اثباتها
+
+17
+00:01:22,170 --> 00:01:25,410
+اليوم لا يعتمد على اللي حكيناه سابقا بما يخص
+
+18
+00:01:25,410 --> 00:01:29,350
+بأمثلة اللي ذكرت فيها ال exponential الان ال
+
+19
+00:01:29,350 --> 00:01:34,310
+exponential function بدنا نثبت وجودها ايش اللي
+
+20
+00:01:34,310 --> 00:01:38,820
+بنقوله نشوف عبر ال theorem 8 3 1 theoremبقول there
+
+21
+00:01:38,820 --> 00:01:44,060
+exists a function U دلّة E من R ل R إذا في عندنا
+
+22
+00:01:44,060 --> 00:01:49,680
+دلّة اسمها E من R ل R such that الـ E prime of X
+
+23
+00:01:49,680 --> 00:01:55,280
+لها بساول EX لكل X element in Rإتنين E of Zero
+
+24
+00:01:55,280 --> 00:01:58,820
+بساوي إيش واحد يعني الآن النظرية دي بتقولي إنه
+
+25
+00:01:58,820 --> 00:02:02,920
+يوجد عندنا دالة domainها كل ال R و rangeها بروح
+
+26
+00:02:02,920 --> 00:02:10,220
+بصوب في ال R هذه الدالة تحقق شرطين اللي هي E prime
+
+27
+00:02:10,220 --> 00:02:14,500
+of X بساوي E of X و E of Zero بساوي إيش واحدالان
+
+28
+00:02:14,500 --> 00:02:19,920
+نجي اللي هو بدنا نثبت وجود هذه الدالة ايه التي
+
+29
+00:02:19,920 --> 00:02:25,380
+تحقق اللي هو الخواص اللي عندنا المذكورة فيه اللي
+
+30
+00:02:25,380 --> 00:02:29,960
+هي نظريا الان خلينا عشان نروح باتجاه اثبات وجود
+
+31
+00:02:29,960 --> 00:02:34,080
+هذه الدالة خلينا ناخد we inductively define a
+
+32
+00:02:34,080 --> 00:02:37,900
+sequence of continuous functions as follows بدي
+
+33
+00:02:37,900 --> 00:02:43,590
+الآن اعرف اللي هو sequence of functionsالأولى
+
+34
+00:02:43,590 --> 00:02:48,790
+اسمها E1 of X بتساوي واحد زائد X طبعا هذه الدالة
+
+35
+00:02:48,790 --> 00:02:52,790
+موجودة E1 of X بتساوي واحد زائد X هي دالة خطية
+
+36
+00:02:52,790 --> 00:02:58,590
+الآن بدي أعرف ال E2 ال E2 of X بساوي ال
+
+37
+00:02:58,590 --> 00:03:04,170
+integration واحد زائد ال integration من سفر لعند X
+
+38
+00:03:04,170 --> 00:03:13,140
+اللي هو E1 of X D أو E1 of T DTإذاً الـ E2 بدي
+
+39
+00:03:13,140 --> 00:03:17,960
+أجيبها من مين؟ من الـ E1 طبعاً بتيجي الـ E والـ E2
+
+40
+00:03:17,960 --> 00:03:23,500
+اللي هي عبارة عن واحد زائد هذه واحد زائد T اللي هو
+
+41
+00:03:23,500 --> 00:03:27,730
+تفاضلها زي ما انتوا عارفين تكملها اللي هي Tزائد
+
+42
+00:03:27,730 --> 00:03:32,910
+اللي هي T تربيع على اتنين من صفر لعند X ويسوا واحد
+
+43
+00:03:32,910 --> 00:03:38,490
+زائد X زائد X على X تربيع على اتنين هذه الدالة من
+
+44
+00:03:38,490 --> 00:03:45,020
+هي E2 of X E3 of Xبتعرفها بنفس الأسلوب بالساوي 1
+
+45
+00:03:45,020 --> 00:03:49,840
+زائد الـ integration من 0 ل X لدالة اللي وجدتها
+
+46
+00:03:49,840 --> 00:03:56,140
+قبلها اللي هي E2 of T DT بضل أسائي ساير في التعريف
+
+47
+00:03:56,140 --> 00:04:03,760
+بقول in general بتعرف ال E N زائد 1 of Xبساوة الـ
+
+48
+00:04:03,760 --> 00:04:11,420
+1 زي ال integration من 0 ل X EN of T DT إذن الآن
+
+49
+00:04:11,420 --> 00:04:16,020
+عرفت اللي هي ال E1 of X بساوة 1 زي X ومنها عرفت
+
+50
+00:04:16,020 --> 00:04:21,840
+اللي هي E2 وE2 عرفت منها E3 وE3 عرفت منها E4 وهكذا
+
+51
+00:04:21,840 --> 00:04:26,120
+ال EN زي ال 1 of X هتساوة 1 زي ال integration من 0
+
+52
+00:04:26,120 --> 00:04:31,440
+ل X لل EN اللي جاب الها ديof D D T لكل N element
+
+53
+00:04:31,440 --> 00:04:36,720
+in N و لكل X element in M in R نيجي الآن نطلع على
+
+54
+00:04:36,720 --> 00:04:40,920
+الملاحظات اللي بدنا نحكيها عشان نستخدمها الان 1
+
+55
+00:04:40,920 --> 00:04:46,840
+زائد X دالة متصلة مش متصلة أصلا بس هي أصلا قابلة
+
+56
+00:04:46,840 --> 00:04:51,900
+للتفاضل أيضا اللي هي differentiable الان بناء عليه
+
+57
+00:04:51,900 --> 00:05:00,140
+مدام ال E1 is continuous هتكون اللي هي E2E2 هي
+
+58
+00:05:00,140 --> 00:05:03,940
+الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 الـ E1
+
+59
+00:05:03,940 --> 00:05:04,180
+هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 الـ
+
+60
+00:05:04,180 --> 00:05:07,840
+E1 هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1
+
+61
+00:05:07,840 --> 00:05:11,080
+الـ E1 هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ
+
+62
+00:05:11,080 --> 00:05:12,820
+E1 الـ E1 هي الانتجراش للـ E1 الـ E1 هي الانتجراش
+
+63
+00:05:12,820 --> 00:05:14,980
+للـ E1 الـ E1 هي الانتجراش للـ E1 الـ E1 هي
+
+64
+00:05:14,980 --> 00:05:18,980
+الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 الـ E1
+
+65
+00:05:18,980 --> 00:05:22,820
+هي الانتجراش للـ E1 الـ E1 هي الانتجراش للـ E1 ال
+
+66
+00:05:25,750 --> 00:05:27,270
+الآن F.E.L
+
+67
+00:05:31,050 --> 00:05:34,950
+in on R then it is integrable over any bounded
+
+68
+00:05:34,950 --> 00:05:39,590
+interval زي ما قلنا مدام هذا continuous اللي هي E
+
+69
+00:05:39,590 --> 00:05:45,210
+اللي هي 2 continuous ومن هنا هتطلع E 3 continuous
+
+70
+00:05:45,210 --> 00:05:49,530
+وE 4 continuous إذا صارت هذي دايما continuous وده
+
+71
+00:05:49,530 --> 00:05:53,170
+continuous وده integration exist و by fundamental
+
+72
+00:05:53,170 --> 00:05:57,250
+theorem هذا ال integration كله على بعض can be
+
+73
+00:05:57,250 --> 00:06:01,160
+differentiatedوهتكون الهو ايش is differentiable
+
+74
+00:06:01,160 --> 00:06:05,520
+ومنه so EN زائد واحد is well defined by the above
+
+75
+00:06:05,520 --> 00:06:09,300
+formula moreover زي ما قلت it is from fundamental
+
+76
+00:06:09,300 --> 00:06:12,400
+theorem of calculus ال second form اللي هي سبعة
+
+77
+00:06:12,400 --> 00:06:15,920
+تلاتة خمسة هيكون عند ال EN زائد واحد is
+
+78
+00:06:15,920 --> 00:06:19,280
+differentiable ومش هيك وتفاضل هذه زي ما احنا
+
+79
+00:06:19,280 --> 00:06:24,540
+عارفين بساوي بنشيل ال integration طبعا التفاضل بلغ
+
+80
+00:06:24,540 --> 00:06:29,220
+ال integrationبصير en of x فبصير عندي ال en زائد
+
+81
+00:06:29,220 --> 00:06:34,240
+واحد prime of x موجودة ويساوي en x for all n
+
+82
+00:06:34,240 --> 00:06:37,720
+element in N إذن الآن عملنا sequence ال sequence
+
+83
+00:06:37,720 --> 00:06:40,580
+هذه طلعت sequence of differentiable functions و ال
+
+84
+00:06:40,580 --> 00:06:43,860
+derivative لل en زائد واحد prime هي بترجع لمين
+
+85
+00:06:43,860 --> 00:06:50,320
+بتيجي اللي هي ال en of xطيب الان هذا كله و ده
+
+86
+00:06:50,320 --> 00:06:53,900
+خليني اسميها تلاتة و خليني نحضر حالنا نصل للي بدنا
+
+87
+00:06:53,900 --> 00:06:59,500
+ياجولكم وين هنصل في الآخر هوصلكم انه اللي هو ال
+
+88
+00:06:59,500 --> 00:07:05,400
+limit لهذه ال sequence او لهذه ال sequence هي ال E
+
+89
+00:07:05,400 --> 00:07:12,300
+of X اللي انا بثبت وجودهاوستكون اللي هي بتحقق
+
+90
+00:07:12,300 --> 00:07:16,440
+الشروط اللي حكيناها خلّينا نشوف ما لاستعجلش نشوف
+
+91
+00:07:16,440 --> 00:07:19,900
+إيش اللي بدنا نصلله إذا اللي عملناه كوّننا
+
+92
+00:07:19,900 --> 00:07:23,380
+sequence sequence زي ما قلنا اللي هي ال sequence
+
+93
+00:07:23,380 --> 00:07:28,160
+بدأت عشان يبقى لكم الذاكرين E1 of X بساوي واحد
+
+94
+00:07:28,160 --> 00:07:34,760
+زائد X E and زائد واحد of X بساوي الانتجرأت واحد
+
+95
+00:07:35,450 --> 00:07:39,790
+بسوء واحدة زي الـ integration من صفر لعدد X E N of
+
+96
+00:07:39,790 --> 00:07:47,450
+T DT خلّين هذولة أمامنا طبعاً N element in N عندي
+
+97
+00:07:47,450 --> 00:07:54,630
+و X أي element وين in Rطيب إذا الان سار عندي اللي
+
+98
+00:07:54,630 --> 00:07:58,430
+هو ال .. ده اللي هذي is differential لان بقوللي
+
+99
+00:07:58,430 --> 00:08:03,230
+انه ابن الدعي ويمكن لو حد شاف قبل بشوية ما وصلنا ل
+
+100
+00:08:03,230 --> 00:08:08,450
+E2 E2 كانت عبارة عن واحد زي دكستر بيه على اتنين
+
+101
+00:08:08,450 --> 00:08:13,070
+اللي هو اللي هي اتنين factorialلو كملنا هيكون E N
+
+102
+00:08:13,070 --> 00:08:16,910
+of X بتساوي 1 زياد X على 1 factorial X تربيه على 2
+
+103
+00:08:16,910 --> 00:08:21,170
+factorial زياد X وصف N على 100 على N factorial لكل
+
+104
+00:08:21,170 --> 00:08:25,750
+X element in R هذه الـ N صحيحة اللي هي لكل N
+
+105
+00:08:25,750 --> 00:08:31,470
+element in R اللي هو طبعا اثباتها سهل نثبتها by
+
+106
+00:08:31,470 --> 00:08:36,010
+induction خلينا نشوف كيفنا نثبت أربعة by induction
+
+107
+00:08:58,380 --> 00:09:01,020
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+108
+00:09:01,020 --> 00:09:04,640
+أربعة
+
+109
+00:09:04,640 --> 00:09:06,540
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+110
+00:09:06,540 --> 00:09:06,720
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+111
+00:09:06,720 --> 00:09:06,900
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+112
+00:09:06,900 --> 00:09:06,900
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+113
+00:09:06,900 --> 00:09:06,900
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+114
+00:09:06,900 --> 00:09:06,900
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+115
+00:09:06,900 --> 00:09:06,900
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+116
+00:09:06,900 --> 00:09:08,610
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أfour is
+
+117
+00:09:08,610 --> 00:09:16,450
+a true four and بتساوي كتابة يعني صار عند الالالـ
+
+118
+00:09:16,450 --> 00:09:23,550
+E K of X بتساوي 1 زائد X على 1 factorial زائد X
+
+119
+00:09:23,550 --> 00:09:29,170
+تربيع على 2 factorial زائد X أُس K على K factorial
+
+120
+00:09:29,170 --> 00:09:33,890
+هذا لما نفرض إن اللي هي .. اللي هي الأربعة is true
+
+121
+00:09:33,890 --> 00:09:39,150
+for N بتساوي K بدنا نثبت إن E K زائد 1 هتطلع اللي
+
+122
+00:09:39,150 --> 00:09:43,870
+هي هذهزائد x أس k على k زائد واحد فيكتوريا اللي
+
+123
+00:09:43,870 --> 00:09:48,790
+على ال net بتطلع أربعة صحيحة for k زائد واحد ده
+
+124
+00:09:48,790 --> 00:09:56,070
+نحسب خلّينا نحسب الآن E k زائد واحد of x حسب اللي
+
+125
+00:09:56,070 --> 00:10:01,370
+احنا مفترضينه أو معرفين ال sequence على أساسه E k
+
+126
+00:10:01,370 --> 00:10:04,830
+زائد واحد of x أيش بتساوي واحد زائد ال integration
+
+127
+00:10:04,830 --> 00:10:14,410
+من صفر ل X E k of T DTمظبوط؟ طيب الان بدي اعوض عن
+
+128
+00:10:14,410 --> 00:10:20,030
+E K of T احنا مفترضينها صحيحة ل K اذا E K of X
+
+129
+00:10:20,030 --> 00:10:24,230
+هيها اذا باجي بعوض بيصير Y ساوي واحد زائد ال
+
+130
+00:10:24,230 --> 00:10:29,250
+integration من صفر ل X E K of T اللي هي واحد زائد
+
+131
+00:10:29,250 --> 00:10:33,170
+T زائد T تربيع طبعا واحد فيكتوريال اللي هي واحد
+
+132
+00:10:33,170 --> 00:10:40,080
+على اتنين فيكتوريال زائد لما أصل X أو T أس Kعلى K
+
+133
+00:10:40,080 --> 00:10:46,520
+فكتوريال الكل إشماله DT لأن اللي هي أكيد وضحت
+
+134
+00:10:46,520 --> 00:10:49,660
+الصورة بدل الفاضل نطلع قيمة التفاصيل الكامل و نطلع
+
+135
+00:10:49,660 --> 00:10:54,360
+قيمة التكامل و يساوي واحد هيوزايد ما هو جاعد زاد
+
+136
+00:10:54,360 --> 00:11:00,520
+هذا ال integration اللي هو عبارة عن Tزائد T تربيع
+
+137
+00:11:00,520 --> 00:11:06,140
+على 2 في 1 يعني 2 factorial زائد T تكعيب على 3 في
+
+138
+00:11:06,140 --> 00:11:10,920
+2 factorial يعني 3 factorial زائد لما أصل لآخر 1 T
+
+139
+00:11:10,920 --> 00:11:15,640
+أُس K زائد 1 على K زائد 1 في K factorial هي K زائد
+
+140
+00:11:15,640 --> 00:11:22,230
+1 لكل factorial هذا الكلام من 0 لمين؟لعند X واضحة
+
+141
+00:11:22,230 --> 00:11:26,550
+الصورة ويساوي عبارة عن لما اعوض من 0 ل X بيصير 1
+
+142
+00:11:26,550 --> 00:11:32,090
+زائد X زائد X تربيع على 2 factorial لما أصل لأخر
+
+143
+00:11:32,090 --> 00:11:38,210
+واحد X K زائد 1 على K زائد 1فاكتوريال إذا فعلاً
+
+144
+00:11:38,210 --> 00:11:42,110
+طلعت عندي a k زائد واحد بساوي هذا المقدار يعني
+
+145
+00:11:42,110 --> 00:11:46,450
+بمعنى آخر أربعة طلعت ال true for n بتساوي k زائد
+
+146
+00:11:46,450 --> 00:11:51,830
+واحد إذا من كل هذا ال induction بنكون أثبتنا أن e
+
+147
+00:11:51,830 --> 00:11:56,430
+n of x بساوي هذا الكلام لكل x element in R لكل n
+
+148
+00:11:56,430 --> 00:12:00,630
+element in Nإذاً هذه صورة اللي هي الـEN of X صورة
+
+149
+00:12:00,630 --> 00:12:05,150
+غير الصورة اللي عرفناها فوق استنتجناها منها الآن
+
+150
+00:12:05,150 --> 00:12:11,770
+خلّينا نروح باتجاه إثبات إنه ال limit للـEN هذه أو
+
+151
+00:12:11,770 --> 00:12:17,910
+الـEK أو الـEN أو اللي هي is uniformly convergent
+
+152
+00:12:18,680 --> 00:12:23,900
+to some function هذه الـ some function هي اللي
+
+153
+00:12:23,900 --> 00:12:29,120
+بتدعي انها هتكون ال exponential طيب اللي بنسميها
+
+154
+00:12:29,120 --> 00:12:32,840
+exponential بعد شوية اللي هي بتحقق شرطين اللي
+
+155
+00:12:32,840 --> 00:12:35,400
+حكينا عنهم لسه احنا بنعرف ال exponential احنا
+
+156
+00:12:35,400 --> 00:12:38,340
+بنعرف الدالة هذه لكن لأن معلوماتنا عارفين من اول
+
+157
+00:12:38,340 --> 00:12:43,000
+ال exponentialالان احنا الدالة هذه اللى هنثبت
+
+158
+00:12:43,000 --> 00:12:46,540
+وجودها اليوم هي اللى بعد شوية بعد ما نثبت ال
+
+159
+00:12:46,540 --> 00:12:50,880
+uniqueness لها بنسميها ال exponential زي ما هنشوف
+
+160
+00:12:50,880 --> 00:12:56,620
+بعد شوية الان اذا ال sequence اللى عندى هذه
+
+161
+00:12:56,620 --> 00:13:05,300
+هيوضعها الان قلنا E Nof X هذه المعادلة التانية هي
+
+162
+00:13:05,300 --> 00:13:11,560
+واحد زائد X زائد X تربيع على اتنين factorial زائد
+
+163
+00:13:11,560 --> 00:13:15,600
+X أُس N على N factorial وهذا الشكل طبعا أنتوا مش
+
+164
+00:13:15,600 --> 00:13:20,240
+غريب عليكم بتعرفوه الآن خليني أخد الان let A أكبر
+
+165
+00:13:20,240 --> 00:13:24,120
+من سفر بيه given افترض ان A اني اللي هو real
+
+166
+00:13:24,120 --> 00:13:28,660
+number أكبر من مين من سفر باخده arbitrarily لكن
+
+167
+00:13:28,660 --> 00:13:33,470
+خليني نحكي عن A محددةالان if absolute value of X
+
+168
+00:13:33,470 --> 00:13:37,910
+أصغر أو تساوي A يعني بتحكي الحديث هان على ال Xات
+
+169
+00:13:37,910 --> 00:13:43,590
+اللي في ال R اللي من عند ناقص A لعند مين ال A يعني
+
+170
+00:13:43,590 --> 00:13:48,610
+ال absolute value لهن هذولة أصغر أو تساوي ال A
+
+171
+00:13:48,610 --> 00:13:52,390
+يعني في الفترة المغلقة اللي أمامي اللي بين ناقص ال
+
+172
+00:13:52,390 --> 00:13:58,870
+A و ال A بتتحدث شوف الآن احسبلي Em of X ناقص En of
+
+173
+00:13:58,870 --> 00:14:03,750
+Xو يساوي و بدنا نفترض لكم ان الان ايه شمالها اكبر
+
+174
+00:14:03,750 --> 00:14:07,910
+من الان و الان اكبر من اتنين ايه اتنين ايه مكتوب
+
+175
+00:14:07,910 --> 00:14:10,850
+اتنين ايه لغرض الحسابات اللي جيت منشوفها بنفع
+
+176
+00:14:10,850 --> 00:14:13,270
+تلاتة ايه، بنفع اربعة ايه، بنفع خمسة ايه، بنفع ستة
+
+177
+00:14:13,270 --> 00:14:16,550
+ايه، بنفع كله بنفع هذا الكلام على اساس انك ماينفعش
+
+178
+00:14:16,550 --> 00:14:19,550
+اقول نص ايه او تلت ايه او ربع ايه لأنها مش هتقد
+
+179
+00:14:19,550 --> 00:14:23,910
+الغرض اللي بدي انالأن مين اخترت أنا اخترت اللي هو
+
+180
+00:14:23,910 --> 00:14:29,650
+الأمات والأنات اللي أكبر منين من اتنين في الـA
+
+181
+00:14:29,650 --> 00:14:34,390
+اللي هي قيبة مين الـA اللي هي نص الفترة اللي عندي
+
+182
+00:14:34,390 --> 00:14:39,210
+أو طول نص الفترة طيب، احسبلي ايه M of X ناقص Y of
+
+183
+00:14:39,210 --> 00:14:44,360
+X؟E M of X اللي هي عبارة عن واحد زائد X زائد X
+
+184
+00:14:44,360 --> 00:14:49,360
+تربيع و هجابل في الطريق من ال X M لأنه M أكبر X
+
+185
+00:14:49,360 --> 00:14:52,720
+تربيع على M فكتوريال زائد X M زائد واحد على M زائد
+
+186
+00:14:52,720 --> 00:14:57,280
+واحد فكتوريال لما أصل الأخر واحدة من X أُس M على M
+
+187
+00:14:57,280 --> 00:15:03,400
+فكتوريال يعني الآن هذي هيكون زي هيك لما أصل طبعا X
+
+188
+00:15:03,400 --> 00:15:10,500
+M زائد واحد على Mزائد واحد factorial زائد لمّا أصل
+
+189
+00:15:10,500 --> 00:15:15,760
+لعند X أُس M على M factorial هذه مين هي هذه عبارة
+
+190
+00:15:15,760 --> 00:15:24,220
+عن ال EM يعني ال EM هتساوي اللي هي E of XE N of X
+
+191
+00:15:24,220 --> 00:15:30,020
+زائد المتبقي هذا الان حاصل طرح الاتنتين هيكون
+
+192
+00:15:30,020 --> 00:15:33,480
+عبارة عن لإن المفترض ال M أكبر من L زي ما قلنا
+
+193
+00:15:33,480 --> 00:15:37,700
+حاصل طرح اللي هيكون اللي هو المتبقي هذا X N زائد
+
+194
+00:15:37,700 --> 00:15:40,840
+واحد على N زائد واحد فيكتوريال لما أصل ل X M على M
+
+195
+00:15:40,840 --> 00:15:46,240
+إيش فيكتوريال ماشي الحال إذا الأن أوصلنا لحاصل طرح
+
+196
+00:15:46,240 --> 00:15:51,340
+دولة بساوي هذا المقدر نيجي نكمل الأن عندي
+
+197
+00:15:53,560 --> 00:15:58,460
+عند ال absolute value لل X أصغر من 100 من A
+
+198
+00:16:10,590 --> 00:16:17,130
+زائد absolute value زائد xn زائد اتنين على n زائد
+
+199
+00:16:17,130 --> 00:16:22,710
+اتنين factorial زائد لما أصل لأخر واحد x أسم م على
+
+200
+00:16:22,710 --> 00:16:28,150
+m factorial ماشي الحال طيب الآن ان ان كل x من
+
+201
+00:16:28,150 --> 00:16:31,270
+هدولة ال absolute value هي أصغر يساوي منين ايه إذا
+
+202
+00:16:31,270 --> 00:16:36,650
+صار هذا المقدار أصغر أو يساوي هذا المقدار اللي هنا
+
+203
+00:16:36,650 --> 00:16:45,550
+أصغر أو يساوي Mزائد واحد على N آسف A أُس N زائد
+
+204
+00:16:45,550 --> 00:16:49,970
+واحد لأن ال absolute value X أصغر تساوي A إذا X N
+
+205
+00:16:49,970 --> 00:16:54,510
+زائد واحد أصغر أو ساوي ال A أُس N زائد واحد على N
+
+206
+00:16:54,510 --> 00:17:00,870
+زائد واحد factorial زائد التاني اللي هو A N زائد
+
+207
+00:17:00,870 --> 00:17:07,130
+اتنينعلى n زائد 2 factorial زائد لما أصل لآخر واحد
+
+208
+00:17:07,130 --> 00:17:14,870
+اللي هو عبارة عن a أس m على m factorial ماشي الحال
+
+209
+00:17:14,870 --> 00:17:21,080
+طيبالان خليني اخد من هدولة ال a n زائد واحد على ال
+
+210
+00:17:21,080 --> 00:17:24,480
+n زائد واحد factorial عامل مشترك قبل ما اصلح هذه
+
+211
+00:17:24,480 --> 00:17:28,520
+الخطوة لسه اه خليني اخد عامل مشترك بيصير عندي a n
+
+212
+00:17:28,520 --> 00:17:33,180
+زائد واحد على n زائد واحد factorial فاش اللي بيضل
+
+213
+00:17:33,180 --> 00:17:39,420
+هنا فيه اللي بيضل هنا واحد زائد هنا بيضل a على n
+
+214
+00:17:39,420 --> 00:17:46,280
+زائد اتنين اكيد زائد اللي بعدها a تربيع على nزائد
+
+215
+00:17:46,280 --> 00:17:52,160
+اتنين فان زائد تلاتة زائد لما أصل لآخر واحد مين
+
+216
+00:17:52,160 --> 00:17:57,080
+آخر واحد بشيل منه ان زائد واحد بيصير a أس ام ناقص
+
+217
+00:17:57,080 --> 00:18:03,000
+ان ناقص واحد على اللي بيضل من ان زائد اتنين مضروب
+
+218
+00:18:03,000 --> 00:18:09,250
+لعند ان ام ناقص ان ناقص واحد هذول الأنماشي الحال
+
+219
+00:18:09,250 --> 00:18:13,470
+هذا أخد تمين يا جماعة ماعليش دخل الكلام مع بعضه بس
+
+220
+00:18:13,470 --> 00:18:18,130
+أكيد أنتوا مستوعبين إيش بقول طلعت ال a n زائد واحد
+
+221
+00:18:18,130 --> 00:18:21,090
+على n زائد واحد في كتوريا العام المشترك طلع عندي
+
+222
+00:18:21,090 --> 00:18:26,550
+هذا المقدار الان عندي أكيد ال n زائد اتنين أكبر من
+
+223
+00:18:26,550 --> 00:18:32,050
+مين من ال end فمقلوبه أصغرأه فبصير عندى اللى هو
+
+224
+00:18:32,050 --> 00:18:38,050
+عندى اللى هى هذا المقدار a n على l زائد 2 أصغر أو
+
+225
+00:18:38,050 --> 00:18:42,170
+شاوي a على n و اللى بعده a تربيع أصغر أو شاوي ا ا
+
+226
+00:18:42,170 --> 00:18:44,370
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+227
+00:18:44,370 --> 00:18:44,410
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+228
+00:18:44,410 --> 00:18:45,090
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+229
+00:18:45,090 --> 00:18:46,010
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+230
+00:18:46,010 --> 00:18:47,730
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+231
+00:18:47,730 --> 00:18:47,730
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+232
+00:18:47,730 --> 00:18:48,010
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+233
+00:18:51,320 --> 00:18:55,380
+أكبر من أنه وهذه أكبر من أنه فمقلوبهم بيصير هذا
+
+234
+00:18:55,380 --> 00:19:00,980
+المقدار أصغر اللي هو أو يساوي المقدار اللي بعده
+
+235
+00:19:00,980 --> 00:19:07,730
+بيصير عندى هذا المقدارأصغر أو يساوي هذا زي ما هو و
+
+236
+00:19:07,730 --> 00:19:13,670
+هذه واحد هذه a على n لأنها هتكون أكبر a تربيع على
+
+237
+00:19:13,670 --> 00:19:19,170
+n تربيع ان تربيع هتكبر لما أصل ل a m minus n نقص
+
+238
+00:19:19,170 --> 00:19:25,420
+واحد على m minus n نقص واحد لأن هنا دولة عددهمن
+
+239
+00:19:25,420 --> 00:19:30,200
+نقص واحد من الانز هيكون ان طبعا استبدالت كل واحدة
+
+240
+00:19:30,200 --> 00:19:34,400
+بان فهيطلع بالشكل هذا وبتظل ال inequality صحيحة
+
+241
+00:19:34,400 --> 00:19:38,540
+خلصنا من هذا طيب دعونا نشوف كيف أضبح لكم هذا دعونا
+
+242
+00:19:38,540 --> 00:19:48,770
+نخلص منه نجي الآن اللي هو نرجعانكمل الحسبة هذا
+
+243
+00:19:48,770 --> 00:19:57,670
+الان المقدار عندى اللى هو المقدار هذا هيه اتطلعوا
+
+244
+00:19:57,670 --> 00:20:06,710
+عندى ال a ال a على n ايش انا ماخد ال n ماخد ال n
+
+245
+00:20:06,710 --> 00:20:12,930
+اكبر من مين من اتنين a يعني ال a اصغر من n على مين
+
+246
+00:20:13,680 --> 00:20:21,900
+على اتنين مظبوط ال A أصغر من N على اتنين واضحة جسم
+
+247
+00:20:21,900 --> 00:20:25,660
+ال N على اتنين و N على اتنين صارت N على اتنين أكبر
+
+248
+00:20:25,660 --> 00:20:29,940
+من مين من ايه بدي استخدمها الآن هذه ال N بصير أصغر
+
+249
+00:20:29,940 --> 00:20:34,020
+أو يساوي هذا المقدار بصير أصغر أو يساوي هذا بحكي
+
+250
+00:20:34,020 --> 00:20:39,590
+عن هذا بصير أصغر أو يساوي اللي هو Aأُس ان زائد
+
+251
+00:20:39,590 --> 00:20:45,410
+واحد على ان زائد واحد الكل فكتوريال فيه اللي هو
+
+252
+00:20:45,410 --> 00:20:56,830
+واحد زائد ا على ان زائد ا تربية على ان تربية زائد
+
+253
+00:20:56,830 --> 00:21:06,530
+ا اللي هو ا تكعيب على ان تكعيبزائد مش بتصل لهذا
+
+254
+00:21:06,530 --> 00:21:11,670
+زائد و بتظل ماشيها يشمالها إلى ما لا نهاية يعني
+
+255
+00:21:11,670 --> 00:21:17,110
+بتضيف عليها a على n أس ام ناقص n a على n أس ام
+
+256
+00:21:17,110 --> 00:21:20,290
+ناقص n زائد واحد وهكذا تظلها إلى ما لا نهاية يعني
+
+257
+00:21:20,290 --> 00:21:23,850
+بتحولها لمين ل infinite series طيب احنا قلنا ال a
+
+258
+00:21:23,850 --> 00:21:28,670
+أصغر من n على 2يعني ال a n على n أصغر من مين؟ من
+
+259
+00:21:28,670 --> 00:21:32,930
+نص عرفته الأن إيش بدأ أسأل صار عندي هذا المقدار
+
+260
+00:21:32,930 --> 00:21:39,310
+أصغر أو يساوي a أس n زائد واحد على n زائد واحد لكل
+
+261
+00:21:39,310 --> 00:21:45,690
+factorial مضروب في مين؟ اللي هو واحد زائد نص زائد
+
+262
+00:21:45,690 --> 00:21:50,670
+نص تربيع أه لأن a على n أصغر من مين يا جماعة؟ من
+
+263
+00:21:50,670 --> 00:21:57,850
+نص زائدتربيع زاد نص تتعيد زاد الآخرين لأن هذه صارت
+
+264
+00:21:57,850 --> 00:22:02,470
+عبارة عن geometric series مجموحها هذه بتساوي مجموح
+
+265
+00:22:02,470 --> 00:22:07,050
+هذه عبارة عن واحد على واحد ناقصه اللي هو نص وهي
+
+266
+00:22:07,050 --> 00:22:12,730
+ساوي جداش اتنينماشي إذا هذا المقدار اللي هو صار
+
+267
+00:22:12,730 --> 00:22:16,510
+عبارة عن اتنين في هذا المقدار اللي هو وصلنا له
+
+268
+00:22:16,510 --> 00:22:20,650
+أصغر أو يساوي a n زائد واحد على n زائد واحد
+
+269
+00:22:20,650 --> 00:22:23,890
+فيكتوريا مضروب في مين؟ في اتنين يعني حسابات هذه
+
+270
+00:22:23,890 --> 00:22:28,770
+طيب إذا صار عندي الآن هاي اللي بدي أصله و اللي
+
+271
+00:22:28,770 --> 00:22:31,630
+كاتبه باختصار هو لإنه بيعتبر ان الباقية حساباتي
+
+272
+00:22:31,630 --> 00:22:36,950
+بتعرفوا تحسبوها em-n of x of x أصغر أو يساوي هذا
+
+273
+00:22:36,950 --> 00:22:43,450
+المقدار على مين؟ على اتنينالان شوف ما يليه الان as
+
+274
+00:22:43,450 --> 00:22:49,590
+n goes to infinity هذا المقدار هذا المقدار as n
+
+275
+00:22:49,590 --> 00:22:54,230
+goes to infinity ال limit بتروح للصفر لأن a n زائد
+
+276
+00:22:54,230 --> 00:22:57,110
+واحد على n زائد واحد كل factorial as n goes to
+
+277
+00:22:57,110 --> 00:23:01,190
+infinity ايش بده يروح للصفر يعني بمعنى اخر مدام
+
+278
+00:23:01,190 --> 00:23:04,430
+بده يروح للصفر طبعا وذا كبرت الان بتكبر مين برضه
+
+279
+00:23:04,430 --> 00:23:07,850
+مباشرة ام لأن ام اكبر منها اذا four
+
+280
+00:23:10,880 --> 00:23:19,800
+for large ن و أم we get
+
+281
+00:23:23,490 --> 00:23:31,050
+E M of X ناقص E N of X اللي هي أصغر أو يساوي من
+
+282
+00:23:31,050 --> 00:23:38,070
+هذه هذه أصلا for large N as N goes to infinity هذا
+
+283
+00:23:38,070 --> 00:23:43,470
+المقدار بيصير أصغر من أي ي في الدنيا اللي هي بيصير
+
+284
+00:23:43,470 --> 00:23:49,330
+أصغر من مين من ي أو أصغر أو يساوي ي as N و M
+
+285
+00:23:49,330 --> 00:23:54,630
+become very very largeماشي الحال لإنه ال limit لل
+
+286
+00:23:54,630 --> 00:23:59,110
+a n على n فكتوره ليش بيساوي بيساوي سفر إذا صار
+
+287
+00:23:59,110 --> 00:24:05,950
+عندي الآن اللي هي E m of X E n of X أصغر وشوى Y
+
+288
+00:24:05,950 --> 00:24:15,250
+لكل X وين موجودة في الفترة A ماقص A أو A ماشي
+
+289
+00:24:15,250 --> 00:24:23,160
+الحال الآن بناء عليهالان لكل X بغض النظر على ال X
+
+290
+00:24:23,160 --> 00:24:28,000
+اللي هو بيكون عندي أنه I'm very large وبيعطيني هذا
+
+291
+00:24:28,000 --> 00:24:32,560
+أصغر وسوء من إبسلون وهذه اللي سميناها Cauchy's
+
+292
+00:24:32,560 --> 00:24:37,470
+criterion for uniformاللي هو convergence في ال ..
+
+293
+00:24:37,470 --> 00:24:43,590
+اللي هو section 81 بناء عليها بطلع عندى E and اللي
+
+294
+00:24:43,590 --> 00:24:47,090
+هو converges uniformly to some function مش
+
+295
+00:24:47,090 --> 00:24:51,410
+عارفينها اللي هي .. اللي هي converges uniformly on
+
+296
+00:24:51,410 --> 00:24:59,770
+mean سالب a أو a باشي الحالة الالالآن عندي it
+
+297
+00:24:59,770 --> 00:25:02,610
+follows the sequence a and a converge uniformly on
+
+298
+00:25:02,610 --> 00:25:07,210
+the interval ناقص a و a where a أكبر من 0 لكن a
+
+299
+00:25:07,210 --> 00:25:11,670
+أكبر من 0 was a شمالها arbitrarily يعني اللي وصلنا
+
+300
+00:25:11,670 --> 00:25:18,110
+له ما ياليا يا جماعة اللي وصلنا له أنهعندي اللي هي
+
+301
+00:25:18,110 --> 00:25:23,210
+الـ sequence هذه لو جيت أخدت for every a element
+
+302
+00:25:23,210 --> 00:25:27,130
+in R و a أكبر من سفر لو وصلنا له اللي كانت a
+
+303
+00:25:27,130 --> 00:25:32,130
+arbitrarily وجدنا أنه هيكون عند الـ EL converges
+
+304
+00:25:32,130 --> 00:25:39,550
+uniformly on ماقص a و مين و a ماشي الحال طيب بناء
+
+305
+00:25:39,550 --> 00:25:48,200
+عليه لو أنت جيت أخدت خد الآن letX element in R، أي
+
+306
+00:25:48,200 --> 00:25:53,540
+X element in R، مدام X في R، إذا أكيد الـ X عشر،
+
+307
+00:25:53,540 --> 00:25:59,250
+عشرين، تلاتين، مليون، ممكن ما تكون،بقدر ألاقي A
+
+308
+00:25:59,250 --> 00:26:05,890
+بحيث أن X تنتمي إلى الفترة من ناقص A لعند مين لعند
+
+309
+00:26:05,890 --> 00:26:11,590
+إيه يعني مثلا ال X لجيتها 100 باخد ال A 110 بصير
+
+310
+00:26:11,590 --> 00:26:17,850
+ال X بين اللي هي ناقص 110 و100 إيش ما تيجي X بلاقي
+
+311
+00:26:17,850 --> 00:26:24,470
+لها Aإذا there exists a such that x element in a
+
+312
+00:26:24,470 --> 00:26:31,410
+minus a أكبر من صفر طبعا minus a ومين أو a أكيد طب
+
+313
+00:26:31,410 --> 00:26:34,390
+ما هو احنا قد أثبتنا انه لكل a element in R
+
+314
+00:26:38,870 --> 00:26:44,730
+Converge uniformly للـ A اللي لاجناها هذه On ناقص
+
+315
+00:26:44,730 --> 00:26:49,690
+A و A لهذه الـ A يعني بمعنى معناه مادام Converge
+
+316
+00:26:49,690 --> 00:26:55,030
+uniformly لإذا E N of Xاللي هو converges point
+
+317
+00:26:55,030 --> 00:26:58,250
+-wise to some function عند مين؟ عند الـ X اللي
+
+318
+00:26:58,250 --> 00:27:03,670
+أخدتها هانا هذه إذا الأن for any X element in R
+
+319
+00:27:03,670 --> 00:27:11,450
+for any X element in R هنلاقي E N of X convergesما
+
+320
+00:27:11,450 --> 00:27:15,250
+دام ال E N of X is convergent for every X element
+
+321
+00:27:15,250 --> 00:27:22,230
+in R إذا صارت عندي limit ال E N of X as N goes to
+
+322
+00:27:22,230 --> 00:27:27,830
+infinity exists for every X element in R ما دام
+
+323
+00:27:27,830 --> 00:27:34,210
+exist حسب اللي قلناها إذا الآن شرعت لتعريف الدالة
+
+324
+00:27:34,210 --> 00:27:40,600
+التالية الآن أنا بقول إنه احنا صار عندنااللي هو
+
+325
+00:27:40,600 --> 00:27:47,760
+مشروع ان نقول we define E من R لR by limit E N of
+
+326
+00:27:47,760 --> 00:27:53,940
+X اللي هي موجودة سميتها إيش اسمها E of X for X
+
+327
+00:27:53,940 --> 00:28:00,760
+element of Rوجود اللي هو دالة اسمها E أنا سميتها E
+
+328
+00:28:00,760 --> 00:28:06,400
+من R لعند R بحيث ان E of X هي limit ال E أنه VIX
+
+329
+00:28:06,400 --> 00:28:11,480
+اللي أثبتت وجوده بدي أثبتلك الأن أن E of X هذه هي
+
+330
+00:28:11,480 --> 00:28:16,120
+الدالة المبتغة اللي بتحقق الشروط اللي طلبها في
+
+331
+00:28:16,120 --> 00:28:21,740
+النظرية نشوف كيف طيب صلوا على النبي عليه الصلاة
+
+332
+00:28:21,740 --> 00:28:22,160
+والسلام
+
+333
+00:28:35,970 --> 00:28:39,830
+الان عندى ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+334
+00:28:39,830 --> 00:28:39,910
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+335
+00:28:39,910 --> 00:28:39,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+336
+00:28:39,970 --> 00:28:40,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+337
+00:28:40,290 --> 00:28:42,410
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+338
+00:28:42,410 --> 00:28:42,810
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+339
+00:28:42,810 --> 00:28:44,810
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+340
+00:28:44,810 --> 00:28:44,810
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+341
+00:28:44,810 --> 00:28:49,770
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+342
+00:28:49,770 --> 00:28:51,450
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+343
+00:28:51,450 --> 00:28:51,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+344
+00:28:51,610 --> 00:28:51,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+345
+00:28:51,610 --> 00:28:52,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+346
+00:28:52,610 --> 00:28:55,710
+.. ال ..
+
+347
+00:29:00,330 --> 00:29:06,370
+converge such that x element ناقص a أو a كلها هذه
+
+348
+00:29:06,370 --> 00:29:12,330
+الـen converged uniformly الان لمن؟ للـe معايا
+
+349
+00:29:12,330 --> 00:29:19,190
+converged uniformly للـe for every أو on ناقص a أو
+
+350
+00:29:19,190 --> 00:29:23,010
+a لأنه سمناها إيش اللي هي ال limit بتروحلها اسمها
+
+351
+00:29:23,010 --> 00:29:27,670
+إيه الآن en اتفجنا إنه أثبتناها إنها إيش معالها
+
+352
+00:29:28,810 --> 00:29:34,050
+continuous مادام continuous و en اللي هو طبعا
+
+353
+00:29:34,050 --> 00:29:36,330
+continuous مش بس على ناقص a و a continuous وين
+
+354
+00:29:36,330 --> 00:29:39,690
+مكان احنا الآن هنحكي عن ناقص a و a continuous صارت
+
+355
+00:29:39,690 --> 00:29:42,910
+ال en continuous sequence converts uniformly to e
+
+356
+00:29:42,910 --> 00:29:48,110
+على ناقص a و a إذا صارت ال e هذه حسب نظريتنا هتكون
+
+357
+00:29:48,110 --> 00:29:53,560
+continuous نظرية الأولىفي سيكشن 8 اللي هو 2 هتكون
+
+358
+00:29:53,560 --> 00:29:57,800
+الـ E is continuous على ناقص A و A قولنا if E N is
+
+359
+00:29:57,800 --> 00:30:00,200
+a sequence of continuous functions that converge
+
+360
+00:30:00,200 --> 00:30:03,200
+uniformly to some function then this function or
+
+361
+00:30:03,200 --> 00:30:06,880
+some function is continuous on ناقص A و Eإذا صارت
+
+362
+00:30:06,880 --> 00:30:10,200
+ال E continuous على نقص A و A يعني ال E continuous
+
+363
+00:30:10,200 --> 00:30:14,520
+عند من؟ عند ال X و since X was arbitrary in R then
+
+364
+00:30:14,520 --> 00:30:21,180
+E هتكون is continuous على كل ال R إذا صارت عندي E
+
+365
+00:30:21,180 --> 00:30:26,560
+is continuous at any X element in R الآن لو جينا
+
+366
+00:30:26,560 --> 00:30:31,600
+حسبنا ال E N of 0 و E 1 of 0 و E 1 of 0 أشو
+
+367
+00:30:31,600 --> 00:30:39,410
+بالساوية؟ هي واحدE اللي هو N زائد واحد of Zero
+
+368
+00:30:39,410 --> 00:30:45,630
+اللي هو بساوي من سفر لسفر هيطلع سفر وهذا واحد يعني
+
+369
+00:30:45,630 --> 00:30:52,470
+دايما ال E N of Zero هتطلع إيش؟ Zero مدام E N of
+
+370
+00:30:52,470 --> 00:31:00,670
+Zero Zero وبما أنه E is continuous إذن limit ال Eن
+
+371
+00:31:00,670 --> 00:31:05,930
+of zero as n goes to infinity بسوء اللي هو E of
+
+372
+00:31:05,930 --> 00:31:10,990
+zero أو E of X أسف E of X as n goes to infinity
+
+373
+00:31:10,990 --> 00:31:18,450
+بسوء E of X وبما أنه اللي هواللي هي ال ال ال ال ال
+
+374
+00:31:18,450 --> 00:31:20,590
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+375
+00:31:20,590 --> 00:31:21,370
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+376
+00:31:21,370 --> 00:31:22,190
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+377
+00:31:22,190 --> 00:31:25,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+378
+00:31:25,670 --> 00:31:30,470
+ال ال ال ال ال ال ال ال ال ال
+
+379
+00:31:30,470 --> 00:31:32,430
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+380
+00:31:32,430 --> 00:31:32,790
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+381
+00:31:32,790 --> 00:31:32,790
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+382
+00:31:32,790 --> 00:31:32,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+383
+00:31:32,950 --> 00:31:32,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+384
+00:31:32,950 --> 00:31:32,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+385
+00:31:32,950 --> 00:31:32,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+386
+00:31:32,950 --> 00:31:35,550
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+387
+00:31:35,550 --> 00:31:39,680
+ال الأنا كنت بخلطها أنا بقول E n of 0 بساوي 1
+
+388
+00:31:39,680 --> 00:31:43,540
+limit E n of X بساوي E of X وال E is continuous
+
+389
+00:31:43,540 --> 00:31:48,900
+إذا الحيكون ال E of 0 هذه هتساوي إيش؟ هيساوي 1
+
+390
+00:31:48,900 --> 00:31:53,800
+لأنه limit E n of 0 point twice بساوي E of 0 اللي
+
+391
+00:31:53,800 --> 00:31:58,580
+هي 0الان e n of zero بتساوي واحد for all and infim
+
+392
+00:31:58,580 --> 00:32:04,940
+therefore e of zero بتساوي واحد لإن اللي هي e
+
+393
+00:32:04,940 --> 00:32:11,240
+نفسها is continuous إذا حصلنا على اللي هو الجزء
+
+394
+00:32:11,240 --> 00:32:16,080
+الأول أذكركم في الظاهرية على اللي هو المطلوب أو
+
+395
+00:32:16,080 --> 00:32:20,770
+الخاصية الأولىالخاصية الأولى هى الخاصية الأولى هى
+
+396
+00:32:20,770 --> 00:32:25,430
+عندى أثبتنا .. التانى أسف أثبتنا E اللى هى E of
+
+397
+00:32:25,430 --> 00:32:29,370
+Zero بالساوية واحدة بدى أثبتلك الأن E prime of X
+
+398
+00:32:29,370 --> 00:32:34,750
+هتساوي E of X عشان أثبتها بدنا نذكركم في نظرية
+
+399
+00:32:34,750 --> 00:32:45,750
+أخدناها المرة الماضية اللى هى بتقول ما يليه أذكركم
+
+400
+00:32:45,750 --> 00:32:51,350
+يا جماعةبالنظرية اللي بستخدمها كانت ان عندي لو في
+
+401
+00:32:51,350 --> 00:32:56,330
+عندي fn sequence of functions و هذه fn ال
+
+402
+00:32:56,330 --> 00:33:00,050
+differentiable لأن fn برايم بتروح ل g uniformly
+
+403
+00:33:00,050 --> 00:33:08,330
+ماشي on some interval on some j وكان عندي fn of x
+
+404
+00:33:08,330 --> 00:33:11,050
+not converge
+
+405
+00:33:12,940 --> 00:33:21,240
+converts to f of x not مثلا on j اه for x not
+
+406
+00:33:21,240 --> 00:33:31,300
+element in j then بقول لي اللي هو ال f هذه f prime
+
+407
+00:33:31,300 --> 00:33:39,230
+existsو FN converts uniformly to this F او FN
+
+408
+00:33:39,230 --> 00:33:46,950
+converts uniformly to this F and F' هي مين هي الـ
+
+409
+00:33:46,950 --> 00:33:50,370
+G هذا حكيناه المرة الماضية طيب، بدأ استخدمها الآن
+
+410
+00:33:50,370 --> 00:33:54,510
+شوف عنده، ان شوف عنده الـ N أثبتنا او الـ N
+
+411
+00:33:54,510 --> 00:33:57,110
+interval لاقصية و ايه؟ we have the uniform
+
+412
+00:33:57,110 --> 00:34:02,350
+convergence of the sequence EN اللي هو هتكون EN
+
+413
+00:34:04,720 --> 00:34:12,400
+converge uniformly ماشي الحالة of you of me of
+
+414
+00:34:12,400 --> 00:34:15,900
+تلاتة اللي هو تلاتة اللي حكيناها قبل بشوية خليني
+
+415
+00:34:15,900 --> 00:34:21,540
+بس نذكركم فيها اللي هي تلاتة هي عندي اللي هي تلاتة
+
+416
+00:34:21,840 --> 00:34:25,980
+عندي الان conversion formally to some function E
+
+417
+00:34:25,980 --> 00:34:30,140
+سمناها الان بناء عليه بدلا من الان زائد واحد هي
+
+418
+00:34:30,140 --> 00:34:34,820
+سافسة الان إذا صارت الان زائد واحد prime برضه
+
+419
+00:34:34,820 --> 00:34:38,140
+conversion هادي هادي أصلا conversion formally to
+
+420
+00:34:38,140 --> 00:34:46,280
+مين؟ to ال E اللي عندي الان وضحت الصورة الان صارت
+
+421
+00:34:46,280 --> 00:34:53,410
+الصورة واضحة الان اللي حصلنا انهانتبه عليا، on any
+
+422
+00:34:53,410 --> 00:34:56,010
+interval ناقص a و a, we have the inferred
+
+423
+00:34:56,010 --> 00:35:01,170
+convergence of E n وفي ضوء اللي هو تلاتة, we also
+
+424
+00:35:01,170 --> 00:35:04,290
+have the inferred convergence E n prime of the
+
+425
+00:35:04,290 --> 00:35:08,350
+derivatives الآن من ال theorem 8.2.3 اللي حكيتها
+
+426
+00:35:08,350 --> 00:35:13,700
+هنا، مدام F n prime converges ل Gماشي الحال و ال
+
+427
+00:35:13,700 --> 00:35:17,160
+.. او ال Fn X0 بتروح ل F of X0 for X0 اللي بتنجح
+
+428
+00:35:17,160 --> 00:35:21,880
+اللي هو اكتر من النقطة و اصلا على اساس عرفنا ان Fn
+
+429
+00:35:21,880 --> 00:35:27,420
+of X بالساوي اللي هو مين E of X بتروح لمين لل E of
+
+430
+00:35:27,420 --> 00:35:31,780
+X اذا اكيد هذه متحققة كمان بالنسبة لمين لل E N
+
+431
+00:35:31,780 --> 00:35:36,760
+صارت هذه متحققة و هذه متحققة من التحقق هذههذه يا
+
+432
+00:35:36,760 --> 00:35:42,140
+عزيزي التحقق هذه إذا إذا هيكون عنده ال F N بتروح
+
+433
+00:35:42,140 --> 00:35:46,020
+لل F اللي هي ال E N بتروح لل E صنادر أثبتناها بس
+
+434
+00:35:46,020 --> 00:35:51,720
+إيش المهم أنه ال F prime لهذه اللي بتروحلها هذه
+
+435
+00:35:51,720 --> 00:35:57,080
+اللي هي ال E prime هي مين اللي هي اللي بتروحلها ال
+
+436
+00:35:57,080 --> 00:36:02,340
+E N ال F ال F N prime عند ال E N زائد واحد prime
+
+437
+00:36:02,340 --> 00:36:03,260
+بتروح لل E
+
+438
+00:36:06,460 --> 00:36:13,560
+إذا من نظرية إيان ستذهب إلى الـ E برضه وليس كذلك
+
+439
+00:36:13,560 --> 00:36:20,250
+الـ E' لهذههي هذه يعني بمعنى آخر E N زي دول برايم
+
+440
+00:36:20,250 --> 00:36:25,830
+برايم limitها ال E برايم زي ما هي مين ال E يعني
+
+441
+00:36:25,830 --> 00:36:29,950
+مدام الان limitها هي ال E و هي نفسها limitها من
+
+442
+00:36:29,950 --> 00:36:33,370
+النظرية اللي بنستنتجها E برايم إذا صارت ال E هي
+
+443
+00:36:33,370 --> 00:36:38,610
+مين ال E برايم أو بطريقة أخرى limit ال E N برايم
+
+444
+00:36:38,610 --> 00:36:43,440
+حسب النظرية بتساوي ال E برايمومن جهة أخرى limit en
+
+445
+00:36:43,440 --> 00:36:50,500
+براي هو نفسه limit en نفسهاو limit en اللي هي طبعا
+
+446
+00:36:50,500 --> 00:36:53,280
+انا مسميها n و n نقص واحد احنا مسميينها n و n زاد
+
+447
+00:36:53,280 --> 00:36:57,740
+واحد طبيعي en برايم هي limit من limit en نقص واحد
+
+448
+00:36:57,740 --> 00:37:02,620
+لحالها لأن هذه بتساوي هذه و هذه اصلا limit احنا
+
+449
+00:37:02,620 --> 00:37:07,140
+اثبتنا ايش بساوي ال E اذا صارت عند ال E برايم هي
+
+450
+00:37:07,140 --> 00:37:10,720
+ايش بتساوي ال E يعني هذه ال E برايم استنتاجا من
+
+451
+00:37:10,720 --> 00:37:16,260
+النظريةو هذه اللي هو من اللي أثبتنا في البداية و
+
+452
+00:37:16,260 --> 00:37:19,800
+أيضا نقدر نستخدم .. لسه نتجه من النظرية لكن أحنا
+
+453
+00:37:19,800 --> 00:37:25,540
+أثبتنا فيها قبل ما نستعمل المظلةطيب هذا الكلام
+
+454
+00:37:25,540 --> 00:37:30,680
+صحيح وين لكل x وين موجودة في ناقص a و a لكن a احنا
+
+455
+00:37:30,680 --> 00:37:35,600
+أخدناها أجمالها arbitrary يعني الآن بيصير عندي
+
+456
+00:37:35,600 --> 00:37:40,740
+اللي هو لكل x بلقي لواحدة زي هيك بتحقق الكلام هذا
+
+457
+00:37:40,740 --> 00:37:44,560
+الآن فبصير عندي a prime of x بسوية of x لكل x
+
+458
+00:37:44,560 --> 00:37:50,720
+element in R وهيك بيكون احنا أثبتنا وجود اللي هو
+
+459
+00:37:50,720 --> 00:37:58,390
+ال E of Xأثبتنا وجود دالة أثبتنا
+
+460
+00:37:58,390 --> 00:38:06,100
+وجود دالة سمناها E of Xهذه الدالة بتحقق شرطين اللي
+
+461
+00:38:06,100 --> 00:38:11,900
+هو E prime of X بساوي E of X وبتحقق الشرط التاني E
+
+462
+00:38:11,900 --> 00:38:20,680
+of 0 بساوي 1 السؤال الآن هل في غيرها؟ هل في غيرها
+
+463
+00:38:20,680 --> 00:38:25,860
+ولا لأ؟ طبعا لحظة الحظ أنه لا يوجد دالة غير هذه
+
+464
+00:38:25,860 --> 00:38:31,140
+الدالة اللي بتحقق هذا الكلامبس قبل ما نثبت الـ
+
+465
+00:38:31,140 --> 00:38:35,740
+uniqueness خلّينا ناخد بعض النتائج بشكل سريع و
+
+466
+00:38:35,740 --> 00:38:39,900
+نتائج سهلة و اللي هي ان شاء الله متاخدش وقتها
+
+467
+00:38:39,900 --> 00:38:43,040
+شوفوا يا جماعة صلوا على النبي عليه الصلاة والسلام
+
+468
+00:38:43,040 --> 00:38:48,080
+الـ function E has a derivative of every order and
+
+469
+00:38:48,080 --> 00:38:51,260
+E N of X بيساوي E of X for all N element in N و X
+
+470
+00:38:51,260 --> 00:38:54,480
+element in Rيعني الآن لو فضلناها كمان مرة و مرتين
+
+471
+00:38:54,480 --> 00:38:56,980
+و تلاتة و أربعة هتطلع أيش نفس الدالة طبعا هذا
+
+472
+00:38:56,980 --> 00:39:00,360
+الكلام سهل و by induction زي ما انتوا عارفين أول
+
+473
+00:39:00,360 --> 00:39:03,120
+حاجة ماثبتها فوران بالساوية واحد فوران بالساوية
+
+474
+00:39:03,120 --> 00:39:06,480
+واحد ماحنا أثبتنا E prime of X أيش بالساوية E of X
+
+475
+00:39:06,480 --> 00:39:11,070
+إذا هذه is true فوران بالساوية واحدطيب لان افترض
+
+476
+00:39:11,070 --> 00:39:15,510
+انها هذه صحيحة في القرآن بيساوي K بيصير E K of X
+
+477
+00:39:15,510 --> 00:39:20,010
+بيساوي E of X لما ان اتبتها ل K زائد واحد طيب ل K
+
+478
+00:39:20,010 --> 00:39:23,870
+زائد واحد خد A K زائد واحد of X ايش هذه؟ هذه اللي
+
+479
+00:39:23,870 --> 00:39:30,840
+هي A K of X الكل اشمالها إبراهيمالان a k of x
+
+480
+00:39:30,840 --> 00:39:33,540
+فرضناها ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+481
+00:39:33,540 --> 00:39:33,940
+بالساوية ايه بالساوية ايه بالساوية ايه بالساوية
+
+482
+00:39:33,940 --> 00:39:34,880
+ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+483
+00:39:34,880 --> 00:39:34,880
+بالساوية ايه بالساوية ايه بالساوية ايه بالساوية
+
+484
+00:39:34,880 --> 00:39:35,180
+ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+485
+00:39:35,180 --> 00:39:37,200
+بالساوية ايه بالساوية ايه بالساوية ايه بالساوية
+
+486
+00:39:37,200 --> 00:39:43,180
+ايه بالساوية ايه بالساوية ايه بالساوية ايه
+
+487
+00:39:43,180 --> 00:39:54,500
+بالساوية ايه بالساوية ايه بالسا
+
+488
+00:39:55,640 --> 00:40:01,620
+وضلك فاضل إلى ما لا نهاية حيظل تطلع نفس الدالة نجي
+
+489
+00:40:01,620 --> 00:40:07,340
+الآن لـ Corollary أو الخاصية اللي بعدها لهذه
+
+490
+00:40:07,340 --> 00:40:15,040
+الدالة هذه الدالة Fx أكبر من 0 بقولك دايماً حيكون
+
+491
+00:40:15,040 --> 00:40:21,280
+الواحد زائد X strictly أصغر من مين من E of X من E
+
+492
+00:40:21,280 --> 00:40:32,910
+of X ان انعندي اللي هي أربعة أربعة عشان تشوف أيش
+
+493
+00:40:32,910 --> 00:40:40,550
+أربعة الأربعة اللي هي ال E prime of X أظن هيك كنا
+
+494
+00:40:40,550 --> 00:40:51,590
+حاكين ال E الناس في ال E of X عندي
+
+495
+00:40:51,590 --> 00:40:53,390
+E
+
+496
+00:40:55,380 --> 00:41:03,750
+انا of Xأقبى أو أصغر strictly من E N زائد واحد of
+
+497
+00:41:03,750 --> 00:41:09,850
+X لكل X أكبر من مين من صفر ليه؟ لأن هذه هيزيد
+
+498
+00:41:09,850 --> 00:41:12,630
+عليها term اللي هو X أسوان زائد واحد على N زائد
+
+499
+00:41:12,630 --> 00:41:15,630
+واحد فكتوريا وهذا ال term الاكساتي اللي أكبر من
+
+500
+00:41:15,630 --> 00:41:19,810
+صفر أشماله اللي هو مودة إذا صارت ال sequence اللي
+
+501
+00:41:19,810 --> 00:41:25,010
+عندي يا جماعة هذه عبارة عن strictly increasing
+
+502
+00:41:25,680 --> 00:41:29,120
+sequence strictly increasing sequence بناءً عليه
+
+503
+00:41:29,120 --> 00:41:36,240
+هيكون عند E1 of X أصغر strictly من E2 of X وهذا
+
+504
+00:41:36,240 --> 00:41:42,020
+أصغر strictly من E N of X لكل N أكبر أو يساوي
+
+505
+00:41:42,020 --> 00:41:51,440
+تلاتة وال X أشمالها أكبر من سفر ماشي الحال طيب E1
+
+506
+00:41:51,440 --> 00:42:02,170
+of X مين هي؟ واحد زاد Xوهذا أصغر من E2 of X وهذا
+
+507
+00:42:02,170 --> 00:42:08,170
+أصغر من E N of X إذا نخد ال limit لكل الجهات as N
+
+508
+00:42:08,170 --> 00:42:10,670
+goes to infinity وهذا independent of N وهذا
+
+509
+00:42:10,670 --> 00:42:15,590
+independent of N إذا سيصبح أصغر أو يساوي limit E N
+
+510
+00:42:15,590 --> 00:42:20,430
+of X as N goes to infinityو limit E n of X as n
+
+511
+00:42:20,430 --> 00:42:25,350
+goes to infinity هو عبارة عن مين قلنا عنه E of X
+
+512
+00:42:25,350 --> 00:42:31,350
+إذا صارت 1 زائد X strictly أصغر من E of X أو E of
+
+513
+00:42:31,350 --> 00:42:39,850
+X أكبر strictly من 1 زائد Xطيب نيجي اللي هو نثبت
+
+514
+00:42:39,850 --> 00:42:45,310
+الـ uniqueness للدالة اللي أثبتنا وجودها الآن إذا
+
+515
+00:42:45,310 --> 00:42:51,290
+أثبتنا وجود دالة سميناها E of X هذه الدالة تحقق
+
+516
+00:42:51,290 --> 00:43:01,390
+الشرطين اللي قلناهن اللي هو E of E primeof X بساوي
+
+517
+00:43:01,390 --> 00:43:07,430
+E of X لكل X element in R الشرط الأول والشرط
+
+518
+00:43:07,430 --> 00:43:14,350
+التاني اللي هو E of Zero بتساوي إياش واحد الآن هذه
+
+519
+00:43:14,350 --> 00:43:17,390
+الشرط ده اللي أكبرنا وجودها لنتبت إنها إياش وحيدة
+
+520
+00:43:17,700 --> 00:43:22,860
+الأن الـ function E من R لـ R that satisfies I and
+
+521
+00:43:22,860 --> 00:43:29,200
+I I هكذا of theorem 8.3.1 is unique إذا ما لها هذه
+
+522
+00:43:29,200 --> 00:43:32,940
+الدالة وحيدة ونشوف كيف نثبت وحيدة طبعا انتوا
+
+523
+00:43:32,940 --> 00:43:36,140
+عارفين ال .. الاستراتيجية تثبت انها وحيدة ونفترض
+
+524
+00:43:36,140 --> 00:43:39,340
+ان في دالتين وفي الآخر يا بنسأل لتناقض أو بنسأل
+
+525
+00:43:39,340 --> 00:43:43,260
+لإن الدالتين إشمالهم متساويتين خلينا نشوف
+
+526
+00:43:47,010 --> 00:43:52,110
+لأن let E1 and E2 be two functions on R ماشي الحال
+
+527
+00:43:52,110 --> 00:43:59,470
+E1 وE2 عبارة عن دالتين من R لR تحقيقان البرو بارتز
+
+528
+00:43:59,470 --> 00:44:03,010
+I and I I of T والمتمنى هو تلاتة واحد اللي كتبه ان
+
+529
+00:44:03,010 --> 00:44:08,700
+انا على الجنب هناكالان و خلّينا نسمي E1-E2 يتساوي
+
+530
+00:44:08,700 --> 00:44:14,840
+F رايحكم باتجاهة F يتساوي 0 إذا أثبتنا F يتساوي 0
+
+531
+00:44:14,840 --> 00:44:21,630
+إذا سيصبح E1 يتساوي E2 يكون خلصناطيب then فضلي هذه
+
+532
+00:44:21,630 --> 00:44:24,510
+.. فضلي هذه لأن هذا قبل التفاضل و هذا قبل التفاضل
+
+533
+00:44:24,510 --> 00:44:27,350
+إذا F prime of X بيساوي E1 prime of X ناقص E2
+
+534
+00:44:27,350 --> 00:44:32,230
+prime of X E1 prime of X إيش هتساوي اللي هو نفسها
+
+535
+00:44:32,230 --> 00:44:35,730
+لأن مفترضين احنا و E2 prime of X برضه هتساوي نفسها
+
+536
+00:44:35,730 --> 00:44:39,770
+إذا E1 ناقص E2 يعني مين بيساوي F يعني صارت F prime
+
+537
+00:44:39,770 --> 00:44:44,610
+تبعتنا مين هي بيساوي F of X لكل X element المين
+
+538
+00:44:44,610 --> 00:44:50,090
+إنا احسب اللي دي إيش يا جماعة احسب لولي F في صفرأف
+
+539
+00:44:50,090 --> 00:44:53,350
+اف صفر بيساوي ا واحد اف صفر ناقص اتنين اف صفر ا
+
+540
+00:44:53,350 --> 00:44:56,710
+واحد اف صفر واحد و اتنين اف صفر برضه اش بتساوي
+
+541
+00:44:56,710 --> 00:44:59,510
+واحد لإن مفترضين ا واحد و اتنين بتحفق اللي هي
+
+542
+00:44:59,510 --> 00:45:02,970
+الشطن الأمامنا إذا بيساوي واحد ناقص واحد و اي ساوي
+
+543
+00:45:02,970 --> 00:45:04,350
+اش صفر
+
+544
+00:45:07,320 --> 00:45:13,380
+by induction f double prime هتساوي f نفسها f
+
+545
+00:45:13,380 --> 00:45:18,060
+triple بتساوي f نفسها fn of x بيساوي f of x وعملت
+
+546
+00:45:18,060 --> 00:45:21,920
+قبل بشوية واحدة زيها إذا by induction fn of x
+
+547
+00:45:21,920 --> 00:45:28,280
+بيساوي f of x لكل x element in R إذا حققت الآن f
+
+548
+00:45:28,280 --> 00:45:34,500
+of 0 بيساوي 0 و fn of x بيساوي مين؟ f of x شوف
+
+549
+00:45:34,500 --> 00:45:42,870
+الآنأذا صار عندي F of Zero بساوي Zero أو F
+
+550
+00:46:10,090 --> 00:46:17,830
+بساوة 0طب ايش علاقتنا ابوها الجيت بتشوف عشان بدنا
+
+551
+00:46:17,830 --> 00:46:20,690
+نطبق اللي هو taylor's theorem تبعت ال derivative
+
+552
+00:46:20,690 --> 00:46:25,930
+نص اللي اللي بدنا يعني برهان حلو let x element in
+
+553
+00:46:25,930 --> 00:46:29,550
+R be arbitrary أخدنا إذا x element in R arbitrary
+
+554
+00:46:29,550 --> 00:46:33,810
+x اللي يعني let I x be the closed interval with
+
+555
+00:46:33,810 --> 00:46:40,760
+end point 0x يعني I xهناخدها بتساوي 0 و X أو اللي
+
+556
+00:46:40,760 --> 00:46:47,080
+هي X و 0 على .. على اللي هو اللي هي حسب X اللي هي
+
+557
+00:46:47,080 --> 00:46:51,980
+سالبة أو مجبة إذا أخدنا ال I X عبارة عن اللي هي ال
+
+558
+00:46:51,980 --> 00:46:56,600
+closed interval اللي within point 0 X الآن F is
+
+559
+00:46:56,600 --> 00:47:01,020
+continuous on I Xعلى الـ closed interval مدام
+
+560
+00:47:01,020 --> 00:47:03,320
+continuous على closed interval and function that
+
+561
+00:47:03,320 --> 00:47:06,460
+is continuous على closed interval then it is
+
+562
+00:47:06,460 --> 00:47:09,200
+bounded on this interval يعني بمعنى أخر there
+
+563
+00:47:09,200 --> 00:47:12,880
+exist k بحيث أن absolute value of f of t أصغر أو
+
+564
+00:47:12,880 --> 00:47:17,960
+يساوي k for all t element in I X يعني f is bounded
+
+565
+00:47:17,960 --> 00:47:23,580
+on this intervalالان بدنا نطبق if we apply
+
+566
+00:47:23,580 --> 00:47:27,540
+taylor's theorem 6 4 1 to F بدنا نطبقها على
+
+567
+00:47:27,540 --> 00:47:31,800
+النقطتين النقطة الأولى اللى هى ال X X و X naught 0
+
+568
+00:47:31,800 --> 00:47:35,640
+يعني بنطبقها على مين اللى هى X X اللى هى طبعا
+
+569
+00:47:35,640 --> 00:47:41,370
+انتوا متذكرين F of Xأف of X تيلر سيوريم there
+
+570
+00:47:41,370 --> 00:47:46,370
+exists C in اللي هي ال interval مثلا X not و X
+
+571
+00:47:46,370 --> 00:47:52,690
+such that F of X بيساوي اللي هو F of X not زائد F
+
+572
+00:47:52,690 --> 00:47:58,490
+prime of X not على واحد factorial في X minus X not
+
+573
+00:47:58,490 --> 00:48:05,910
+زائد زائد Fn of x0 على n factorial في x minus x0
+
+574
+00:48:05,910 --> 00:48:11,610
+الكلوس n زائد ال remainder اللي هو fn زائد واحد of
+
+575
+00:48:11,610 --> 00:48:15,730
+اللي هي ال c اللي لاجيناها there exists c اللي هي
+
+576
+00:48:15,730 --> 00:48:19,170
+of c طبعا ال c هنا هتعتمد على ال n اللي احنا
+
+577
+00:48:19,170 --> 00:48:24,850
+اختارناها واشتغلنا عليها هو مسميها cn على اللي هو
+
+578
+00:48:24,850 --> 00:48:28,670
+n زائد واحد factorial في x
+
+579
+00:48:33,180 --> 00:48:37,920
+الـ N هو
+
+580
+00:48:37,920 --> 00:48:42,580
+ما خدها لعند مين بدل ما هو remainder N زائد واحد
+
+581
+00:48:42,580 --> 00:48:45,880
+نسميه remainder N نفس الشيء مافيش مشكلة احنا
+
+582
+00:48:45,880 --> 00:48:51,880
+كملناها يعني بدل ما اشتغل على N زي ما اشتغل على N
+
+583
+00:48:51,880 --> 00:48:54,460
+زائد واحد اشتغل على ال N هو اما هي ال Taylor's
+
+584
+00:48:54,460 --> 00:48:59,460
+theorem طيب المهم انتبهوا عن ديلنبن Taylor's
+
+585
+00:48:59,460 --> 00:49:03,580
+theorem على ال interval Ix اللي X0 بيساوي 0
+
+586
+00:49:03,580 --> 00:49:08,040
+وخلّينا نستخدم Fk of 0 اللي كتبتها هناك اللي هو
+
+587
+00:49:08,040 --> 00:49:12,020
+هتساوي Fk of 0 هتساوي 0 دايما اللي هو و لكل k
+
+588
+00:49:12,020 --> 00:49:15,740
+element n it follows thatfor each n unlimited on
+
+589
+00:49:15,740 --> 00:49:20,000
+there exist a point cn unlimited on x هذه اللي هي
+
+590
+00:49:20,000 --> 00:49:23,920
+ال cn بتعتمد على مين على n يعني الأن لو أخدت ببدل
+
+591
+00:49:23,920 --> 00:49:28,860
+اللي هنا على اللي هي on بتساوي مثلا اتنين أخد on
+
+592
+00:49:28,860 --> 00:49:31,660
+بتساوي تلتة أخد بتساوي on بتساوي أربعة ده هتختلف
+
+593
+00:49:31,660 --> 00:49:35,740
+من ال cn اللي بنلاقيها such that f of x بيساوي f
+
+594
+00:49:35,740 --> 00:49:39,420
+of zero زيد f prime of zero على واحد factorial في
+
+595
+00:49:39,420 --> 00:49:44,390
+xطبعاً نقص صفر X هتظلها زائد FN نقص واحد لأن نقص
+
+596
+00:49:44,390 --> 00:49:47,630
+واحد factorial في X minus X note اللي هي صفر طبعاً
+
+597
+00:49:47,630 --> 00:49:52,830
+هتصير X نقص واحد زائد FN of CN على N factorial X
+
+598
+00:49:52,830 --> 00:49:56,530
+أثن يعني هنا ناخد ال remainder اللي هو RN مش RN
+
+599
+00:49:56,530 --> 00:50:01,410
+زائد واحد زي ما نعمله طبعاً ماتفرجشبتزيده و بتشتغل
+
+600
+00:50:01,410 --> 00:50:04,910
+عليه نفس الاشي الان بس ال cn اللي بتختلف من n زائد
+
+601
+00:50:04,910 --> 00:50:07,650
+واحد بصير cn زائد واحد مثلا لأنه حاجة تانية ممكن
+
+602
+00:50:07,650 --> 00:50:11,290
+تيجي غير ال cn اللي لاجيناها حسب النظرية و يساوي
+
+603
+00:50:11,290 --> 00:50:16,350
+لأن كل هدول التاريج زي شمال هي الصفار لإنه fk of
+
+604
+00:50:16,350 --> 00:50:21,290
+00 إذا هذا سفر وهذا سفر طبعا هذا عند مين محسب عند
+
+605
+00:50:21,290 --> 00:50:25,800
+السفر وهذا عند السفر إلى آخرهإذا كل هذول هيكون
+
+606
+00:50:25,800 --> 00:50:30,700
+الصفار هيظل عندى بس القيمة هذه ايش القيمة هذه اللي
+
+607
+00:50:30,700 --> 00:50:35,320
+هي fn of cn طبيعي هتكون f of min of cn لأنه احنا
+
+608
+00:50:35,320 --> 00:50:41,070
+عرفنا انه ال derivative f primeأف دابل برايم أف
+
+609
+00:50:41,070 --> 00:50:45,710
+تريبل كل نياش بيساوي الأف إذا حيكون أف of CN على N
+
+610
+00:50:45,710 --> 00:50:50,710
+فيكتوريال في X أُس N إذا وصلنا له الآن أنه بعد ما
+
+611
+00:50:50,710 --> 00:50:57,170
+طبقنا Taylor's theorem طلع عندي الآن F of X هذه
+
+612
+00:50:57,170 --> 00:51:04,710
+اللي بنصبه إلى أن نثبتها بتساوي صفر طلعت عندي F of
+
+613
+00:51:04,710 --> 00:51:10,230
+X بيساوي F of CN على N فيكتوريال في X أُس Nالان خد
+
+614
+00:51:10,230 --> 00:51:14,510
+لل absolute value لها absolute value لل F of X
+
+615
+00:51:14,510 --> 00:51:20,090
+هيصير اصغر او يساوي ال absolute value او بيساوي
+
+616
+00:51:20,090 --> 00:51:26,870
+بالظبط absolute value F of C N فال absolute value
+
+617
+00:51:27,400 --> 00:51:33,440
+للـ X أُس N على N فكتوريال، مظبوط؟ لكن F of C N
+
+618
+00:51:33,440 --> 00:51:37,200
+هذه is .. الـ F is bounded على الفترة اللي لجيناها
+
+619
+00:51:37,200 --> 00:51:40,180
+اللي هي الفترة اليمين اللي قلت عنها اللي هي الـ I
+
+620
+00:51:40,180 --> 00:51:44,380
+X مدان bounded قلنا هذه أصغر أو يساوي الـ K إذا
+
+621
+00:51:44,380 --> 00:51:47,380
+هذه بيصير أصغر أو يساوي الـ K في ال absolute value
+
+622
+00:51:47,380 --> 00:51:52,750
+X أس N على N فكتوريال نيجي الآنهذه as n goes to
+
+623
+00:51:52,750 --> 00:51:56,770
+infinity هذه independent of n هذه أكبره يساوي سفر
+
+624
+00:51:56,770 --> 00:51:59,430
+و أصغره يساوي هذه as n goes to infinity هذه بتروح
+
+625
+00:51:59,430 --> 00:52:05,590
+للسفر إذا هذه بتروح أشمالها بدها تصير f of x تساوي
+
+626
+00:52:05,590 --> 00:52:11,230
+السفر ومنه ال E1 بتساوي ال E2 لأن f بتساوي E1 ناقص
+
+627
+00:52:11,230 --> 00:52:17,350
+Eإتنين وهو المطلوب وهذا الكلام صحيح لكل X element
+
+628
+00:52:17,350 --> 00:52:25,050
+in R لأن X اللي أخدناها arbitrary element in R هيك
+
+629
+00:52:25,050 --> 00:52:31,990
+بنكون أثبتنا وجود ال E واحد ال E التي تحقق الشرطين
+
+630
+00:52:31,990 --> 00:52:38,590
+اللي عندنا وفي نفس الوقت أثبتنا أن هذه الدالة اللي
+
+631
+00:52:38,590 --> 00:52:46,680
+بتحقق الشرطينهي دالة وحيدةمدام الدالة واحدة إذن
+
+632
+00:52:46,680 --> 00:52:53,280
+الآن يعني شرّعنا إنه نعطيها اسم إنه نقدر نعرف
+
+633
+00:52:53,280 --> 00:52:59,200
+الدالة اللي بتحقق هذول الشرطين إنها اسمها كذا the
+
+634
+00:52:59,200 --> 00:53:02,660
+unique definition ثمانية تلاتة خمسة the unique
+
+635
+00:53:02,660 --> 00:53:06,140
+function E من R لR such that E prime of X في سوء E
+
+636
+00:53:06,140 --> 00:53:10,120
+of X for all X elements in R وتحقق ال E زيرو
+
+637
+00:53:10,120 --> 00:53:15,190
+بالسوء واحد موجودةووحيدة إذا بحق اللي أقول is
+
+638
+00:53:15,190 --> 00:53:18,450
+called the exponential function وهي الـ
+
+639
+00:53:18,450 --> 00:53:22,350
+exponential اللي أنتوا مبسوطين عليها و بتستخدموها
+
+640
+00:53:22,350 --> 00:53:27,530
+أثبتنا الآن من خلال اللي هو اللي هي الترتيب اللي
+
+641
+00:53:27,530 --> 00:53:31,690
+رتبناه في المادة differentiability integrability و
+
+642
+00:53:31,690 --> 00:53:36,350
+بعدين اللي هو sequences of functions وصلنا إلى
+
+643
+00:53:36,350 --> 00:53:41,190
+اللي هو ال exponential هذه function existsالتي
+
+644
+00:53:41,190 --> 00:53:43,850
+سمناها الـ Exponential Function
+
+645
+00:53:48,710 --> 00:53:53,850
+بدنا نسمي الـ E of واحد قيمة الدالة القيمة الدالة
+
+646
+00:53:53,850 --> 00:53:58,650
+الـ E هذه عند الواحد بدنا نسميها E E و هذا اللي
+
+647
+00:53:58,650 --> 00:54:04,410
+بنسميه Ehlers number و احنا يعني بعد هيك هيصير
+
+648
+00:54:04,410 --> 00:54:09,410
+عندي اللي هو الرمز E of X ان هو ال exponential X
+
+649
+00:54:09,410 --> 00:54:15,710
+او أسهلنا في الاستخدام ال E of X ايش هتساويالـ E X
+
+650
+00:54:15,710 --> 00:54:21,530
+هذا الـ E واحد قيمة الدالة عند مين عند اللي هو
+
+651
+00:54:21,530 --> 00:54:26,750
+الرقم واحد سمناها E ماشي الحالة الان E of X
+
+652
+00:54:26,750 --> 00:54:32,610
+بالساوي E to the X هذه عبارة عن اللي هي الدالة E
+
+653
+00:54:32,610 --> 00:54:37,550
+of X بالساوي X notation لها لكن بعد شوية هنلاقي ال
+
+654
+00:54:37,550 --> 00:54:42,310
+notation consistent of اللي هو مع مين مع اللي هو
+
+655
+00:54:42,310 --> 00:54:47,480
+ال exponentيعني هيصير الـ E to the exponent X هو
+
+656
+00:54:47,480 --> 00:54:51,960
+عبارة عن بالظبط اللي هو قيمة الـ E of X لأن الـ E
+
+657
+00:54:51,960 --> 00:54:54,620
+of X بيساوي E to the X و ال E of واحد بيساوي E
+
+658
+00:54:54,620 --> 00:54:59,440
+واحد بيصير عندي E لما أرفحها للقوة X يطلع قيمتها
+
+659
+00:54:59,440 --> 00:55:05,840
+هي عبارة عن اللي هي قيمة دل E of X حسب اللي احنا
+
+660
+00:55:05,840 --> 00:55:11,550
+معرفينه هنايعني من الإحسابات ومن تعريفنا للدالة
+
+661
+00:55:11,550 --> 00:55:23,070
+هيكون فيه consistent it is consistent في الحالتين
+
+662
+00:55:23,070 --> 00:55:28,990
+طيبنجي الآن لما الكلام هذا ال number E can be
+
+663
+00:55:28,990 --> 00:55:32,570
+obtained as a limit and thereby approximated in
+
+664
+00:55:32,570 --> 00:55:36,410
+several different ways طبيعا احنا مادام عنده اللي
+
+665
+00:55:36,410 --> 00:55:42,990
+هو عبارة عن limit لل E N of Xاللي هي بتطلع عندى
+
+666
+00:55:42,990 --> 00:55:47,450
+limit عند ال .. ال .. ال .. ال end of واحد لأنها
+
+667
+00:55:47,450 --> 00:55:52,130
+continuous بصير عندى مدام limit إذا بصير أقدر أقرب
+
+668
+00:55:52,130 --> 00:55:56,490
+هذه القيمة اللي هي و نحصل على قيمة تقريبية بال E و
+
+669
+00:55:56,490 --> 00:56:00,010
+هذا مش شغلنا شغل تبعين اللي هو numerical analysis
+
+670
+00:56:00,010 --> 00:56:05,530
+أو الناس اللي بدأت .. اللي هي تشتغل في التقريب أو
+
+671
+00:56:05,530 --> 00:56:09,270
+مش شغل نهاني يعني بصديإلى أن الـ use of notation E
+
+672
+00:56:09,270 --> 00:56:15,050
+و X of E X زي ما قلنا كله تمام تمام consistent إلى
+
+673
+00:56:15,050 --> 00:56:19,910
+أن يجي اللي هو لبعض الخواص الأخرى لهذه اللي هي
+
+674
+00:56:19,910 --> 00:56:24,130
+الدالة إلى أن الـ exponential function satisfies
+
+675
+00:56:24,130 --> 00:56:26,150
+the following properties
+
+676
+00:56:32,620 --> 00:56:35,960
+أول حاجة أن الـ E of X لا تساوي سفر لكل X element
+
+677
+00:56:35,960 --> 00:56:40,140
+in R هي أول حاجة أن هذه الدالة دايما لا تساوي سفر
+
+678
+00:56:40,140 --> 00:56:45,980
+طبعا شغالة على R E of X زي Y بسوء E of X في E of Y
+
+679
+00:56:45,980 --> 00:56:50,880
+for all X element .. Y element in R الآن E of R
+
+680
+00:56:50,880 --> 00:56:56,080
+هنا اللي هي E of R قيمة الـ function هذه هتطلع لنا
+
+681
+00:56:56,080 --> 00:57:00,260
+بالظبطهي عبارة عن الـ E اللي قلنا عنها الرقم اللي
+
+682
+00:57:00,260 --> 00:57:06,000
+قبل و شوية لما نرفع للقوة R فبصير الان consistency
+
+683
+00:57:06,000 --> 00:57:11,440
+between the definition of the exponential and the
+
+684
+00:57:11,440 --> 00:57:15,700
+exponent of E to the power R بس هذي الـ R إيش اللي
+
+685
+00:57:15,700 --> 00:57:21,880
+من الين؟ NQ لان ماشي الحالة ده نشوف نبرهن اللي هو
+
+686
+00:57:21,880 --> 00:57:27,390
+الأولى by contradictionبدي افترض انه في عندي E of
+
+687
+00:57:27,390 --> 00:57:31,930
+α for some α element in R والـ E of α ايش تساوي
+
+688
+00:57:31,930 --> 00:57:35,870
+تساوي سفر ونوصل لcontradiction لان suppose that
+
+689
+00:57:35,870 --> 00:57:39,550
+there exists α element in R such that E of α ايش
+
+690
+00:57:39,550 --> 00:57:44,750
+بساوي بساوي سفرالآن and let G α be the closed
+
+691
+00:57:44,750 --> 00:57:49,710
+interval with endpoints mean α و 0 يعني الـ G of α
+
+692
+00:57:49,710 --> 00:57:54,230
+زي اللي فوق يا بساوي اللي هو 0 ألفة أو ألف و زيره
+
+693
+00:57:54,230 --> 00:57:59,440
+حسب قيمة الألف موجبة أو سالبة طيبالان زي ما قلت
+
+694
+00:57:59,440 --> 00:58:02,480
+قبل بشوية بما ان E is continuous on a closed
+
+695
+00:58:02,480 --> 00:58:07,700
+interval Iα او Jα اللي هو مسميها then there exist
+
+696
+00:58:07,700 --> 00:58:10,280
+case such that اللي هو ال absolute value E of D
+
+697
+00:58:10,280 --> 00:58:16,030
+أصفر سوى K لكل T element in Gالأن مشابه للي قبل دي
+
+698
+00:58:16,030 --> 00:58:19,930
+ربالكم الان بدنا نستخدم mean taylor theorem اللي
+
+699
+00:58:19,930 --> 00:58:24,890
+هو على اللي هي ال function اللي عندي هذه اللي هو
+
+700
+00:58:24,890 --> 00:58:29,310
+بس في مين الآن في ال end points ألف ومين ألف وصفر
+
+701
+00:58:29,310 --> 00:58:32,610
+اذا there exist cn element in dn such that مسرع
+
+702
+00:58:32,610 --> 00:58:35,950
+لإنه قاعد بعيد نفس البرهان اللي قبله شوية such
+
+703
+00:58:35,950 --> 00:58:42,200
+that اللي هو E of صفربطبق عند e of 0 بساوي e of
+
+704
+00:58:42,200 --> 00:58:44,340
+alpha زائد e prime of alpha على واحد factorial في
+
+705
+00:58:44,340 --> 00:58:47,280
+ناقص alpha اللي هي zero ناقص alpha زائد e n ناقص
+
+706
+00:58:47,280 --> 00:58:50,780
+واحد على ناقص واحد factorial alpha ناقص alpha أُس
+
+707
+00:58:50,780 --> 00:58:54,160
+n ناقص واحد لما أصل لعند ال remainder e n of alpha
+
+708
+00:58:54,160 --> 00:59:00,060
+على n factorial في ناقص alpha أُس n الآن اخلق هذه
+
+709
+00:59:00,060 --> 00:59:05,770
+مش e alpha هذه الـCnهذه الـ C أنا مخربط بصيحة الله
+
+710
+00:59:05,770 --> 00:59:11,430
+ماشي الحالة الان E of Zero طبيعي ايش يساوي واحد
+
+711
+00:59:11,430 --> 00:59:14,510
+ماحنا عارفين ان خلاص عرضناها الدالة هذه E of Zero
+
+712
+00:59:14,510 --> 00:59:17,630
+بتساوي واحد اتساوي واحد يساوي E of Zero و يساوي
+
+713
+00:59:20,060 --> 00:59:23,400
+الأن E of Alpha فرضناها إيش بالساوية سفر هيك
+
+714
+00:59:23,400 --> 00:59:28,280
+مفترضينها E prime of Alpha اللي هي نفس E of Alpha
+
+715
+00:59:28,280 --> 00:59:32,880
+إذا سفر برضه وهذا نفس الشيء إذا كلنا دول أصفر مع
+
+716
+00:59:32,880 --> 00:59:36,100
+دمين الأخيرة إذا هتساوي E of Cn على N factorial
+
+717
+00:59:36,100 --> 00:59:42,340
+ناقص Alpha أسعى وزي ما قلنا إنه احنا الآن هذا
+
+718
+00:59:42,340 --> 00:59:48,390
+المقدار عندي صار .. نوضح لكم هذهنشوف كيف نصل لـ
+
+719
+00:59:48,390 --> 00:59:53,770
+contradiction هال gate صار عند مايا ليه يا جماعة
+
+720
+00:59:53,770 --> 00:59:57,190
+صارت عند الواحد هذه اللي بيساوي E to the zero
+
+721
+00:59:57,190 --> 01:00:03,630
+بيساوي E to the zero اللي هي أصغر أو يساوي ال
+
+722
+01:00:03,630 --> 01:00:07,510
+absolute value لهذه بيساويها بعد إنه أصغر أو يساوي
+
+723
+01:00:07,510 --> 01:00:14,420
+بيساوي ال absolute value E of CL على N factorialفي
+
+724
+01:00:14,420 --> 01:00:22,320
+absolute value ناقص Alpha أُس N و هذه زي ما قلنا E
+
+725
+01:00:22,320 --> 01:00:25,880
+of C N إيش ما اللي قلنا قبل بشوية هذه أصغر أوي و
+
+726
+01:00:25,880 --> 01:00:32,960
+ساوي K إذا K على N factorial في ناقص Alpha أُس N
+
+727
+01:00:32,960 --> 01:00:38,710
+ماشي الآن هذا المقدارas n goes to infinity بيروح
+
+728
+01:00:38,710 --> 01:00:42,910
+لـ0 هذا independent of n و هذا independent of n
+
+729
+01:00:42,910 --> 01:00:48,650
+صار عندى الان هذا الان هي الواحد أصغر أو يساوي
+
+730
+01:00:48,650 --> 01:00:53,390
+اللي هو هذا المقدار خد ال limit as n goes to
+
+731
+01:00:53,390 --> 01:00:57,430
+infinity بيصير الواحد أصغر أو يساوي سفر و هذا إيش
+
+732
+01:00:57,430 --> 01:01:03,250
+ماله contradictionإذا صار في عندي الفرضية الأولى
+
+733
+01:01:03,250 --> 01:01:07,770
+خاطئة إذا there is no such Alpha اللي هو بتكون
+
+734
+01:01:07,770 --> 01:01:10,530
+عندها ال K of Alpha بتساوي سفر إذا ال K of Alpha
+
+735
+01:01:10,530 --> 01:01:16,090
+بتساوي أكبر لا تساوي سفر دائما إذا صار عندي اللي
+
+736
+01:01:16,090 --> 01:01:22,150
+هو قيمة اللي هي E to the X لا تساوي سفر أبدا نيجي
+
+737
+01:01:22,150 --> 01:01:29,110
+الآن إن بدنا نثبت أنهنثبت الخاصية اللي بعدها اللي
+
+738
+01:01:29,110 --> 01:01:38,430
+هي عبارة عن E of X زائد Y بساوة E of X في E of Y
+
+739
+01:01:38,430 --> 01:01:42,670
+لكل X و Y element in R هذه الخاصية اللي بدنا
+
+740
+01:01:42,670 --> 01:01:48,410
+نثبتها شوف طريقته حلوة في الإثبات بيقول ليه نفترض
+
+741
+01:01:48,410 --> 01:01:53,030
+Y fixed arbitrary لكن ليهاش fixed بنحكي عن Y محددة
+
+742
+01:01:53,030 --> 01:01:59,760
+arbitrary لكن نحكي عن Y محددةالان مادام Y اللي هي
+
+743
+01:01:59,760 --> 01:02:05,240
+ال E of Y أكيد يشملها لا تساوي سفر اتفجنا عليها
+
+744
+01:02:05,240 --> 01:02:11,520
+الان عرفلي الان function G من R لR عرفها كيف؟G of
+
+745
+01:02:11,520 --> 01:02:15,720
+X المتغير X الان Y اللي هي عبارة عن اشي Fix ثابت
+
+746
+01:02:15,720 --> 01:02:19,080
+بحكي عنه لكن كان arbitrary اللي هي G of X بيساوي E
+
+747
+01:02:19,080 --> 01:02:24,420
+of X زائد Y على E of Y for X element in R أخدنا
+
+748
+01:02:24,420 --> 01:02:30,060
+هذه الدالة الآن شوف هذه الدالة اعمله G prime لها G
+
+749
+01:02:30,060 --> 01:02:33,920
+prime of X بالفضل بالنسبالي XY ثابتة اللي هي بيصير
+
+750
+01:02:33,920 --> 01:02:38,280
+هذه E prime of X زائد Y على E of Y عدد ما لاش
+
+751
+01:02:38,280 --> 01:02:43,080
+علاقة فيه Y ساويالـ E' هي نفس مين؟ الـ E of X زي Y
+
+752
+01:02:43,080 --> 01:02:48,720
+على E of Y ماشي؟ طيب، الآن صار هذا الـ E X زي Y
+
+753
+01:02:48,720 --> 01:02:53,280
+على E of Y هو مين؟ رجع G إذا رجعت إن الـ G' مش
+
+754
+01:02:53,280 --> 01:03:01,770
+بيساوي الـ G الآن andأحسب لي g of 0 بساوية e of 0
+
+755
+01:03:01,770 --> 01:03:06,070
+زائد y على e of y يعني بساوية واحدة إذا الدالة
+
+756
+01:03:06,070 --> 01:03:11,050
+اللي عرفناها هذه g of x طلعت لي g prime لها نفسها
+
+757
+01:03:11,050 --> 01:03:15,310
+وطلعت لي g of 0 واحدة وعلمة قبل قليل عمال بيقول
+
+758
+01:03:15,310 --> 01:03:18,610
+مافيش لغير واحدة في الدنيا بتهبها الخاصيتين اللي
+
+759
+01:03:18,610 --> 01:03:23,190
+هي مين ال E of X إذا هذه غصب عننا لازم تطلع مين ال
+
+760
+01:03:23,190 --> 01:03:27,080
+E of X because of the uniqueness of Eإذا صحيح أنا
+
+761
+01:03:27,080 --> 01:03:31,000
+عندي E of X بساوي E X Z Y على E E of Y يعني E X Z
+
+762
+01:03:31,000 --> 01:03:37,940
+Y بساوي E of Y في ال E of X و هو المطلوب طيب نيجي
+
+763
+01:03:37,940 --> 01:03:46,800
+الآن نثبت اللي بعدها اللي هي بدنا نثبت E of R
+
+764
+01:03:46,800 --> 01:03:54,870
+بساوي E to the RR المنتنين LQ اللي هو rational
+
+765
+01:03:54,870 --> 01:04:00,870
+number طيب جماعة فيكم تصل على النبي عليه الصلاة
+
+766
+01:04:00,870 --> 01:04:09,370
+والسلام لنشوف كيف نيجي
+
+767
+01:04:09,370 --> 01:04:14,690
+البرهن اللي هو الجزء الثالث أو هذا جزء من النظرية
+
+768
+01:04:14,690 --> 01:04:18,830
+أول
+
+769
+01:04:18,830 --> 01:04:24,560
+حاجةهذه صحيحة لكل أنهي المتنانة كيف؟ by induction
+
+770
+01:04:24,560 --> 01:04:53,330
+E of X بساوي E of Xأكيد أكيد أكيد أكيد أكيد
+
+771
+01:04:53,330 --> 01:04:56,270
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+772
+01:04:56,270 --> 01:04:56,330
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+773
+01:04:56,330 --> 01:04:57,110
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+774
+01:04:57,110 --> 01:05:00,170
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+775
+01:05:00,170 --> 01:05:00,170
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+776
+01:05:00,170 --> 01:05:00,170
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد
+
+777
+01:05:00,170 --> 01:05:02,740
+أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكيد أكE
+
+778
+01:05:02,740 --> 01:05:08,660
+of K في X زائد X ويساوي من الخاصية اللي احنا لسه
+
+779
+01:05:08,660 --> 01:05:12,880
+ماخلصنهاش هذه بساوي E للأول زايد في E للتاني اللي
+
+780
+01:05:12,880 --> 01:05:17,960
+هي E للأول اللي هو KX في E للتاني اللي هي EX
+
+781
+01:05:17,960 --> 01:05:22,780
+ويساوي EKX اللي هو E of X أُس K لأنه فرضينا أنا
+
+782
+01:05:22,780 --> 01:05:31,260
+صحيحة اللي هي K بيصير عندي E of X أُس K في E of Xو
+
+783
+01:05:31,260 --> 01:05:39,800
+يساوي E of X الكل أُس K زائد واحد إذا صارت
+
+784
+01:05:39,800 --> 01:05:49,580
+هذه is true for all N element in N طيب .. الآن شوف
+
+785
+01:05:49,580 --> 01:05:53,920
+ما يليه نلاحظ ما يليه
+
+786
+01:06:02,460 --> 01:06:06,080
+Lit x بتساوي ايش؟ واحدة على ان ناخد الـ x ايش
+
+787
+01:06:06,080 --> 01:06:10,540
+بتساوي واحدة على ان؟ بتصير هذا E of واحد لأن ان في
+
+788
+01:06:10,540 --> 01:06:13,840
+واحدة على ان واحد ال E of واحد رمزناها من رمز ايش
+
+789
+01:06:13,840 --> 01:06:17,940
+يا جماعة؟ E وهذا اللي بدأ اصليه هذا رمزناها من رمز
+
+790
+01:06:17,940 --> 01:06:22,420
+E وال E عبارة عن رقم ال E of واحد هي قيمة الدالة
+
+791
+01:06:22,420 --> 01:06:28,100
+اللي تبعتنا عند اللي هي الواحد سمينها Eالان E of N
+
+792
+01:06:28,100 --> 01:06:33,380
+في 1 على N تساوي اللي هي عبارة عن ال X هذه اللي هي
+
+793
+01:06:33,380 --> 01:06:40,720
+عبارة عن 1 على N E of 1 على N الكل اسمه أُس N يعني
+
+794
+01:06:40,720 --> 01:06:48,380
+الآن عندي هذه ال X E N X بساوي E X أُس N X مين 1
+
+795
+01:06:48,380 --> 01:06:53,210
+على N E of 1 على N أُس Nإذا صار عندى الآن هي هذا
+
+796
+01:06:53,210 --> 01:06:59,010
+القيمة بساوية هذا إذا بمعنى آخر E of واحدة الان
+
+797
+01:06:59,010 --> 01:07:05,830
+بساوية E العدد أس واحد على N هذا الان E of واحدة
+
+798
+01:07:05,830 --> 01:07:14,050
+الان بساوية E أس واحد على N الآن من جهة أخرى لو
+
+799
+01:07:14,050 --> 01:07:23,700
+جيت E أس minus Mهتساوي واحد على E أُس M خد
+
+800
+01:07:23,700 --> 01:07:26,760
+ال
+
+801
+01:07:26,760 --> 01:07:33,460
+E of M ناقص M اللي هي بيساوي E of Zero اللي هي
+
+802
+01:07:33,460 --> 01:07:41,020
+بيساوي واحد صح وإيه ساوي E of Mفي E of ناقص M حسب
+
+803
+01:07:41,020 --> 01:07:45,900
+الخاصية اللي هي زائد ناقص M هذه X وهذه ال Y E
+
+804
+01:07:45,900 --> 01:07:49,760
+الأولى في E التانية الان صار عندى هذا المقدار
+
+805
+01:07:49,760 --> 01:07:57,600
+بساوي واحد يعني إذا E of ناقص M بساوي بنجل هدهان
+
+806
+01:07:57,600 --> 01:08:03,260
+واحد على E of M إذا صارت عندى E of ناقص M بساوي
+
+807
+01:08:03,260 --> 01:08:09,360
+واحد على E of M وال E of M ال E of Mمن فوق E of M
+
+808
+01:08:09,360 --> 01:08:14,280
+هذا X بواحد يعني بيساوي E of واحد أُس M يعني عبارة
+
+809
+01:08:14,280 --> 01:08:19,500
+عن E أُس M وهي فوق إيش واحد الآن هذه اللي هو عدد
+
+810
+01:08:19,500 --> 01:08:23,800
+عادي اللي هو E مرفوع للأُس M اللي هو نفسه E to the
+
+811
+01:08:23,800 --> 01:08:27,360
+minus M لأن هذه معلومة قديمة لذا انصار عندي الآن E
+
+812
+01:08:27,360 --> 01:08:34,820
+of minus M بيساوي E أُس ماقص M وال E أُس واحد على
+
+813
+01:08:34,820 --> 01:08:43,460
+N بيساوي Eأُس واحد على N نجي
+
+814
+01:08:43,460 --> 01:08:46,780
+الآن احنا غايتنا مين؟ E of R الـ R إيش اللي نقدر
+
+815
+01:08:46,780 --> 01:08:50,640
+نكتبها؟ الـ R في الـ Q إذا الـ R بتنكتب على صورة M
+
+816
+01:08:50,640 --> 01:08:54,780
+على N إذا نخد R في اللي نمتني Q إذا there exists M
+
+817
+01:08:54,780 --> 01:08:58,820
+و N اي واحدة في زد واحدة في N صحيح ده؟ R بتساوي M
+
+818
+01:08:58,820 --> 01:09:03,320
+على N بتثبتلك إن E of M على N بساوي E to the M على
+
+819
+01:09:03,320 --> 01:09:12,580
+N شوف كيفE of M على N ايش هيساوي E أُس واحدة ل N
+
+820
+01:09:12,580 --> 01:09:21,400
+الكل A شماله أُس M أُس M E of واحدة ل N أُس M مين
+
+821
+01:09:21,400 --> 01:09:28,870
+اللي شرعلي اللي هوعندي اللي هي E-M و هي سالبة طلعت
+
+822
+01:09:28,870 --> 01:09:33,870
+E أص مينس M و اللي شرعلي E و واحدة ل N و N مودبة
+
+823
+01:09:33,870 --> 01:09:41,130
+هي E أص واحد على N فبصير عندي الأن E أص M على N أص
+
+824
+01:09:41,130 --> 01:09:45,970
+M على N بساوي E أص واحد على N هذه اللي جوا الكل
+
+825
+01:09:45,970 --> 01:09:53,650
+أسمين الكل أص M ماشي الحال هو يساوي E
+
+826
+01:09:58,010 --> 01:10:03,730
+هذه شرعات لإي و واحدة الان كل اس ام وهذا عدد عادي
+
+827
+01:10:03,730 --> 01:10:08,730
+الان وهذا عدد عادية بيصير اي أس ام عالميا على ان و
+
+828
+01:10:08,730 --> 01:10:14,850
+هذه بيكون عندي اي أس اي او ام على ان بساوي اللي هو
+
+829
+01:10:14,850 --> 01:10:18,870
+عبارة عن اي أس ام على ان و ام على ان was our
+
+830
+01:10:18,870 --> 01:10:21,710
+arbitral rational number اذا صار عندي اي أس ار
+
+831
+01:10:21,710 --> 01:10:24,210
+بساوي اي أس ار
+
+832
+01:10:29,400 --> 01:10:35,160
+نجي الآن للنظرية اللي هي تمانية تلاتة سبعة اللي هي
+
+833
+01:10:35,160 --> 01:10:39,980
+النظرية الأخيرة في اللي هي الحديث عن اللي هو ال
+
+834
+01:10:39,980 --> 01:10:45,260
+exponential function و بعدها طبعا بنحكي عن اللي هو
+
+835
+01:10:45,260 --> 01:10:48,060
+ال logarithmic function بس خلينا الآن نحكي عالميا
+
+836
+01:10:48,060 --> 01:10:54,340
+انكمل نظريتنا على ال exponential function بنشوف
+
+837
+01:10:55,540 --> 01:11:00,240
+الأن بقولي الـ exponential function E is strictly
+
+838
+01:11:00,240 --> 01:11:04,840
+increasing on R يعني الـ derivative إلها أكبر من
+
+839
+01:11:04,840 --> 01:11:11,460
+سفر ماشي؟ and this range اللي هو Y المتنرسج ده Y
+
+840
+01:11:11,460 --> 01:11:16,720
+أكبر من سفر يعني الـ E هتكون بالظبط ده اللي من R
+
+841
+01:11:16,720 --> 01:11:24,080
+بتصب إلى R positive إلى R positive يعني عبارة عن
+
+842
+01:11:24,080 --> 01:11:31,370
+Zeroومالة نهاية هي التي هي range دالة range دالة
+
+843
+01:11:31,370 --> 01:11:34,610
+هذه هي من سفر إلى مالة نهاية لأن كتابة على سورة
+
+844
+01:11:34,610 --> 01:11:40,210
+function is on to طيب مش هيك limit E of X لما X
+
+845
+01:11:40,210 --> 01:11:43,470
+تروح لسالب مالة نهاية بتساوي سفر and limit E of X
+
+846
+01:11:43,470 --> 01:11:47,110
+لما X تروح لمالة نهاية ايش بتساوي؟ بتساوي مالة
+
+847
+01:11:47,110 --> 01:11:55,670
+نهايةيعني الدالة هذه في حالة ال ال E of X اللي
+
+848
+01:11:55,670 --> 01:11:59,070
+احنا سميناها ال X exponential لل X هذه الدالة هذه
+
+849
+01:11:59,070 --> 01:12:03,130
+الدالة زي ما انتوا عارفين لما X تروح إلى سالب ماله
+
+850
+01:12:03,130 --> 01:12:06,830
+نهاية هذا هيروح للسفر ال E of X هتروح للسفر و لما
+
+851
+01:12:06,830 --> 01:12:10,890
+ال X تروح لماله نهاية ال E of X هتروح إيش إلى ماله
+
+852
+01:12:10,890 --> 01:12:14,810
+نهاية نشوف أول شي بالنسبة لمن؟ لل range
+
+853
+01:12:19,570 --> 01:12:24,250
+الان we know that E of 0 بيساوي Eاش واحد اكبر من
+
+854
+01:12:24,250 --> 01:12:29,770
+Eاش من سفر اكيد،ظبط ولا لا؟ and E of X ده بيساوي
+
+855
+01:12:29,770 --> 01:12:36,390
+سفر for X element in R صار عندى الان هاي دالة E of
+
+856
+01:12:36,390 --> 01:12:38,650
+0 إلها واحد،ماشي؟
+
+857
+01:12:40,360 --> 01:12:46,000
+أو E of X مش سفر يعني إيه شمالها لا تقطع محور
+
+858
+01:12:46,000 --> 01:12:51,910
+السينات إطلاقااللي E of X نفسها و 0 من سفرها الأن
+
+859
+01:12:51,910 --> 01:12:57,110
+أنا بقول مستحيل تكون في إيها قيم سالبة يعني مستحيل
+
+860
+01:12:57,110 --> 01:13:02,030
+نلاقي E of X naught اللي هي أصغر من 0 ليش؟ لأنه لو
+
+861
+01:13:02,030 --> 01:13:05,990
+لجينا E of X naught سالبة لو هالجيت عندنا X naught
+
+862
+01:13:05,990 --> 01:13:09,910
+و هيها قيمتها E of X naught اللي هو سالبة يعني
+
+863
+01:13:09,910 --> 01:13:16,460
+هتكون تحتطب ما هي الدالة متصلة مدام متصلة إذا غصب
+
+864
+01:13:16,460 --> 01:13:20,940
+عنها هتيجي تقطع اللي هو ما هتيجي منها لها هتقطع
+
+865
+01:13:20,940 --> 01:13:24,760
+محور السينات إذا هتصير سفر وهذا Contradiction من
+
+866
+01:13:24,760 --> 01:13:28,380
+أين الكلام هذا؟ By Bolzano Intermediate Value
+
+867
+01:13:28,380 --> 01:13:32,760
+Theorem بما أنه احنا في عندنا X0 فرضناها ال E of
+
+868
+01:13:32,760 --> 01:13:39,260
+X0 أصغر من سفر وفي عندي اللي هي E of Zero بساوي
+
+869
+01:13:39,260 --> 01:13:40,980
+واحد اللي هي
+
+870
+01:13:44,440 --> 01:13:48,620
+أه لو فرضنا ان في اكس نوت اكس نوت تكون اللي هو
+
+871
+01:13:48,620 --> 01:13:56,300
+سالبة اكس نوت اصغر من سفر فعندي E of X naught اصغر
+
+872
+01:13:56,300 --> 01:14:05,740
+من سفر وعندي اللي هو في اللي هو E of X بساوي
+
+873
+01:14:05,740 --> 01:14:14,470
+واحد اه وهادي اكبر من سفرأه وفرضنا وجود هذه وفرضنا
+
+874
+01:14:14,470 --> 01:14:18,810
+وجود هذه اذا by intermediate value theorem غصبن
+
+875
+01:14:18,810 --> 01:14:23,650
+عنها there exists c element الفترة اللي احنا بنحكي
+
+876
+01:14:23,650 --> 01:14:28,510
+عنها R such that f of هذه الـ c اللي هي E of C
+
+877
+01:14:28,510 --> 01:14:33,330
+بتساول كمية اللي بينين اللي هي اسمها سفر وهذا
+
+878
+01:14:33,330 --> 01:14:41,860
+contradictionبالتالي بيحقق البلزان انها مستمرة على
+
+879
+01:14:41,860 --> 01:14:47,060
+اي انتقال مغلق على كل أرض لانها بيحقق البلزان انها
+
+880
+01:14:47,060 --> 01:14:47,260
+مستمرة على اي انتقال مغلق على كل أرض لانها بيحقق
+
+881
+01:14:47,260 --> 01:14:47,280
+البلزان انها مستمرة على اي انتقال مغلق على كل أرض
+
+882
+01:14:47,280 --> 01:14:47,700
+لانها بيحقق البلزان انها مستمرة على اي انتقال مغلق
+
+883
+01:14:47,700 --> 01:14:48,880
+على كل أرض لانها بيحقق البلزان انها مستمرة على اي
+
+884
+01:14:48,880 --> 01:14:49,100
+انتقال مغلق على كل أرض لانها بيحقق البلزان انها
+
+885
+01:14:49,100 --> 01:14:51,280
+مستمرة على اي انتقال مغلق على كل أرض لانها بيحقق
+
+886
+01:14:51,280 --> 01:14:54,390
+البلزان انها مستمرة على اي انتقمن سفر طيب مدام ال
+
+887
+01:14:54,390 --> 01:14:57,010
+E of X أكبر من سفر و احنا بنعرف ان ال E prime of X
+
+888
+01:14:57,010 --> 01:15:00,690
+بيتساوي E of X اذا صارت ال E prime أكبر من مين من
+
+889
+01:15:00,690 --> 01:15:04,890
+سفر كل X element ال R ومن ثم هذا معناته ان E is
+
+890
+01:15:04,890 --> 01:15:10,450
+strictly increasing on R اذا اللي هو المطلوب الأول
+
+891
+01:15:10,450 --> 01:15:15,810
+أثبتناه ان E is strictly increasing on R طيب
+
+892
+01:15:24,230 --> 01:15:30,250
+عندي اتنين strictly increasing ال function مظبوط
+
+893
+01:15:30,250 --> 01:15:41,510
+يعني اتنين اصغر من مين من اياش من ال E ليش لأن
+
+894
+01:15:41,510 --> 01:15:53,730
+عندي الواحد E واحد او E of Xقلنا أصغر strictly ولا
+
+895
+01:15:53,730 --> 01:15:57,890
+أكبر strictly من واحد زاد X صح؟ هذه الكورولا
+
+896
+01:15:57,890 --> 01:16:02,810
+remained تمانية تلاتة تلاتة اثبتناها إذا صار عند E
+
+897
+01:16:02,810 --> 01:16:08,050
+of واحدأكبر strictly من واحد زائد وا أكبر strictly
+
+898
+01:16:08,050 --> 01:16:13,970
+من واحد زائد واحد وال E of واحد مين هو E أس واحد
+
+899
+01:16:13,970 --> 01:16:17,390
+مش هيك اتفاجنا يعني هذا إياش اتنين يعني ال E أكبر
+
+900
+01:16:17,390 --> 01:16:22,450
+strictly من مين من الاتنين اتفاجنا طيب اتفاجنا إذا
+
+901
+01:16:22,450 --> 01:16:26,410
+صار عند ال E of اتنين أكبر strictly ال E أكبر من
+
+902
+01:16:26,410 --> 01:16:29,950
+مين من اتنين خلينا نبدأ عليها هذه ال E أكبر من
+
+903
+01:16:29,950 --> 01:16:41,000
+إياش من اتنينالان اكيد عنده ال E of R اللي بيسوي E
+
+904
+01:16:41,000 --> 01:16:48,440
+R او E N خليني اقول E N اكبر من اتنين هتكون اصغر
+
+905
+01:16:48,440 --> 01:16:53,700
+اللي هي اكبر من اتنين أُس N الان as N goes to
+
+906
+01:16:53,700 --> 01:16:57,680
+infinity اذا
+
+907
+01:16:57,680 --> 01:17:04,230
+اكيد هذه هتروح لمين لإنفينيتيوالـ E نفسها اللي هي
+
+908
+01:17:04,230 --> 01:17:08,750
+is strictly increasing is strictly increasing إذا
+
+909
+01:17:08,750 --> 01:17:12,370
+ال E of X تبعتها برضه هتروح لمين ل Infinity لما X
+
+910
+01:17:12,370 --> 01:17:18,650
+تروح إلى وين إلى مالة نهاية ليش لأن لكل L في X
+
+911
+01:17:18,650 --> 01:17:24,670
+أكبر منهابحيث انه اللي هو تصير E of X اللي هي
+
+912
+01:17:24,670 --> 01:17:30,110
+بيساوي E to the X أكبر من E to the N لكل N في X
+
+913
+01:17:30,110 --> 01:17:33,850
+أكبر منها بتصير E of X أكبر منها لأنها strictly
+
+914
+01:17:33,850 --> 01:17:37,710
+increasing فلان لما تروح هذه إلى مالة نهاية الكبار
+
+915
+01:17:37,710 --> 01:17:41,170
+تبعتها وهذه طبعا أكبر دايما موجودة هذا هتروح إلى
+
+916
+01:17:41,170 --> 01:17:45,540
+أين برضه إلى مالة نهاية يعني limit ال E of Xلما X
+
+917
+01:17:45,540 --> 01:17:48,980
+تروح إلى مالة نهاية بتساوي مالة نهاية وقلكم اللي
+
+918
+01:17:48,980 --> 01:17:54,040
+هو لو تجربته اللي هو تثبته أنه بما أنه limit E of
+
+919
+01:17:54,040 --> 01:17:58,840
+N بتروح إلى مالة نهاية by اللي هي limit definition
+
+920
+01:17:58,840 --> 01:18:03,020
+إذا limit E of X لما X تروح إلى مالة نهاية بتساوي
+
+921
+01:18:03,020 --> 01:18:08,080
+مالة نهاية الآن similarly for mean for اللي هو
+
+922
+01:18:08,080 --> 01:18:11,120
+limit
+
+923
+01:18:12,620 --> 01:18:16,560
+الـ E of X لما X تروح لسالب ملا نهاية هذه الان
+
+924
+01:18:16,560 --> 01:18:22,840
+بيصير اتنين أو minus N أكبر من E أو minus N ماشي
+
+925
+01:18:22,840 --> 01:18:28,000
+الحال الان ال limit لهذه as N goes to infinity
+
+926
+01:18:28,000 --> 01:18:31,940
+أكبر أو ساوي ال limit لهذه as N goes to infinity
+
+927
+01:18:31,940 --> 01:18:33,420
+الان
+
+928
+01:18:35,300 --> 01:18:40,100
+هذه اش مالها بيساوي سفر وهذه اوتوماتيك هيساوي ايش؟
+
+929
+01:18:40,100 --> 01:18:44,840
+هيساوي سفر الان as N goes to infinity يعني ال E to
+
+930
+01:18:44,840 --> 01:18:49,720
+the minus N بتروح للسفر من وين؟من اليمين، مظبوط أو
+
+931
+01:18:49,720 --> 01:18:53,060
+تروح للـ Zero، مظبوط لأن at E minus N تروح لما
+
+932
+01:18:53,060 --> 01:18:57,440
+لنهاية As N goes to infinity E to the minus N تروح
+
+933
+01:18:57,440 --> 01:19:03,460
+لإنفينيتي لأن as X بتروح إلى سالب ما لنهاية ال E
+
+934
+01:19:03,460 --> 01:19:07,560
+to the minus X برضه هتروح إلى وين؟ إلى السفر يعني
+
+935
+01:19:07,560 --> 01:19:11,220
+ال E to the X نفسها لما ناخد ال limit لما X تروح
+
+936
+01:19:11,220 --> 01:19:14,580
+بدل ما لنهاية تروح إلى مين؟ سالب ما لنهاية برضه
+
+937
+01:19:14,580 --> 01:19:20,200
+هتساوي إيش؟ السفرإذا صار عندى limit E ضو X لما X
+
+938
+01:19:20,200 --> 01:19:23,560
+تروح السلمة لها يابسة أو سفر و بعتمد على اللى هو
+
+939
+01:19:23,560 --> 01:19:26,780
+الجهتين على ال strictly increasing تبع ال E و
+
+940
+01:19:26,780 --> 01:19:30,580
+التفاصيل اللى هى ال definition بتظهر عندكم أنا
+
+941
+01:19:30,580 --> 01:19:34,220
+مافصلتاش لإنه هو إيه هذا القائم
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2__gojdcGsw_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2__gojdcGsw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..965fc060c36529ff49bca3920d56a7cdece6db4e
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/2__gojdcGsw_postprocess.srt
@@ -0,0 +1,1560 @@
+1
+00:00:04,940 --> 00:00:07,660
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,660 --> 00:00:10,500
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:10,500 --> 00:00:17,340
+أجمعين هذه هي المحاضرة رقم 23 في مساق تحليل حقيقة
+
+4
+00:00:17,340 --> 00:00:22,200
+نيل طلاب وطالبات الجامعة الإسلامية قسم الرياضيات
+
+5
+00:00:22,200 --> 00:00:27,900
+كلية العلومالمحاضرة اللي هي اليوم هي عبارة عن
+
+6
+00:00:27,900 --> 00:00:33,180
+تكملة ل section تمانية تلاتة الجزء الثاني من .. من
+
+7
+00:00:33,180 --> 00:00:36,580
+.. من هذا .. اللي هو ال chapter الجزء الأول من هذا
+
+8
+00:00:36,580 --> 00:00:39,320
+ال section الجزء الأول اتحدثنا عن ال exponential
+
+9
+00:00:39,320 --> 00:00:44,670
+function وكيف أثبتنا وجودهاواخدنا خواصها الآن بدنا
+
+10
+00:00:44,670 --> 00:00:47,910
+نحكي عن الجزء التاني من اللي هو ال section اللي هو
+
+11
+00:00:47,910 --> 00:00:51,050
+ال logarithmic function ال logarithmic function
+
+12
+00:00:51,050 --> 00:00:55,290
+اللي هو نشوف كيف بدنا نثبت وجودها وكيف اللي هو
+
+13
+00:00:55,290 --> 00:01:00,410
+ناخد خواصها بنفس البناء اللي أو نبنع البناء اللي
+
+14
+00:01:00,410 --> 00:01:05,820
+بنناه المحاضرة الماضيةالان لما حكينا عن ال
+
+15
+00:01:05,820 --> 00:01:10,020
+exponential function E لجينا ان ال exponential E
+
+16
+00:01:10,020 --> 00:01:12,780
+is strictly increasing differentiable function
+
+17
+00:01:12,780 --> 00:01:18,160
+with domain R and range اللي هو Y أكبر من 0 يعني
+
+18
+00:01:18,160 --> 00:01:22,480
+لما حكينا عن ال E حكينا عن ال E من R اللي هي ال
+
+19
+00:01:22,480 --> 00:01:26,600
+exponential لعند الفترة 0 و مالا نهاية هذه ال
+
+20
+00:01:26,600 --> 00:01:31,560
+function هي rangeها و هي domainها و كانت strictly
+
+21
+00:01:31,560 --> 00:01:35,700
+increasingStrictly increasing معناته اللي هو عبارة
+
+22
+00:01:35,700 --> 00:01:40,020
+عن 120 يعني بمعنى أخر في إلها ال function هذه on
+
+23
+00:01:40,020 --> 00:01:43,940
+two وكانت differentiable الآن ال function اللي هي
+
+24
+00:01:43,940 --> 00:01:46,840
+ال exponential طبعا ما أنتوا عارفين كيف رسمتها لو
+
+25
+00:01:46,840 --> 00:01:50,460
+جينا جربنا نرسمها هنلاقي الرسمة اللي هو هذه اللي
+
+26
+00:01:50,460 --> 00:01:56,180
+هي عبارة عن رسمة ال exponentialالان انا بدى اجى
+
+27
+00:01:56,180 --> 00:02:00,300
+اللى هو من خلال اللى هو ال function ال exponential
+
+28
+00:02:00,300 --> 00:02:05,980
+اعرف ال inverse لها واسميه اللى هو logarithmic
+
+29
+00:02:05,980 --> 00:02:10,860
+function او بدى اسميه ال logarithm الطبيعى اللى هى
+
+30
+00:02:10,860 --> 00:02:16,020
+ال len functionمشروع الكلام اه لإن ايه عبارة عن
+
+31
+00:02:16,020 --> 00:02:19,240
+function one to one و one to Hana إذا صار ال
+
+32
+00:02:19,240 --> 00:02:23,580
+inverse لها موجود لإنها strictly increasing إذا
+
+33
+00:02:23,580 --> 00:02:29,560
+صار ال L من عند zero و مالة نهاية لعند ال R هادي
+
+34
+00:02:29,560 --> 00:02:34,100
+اللي هيالـ function الجديدة هي اللي بدي أسميها الـ
+
+35
+00:02:34,100 --> 00:02:38,320
+logarithmic function وهي رسمتها اللي أمامنا اللي
+
+36
+00:02:38,320 --> 00:02:42,460
+هي ال inverse لهذه الدالة اللي بدي أعرفها الآن
+
+37
+00:02:42,460 --> 00:02:47,000
+وتعريف الآن صار شرعي بناء على وجود ال exponential
+
+38
+00:02:47,000 --> 00:02:50,930
+اللي بدي أعرفه اللي هو ال inverse سبعتهاالعمل
+
+39
+00:02:50,930 --> 00:02:57,030
+المعرفي للـ E هو
+
+40
+00:02:57,030 --> 00:03:02,850
+الـ Logarithm أو الـ Nature Logarithm اللي هي It
+
+41
+00:03:02,850 --> 00:03:07,870
+will be denoted by L or by Lin الأكتر شيوعا طبعا
+
+42
+00:03:07,870 --> 00:03:11,810
+اللي هو مين الـ Lin لأن بما أن الـ E و L انفرس
+
+43
+00:03:11,810 --> 00:03:17,110
+لبعض إذا أكيد الـ E composite L composite E of X
+
+44
+00:03:17,110 --> 00:03:22,920
+هيساوي الـ Xلكل الـ x و اللي موجودة في الـ R لأن
+
+45
+00:03:22,920 --> 00:03:26,540
+الـ E بتشتغل على كل الإكسات اللي في الـ R لأن
+
+46
+00:03:26,540 --> 00:03:30,740
+بينما E composite L of Y E composite L of Y الـ L
+
+47
+00:03:30,740 --> 00:03:34,660
+بتشتغل .. بتشتغل مين على مين بس على الـ positive E
+
+48
+00:03:34,660 --> 00:03:38,240
+composite L of Y بيساوي لكل Y element in R و Y
+
+49
+00:03:38,240 --> 00:03:44,900
+أشملها أكبر من 0الان connotations .. connotations
+
+50
+00:03:44,900 --> 00:03:49,860
+بناء عليه الـ N الـ E of X لأن الـ N هي الـ L والـ
+
+51
+00:03:49,860 --> 00:03:53,880
+E هي الـ E وعندي الـ E to the N اللي هو بسوء الـ Y
+
+52
+00:03:53,880 --> 00:03:57,780
+وهو بسوء الـ X بناء على أن الواحدة inverse للتانية
+
+53
+00:04:01,010 --> 00:04:04,750
+أو كل واحدة inverse للاخرى الـ logarithm is a
+
+54
+00:04:04,750 --> 00:04:08,630
+strictly increasing function L with domain اللي هو
+
+55
+00:04:08,630 --> 00:04:12,150
+مين اللي هو ال domain اللي عندي اللي هو تعرفنا هيك
+
+56
+00:04:12,150 --> 00:04:16,210
+أصلا الان ال derivative of L is given by L prime
+
+57
+00:04:16,210 --> 00:04:19,750
+of X ايش بتساوي واحدة ل X for X أكبر من سفر الان
+
+58
+00:04:19,750 --> 00:04:23,430
+ال logarithm satisfy the functional equation تحقق
+
+59
+00:04:23,430 --> 00:04:27,010
+المعادلة الدالية التالية اللي هي L of X في Y بساوي
+
+60
+00:04:27,010 --> 00:04:31,000
+L of X زائد LL of Y for X أكبر من سفر Y أكبر من
+
+61
+00:04:31,000 --> 00:04:34,560
+سفر Y أكبر
+
+62
+00:04:34,560 --> 00:04:38,260
+من سفر
+
+63
+00:04:38,260 --> 00:04:40,560
+Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر
+
+64
+00:04:40,560 --> 00:04:40,580
+من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y
+
+65
+00:04:40,580 --> 00:04:40,640
+أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من
+
+66
+00:04:40,640 --> 00:04:40,700
+سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y
+
+67
+00:04:40,700 --> 00:04:41,020
+سفر Y أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y
+
+68
+00:04:41,020 --> 00:04:47,140
+أكبر من سفر Y أكبر من سفر Y أكبر من سفر Y أكبرL of
+
+69
+00:04:47,140 --> 00:04:51,420
+XR بيساوي R لL of X لإن X أكبر من 0 وR المتر كيوه
+
+70
+00:04:51,420 --> 00:04:54,840
+كلهن اللي هي خواص انتوا بتعرفوهم قبل هيك بس الآن
+
+71
+00:04:54,840 --> 00:04:58,440
+بدنا نبرهنهم و نثبت صحتهم limit L of X لما X تروح
+
+72
+00:04:58,440 --> 00:05:01,740
+لـ0 من اليمين بساوي سالب infinity and limit L of X
+
+73
+00:05:01,740 --> 00:05:07,340
+لما X تروح لمال النهاية بتساوي مال النهاية خلينا
+
+74
+00:05:07,340 --> 00:05:14,840
+احنا نشوف نبرهن اللي هي اللي مطلوبالأن الـ L is
+
+75
+00:05:14,840 --> 00:05:17,560
+strictly increasing with domain X element alone
+
+76
+00:05:17,560 --> 00:05:20,880
+and range R follows from the fact that E is
+
+77
+00:05:20,880 --> 00:05:24,840
+strictly increasing with domain R and range اللي
+
+78
+00:05:24,840 --> 00:05:33,320
+هو اللي عندي الان عندي ال L is strictly increasing
+
+79
+00:05:33,320 --> 00:05:37,560
+بناء على مين على ال E نفسها strictly increasing
+
+80
+00:05:37,560 --> 00:05:48,560
+الان EComposite L E Composite L of Y ايش بتساوي؟ Y
+
+81
+00:05:48,560 --> 00:05:55,320
+لكل Y وY الموجودة لكل Y element in سفر وملا نهاية،
+
+82
+00:05:55,320 --> 00:06:00,780
+مظبوط؟ الان فاضلول الجهتين الان طبعا احنا بنعرف
+
+83
+00:06:00,780 --> 00:06:06,360
+انه من الاصل مدامة ال E isاللي هو differentiable
+
+84
+00:06:06,360 --> 00:06:10,480
+أكيد اللي هي ال inverse إلها is differentiable by
+
+85
+00:06:10,480 --> 00:06:14,680
+theorem 6 9 كده مش عارف إيش في اللي هو chapter 6
+
+86
+00:06:14,680 --> 00:06:18,200
+قدامة ال function اللي هي is differentiable ال
+
+87
+00:06:18,200 --> 00:06:20,880
+inverse إلها برضه is differentiable في حالة وجودها
+
+88
+00:06:20,880 --> 00:06:27,480
+الآن E فاضل الجهتين بيصير عندي E prime of L of Y
+
+89
+00:06:27,480 --> 00:06:36,600
+فL prime of Y بساوي إيش واحد ماشي الحال الآنواضح
+
+90
+00:06:36,600 --> 00:06:41,900
+أن هذا حاصل الضرب صار أكبر من مين strictly من 0
+
+91
+00:06:41,900 --> 00:06:47,920
+وبما أن الـ E is strictly increasing أثبتنا E' of
+
+92
+00:06:47,920 --> 00:06:53,420
+L of Y is strictly أكبر من 0 إذا بيظلها L' of Y is
+
+93
+00:06:53,420 --> 00:06:57,180
+strictly أكبر من 0 لكل Y هنا إذا صارت الـ L is
+
+94
+00:06:57,180 --> 00:07:02,740
+strictly increasingالان طبعا ال domain مدام ان هذه
+
+95
+00:07:02,740 --> 00:07:07,000
+ال inverse ل ال E ال domain اللي هو ال inverse هو
+
+96
+00:07:07,000 --> 00:07:11,380
+range ال function الأصلية و بيصير sub wave في
+
+97
+00:07:11,380 --> 00:07:18,460
+الفئر اذا الان احنا اثبتنا ان ال is strictly
+
+98
+00:07:18,460 --> 00:07:23,530
+increasingالان و rangeها اللي هو صار domain اللي
+
+99
+00:07:23,530 --> 00:07:28,310
+هو او range اللي هو ال .. هذي اللي صار domainها
+
+100
+00:07:28,310 --> 00:07:32,990
+domain ال L و هذي صارت اللي هو range ال L زي ما
+
+101
+00:07:32,990 --> 00:07:37,330
+قلنا قبل بشوية او عندي الان بدنا نثبت اللي هو
+
+102
+00:07:37,330 --> 00:07:42,070
+الجزء الثاني من النظرية خليني نكتب هنا عشان نتذكر
+
+103
+00:07:42,070 --> 00:07:48,430
+ايش اللي بدنا نثبته الان بدنا نثبت اين أثبتنا
+
+104
+00:07:48,430 --> 00:07:54,230
+الأولىاللي فى النص بتقلّى prime of X اللى نكتبهن
+
+105
+00:07:54,230 --> 00:07:59,330
+اللى بدنا نثبتهن عشان نتذكرهن
+
+106
+00:07:59,330 --> 00:08:12,240
+قلّى prime I او VIII قلّى primeof X بسوة واحدة ل X
+
+107
+00:08:12,240 --> 00:08:19,680
+اتنين اللي هو L of XY بسوة L X زائد L Y طبعا ال Y
+
+108
+00:08:19,680 --> 00:08:25,780
+هناك ال L of واحد بسوة سفر L of E بسوة واحد كلهم
+
+109
+00:08:25,780 --> 00:08:34,440
+بسيطاتL prime L of X to the R سوى R L of X و Limit
+
+110
+00:08:34,440 --> 00:08:39,720
+L of X لما X تروح إلى Zero من اليمين سوى سالب لما
+
+111
+00:08:39,720 --> 00:08:45,140
+لنهاية و Limit لL of X لما X تروح إلى ما لنهاية
+
+112
+00:08:45,140 --> 00:08:48,520
+سوى ما لنهاية خلّيني أشوف أن دول على السريع فانوا
+
+113
+00:08:48,520 --> 00:08:53,640
+كلها شغلات يعني بأعتقد أنه سهل أنك نثبتها
+
+114
+00:08:55,730 --> 00:09:02,210
+عندي لأن زي ما عملت قبل بشوية اللي هو لما فضلت هذه
+
+115
+00:09:02,210 --> 00:09:07,290
+تفاضله E composite L of X لما عملتها قبل بشوية
+
+116
+00:09:07,290 --> 00:09:14,250
+اللي هي كانت عندي هين أعمل E composite L of X الكل
+
+117
+00:09:14,250 --> 00:09:19,370
+اللي هي بساوي ال X فاضل هذا يصير E prime
+
+118
+00:09:26,060 --> 00:09:29,100
+بنسبة لـ x أقل الـ prime of x
+
+119
+00:09:34,780 --> 00:09:40,160
+اللي هو واحد على الـ E prime of L of X إذا الـ E
+
+120
+00:09:40,160 --> 00:09:44,300
+القلي برايم of X بيساوي واحد على E prime composite
+
+121
+00:09:44,300 --> 00:09:48,340
+L of X والـ E prime هي نفس الـ E زي ما قلنا إذا
+
+122
+00:09:48,340 --> 00:09:51,140
+بيصير واحد على E composite L of X إلى ال E
+
+123
+00:09:51,140 --> 00:09:54,640
+composite L of X زي ما قلنا إيش بتساوي بساوي X
+
+124
+00:09:54,640 --> 00:09:57,660
+فبساوي واحد على X فالقلي برايم بيساوي واحد على X
+
+125
+00:09:57,660 --> 00:10:02,910
+لكل X في الموجودة في الفترة Zeroو 1 نيجي الآن نشوف
+
+126
+00:10:02,910 --> 00:10:06,710
+اللي هي اللي بعدها الخاصية اللي بعدها خلّينا نثبت
+
+127
+00:10:06,710 --> 00:10:12,690
+اللي هو L of X في Y بسوا L of X زائد مين زائد L of
+
+128
+00:10:12,690 --> 00:10:17,270
+Y برضه الإثبات سهل وانتبهوا معايا وسهلس عندى الآن
+
+129
+00:10:24,240 --> 00:10:27,240
+F X أكبر من صفر Y أكبر من صفر F X أكبر من صفر Y
+
+130
+00:10:27,240 --> 00:10:27,740
+أكبر من صفر F X أكبر من صفر Y أكبر من صفر F X أكبر
+
+131
+00:10:27,740 --> 00:10:27,900
+من صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+132
+00:10:27,900 --> 00:10:28,100
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+133
+00:10:28,100 --> 00:10:28,700
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+134
+00:10:28,700 --> 00:10:28,920
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+135
+00:10:28,920 --> 00:10:32,100
+صفر F X أكبر من صفر F X أكبر من صفر F X أكبر من
+
+136
+00:10:32,100 --> 00:10:43,400
+صفر F X أكبر من صفر F X أكبر من صفر F X
+
+137
+00:10:43,400 --> 00:10:51,850
+أكبر من صفر F Xلأن الـ E والـ L انفرسة بعض الان من
+
+138
+00:10:51,850 --> 00:10:55,130
+الخاصية تبع الـ exponential بدنا نصل لمن؟ لل
+
+139
+00:10:55,130 --> 00:11:00,970
+logarithmic إذا أضرب ل X في Y بيطلع عند X في Y
+
+140
+00:11:00,970 --> 00:11:05,190
+بتساوي E of U في E of V E of U في E of V إيش
+
+141
+00:11:05,190 --> 00:11:10,010
+بتساوي؟ E of U زائد V أثبتناها إذا من هذا الكلام
+
+142
+00:11:10,970 --> 00:11:15,270
+خُد الـ L للجهتين لإنه اللي هي ال inverse لبعض
+
+143
+00:11:15,270 --> 00:11:20,450
+بيصير عندي L of X في Y بساوي L of E of U زائد V
+
+144
+00:11:20,450 --> 00:11:24,410
+اللي هي إيش بتساوي U زائد V U اللي هي عبارة عن L
+
+145
+00:11:24,410 --> 00:11:30,750
+of X و V عبارة عن L of Y إذا أثبتت L of X زائد X
+
+146
+00:11:30,750 --> 00:11:39,370
+في Y بساوي L of X زائد L of Yالان عندى اللى هى E
+
+147
+00:11:39,370 --> 00:11:47,050
+of Zero بيساوي واحد خدلى ال L الجهتين بيصير ZL of
+
+148
+00:11:47,050 --> 00:11:53,010
+E of Zero بيساوي L of واحد ال L of E of Zero هدك
+
+149
+00:11:53,010 --> 00:11:59,450
+inverse التانية بيساوي Zero نفس الاشيالـ L of E of
+
+150
+00:11:59,450 --> 00:12:07,270
+1 بيساوي L of E، مظبوط؟ الـ L of E of 1 بيساوي 1،
+
+151
+00:12:07,270 --> 00:12:12,230
+بيصير L of E بيساوي 1 بيصير أثبتنا L of E بيساوي 1
+
+152
+00:12:12,230 --> 00:12:19,730
+و L of 1 بيساوي 0 وهذا الكلام كلام سهل، طيب بيصير
+
+153
+00:12:19,730 --> 00:12:23,710
+علاقة أنه سهل اللي بنحكيه، الآن
+
+154
+00:12:27,210 --> 00:12:32,730
+نأتي نثبت اللي هو اللي هي L of X to the R بساوة
+
+155
+00:12:32,730 --> 00:12:37,010
+Zero بساوة R في L of X هذه برضه بقاش By
+
+156
+00:12:37,010 --> 00:12:41,910
+Mathematical Induction عملناها قبل هيكة باللي هو
+
+157
+00:12:41,910 --> 00:12:47,330
+ال section اللي جابله أو اللي هو ال exponential
+
+158
+00:12:47,330 --> 00:12:52,830
+على السريع نشوف التفاصيل لإنه التفاصيل معادة
+
+159
+00:13:07,050 --> 00:13:11,430
+التفاصيل هتلاجوها معادة فخليني بسرعة نمر عليها
+
+160
+00:13:11,430 --> 00:13:17,730
+عندي we show by induction L of X بسوا L L of X زي
+
+161
+00:13:17,730 --> 00:13:21,850
+ما قلنا عشان لثبتها هذه أثبتنا اللي قبل بشوية L of
+
+162
+00:13:21,850 --> 00:13:27,190
+X عارفش الرزوم أصلا أفصل ولا لأ لكن بدي أفصل لو
+
+163
+00:13:27,190 --> 00:13:32,790
+أنتوا عندى لو اتفجنا أن نفصل ولا لأ L of X في Y
+
+164
+00:13:32,790 --> 00:13:39,580
+بسوا L of X في L of Yof x was n بساوي n في L of x
+
+165
+00:13:39,580 --> 00:13:44,060
+طبعا for n بتساوي واحد اللي هي a trivial نفترض
+
+166
+00:13:44,060 --> 00:13:48,180
+أنها صحيحة ل L ل n بتساوي k بيصير L of x was k
+
+167
+00:13:48,180 --> 00:13:53,080
+بساوي k L of x الآن بدنا نحسب ل L of x was k زائد
+
+168
+00:13:53,080 --> 00:13:59,480
+واحد اللي هي بساوي L of x was k في xهذه الـ L لها
+
+169
+00:13:59,480 --> 00:14:04,760
+حسب اللي هي الخاصية هذه بسوء L الأولى X plus K في
+
+170
+00:14:04,760 --> 00:14:09,860
+L التاني L of X اللي هو مفترض إنها صحيحة على K ده
+
+171
+00:14:09,860 --> 00:14:19,600
+بسوء K في L of X آسف زائد هذه بسوء K L of Xلأنها
+
+172
+00:14:19,600 --> 00:14:26,400
+صحيحة لـ K زائد L of X ويساوي K زائد واحد في L of
+
+173
+00:14:26,400 --> 00:14:31,520
+X إذا صارت هذه صحيحة اللي هي L ل K زائد واحد إذا
+
+174
+00:14:31,520 --> 00:14:36,760
+صارت صحيحة لكل من لكل N element in N حسب اللي هو
+
+175
+00:14:36,760 --> 00:14:43,080
+ال induction اللي بنحكي فيه إذا الأن أثبتنا أن L
+
+176
+00:14:43,080 --> 00:14:49,710
+of X هو N لL of X لكل اللي هي عنديالان by VI اللي
+
+177
+00:14:49,710 --> 00:14:53,530
+هو زي .. مشابه للي حكيناها قبل بشوية بالظبط في حد
+
+178
+00:14:53,530 --> 00:14:58,890
+ال exponential بس خليني مش وشكلة بتعيده الان شوف L
+
+179
+00:14:58,890 --> 00:15:03,680
+of XM minus M أيش بتساوي؟ L of واحداللي هي لأن هذا
+
+180
+00:15:03,680 --> 00:15:05,860
+X هو السفر اللي هي L of واحد L of واحد مش قولنا
+
+181
+00:15:05,860 --> 00:15:11,040
+عنها سفر هو يسوى L of XM في XM minus واحد ال
+
+182
+00:15:11,040 --> 00:15:16,300
+logarithmic بطلح انجمع L of XM زائد L of X minus M
+
+183
+00:15:16,300 --> 00:15:21,920
+لأن هذه أثبتناها عبارة عن M L of X زائدL of X
+
+184
+00:15:21,920 --> 00:15:27,500
+minus M صار عندي الان M في L of X زائد L of X
+
+185
+00:15:27,500 --> 00:15:32,040
+minus M بسوا سفر انجلي هذا على الجهة الثانية بطلع
+
+186
+00:15:32,040 --> 00:15:35,760
+L of X minus M اللي قعدت لحالها بسوا ناقص M في L
+
+187
+00:15:35,760 --> 00:15:41,720
+of X اذا صار عندي الان لكل M سواء موجبة او سالبة
+
+188
+00:15:41,720 --> 00:15:48,940
+بطلع عندي اللي هي L of X قص Mبساوة M في L of X
+
+189
+00:15:48,940 --> 00:15:53,860
+سواء كانت وجبة أو سالبة نيجي الآن منها بدنا ناخد
+
+190
+00:15:53,860 --> 00:15:57,360
+لمين لأ اللي هي ال R لان therefore for any M
+
+191
+00:15:57,360 --> 00:16:02,800
+element in Z و N element in Nعندي احسبلي الان L of
+
+192
+00:16:02,800 --> 00:16:07,020
+X أس M على N بس ضربليها في N بعد إذنك Y ساوي اللي
+
+193
+00:16:07,020 --> 00:16:12,460
+هي L of X أس M على N لكل ما له أس N لإنه صحيحة هذه
+
+194
+00:16:12,460 --> 00:16:18,080
+لل N اللي هي في N واتفجنا عليها الان هذه بتساوي
+
+195
+00:16:18,080 --> 00:16:21,520
+هذه واضحة لإن هذه هي ال X تبعتنا وهذه ال N بتطلع
+
+196
+00:16:21,520 --> 00:16:27,410
+براالان هذه الان مع الان بيصير L of X plus M L of
+
+197
+00:16:27,410 --> 00:16:30,870
+X plus M قبل بشوية بقى قولنا عنها بيساوي M L of X
+
+198
+00:16:30,870 --> 00:16:34,270
+سواء كانت M positive أو اللي هو negative صار هذه
+
+199
+00:16:34,270 --> 00:16:40,930
+بتساوي هذه إذا انجلي الآنالان هذه ان بيصير عندي L
+
+200
+00:16:40,930 --> 00:16:44,910
+of X of M على N بيسوي M على N في L of X إذا صار
+
+201
+00:16:44,910 --> 00:16:49,490
+عندي لأي rational number صار عندي L of X R بيسوي R
+
+202
+00:16:49,490 --> 00:16:55,670
+L of X لكل R اللي بنتميين NQ نيجي الآن لأ اللي هي
+
+203
+00:16:55,670 --> 00:16:57,230
+الجزء الأخير من النظرية
+
+204
+00:17:08,180 --> 00:17:11,120
+الكلام مشابه للي حكيناها قبل بشوية في الإثبات اللي
+
+205
+00:17:11,120 --> 00:17:15,260
+هو ال limit تبع ال exponential عند 2 أصغر من E
+
+206
+00:17:15,260 --> 00:17:19,380
+وقلنا ليش الان ال E n هنا بيصير 2 أصغر من E أصغر
+
+207
+00:17:19,380 --> 00:17:19,920
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+208
+00:17:19,920 --> 00:17:21,140
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+209
+00:17:21,140 --> 00:17:22,840
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+210
+00:17:22,840 --> 00:17:23,240
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+211
+00:17:23,240 --> 00:17:26,700
+من E أصغر من E أصغر من E أصغر من E أصغر من E أصغر
+
+212
+00:17:26,700 --> 00:17:30,620
+من E أصغ
+
+213
+00:17:33,960 --> 00:17:39,580
+لكن اللي هو L of E N بسوء N and اللي هي L of E
+
+214
+00:17:39,580 --> 00:17:44,020
+minus N بسوء نقص N خليني في الذاكر هذول اذا for
+
+215
+00:17:44,020 --> 00:17:47,480
+every N element in R there exists X element in R
+
+216
+00:17:47,480 --> 00:17:52,670
+بحيث ان X أكبر من مين من Nلكل N element in N في X
+
+217
+00:17:52,670 --> 00:17:56,350
+element in R أكيد X أكبر من مين من E N لأنه أخسرت
+
+218
+00:17:56,350 --> 00:18:00,590
+N بين إيديا حسبت ال E N طلع عند رقم أخدت ال X أكبر
+
+219
+00:18:00,590 --> 00:18:03,310
+منها كيد بالله طيب لأنه unbounded real numbers
+
+220
+00:18:03,310 --> 00:18:06,710
+then L في هذه أكبر أو من L في هذه لأنه ال L
+
+221
+00:18:06,710 --> 00:18:10,810
+strictly increasing إذا صار L في X أكبر من مين من
+
+222
+00:18:10,810 --> 00:18:16,130
+ال NA ألوف E أن يعني أكبر من الان لأن limit هذه as
+
+223
+00:18:16,130 --> 00:18:21,210
+x goes to infinity اللي هو بيكون أكبر أساوي اللي
+
+224
+00:18:21,210 --> 00:18:23,950
+هي limit هذه as n goes to infinity ويساوى infinity
+
+225
+00:18:23,950 --> 00:18:27,550
+لأن لكل لما الان تروح لما لنهاية أكيد ال X بتروح
+
+226
+00:18:27,550 --> 00:18:31,270
+لمين إلى ما لنهاية فصار عندي هذه بتروح إلى ما
+
+227
+00:18:31,270 --> 00:18:34,970
+لنهاية الآن صار عندي limit L of X لما X تروح لما
+
+228
+00:18:34,970 --> 00:18:41,040
+لنهاية بيساوي ما لنهاية similarlyالان لكل نقص any
+
+229
+00:18:41,040 --> 00:18:43,100
+element in z positive بلاقي x element in r
+
+230
+00:18:43,100 --> 00:18:45,740
+positive بحيث ان x أكبر من صفر و أصغر من صفر و
+
+231
+00:18:45,740 --> 00:18:46,340
+أصغر من صفر و أصغر من صفر و أصغر من صفر و أصغر من
+
+232
+00:18:46,340 --> 00:18:47,840
+صفر و أصغر من صفر و أصغر من صفر و أصغر من صفر و
+
+233
+00:18:47,840 --> 00:18:51,500
+أصغر من صفر و أصغر من صفر و أصغر من صفر و أصغر من
+
+234
+00:18:51,500 --> 00:18:57,960
+صفر و أصغر من صفر و أصغر من صفر و أصغر من صفر و
+
+235
+00:18:57,960 --> 00:19:02,520
+أصغر من صفر و أصغر من صفر و أصغر من صفر و أصغر من
+
+236
+00:19:02,520 --> 00:19:09,620
+صفر و أصغر من صفر و أصغر من صفر و أطيب then L of X
+
+237
+00:19:09,620 --> 00:19:13,660
+هيكون أصغر يساوي ال E to the minus N يعني L of X
+
+238
+00:19:13,660 --> 00:19:17,800
+اللي هي أصغر يساوي ناقص N إذا as N goes to
+
+239
+00:19:17,800 --> 00:19:22,700
+infinity as N goes to infinity اللي هو ال E to the
+
+240
+00:19:22,700 --> 00:19:26,540
+minus N بيروح لل0 من اليمين إذا ال X بتروح لل0 من
+
+241
+00:19:26,540 --> 00:19:30,820
+اليمين إذا عندي ال X بتروح لل 0 من اليميناللي هو
+
+242
+00:19:30,820 --> 00:19:34,580
+أصغر لما الـ limit L of X أصغر من limit E to the
+
+243
+00:19:34,580 --> 00:19:37,900
+minus N لما هذا يروح لـ 0 من اليمين أو بمعنى أخر
+
+244
+00:19:37,900 --> 00:19:41,680
+لما الـ N تروح لمهة لنهاية و هذا بيروح لمين؟ لـ
+
+245
+00:19:41,680 --> 00:19:44,760
+Infinity إذا limit L of X لما X تروح لمهة لنهاية
+
+246
+00:19:44,760 --> 00:19:50,920
+بساوي سالب Infinity و هو المطلوب hence limit L of
+
+247
+00:19:50,920 --> 00:19:54,460
+X لما X تروح لـ 0 من اليمين بساوي سالب Infinity
+
+248
+00:19:54,460 --> 00:19:58,500
+طيب
+
+249
+00:20:12,260 --> 00:20:16,320
+الان سارعنا الان نقدر ان اللي هو نحكي عن ال bar
+
+250
+00:20:16,320 --> 00:20:20,080
+functions بدنا نعرف ال bar functions اللي هي بناء
+
+251
+00:20:20,080 --> 00:20:25,060
+على اللي حكيناه و اللي هي موضوع ال bar functions
+
+252
+00:20:25,060 --> 00:20:28,880
+كل ما فيه تقريبا يعني بنعتبره exercises احنا لكن
+
+253
+00:20:28,880 --> 00:20:32,520
+خلينا نعرف التعريفات و النظريات بتكون اللي هي
+
+254
+00:20:32,520 --> 00:20:35,900
+معاكم exercises بسيطة بناء على التعريف اللي
+
+255
+00:20:35,900 --> 00:20:40,720
+بنعرفها اللي هناخد α يليمنتان R و X أكبر من 0The
+
+256
+00:20:40,720 --> 00:20:43,320
+number X to the Alpha is defined to be .. الآن بدي
+
+257
+00:20:43,320 --> 00:20:46,940
+أعرف حاجة اسمها X to the Alpha X to the Alpha بدي
+
+258
+00:20:46,940 --> 00:20:49,900
+أعرفها .. إيش بدي أعرفها؟ بإيشي أنا معرف عندي من
+
+259
+00:20:49,900 --> 00:20:54,440
+الأصل ال exponential معرفة .. خلصنا منها و ال len
+
+260
+00:20:54,440 --> 00:20:59,000
+معرفة .. إذا E to the Alpha في لن ال X هذه المقدار
+
+261
+00:20:59,000 --> 00:21:03,820
+لهذا معرف و هذا معرف بدي أسمي X to the Min to the
+
+262
+00:21:03,820 --> 00:21:07,400
+Alpha اللي هو في الواقع عبارة عن Min E to the
+
+263
+00:21:07,400 --> 00:21:12,040
+AlphaL of X L of X معرفة والـ E معرفة إذا كل هذه
+
+264
+00:21:12,040 --> 00:21:16,000
+معرفة بتسميها X to the main to the alpha الآن صارت
+
+265
+00:21:16,000 --> 00:21:19,540
+عندي يعني قيمة الـ X under this function اللي
+
+266
+00:21:19,540 --> 00:21:23,120
+عرفتها لجديدة يعني إذا بتسميها دي ال function الـ
+
+267
+00:21:23,120 --> 00:21:28,240
+R of X إيش عرفتها أنا بتساوي X to the alpha؟يعني
+
+268
+00:21:28,240 --> 00:21:31,680
+كل ال X بتصير يشمل X to the Alpha و X أكبر من 0
+
+269
+00:21:31,680 --> 00:21:36,780
+هذه ال X to the Alpha هي اللي بدي أسميها ال power
+
+270
+00:21:36,780 --> 00:21:42,000
+function بدي أسميها power function with exponent
+
+271
+00:21:42,000 --> 00:21:47,540
+mean Alpha و ال X هي أشمالها المتغيرة اللي أكبر من
+
+272
+00:21:47,540 --> 00:21:54,340
+0 شوف الآن نشوف بعض الخواص اللي هو هذه اللي هي
+
+273
+00:21:54,340 --> 00:21:56,460
+الدالة طيب
+
+274
+00:22:04,730 --> 00:22:08,690
+الان if x أكبر من 0 and alpha بساوة m على n where
+
+275
+00:22:08,690 --> 00:22:12,770
+m element in z و n element in n then we define x
+
+276
+00:22:12,770 --> 00:22:17,790
+to the alpha بساوة x to the m أسواحد على n in
+
+277
+00:22:17,790 --> 00:22:23,110
+section mean خمسة ستة هتعرفناها زمان انه في حالة
+
+278
+00:22:23,110 --> 00:22:26,570
+بس اللي هي ال rational number عرفنا x to the m على
+
+279
+00:22:26,570 --> 00:22:30,630
+n بساوة x to the m لكل أسواحد على nماشي الحال
+
+280
+00:22:30,630 --> 00:22:34,510
+..الان بدنا نشوف هذا التعريف مطابق لتعريفنا اليوم
+
+281
+00:22:34,510 --> 00:22:41,670
+ولا لأ hence we have لن ال X to the Alpha لن ال X
+
+282
+00:22:41,670 --> 00:22:45,370
+to the Alpha لن ال X to the Alpha بساوي Alpha لن
+
+283
+00:22:45,370 --> 00:22:51,540
+ال Xعرفناها هذه طيب where X to the Alpha بيسوا E
+
+284
+00:22:51,540 --> 00:22:56,260
+to the Lin X to the Min to the Alpha اللي هو بيسوا
+
+285
+00:22:56,260 --> 00:23:01,020
+E to the Alpha في Min في Lin ال X كلام كله سهل ال
+
+286
+00:23:01,020 --> 00:23:05,740
+X to the Alpha هو اللي عرفناها اللي عبارة عن E
+
+287
+00:23:05,740 --> 00:23:10,570
+بتصير to the Lin X to the Alphaلأنه استبدلت الـ x
+
+288
+00:23:10,570 --> 00:23:15,090
+to the alpha بقيمتها اللي هي عبارة عن اللي هي
+
+289
+00:23:15,090 --> 00:23:18,630
+alpha ln x اللي هي بالساوية e to the ln x to the
+
+290
+00:23:18,630 --> 00:23:24,510
+mean to the alpha إذا سواء احنا بالتعريف اللي هو
+
+291
+00:23:24,510 --> 00:23:28,190
+احنا هذا بال exponent أو بال ال function اللي
+
+292
+00:23:28,190 --> 00:23:33,110
+عرفناها بالشكل هذا هيطلع عندي اللي هو القيمتين نفس
+
+293
+00:23:33,110 --> 00:23:34,790
+القيمة طيب
+
+294
+00:23:37,160 --> 00:23:42,300
+نجي الآن لبعض الخواص اللي هي تبعت ال exponential
+
+295
+00:23:42,300 --> 00:23:47,180
+ال power function و الخواص هنتركه لكم إياه لأنها
+
+296
+00:23:47,180 --> 00:23:54,600
+مباشرة على التعريف تبعنا مباشرة
+
+297
+00:23:54,600 --> 00:24:01,100
+على اللي هي التعريف اللي عندنا و هيكون في عندي
+
+298
+00:24:01,100 --> 00:24:05,760
+الآن النظرية الأولىاللي هي 8 3 11 لو كانت Alpha
+
+299
+00:24:05,760 --> 00:24:11,340
+element in R و X و Y اللي هو تنتمي للفترة Zero و
+
+300
+00:24:11,340 --> 00:24:16,500
+تمانية Zero و ما لنهاية آسف then معلش عشان ده طلعت
+
+301
+00:24:16,500 --> 00:24:20,450
+الكهربا قعد نقلف الكهربا أناIf α element in R و X
+
+302
+00:24:20,450 --> 00:24:26,350
+Y belongs to 0 α then 1 to the α بسوء 1 و X to the
+
+303
+00:24:26,350 --> 00:24:30,270
+α أكبر من 0 و X Y to the α بسوء X to the α و Y to
+
+304
+00:24:30,270 --> 00:24:35,590
+the α و X على Y to the α بسوء X to the α على Y to
+
+305
+00:24:35,590 --> 00:24:39,370
+the α هذه اللي هي النظرية طبعا اللي هي مباشرة على
+
+306
+00:24:39,370 --> 00:24:45,100
+تعريفنا اللي هو X to the α بسوء Eof α لن X يعني
+
+307
+00:24:45,100 --> 00:24:49,800
+بدك تيجي تستخدم تعريفك اللي هو اللي عرفناه وعليه
+
+308
+00:24:49,800 --> 00:24:53,480
+اللي هو بتبدأ تشتغل و تبني اللي هو اللي هي
+
+309
+00:24:53,480 --> 00:24:57,680
+القوانين اللي بنحكي عنها اللي هو تعريفنا اللي هو X
+
+310
+00:24:58,570 --> 00:25:05,210
+to the alpha بتساوي E of alpha len اللي هي L of X
+
+311
+00:25:05,210 --> 00:25:10,650
+أو حسب ال notation تبعتنا E to the alpha len ال X
+
+312
+00:25:10,650 --> 00:25:15,710
+هذا الآن التعريف اللي عليه بدك اللي هو تبدأ اللي
+
+313
+00:25:15,710 --> 00:25:23,290
+هو تشتغل على اللي هي النظريةوتبرهنها اللي عندنا
+
+314
+00:25:23,290 --> 00:25:27,630
+نظرية الأولى اللي ذكرناها قبل بشوية اللي هي هذه
+
+315
+00:25:27,630 --> 00:25:32,090
+النظرية على التعريف مباشرة ونظرية تانية أيضا برضه
+
+316
+00:25:32,090 --> 00:25:35,670
+من الخواص إذا كانت Alpha و Beta element ر و X في
+
+317
+00:25:35,670 --> 00:25:40,640
+الفترة Zero ولا نهاية إذا Xتو دا ألفة زيادة بيتا
+
+318
+00:25:40,640 --> 00:25:44,040
+برضه نفس الاشياء طبعا هتلاقي اللي هو انت لما تيجي
+
+319
+00:25:44,040 --> 00:25:48,320
+تفرد هذه هتصير تستخدم خواص المعرفة اللي هي
+
+320
+00:25:48,320 --> 00:25:52,360
+بواسطتها معرفة هتستخدم خواص ال X exponential والن
+
+321
+00:25:52,360 --> 00:25:55,420
+اللي قبله بشوية هتلاقي حالك بتصل X تو دا ألفة
+
+322
+00:25:55,420 --> 00:25:58,310
+زيادة بيتا بسوء X تو دا ألفة في X تو دا بيتاو نفس
+
+323
+00:25:58,310 --> 00:26:05,170
+الشيء x²α²β بيساوي x α beta و يساوي x²β²α و هتيجي
+
+324
+00:26:05,170 --> 00:26:08,830
+.. اللي هي كلها قوانين احنا بنعرفها x²-α بيساوي 1
+
+325
+00:26:08,830 --> 00:26:12,270
+على x²α و نفس الشيء إذا كانت alpha أصغر من beta
+
+326
+00:26:12,270 --> 00:26:17,770
+هيكون x²α أصغر من x²β لما ان x تكون أكبر من 1 و
+
+327
+00:26:17,770 --> 00:26:22,130
+هذه كلها بتكون x resources معاكم اللي هي مباشرة
+
+328
+00:26:22,130 --> 00:26:31,830
+على هذه التعريفالنظرية اللي عندنا على السريع let
+
+329
+00:26:31,830 --> 00:26:35,010
+alpha element in R then the function x بالتروح للـ
+
+330
+00:26:35,010 --> 00:26:37,670
+x alpha من 0 و 1 to R is continuous and
+
+331
+00:26:37,670 --> 00:26:41,210
+differentiable and اللي هو ال derivative لل x to
+
+332
+00:26:41,210 --> 00:26:43,630
+the alpha بسوء alpha to the x to the alpha minus 1
+
+333
+00:26:43,630 --> 00:26:47,650
+for x element in 0 و 1 طبيعي أصلا هي composition
+
+334
+00:26:47,650 --> 00:26:54,490
+of two هي عندى function هذه اللي هي continuousهذا
+
+335
+00:26:54,490 --> 00:26:57,650
+كلها على بعض الـ E كمان continuous ده اللي هتطلع
+
+336
+00:26:57,650 --> 00:26:59,850
+هذا continuous و هذا continuous و نفس الاشي ال
+
+337
+00:26:59,850 --> 00:27:02,870
+differentiability إذا أكيد اللي هي ال function
+
+338
+00:27:02,870 --> 00:27:05,890
+اللي عندنا X to the X to the Alpha حسب تعريفنا is
+
+339
+00:27:05,890 --> 00:27:09,410
+continuous and differentiable و لو بدك تسمي اللي
+
+340
+00:27:09,410 --> 00:27:13,710
+هو هذه ال derivative و بدك تبدأ تفاضل دي اتفاضل DX
+
+341
+00:27:13,710 --> 00:27:17,050
+Alpha يعني بدك تتفاضل هذه كيف تتفاضل هذه ال
+
+342
+00:27:17,050 --> 00:27:20,860
+exponential اللي هي E to the Alpha لإن ال Xفى
+
+343
+00:27:20,860 --> 00:27:25,580
+التفاضل اللى هو اللى جوا اللى هو Alpha فى واحد على
+
+344
+00:27:25,580 --> 00:27:30,120
+X ماشي الحال اللى هى بمعنى آخر بصير عندى اللى هو
+
+345
+00:27:30,120 --> 00:27:35,260
+عبارة عن E to the Alpha لن ال X اللى هى عبارة عن
+
+346
+00:27:35,260 --> 00:27:38,480
+ال X to the Alpha نفسها فى التفاضل هذه اللى هى
+
+347
+00:27:38,480 --> 00:27:43,080
+Alpha على X بيساوى Alpha أس X اللى هى هذه بتطلع
+
+348
+00:27:43,080 --> 00:27:46,680
+ناقص واحد Alpha مانس واحد for X element in zero
+
+349
+00:27:46,680 --> 00:27:53,250
+وملا نهايةالان بعض الملاحظات الأخرى اللي بيقولك
+
+350
+00:27:53,250 --> 00:28:01,010
+إياها على هذه الدالة بيقولبقول لك اللي هو عندي إذا
+
+351
+00:28:01,010 --> 00:28:07,610
+كانت Alpha أكبر من 0 فبصير
+
+352
+00:28:07,610 --> 00:28:11,970
+عندي اللي هي ال function من X and X alpha is
+
+353
+00:28:11,970 --> 00:28:15,930
+strictly increasing على فترة 0 و ملا نهاية طبيعي
+
+354
+00:28:15,930 --> 00:28:19,890
+لما Alpha أكبر من 0 هيصير عندي الان المقدر هذا
+
+355
+00:28:19,890 --> 00:28:24,120
+بظله موجبو هذه ألف أكبر من سفر بيكون بيبدو أكبر من
+
+356
+00:28:24,120 --> 00:28:27,180
+سفر إذا صارت عندي اللي هي ال derivative أكبر من
+
+357
+00:28:27,180 --> 00:28:31,160
+سفر إذا صارت عند الدلة strictly increasing لو كانت
+
+358
+00:28:31,160 --> 00:28:34,520
+ألف أصغر من سفر هتصير اللي هي العكس strictly
+
+359
+00:28:34,520 --> 00:28:38,420
+decreasing لإنه هتكون هذه سالبة وهذه مدلة موجبة
+
+360
+00:28:38,420 --> 00:28:42,180
+بتظل هذه كلها موجبة إذا صارت strictly decreasing
+
+361
+00:28:42,180 --> 00:28:45,360
+عند ألف بتساوي سفر بيكون احنا ال derivative للواحد
+
+362
+00:28:45,360 --> 00:28:48,880
+اللي هو بيكون عبارة عن constant function اللي هو
+
+363
+00:28:48,880 --> 00:28:51,300
+في حالة الألف بتساوي سفر
+
+364
+00:28:53,910 --> 00:29:02,970
+الان نيجي الى اللي هي هيك بنكون اللي هو وصلنا
+
+365
+00:29:02,970 --> 00:29:09,190
+لآخر تعريف بده يعرف اللي هو ال log function للأساس
+
+366
+00:29:09,190 --> 00:29:13,090
+a احنا اللي عرفناه ال len اللي هو للأساس e بمعنى
+
+367
+00:29:13,090 --> 00:29:16,530
+آخر كيف بده اعرفه الآن احنا لسه ماعرفش الأساسات
+
+368
+00:29:16,530 --> 00:29:19,930
+هدا كصمنا ال len و ال exponential الان بدنا نعرف
+
+369
+00:29:19,930 --> 00:29:25,920
+اللي هو نسمي ال logاللغاريثم للأساس A نفترض أن A
+
+370
+00:29:25,920 --> 00:29:28,860
+أكبر من 0 و A لات سوى 1 it is sometimes useful to
+
+371
+00:29:28,860 --> 00:29:34,820
+define the function log للأساس A كمالي الان log A
+
+372
+00:29:34,820 --> 00:29:39,560
+of X كده اللي بيساوي لن ال X على لن ال A حيث ال A
+
+373
+00:29:39,560 --> 00:29:43,940
+عدد ثابت ماشي الحال هذه الآن صارت اللي هي ال log
+
+374
+00:29:43,940 --> 00:29:49,540
+العامة هي نفس ال exponential بس مضروبة في ثابتالأن
+
+375
+00:29:49,540 --> 00:29:52,920
+إذا الـ exponential الأصلية عليها هو معرف الان
+
+376
+00:29:52,920 --> 00:29:59,140
+بقولك إنه اللي هي هذه بنسميها log أو ال logarithm
+
+377
+00:29:59,140 --> 00:30:04,620
+للأساس A لو كان الأساس E هذا بصير لن ال E واحد
+
+378
+00:30:04,620 --> 00:30:09,320
+بنصير نرجع لن ال X اللي هي الدالة الأصلية إذا لو
+
+379
+00:30:09,320 --> 00:30:14,000
+كانت ال A هي ال E بنرجع للدالة الأصلية اللي هي زي
+
+380
+00:30:14,000 --> 00:30:17,060
+ما قلنا is called the logarithm of X to the base A
+
+381
+00:30:19,560 --> 00:30:23,400
+Yields دا الـ logarithm العادي الان اللي مشهور
+
+382
+00:30:23,400 --> 00:30:28,020
+عندنا للحسابات اللي هو للأساس عشرة اللي هو بنسمي
+
+383
+00:30:28,020 --> 00:30:32,220
+اللي هو log to the base عشرة أو اللي بنسمي common
+
+384
+00:30:32,220 --> 00:30:36,720
+logarithm اللي هو اللي بنستخدمه عادة في الحسابات و
+
+385
+00:30:36,720 --> 00:30:41,620
+هيك بكون عندنا احنا انهينا اللي هو ال section اللي
+
+386
+00:30:41,620 --> 00:30:46,180
+هو تمانية تلاتة و بكون خلصنا اللي هيالجزء الثاني
+
+387
+00:30:46,180 --> 00:30:52,240
+من المحاضرة اللي هو ما يتعلق بال .. اللي هو ال
+
+388
+00:30:52,240 --> 00:30:54,660
+logarithmic function وال power function وال
+
+389
+00:30:54,660 --> 00:31:00,040
+logarithmic للأساس اللي هو زي ما قلنا ايه و إلى
+
+390
+00:31:00,040 --> 00:31:00,640
+لقاء
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0229173181dabf0de30b6b1766e9261331cc2d24
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/7kAGhF5ugUM.srt
@@ -0,0 +1,2591 @@
+1
+00:00:10,580 --> 00:00:15,760
+إيش يا أبو حسين؟ بسم الله الرحمن الرحيم الحمد لله
+
+2
+00:00:15,760 --> 00:00:18,980
+رب العالمين والصلاة والسلام على سيد المرسلين سيدنا
+
+3
+00:00:18,980 --> 00:00:24,540
+محمد وعلى آله وصحبه أجمعين هذه هي المحاضرة رقم 17
+
+4
+00:00:24,540 --> 00:00:29,900
+في مساق تحليل حقيقي 2 لطلاب وطالبات الجامعة
+
+5
+00:00:29,900 --> 00:00:37,170
+الإسلامية كلية العلوم قسم الرياضيات بدأنا اليوم
+
+6
+00:00:37,170 --> 00:00:41,490
+استكمالًا للي بدأنا المرة الماضية حكينا المرة
+
+7
+00:00:41,490 --> 00:00:48,070
+الماضية عن الـ integration as a limit قلنا إحنا 
+
+8
+00:00:48,070 --> 00:00:51,970
+قبل كنا عارفين ال integration أنه موجود على أساس
+
+9
+00:00:51,970 --> 00:00:56,950
+أن ال upper integral U of F يساوي ال lower
+
+10
+00:00:56,950 --> 00:01:01,710
+integral L of F قلنا المرة الماضية أن إحنا بدنا
+
+11
+00:01:01,710 --> 00:01:07,300
+نروح باتجاه إنه نصل في النهاية إنه هذا الكلام اللي
+
+12
+00:01:07,300 --> 00:01:11,440
+هو الـ Integrability يكافئ إن نصل إنه ال limit
+
+13
+00:01:11,440 --> 00:01:14,760
+طبعًا وفي حالة وجوده هنسميه بساوي ال integration من
+
+14
+00:01:14,760 --> 00:01:19,940
+a لـ b of x dx قلنا المرة الماضية إنه هنصل في
+
+15
+00:01:19,940 --> 00:01:25,600
+النهاية في نهاية ال section 7-4 إنه هذا اللي هو ال
+
+16
+00:01:25,600 --> 00:01:28,840
+condition أو هذا ال definition يكافئ إنه نقول
+
+17
+00:01:28,840 --> 00:01:35,640
+limit اللي هو SB و F as norm B أو الـ mesh تبع الـ B
+
+18
+00:01:35,640 --> 00:01:41,100
+بيروح لـ 0 وفي هذه الحالة إذا كان هذا exist بيصير
+
+19
+00:01:41,100 --> 00:01:45,380
+... هيساوي ال integration من A لـ B F of X DX يعني
+
+20
+00:01:45,380 --> 00:01:49,500
+بمعنى آخر... بمعنى آخر أنه اللي هو هذا طبعًا الـ
+
+21
+00:01:49,500 --> 00:01:55,460
+Riemann Sum أن الـ limit لل Riemann sum as الـ
+
+22
+00:01:55,460 --> 00:02:00,020
+partition B بيروح للـ 0 لو كان exist هيصير اللي هي
+
+23
+00:02:00,020 --> 00:02:04,220
+F is integrable والـ integration لها هو عبارة عن
+
+24
+00:02:04,220 --> 00:02:09,520
+قيمة هذا الـ limit ولو كان ال integration exist
+
+25
+00:02:09,520 --> 00:02:14,040
+طبعًا بالمفهوم اللي هو هذا هيكون عنده ال limit هذا
+
+26
+00:02:14,040 --> 00:02:18,300
+exist وهيساوي قيمة مين؟ ال integration هذا اللي
+
+27
+00:02:18,300 --> 00:02:22,260
+حنصل إليه في النهاية اللي حكيناه المرة الماضية
+
+28
+00:02:22,260 --> 00:02:27,380
+بشكل سريع اللي هو عرفنا إيش هو معنى اللي هو ال
+
+29
+00:02:27,380 --> 00:02:32,080
+Riemann Sum اللي أمامنا هذا بعد هيك اللي هو إيجينا
+
+30
+00:02:32,080 --> 00:02:36,600
+أخذنا اللي هي الخاصية الأولى قلنا دائمًا ال Riemann
+
+31
+00:02:36,600 --> 00:02:41,140
+Sum بين اللي هو ال lower sum وبين ال upper sum و
+
+32
+00:02:41,140 --> 00:02:46,080
+بعدين اللي هو إيجينا قلنا اللي هو النظرية ال... ال
+
+33
+00:02:46,080 --> 00:02:47,220
+... ال... ال... ال... ال... ال... ال... ال... ال...
+
+34
+00:02:47,220 --> 00:02:47,280
+ال... ال... ال... ال... ال... ال... ال... ال... ال
+
+35
+00:02:47,280 --> 00:02:48,000
+ال... ال... ال... ال... ال... ال... ال... ال... ال
+
+36
+00:02:48,000 --> 00:02:48,120
+... ال... ال... ال... ال... ال... ال... ال... ال...
+
+37
+00:02:48,120 --> 00:02:49,580
+ال... ال... ال... ال... ال... ال... ال... ال... ال
+
+38
+00:02:49,580 --> 00:02:49,700
+... ال... ال... ال... ال... ال... ال... ال... ال...
+
+39
+00:02:49,700 --> 00:02:50,220
+ال... ال... ال... ال... ال... ال... ال... ال... ال
+
+40
+00:02:50,220 --> 00:02:59,260
+... ال... ال... ال... ال... ال... ال... ال... إذا
+
+41
+00:02:59,260 --> 00:03:03,200
+كانت F Integrable إذا لكل Y أكبر من 0 نجد نلاقي
+
+42
+00:03:03,200 --> 00:03:07,220
+partition بي إبسلون و by such that إذا كانت بي أي
+
+43
+00:03:07,220 --> 00:03:10,600
+اللي هو refinement partition refinement للبي
+
+44
+00:03:10,600 --> 00:03:14,260
+إبسلون يعني يحتوي البي إبسلون هيكون وكان عند ال
+
+45
+00:03:14,260 --> 00:03:18,540
+S P U F عبارة عن اللي هو ال Riemann Sum بكون الـ absolute
+
+46
+00:03:18,540 --> 00:03:21,300
+value ال integration بين S بي و F مقصد ال
+
+47
+00:03:21,300 --> 00:03:24,840
+integration إيش ماله؟ أصغر من مين؟ من إبسلون يعني لو
+
+48
+00:03:24,840 --> 00:03:28,460
+F is integrable هنلاقي بي إبسلون بحيث كل الـ B
+
+49
+00:03:28,460 --> 00:03:31,540
+بتحتوي بي إبسلون هيكون ال absolute value بين
+
+50
+00:03:31,540 --> 00:03:36,400
+ال Riemann Sum هذا أصغر من مين؟ من اللي هي إيش؟ إبسلون
+
+51
+00:03:36,820 --> 00:03:41,900
+طيب بعد هيك كتبنا عن البرهان هذا وصار في عندي الآن
+
+52
+00:03:41,900 --> 00:03:46,240
+اللي هو النظرية الثانية أيضًا برهناها والنظرية
+
+53
+00:03:46,240 --> 00:03:52,110
+الثانية كانت تقول أن لو كانت F is bounded الآن...
+
+54
+00:03:52,110 --> 00:03:57,250
+وقدرنا... وبدنا الآن نفترض أن لجينا اللي هو
+
+55
+00:03:57,250 --> 00:04:01,830
+number a يحقق ماله إيش؟ هذا number a يحقق أن لكل
+
+56
+00:04:01,830 --> 00:04:04,890
+epsilon أكبر من 0 ونلاقي بي إبسلون بحيث أن أي بي
+
+57
+00:04:04,890 --> 00:04:11,040
+يحتوي بي إبسلون و S اللي هي أي Riemann Sum و then اللي
+
+58
+00:04:11,040 --> 00:04:16,060
+هي S, B و F ناقص a أصغر من إبسلون إذا كان هذا الكلام
+
+59
+00:04:16,060 --> 00:04:19,480
+كله على بعضه اتحقق لما نلاقي a بحيث يقول لكل إبسلون
+
+60
+00:04:19,480 --> 00:04:24,180
+أكبر من صفر اللي هو نلاقي بي إبسلون لو كان بي
+
+61
+00:04:24,180 --> 00:04:27,740
+إبسلون بحيث أن بي بتحتوي بي إبسلون وهذا ال Riemann
+
+62
+00:04:27,740 --> 00:04:32,030
+Sum هيعطيني هذا هذا كله على بعضه ال conditions زي ما
+
+63
+00:04:32,030 --> 00:04:35,410
+قلنا المرة الماضية بيعطينا أن F إيش مالها؟
+
+64
+00:04:35,410 --> 00:04:39,270
+Integrable وهذا الـ A اللي حقق هذه الشروط هنا هو
+
+65
+00:04:39,270 --> 00:04:44,050
+قيمة ال integration هذا اللي حكيناه المرة الماضية
+
+66
+00:04:44,050 --> 00:04:51,120
+وبعدين اللي هو إحنا إيجينا وعرفنا شو معنى ال mesh أو
+
+67
+00:04:51,120 --> 00:04:54,800
+ال norm إذا بذكركم ال mesh أو ال norm هو عبارة عن ال
+
+68
+00:04:54,800 --> 00:05:00,140
+supremum لاللي هي أطوال ال subintervals تبعات ال
+
+69
+00:05:00,140 --> 00:05:03,060
+partition قلنا ال norm للبيبس أو ال supremum لهذه
+
+70
+00:05:03,060 --> 00:05:07,280
+اللي هي الأطوال تبعات ال subintervals اللي ناتجة
+
+71
+00:05:07,280 --> 00:05:11,550
+من ال partition B هذا اسمنا ال mesh أو ال norm أخذنا
+
+72
+00:05:11,550 --> 00:05:17,230
+بعض اللي هي الخواص وصغفنا عند مين؟ عند Darboux's
+
+73
+00:05:17,230 --> 00:05:20,690
+theorem اليوم بدنا نبدأ نشرح في مين؟ في Darboux's
+
+74
+00:05:20,690 --> 00:05:24,230
+theorem نشوف إيش Darboux's theorem بتقول الآن بقول
+
+75
+00:05:24,230 --> 00:05:28,990
+لي let i بتساوي a و b اللي هي bounded interval و F
+
+76
+00:05:28,990 --> 00:05:32,910
+من I لعنب R Integrable on I in the sense of
+
+77
+00:05:32,910 --> 00:05:38,050
+definition 716 يعني بقول لي نفترض أن F is an
+
+78
+00:05:38,050 --> 00:05:42,830
+integrable function حسب تعريف 716 يعني ال
+
+79
+00:05:42,830 --> 00:05:46,470
+upper integral بيساوي ال lower integral بيساوي ال
+
+80
+00:05:46,470 --> 00:05:50,350
+integration هذا اللي هو ال definition 716 الآن
+
+81
+00:05:50,350 --> 00:05:56,710
+بقول لي then for every epsilon أكبر من 0 then for
+
+82
+00:05:56,710 --> 00:06:02,450
+every epsilon أكبر من صفر there exists delta such
+
+83
+00:06:02,450 --> 00:06:07,150
+that الآن لو كان P is any partition of I وال
+
+84
+00:06:07,150 --> 00:06:11,710
+norm P أصغر من Delta وكان عند ال S P و F اللي
+
+85
+00:06:11,710 --> 00:06:15,810
+هو is any corresponding Riemann sum then ال
+
+86
+00:06:15,810 --> 00:06:19,450
+integration بين ال S P... البعد بين ال integration
+
+87
+00:06:19,450 --> 00:06:23,670
+بين ال S P وال integration أصغر من مين؟ أصغر من
+
+88
+00:06:23,670 --> 00:06:28,990
+Epsilon بس
+
+89
+00:06:28,990 --> 00:06:29,910
+بقى في دقيقة يا أبو حسن
+
+90
+00:06:59,460 --> 00:07:03,900
+أيوة أنا في محاضرة... أنا في محاضرة وبسجل... أيوة
+
+91
+00:07:03,900 --> 00:07:08,400
+أه في
+
+92
+00:07:08,400 --> 00:07:16,360
+كلية العلوم؟ من قال لك في كلية العلوم؟
+
+93
+00:07:16,360 --> 00:07:18,500
+لأ يا عم أنا روحت على دراسات العلوم اللي قالولي
+
+94
+00:07:18,500 --> 00:07:27,580
+طلعن أه... بعرفش... بعرفش كلام هو صحيح ولا لأ لأ
+
+95
+00:07:27,580 --> 00:07:33,080
+لأ بقى طيب يا راجل أنا في المحاضرة ماشي مع السلام
+
+96
+00:07:33,080 --> 00:07:40,800
+... ماشي بقى كله مروح مع السلام ليش؟
+
+97
+00:07:40,800 --> 00:07:44,040
+مع السلام... بس شوف كيف مع السلام
+
+98
+00:08:32,780 --> 00:08:36,900
+اعطيني بس تليفون هذا في العلوم 1600 أنا عارف الله
+
+99
+00:08:36,900 --> 00:08:41,780
+ده
+
+100
+00:08:41,780 --> 00:08:45,660
+الدس
+
+101
+00:08:45,660 --> 00:08:50,040
+اه هو كده روح إذا أبو بلال الموجود روح
+
+102
+00:09:15,660 --> 00:09:18,500
+وعليكم السلام عليك يا أبو سامي كيف حالك؟ كيف صحتك؟
+
+103
+00:09:18,500 --> 00:09:21,980
+الله يبارك فيك الحمد لله الله عزيزي عنك هل في إلي
+
+104
+00:09:21,980 --> 00:09:28,260
+عندكم رسالة تابعة السنّاق؟ وتابعة ياسر؟ طب... طب
+
+105
+00:09:28,260 --> 00:09:33,820
+... مين عندك؟ قاعد بتسأل عليه لو... لو أبو أكرم
+
+106
+00:09:33,820 --> 00:09:36,880
+أخذن بس وحطن في غرفتي لأنه أنا قاعد بصور والله
+
+107
+00:09:36,880 --> 00:09:42,060
+يبقى اه... اه... اه... الله يبارك فيك يا عزيزي أنا
+
+108
+00:09:42,060 --> 00:09:50,370
+بجيبها المفتاح هو اه اه ماشي
+
+109
+00:09:50,370 --> 00:09:54,770
+لو حتى أنا يعني أنا موجود بس بنتأخر يعني التصوير
+
+110
+00:09:54,770 --> 00:09:59,950
+ممكن أظل الثلاثة ماشي ماشي الله بقى أرفع حاجة
+
+111
+00:09:59,950 --> 00:10:03,290
+لأنه بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+112
+00:10:03,290 --> 00:10:03,490
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+113
+00:10:03,490 --> 00:10:06,830
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+114
+00:10:06,830 --> 00:10:08,250
+ب
+
+115
+00:10:27,230 --> 00:10:30,330
+إذن Darboux's theorem زي ما قلنا إن لو كانت F
+
+116
+00:10:30,330 --> 00:10:34,600
+integrable function بقول إذا لكل إبسلون أكبر من 0
+
+117
+00:10:34,600 --> 00:10:38,780
+بقدر ألاقي Delta أكبر من 0 بحيث أن لو كان بي أي
+
+118
+00:10:38,780 --> 00:10:41,620
+partition بحيث أن ال... اللي هو ال... ال... ال
+
+119
+00:10:41,620 --> 00:10:44,980
+norm للـ B أصغر من Delta و S, B و F أي
+
+120
+00:10:44,980 --> 00:10:49,420
+corresponding Riemann Sum بالنسبة للـ B هيعطيني أن
+
+121
+00:10:49,420 --> 00:10:52,860
+ال absolute value بين اللي هو أو البعد بين S, B و
+
+122
+00:10:52,860 --> 00:10:57,780
+F ناقص ال integration أصغر من إبسلون يعني وكأنه
+
+123
+00:10:57,780 --> 00:11:02,190
+بقول من تحت بطنانه ال integration ال integration
+
+124
+00:11:02,190 --> 00:11:08,710
+لل F لو F is integrable بيعطينا أن بمفهوم اللي هو
+
+125
+00:11:08,710 --> 00:11:18,140
+716 بكون عنده limit ال SB و F as norm B
+
+126
+00:11:18,140 --> 00:11:24,320
+بيروح للصفر بيساوي بالظبط integration من A لـ B F of X
+
+127
+00:11:24,320 --> 00:11:29,260
+DX لأن إيش معناه هذا؟ معناه هذا اللي هو حسب الـ
+
+128
+00:11:29,260 --> 00:11:32,160
+epsilon delta Definition for every epsilon أكبر من
+
+129
+00:11:32,160 --> 00:11:36,740
+صفر there exists delta أكبر من صفر such that if
+
+130
+00:11:36,740 --> 00:11:43,170
+norm B أصغر، ناقص الصفر أصغر من دلتا then هيعطيني
+
+131
+00:11:43,170 --> 00:11:46,810
+الـ absolute value للـ S, P و F ناقص ال
+
+132
+00:11:46,810 --> 00:11:52,650
+integration من A لـ B F of X DX كله أصغر من مين؟ من
+
+133
+00:11:52,650 --> 00:11:56,790
+إبسلون إذا اللي بدنا نثبته بدنا لكل إبسلون نلاقي
+
+134
+00:11:56,790 --> 00:12:01,870
+Delta بحيث أن لما أي partition نورمه أصغر من Delta
+
+135
+00:12:01,870 --> 00:12:05,510
+يعطيني الفرق بين الـ Riemann Sum وبين الـ
+
+136
+00:12:05,510 --> 00:12:08,910
+Integration يكون أصغر من مين؟ من Epsilon هذه اللي
+
+137
+00:12:08,910 --> 00:12:11,990
+هي اللي بتقول لنا Darboux's Theorem أن لو F is
+
+138
+00:12:11,990 --> 00:12:15,610
+integrable إذا اللي هو الـ limit لاللي هو الـ
+
+139
+00:12:15,610 --> 00:12:18,730
+Riemann Sum هو حيساوي هذا ال integration اللي
+
+140
+00:12:18,730 --> 00:12:23,330
+فرضنا إحنا إيش ماله؟ أنه موجود خلينا نشوف كيف بدنا 
+
+141
+00:12:23,330 --> 00:12:29,380
+انبرهن النظرية و ركزوا معي واتبعوا إيش اللي بدنا 
+
+142
+00:12:29,380 --> 00:12:35,200
+نحكيه عشان نصل للي هو المطلوب طيب صلى الله عليه 
+
+143
+00:12:35,200 --> 00:12:41,370
+الصلاة والسلام أول شيء بما أن F is integrable الـ
+
+144
+00:12:41,370 --> 00:12:42,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+145
+00:12:42,290 --> 00:12:42,330
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+146
+00:12:42,330 --> 00:12:43,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+147
+00:12:43,190 --> 00:12:43,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+148
+00:12:43,510 --> 00:12:44,470
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+149
+00:12:44,470 --> 00:12:50,750
+ال .. ال .. ال .. ال .. ال ..
+
+150
+00:12:50,750 --> 00:12:52,070
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+151
+00:12:52,070 --> 00:12:53,590
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+152
+00:12:53,590 --> 00:12:53,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+153
+00:12:53,750 --> 00:12:54,490
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+154
+00:12:54,490 --> 00:12:54,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+155
+00:12:54,910 --> 00:13:02,270
+.. ال .. ال .. ال .. الإذن الآن أخفرضت epsilon 
+
+156
+00:13:02,270 --> 00:13:06,870
+arbitrary بدي أدور على الـ delta اللي لما ال 
+
+157
+00:13:06,870 --> 00:13:10,630
+norm بيه أصغر من delta يعطيني الفرق بين هذه و
+
+158
+00:13:10,630 --> 00:13:14,710
+هذه أصغر من مين من epsilon لذا هيك رايح أنا لأن 
+
+159
+00:13:14,710 --> 00:13:19,400
+إذن بما أن أفنتي جربت لكل epsilon أكبر من 0 بقدر 
+
+160
+00:13:19,400 --> 00:13:23,980
+ألاقي partition الآن سميته بي إبسلون اللي هو x0 و 
+
+161
+00:13:23,980 --> 00:13:29,400
+x1 لعندي xn such that ال U ال upper sum لل بي 
+
+162
+00:13:29,400 --> 00:13:32,340
+إبسلون و F ناقص ال lower sum لل بي إبسلون و F أصغر 
+
+163
+00:13:32,340 --> 00:13:35,780
+من مين من إبسلون سميتهاش أنا إبسلون على تلاتة
+
+164
+00:13:35,780 --> 00:13:38,700
+للحسابات طبعا أصغر من إبسلون في الدنيا من ضمنها 
+
+165
+00:13:38,700 --> 00:13:45,040
+الإبسلون على تلاتة هذا حسب الريمان criterion أو ال 
+
+166
+00:13:45,040 --> 00:13:51,190
+integrable criterion طيب moreover لأن لو كانت عندي
+
+167
+00:13:51,190 --> 00:13:55,650
+ال B أي B partition بحتوى ال بي إبسلون أكيد هيكون 
+
+168
+00:13:55,650 --> 00:13:59,550
+اللي هو ال .. ال .. ال .. هذا بيصير refinement
+
+169
+00:13:59,550 --> 00:14:04,410
+مدام refinement ال refinement التحسين ال lower
+
+170
+00:14:04,410 --> 00:14:09,670
+بعله و ال upper بقاشه بينزل يعني بمعنى آخر هيكون 
+
+171
+00:14:09,670 --> 00:14:13,030
+ال lower لل refine .. لل refinement أو التحسين
+
+172
+00:14:13,030 --> 00:14:17,240
+أكبر أوي سوى مين ال lower للأصل ال بي إبسلون وأكيد 
+
+173
+00:14:17,240 --> 00:14:20,840
+الـ lower لل B و ال F أكيد أصغر أو سوء القبر لل B 
+
+174
+00:14:20,840 --> 00:14:24,780
+و ال F in general و القبر لل B و F قلنا مدامه 
+
+175
+00:14:24,780 --> 00:14:29,600
+تحسين إذا أكيد بنزل بصغر عن مين عن اللي صار له 
+
+176
+00:14:29,600 --> 00:14:34,960
+تحسين اللي هو مين U, B, Y و F إذا صار عندي الآن ..
+
+177
+00:14:34,960 --> 00:14:45,230
+هي عندي ال L .. ال L, B, Y و F وهذا L, B و F وهذا
+
+178
+00:14:45,230 --> 00:14:51,650
+الـ U, B و F وهذا الـ U, B, E, F واضح إن المسافة
+
+179
+00:14:51,650 --> 00:14:58,430
+بين الـ U, B, E, F و الـ L, B, E, F أكيد أكبر أو 
+
+180
+00:14:58,430 --> 00:15:02,550
+تساوي المسافة بين الـ U و الـ L للـ B و الـ F يعني
+
+181
+00:15:02,550 --> 00:15:05,710
+هذه المسافة واضح إنها أكبر أو تساوي هذه المسافة 
+
+182
+00:15:05,710 --> 00:15:12,000
+يعني بمعنى آخر هيكون الـ U, B, F نقص lbf أصغر أو
+
+183
+00:15:12,000 --> 00:15:15,240
+يساوي لـ U بي إبسلون نقص ل L بي إبسلون و F هذا
+
+184
+00:15:15,240 --> 00:15:21,260
+لمين؟ عدي ال .. ال .. ال بي إبسلون من فوق حصلنا 
+
+185
+00:15:21,260 --> 00:15:24,940
+عنها أصغر من إبسلون ع تلاتة إذا صار عند ال U بي إف 
+
+186
+00:15:24,940 --> 00:15:29,500
+و ال L بي إف المسافة بينهم برضه أصغر من مين؟ من 
+
+187
+00:15:29,500 --> 00:15:35,360
+إبسلون ع تلاتة إذا الآن صار عند أيب لجأت الـ
+
+188
+00:15:35,360 --> 00:15:39,840
+بإبسلون و أي بي بيحتوى الـ بإبسلون لجئنا المسافة 
+
+189
+00:15:39,840 --> 00:15:47,880
+بين الـ U بي و F ناقص الـ L بي و F أصغر من مين من 
+
+190
+00:15:47,880 --> 00:15:53,710
+إبسلون على 3 ماشي الحال هذا اللي حصلناه في الأول
+
+191
+00:15:53,710 --> 00:15:57,170
+الآن احنا زي ما قلنا ادورتنا ع مين يا جماعة
+
+192
+00:15:57,170 --> 00:16:01,210
+ادورتنا على الـ Delta اللي لما ال Norm بيه أصغر
+
+193
+00:16:01,210 --> 00:16:04,330
+من Delta يعطينا المسافة بين الريمان صموا ال
+
+194
+00:16:04,330 --> 00:16:08,670
+integration أصغر من إيش من أبسلون الآن أنا بتدعي
+
+195
+00:16:08,670 --> 00:16:15,060
+أو الكاتب بتدعي أنههناخد Delta بقيمة معينة و هتشوف
+
+196
+00:16:15,060 --> 00:16:17,960
+إنها فعلاً هذه الـ Delta بتحقق طبعاً الـ Delta هذه
+
+197
+00:16:17,960 --> 00:16:22,160
+نتيجة إحسابات اللي هو بيبقى مشة على برهان كامل و
+
+198
+00:16:22,160 --> 00:16:26,400
+في الآخر لجأ الإحساب اللي بيخلي اللي هو قيمة هنا 
+
+199
+00:16:26,400 --> 00:16:30,540
+Epsilon الدلتة اللي بياخدها الآن طيب، قبل ما نقول 
+
+200
+00:16:30,540 --> 00:16:34,560
+إيش الـ Delta بدنا نعطي الرمز الـ F is bounded,
+
+201
+00:16:34,740 --> 00:16:37,220
+integrable لإنها مدام bounded أو integrable
+
+202
+00:16:37,220 --> 00:16:41,460
+السبريمم إلها على كل الفترة موجود خذ الـ Supremum
+
+203
+00:16:41,460 --> 00:16:45,200
+لقيمة الدالة F of X للـ X element in the interval
+
+204
+00:16:45,200 --> 00:16:49,940
+I سميها إيش بتساوي؟ سميها بتساوي M Capital، ماشي
+
+205
+00:16:49,940 --> 00:16:54,360
+الحال، الآن بادعي الآن إن دلتا اللي هتظبط معنى و
+
+206
+00:16:54,360 --> 00:16:57,320
+تجيبلنا اللي هو القيمة اللي بدنا إياها اللي هي
+
+207
+00:16:57,320 --> 00:17:00,180
+أصغر من إبسلون، اللي هي دلتا بتساوي إبسلون على
+
+208
+00:17:00,180 --> 00:17:05,140
+اثنا عشر N في مين في M N مين هذه، N اللي ظهرت في ال
+
+209
+00:17:05,140 --> 00:17:09,750
+partition هنا اللي هو عدد عناصر ال partition اللي
+
+210
+00:17:09,750 --> 00:17:14,490
+جزأني الفترة هي N زائد 1 هذا مين ال partition اللي
+
+211
+00:17:14,490 --> 00:17:19,790
+لجيته في الريمان من خلال ال integrability للأف إذاً
+
+212
+00:17:19,790 --> 00:17:24,370
+where الـ N زائد واحد is the number of parts in B
+
+213
+00:17:24,370 --> 00:17:29,190
+إبسلون يعني الـ Delta بتساوي إبسلون على 12 في N
+
+214
+00:17:29,190 --> 00:17:33,370
+الـ N ارتبطت بال partition اللي لجيته والـ M هي 
+
+215
+00:17:33,370 --> 00:17:39,250
+عبارة عن ال supremum لكل الدالة على كل الفترة 
+
+216
+00:17:39,250 --> 00:17:41,410
+المذكورة نيجي الآن 
+
+217
+00:17:46,350 --> 00:17:53,750
+Now let Q بيساوي Y not Y واحد و Y اتنين لعند Y M
+
+218
+00:17:53,750 --> 00:17:59,890
+مش N، Y M ماشي بـ any partition of I with ال
+
+219
+00:17:59,890 --> 00:18:03,550
+absolute value للـQ أو ال norm للـQ أصغر من Delta
+
+220
+00:18:04,420 --> 00:18:08,500
+أيش يا جماعة قاعد أنا أحاول أصل للي بديها؟ أيش 
+
+221
+00:18:08,500 --> 00:18:12,080
+غرضي؟ إن لكل epsilon أكبر من 0 بدي ألاقي delta
+
+222
+00:18:12,080 --> 00:18:16,600
+بحيث أنه أي partition أصغر من delta norm يعطيني
+
+223
+00:18:16,600 --> 00:18:21,320
+الفرق بين رمان صمه وال integration أصغر من epsilon
+
+224
+00:18:21,320 --> 00:18:27,660
+وكأنه الآن بدأت أحط أيدي على الجرح وأصل أقول let Q
+
+225
+00:18:27,660 --> 00:18:34,780
+بيساوي Y0 Y1 YM بأي partition Norm أصغر من مين؟ 
+
+226
+00:18:34,780 --> 00:18:40,260
+من Delta متوقع أنا أنه في النهاية عشان أخلص 
+
+227
+00:18:40,260 --> 00:18:47,200
+النظرية أثبتلك أنه ال absolute value لأ اللي هو ال 
+
+228
+00:18:47,200 --> 00:18:55,230
+S ال UF ناقص ال integration من قلبي f of x dx يطلع 
+
+229
+00:18:55,230 --> 00:19:00,290
+لي أصغر من مين من إبسلون إذا أثبتت هذا بناء على 
+
+230
+00:19:00,290 --> 00:19:05,830
+اختياري للـ Delta اللي عندي وبناء على كل ال cues
+
+231
+00:19:05,830 --> 00:19:10,490
+اللي نورهم أصغر من Delta يعطيني هذا ناقص هذا أصغر 
+
+232
+00:19:10,490 --> 00:19:14,210
+من إبسلون وبقول خلصت وبرهنت اللي هي نظريتي
+
+233
+00:19:14,210 --> 00:19:19,350
+Darboux theorem خلّينا نشوف كيف بدنا نروح لهذه
+
+234
+00:19:19,350 --> 00:19:24,810
+اللي هي نثبتها إنها أصغر من إبسلون تعالي شوية الآن
+
+235
+00:19:24,810 --> 00:19:31,630
+لأن let Q*) بسوى Q اتحادين بإبسلون هذه بي إبسلون
+
+236
+00:19:31,630 --> 00:19:37,210
+مين اللي لجيتها فوق اللي هي عبارة عن بي إبسلون
+
+237
+00:19:38,430 --> 00:19:43,870
+بإبسلون هي الفترة من a لعند b بإبسلون اللي هي أش 
+
+238
+00:19:43,870 --> 00:19:50,850
+جزأة للفترة هذه هذي x note هذي x1 هذي x2 هذي x3
+
+239
+00:19:50,850 --> 00:19:56,430
+لما أصل xn ناقص واحد لما أصل هنا عند مين xn اللي 
+
+240
+00:19:56,430 --> 00:20:01,390
+هي مين ال b هذي مين جزأها جزء الفترة هذه واحدة 
+
+241
+00:20:01,390 --> 00:20:08,190
+اسمها بإبسلون نيجي الآن اتجزأت الفترة بمين بالـ Q
+
+242
+00:20:08,190 --> 00:20:17,270
+الـ Q مين هي بدأت ب Y note طبعا هي ايه Y1 و Y2 و 
+
+243
+00:20:17,270 --> 00:20:24,950
+Y3 لعند مؤصل لعند Y M ناقص واحد وهنا اللي هي YM
+
+244
+00:20:24,950 --> 00:20:29,730
+اللي هي طبعاً مين هي اللي هي الـB هذه الـQ جزقتها 
+
+245
+00:20:29,730 --> 00:20:33,430
+بشكلها اللي أمامي مع العلم إن الـQ هي تبعتنا
+
+246
+00:20:33,430 --> 00:20:38,950
+لنورمها أصغر من مين من Delta الآن بيقوللي خد Q*)
+
+247
+00:20:38,950 --> 00:20:46,150
+إيش بتساوي؟ الـQ اتحاد من الـBإبسلون صارت الآن 
+
+248
+00:20:46,150 --> 00:20:54,880
+الـQ هذه بساوة بي بي ستار اتحاد لـ Q هذه مين هي الـ 
+
+249
+00:20:54,880 --> 00:21:01,100
+Q star طبعا النقطة الأولى X not هي نفسها Y not
+
+250
+00:21:01,100 --> 00:21:06,840
+والـ Xn هي مين الـ Yn اللي يعني ممكن يكون
+
+251
+00:21:06,840 --> 00:21:11,380
+المختلفات اللي هي من X واحد لعند Xn نقص واحد يكون 
+
+252
+00:21:11,380 --> 00:21:16,890
+المختلفات عن هدول الاتحاد أقصى حدودهم يعني إذا بدهم
+
+253
+00:21:16,890 --> 00:21:21,430
+يعملنّي sub intervals زيادات هيكون أقصى حدودهم 
+
+254
+00:21:21,430 --> 00:21:27,290
+اللي لنا اللي هي X1 و X2 و X3 و X-1 ماتنطبقش ولا 
+
+255
+00:21:27,290 --> 00:21:33,810
+على أي Y1 ولا Y2 ولا Y3 ولا Y أم minus 1 متى ما 
+
+256
+00:21:33,810 --> 00:21:38,410
+انطبقلنش معناته أنه هيكونين وين موجودات في داخل ال 
+
+257
+00:21:38,410 --> 00:21:42,630
+intervals معناته كل واحدة عملتلها إلا عن فترة تاني
+
+258
+00:21:42,630 --> 00:21:46,550
+جداد اللي هو في الفترة تانية الإجداد يعني لو إجت
+
+259
+00:21:46,550 --> 00:21:51,390
+هنا الـ X1 هنا مثلا بيكون هذه عملة فترة تانية لو
+
+260
+00:21:51,390 --> 00:21:58,930
+إجينا سمينا هذه المنطقة اللي هو M1 star اللي هو M1
+
+261
+00:21:58,930 --> 00:22:02,470
+مين اللي هو ال maximum أو ال supreme على مين على 
+
+262
+00:22:02,470 --> 00:22:09,510
+ال partition الجديد Q star وهذه سمناها هتكون M2*)
+
+263
+00:22:09,510 --> 00:22:15,670
+هيصير الـ M1*) بتختلف لأن هذه عبارة عن الـ 
+
+264
+00:22:15,670 --> 00:22:20,490
+Supremum على المنطقة هذه بينما بالنسبة للـ Q لو
+
+265
+00:22:20,490 --> 00:22:27,030
+أجينا لـ Maximum تبعها أو Supremum تبعها هنسميه M1
+
+266
+00:22:27,030 --> 00:22:32,970
+هذا الـ M1 قد يختلف عن الـ M1 Star وعن مين الـ M2
+
+267
+00:22:32,970 --> 00:22:37,610
+Star لأن الـ M1 على هذه كلها بينما الـ M1 Star على
+
+268
+00:22:37,610 --> 00:22:41,070
+هذه والـ M2 Star على هذه اللي هو الـ Supremum
+
+269
+00:22:41,070 --> 00:22:44,670
+للدالة على الجزء من هذا أو الجزء من هذا قد يختلف 
+
+270
+00:22:44,670 --> 00:22:49,860
+عن الـ Supremum عن الجزء هذا يعني الآن الـ الـ الـ
+
+271
+00:22:49,860 --> 00:22:55,060
+الـ الـ subintervals جديدة هتولدلي M1 maximum
+
+272
+00:22:55,060 --> 00:23:00,700
+لعناصر للـ function على اللي هي الكلي بختلف عن مين
+
+273
+00:23:00,700 --> 00:23:07,240
+عن الجزء قد يختلف الـ N لكن اللي .. اللي .. لو كانت
+
+274
+00:23:07,240 --> 00:23:12,420
+اللي هي عدد هنا دولة اللي هي الـ N أكبر من الـ N
+
+275
+00:23:12,420 --> 00:23:19,420
+هتتوزع .. هتتوزع اللي هو الـ X1 والـ X2 لإذا 
+
+276
+00:23:19,420 --> 00:23:23,280
+اختلفن كمان واتوزعن مختلفات هيتوزعن وين؟ في 
+
+277
+00:23:23,280 --> 00:23:28,870
+المناطق اللي هيجبل ما نخلص الـ YM يعني هتلاقيها كل 
+
+278
+00:23:28,870 --> 00:23:33,970
+واحدة مكان لأن الـ M أكبر من الـ N اللي بتضال بدون 
+
+279
+00:23:33,970 --> 00:23:39,870
+ما تدخلها واحدة من الـ X1 أو X2 أو X3 هتسير في ال
+
+280
+00:23:39,870 --> 00:23:43,810
+partition الجديد Q هي نفسها في الاصل في ال 
+
+281
+00:23:43,810 --> 00:23:50,140
+partition main الـ Q يعني هيكون الـ M هنا الـ star و ال
+
+282
+00:23:50,140 --> 00:23:56,440
+M نفسها هيكون زي بعض يعني هيكون التنتين بنفس 
+
+283
+00:23:56,440 --> 00:24:02,600
+القيمة عشان هيك لو أجينا طرحنا اللي هو .. اللي هي
+
+284
+00:24:02,600 --> 00:24:09,860
+قيمة ال lower sum ال upper sum على ال Q star مع ال
+
+285
+00:24:09,860 --> 00:24:16,340
+upper sum على ال Q هيصير عندي اللي هنا يظهر اللي
+
+286
+00:24:16,340 --> 00:24:22,810
+هو M من العادية أو M من الـ Star ناقص الـ M من الـ
+
+287
+00:24:22,810 --> 00:24:27,350
+Star لأنه بيكون قد يكون المختلفات لكن اللي هان مش
+
+288
+00:24:27,350 --> 00:24:31,050
+هيظهر لأنه هيصير الـ M ناقص M من الـ Star صفر إذن
+
+289
+00:24:31,050 --> 00:24:36,110
+هيصير عندي ظهور هذولة في كم فترة عن أكثر هاي
+
+290
+00:24:36,110 --> 00:24:41,710
+واحدة تنتين بضل أمشي لـ N ناقص واحد لإن عددنا دولة
+
+291
+00:24:41,710 --> 00:24:45,330
+من X1 عند XN ناقص واحدة كم واحدة N ناقص واحد يعني
+
+292
+00:24:45,330 --> 00:24:49,130
+على الأكثر هيكون عدد ال sub intervals اللي اجداد
+
+293
+00:24:49,130 --> 00:24:54,390
+عملاً اللي هو 2 في N ناقص واحد اللي اتجسمت تنتين
+
+294
+00:24:54,390 --> 00:25:00,590
+تنتين الآن فبصير عندي ال summation هذا لو جينا لو
+
+295
+00:25:00,590 --> 00:25:08,230
+أخدنا لك الـ U الـ U star مع الـ اللي الـ F ناقص الـ U
+
+296
+00:25:08,230 --> 00:25:14,910
+الـ QF هيكون عبارة عن إيش يا جماعة اللي هنا هيتصفر
+
+297
+00:25:14,910 --> 00:25:19,070
+حيساوي الصميه كم واحدة من هذولة هيكون على الأكثر
+
+298
+00:25:19,070 --> 00:25:23,790
+الشكل هذا واحدة اسمها مثلا MK MJ زي ما هو مسميها
+
+299
+00:25:23,790 --> 00:25:28,870
+والتاني M star K هذولة على الأكثر على الأكثر على
+
+300
+00:25:28,870 --> 00:25:34,900
+الأكثر هيكون عددهم قداش عددهم عبارة عن اثنين فئة
+
+301
+00:25:34,900 --> 00:25:40,240
+ناقص واحد مضروبات في طول الفترة هذه الفترة الصغيرة
+
+302
+00:25:40,240 --> 00:25:43,680
+اللي هي .. اللي هي الفترة تبعت .. اللي هي مين
+
+303
+00:25:43,680 --> 00:25:48,720
+الـ Q*) اللي هي .. واسميها مثلا ZK ناقص ZK ماينص
+
+304
+00:25:48,720 --> 00:25:53,700
+واحد يعني عددهم هذولة اللي بظهر الـU ناقص الـU
+
+305
+00:25:53,700 --> 00:25:59,270
+بظهر عبارة عن كم واحدة من هذولة summation لهم عبارة عن
+
+306
+00:25:59,270 --> 00:26:04,390
+الـ two فئة ناقص واحد من الـ terms نجي الآن إيش
+
+307
+00:26:04,390 --> 00:26:12,830
+اللي كاتبوا شوف قلنا لـ Q star بيساوي Q اتحاد من
+
+308
+00:26:12,830 --> 00:26:17,930
+الـ B إبسلون الـ Q star صار refinement لمين؟ للـ B
+
+309
+00:26:17,930 --> 00:26:23,620
+إبسلون إذا الـ Q*) حسب اللي حكيته هناك has at most
+
+310
+00:26:23,620 --> 00:26:28,540
+N ناقص واحد more than points than main Q على
+
+311
+00:26:28,540 --> 00:26:32,660
+الأكثر هيكون عدد اللي في الـ Q*) العناصر اللي في
+
+312
+00:26:32,660 --> 00:26:38,040
+Q*) عند Canon اللي في الـ Q اللي في ال .. أمسح 
+
+313
+00:26:38,040 --> 00:26:45,900
+اللي فوق بس زي ما قلت اللي في الـ By اللي في الـ
+
+314
+00:26:45,900 --> 00:26:54,870
+By هي عبارة عن X0X1 Xm-1 لعند Xm اللي في ال Q هي
+
+315
+00:26:54,870 --> 00:27:04,190
+عبارة عن Y0 Y1 Ym-1 لعند Ym اللي في ال Q*) إيش
+
+316
+00:27:04,190 --> 00:27:10,910
+هيصير أن أكيد هذي و هذي هم نفسهم فأكيد لو بدأنا ب
+
+317
+00:27:10,910 --> 00:27:17,650
+Z0 و انتهينا بأخر واحدة Z مين ZB مثلا هيكون اللي
+
+318
+00:27:17,650 --> 00:27:23,390
+هو على الأكثر، على الأكثر، على الأكثر الـ Q*) بتزيد عن
+
+319
+00:27:23,390 --> 00:27:30,170
+الـ Q بقداش بالنقاط هذولة اللي لو كانت مش مكررات من
+
+320
+00:27:30,170 --> 00:27:35,430
+هنا خالص اللي هي بيصير عندي في داخل هذه عدد عناصر
+
+321
+00:27:35,430 --> 00:27:41,890
+الـ Q*) أكثر من عدد عناصر الـ Q بـ على الأكثر N ناقص واحد
+
+322
+00:27:42,200 --> 00:27:50,720
+وكل هذا تبع اللي هو النقاط اتكررت معها دولة أو ما
+
+323
+00:27:50,720 --> 00:27:57,000
+اتكررتش ما اتكررتش بالمرة بيكون بالظبط عددهم اللي
+
+324
+00:27:57,000 --> 00:28:03,000
+هو ال YM زائد ال N ناقص واحد لو ما اتكررتش ولا
+
+325
+00:28:03,000 --> 00:28:07,700
+واحدة يعني بمعنى آخر ال Q start زيد عن ال Q بـ N
+
+326
+00:28:07,700 --> 00:28:10,740
+ناقص واحد من النقاط
+
+327
+00:28:12,960 --> 00:28:17,560
+طيب زي ما قال إذن So Q star تحتوي B إبسلون and Q
+
+328
+00:28:17,560 --> 00:28:21,780
+star has at most N نقص واحد more points than Q
+
+329
+00:28:21,780 --> 00:28:26,220
+namely those points among اللي هي النقاط اللي من
+
+330
+00:28:26,220 --> 00:28:30,080
+مين اللي بيكون الزيادات من ال X واحد لعندي ال X N
+
+331
+00:28:30,080 --> 00:28:35,200
+ال X N نقص واحد that is belongs to B star but not
+
+332
+00:28:35,200 --> 00:28:40,560
+to مين to Q اللي هدول اللي بتكون الزيادات طيب نطلع
+
+333
+00:28:40,560 --> 00:28:48,130
+لفوق الآن بما أن الـ Q صار تحتوي لـ Q إذا أكيد الـ
+
+334
+00:28:48,130 --> 00:28:53,850
+UQ ناقص الـ UQ صار أكبر سواء 0 طبعا عارفين ليش لأن
+
+335
+00:28:53,850 --> 00:28:58,890
+الـ refinement دائما لل upper sum بيجلله ماشي عشان
+
+336
+00:28:58,890 --> 00:29:02,670
+يصير refinement عشان يبطل يطلع فوق ينزل إشي بسيط
+
+337
+00:29:02,670 --> 00:29:07,730
+فهذا في الـ refinement معناته بيصير الـ UQ أصغر من
+
+338
+00:29:07,730 --> 00:29:11,790
+مين؟ أكبر من مين؟ من الـ UQ UQ star لأنه في
+
+339
+00:29:11,790 --> 00:29:15,630
+الـ refinement الأعلى بيجلد مدام بجلد إذا هذا UQ
+
+340
+00:29:15,630 --> 00:29:20,610
+ناقص UQ star أكبر أو يساوي صفر الآن زي ما سمينا if
+
+341
+00:29:20,610 --> 00:29:25,170
+we write UQ star بيساوي Z node Z واحد عند مين؟ عند
+
+342
+00:29:25,170 --> 00:29:34,610
+ZB then لو أجينا بدنا نحسب الآن UQ F ناقص UQ star
+
+343
+00:29:34,610 --> 00:29:42,230
+و F خليني أوضح لك
+
+344
+00:29:42,230 --> 00:29:53,010
+خليني اكتبها معليش عندي U Q و
+
+345
+00:29:53,010 --> 00:29:59,290
+F ناقص U Q Star و F
+
+346
+00:30:02,130 --> 00:30:07,370
+الـ summation الأولى العبارة عن الـ summation له
+
+347
+00:30:07,370 --> 00:30:19,310
+اللي هي M J في 100 في الـ Q اللي هو Y J minus Y J
+
+348
+00:30:19,310 --> 00:30:25,130
+minus 1 J من عند 1 لعند الـ M ناقص ال summation
+
+349
+00:30:25,130 --> 00:30:37,430
+للتانية اللي هي MK Star في مين؟ في Z K-Z K-1 K من
+
+350
+00:30:37,430 --> 00:30:42,750
+عند 1 لعند مين؟ لعند الـ B اللي فرضناها إيش اسمها
+
+351
+00:30:42,750 --> 00:30:49,190
+اللي هي الـ B زي ما قلت قبل بشوية لو كان هذولة
+
+352
+00:30:49,190 --> 00:30:53,870
+اللي صارن زيادات هنا اللي صارن زيادات هنا ال X
+
+353
+00:30:53,870 --> 00:30:59,410
+نقطة من X واحد لعند X ناقص واحد لو توزع بين هذولة
+
+354
+00:31:00,990 --> 00:31:04,390
+يعني بمعنى آخر كل هدف في حالة الـ M أكبر من N
+
+355
+00:31:04,390 --> 00:31:10,430
+توزع بينهين هيعمل اللي هو ال intervals زي ما قلنا
+
+356
+00:31:10,430 --> 00:31:15,850
+2 في N ناقص 1 في هذه ال intervals هيكون اللي هو
+
+357
+00:31:15,850 --> 00:31:22,460
+الـ Mj و الـ Mk قد يكون المختلفات لكن في الباقي
+
+358
+00:31:22,460 --> 00:31:28,400
+اللي أصلا ما دخلهنش إشي جديد وضلت الـ Q زي الـ Q*)
+
+359
+00:31:28,400 --> 00:31:35,680
+فبتكون M تبعت الـ Q و M*) تبعت الـ Q*) زي بعض فبصير
+
+360
+00:31:35,680 --> 00:31:40,360
+هذه ناقص هذه بيساوي 0 اللي هي الـ MJ والمك بيساوي 0
+
+361
+00:31:40,360 --> 00:31:47,070
+يعني بمعنى آخر الـ terms اللي هتكون على صورة MJ ناقص
+
+362
+00:31:47,070 --> 00:31:52,110
+MK star على الأكثر على الأكثر اللي ممكن يكون المختلفات
+
+363
+00:31:52,110 --> 00:31:57,550
+عبارة عن قداش يا جماعة اثنين في N ناقص واحد يعني هذول
+
+364
+00:31:57,550 --> 00:32:01,950
+عدد هنا على الأكثر طبعا في ZK minus ZK minus واحد
+
+365
+00:32:01,950 --> 00:32:04,770
+تبعي اللي هو التجزئة الجديدة لإن هذه التجزئة اللي
+
+366
+00:32:04,770 --> 00:32:08,950
+بتجسمها ل sub intervals يعني على الأكثر هذول عدد هنا
+
+367
+00:32:08,950 --> 00:32:13,180
+قداش اثنين في N ناقص واحد هذا أنا قلته لما في حالتي
+
+368
+00:32:13,180 --> 00:32:18,610
+الام أكبر من N في حالة الـ M أصغر أو يساوي N
+
+369
+00:32:18,610 --> 00:32:23,890
+بيصير اللي هو في الشيء .. بيصير اللي هو غصبًا عنها
+
+370
+00:32:23,890 --> 00:32:30,270
+مدام الـ N أكبر وبدها تدخل الـ X1 عليهم غصبًا عنها
+
+371
+00:32:30,270 --> 00:32:35,210
+هيكون في الداخل انطبج على مين؟ على إيش من هان يعني
+
+372
+00:32:35,210 --> 00:32:39,630
+مش هيعمل أن 2 في N ناقص 1 هيعمل أن أجل من هيك إلا
+
+373
+00:32:39,630 --> 00:32:42,150
+في حالة اللي هي M بتساوي N بتطلع اللي هو على
+
+374
+00:32:42,150 --> 00:32:47,560
+الأكثر ممكن يطلع 2 في N-1 لأنه ما بيظلش فيه عنده
+
+375
+00:32:47,560 --> 00:32:53,580
+اللي هو مكان بين هذوله يدخلن فبضطر أن اللي هو أكيد
+
+376
+00:32:53,580 --> 00:32:58,140
+هيكون من منين من جواك اللي هي هذه أو بكون اللي جوا
+
+377
+00:32:58,140 --> 00:33:03,760
+برضه مش هيزيدن عن اثنين في الـ N-1 إذا اللي هي دخلت
+
+378
+00:33:04,020 --> 00:33:09,620
+على أماكن غير مين حتى في حالة ال M ال M أصغر من N
+
+379
+00:33:09,620 --> 00:33:14,000
+لأ هيدخلن هيدخلن يعملن sub intervals هيختلفن برضه
+
+380
+00:33:14,000 --> 00:33:18,640
+نفس الشيء يعني لو دخلت X1 هنا و X2 هنا فبصير برضه
+
+381
+00:33:18,640 --> 00:33:22,550
+يعملن sub intervals في مجملها لن يتجاوز أن اثنين
+
+382
+00:33:22,550 --> 00:33:29,230
+في N ناقص واحد لأن عدد N ناقص واحد من النقاط
+
+383
+00:33:29,230 --> 00:33:33,550
+الجديدة X1 X2 عند Xn ناقص واحد إن شاء الله تكون
+
+384
+00:33:33,550 --> 00:33:39,490
+واضحة هذه الصورة يعني مختصرها أن اللي ممكن ما
+
+385
+00:33:39,490 --> 00:33:47,270
+يحفظلش على اللي هو الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+386
+00:33:47,270 --> 00:33:48,310
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+387
+00:33:48,310 --> 00:33:48,670
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+388
+00:33:48,670 --> 00:33:48,690
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+389
+00:33:48,690 --> 00:33:48,810
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+390
+00:33:48,810 --> 00:33:49,030
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+391
+00:33:49,030 --> 00:33:52,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الاللي
+
+392
+00:33:52,480 --> 00:33:57,120
+هي بس اللي هي N ناقص واحد من النقاط اللي هتصنعني
+
+393
+00:33:57,120 --> 00:34:02,180
+بس اثنين في N ناقص واحد على الأكثر من ال .. اللي
+
+394
+00:34:02,180 --> 00:34:10,840
+هي الـ M واحد أو الـ Mj تختلف عن الـ M كستار طيب،
+
+395
+00:34:10,840 --> 00:34:13,940
+ماشي الحالة إن شاء الله تكون المضحكة هذه لأن هي بس
+
+396
+00:34:13,940 --> 00:34:17,840
+هذه النقطة اللي بدها توضيح في الباقي هيكون بإذن
+
+397
+00:34:17,840 --> 00:34:23,040
+الله سعيد إذا صار زي ما قلنا نرجع لهذا then U Q F
+
+398
+00:34:23,040 --> 00:34:27,200
+نقص U Q Star و F can be written as the sum of at
+
+399
+00:34:27,200 --> 00:34:31,920
+most اثنين في M نقص واحد terms of the form M J نقص
+
+400
+00:34:31,920 --> 00:34:37,460
+M K Star في Z K minus Z K minus واحد لأن عدد هذه
+
+401
+00:34:37,460 --> 00:34:41,680
+الدولة على الأكثر اللي هو بالشكل هذا إذا الآن لو
+
+402
+00:34:41,680 --> 00:34:51,060
+أجينا بدي أحسب لك اللي هو الـ M J نقص M K Star هذه
+
+403
+00:34:51,060 --> 00:35:00,000
+هيكون أصغر أو يساوي مج زائد مك
+
+404
+00:35:01,360 --> 00:35:05,180
+وكل واحدة طبعاً هذا supremum على فترتها وهذا
+
+405
+00:35:05,180 --> 00:35:09,240
+supremum لل F على فترتها أكيد أصغر أو يساوي ال M
+
+406
+00:35:09,240 --> 00:35:13,160
+زائد ال M لأن هذا ال M عبارة عن ال supremum على كل
+
+407
+00:35:13,160 --> 00:35:16,360
+ال interval A و B هذا على جزءه هذا على كل ال
+
+408
+00:35:16,360 --> 00:35:19,240
+interval A و B هذا على جزءه يعني في النهاية هذا
+
+409
+00:35:19,240 --> 00:35:25,460
+أصغر أو يساوي قداش 2 في M يعني هيصير عندي الآن ال
+
+410
+00:35:25,460 --> 00:35:32,980
+absolute value لل M J ناقص M K Star في ZK-ZK-1
+
+411
+00:35:32,980 --> 00:35:39,970
+هيكون أصغر أو يساوي 2M في مين؟ في اللي هي طول ال
+
+412
+00:35:39,970 --> 00:35:43,550
+interval هذه طول ال interval هذه طب هذه الـ
+
+413
+00:35:43,550 --> 00:35:50,170
+interval zk minus zk minus 1 أكيد أصغر أو يساوي
+
+414
+00:35:50,170 --> 00:35:56,410
+مين؟ norm لـ Q star مين norm لـ Q star؟ اللي هو ال
+
+415
+00:35:56,410 --> 00:36:01,510
+supremum على مين؟ على أطوال ال subintervals ال
+
+416
+00:36:01,510 --> 00:36:05,750
+supremum أكيد أكبر أو يساوي واحدة منهم طول واحدة
+
+417
+00:36:05,750 --> 00:36:13,190
+منهم لكلّهم وهذه دائماً لما نزيد العدد قلنا لما نكون
+
+418
+00:36:13,190 --> 00:36:19,630
+Q يحتوي Q*) automatic norm لـ Q*) زي ما قلنا المرة
+
+419
+00:36:19,630 --> 00:36:24,710
+الفاية هيكون أصغر أو يسوي .. آسف لما يكون Q
+
+420
+00:36:24,710 --> 00:36:28,370
+substantive لـ Q*) يكون norm لـ Q*) عكسه أصغر أو 
+
+421
+00:36:28,370 --> 00:36:34,420
+يشوي norm من الـ Q إذا الـ N هذا أصغر أو يساوي هذا و
+
+422
+00:36:34,420 --> 00:36:38,940
+هذا نفسه أصغر أو يساوي من؟ الـ Q و الـ Normal Q
+
+423
+00:36:38,940 --> 00:36:42,720
+أصغر من من؟ من دلتا ما احنا على أساسه اللي هي
+
+424
+00:36:42,720 --> 00:36:48,120
+اشتغلنا إذا صار عندي هذا Normal أصغر من دلتا يعني
+
+425
+00:36:48,120 --> 00:36:53,380
+نرجع لهذا هذا المقدار كل واحد لحاله أصغر من اثنين 
+
+426
+00:36:53,380 --> 00:36:58,350
+أم في من بيصير؟ في دلتا الآن عدد هذول اللي ممكن
+
+427
+00:36:58,350 --> 00:37:07,870
+يظهر في UQ ناقص UQ star عبارة عن 2M ناقص 1 يعني في
+
+428
+00:37:07,870 --> 00:37:14,330
+النهاية هذا أصغر أو يساوي اللي هو عدد الـ 2M ناقص
+
+429
+00:37:14,330 --> 00:37:22,940
+1 مضروب في من؟ في اللي هي 2M 2M في Delta لأن هذا
+
+430
+00:37:22,940 --> 00:37:28,390
+نفسه أصغر أو يساوي 2M و هذا نفسه أصغر أو يساوي Delta الآن
+
+431
+00:37:28,390 --> 00:37:33,030
+هدولة بتكرر على الأكثر اثنين فئة ناقص واحد هذا ..
+
+432
+00:37:33,030 --> 00:37:36,750
+هذا بتكرر في هذا المقدار على الأكثر في هذا و
+
+433
+00:37:36,750 --> 00:37:40,370
+الباقية هيتصفر زي ما قلنا إذا صار هيكون هذا أصغر
+
+434
+00:37:40,370 --> 00:37:44,750
+أو يساوي عدد تكرار من اثنين فئة ناقص واحد في اثنين
+
+435
+00:37:44,750 --> 00:37:51,010
+M في من في Delta فإذا صار عندي الآن ال UQF ناقص
+
+436
+00:37:51,010 --> 00:37:55,050
+ال UQ star و F أصغر أو يساوي اثنين فئة ناقص واحد في
+
+437
+00:37:55,050 --> 00:38:01,350
+اثنين M في من في delta مضروب اللي هو هذا عبارة عن
+
+438
+00:38:01,350 --> 00:38:13,090
+قد إيش جماعة نيجي نحسبها عشان نصل للي بدنا إياه صار
+
+439
+00:38:13,090 --> 00:38:26,230
+عندي اللي هو ال U Q F U star و F Q F ناقص U
+
+440
+00:38:32,930 --> 00:38:38,230
+UQF-UQF UQF
+
+441
+00:38:38,230 --> 00:38:44,130
+-UQF UQF
+
+442
+00:38:44,130 --> 00:38:45,750
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+443
+00:38:45,750 --> 00:38:45,850
+-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF-UQF UQF
+
+444
+00:38:45,850 --> 00:38:54,050
+-UQF UQF-UQF UQF-UQF UQF في اللي هو M في Delta اللي
+
+445
+00:38:54,050 --> 00:38:59,870
+هو أكيد هذا أصغر من أربعة في N في M في Deltaمظهرة
+
+446
+00:38:59,870 --> 00:39:03,790
+ولا لأ؟ لأن الـ N أكبر من من؟ من الـ N ناقص واحد
+
+447
+00:39:03,790 --> 00:39:06,370
+الـ Delta إيش اخترناها؟ ما هي الحسابات من الأول
+
+448
+00:39:06,370 --> 00:39:12,010
+حاسبينها احنا اخترنا الـ Delta فوق عبارة عن جداش
+
+449
+00:39:12,010 --> 00:39:15,710
+لأن احنا كنا عارفين حالنا أصلا بنصل لها المرحلة
+
+450
+00:39:15,710 --> 00:39:19,730
+فبدنا نخلي هذه ي على ثلاثة ليش ي على ثلاثة؟ بعد
+
+451
+00:39:19,730 --> 00:39:26,470
+شوية تشوف اللي هي عبارة عن ي هذه ي على 12N في من
+
+452
+00:39:26,470 --> 00:39:31,170
+في N هذه الآن لما أشيل هذه و أضرب هذه فيها بيصير
+
+453
+00:39:31,170 --> 00:39:34,770
+أربعة في واحد و الآن مع الآن و الام مع الام و هذه
+
+454
+00:39:34,770 --> 00:39:41,750
+بيصير جداش ثلاثة إذا صار عندي الآن U Q و F ناقص U
+
+455
+00:39:41,750 --> 00:39:48,000
+Q Star و F أصغر من epsilon ع ثلاثة يعني بمعنى آخر
+
+456
+00:39:48,000 --> 00:39:55,380
+صار عند الـ U Q و F أصغر من إبسلون ع ثلاثة زائد U
+
+457
+00:39:55,380 --> 00:40:01,420
+Q star من و F ماشي الحال إذا هذه ال in quality
+
+458
+00:40:01,420 --> 00:40:06,160
+الثانية اللي وصلناها اللي هتوصلني في النهاية للي
+
+459
+00:40:06,160 --> 00:40:11,490
+بدي إياه ونشوف كيف هتوصلني طيب يا جماعة صلوا على النبي
+
+460
+00:40:11,490 --> 00:40:17,670
+عليه الصلاة والسلام تنسواش أنه احنا في الأول حصلنا
+
+461
+00:40:17,670 --> 00:40:21,730
+على U بي و أف ماينص أل بي و أف أصغر من من
+
+462
+00:40:21,730 --> 00:40:24,930
+إبسلون على ثلاثة وحصلنا على U بي و إبسلون هذا أصغر
+
+463
+00:40:24,930 --> 00:40:27,910
+من إبسلون على ثلاثة هنحتاجها بعد شوية خليني أكتبها
+
+464
+00:40:27,910 --> 00:40:35,630
+الثانية عند حصلنا قبل هيك على ال U بي و أف ماينص أل
+
+465
+00:40:35,630 --> 00:40:42,970
+بي و أف أصغر من epsilon ع ثلاثة وطبعا أكيد اللي هي
+
+466
+00:40:42,970 --> 00:40:46,870
+أصغر من u بي إبسلون و اف عشان لا نرجع الهاشمون
+
+467
+00:40:46,870 --> 00:40:51,970
+اقصال بي إبسلون و اف كله أصغر من إبسلون ع ثلاثة
+
+468
+00:40:51,970 --> 00:41:00,930
+هاي كمان هدول التنتين حصلناها ماشي طيب الآن
+
+469
+00:41:00,930 --> 00:41:09,000
+اللي عملنا هذا اللي هو مع ال upper sum بنعمل نفسه
+
+470
+00:41:09,000 --> 00:41:14,680
+مع من مع اللي هو lower sum هنلاقي اللي هو LQ يعني
+
+471
+00:41:14,680 --> 00:41:19,060
+LQ star و F ناقص LQ F هنلاقيه هنا على الأكثر
+
+472
+00:41:19,060 --> 00:41:23,020
+باختلاف أنه هو التو فئة ناقص واحد من التلزمه و و و
+
+473
+00:41:23,020 --> 00:41:26,640
+الاخر و بنكمل نفس الشيء بطل عند LQ star و F ناقص
+
+474
+00:41:26,640 --> 00:41:30,600
+إبشر على ثلاثة أصغر من من من LQ F إذا similarly
+
+475
+00:41:30,600 --> 00:41:35,120
+for هذه اللي عملناها هذه ما حد بنعمله مع اللي هو
+
+476
+00:41:35,730 --> 00:41:47,930
+الـ L L of Q star و F ماينص اللي هو إبسلون ع ثلاثة
+
+477
+00:41:47,930 --> 00:41:55,890
+أصغر من L Q O mean O F ماشي الحال، طيب and exactly
+
+478
+00:41:55,890 --> 00:42:00,310
+زي ما بنقول similar argument symbolize that اللي
+
+479
+00:42:00,310 --> 00:42:07,870
+كتبناه لنبدأ نجمع معلوماتنا عشان نصل لإنه الـ
+
+480
+00:42:07,870 --> 00:42:11,530
+Riemann Sum ناقص الـ integration يكون إيه شماله
+
+481
+00:42:11,530 --> 00:42:15,890
+اللي هو أصغر من إبسلون، انتبهوا كيف عشان يمكن هيك
+
+482
+00:42:15,890 --> 00:42:23,210
+تكون أسهل لنا نرسم خط الأعداد وهنا هخلينا اللي هو
+
+483
+00:42:23,210 --> 00:42:43,920
+نحط الـ U أكي و FU Q F هي أصغر من
+
+484
+00:42:43,920 --> 00:42:55,420
+إبسلون على ثلاثة زي U U أستار U F عندي
+
+485
+00:42:55,420 --> 00:42:57,860
+U Q F
+
+486
+00:43:00,380 --> 00:43:07,380
+بس خليني عشان أحط ال L قبل ال L قبل هه عشان مفيش
+
+487
+00:43:07,380 --> 00:43:14,800
+وسع أنا جماعة بعد أذنكم خليني بس هكتب الأول أشنب
+
+488
+00:43:14,800 --> 00:43:27,870
+ده بمن ب L L Q و F الـ Refinement طبعا لـ L, Q,
+
+489
+00:43:27,970 --> 00:43:36,450
+Star و F قبلها زي ما أنتو عارفين L, Q و F خليني
+
+490
+00:43:36,450 --> 00:43:41,090
+أعمل هذه قبلها عشان تظبط أحسن L, Q, Star و F ناقص
+
+491
+00:43:41,090 --> 00:43:50,640
+بإبسلون ع ثلاثة وهذه LUQF معايا هي هذه بتكون قبل هذه
+
+492
+00:43:50,640 --> 00:43:59,300
+طيب ال QF أكيد بعدها من UQF صح ولا لأ أكيد طيب
+
+493
+00:43:59,300 --> 00:44:07,420
+بعد ال UQF إيش بتيجي بتيجي هنا إبسلون ع ثلاثة زائد
+
+494
+00:44:07,420 --> 00:44:15,340
+UQ star و F مظبوط مظبوط أكيد؟ طيب إذا أنا اجيت لخصت
+
+495
+00:44:15,340 --> 00:44:21,120
+المعلومة هذه و لخصت المعلومة هذه اللي هي أصغر من
+
+496
+00:44:21,120 --> 00:44:28,460
+epsilon ع ثلاثة UQF UQF ولا ال PUF هذه المسافة
+
+497
+00:44:28,460 --> 00:44:32,910
+بينهم إيه اشمل يا جماعة؟ أصغر من إبسلون ع ثلاثة
+
+498
+00:44:32,910 --> 00:44:37,130
+واضح أه؟ ومن هنا قال لك U square of F ناقص هذه وهذه
+
+499
+00:44:37,130 --> 00:44:43,050
+إبسلون وهذه بالترتيب اللي احنا حصلنا عليه طيب الآن
+
+500
+00:44:43,050 --> 00:44:48,230
+طبيعي اللي هو ال remansum و ال integration هيكون
+
+501
+00:44:48,230 --> 00:44:52,030
+بين ال lower و بين main اللي هو إيش الأبر إذن
+
+502
+00:44:52,030 --> 00:44:57,110
+أكيد أكيد أكيد ال remansum تبعنا هي بدينا نصل للي
+
+503
+00:44:57,110 --> 00:45:04,400
+جدنا إياه ال CQF واللي هو ال integration من a إلى
+
+504
+00:45:04,400 --> 00:45:08,720
+b إلى ال F هيكون بين ال lower و بين ال upper ال
+
+505
+00:45:08,720 --> 00:45:11,720
+integration موجود لأن مراس الدور جللنا إذا هذوله
+
+506
+00:45:11,720 --> 00:45:17,800
+صار اللي هو بين هذه و بين هذه إذا صار هذه و هذه
+
+507
+00:45:17,800 --> 00:45:26,120
+بين هذه الدنتين و هذه طبعا ال U Q F و اللي قاله Q F
+
+508
+00:45:26,120 --> 00:45:31,780
+واضح .. واضح إنه اللي هو وين في داخل الفترة اللي
+
+509
+00:45:31,780 --> 00:45:36,660
+هي L Q Star و F ناقص إبسلون على ثلاثة و U Q Star و F
+
+510
+00:45:36,660 --> 00:45:42,500
+إبسلون على ثلاثة يعني بين .. هذه طبعا .. بين هذه و
+
+511
+00:45:42,500 --> 00:45:47,200
+بين من و بين ال interval هذه يعني subset من من
+
+512
+00:45:47,200 --> 00:45:53,460
+جايل من I إبسلون اللي هي I Epsilon بتساوي اللي هو
+
+513
+00:45:53,460 --> 00:45:59,440
+الفترة هذه من هنا لعند الـ hand هو اللي مسمينها
+
+514
+00:45:59,440 --> 00:46:05,740
+احنا شماله I Epsilon بين L Q Star و F ناقص
+
+515
+00:46:05,740 --> 00:46:11,860
+Epsilon ع ثلاثة و U Q Star F و Epsilon ع ثلاثة
+
+516
+00:46:11,860 --> 00:46:20,060
+الآن U Q Star و F ناقص قالك U Star و F ما مسحتاش
+
+517
+00:46:20,060 --> 00:46:28,200
+لسه أنا U Q Star F و قالك U Star F أصغر من من
+
+518
+00:46:28,200 --> 00:46:36,520
+إبسلون ع ثلاثة لأ اللي هي U
+
+519
+00:46:36,520 --> 00:46:42,670
+Q Star F و قال الـ Q star F حصلنا عليها قبل هيك أنها
+
+520
+00:46:42,670 --> 00:46:46,650
+أصغر من من من إبسلون ع ثلاثة طبعا من وين بنحصلها؟
+
+521
+00:46:46,650 --> 00:46:49,650
+ممكن نحصلها مبقى من هنا ده كما حصلناش أن الـ Q
+
+522
+00:46:49,650 --> 00:46:54,430
+star و F و الـ By بتحتوي الـ By فهيكون الـ U اللي
+
+523
+00:46:54,430 --> 00:47:00,090
+حصلنا أولاً بالنسبة لمن؟ للي هي الـ By حصلنا قبل
+
+524
+00:47:00,090 --> 00:47:06,400
+هيك أن الـ U بإبسلون و ال ال بإبسلون الفرق بينهم إيش
+
+525
+00:47:06,400 --> 00:47:10,840
+إبسلون على ثلاثة و ال Q star refinement إذا أكيد
+
+526
+00:47:10,840 --> 00:47:14,920
+المسافة بين ال other طبعا في ال refinement المسافة
+
+527
+00:47:14,920 --> 00:47:20,440
+بين ال other و ال other هتصغر لكل refinement ال U
+
+528
+00:47:20,440 --> 00:47:28,340
+بما أن هذه refinement إذا ال U لأ الـ Q star و F
+
+529
+00:47:28,340 --> 00:47:34,960
+ناقص L Q star و F أصغر أو يساوي لأنها صارت تحسين
+
+530
+00:47:34,960 --> 00:47:38,400
+عليها ما زالت صارت تحسين يعني بتجلل مسافة بين ال
+
+531
+00:47:38,400 --> 00:47:40,780
+Upper و الLower عشان نروح في الآخر لل integration
+
+532
+00:47:40,780 --> 00:47:51,520
+ناقص أصغر أو يساوي ل L B epsilon و F U ناقص L B
+
+533
+00:47:51,520 --> 00:47:56,980
+epsilon و F اللي هي هذه أصغر من 100 من إبسلون وينها
+
+534
+00:47:56,980 --> 00:48:03,400
+أصغر من إبسلون ع ثلاثة أصغر من إبسلون ع ثلاثة إذا
+
+535
+00:48:03,400 --> 00:48:10,320
+فعلاً عرفنا من وين اجت هذه أصغر من من إبسلون ع
+
+536
+00:48:10,320 --> 00:48:18,460
+ثلاثة إذا صار عندي ال length لهذه ال length لهذه
+
+537
+00:48:18,460 --> 00:48:23,240
+سهل نوجدها عليش خلّيني أكتب فوق عشان لو جبتلكم ال
+
+538
+00:48:23,240 --> 00:48:29,780
+length إلها عشان أقولكم إنه هذه و هذه هيكون اللي
+
+539
+00:48:29,780 --> 00:48:38,900
+هو بالبعد المطلوب تحسبلي الآن هذه ناقص هذه بيصير
+
+540
+00:48:38,900 --> 00:48:48,940
+عبارة عن طول ال interval mean Iy بساوي ال UQ star
+
+541
+00:48:48,940 --> 00:48:55,780
+و F زائد إبسلون على ثلاثة ناقص تبعين معيار ال Q
+
+542
+00:48:55,780 --> 00:49:01,720
+star و F ناقص ناقص بيصير زائد إبسلون على ثلاثة و
+
+543
+00:49:01,720 --> 00:49:04,900
+يساوي اللي هو إبسلون على ثلاثة و إبسلون على ثلاثة
+
+544
+00:49:04,900 --> 00:49:12,180
+اثنين إبسلون على ثلاثة زائد U Q star و F ناقص ال Q
+
+545
+00:49:12,180 --> 00:49:18,800
+star و F اللي هم هذولة هذه اللي كتبتها لسه ما حتنش
+
+546
+00:49:18,800 --> 00:49:23,400
+أصغر من من يبسلون على ثلاثة فبتصير هذه طولها
+
+547
+00:49:23,400 --> 00:49:26,700
+أصغر من اثنين يبسلون على ثلاثة زائد يبسلون على
+
+548
+00:49:26,700 --> 00:49:31,620
+ثلاثة ويساوي يبسلون إذا صار عندي طول الـ interval
+
+549
+00:49:31,620 --> 00:49:40,520
+اللي أسي Qf و ال integration A وB موجودة في كل
+
+550
+00:49:40,520 --> 00:49:46,660
+الفترة هذه اللي هي المسافة بينهم عبارة عن أصغر من
+
+551
+00:49:46,660 --> 00:49:53,460
+من من Epsilon إذا صار عندي الآن ال integration
+
+552
+00:49:53,460 --> 00:50:05,480
+أين أكتب ال integration إذا صار عندي إذا صار عندي
+
+553
+00:50:05,480 --> 00:50:12,380
+المسافة بين هذه و هذه SQF نقص ال integration من A B
+
+554
+00:50:12,380 --> 00:50:16,900
+ل F أصغر من من يا جماعة من يبسط من من هذا تحت
+
+555
+00:50:16,900 --> 00:50:23,360
+شرط من إنه normally Q هذا أصغر من A H من دلتا
+
+556
+00:50:23,360 --> 00:50:29,200
+أصغر من دلتا بقول إيه احنا خلصنا اللي بدنا إياه
+
+557
+00:50:29,200 --> 00:50:32,280
+نوقف
+
+558
+00:50:32,280 --> 00:50:33,020
+الجيجا بحثها
+
+559
+00:51:39,830 --> 00:51:44,830
+أه يا أبو حسن بقول هيك احنا خلصنا برهان نظرية أول
+
+560
+00:51:44,830 --> 00:51:48,490
+حد يقول لي إنه اللي هو المسافة بين U وQ قال الـ Q
+
+561
+00:51:48,490 --> 00:51:50,950
+أصغر من إبسيلون على تلاتة لأ احنا ما قلناش هيك
+
+562
+00:51:50,950 --> 00:51:53,950
+المسافة بين الأصغر من إبسيلون على تلاتة اللي هو الـ
+
+563
+00:51:53,950 --> 00:51:58,190
+P إبسيلون الـ U P إبسيلون والـ L P إبسيلون وأي
+
+564
+00:51:58,190 --> 00:52:01,010
+refinement له بس الـ Q هنا مش refinement هذا بس
+
+565
+00:52:01,010 --> 00:52:04,830
+اللي بنعرف أنه norm لـ Q أصغر من مين من دلتا أصلا
+
+566
+00:52:04,830 --> 00:52:08,960
+احنا بدنا نصل لإنه المسافة بين هذولة اللي هو أصغر
+
+567
+00:52:08,960 --> 00:52:13,300
+من إبسيلون وعلى طول منها بنستنتج هذه فكيف وصلنا
+
+568
+00:52:13,300 --> 00:52:16,160
+بإننا قلنا اللي هو ال integration هذه في هذه
+
+569
+00:52:16,160 --> 00:52:19,780
+الفترة والفترة هذه جزء من هذه وهذه قلنا هذه طولها
+
+570
+00:52:19,780 --> 00:52:22,960
+على الأكثر بساوي إبسيلون عشان هيك صارت المسافة بين
+
+571
+00:52:22,960 --> 00:52:28,000
+هذه وهذا أصغر من إبسيلون وهو المطلوب طيب نيجي الآن
+
+572
+00:52:28,000 --> 00:52:34,060
+ده اللي هي النظرية اللي بعدها theorem
+
+573
+00:52:35,670 --> 00:52:45,070
+لت I بتساوي A وB و لت F من I لعند R بيكون فانكشن
+
+574
+00:52:46,090 --> 00:52:49,330
+suppose there exists a number B such that لكل Y
+
+575
+00:52:49,330 --> 00:52:54,110
+أكبر من 0 if B is any partition of I with norm B
+
+576
+00:52:54,110 --> 00:52:58,030
+أصغر من Delta and S of Bi is any corresponding
+
+577
+00:52:58,030 --> 00:53:01,950
+Riemann sum اللي هو then لهذا أصغر من إبسيلون then
+
+578
+00:53:01,950 --> 00:53:06,310
+F is integrable on I in the sense of definition
+
+579
+00:53:06,310 --> 00:53:12,590
+716 يعني وكأننا جاعدين بنقول conversely إيش بنقول؟
+
+580
+00:53:12,590 --> 00:53:13,610
+بنقول
+
+581
+00:53:16,710 --> 00:53:24,890
+إنه لو كان عندي اللي هو limit لو كان عندي limit
+
+582
+00:53:24,890 --> 00:53:32,330
+اللي هو الـ S أو B و F as norm B بروح للسفر
+
+583
+00:53:32,330 --> 00:53:38,190
+exist و بسوء some number B إذن هذا الـ B بسوء ال
+
+584
+00:53:38,190 --> 00:53:43,410
+integration من A لB F of X DX يعني بقوللي لو كان
+
+585
+00:53:43,410 --> 00:53:50,850
+هذا متحقق لو كان هذا متحقق بيعطيني إنه هذا هو هيطلع
+
+586
+00:53:50,850 --> 00:53:55,110
+اللي هي هتطلع F-integrable وهيكون بيه هذا اللي هو
+
+587
+00:53:55,110 --> 00:53:59,030
+ال limit هذا هو قيمة مين ال integration ليش؟ لأن
+
+588
+00:53:59,030 --> 00:54:02,490
+هذا اصلا شو معناته؟ هذا معناته for every epsilon
+
+589
+00:54:02,490 --> 00:54:07,490
+أكبر من صفر there exist اللي هو delta أكبر من صفر
+
+590
+00:54:07,490 --> 00:54:14,370
+such that b أصغر من delta بيؤدي إلى S B و F ناقص
+
+591
+00:54:14,370 --> 00:54:17,630
+ال B اللي مفترضين أصغر من مين ال epsilon هذا هو
+
+592
+00:54:17,630 --> 00:54:23,290
+معناته هذا يعني أن اللي هو المعطى طبعا f bounded من
+
+593
+00:54:23,290 --> 00:54:30,590
+رأس الدور لجهنا number b بحيث ان لكل epsilon أو fb
+
+594
+00:54:30,590 --> 00:54:33,270
+is any partition بحيث ان normal b أعلى من delta
+
+595
+00:54:34,000 --> 00:54:39,600
+وكانت اللي هي المسافة بين الـ B أصغر من Epsilon
+
+596
+00:54:39,600 --> 00:54:44,440
+هذا .. ده متحقق اللي هو هذا كله عبارة هو عبارة عن
+
+597
+00:54:44,440 --> 00:54:47,940
+limit S بي و F as and norm B اللي هو سفر
+
+598
+00:54:47,940 --> 00:54:52,160
+بساول B إذا .. إذا اتحقق هذا بتكون اللي هي F
+
+599
+00:54:52,160 --> 00:54:55,440
+integrable وقيمة الـ B هذه اللي هي قيمة ال limit
+
+600
+00:54:55,440 --> 00:54:59,420
+بساول integration هذه اللي هي عبارة عن .. النظرية
+
+601
+00:54:59,420 --> 00:55:04,470
+عبارة عن اللي هو بن .. اللي هي دمج بين اللي هي
+
+602
+00:55:04,470 --> 00:55:08,190
+نظريات السابقة المرة الماضية نشوف كيف اللي هو
+
+603
+00:55:08,190 --> 00:55:14,100
+البرهان برهان بسيط لإنه بعتمد عليه بشكل سريع لت y
+
+604
+00:55:14,100 --> 00:55:17,440
+أكبر من 0 و delta أكبر من 0 as in the theorem اللي
+
+605
+00:55:17,440 --> 00:55:20,180
+هو اللي في الـ theorem اللي فوق المقصود فيها النص
+
+606
+00:55:20,180 --> 00:55:25,820
+هذه قدت بي إبسيلون بي partition of I with نفترض أنه
+
+607
+00:55:25,820 --> 00:55:30,080
+norm بي إبسيلون أصغر من 200 من دلتا هذا المعطى ماشي
+
+608
+00:55:30,080 --> 00:55:36,240
+الحال نفترض أنه إبسيلون أكبر من 0 arbitrarily و
+
+609
+00:55:36,240 --> 00:55:41,190
+delta أكبر من 0 أو نفترض أن بي إبسيلون أي partition
+
+610
+00:55:41,190 --> 00:55:45,310
+بحيث أنه نورمه إيه شماله أصغر من دلتا لكن لو جينا
+
+611
+00:55:45,310 --> 00:55:48,930
+أخدنا بيه أي partition آخر و بيه محتوى بيه إبسيلون
+
+612
+00:55:48,930 --> 00:55:53,770
+هيكون norm ال partition بيه هذا اللي هو ال
+
+613
+00:55:53,770 --> 00:55:57,470
+refinement أكيد أصغر أو يساوي norm مين الأصلي اللي
+
+614
+00:55:57,470 --> 00:56:01,030
+هو أصغر من دلتا صار عنده الآن لكل إبسيلون أكبر من
+
+615
+00:56:01,030 --> 00:56:06,470
+صفر there exists دلتا بحيث أنه norm البي إبسيلون
+
+616
+00:56:06,470 --> 00:56:11,740
+أصغر من دلتا لأي partition بي refinement لبيبسلون
+
+617
+00:56:11,740 --> 00:56:17,260
+صار norm أصغر من delta إذا من اللي هو ال .. بواسطة
+
+618
+00:56:17,260 --> 00:56:21,740
+اللي هو النظرية السابقة حيكون عند ال S minus البي
+
+619
+00:56:21,740 --> 00:56:27,580
+أصغر من إبسيلون يؤدي إلى هذا بيبساو ال integration
+
+620
+00:56:27,580 --> 00:56:32,020
+لإن إيش كانت نظرية سبعة أربعة تلاتة بتشترط تشترط
+
+621
+00:56:32,020 --> 00:56:33,840
+إنه نلاقي لكل إبسيلون
+
+622
+00:56:36,480 --> 00:56:42,920
+أي بارتشن بي إبسيلون بحيث أن أي بي بتحتول بي إبسيلون
+
+623
+00:56:43,910 --> 00:56:48,530
+يؤدي إلى هذا أصغر من إبسيلون كله على بعض بيؤدي F
+
+624
+00:56:48,530 --> 00:56:53,790
+أشماله is integrable إذا بيواصل 7 4 3 مدام حصلنا
+
+625
+00:56:53,790 --> 00:56:57,910
+على ال S بي و F نقص ال V أصغر من إبسيلون بيكون هذا
+
+626
+00:56:57,910 --> 00:57:01,190
+اللي حصلنا عليه اللي هو P بساوة ال integration لل
+
+627
+00:57:01,190 --> 00:57:06,630
+F على الفترة من A لB يعني بمعنى آخر احنا اللي
+
+628
+00:57:06,630 --> 00:57:13,530
+حصلنا الآن من النظريتين أن F is integrable F is
+
+629
+00:57:13,530 --> 00:57:19,050
+integrable if and only if limit الـ S,B وF من
+
+630
+00:57:19,050 --> 00:57:23,890
+norm B بيروح للسفر exist وبساوي قيمة ال
+
+631
+00:57:23,890 --> 00:57:28,550
+integration يعني الآن ال integration أوصلنا له عبر
+
+632
+00:57:28,550 --> 00:57:34,330
+طريقين إما عبر طريق اللي هو limit للرمان sum يكون
+
+633
+00:57:34,330 --> 00:57:38,690
+exist أو عبر الطريق الآخر لأن ال upper .. ال upper
+
+634
+00:57:38,690 --> 00:57:42,930
+integral والlower integral يكون جد بعض ومتساويين
+
+635
+00:57:42,930 --> 00:57:52,690
+وحيكون في هذه الحالة هم ال integration وقف
+
+636
+00:57:52,690 --> 00:57:59,570
+هنا يا أبو حسن كم ساعة .. كم
+
+637
+00:57:59,570 --> 00:58:00,810
+عندك الوقت؟
+
+638
+00:58:03,290 --> 00:58:10,650
+نخلصها هيك و نبدأ تانية؟ لأن الجزء الثاني هذا اللي
+
+639
+00:58:10,650 --> 00:58:17,070
+هو ال improper integral بس بطولش بياخد نص ساعة انت
+
+640
+00:58:17,070 --> 00:58:22,090
+قاعد معايا للجد إيش؟ أكيد؟ ما بديش أضغط عليك يا أبو
+
+641
+00:58:22,090 --> 00:58:30,390
+حسن طيب لأ خلينا نخلص هذه ما هو درس 17 ها؟ هلجيت
+
+642
+00:58:30,390 --> 00:58:31,270
+18؟
+
+643
+00:58:41,590 --> 00:58:48,290
+هي الآن بتبدأ في المحاضرة 18 خلصنا 17 كيف؟
+
+644
+00:58:54,810 --> 00:58:59,850
+هيك مكون احنا خلصنا المحاضرة رقم 17 اللي هو ال
+
+645
+00:58:59,850 --> 00:59:03,610
+integration as a limit بعد شوية هنكمل ال section
+
+646
+00:59:03,610 --> 00:59:08,490
+هذا مظبوط بس هنكمله بموضوع جديد اللي هو عبارة عن
+
+647
+00:59:08,490 --> 00:59:12,510
+ال improper integral وإلى لقاء آخر والسلام عليكم
+
+648
+00:59:12,510 --> 00:59:13,670
+ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/A0riuruZYaI_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/A0riuruZYaI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b748194a393e0c1e1c2316d7c4b9a9991c329f6f
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/A0riuruZYaI_raw.srt
@@ -0,0 +1,2004 @@
+1
+00:00:05,740 --> 00:00:08,920
+بسم الله الرحمن الرحيم الجزء الثاني من المحاضرة
+
+2
+00:00:08,920 --> 00:00:14,780
+التاسعة هيكون اللي هو عبارة عن discussionأو مناقشة
+
+3
+00:00:14,780 --> 00:00:22,060
+لـ Section 6.2 و6.3 اللي هو مناقشة لـ Main Value
+
+4
+00:00:22,060 --> 00:00:25,220
+Theorem and its Applications ومناقشة أيضًا لـ
+
+5
+00:00:25,220 --> 00:00:30,560
+Lobitals Rules نيجي الآن لـ 6.2 الأسئلة المطلوبة
+
+6
+00:00:30,560 --> 00:00:35,720
+هي كما يلي نبدأ في سؤال 6.2 ادخلنا على الكتاب
+
+7
+00:00:35,720 --> 00:00:39,160
+خلينا نشوف ال .. ال .. ال .. المثال .. السؤال من
+
+8
+00:00:39,160 --> 00:00:45,790
+الكتاب نبدأ الآن بسؤال 5السؤال الخامسة هو كما يلي
+
+9
+00:00:45,790 --> 00:00:49,550
+let a أكبر من سفر و b أكبر من سفر و a strictly
+
+10
+00:00:49,550 --> 00:00:55,570
+أكبر من b طبعا كل العلاقة strictly وبنفترض أن n
+
+11
+00:00:55,570 --> 00:01:00,290
+أكبر أساوي اتنين prove that a أس واحدة لأ ناقص b
+
+12
+00:01:00,290 --> 00:01:05,290
+أس واحدة لأ ن أصغر من a minus b أس واحد عليا الان
+
+13
+00:01:05,290 --> 00:01:10,490
+لو جينا لاحظنا على اللي هو المطلوب عند خمسةبقولي
+
+14
+00:01:10,490 --> 00:01:16,710
+أن a أكبر من b أكبر من 0 أو n أكبر أو يساوي 2
+
+15
+00:01:16,710 --> 00:01:23,070
+بقولي prove that أن a أس واحد على n ناقص b أس واحد
+
+16
+00:01:23,070 --> 00:01:30,710
+على n أصغر من a ناقص b الكل أس واحد على n نيجي
+
+17
+00:01:30,710 --> 00:01:36,890
+للبرهان لو جينا لاحظناإنه عندي ال .. نيجي للسؤال
+
+18
+00:01:36,890 --> 00:01:40,770
+بس كيف نفكر في السؤال هو ماعطيني hint في الكتاب
+
+19
+00:01:40,770 --> 00:01:45,190
+لكن خلينا نشوف كيف .. كيف حصل على ال hint لو ادينا
+
+20
+00:01:45,190 --> 00:01:50,490
+جسمنا الجهتين هذا مش من ضمن الحل طبعا عندي a على b
+
+21
+00:01:51,290 --> 00:01:55,270
+الكل أس واحدة لأن ناقص جسمة على اللي هو بي أس
+
+22
+00:01:55,270 --> 00:01:59,510
+واحدة لأن الجهتين طبعا والبي طبعا موجبة ففيش إشي
+
+23
+00:01:59,510 --> 00:02:05,290
+بتغير بيصير a على بي ناقص واحد الكل أس واحدة لأن
+
+24
+00:02:05,290 --> 00:02:10,710
+لو نجلنا هذه a على بي أس واحدة لأن ناقص ال a على
+
+25
+00:02:10,710 --> 00:02:16,150
+بي ناقص واحد أس واحدة لأن أصغر من مين من واحد الان
+
+26
+00:02:16,700 --> 00:02:21,940
+عندي هذا الأن كله على بعض هو نفسه اللهان فممكن
+
+27
+00:02:21,940 --> 00:02:27,680
+نستقل الدالة من خلاله أنه ناخد ال F of X لت F of X
+
+28
+00:02:27,680 --> 00:02:35,690
+و هتوصلنا بساوي X أسواحة ده الأن ناقصx ناقص واحد
+
+29
+00:02:35,690 --> 00:02:42,810
+واس واحد علان وطبعا هو الان معطيني في السؤال a
+
+30
+00:02:42,810 --> 00:02:47,790
+أكبر من b أكبر من 0 لو طلعنا نلاقي الدالة هذه
+
+31
+00:02:47,790 --> 00:02:56,610
+ولاحظنا أوجدنا ال f prime لها f prime of xخلّينا
+
+32
+00:02:56,610 --> 00:03:02,130
+ناخد ال X عنده ال X أكبر أو يساوي واحد و هنشوف
+
+33
+00:03:02,130 --> 00:03:05,730
+اللي هو ليش عنده ال X أكبر أو يساوي واحد برضه
+
+34
+00:03:05,730 --> 00:03:09,070
+بتظبط في حالتنا لإن اللي بنينا على أساسها اللي هي
+
+35
+00:03:09,070 --> 00:03:13,290
+ال A على B نفسها أكبر strictly من مين من واحد
+
+36
+00:03:13,290 --> 00:03:17,150
+فالأمور متناسقة مع بعض و لو بدنا نطبق حللها جي جي
+
+37
+00:03:17,150 --> 00:03:20,670
+اللي هو تطبيق معقول اللي هنقف ال prime of X بساوي
+
+38
+00:03:20,670 --> 00:03:26,200
+واحد على N في X أسوا واحد على N ناقص واحد ناقصاللي
+
+39
+00:03:26,200 --> 00:03:30,720
+هو واحدة لان في x ناقص واحد واس واحدة لان ناقص
+
+40
+00:03:30,720 --> 00:03:36,520
+واحد ويسوى واحدة لان في x اس واحدة لان ناقص واحد
+
+41
+00:03:36,520 --> 00:03:44,840
+ناقص اللي هو x ناقص واحد اللي هو على واحدة لان
+
+42
+00:03:44,840 --> 00:03:50,460
+ناقص واحد الآن لو طلعنا للي عندي هذا
+
+43
+00:03:53,450 --> 00:03:56,930
+لو طلعنا للمقدار اللي عندي ال X أكبر أو يساوي إيش
+
+44
+00:03:56,930 --> 00:04:02,450
+واحد يعني الآن ال X أكبر يساوي واحد لذا لما عندي
+
+45
+00:04:02,450 --> 00:04:06,950
+الأس اللي هان أس إيش ماله بالسالب أو صفر على سوء
+
+46
+00:04:06,950 --> 00:04:10,130
+الظروف اللي هو بالسالب معناته اللي هو بده يصير
+
+47
+00:04:10,130 --> 00:04:16,070
+واحد على X الواحد على X عبارة عن كسر، مظبوط؟ الآن
+
+48
+00:04:16,070 --> 00:04:20,430
+بيصير عندي المقدار اللي عندي العلاقة بين هذا و هذا
+
+49
+00:04:20,940 --> 00:04:26,360
+x أكيد أكبر من x نقص واحد صح ولا لأ لكن لأن
+
+50
+00:04:26,360 --> 00:04:31,240
+مقلوبها هيصير ايش ماله هيصير أصغر فهيصير المقدار
+
+51
+00:04:31,240 --> 00:04:35,440
+هذا أصغر من هذا المقدار ماشي فبصير عندي المقدار
+
+52
+00:04:35,440 --> 00:04:40,180
+هذا كله على بعض أصغر من مين من سفر فالآن صارت عندي
+
+53
+00:04:40,180 --> 00:04:45,720
+f' أصغر strictly من مين من سفر إذا صار عندي إذا f
+
+54
+00:04:45,720 --> 00:04:47,160
+is strictly
+
+55
+00:04:50,230 --> 00:04:54,310
+Decreasing بدى استخدم الخاصية هذه مدام Strictly
+
+56
+00:04:54,310 --> 00:04:59,390
+Decreasing وانا عندى a أكبر من b هسينا عندى a على
+
+57
+00:04:59,390 --> 00:05:06,110
+b أكبر من واحد و ال b طبعا لا تسوى سفر اذا بما ان
+
+58
+00:05:06,110 --> 00:05:11,930
+F is strictly decreasing اذا F of a على b أكبر من
+
+59
+00:05:11,930 --> 00:05:18,440
+F of واحدأف of a على b دلتنا بيجيب العوض فوق بيصير
+
+60
+00:05:18,440 --> 00:05:26,380
+عندي اللي هو .. آسف أصغر عندي أف of a على b إيش
+
+61
+00:05:26,380 --> 00:05:30,920
+هتساويك؟ قولوا معايا اللي هو a على b أس واحد على n
+
+62
+00:05:30,920 --> 00:05:40,360
+ناقص a على b ناقص واحد وكل أس واحد على n هذا إيش
+
+63
+00:05:40,360 --> 00:05:45,310
+ماله؟ أصغر من مين؟من F of واحد F of واحد حسب لي F
+
+64
+00:05:45,310 --> 00:05:50,290
+of واحد هذه واحد وهذه سفر فبصير عبارة عن اصغر من
+
+65
+00:05:50,290 --> 00:05:53,350
+واحد طبعا هذه اللي هو بنعمل عملية عكسية للي
+
+66
+00:05:53,350 --> 00:05:57,530
+عملناها فوق فبصير عندى اضرب الجهتين في B أس واحدة
+
+67
+00:05:57,530 --> 00:06:04,260
+لان فبصير A أس واحدة لان ناقصA ناقص B أس واحد على
+
+68
+00:06:04,260 --> 00:06:10,940
+N أصغر من مين من B أس واحد على N ضربت كله في مين؟
+
+69
+00:06:10,940 --> 00:06:14,980
+في B أس واحد على N إن جلّي الأن بصير عندي A أس
+
+70
+00:06:14,980 --> 00:06:20,320
+واحد على N ناقص B أس واحد على N أصغر من A minus B
+
+71
+00:06:20,320 --> 00:06:26,530
+الكل أس واحد على Nوهو المطلوب وهذا اللي هو بدهيا
+
+72
+00:06:26,530 --> 00:06:32,150
+يلا إيه بعده؟ خلينا نيجي للسؤال اللي المطلوب الآخر
+
+73
+00:06:32,150 --> 00:06:38,570
+اللي هو use the mean value theorem سؤال 6 use the
+
+74
+00:06:38,570 --> 00:06:42,830
+mean value theorem to prove that sin x minus sin y
+
+75
+00:06:42,830 --> 00:06:47,070
+أصغر أو يسوى x minus y for all x, y in R هذا
+
+76
+00:06:47,070 --> 00:06:50,610
+السؤال حلنا زيه بالظبط اللي هو mean اللي هو ال
+
+77
+00:06:50,610 --> 00:06:52,070
+cosine، مظبوط؟
+
+78
+00:06:57,300 --> 00:07:03,320
+الان ماعرفش فيه داعي نحله ولا ان هو نفسي او مصور
+
+79
+00:07:03,320 --> 00:07:06,740
+عملناه
+
+80
+00:07:06,740 --> 00:07:12,000
+ولا لا اللي هي ال cosine عملناها بنفس الأسلوب ومش
+
+81
+00:07:12,000 --> 00:07:14,340
+هيختلف اللي هو الحل
+
+82
+00:07:22,460 --> 00:07:27,840
+أحلو ولا خلصت؟ الان عندي اللي هو سبعة use the mean
+
+83
+00:07:27,840 --> 00:07:32,580
+value theorem to prove that X-1 على X أصغر من X
+
+84
+00:07:32,580 --> 00:07:39,160
+أصغر من X واحد for X أكبر من واحد اللي هو عند ..
+
+85
+00:07:39,160 --> 00:07:45,440
+احنا حلينا واحد زاد X هذه الآن اللي هي عبارة عن
+
+86
+00:07:45,440 --> 00:07:51,040
+مين؟عن اللي هو ln LX الدلة اللي هي F of X بساوي ln
+
+87
+00:07:51,040 --> 00:07:56,440
+LX وبنستخدم ال mean value theorem وبنفس الأسلوب في
+
+88
+00:07:56,440 --> 00:08:00,540
+داعي نحله؟ خلّينا نحله، خلّينا نحله عشان بنصور
+
+89
+00:08:00,540 --> 00:08:12,360
+الآن سؤال سبعة الآن عندي بدأ أثبت أن ln LX أصغر من
+
+90
+00:08:12,360 --> 00:08:20,000
+X ناقص واحدو أكبر من x minus واحد عالميا على x
+
+91
+00:08:20,000 --> 00:08:26,400
+solution العالمين value theorem عالمين value
+
+92
+00:08:26,400 --> 00:08:29,960
+theorem نحله عالمين value theorem لأنه لسه ما
+
+93
+00:08:29,960 --> 00:08:35,980
+خدناش اللي هو Taylor's theorem مش
+
+94
+00:08:35,980 --> 00:08:39,340
+فاهم
+
+95
+00:08:39,340 --> 00:08:42,110
+عليكبينفع الحلقة باستخدام Taylor and X not
+
+96
+00:08:42,110 --> 00:08:44,690
+بيساومها يعني ال mainly طيب اه احنا .. احنا عشان
+
+97
+00:08:44,690 --> 00:08:48,850
+لسه ماخدناش Taylor's theorem بدنا نحلها على مين؟
+
+98
+00:08:48,850 --> 00:08:51,970
+على ال mean value theorem ليش؟ لأنه احنا لسه
+
+99
+00:08:51,970 --> 00:09:00,070
+ماخدناش Taylor's theorem طيب الان let F of X
+
+100
+00:09:00,070 --> 00:09:07,330
+بتساوي لين ال X؟ وعندي ال X أكبر من مين؟ أكبر أو
+
+101
+00:09:07,330 --> 00:09:11,800
+تساوي الواحد، ولا لأ؟عندي الـ x أكبر من 100 من 0
+
+102
+00:09:11,800 --> 00:09:14,940
+for
+
+103
+00:09:14,940 --> 00:09:23,100
+x أكبر من 0 مش عايز أني ماشي الحين نيجي اللي هو أن
+
+104
+00:09:23,100 --> 00:09:26,540
+نستخدم ال main value theorem continuous و claw و
+
+105
+00:09:26,540 --> 00:09:31,300
+differentiable وكل الأمور هذه أشملها متحققة إذا
+
+106
+00:09:31,300 --> 00:09:38,150
+there exist c element in a و bC عندي اللي هو
+
+107
+00:09:38,150 --> 00:09:42,290
+element معايا؟
+
+108
+00:09:42,290 --> 00:09:52,610
+طيب لأن let F of X بيساوي لن X و X أكبر من 0 وعندي
+
+109
+00:09:52,610 --> 00:09:57,430
+المطلوب في ال inequality اللي هي X أكبر من 1 يعني
+
+110
+00:09:57,430 --> 00:10:02,870
+X سنتمي إلى الواحد وما لا نهاية معايا؟ إذا there
+
+111
+00:10:02,870 --> 00:10:11,590
+exists Cلذن بدى اطبق الان we apply mean value
+
+112
+00:10:11,590 --> 00:10:18,570
+theorem on وين قول معايا on واحد و X there exists
+
+113
+00:10:18,570 --> 00:10:25,090
+C element واحد و X such that معايا such that اللي
+
+114
+00:10:25,090 --> 00:10:36,890
+هو F prime of C سوى F of X نقص F واحدعلى x ناقص
+
+115
+00:10:36,890 --> 00:10:48,110
+اياش ناقص واحد اه فالان عندي f of x جديش ويساوي لن
+
+116
+00:10:48,110 --> 00:10:56,450
+ال x ناقص لن الواحد جديش سفر على x ناقص واحد وهذا
+
+117
+00:10:56,450 --> 00:11:02,050
+مين هو f prime of c عبارة عن لن الواحد على c مظبوط
+
+118
+00:11:02,870 --> 00:11:06,570
+إذا صار عندى الآن بدأ أجيب لإن ال X أصغر من مين من
+
+119
+00:11:06,570 --> 00:11:12,270
+X ماينس واحد صار عندى إذا لإن ال X بساوي واحد على
+
+120
+00:11:12,270 --> 00:11:18,390
+C في X ماينس واحد واللي عند C أشمالة باخدها أنا
+
+121
+00:11:18,390 --> 00:11:23,050
+أكبر من واحد مدام أكبر من واحد إذا واحد على C اللي
+
+122
+00:11:23,050 --> 00:11:28,390
+هو أصغر من واحد مظبوط إذا هذا أكيد هذا أصغر من X
+
+123
+00:11:28,390 --> 00:11:35,440
+ماينس واحدمظبوط؟ لأن الواحد على الـC أشمالها عبارة
+
+124
+00:11:35,440 --> 00:11:43,990
+عن كسر الآن من جهة أخرى عندي اللي هو لن ال Xبساوي
+
+125
+00:11:43,990 --> 00:11:49,410
+واحد على C في X ناقص واحد لكن الـ X أنا C إيش
+
+126
+00:11:49,410 --> 00:11:54,190
+معناها بين الواحد والإكس يعني C أصغر من مين C أصغر
+
+127
+00:11:54,190 --> 00:11:59,430
+من X يعني الواحد على X اللي هو أصغر من مين الآن C
+
+128
+00:11:59,430 --> 00:12:05,890
+أصغر من X إذا واحد على C أكبر من واحد على X فبصير
+
+129
+00:12:05,890 --> 00:12:13,190
+عند هذا أكبرمن 1 على x في x minus 1 يعني بمعنى آخر
+
+130
+00:12:13,190 --> 00:12:18,230
+صار عند لن ال x اللي هو أكبر من x minus 1 على ال x
+
+131
+00:12:18,230 --> 00:12:21,550
+هي عند ال inequality التانية و هي عند ال
+
+132
+00:12:21,550 --> 00:12:26,690
+inequality الأولى من التنتين إذا لن ال x أشمله
+
+133
+00:12:26,690 --> 00:12:32,790
+أصغر من x minus 1 مظبوط اللي بعمله و أكبر من x
+
+134
+00:12:32,790 --> 00:12:41,190
+minus 1 عالميا على xوهو المطلوب إيش السؤال اللي
+
+135
+00:12:41,190 --> 00:12:49,550
+بعده؟ الآن سؤال تمانية Let F من A لعند B
+
+136
+00:13:11,390 --> 00:13:17,630
+سؤال تمانية let
+
+137
+00:13:17,630 --> 00:13:30,470
+f من a و b لعند r اشمل بي continuous او
+
+138
+00:13:30,470 --> 00:13:37,190
+differentiable on
+
+139
+00:13:37,190 --> 00:13:45,370
+meanon open interval a و b show
+
+140
+00:13:45,370 --> 00:13:51,730
+that if limit f prime of x عندي limit f prime of x
+
+141
+00:13:51,730 --> 00:14:01,630
+لما x تروح لل a بساوي a capital then اللي هي f
+
+142
+00:14:01,630 --> 00:14:11,990
+prime of aF prime of A exists and equals A
+
+143
+00:14:11,990 --> 00:14:21,750
+solution أو proof ماعطيني
+
+144
+00:14:21,750 --> 00:14:28,650
+F is differentiable على اللي هي الفترة من A وB أو
+
+145
+00:14:28,650 --> 00:14:33,350
+continuous طبعاً open أو continuous على close من A
+
+146
+00:14:34,120 --> 00:14:39,860
+وب عندي limit f prime of x معطينيها لما x تروح إلى
+
+147
+00:14:39,860 --> 00:14:50,180
+ال a ايش بساوي بساوي اللي هو a capital اطلع
+
+148
+00:14:50,180 --> 00:14:58,560
+لفوق الان عندي الان ال f prime of a تعريفهااللي هي
+
+149
+00:14:58,560 --> 00:15:04,600
+limit F of X ناقص F of A على X minus A لما X تروح
+
+150
+00:15:04,600 --> 00:15:09,940
+للـA ماشي الحال هذا اللي هو إذا كان ال limit had
+
+151
+00:15:09,940 --> 00:15:13,500
+exist إذا أثبتنا إن ال limit had exist بتكون ال F
+
+152
+00:15:13,500 --> 00:15:18,440
+prime of A أشمالها اللي هي exist ماشي الحال الآن
+
+153
+00:15:18,440 --> 00:15:21,200
+هو ماعطيني limit F prime of X لما X تروح لـA
+
+154
+00:15:21,200 --> 00:15:28,290
+أشمالها هي ال existواضح اه؟ لان بدي اطبق الـ Mean
+
+155
+00:15:28,290 --> 00:15:33,290
+Value Theorem لان في البداية على أي X وين في
+
+156
+00:15:33,290 --> 00:15:39,170
+الفترة A وB في الفترة A وB لو أخدنا X في ال A وB
+
+157
+00:15:39,170 --> 00:15:44,380
+بالـ Mean Value Theoremبين على الـ A و الـ X على
+
+158
+00:15:44,380 --> 00:15:47,920
+الفترة الـ A و الـ X there exists CX ما لها
+
+159
+00:15:47,920 --> 00:15:52,340
+between X and A such that F of X ناقص F of A بساوي
+
+160
+00:15:52,340 --> 00:15:57,240
+F prime C of X في X minus A هذه اللي هي تطبيق الـ
+
+161
+00:15:57,240 --> 00:16:02,860
+Mean Value Theorem على الفترة A و B and so و منه
+
+162
+00:16:02,860 --> 00:16:07,700
+اللي هي بنقول F prime C of X بساوي اللي هو F of X
+
+163
+00:16:07,700 --> 00:16:15,920
+ناقص F of A على X minus Aالان عندى
+
+164
+00:16:15,920 --> 00:16:22,520
+.. خلّينا نيجى ناخد هذه المنطقة اه عشان لسه بدات
+
+165
+00:16:22,520 --> 00:16:26,600
+بين F prime of A أشمالها موجودة بساوي limit ال F
+
+166
+00:16:26,600 --> 00:16:31,180
+prime CX لما X تروح لمين؟ لل A، ماشي الحال، هذه
+
+167
+00:16:31,180 --> 00:16:36,610
+الآن لو exist بتكون F prime of A أشمالها existالان
+
+168
+00:16:36,610 --> 00:16:40,510
+لاحظ احنا طبقنا اللى هى ال mean value theorem على
+
+169
+00:16:40,510 --> 00:16:46,910
+مين على الفترة من a لعند مين لعند x لجينا ال cx
+
+170
+00:16:46,910 --> 00:16:53,290
+وين موجودة بين ال a و ال x الان لما cx تروح لل a
+
+171
+00:16:53,290 --> 00:17:00,050
+اكيد ال x هتروح لمين لل a ماشي الحال طيب الان
+
+172
+00:17:00,050 --> 00:17:05,700
+بيصير عندىهو ماعطيني أصلا limit f prime of x لما x
+
+173
+00:17:05,700 --> 00:17:10,600
+تروح للإيه exist ماشي فبصير عندي لأن limit f prime
+
+174
+00:17:11,520 --> 00:17:17,760
+of CX لما ال X تروح لل A هي نفسها as X goes to A
+
+175
+00:17:17,760 --> 00:17:21,700
+CX وين هتروح لما X تروح لل A اتوماتيك CX هتروح لل
+
+176
+00:17:21,700 --> 00:17:26,480
+A فبصير عندى لقى limit F prime of CX لما X تروح لل
+
+177
+00:17:26,480 --> 00:17:29,880
+A هو نفس limit F prime of CX لما A CX تروح لل A
+
+178
+00:17:29,880 --> 00:17:34,580
+وهذا هو ماعطينى ايش اسمه ان existence هو ايه، اذا
+
+179
+00:17:34,580 --> 00:17:39,500
+صار هذا ال limitexist يعني هذا اللي هو اللي مساوي
+
+180
+00:17:39,500 --> 00:17:42,620
+لل limit هذا اللي بنين عليه إذا حيكون ال F prime
+
+181
+00:17:42,620 --> 00:17:46,920
+of A exist و برضه حيساوي مين؟ حيساوي إيه؟ اطلع على
+
+182
+00:17:46,920 --> 00:17:53,100
+لدك اللي بالك نخلص نعم لا اطلع على اللي بعده أيوة
+
+183
+00:17:53,100 --> 00:17:55,420
+السؤال اللي بعده
+
+184
+00:18:06,430 --> 00:18:13,030
+كبر هذا السؤال اللي سألتني عنه يا محمد
+
+185
+00:18:13,030 --> 00:18:18,450
+قبل هيك اطلعلي .. خليه بس اطلعلي على الكتاب على
+
+186
+00:18:18,450 --> 00:18:28,770
+628 النظرية 628 انزل انزل 628 اطلعلي عليها النظرية
+
+187
+00:18:28,770 --> 00:18:36,630
+عشان نقولك ايش هو السؤال علىلأنه مهم نعرف عن إيش،
+
+188
+00:18:36,630 --> 00:18:40,410
+الآن إذا بتتذكروا أخدنا اللي هو ال first
+
+189
+00:18:40,410 --> 00:18:45,390
+derivative test for extrema بتقول إذا كان لجينا
+
+190
+00:18:45,390 --> 00:18:47,870
+neighborhood Hannah subset من I such that F double
+
+191
+00:18:47,870 --> 00:18:51,950
+prime أكبر ساعة و سفر و X ال .. ال .. ال .. لو F
+
+192
+00:18:51,950 --> 00:18:54,350
+double prime أكبر ساعة و سفر مرة ع اليمين و مرة ع
+
+193
+00:18:54,350 --> 00:18:59,350
+اليسار إذا F has إيش مالها relative إيش مالها
+
+194
+00:18:59,350 --> 00:19:05,280
+maximum اللي هو اللي بتغير شرطهامن موجب إلى سالب
+
+195
+00:19:05,280 --> 00:19:09,260
+فبتكون عندي relative maximum، الآن هل العكس صحيح؟
+
+196
+00:19:09,260 --> 00:19:12,440
+يعني لو كان في عندنا relative maximum، هل شرط إنها
+
+197
+00:19:12,440 --> 00:19:17,950
+تغير إشارتها في اللي دا؟أطلع لفوق شوية عشان أورجيك
+
+198
+00:19:17,950 --> 00:19:21,170
+السؤال وين كان موجود هان remark the converse of
+
+199
+00:19:21,170 --> 00:19:25,410
+the first derivative test is not true مهم الكلام
+
+200
+00:19:25,410 --> 00:19:28,610
+هذا for example there exists a differentiable
+
+201
+00:19:28,610 --> 00:19:31,610
+function f من R لR with absolute minimum at x
+
+202
+00:19:31,610 --> 00:19:35,210
+بالساوية سفر but such that f prime takes on both
+
+203
+00:19:35,210 --> 00:19:39,110
+positive and negative values on both sides of اللي
+
+204
+00:19:39,110 --> 00:19:45,000
+هي x بتساوي عياش بساوية سفرماشي الحال إذا هذا الآن
+
+205
+00:19:45,000 --> 00:19:49,920
+هذا الحديث هو سؤالنا اللي عندنا اللي بدنا نحكي فيه
+
+206
+00:19:49,920 --> 00:19:52,880
+اللي هو exercise قداش تسعة ارجعلي على exercise
+
+207
+00:19:52,880 --> 00:19:56,560
+تسعة إذا ال exercise تسعة هو عبارة عن إيش يقول ليه
+
+208
+00:19:56,560 --> 00:20:00,280
+ان ال converts of this theorem need not to be true
+
+209
+00:20:00,280 --> 00:20:04,930
+in generalبالظبط ايش بيقول؟ بيقول لت F من R ل R بي
+
+210
+00:20:04,930 --> 00:20:08,910
+define by F of X بيساوة 2 X plus 4 زاد X plus 4
+
+211
+00:20:08,910 --> 00:20:12,770
+Sine 1 علي X For X لا تساوي سفر عند F of 0 ايش
+
+212
+00:20:12,770 --> 00:20:16,450
+بيساوي Zero إذا أنا معرفت دالة ال F بهذه الطريقة
+
+213
+00:20:16,450 --> 00:20:20,450
+بهذه لما X لا تساوي سفر وعند X بيساوي سفر عرفها F
+
+214
+00:20:20,450 --> 00:20:25,120
+of 0 بيساوي أيش؟ Zeroبقول لشهدات أول إشي F has an
+
+215
+00:20:25,120 --> 00:20:30,440
+absolute minimum when عند الـ 0 but that its
+
+216
+00:20:30,440 --> 00:20:34,820
+derivative has both positive and negative values
+
+217
+00:20:34,820 --> 00:20:40,280
+everywhere اللي هو إيش في neighborhood حوالين مين؟
+
+218
+00:20:40,280 --> 00:20:49,380
+حوالين الصفر واضحطيب، نشوف الآن، عملية فيه
+
+219
+00:20:49,380 --> 00:20:54,280
+absolute minimum مش صعبة، اللي هي بس خلينا نتطلع
+
+220
+00:20:54,280 --> 00:20:58,140
+على الحسابات، لإن الحسابات بتاخد وجه، فخلينا نتطلع
+
+221
+00:20:58,140 --> 00:21:02,900
+على اللي عندنا محسوبة وخالصلأن لأي x الينتن ار
+
+222
+00:21:02,900 --> 00:21:07,360
+اكيد ال x الاربعة ايه شماله اكبر ويساوي سفر وال
+
+223
+00:21:07,360 --> 00:21:11,900
+sign الواحد على x اكبير اكيد اكبر ويساوي مين ناقص
+
+224
+00:21:11,900 --> 00:21:16,300
+واحد اضرب الجهتين في x الاربعة فبصير x الاربعة في
+
+225
+00:21:16,300 --> 00:21:20,680
+هذا اكبر ويساوي ناقص ايش x الاربعة اضيف للجهتين
+
+226
+00:21:20,680 --> 00:21:26,110
+اتنين x الاربعةفبصير 2x أس 4 زائد هذا أكبر أو
+
+227
+00:21:26,110 --> 00:21:30,470
+يساوي اللي ضفت 2x أس 4 زائد اللي هو ياش ناقص اللي
+
+228
+00:21:30,470 --> 00:21:34,930
+هي x أس 4 اللي هو بيطلع جداش x أس 4 اللي هو أكيد
+
+229
+00:21:34,930 --> 00:21:39,270
+أكبر أو يساوي 0 صارت عند قيمة ال function f of x
+
+230
+00:21:39,270 --> 00:21:44,770
+اللي احنا بنحكي عنها دايما أكبر أو يساوي 0 اللي هو
+
+231
+00:21:44,770 --> 00:21:49,650
+مين بيساوي اللي عرفناه F0 إذا صار في عندي F has
+
+232
+00:21:49,650 --> 00:21:58,450
+absoluteminimum at mean at zero لكن عندي لطبيعة
+
+233
+00:21:58,450 --> 00:22:02,590
+الـ sine و طبيعة ال cosine لو جيت الآن أخدت أي
+
+234
+00:22:02,590 --> 00:22:06,990
+neighborhood حوالين ناقص delta و delta بدي أثبتلك
+
+235
+00:22:06,990 --> 00:22:12,410
+أن F prime مرة ممكن تسويلي أصغر من سفر و مرة تكون
+
+236
+00:22:12,410 --> 00:22:21,190
+أشمالها أكبر من سفر واضح؟ إذا تعالى شوفعندي خد لأي
+
+237
+00:22:21,190 --> 00:22:25,370
+neighborhood حوالين اللي هو الـ Zero خده من ناقص
+
+238
+00:22:25,370 --> 00:22:29,850
+Delta وDelta لأي Delta في الدنيا أو لأي أمثلون في
+
+239
+00:22:29,850 --> 00:22:34,450
+الدنيا عندي هي ال neighborhood اللي بحكي فيه
+
+240
+00:22:40,490 --> 00:22:45,390
+النقطة الداخلية اللي احنا مستهد فينا اللي هي الصفر
+
+241
+00:22:45,390 --> 00:22:51,500
+خد أي neighbor حواليه ناقص دلتا او ديلتابقدر ألادي
+
+242
+00:22:51,500 --> 00:22:58,220
+n اكبر او يساوي اتنين very large اللي
+
+243
+00:22:58,220 --> 00:23:04,540
+بيكون ان اشمالهن very close to zero ماشي يعني مهما
+
+244
+00:23:04,540 --> 00:23:09,300
+زغرتلي ال delta براجيلك n كبيرة كفاية انها تضلها
+
+245
+00:23:09,300 --> 00:23:18,320
+في هذا الجوار وتحقق ما يليه ايش أخدتها اخدت النقطة
+
+246
+00:23:18,320 --> 00:23:22,460
+واحد على اتنين and byطبعا الان هذا بزغرها جد ما
+
+247
+00:23:22,460 --> 00:23:28,120
+بده بتكبير الان و نفس الاشي 2 على 4 ان زاد واحد في
+
+248
+00:23:28,120 --> 00:23:30,780
+باقي طبعا ليش أخدت هيك عشان واحدة تخليلي ال sign
+
+249
+00:23:30,780 --> 00:23:34,620
+صفر و واحدة تخليلي ال cosine إيه عشان صفر واضح و
+
+250
+00:23:34,620 --> 00:23:37,580
+في نفس الوجه بتخليلي ال sign واحد و ال cosine واحد
+
+251
+00:23:37,580 --> 00:23:44,380
+بشكل معاكس ده فنشوف أشي اللي بقولهالان هذه الان و
+
+252
+00:23:44,380 --> 00:23:47,380
+هذه الان اخترت الان اللي تخليني إياها موجودة في
+
+253
+00:23:47,380 --> 00:23:51,060
+نقص delta و delta هذولا النقطين في وين في الجوار
+
+254
+00:23:51,060 --> 00:23:56,880
+اللي اعطيتني إياه أي جوار بتعطيني يا بدأ جيلك الان
+
+255
+00:23:56,880 --> 00:24:01,300
+المناسبة إليه احسبلي الان F prime F prime of X
+
+256
+00:24:01,300 --> 00:24:04,040
+بتعرف .. نعرف نحسبها خلينا نحسب F prime of X على
+
+257
+00:24:04,040 --> 00:24:08,580
+جهها لإنه مش هحسبها عشان تكون قدامكم F prime of X
+
+258
+00:24:10,740 --> 00:24:18,560
+أف برايم of x ايش بتساوي تمانية x تكعيب زائد أربعة
+
+259
+00:24:18,560 --> 00:24:28,300
+x تكعيب sign واحد على x ناقص اللي هو ليش
+
+260
+00:24:28,300 --> 00:24:34,800
+زائد ناقص x أصبح أربعة بيصير x تربيع sign واحد على
+
+261
+00:24:34,800 --> 00:24:41,650
+x صحيح؟هذه اليومين f prime of x بدّي الآن نعوض على
+
+262
+00:24:41,650 --> 00:24:47,310
+f عند النقطة أول إشي النقطة الأولى عبارة عن واحد
+
+263
+00:24:47,310 --> 00:24:52,450
+على اتنين and by عوضنا عنها في تمانية x سكعيب هي
+
+264
+00:24:52,450 --> 00:24:57,210
+تمانية في x سكعيب زاد أربعة هي x سكعيب وهي sin
+
+265
+00:24:57,210 --> 00:25:01,820
+واحد على x بيصير sin اتنين and byعشان هيك الاختيار
+
+266
+00:25:01,820 --> 00:25:05,020
+زائد واحد على اتنين and by أُس أربع اللي هي ..
+
+267
+00:25:05,020 --> 00:25:11,580
+اللي هي .. بحها دي بيصير أُس اتنين أه و هاي الناقص
+
+268
+00:25:11,580 --> 00:25:16,900
+فاهمين؟ X تربيع ها دي محادي اللي هي بيصير X تربيع
+
+269
+00:25:16,900 --> 00:25:23,800
+بالسالبواضح هه في cosine من اللي هو 2 unbi الان
+
+270
+00:25:23,800 --> 00:25:27,580
+هذا المقدار اللي في النص كله ايش حباله هيصير سفر
+
+271
+00:25:27,580 --> 00:25:32,160
+لأنه sin 2 unbi سفر هذا المقدار عبارة عن اللي هو
+
+272
+00:25:32,160 --> 00:25:34,860
+تمانية بتروح مع تمانية اللي هم يصير واحد على unbi
+
+273
+00:25:34,860 --> 00:25:39,880
+كل تكعيب هذا ال cosine ايش بيساوي واحد اذا بيظل من
+
+274
+00:25:39,880 --> 00:25:47,480
+عنده اللي هو هذا سالب تربيع ايه الانواخد 1 على
+
+275
+00:25:47,480 --> 00:25:52,120
+unbi عام المشترك تربيع بيظل عندى اللى هنا عبارة عن
+
+276
+00:25:52,120 --> 00:25:59,560
+اللى هى 4 unbi لأنه ماخد هنا اللى هى 1 على 2 unbi
+
+277
+00:25:59,560 --> 00:26:03,720
+لكل تربيع اللى هو عام المشترك بيظل 4 على unbi ناقص
+
+278
+00:26:03,720 --> 00:26:08,840
+ايه اش واحدواضح الاربع على n by لل n أكبر أو يساوى
+
+279
+00:26:08,840 --> 00:26:14,660
+2 أن هذا المقدار بصير يصغر لدرجة أنه أصغر من
+
+280
+00:26:14,660 --> 00:26:18,320
+الواحد لل n أكبر يساوى 2 إذا صار هذا المقدار عبارة
+
+281
+00:26:18,320 --> 00:26:22,460
+عن سالب في موجة بيطلع أصغر من 0 إذا F براين طلعت
+
+282
+00:26:22,460 --> 00:26:29,390
+أصغر من 0في نفس الوقت أف برايم ل 2 على كذا على 4n
+
+283
+00:26:29,390 --> 00:26:34,130
+زائد 1 في πاي أضربها أحسبها بيصير تمانية وعوض وعوض
+
+284
+00:26:34,130 --> 00:26:38,150
+وعوض الان مش ال sign اللي هتت cancel هتت cancel
+
+285
+00:26:38,150 --> 00:26:43,110
+مين ال cosine فهيطلع عندى هذا المقدار هيه وهيه هذا
+
+286
+00:26:43,110 --> 00:26:48,390
+المقدارالتنين المقدارين موجبات، إذا هيكون أكبر من
+
+287
+00:26:48,390 --> 00:26:53,510
+مين؟ من سفر، إذا في كل المنطقة، في كل المنطقة،
+
+288
+00:26:53,510 --> 00:26:58,050
+هتلاقي اللي هو جانب بعض، جانب بعض، مرة أكبر من
+
+289
+00:26:58,050 --> 00:27:00,530
+سفر، مرة أصغر من سفر، مرة أكبر من سفر، مرة أصغر من
+
+290
+00:27:00,530 --> 00:27:05,070
+سفر، ففيش عندك اللي هو تغير إشارتها من موجب إلى
+
+291
+00:27:05,070 --> 00:27:09,750
+سالب، لأ، هم جانب بعض، هذولة تنفج يا واحدة تنساشفي
+
+292
+00:27:09,750 --> 00:27:14,570
+جهة واحدة من الـ neighborhood مش على الجهتين هو ال
+
+293
+00:27:14,570 --> 00:27:18,270
+test اللي بنعرفه أشمل بيقولك لو اتغير من قبل ال ..
+
+294
+00:27:18,270 --> 00:27:21,690
+قبل .. في ال neighborhood قبل النقطة ال X note من
+
+295
+00:27:21,690 --> 00:27:26,990
+موجب إلى سالب بيصير maximum من سالب إلى موجب بيصير
+
+296
+00:27:26,990 --> 00:27:34,400
+موجب بيصير minimum الآنأحنا لجينا relative minimum
+
+297
+00:27:34,400 --> 00:27:38,800
+أو absolute minimum لكن في النقاط من ناقص ذلت
+
+298
+00:27:38,800 --> 00:27:44,180
+العين دلت هاين اختارتلك هنا وهنا جان بعض و جرب
+
+299
+00:27:44,180 --> 00:27:48,650
+كمان بلا جيلك كمان اللي هو بحيث انها تكون موجبةو
+
+300
+00:27:48,650 --> 00:27:53,050
+سالبة و موجبة و سالبة يعني فش derivative هنا تكون
+
+301
+00:27:53,050 --> 00:27:57,690
+موجبة كلها و هنا سالبة كلها عشان تحكم max .. تقول
+
+302
+00:27:57,690 --> 00:28:01,190
+اللي هو .. اللي هي ال .. و .. و .. و فقط اللي هي
+
+303
+00:28:01,190 --> 00:28:04,750
+ال converse in and the converse need not to be
+
+304
+00:28:04,750 --> 00:28:09,990
+true in general واضح؟ في الجوارين
+
+305
+00:28:09,990 --> 00:28:14,830
+.. هذا .. هذا من هنا .. من هنا لعين دلها فش إشارة
+
+306
+00:28:14,830 --> 00:28:19,040
+واحدة و من هنا لعين دلها فش إشارة واحدةإذا the
+
+307
+00:28:19,040 --> 00:28:22,320
+converse need not to be true in general واضح و
+
+308
+00:28:22,320 --> 00:28:30,400
+الله واضح و أعيد واضح يا محمد اه طيب اللي بعده
+
+309
+00:28:30,400 --> 00:28:34,120
+برضه في ال .. في ال .. في ال .. في المثال ارجعلي
+
+310
+00:28:34,120 --> 00:28:38,700
+للكتاب عشان أقولك هذا برضه بخدمين السؤال قبلها
+
+311
+00:28:38,700 --> 00:28:42,160
+انزل اطلع قبل النظرية قبل النظرية قبل النظرية في
+
+312
+00:28:42,160 --> 00:28:45,520
+عندي مثال هيو او لا .. ايو ال remark ال remark
+
+313
+00:28:45,520 --> 00:28:52,760
+أيوة اطلع ال remark هذهالان اذا بتتذكروا سؤال عشر
+
+314
+00:28:52,760 --> 00:28:55,260
+اللي بناحكيها الجد حكيها ان احنا قولنا it is
+
+315
+00:28:55,260 --> 00:28:59,420
+reasonable to define a function to be increasing
+
+316
+00:28:59,420 --> 00:29:04,170
+at a pointإذا كانت هناك مقارنة للمقارنة في
+
+317
+00:29:04,170 --> 00:29:13,750
+المقارنة اللي حوالها، إذا
+
+318
+00:29:13,750 --> 00:29:18,810
+كانت هناك مقارنة في المقارنة اللي حوالها، إذا كانت
+
+319
+00:29:18,810 --> 00:29:19,510
+هناك مقارنة في المقارنة اللي حوالها،
+
+320
+00:29:22,640 --> 00:29:27,460
+من الممكن أن يكون الـ derivative صحيح بشكل صحيح في
+
+321
+00:29:27,460 --> 00:29:35,840
+نقطة فالعمل يزيد في هذه النقطة ولكن هذا الوضع غير
+
+322
+00:29:35,840 --> 00:29:40,960
+صحيح يعني هذا الكلام إيش ماله ليس شرط انه صحيح انه
+
+323
+00:29:40,960 --> 00:29:44,500
+عندي اللي هنلاقي اللي هو الـ derivative صحيح بشكل
+
+324
+00:29:44,500 --> 00:29:49,220
+صحيح لكن مافيش .. ماقدرش نقول عنها إيش مالها is
+
+325
+00:29:49,220 --> 00:29:53,460
+increasing at this pointهذا في الـ Interval صحيح
+
+326
+00:29:53,460 --> 00:29:57,020
+لكن في الـ Point إيش ماله need not to be true in
+
+327
+00:29:57,020 --> 00:30:01,860
+general وهي مثال G of X هيه اللي هو بحيث انه G'
+
+328
+00:30:02,240 --> 00:30:07,940
+للـ 0 بساوي 1 لكن الـ G is not increasing in any
+
+329
+00:30:07,940 --> 00:30:14,260
+neighbourhood حوالين مين الصفر، هذا مثال على G' of
+
+330
+00:30:14,260 --> 00:30:20,200
+0 بساوي 1 اللي هو strictly أكبر من 0 butاللي هو في
+
+331
+00:30:20,200 --> 00:30:24,940
+هذا ال .. عند هذا النقطة اللي هو في الجوار تبعها
+
+332
+00:30:24,940 --> 00:30:30,260
+لا يمكن انها تكون اللي هي increasing في أي جوار
+
+333
+00:30:30,260 --> 00:30:35,610
+حواليهاهذا مثلنا يلّا خلّيني نحل السؤال الان هاي
+
+334
+00:30:35,610 --> 00:30:40,090
+سؤالنا let g من R لR be defined by g of X بيساوي X
+
+335
+00:30:40,090 --> 00:30:44,410
+زي 2 X ثانوية صين واحدة ل X for X تتساوي سفر and g
+
+336
+00:30:44,410 --> 00:30:47,550
+of 0 بيساوي 0 show that g prime of 0 ايش بيساوي
+
+337
+00:30:47,550 --> 00:30:53,030
+واحد but in every neighborhoodof zero, the
+
+338
+00:30:53,030 --> 00:30:57,430
+derivative g prime takes on both positive and
+
+339
+00:30:57,430 --> 00:31:01,710
+negative values. Thus, g is not monotonic in any
+
+340
+00:31:01,710 --> 00:31:05,830
+neighborhood. هنلاقي في المنطقة هذه، وين ما كان،
+
+341
+00:31:05,830 --> 00:31:13,210
+هنلاقي الـ g prime اللي هيأكبر من سفر وأصغر من سفر
+
+342
+00:31:13,210 --> 00:31:18,410
+يعني مش هنلاقي في أي neighborhood أن الـ G' أكبر
+
+343
+00:31:18,410 --> 00:31:25,410
+من سفر لحالها أو الـ G' للـ X هي أكبر من حالها أو
+
+344
+00:31:25,410 --> 00:31:33,910
+أصغر من حالها في كل .. من سفر في كل الجوارG' مش
+
+345
+00:31:33,910 --> 00:31:38,930
+هتكون أصغر من سفر في كل الجوار ولا أكبر من سفر في
+
+346
+00:31:38,930 --> 00:31:46,630
+كل الجوار هنلاقي إلها متذبذبة في الإشارة كيف؟
+
+347
+00:31:48,510 --> 00:31:54,930
+الحل شبهه صحيح الحل شبهه بس هذا الان موظف لمين لا
+
+348
+00:31:54,930 --> 00:31:58,990
+اللي هي اللي هو counter example على اللي هي ال
+
+349
+00:31:58,990 --> 00:32:02,630
+remark اللي عندنا وده counter example على اللي هي
+
+350
+00:32:02,630 --> 00:32:08,010
+النظرية هذك بوضح ان ال theorem need not to be true
+
+351
+00:32:08,010 --> 00:32:12,170
+in general وهنا اللي هو بوضح انه اللي هو ال
+
+352
+00:32:12,170 --> 00:32:18,000
+strictly increasing عند نقطةلأ .. لأ .. لأ .. لأ
+
+353
+00:32:18,000 --> 00:32:18,380
+.. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ ..
+
+354
+00:32:18,380 --> 00:32:18,540
+لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ
+
+355
+00:32:18,540 --> 00:32:19,120
+.. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ ..
+
+356
+00:32:19,120 --> 00:32:19,800
+لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ
+
+357
+00:32:19,800 --> 00:32:26,540
+.. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ
+
+358
+00:32:26,540 --> 00:32:29,660
+..
+
+359
+00:32:29,660 --> 00:32:31,300
+لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ
+
+360
+00:32:31,300 --> 00:32:31,300
+.. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ ..
+
+361
+00:32:31,300 --> 00:32:32,100
+لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ
+
+362
+00:32:32,100 --> 00:32:39,020
+.. لأ .. لأ
+
+363
+00:32:39,020 --> 00:32:46,020
+.. لأأيش بعمل قاعد بدي أحاول أثبت انه g prime of 0
+
+364
+00:32:46,020 --> 00:32:51,600
+اللي هو بيساوي واحد هاي التعريف هاي عنده y ساوي
+
+365
+00:32:51,600 --> 00:32:55,180
+جسمنا عليه بيصير واحد زاد اتنين limit x sin واحد
+
+366
+00:32:55,180 --> 00:33:00,380
+على x اللي هو هذا ايه شماله؟بساوة صفر لأن الـ
+
+367
+00:33:00,380 --> 00:33:03,720
+absolute value للـ X صين واحد على X أكبر بساوة صفر
+
+368
+00:33:03,720 --> 00:33:07,740
+و أصغر أو يساوي الـ absolute value للـ X اللي هو
+
+369
+00:33:07,740 --> 00:33:11,020
+by Sandwich theorem اللي هو ال limit هذا إيش بساوة
+
+370
+00:33:11,020 --> 00:33:15,040
+صفر إذا ال limit على بعض و كله إيش بساوة واحد إذا
+
+371
+00:33:15,040 --> 00:33:17,740
+D prime of zero بساوة واحد اطلع لفوق
+
+372
+00:33:20,460 --> 00:33:26,260
+عندي for x تتساوى 0 الـ g prime سهل أن انا اجدها
+
+373
+00:33:26,260 --> 00:33:30,300
+عبارة عن واحد زائد تفاضل قاعد اربع x sin واحد على
+
+374
+00:33:30,300 --> 00:33:34,080
+x ناقص اتنين cosine واحد على x لان بالظبط as above
+
+375
+00:33:34,080 --> 00:33:37,520
+for any neighborhood زي اللي حكينا قبل شوية for
+
+376
+00:33:37,520 --> 00:33:43,340
+any neighborhood ناقص دلتا ودلتا حول الصفر بقدر
+
+377
+00:33:43,340 --> 00:33:49,200
+الاقي اد اكبر سواء واحد بحيث انههذا وهذا يكون في
+
+378
+00:33:49,200 --> 00:33:54,160
+الجوار لكن جي برايم عند الأولى أصغر من سفر وجي
+
+379
+00:33:54,160 --> 00:33:58,480
+برايم عند الثانية أشمالها أكبر من سفر بحسابات
+
+380
+00:33:58,480 --> 00:34:01,580
+مشابهة أي سؤال؟
+
+381
+00:34:05,050 --> 00:34:09,570
+طيب نيجي لسؤال 12 سؤال 12 بيقول إذا كانت h of x
+
+382
+00:34:09,570 --> 00:34:13,590
+بيساوي 0 إذا كانت x أصغر من 0 و 1 إذا كانت x أكبر
+
+383
+00:34:13,590 --> 00:34:16,650
+بيساوي 0 prove that there does not exist a
+
+384
+00:34:16,650 --> 00:34:21,310
+function f من R لR such that f prime of x أشمالها
+
+385
+00:34:21,310 --> 00:34:26,190
+بيساوي h of x هذا حلنا زيه برضه اللي هو درابوكس
+
+386
+00:34:26,190 --> 00:34:29,270
+theorem using ايش درابوكس theorem ايش بنقول
+
+387
+00:34:29,270 --> 00:34:37,360
+suppose notمظبوط صبّق الان هي عند H of X هيهابقول
+
+388
+00:34:37,360 --> 00:34:42,920
+لأثبت أنه فيش ولا function F لو فضلناها بتطلع مين؟
+
+389
+00:34:42,920 --> 00:34:46,540
+H of X بدنا نفترض العكس، نفترض أنه في function
+
+390
+00:34:46,540 --> 00:34:51,260
+اسمها F بحيث أن F' إيش بتساوي H صارت H نفسها
+
+391
+00:34:51,260 --> 00:34:54,400
+differentiable، ماشي آسف، F إيش ما لا؟
+
+392
+00:34:54,400 --> 00:34:57,880
+differentiable، مظبوط؟ مدام F differentiable، إذا
+
+393
+00:34:57,880 --> 00:35:03,120
+by مين؟ By Daraboux's theorem اللي هو there existو
+
+394
+00:35:03,120 --> 00:35:07,640
+طبعا و احنا عارفين النص بين مين؟ بين الـ 0 و الـ 1
+
+395
+00:35:07,640 --> 00:35:12,880
+اذا by Daraboux's theorem there exist اللي هو ..
+
+396
+00:35:12,880 --> 00:35:19,840
+اللي هي C بين الـ X1 و X2 بحيث انه G of C بسوء أفه
+
+397
+00:35:19,840 --> 00:35:24,940
+prime of C و يسوى نص which is impossible أسرعت
+
+398
+00:35:24,940 --> 00:35:32,940
+عليكم، مظبوط؟ الآن يا جماعةبدي افترض ان العكس صحيح
+
+399
+00:35:32,940 --> 00:35:37,880
+يعني بدي افترض ان F من R ل R بحيث ان F prime of X
+
+400
+00:35:37,880 --> 00:35:42,740
+ايش بتساوي؟ X لكل X element in R ماشي الحال اتفجن
+
+401
+00:35:42,740 --> 00:35:47,840
+الهن اذا F نفسها بناء على هذا الحديث F is
+
+402
+00:35:47,840 --> 00:35:52,340
+differentiable على Rمن جهة أخرى أخرى لاحظ إن النص
+
+403
+00:35:52,340 --> 00:35:55,160
+بين الـ 0 والـ 1، مين هو الـ 0 والـ 1؟ الـ 0 والـ
+
+404
+00:35:55,160 --> 00:35:58,060
+1 هي قيم الـ function هذه اللي بحكي عنها، يعني الـ
+
+405
+00:35:58,060 --> 00:36:03,840
+0 والـ 1 هتكون الـ 0 عبارة عن أشوف X1 و الـ A1
+
+406
+00:36:03,840 --> 00:36:09,390
+أشوف X2، مين X1 و X2؟ اخترت الـ X1 أصغر من 0؟و X2
+
+407
+00:36:09,390 --> 00:36:13,690
+أكبر من 0 صار عند نقطين X1 و X2 واحد أصغر من 0
+
+408
+00:36:13,690 --> 00:36:18,030
+واحد أكبر من 0 يعني التمتين عملين لفترة إذا صار
+
+409
+00:36:18,030 --> 00:36:24,870
+عند نص في الفترة بين 0 و 1 اللي هو عبارة عن بين H
+
+410
+00:36:24,870 --> 00:36:31,520
+of X1 و H of X2 لكن H of X1 و H of X2 من هم؟F' of
+
+411
+00:36:31,520 --> 00:36:36,900
+X1 و F' of X2 إذا صارت اللي هي درابوكس theorem
+
+412
+00:36:36,900 --> 00:36:41,260
+محققة F is differentiable و نص تنتمي للفترة بيه
+
+413
+00:36:41,260 --> 00:36:47,340
+اللي هي F' of X1 و F' of X2 of X2 إذا حسب اللي هي
+
+414
+00:36:47,340 --> 00:36:51,340
+درابوكس theorem أي حاجة بينهم لازم يكون لها أصل
+
+415
+00:36:51,340 --> 00:36:57,190
+إذا there exists Cبين الـ x1 و الـ x2 بحيث أنه
+
+416
+00:36:57,190 --> 00:37:02,450
+اللي هو f prime للـ c هذه اللي اللي جاتها بين x1 و
+
+417
+00:37:02,450 --> 00:37:08,770
+x2 هي مين النص يعني زي بمسح كل القيم اللي بين f of
+
+418
+00:37:08,770 --> 00:37:13,080
+x1 و f of x2 مش هيك تدربت في تستيرون بتقولإذا صارت
+
+419
+00:37:13,080 --> 00:37:17,460
+عيدي في c بين هذه و هذه بحيث أن f prime of c بساوة
+
+420
+00:37:17,460 --> 00:37:21,480
+نص يعني g of c بساوة نص طب هذا مستحيل لأن اصلا g
+
+421
+00:37:21,480 --> 00:37:25,100
+.. h طبعا هذا مش g .. h of c .. هذا مستحيل ليش
+
+422
+00:37:25,100 --> 00:37:28,760
+مستحيل؟ لأن h أصلا ماتاخدش رقم تاني، يا سفر يا
+
+423
+00:37:28,760 --> 00:37:32,020
+واحد إذا contradiction، مدام contradiction إذا
+
+424
+00:37:32,020 --> 00:37:37,940
+there is no function f من R لR بحيث أن f prime of
+
+425
+00:37:37,940 --> 00:37:41,080
+x بساوة f of x for every x
+
+426
+00:37:45,230 --> 00:38:01,830
+في ضايق سؤالين خلنا نمر عليهم هذا
+
+427
+00:38:01,830 --> 00:38:06,130
+حلنا زيها اللي هو let I be an interval and let F
+
+428
+00:38:06,130 --> 00:38:11,110
+من I لR be differentiable on I مفترضين أن F عبارة
+
+429
+00:38:11,110 --> 00:38:16,000
+عن اللي هو differentiable function علىan interval
+
+430
+00:38:16,000 --> 00:38:19,820
+I وقول لي show that إذا كانت F prime is positive
+
+431
+00:38:19,820 --> 00:38:25,000
+on I لو F prime أكبر من 0 على I هتكون ال F أشمالها
+
+432
+00:38:25,000 --> 00:38:29,800
+strictly increasing on I طبعا اللي هو على السريع
+
+433
+00:38:29,800 --> 00:38:34,940
+لنفترض F prime أكبر من 0 لكل X element on I ماشي
+
+434
+00:38:34,940 --> 00:38:41,240
+هو نفسه؟ خلاص اللي بده السؤال موجود في الشريح اللي
+
+435
+00:38:41,240 --> 00:38:44,300
+هو ال main value theorem اتبكّل الله خليني أقوله
+
+436
+00:38:44,300 --> 00:38:50,490
+عنهالأن let I be an interval and let F من I لعند R
+
+437
+00:38:50,490 --> 00:38:55,050
+سواء الـ14 بيه differentiable on I show that if
+
+438
+00:38:55,050 --> 00:38:59,210
+the derivative F' is never zero on I يعني إذا كانت
+
+439
+00:38:59,210 --> 00:39:04,230
+F' أكبر من سفر اللي هي تسوى سفر on I then either
+
+440
+00:39:04,230 --> 00:39:08,430
+F' أكبر من سفر for all X limited on I أو F' أصغر
+
+441
+00:39:08,430 --> 00:39:13,480
+من سفر لكل XA جمالهايعني بيقولّي إذا كانت ال F
+
+442
+00:39:13,480 --> 00:39:17,760
+differentiable على ال interval I وكانت ال F'
+
+443
+00:39:18,160 --> 00:39:23,240
+بتسويش 0 في هذه الحالة ال F' يا هتكون كلها موجة
+
+444
+00:39:23,240 --> 00:39:28,940
+على ال I يا كلها سالب عالميا على ال I مدامت مغيرتش
+
+445
+00:39:28,940 --> 00:39:32,760
+شرطها بالمرة يعني بمعنى أخر يعني مش هتغير شرطها
+
+446
+00:39:32,760 --> 00:39:38,260
+بالمرة مدامت ال F' مش 0 على الفترة إذا إشارتها
+
+447
+00:39:38,260 --> 00:39:43,650
+واحدةيا F أكبر من 0، يا F أكبر من .. أصغر من 0،
+
+448
+00:39:43,650 --> 00:39:47,070
+هدا في ضوء أن F is differentiable، بدنا نفترض
+
+449
+00:39:47,070 --> 00:39:51,170
+العكس ونصل لcontradiction، suppose on the contrary
+
+450
+00:39:51,170 --> 00:39:56,290
+نفترض أن F prime of X أكبر من 0 لنقات .. لبعض
+
+451
+00:39:56,290 --> 00:40:00,390
+النقات في I، و F prime of X أكبر من .. أصغر من 0
+
+452
+00:40:00,390 --> 00:40:04,660
+لبعض النقات في I، يعني مخلوطةوبدّا نصلّمين ل
+
+453
+00:40:04,660 --> 00:40:08,640
+contradiction طيب then there exist a و b element
+
+454
+00:40:08,640 --> 00:40:12,220
+in I such that أف برايم of a أشماله أكبر من سفر و
+
+455
+00:40:12,220 --> 00:40:15,520
+أف برايم بي أصغر من سفر لإن أنا مفترض الآن افترضت
+
+456
+00:40:15,520 --> 00:40:18,200
+أنه في نقاط اللي هي أكبر من سفر عندها ال
+
+457
+00:40:18,200 --> 00:40:20,940
+derivative وفي نقاط أصغر من سفر عندها ال
+
+458
+00:40:20,940 --> 00:40:25,040
+derivative ماشي الحال إذا بنلاقي a و b بالحقق هذه
+
+459
+00:40:25,490 --> 00:40:28,710
+الان اكيد مدام هذا أكبر من صفر وهذا أصغر من صفر،
+
+460
+00:40:28,710 --> 00:40:32,910
+إذا الصفر بين الـF'A والـF'B لأنها واحدة موجة
+
+461
+00:40:32,910 --> 00:40:36,850
+بواحدة مين، مدام الصفر بينهم، إذا حسب Darabowski's
+
+462
+00:40:36,850 --> 00:40:40,990
+theorem، هي بتمسح كل المنطقة اللي بين الصور، لازم
+
+463
+00:40:40,990 --> 00:40:45,570
+كلها يكون اللي هي أصولإذن by Daraboux's theorem
+
+464
+00:40:45,570 --> 00:40:49,430
+there exists c element in I such that f prime of c
+
+465
+00:40:49,430 --> 00:40:52,970
+بيساوي سفر وهذا اللي هو بناقض الفرضية اللي احنا
+
+466
+00:40:52,970 --> 00:40:57,570
+فرضناها أن f prime لا تساوي سفر على كل ال I إذن f
+
+467
+00:40:57,570 --> 00:41:01,730
+prime لا تساوي سفر على كل ال I معناته و
+
+468
+00:41:01,730 --> 00:41:05,670
+differentiable طبعا معناته يا إما كلهن ال f prime
+
+469
+00:41:05,670 --> 00:41:11,950
+وجبات يا إما كلهن إيه شمالهن سالباتيعني يا
+
+470
+00:41:11,950 --> 00:41:15,710
+increasing strictly increasing يا strictly يا
+
+471
+00:41:15,710 --> 00:41:23,230
+شمالها decreasing مافيش أي تغيير للرسم والشعر طيب
+
+472
+00:41:23,230 --> 00:41:28,820
+نيجي لآخر السؤاللت I Be An Interval Prove That If
+
+473
+00:41:28,820 --> 00:41:32,980
+F Is Differentiable On I And The Derivative Of F'
+
+474
+00:41:33,300 --> 00:41:37,820
+Is Bounded On I، Then F Satisfies Lipschitz
+
+475
+00:41:37,820 --> 00:41:43,920
+Condition On I، ماشي الحل، بتقول لي، بتقوللي
+
+476
+00:41:43,920 --> 00:41:48,460
+السؤال ما يعني، Lipschitz Condition
+
+477
+00:41:53,580 --> 00:41:58,020
+خلّينا نشوف إيش اللي بنقوله إذا كانت F
+
+478
+00:41:58,020 --> 00:42:10,320
+differentiable on I و F' bounded on I اثبت إن F
+
+479
+00:42:10,320 --> 00:42:15,680
+satisfies Lipschitz conditions ماشي؟ إيش Lipschitz
+
+480
+00:42:15,680 --> 00:42:23,450
+condition؟ إنه there exists K أكبر من 0 such thatF
+
+481
+00:42:23,450 --> 00:42:30,130
+of X ناقص F of Y أصغر أو ساوي لبس اليود فيها ل X
+
+482
+00:42:30,130 --> 00:42:34,330
+minus Y في مين؟ في K اللي كنا نقول عنها على طول
+
+483
+00:42:34,330 --> 00:42:40,630
+هذي بتعطي إيش ما لها uniformly continuous لكل X و
+
+484
+00:42:40,630 --> 00:42:44,190
+Y لكل X و Y في الفترة اللي بنحكي عنها اللي بشت
+
+485
+00:42:44,190 --> 00:42:48,790
+condition إيش ما لها متحققةإذا الـ Absolute هذا
+
+486
+00:42:48,790 --> 00:42:54,670
+معناه اللي بش تسكندشه نيجي نحققها هذه نيجي نحقق
+
+487
+00:42:54,670 --> 00:42:55,710
+اللي هو
+
+488
+00:42:58,230 --> 00:43:02,930
+الـ Lipschitz condition لت x و y element in I بيه
+
+489
+00:43:02,930 --> 00:43:06,130
+such that x strictly أصغر من 100 من y
+
+490
+00:43:27,180 --> 00:43:30,960
+إذا منها ناخد ال absolute value للجهتين بتطلع عندي
+
+491
+00:43:30,960 --> 00:43:36,260
+اللي أماني واضح لكن F' is bounded مدان bounded F'
+
+492
+00:43:36,740 --> 00:43:41,940
+إذا there exist K بحيث أن F' of C أصغر سوى K لكل C
+
+493
+00:43:41,940 --> 00:43:47,550
+إيه شمالها من ضمن ال C اللي فوقأه لأن أف برايم is
+
+494
+00:43:47,550 --> 00:43:51,870
+bounded على كل ال I و هذه ال K بتنفع لكل مين لكل
+
+495
+00:43:51,870 --> 00:43:54,570
+ال C's اللي في ال I إذا صارت أف برايم في C أصغر أو
+
+496
+00:43:54,570 --> 00:43:58,270
+شويه K بنعود فوق بيصير أف of X ناقص أف of Y أصغر
+
+497
+00:43:58,270 --> 00:44:02,150
+أو شويه K في X minus Y و ال X و ال Y كانت نقش
+
+498
+00:44:02,150 --> 00:44:06,870
+مالهين arbitrary إذا صار هذه أصغر أو شويه K في X
+
+499
+00:44:06,870 --> 00:44:11,790
+minus Y ودخلت المتساوية لأن في حالة ال X بتساوي Y
+
+500
+00:44:11,790 --> 00:44:21,600
+اللي هو it is trivialtherefore I satisfy اللي هو
+
+501
+00:44:21,600 --> 00:44:25,820
+Lipschitz condition و الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0fe1e77efbcbf108e3fabf9108b97f46e2f98add
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_postprocess.srt
@@ -0,0 +1,1500 @@
+1
+00:00:04,910 --> 00:00:09,510
+بسم الله الرحمن الرحيم هذه المحاضرة الخامسة في
+
+2
+00:00:09,510 --> 00:00:15,630
+مساق تحليل حقيقه اتنين لطلبة كلية العلوم تخصص
+
+3
+00:00:15,630 --> 00:00:22,110
+رياضيات في الجامعة الإسلامية بغزا المحاضرة
+
+4
+00:00:22,110 --> 00:00:26,550
+اليوم هي جزئين الجزء الاول اللي هو عبارة عن
+
+5
+00:00:26,550 --> 00:00:31,350
+discussion لست واحد اللي هو مناقشة لموضوع اللي هو
+
+6
+00:00:31,350 --> 00:00:37,410
+derivative او الاشتقاءالجزء الثاني هنكمل اللي هو
+
+7
+00:00:37,410 --> 00:00:43,210
+الحديث عن 6.2 اللي هو الـ Mean Value Theorem أو
+
+8
+00:00:43,210 --> 00:00:47,730
+نظرية القيمة المتوسطة هناخذ بعض التطبيقات لنبدأ
+
+9
+00:00:47,730 --> 00:00:51,750
+الآن اللي هي بالأسئلة اللي احنا طلبناها منكم
+
+10
+00:00:51,750 --> 00:00:57,230
+تحلوها كواجب المرة الماضية أو التي قبلها وكانت
+
+11
+00:00:57,230 --> 00:01:01,210
+الأسئلة هي عبارة عن السؤال الرابع والسؤال السابع
+
+12
+00:01:02,000 --> 00:01:07,420
+والسؤال التاسع و السؤال تلتاشر بالنسبة للسؤال
+
+13
+00:01:07,420 --> 00:01:13,600
+الثالث اللي هو عبارة عن اللي هي برهان نظرية 613A
+
+14
+00:01:13,600 --> 00:01:19,200
+وB وهذه البرهين براهين سهلة اللي كانت ال F
+
+15
+00:01:19,200 --> 00:01:22,960
+differentiableالـ F differentiable والـ Alpha
+
+16
+00:01:22,960 --> 00:01:26,560
+عبارة عن constant بيعطينا الـ Alpha F برضه is
+
+17
+00:01:26,560 --> 00:01:30,200
+differentiable و لو كانت الـ F والـ G
+
+18
+00:01:30,200 --> 00:01:32,700
+differentiable بيعطينا الـ F زائد G is
+
+19
+00:01:32,700 --> 00:01:35,660
+differentiable و احنا برهننا حالة الضرب و حالة
+
+20
+00:01:35,660 --> 00:01:41,500
+القسمة و هدول حالات تعتبر سهلة مباشرة على التعريف
+
+21
+00:01:41,500 --> 00:01:45,900
+لذلك هنبدأ ان شاء الله في الحديث او في حل الأسئلة
+
+22
+00:01:45,900 --> 00:01:52,540
+على السؤال الرابع اللي هو ببول ماليعندي معطيني F
+
+23
+00:01:52,540 --> 00:02:01,760
+من R لـ R بي defined by F of X بساوي اللي هو X
+
+24
+00:02:01,760 --> 00:02:06,420
+تربيع إذا كانت X rational وبساوي سفر إذا كانت X
+
+25
+00:02:06,420 --> 00:02:09,700
+irrational اثبت إن الـ F الـ differential بالقدر X
+
+26
+00:02:09,700 --> 00:02:15,550
+بتساوي سفر أو جد اللي هي F prime of 0لاحظ أن الـ
+
+27
+00:02:15,550 --> 00:02:16,610
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+28
+00:02:16,610 --> 00:02:17,090
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+29
+00:02:17,090 --> 00:02:17,910
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+30
+00:02:17,910 --> 00:02:20,450
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+31
+00:02:20,450 --> 00:02:27,990
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+32
+00:02:27,990 --> 00:02:28,350
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+33
+00:02:28,350 --> 00:02:29,630
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+34
+00:02:29,630 --> 00:02:29,690
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+35
+00:02:29,690 --> 00:02:41,470
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+36
+00:02:41,470 --> 00:02:52,150
+الـ الـ الـFind this value a proof الآن عشان نوجد
+
+37
+00:02:52,150 --> 00:02:56,730
+اللي هي نثبت أن F prime of 0 موجودة خلّيني ألاحظ
+
+38
+00:02:56,730 --> 00:03:00,950
+مالي عند ال function اللي هي X تربيع لما X
+
+39
+00:03:00,950 --> 00:03:07,150
+rational و Zero لما Xاش is irrationalالان بدنا
+
+40
+00:03:07,150 --> 00:03:11,770
+نتوقع اول اشي اللي هو لانه هتلزمني جاي اللي بعدين
+
+41
+00:03:11,770 --> 00:03:15,890
+find this value بدنا نتوقع ايش قيمة اللي هو ال
+
+42
+00:03:15,890 --> 00:03:20,950
+derivative عند الصفر لاحظ انه اللي هو .. اللي ..
+
+43
+00:03:20,950 --> 00:03:25,630
+اللي لو بدنا نقول انه ال derivative ممكن تكون zero
+
+44
+00:03:25,630 --> 00:03:30,510
+كون ان off of x صفر او لو بدها تكون و ال
+
+45
+00:03:30,510 --> 00:03:36,560
+derivative هنا لو قولنا رفل 2xبدو يكون اللي هو لو
+
+46
+00:03:36,560 --> 00:03:40,820
+بدو يكون اللي عند الـ zero اللي هي F prime بدو في
+
+47
+00:03:40,820 --> 00:03:47,220
+النهاية تروح ل اللي هيكون برضه قريبة من انه نقول
+
+48
+00:03:47,220 --> 00:03:52,580
+او نأكد انها صفر عشان هي كالظن الغالب ان F prime
+
+49
+00:03:52,580 --> 00:03:58,660
+هتكون ايش صفر هذه مجرد تفكيرات الانبدي أثبت لك إنه
+
+50
+00:03:58,660 --> 00:04:03,080
+فعلًا هي الـ derivative بتساوي 0 كيف بدي أثبتها؟
+
+51
+00:04:03,080 --> 00:04:11,280
+بدي أثبت لك إنه الـ limit لـ F of X نقص F of 0 على
+
+52
+00:04:11,280 --> 00:04:17,600
+X minus 0 لما X تروح لـ 0 بتساوي 0 بدي أثبت لك
+
+53
+00:04:17,600 --> 00:04:24,240
+هيهاالان واضح ان X تقول الى الصفر X تقول الى الصفر
+
+54
+00:04:24,240 --> 00:04:29,200
+هتمر بال rational وال rational عشان هيك صعب ان انا
+
+55
+00:04:29,200 --> 00:04:32,600
+اتحدث عن اللي هو ايجاد ال derivative مباشرة من
+
+56
+00:04:32,600 --> 00:04:36,130
+الان او من ال two branches اللي عندىلا بقدر أخد من
+
+57
+00:04:36,130 --> 00:04:40,030
+اليمين ولا أخد من اليسار لإنه عندي من اليمين أو من
+
+58
+00:04:40,030 --> 00:04:44,130
+اليسار هيكون عندي اللي هو قابلت اللي هي الأعداد ال
+
+59
+00:04:44,130 --> 00:04:48,110
+rational لل rational فعشانك أسلم إشي إنه نستخدم
+
+60
+00:04:48,110 --> 00:04:52,650
+التعريف في إثبات هذا يعني الآن بدي أثبت هذا الكلام
+
+61
+00:04:53,270 --> 00:04:58,090
+كيف بدي أثبته؟ بدي أثبت ما يعني بدي أصل لكل إبسلون
+
+62
+00:04:58,090 --> 00:05:03,190
+أكبر من 0 بدلاج دلتا أكبر من 0 بدلاجية حاجيلك دلتا
+
+63
+00:05:03,190 --> 00:05:08,350
+بحيث أنه لما يكون ال absolute value ل F of X ناقص
+
+64
+00:05:08,350 --> 00:05:14,630
+F of Zero على X minus Zero يكون ناقص Zero طبعا
+
+65
+00:05:14,630 --> 00:05:19,790
+Zero هذي أصغر من إبسلون هذا متى؟ whenever
+
+66
+00:05:22,670 --> 00:05:28,470
+x-0 أكبر من 0 وأصغر من مين من دلتا هذا اللي بده
+
+67
+00:05:28,470 --> 00:05:33,150
+أصله أو هذا اللي بده أثبته خلّينا نشوف إذا خلّينا
+
+68
+00:05:33,150 --> 00:05:36,530
+نشوف كيف بدنا نوجده عشان أثبت إن ال limit هذا
+
+69
+00:05:36,530 --> 00:05:43,110
+بساوي 0 لاحظ القيمة اللي عندي أول إشي ال absolute
+
+70
+00:05:43,110 --> 00:05:50,530
+value of f of x ناقص f of 0 على x-0 إيش هتساوي؟
+
+71
+00:05:51,590 --> 00:05:57,390
+هتساوي اللي هو ال absolute value of of X عندى يا X
+
+72
+00:05:57,390 --> 00:06:01,070
+تربيع يمين يا سفر خلّينها زي ما هي أول إشي of of X
+
+73
+00:06:01,070 --> 00:06:06,010
+ناقص of of Zero اللي هو جداش بيساوي Zero لإنه of
+
+74
+00:06:06,010 --> 00:06:10,130
+of Zero بيساوي Zero لإنه Zero rational على إذن هذا
+
+75
+00:06:10,130 --> 00:06:16,230
+سفر على X ناقص سفر اللي هو X absolute value هذا
+
+76
+00:06:16,230 --> 00:06:22,790
+القيمة الآن لاحظ بتساوييا إما اللي هو x تربيع على
+
+77
+00:06:22,790 --> 00:06:30,750
+x absolute value في حالة x is rational أو بتساوي
+
+78
+00:06:30,750 --> 00:06:37,450
+اللي هو سفر في حالة x أشمالها is irrational لأن
+
+79
+00:06:37,450 --> 00:06:42,030
+مقيمة f of x يا x تربيع يا سفر حسب اللي هو كتبناه
+
+80
+00:06:42,030 --> 00:06:46,790
+حاليًاالآن هذا بالظبط هو عبارة عن الـ absolute
+
+81
+00:06:46,790 --> 00:06:57,590
+value لل X if X is rational Zero if X is
+
+82
+00:06:57,590 --> 00:07:03,950
+irrational الآن الصورة وضحت خلّينا نسمي هذا اللي
+
+83
+00:07:03,950 --> 00:07:09,900
+هو واحدالان حضرت عشان اصل للنهاية اللى هاني كاتبها
+
+84
+00:07:09,900 --> 00:07:13,800
+هنا واشوف ايش ال delta اللى بتطلع عندى الان بتدعي
+
+85
+00:07:13,800 --> 00:07:17,380
+مالي for every epsilon أكبر من سفر انا بقول there
+
+86
+00:07:17,380 --> 00:07:21,800
+exists delta هتساوي من ال epsilon هتجد تشوفوا ليش
+
+87
+00:07:21,800 --> 00:07:26,980
+there exists delta بساوي epsilon such that if x
+
+88
+00:07:26,980 --> 00:07:35,210
+minus 0 أكبر من سفره أصغر من delta thenهذا معناته
+
+89
+00:07:35,210 --> 00:07:37,870
+إيش أن أبسل يوت فيها ال X أكبر من صفر وأصغر من
+
+90
+00:07:37,870 --> 00:07:41,870
+مين؟ من دلتا إذا اخترت دلتا إيش بتساوي و هي اللي
+
+91
+00:07:41,870 --> 00:07:47,850
+هتخلص من الموضوع then اللي هو F of X نقص F of Zero
+
+92
+00:07:47,850 --> 00:07:50,970
+على
+
+93
+00:07:50,970 --> 00:07:57,790
+X minus Zero هو طبعا نقص الصفر اللي قلنا عنها ال
+
+94
+00:07:57,790 --> 00:08:01,520
+derivative المتوقع عليا هذه بالظبطاللي فوق هذا هو
+
+95
+00:08:01,520 --> 00:08:05,920
+اللي فوق طلع إيش عندي هذا بساوي هذا المقدار إذا
+
+96
+00:08:05,920 --> 00:08:09,760
+كانت X rational و 0 إذا كانت X irrational يعني
+
+97
+00:08:09,760 --> 00:08:15,400
+بمعنى أخر بساوي absolute value ل X if X is
+
+98
+00:08:15,400 --> 00:08:23,530
+rational و 0 if X is irrational in both casesاللي
+
+99
+00:08:23,530 --> 00:08:27,590
+هي إذا كان بساوي absolute value للـ X هيكون أصغر
+
+100
+00:08:27,590 --> 00:08:31,250
+من Delta اللي انا اخترتها أشملها Epsilon هيكون
+
+101
+00:08:31,250 --> 00:08:34,570
+أصغر من Epsilon و أيضا هذه متحققة لإن الـ Epsilon
+
+102
+00:08:34,570 --> 00:08:38,850
+دائما أشملها أكبر من 0 إذا اللي حصلته أنه لكل
+
+103
+00:08:38,850 --> 00:08:42,490
+Epsilon أكبر من 0 اللي جيت Delta لما يكون هذا أصغر
+
+104
+00:08:42,490 --> 00:08:47,130
+من Delta بيعطيني هذا أصغر من Epsilon وهذا يعني
+
+105
+00:08:47,130 --> 00:08:54,370
+hence limitهذا المقدار اللي هو f of x ناقص f of 0
+
+106
+00:08:54,370 --> 00:09:01,690
+على x minus 0 لما x تروح للصفر بساوية اللي هو
+
+107
+00:09:01,690 --> 00:09:12,870
+الصفر وهذا هو تعريف من ال f prime عند 0 that is f
+
+108
+00:09:12,870 --> 00:09:18,740
+prime at 0 بساوية 0 وفي نفس الواجب طبعا أثبتناالـ
+
+109
+00:09:18,740 --> 00:09:25,960
+existence للـ F prime عند الـ zero أي سؤال طيب
+
+110
+00:09:25,960 --> 00:09:30,840
+نيجي الآن نشوف السؤال الثاني خلّال السؤال الأربعة
+
+111
+00:09:30,840 --> 00:09:44,220
+نيجي لسؤال سبعة الان
+
+112
+00:09:44,220 --> 00:09:48,100
+سؤال سبعة اش اللي بقوله سؤال سبعةاللي بيقوله سؤال
+
+113
+00:09:48,100 --> 00:09:52,420
+سبعة مالي عندي
+
+114
+00:09:52,420 --> 00:09:55,740
+suppose
+
+115
+00:09:55,740 --> 00:09:59,320
+that F من R لR is differentiable at C يعني نفترض
+
+116
+00:09:59,320 --> 00:10:04,520
+أنه F قبل الاشتقاق عند Cونفترض ان f of c قيمة الـ
+
+117
+00:10:04,520 --> 00:10:07,920
+function عند c بساوة 0 لان بقول لشهدات ال absolute
+
+118
+00:10:07,920 --> 00:10:10,960
+value لل f of x اللي هي نسميها d of x is
+
+119
+00:10:10,960 --> 00:10:14,080
+differentiable at c if and only if a شمالها f
+
+120
+00:10:14,080 --> 00:10:21,740
+prime of c بتساوة 0 إذا ناخد لك f من R لعند R و
+
+121
+00:10:21,740 --> 00:10:30,810
+جايلك أن f prime عند c exist معطيكي إياهاأو ومعطيك
+
+122
+00:10:30,810 --> 00:10:37,390
+اللي هو f of c بتساوي سفر وبقول لي prove that أنه
+
+123
+00:10:37,390 --> 00:10:42,370
+g of x بساوي ال absolute value لل f of x is
+
+124
+00:10:42,370 --> 00:10:49,810
+differentiable at c if and only if f prime عند ال
+
+125
+00:10:49,810 --> 00:10:57,880
+c ايش بتساوي بساوي سفر، مظبوط؟ طيب شوفالان خلينا
+
+126
+00:10:57,880 --> 00:11:03,380
+افترض اول اشي ان f prime عند c ايش بتساوي سفر نقول
+
+127
+00:11:03,380 --> 00:11:09,320
+suppose proof suppose
+
+128
+00:11:09,320 --> 00:11:15,580
+suppose
+
+129
+00:11:15,580 --> 00:11:23,120
+that f prime at c بتساوي سفر ايش هذا بيعني ان then
+
+130
+00:11:23,120 --> 00:11:25,940
+limit
+
+131
+00:11:27,220 --> 00:11:36,680
+F of X ناقص F of C على X minus C لما X تروح للـ C
+
+132
+00:11:36,680 --> 00:11:40,240
+اللي هو بيساوي سفر لأن هذا تعريف مين F براين
+
+133
+00:11:40,240 --> 00:11:46,000
+بيساوي سفر و F of C إيش معطنية هو بيساوي سفر لأن
+
+134
+00:11:46,000 --> 00:11:53,260
+بيساوي limit F of X على X minus C لما X تروح لمين
+
+135
+00:11:53,260 --> 00:11:58,730
+للـ C مدامة ال limit هذه موجودةإذا ال limit من
+
+136
+00:11:58,730 --> 00:12:02,270
+اليمين وال limit من اليسار أيش برضه مالها موجودة
+
+137
+00:12:02,270 --> 00:12:06,710
+ماشي الحال انا الآن غرضي ان او اثبت ان g of x بسبب
+
+138
+00:12:06,710 --> 00:12:09,190
+absolute value of f of x أيش مالها is
+
+139
+00:12:09,190 --> 00:12:14,110
+differentiable at c ماشي الان ايش اللي بدي اثبته
+
+140
+00:12:14,110 --> 00:12:22,370
+بمعنى اخر بدي اثبتلك انه limitالـ G of X ناقص G of
+
+141
+00:12:22,370 --> 00:12:29,430
+C على X minus C لما X تروح للـ C exist باشي إذا
+
+142
+00:12:29,430 --> 00:12:31,930
+أثبتوا معناته أثبتتوا إن الـ G is differentiable
+
+143
+00:12:31,930 --> 00:12:36,970
+at C أو بمعنى آخر بالدثبت limit لـ absolute value
+
+144
+00:12:36,970 --> 00:12:42,660
+لل F of Xمدلة g of x ناقص ال absolute value of f
+
+145
+00:12:42,660 --> 00:12:48,960
+of c على x minus c لما x بتروح لل c exist بدي أشوف
+
+146
+00:12:48,960 --> 00:12:53,240
+هدا لسه exist ولا لأ يعني بدي أثبت اللي هو limit
+
+147
+00:12:53,240 --> 00:12:58,900
+absolute value of f of x على x minus c as x بتروح
+
+148
+00:12:58,900 --> 00:13:07,520
+لل c أشماله exist ماشي الحال طيب الآن واضح
+
+149
+00:13:08,360 --> 00:13:13,000
+عندي من اللي فوق ال limit لل f of x على x minus c
+
+150
+00:13:13,000 --> 00:13:19,160
+as x بتروح لل c انه ايش بيساوي بيساوي صفر، مظبوط؟
+
+151
+00:13:19,160 --> 00:13:27,160
+اذا هيكون عندي limit اللي هو limit absolute value
+
+152
+00:13:27,160 --> 00:13:33,400
+لل limit خليني اكتبها بس في طريقة أخرى الصفر هذا
+
+153
+00:13:33,400 --> 00:13:43,200
+اللي بدأتبته اه انه existعندي ال absolute value ل
+
+154
+00:13:43,200 --> 00:13:52,020
+limit f of x على x minus c لما x تروح لل c اللي هو
+
+155
+00:13:52,020 --> 00:13:58,020
+من اليمين و من اليسار exist، مظبوط؟ واضحة و يساوي
+
+156
+00:13:58,020 --> 00:14:05,160
+اللي هو limit absolute value لل f of x على x minus
+
+157
+00:14:05,160 --> 00:14:12,420
+c as absolute valueas X بتروح لمين؟ للـ C باشي
+
+158
+00:14:12,420 --> 00:14:16,820
+الحال الآن من اليمين ومن اليسار كله هيكون موجود
+
+159
+00:14:16,820 --> 00:14:20,480
+بناء على هذا أنه موجود خلّيني أخد من اليمين وهنا
+
+160
+00:14:20,480 --> 00:14:25,860
+من اليمين فبصير هذا عبارة عن limit absolute value
+
+161
+00:14:25,860 --> 00:14:32,140
+ل F of X على X minus C لما X بتروح ل C من وين؟ من
+
+162
+00:14:32,140 --> 00:14:38,330
+اليمين يعني هذا المقدارصار موجود وإيش بساوي بساوي
+
+163
+00:14:38,330 --> 00:14:42,350
+سفر هذا خلّيه لإنه هذا اللي بدنا نصلّه لأن limit
+
+164
+00:14:42,350 --> 00:14:47,310
+صار عندي معنى آخر limit absolute value of f of x
+
+165
+00:14:47,310 --> 00:14:53,850
+على x minus c لما x تروح لل c من اليمين بساوي سفر
+
+166
+00:14:53,850 --> 00:14:58,360
+existلاحظا قاعد رايح لأثبت أن هذا exist ده خد الآن
+
+167
+00:14:58,360 --> 00:15:03,520
+من وين؟ من اليسار خد لأن احسب similarly عندي سفر
+
+168
+00:15:03,520 --> 00:15:08,840
+بساوي absolute value of limit f of x على x minus c
+
+169
+00:15:08,840 --> 00:15:15,100
+لما x تروح ل c من وين؟ من اليسار ويساوي عبارة عن
+
+170
+00:15:15,100 --> 00:15:19,960
+limit absolute value of f of x على absolute value
+
+171
+00:15:19,960 --> 00:15:25,900
+of x minus c لما x تروح ل c من وين؟ من اليسارهذه
+
+172
+00:15:25,900 --> 00:15:34,580
+نفسها بساوي limit أو بساوي سالب limit f of x
+
+173
+00:15:34,580 --> 00:15:42,270
+absolute value على x minus c لما x تروحللـ C من
+
+174
+00:15:42,270 --> 00:15:47,030
+اليسار، ليش؟ لأن X أصغر من C، إذا X minus C سالبة
+
+175
+00:15:47,030 --> 00:15:50,230
+إذا الـ absolute value سالب إليها واخدت السالب برا
+
+176
+00:15:50,230 --> 00:15:54,990
+هذا الآن المخضر بيساوي سفر، إذا هذا لحاله برضه إيش
+
+177
+00:15:54,990 --> 00:16:01,270
+ماله؟ سفر، إذا limit absolute value للـ F of X على
+
+178
+00:16:01,270 --> 00:16:04,870
+X minus C، لما X تروح للـ C من اليسار، برضه إيش
+
+179
+00:16:04,870 --> 00:16:10,450
+بيساوي؟ بيساوي سفر، لاحظ إن ال limit من اليمينوالـ
+
+180
+00:16:10,450 --> 00:16:15,890
+limit من اليسار موجود وبساوي 0 متساويين يعني الآن
+
+181
+00:16:15,890 --> 00:16:23,130
+ال limit هذا صار ايش بساوي بساوي 0 إذا الان هذا
+
+182
+00:16:23,130 --> 00:16:29,870
+الآن بنقوله كله تحت هذا وبقول hence اللي هو g
+
+183
+00:16:29,870 --> 00:16:38,310
+prime of c بساوي limit of g of x نقص g of c على x
+
+184
+00:16:38,310 --> 00:16:46,870
+minus cas x → c بساوي حسب اللي عندى من هنا و من
+
+185
+00:16:46,870 --> 00:16:55,310
+هنا و من هنا هيساوي سفر الان conversely بتأفترض
+
+186
+00:16:55,310 --> 00:16:58,090
+طبعا ان ال conversely هيكون الخطوات كثير مشابهه
+
+187
+00:16:58,090 --> 00:17:03,350
+لللي هنا يعني كثير اللي استخدمته هنا هستخدمه في
+
+188
+00:17:03,350 --> 00:17:03,930
+اللي بعدها
+
+189
+00:17:12,670 --> 00:17:17,790
+Conversely suppose that
+
+190
+00:17:17,790 --> 00:17:25,890
+g of x سواء absolute value او f of x اللي
+
+191
+00:17:25,890 --> 00:17:33,550
+هو is differentiable at c بدا وجدلك الان اثبتلك ان
+
+192
+00:17:33,550 --> 00:17:39,650
+f prime of c ايش ما لها بتساوي سفر يعني بدا اثبت
+
+193
+00:17:39,650 --> 00:17:46,880
+limitf of x ناقص f of c اللي هي سفر على x minus c
+
+194
+00:17:46,880 --> 00:17:51,160
+لما x تروح لل c ايش بيساوي بساوي سفر بكون خلصت
+
+195
+00:17:51,160 --> 00:17:58,500
+الان issue مشابه عند الان limit
+
+196
+00:17:58,500 --> 00:18:05,180
+هذا exist عند ال c اذا عندي صار g prime of c exist
+
+197
+00:18:05,180 --> 00:18:10,430
+ويساوي حسب الحديث اللي هنا limitabsolute value of
+
+198
+00:18:10,430 --> 00:18:18,570
+f of x ناقص ال absolute value of f of c صفر على x
+
+199
+00:18:18,570 --> 00:18:26,310
+minus c لما x تروح ل c اشماله exist معايا؟ طيب شوف
+
+200
+00:18:26,310 --> 00:18:34,960
+الآن عندى اذا احسبلي limitf of x اللي حسبناها قبل
+
+201
+00:18:34,960 --> 00:18:39,660
+بشوية بنفس الأسلوب على x minus c لما x تروح ل c من
+
+202
+00:18:39,660 --> 00:18:47,020
+وين؟ من اليمين بساوي limit لل absolute value ل f
+
+203
+00:18:47,020 --> 00:18:53,780
+of x على x minus c لما x تروح ل c من اليمين لأن ال
+
+204
+00:18:53,780 --> 00:19:01,840
+x أكبر من ال c واضحالآن من جهة أخرى احسبلي الـ
+
+205
+00:19:01,840 --> 00:19:08,060
+absolute value لل limit لل F of X طبعا هذا ايش
+
+206
+00:19:08,060 --> 00:19:15,620
+هيساوي بسوى G prime of C، مظبوط؟ بسوى G prime of
+
+207
+00:19:15,620 --> 00:19:23,290
+C، موجود، limit F of Xعلى x minus c لما x تروح ل c
+
+208
+00:19:23,290 --> 00:19:28,570
+من وين؟ من اليسار بساوي زي ما عملنا قبل شوية سالب
+
+209
+00:19:28,570 --> 00:19:33,530
+limit absolute value of f of x على x minus c لما x
+
+210
+00:19:33,530 --> 00:19:41,050
+تروح ل c من وين؟ من اليسار الآن واضح بما أن هذه
+
+211
+00:19:41,050 --> 00:19:51,470
+exist إذا هذا المقدار و هذا المقدار زي بعضالان هذا
+
+212
+00:19:51,470 --> 00:19:56,590
+بيساوي ناقص هذا او بمعنى اخر نشيل الناقص من هنا و
+
+213
+00:19:56,590 --> 00:20:03,390
+نضربه هنا صار عندى المقدرين هدولة بما انه متساويين
+
+214
+00:20:03,390 --> 00:20:10,310
+لإن الاتنين ايش بيساوين ال G prime of C مظبوط اذا
+
+215
+00:20:10,310 --> 00:20:13,390
+صار عندى هذا المقدار بيساوي هذا المقدار اذا صار
+
+216
+00:20:13,390 --> 00:20:20,940
+عندى ال limitF of X على X minus C لما X تروح للـ C
+
+217
+00:20:20,940 --> 00:20:29,560
+من اليمين absolute value بساوي ناقص limit F of X
+
+218
+00:20:29,560 --> 00:20:34,600
+على X minus C لما X تروح للـ C من وين؟ من اليسار
+
+219
+00:20:34,600 --> 00:20:41,500
+واضحة؟ لكن أصلا عندى هذا
+
+220
+00:20:43,370 --> 00:20:49,010
+بساوي اللي هو التنين بساوي نفس القيمة ماشي الحال
+
+221
+00:20:49,010 --> 00:20:55,850
+إذا لازم عندي من هنا جي برايم و جي برايم اللي هو
+
+222
+00:20:55,850 --> 00:21:00,210
+صار بنساوي نفس القيمة إذا هيطلع الجي برايم إيش
+
+223
+00:21:00,210 --> 00:21:05,530
+ماله بساوي سفرإذا صار المقدار هذا كله إش بده يساوي
+
+224
+00:21:05,530 --> 00:21:08,650
+صفر وهذا بيساوي صفر يعني ال limit من اليمين و
+
+225
+00:21:08,650 --> 00:21:12,070
+limit من اليسار متساويين إذا صارت limit F of X على
+
+226
+00:21:12,070 --> 00:21:23,310
+X minus C لما X تروح للـC بدها تساوي صفر أي سؤال؟
+
+227
+00:21:23,310 --> 00:21:31,130
+زي ما حكينا، الآن إحنا قلنا إنه لو كانت D بدينا D
+
+228
+00:21:31,130 --> 00:21:34,600
+بيساوي F of X ال differential بالأد Cجيبنا g prime
+
+229
+00:21:34,600 --> 00:21:37,500
+و كتبناها بالصورة اللي أمامنا بعدين أخدنا ال
+
+230
+00:21:37,500 --> 00:21:40,120
+absolute value لlimit f of x علي x minus c لم x
+
+231
+00:21:40,120 --> 00:21:45,200
+تروح ل c positive طلعت عندي بساوي g prime of c و
+
+232
+00:21:45,200 --> 00:21:48,680
+أخدنا اللي هي ناقص هذه طلعت عندي برضه g prime
+
+233
+00:21:48,680 --> 00:21:53,920
+الاتنين ال c إذا صار هذا بساوي هذا المقدار و احنا
+
+234
+00:21:53,920 --> 00:21:57,640
+بنعرف في الأصل ان f prime of c exist يعني
+
+235
+00:21:57,640 --> 00:22:01,900
+differentiable يعني ال limit هذا اللي هو موجودو من
+
+236
+00:22:01,900 --> 00:22:05,100
+اليمين و من اليسار زي بعض يعني يعني هذا بده يساوي
+
+237
+00:22:05,100 --> 00:22:07,500
+هذا من اليمين و هذا من اليسار يعني في الواقع هذا
+
+238
+00:22:07,500 --> 00:22:10,960
+اللي جوا هو نفسه اللي جوا بساوي limit of of X يعني
+
+239
+00:22:10,960 --> 00:22:15,780
+بمعنى أخر absolute value ل limit of of X على X
+
+240
+00:22:15,780 --> 00:22:22,100
+minus C لما X تروح لل C هو نفسه سالب limit لل of
+
+241
+00:22:22,100 --> 00:22:27,400
+of X على X minus C لما X تروح لل C من وين من
+
+242
+00:22:27,400 --> 00:22:31,540
+اليسار هو نفسه لل C من وين تبت هذالأنه احنا بنقول
+
+243
+00:22:31,540 --> 00:22:34,560
+f prime of c exist يعني ال limit هذا موجود و من
+
+244
+00:22:34,560 --> 00:22:37,360
+اليمين و من اليسار زي بعر إذا صار هذا المقدر نفس
+
+245
+00:22:37,360 --> 00:22:41,200
+هذا المقدر زي ما قلنا إذا صار عند هذا المقدر بساوة
+
+246
+00:22:41,200 --> 00:22:46,800
+سفر لإن التنين بسينا بساوة سفر إذا صار عنده limitF
+
+247
+00:22:46,800 --> 00:22:50,880
+of X على X minus C اللي هو الـ absolute value as X
+
+248
+00:22:50,880 --> 00:22:56,100
+بتروح للـ C بساوة صفر ومن ثم اللي جوا بساوة صفر هو
+
+249
+00:22:56,100 --> 00:22:58,740
+مين هو اللي جوا هذا اللي كنا بدنا نصله من الأول
+
+250
+00:22:58,740 --> 00:23:04,260
+اللي هو F prime of C بتساوة صفر وهو المطلوب هذا
+
+251
+00:23:04,260 --> 00:23:10,300
+توضيح بشكل كامل ل اللي صار في اللي هو الاتجاه
+
+252
+00:23:10,300 --> 00:23:16,200
+الثاني نيجينا سؤال بعد ما خلصنا السؤال سبعةنجي
+
+253
+00:23:16,200 --> 00:23:23,420
+لسؤال تسعة تسعة ايش اللي بقوله تسعة نشوف ايش سؤال
+
+254
+00:23:23,420 --> 00:23:31,360
+تسعة بقول ونحل سؤال تسعة سؤال تسعة بقول ليه
+
+255
+00:23:31,360 --> 00:23:39,110
+باختصار انه لو كان عنده ال function ofعبارة عن من
+
+256
+00:23:39,110 --> 00:23:43,130
+R لـ R even function طبعا عارفين ايش ال even اللي
+
+257
+00:23:43,130 --> 00:23:49,130
+هو F ناقص X بيساوي F X لكل X موجودة في الـ R and
+
+258
+00:23:49,130 --> 00:23:54,310
+has a derivative at every point then F prime is an
+
+259
+00:23:54,310 --> 00:23:58,190
+odd function يعني بيقول لي لو كانت باختصار يعني لو
+
+260
+00:23:58,190 --> 00:24:01,730
+كانت ال F even و ال derivative موجودة بتكون ال
+
+261
+00:24:01,730 --> 00:24:07,010
+derivative odd و لو كانت ال derivative oddبتكون
+
+262
+00:24:07,010 --> 00:24:11,350
+الـ function الـ G prime إيه شمالها is even انحل
+
+263
+00:24:11,350 --> 00:24:16,970
+واحدة من هنا والتانية similarly زيها الآن لنفترض F
+
+264
+00:24:16,970 --> 00:24:29,890
+من عند R لعند R be an odd differentiable function
+
+265
+00:24:29,890 --> 00:24:34,970
+ماشي الحال show that
+
+266
+00:24:36,040 --> 00:24:44,360
+F' is even a proof بدنا نثبت أنه لو كانت الـ F
+
+267
+00:24:44,360 --> 00:24:49,940
+اللي هي odd function بدو يكون عنده و
+
+268
+00:24:49,940 --> 00:24:52,320
+differentiable بدو يكون عنده derivative إلها إيه
+
+269
+00:24:52,320 --> 00:25:03,000
+إيش even لأن let C element in R be arbitrary and
+
+270
+00:25:03,000 --> 00:25:04,180
+fixed
+
+271
+00:25:06,310 --> 00:25:15,930
+NR ناخد الـ R ناخد الـ C أي اللي هو real number in
+
+272
+00:25:15,930 --> 00:25:23,360
+R لكن نحكي عن اي شي محدد الان F prime of Cبدأ
+
+273
+00:25:23,360 --> 00:25:29,060
+أثبتلك أنه هو بسوء F prime of ناقص C يعني F prime
+
+274
+00:25:29,060 --> 00:25:34,920
+is even إذا خد F prime ناقص C وابدأ حسب وواصلك في
+
+275
+00:25:34,920 --> 00:25:39,140
+النهاية بسوء F prime of C إذا F prime is even بسوء
+
+276
+00:25:39,140 --> 00:25:49,380
+limit اللي هي F of X ناقص F of minus C على X minus
+
+277
+00:25:50,570 --> 00:25:57,070
+اللي هو minus C لما X تروح لمين لـ minus C مظبوط
+
+278
+00:25:57,070 --> 00:26:05,550
+طيب و يساوي limit ال F إيش معتنيها عبارة عن odd
+
+279
+00:26:05,550 --> 00:26:12,250
+إيش يعني odd يعني F of ناقص X بيساوي ناقص F of X
+
+280
+00:26:12,250 --> 00:26:16,590
+مظبوط هذه اللي هي إيش ما لها odd function اللي هو
+
+281
+00:26:16,590 --> 00:26:28,550
+بيساوي limit F ofالان اللي هي ناقص f of ناقص x
+
+282
+00:26:28,550 --> 00:26:34,150
+واضح أه؟
+
+283
+00:26:34,150 --> 00:26:37,150
+f of ناقص x بيساوي ناقص f of x يعني f of x بيساوي
+
+284
+00:26:37,150 --> 00:26:41,230
+ناقص f of ناقص x فالجد تعرفوا ليش بعملت هيك لأن
+
+285
+00:26:41,230 --> 00:26:48,570
+ناقص f of ناقص c الان f is odd مظبوط بيصير زائد f
+
+286
+00:26:48,570 --> 00:26:49,330
+of c
+
+287
+00:26:52,220 --> 00:26:58,060
+على خد الان ناقص من هنا عامل مشترك بيصير عبارة عن
+
+288
+00:26:58,060 --> 00:27:08,220
+ناقص X الان ناقص ال C لما X تروح لمين لسالب ال C
+
+289
+00:27:08,220 --> 00:27:14,040
+ال X بتروح لسالب ال C إذا و فقط إذا سالب ال X
+
+290
+00:27:14,040 --> 00:27:22,160
+بتروح لمين إلى ال C الان خد لي Yبساوي سالب ال X
+
+291
+00:27:22,160 --> 00:27:29,240
+واستبدل عشان نضح لك إياه بساوي limit الان خد الان
+
+292
+00:27:29,240 --> 00:27:38,320
+عندي F حكما كان نقص اكسميا ال Y limit ناقص F of Y
+
+293
+00:27:38,320 --> 00:27:49,390
+زائد F of C على اللي هو Y بتروح إلى ال Cوهنا y
+
+294
+00:27:49,390 --> 00:27:57,430
+ناقص ال c وهنا في عندي ايش برضه ناقص برا لان خد من
+
+295
+00:27:57,430 --> 00:28:01,670
+هنا ناقص عام المشترك او ضيعه مع الناقص اللي هنا
+
+296
+00:28:01,670 --> 00:28:11,160
+ماضح اه بيصير عندي y ساوي limit f of yنقص f of c
+
+297
+00:28:11,160 --> 00:28:16,800
+على y minus c لما y تروح لل c وهذا عبارة عن f
+
+298
+00:28:16,800 --> 00:28:22,440
+prime لمين لل c بدأنا ب f prime نقص c وانتهينا ب f
+
+299
+00:28:22,440 --> 00:28:31,520
+prime لل c لذا therefore f prime is even whenever
+
+300
+00:28:31,520 --> 00:28:37,160
+f is odd and f is differentiable
+
+301
+00:28:40,710 --> 00:28:56,810
+السؤال الأخير السؤال 13 السؤال
+
+302
+00:28:56,810 --> 00:29:03,990
+13 هو كما يلي اش
+
+303
+00:29:03,990 --> 00:29:09,200
+اللي بقول السؤال 13سؤال 13 بيقول إذا كانت F من R
+
+304
+00:29:09,200 --> 00:29:12,380
+لـ R is differentiable at C element in R show that
+
+305
+00:29:12,380 --> 00:29:16,840
+F prime of C سوى limit N في F of C زائد 1 لأن ناقص
+
+306
+00:29:16,840 --> 00:29:20,620
+F of C as N goes to infinity يعني لو كانت F
+
+307
+00:29:20,620 --> 00:29:24,900
+differentiable عند الـ C element in R بنقدر نكتب
+
+308
+00:29:24,900 --> 00:29:27,920
+ال derivative اللي هي F prime of C على سورة limit
+
+309
+00:29:27,920 --> 00:29:32,320
+N F of C زائد 1 لأن ناقص F of C as N goes to
+
+310
+00:29:32,320 --> 00:29:38,120
+infinityلكن بيقول لي by example show that the
+
+311
+00:29:38,120 --> 00:29:44,000
+existence of this limit this limit need not اللي
+
+312
+00:29:44,000 --> 00:29:52,300
+هو imply the existence of the derivative نيجي
+
+313
+00:29:52,300 --> 00:30:03,960
+الآن للجزء الأول عندي F من R لRو F prime of C
+
+314
+00:30:03,960 --> 00:30:12,120
+exist لانه يقول لي prove that F prime of C can be
+
+315
+00:30:12,120 --> 00:30:20,760
+written as limit on F of C زائد واحدة لان ناقص F
+
+316
+00:30:20,760 --> 00:30:26,180
+of C as N goes to infinity هذا الجزء الأول الجزء
+
+317
+00:30:26,180 --> 00:30:32,400
+الثاني حنجي الان نقول prove للجزء الأولقبل ما نقول
+
+318
+00:30:32,400 --> 00:30:37,700
+الـ proof نذكركم بس بنظرية سابقة في الـ real واحد
+
+319
+00:30:37,700 --> 00:30:43,840
+إنه لو عندي limit f of x لما x تروح لل c لو كانت
+
+320
+00:30:43,840 --> 00:30:52,780
+بتساوي Lبكون عندى أي sequence xₙ بتروح للـ C لازم
+
+321
+00:30:52,780 --> 00:30:59,020
+يتحقق لها limit f of xₙ as n goes to infinity
+
+322
+00:30:59,020 --> 00:31:05,530
+بساوي برضه الـكنا نتحدث بالحديث، باستبداء الحديث
+
+323
+00:31:05,530 --> 00:31:08,670
+عن الـ limit العادية للـ function S X بتروح للـ C
+
+324
+00:31:08,670 --> 00:31:13,470
+إلى limit لمين للـ sequence أو limit للـ sequences
+
+325
+00:31:13,470 --> 00:31:17,290
+الآن بنستخل هذه اللي هو المعلومة في إثبات اللي
+
+326
+00:31:17,290 --> 00:31:22,630
+بدنايا عند الآن since F prime of C exist بما أنه
+
+327
+00:31:22,630 --> 00:31:29,250
+ال derivative عند C موجودةإذا أكيد عندي صار f
+
+328
+00:31:29,250 --> 00:31:37,010
+prime of c بسهولمة f of x أو اللي هي الـ x عند c
+
+329
+00:31:38,080 --> 00:31:46,140
+زائد h ناقص f of c على h as h goes to mean to zero
+
+330
+00:31:46,140 --> 00:31:49,860
+اللي هو التعريف التعريف ال derivative أو الشكل
+
+331
+00:31:49,860 --> 00:31:52,980
+الآخر للتعريف ال derivative f of c زائد ال
+
+332
+00:31:52,980 --> 00:31:55,560
+increment ناقص f of c على ال increment as ال
+
+333
+00:31:55,560 --> 00:32:01,600
+increment goes to mean to zero ماشي الحل ال L بما
+
+334
+00:32:01,600 --> 00:32:07,480
+أنه اللي هو ال 1 على N sequence بتروح للسفروهذا
+
+335
+00:32:07,480 --> 00:32:11,440
+الـ limit exist لأن حسب النظرية اللي حكيتها قبل
+
+336
+00:32:11,440 --> 00:32:21,100
+بشوية بكون عندي لأن but كذا then F prime of C can
+
+337
+00:32:21,100 --> 00:32:26,580
+be اللي هو إعادة اللي هي rewritten as a limit of a
+
+338
+00:32:26,580 --> 00:32:36,800
+sequence F of اللي هو limit limitF of C زائد but
+
+339
+00:32:36,800 --> 00:32:40,000
+الـ H اللي هي تروح للصفر صارت mean ال sequence
+
+340
+00:32:40,000 --> 00:32:46,380
+واحدة ل N تروح للصفر واحدة ل N ناقص F of C على
+
+341
+00:32:46,380 --> 00:32:52,640
+واحدة ل N as N goes to infinity مدامت ال sequence
+
+342
+00:32:52,640 --> 00:32:57,100
+واحدة ل N بتروح للصفر صارت ال F of واحدة ل N اللي
+
+343
+00:32:57,100 --> 00:33:00,900
+هي عبارة عن F of C زائد واحدة ل N لإن الـ C عبارة
+
+344
+00:33:00,900 --> 00:33:07,740
+عن إياش فالتةواضح أه؟ الان هذا بيساوي اللي هو
+
+345
+00:33:07,740 --> 00:33:14,600
+limit الان as n goes to infinity اللي هو أكيد اللي
+
+346
+00:33:14,600 --> 00:33:21,920
+هو بيصير عندي f n في الجوس f of c زائد واحدة ل n
+
+347
+00:33:21,920 --> 00:33:28,260
+ناقص f of c اللي هو as n goes to infinity هو هذا
+
+348
+00:33:28,260 --> 00:33:35,150
+صار f prime of c وهو المطلوبالان conversely the
+
+349
+00:33:35,150 --> 00:33:37,890
+converse need not to be true in general هيك بيقول
+
+350
+00:33:37,890 --> 00:33:45,390
+ليه يعني بيقوللي if if بيقوللي او اللي بيقول if f
+
+351
+00:33:45,390 --> 00:33:53,670
+برا اللي هو limit f of c زاد واحدة ل n ناقص f of c
+
+352
+00:33:53,670 --> 00:34:01,610
+الكل مضروف في n as n goes to infinity exist if كده
+
+353
+00:34:02,500 --> 00:34:12,640
+then f prime at c need not be exist اصلا مش انه
+
+354
+00:34:12,640 --> 00:34:16,180
+يكون بيسوي هذا او لا need not to be اشمله exist
+
+355
+00:34:16,180 --> 00:34:19,640
+لان لو كان exist على طول بيسوي اما need not to be
+
+356
+00:34:19,640 --> 00:34:28,200
+exist ومااخد مثال جالي consider consider consider
+
+357
+00:34:28,200 --> 00:34:37,000
+f of xبساوي ال absolute value لل X وخد عند ال C أش
+
+358
+00:34:37,000 --> 00:34:46,440
+بتساوي سفر واضح F prime of 0 does not exist لأنها
+
+359
+00:34:46,440 --> 00:34:48,780
+عبارة عن corner point، انتوا عارفين احنا اللي هو
+
+360
+00:34:48,780 --> 00:34:52,480
+ال F prime عند ال zero لل absolute value does not
+
+361
+00:34:52,480 --> 00:34:59,740
+exist لكن هذه متحققة، ليش؟ but limit
+
+362
+00:35:01,280 --> 00:35:10,900
+N في F of 0 زائد 1 على N نقص F of 0 as N goes to
+
+363
+00:35:10,900 --> 00:35:18,840
+infinity بساوي limit N F of 0 زائد 1 على N يعني F
+
+364
+00:35:18,840 --> 00:35:23,560
+of 1 على N F of X بساوي absolute value X ف1 على N
+
+365
+00:35:23,560 --> 00:35:28,960
+مظبوط أه as N goes to infinity طبعا الـ N بتروح
+
+366
+00:35:29,220 --> 00:35:35,100
+يصير عبارة عن ash واحد إذا فعلا جبنا مثال أن ال
+
+367
+00:35:35,100 --> 00:35:39,720
+limit هذه تكون exist و سوى واحد but ال F prime عند
+
+368
+00:35:39,720 --> 00:35:42,640
+هذا النقطة C اللي هي 00 في هذه الحالة does not
+
+369
+00:35:42,640 --> 00:35:47,320
+exist بيكون هيك احنا انتهينا من الجزء الأول من
+
+370
+00:35:47,320 --> 00:35:54,870
+المحاضرة الخامسةاللي هو discussion لأو مناقشة ل
+
+371
+00:35:54,870 --> 00:35:59,910
+section 6-1 اللي هو the derivative والآن سنكمل
+
+372
+00:35:59,910 --> 00:36:05,690
+الحديث في الجزء الثاني من المحاضرة اللي هو عن اللي
+
+373
+00:36:05,690 --> 00:36:09,250
+هو the mean value theorem أو اللي هي نكمل
+
+374
+00:36:09,250 --> 00:36:11,910
+applications على mean value theorem وناخد اللي هو
+
+375
+00:36:11,910 --> 00:36:12,030
+ال
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa8a496058b0c26fa52efb39cc735f8adb72d0f8
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_raw.json
@@ -0,0 +1 @@
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870.32, "word": " بتروح", "probability": 0.8341471354166666}, {"start": 870.32, "end": 870.44, "word": " ل", "probability": 0.8330078125}, {"start": 870.44, "end": 870.56, "word": " C", "probability": 0.435791015625}, {"start": 870.56, "end": 870.76, "word": " من", "probability": 0.9365234375}, {"start": 870.76, "end": 871.98, "word": " وين؟", "probability": 0.8779296875}, {"start": 871.98, "end": 872.14, "word": " من", "probability": 0.98828125}, {"start": 872.14, "end": 872.64, "word": " اليمين", "probability": 0.8865559895833334}, {"start": 872.64, "end": 873.36, "word": " يعني", "probability": 0.903076171875}, {"start": 873.36, "end": 874.1, "word": " هذا", "probability": 0.9482421875}, {"start": 874.1, "end": 874.96, "word": " المقدار", "probability": 0.9228515625}], "temperature": 1.0}, {"id": 35, "seek": 89419, "start": 875.57, "end": 894.19, "text": "صار موجود وإيش بساوي بساوي سفر هذا خلّيه لإنه هذا اللي بدنا نصلّه لأن limit صار عندي معنى آخر limit absolute value of f of x على x minus c لما x تروح لل c من اليمين بساوي سفر exist", "tokens": [9381, 9640, 3714, 29245, 23328, 4032, 28814, 1829, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 8608, 5172, 2288, 23758, 16490, 1211, 11703, 1829, 3224, 5296, 28814, 1863, 3224, 23758, 13672, 1829, 47525, 8315, 8717, 36520, 11703, 3224, 5296, 33456, 4948, 20328, 9640, 18871, 16254, 20449, 1863, 7578, 19753, 34740, 4948, 8236, 2158, 295, 283, 295, 2031, 15844, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016, 24976, 269, 9154, 2423, 32640, 9957, 4724, 3794, 995, 45865, 8608, 5172, 2288, 2514], "avg_logprob": -0.22025602014668016, "compression_ratio": 1.5274725274725274, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 875.57, "end": 875.95, "word": "صار", "probability": 0.63916015625}, {"start": 875.95, "end": 876.37, "word": " موجود", "probability": 0.9705403645833334}, {"start": 876.37, "end": 876.61, "word": " وإيش", "probability": 0.729736328125}, {"start": 876.61, "end": 877.17, "word": " بساوي", "probability": 0.838134765625}, {"start": 877.17, "end": 878.33, "word": " بساوي", "probability": 0.794189453125}, {"start": 878.33, "end": 878.75, "word": " سفر", "probability": 0.7451171875}, {"start": 878.75, "end": 879.53, "word": " هذا", "probability": 0.638671875}, {"start": 879.53, "end": 880.01, "word": " خلّيه", "probability": 0.83818359375}, {"start": 880.01, "end": 880.19, "word": " لإنه", "probability": 0.7928466796875}, {"start": 880.19, "end": 880.33, "word": " هذا", "probability": 0.8857421875}, {"start": 880.33, "end": 880.45, "word": " اللي", "probability": 0.96875}, {"start": 880.45, "end": 880.63, "word": " بدنا", "probability": 0.88134765625}, {"start": 880.63, "end": 881.19, "word": " نصلّه", "probability": 0.8170166015625}, {"start": 881.19, "end": 881.77, "word": " لأن", "probability": 0.774658203125}, {"start": 881.77, "end": 882.35, "word": " limit", "probability": 0.9052734375}, {"start": 882.35, "end": 882.81, "word": " صار", "probability": 0.9736328125}, {"start": 882.81, "end": 883.09, "word": " عندي", "probability": 0.79931640625}, {"start": 883.09, "end": 883.47, "word": " معنى", "probability": 0.96337890625}, {"start": 883.47, "end": 883.89, "word": " آخر", "probability": 0.9248046875}, {"start": 883.89, "end": 884.85, "word": " limit", "probability": 0.94287109375}, {"start": 884.85, "end": 885.89, "word": " absolute", "probability": 0.63623046875}, {"start": 885.89, "end": 886.35, "word": " value", "probability": 0.9873046875}, {"start": 886.35, "end": 886.55, "word": " of", "probability": 0.394775390625}, {"start": 886.55, "end": 886.77, "word": " f", "probability": 0.65869140625}, {"start": 886.77, "end": 886.93, "word": " of", "probability": 0.44384765625}, {"start": 886.93, "end": 887.31, "word": " x", "probability": 0.68017578125}, {"start": 887.31, "end": 888.33, "word": " على", "probability": 0.68310546875}, {"start": 888.33, "end": 888.73, "word": " x", "probability": 0.83935546875}, {"start": 888.73, "end": 889.17, "word": " minus", "probability": 0.69091796875}, {"start": 889.17, "end": 889.47, "word": " c", "probability": 0.83056640625}, {"start": 889.47, "end": 889.79, "word": " لما", "probability": 0.891845703125}, {"start": 889.79, "end": 890.07, "word": " x", "probability": 0.8466796875}, {"start": 890.07, "end": 890.45, "word": " تروح", "probability": 0.994140625}, {"start": 890.45, "end": 890.71, "word": " لل", "probability": 0.68359375}, {"start": 890.71, "end": 891.07, "word": " c", "probability": 0.358642578125}, {"start": 891.07, "end": 892.07, "word": " من", "probability": 0.9921875}, {"start": 892.07, "end": 892.85, "word": " اليمين", "probability": 0.8310546875}, {"start": 892.85, "end": 893.47, "word": " بساوي", "probability": 0.92236328125}, {"start": 893.47, "end": 893.85, "word": " سفر", "probability": 0.9275716145833334}, {"start": 893.85, "end": 894.19, "word": " exist", "probability": 0.6865234375}], "temperature": 1.0}, {"id": 36, "seek": 92472, "start": 895.12, "end": 924.72, "text": "لاحظا قاعد رايح لأثبت أن هذا exist ده خد الآن من وين؟ من اليسار خد لأن احسب similarly عندي سفر بساوي absolute value of limit f of x على x minus c لما x تروح ل c من وين؟ من اليسار ويساوي عبارة عن limit absolute value of f of x على absolute value of x minus c لما x تروح ل c من وين؟ من اليسار", "tokens": [15040, 5016, 19913, 995, 12174, 995, 22488, 12602, 47302, 5016, 5296, 10721, 12984, 3555, 2655, 14739, 23758, 2514, 11778, 3224, 16490, 3215, 6024, 48506, 9154, 4032, 9957, 22807, 9154, 45595, 3794, 9640, 16490, 3215, 5296, 33456, 1975, 5016, 35457, 14138, 18871, 16254, 8608, 5172, 2288, 4724, 3794, 995, 45865, 8236, 2158, 295, 4948, 283, 295, 2031, 15844, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016, 5296, 269, 9154, 4032, 9957, 22807, 9154, 45595, 3794, 9640, 4032, 1829, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 4948, 8236, 2158, 295, 283, 295, 2031, 15844, 8236, 2158, 295, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016, 5296, 269, 9154, 4032, 9957, 22807, 9154, 45595, 3794, 9640], "avg_logprob": -0.22729700905644995, "compression_ratio": 2.053921568627451, "no_speech_prob": 6.735324859619141e-06, "words": [{"start": 895.12, "end": 895.72, "word": "لاحظا", "probability": 0.7103271484375}, {"start": 895.72, "end": 895.98, "word": " قاعد", "probability": 0.633056640625}, {"start": 895.98, "end": 896.32, "word": " رايح", "probability": 0.7725423177083334}, {"start": 896.32, "end": 897.18, "word": " لأثبت", "probability": 0.821630859375}, {"start": 897.18, "end": 897.28, "word": " أن", "probability": 0.6357421875}, {"start": 897.28, "end": 897.48, "word": " هذا", "probability": 0.76904296875}, {"start": 897.48, "end": 897.8, "word": " exist", "probability": 0.422119140625}, {"start": 897.8, "end": 898.02, "word": " ده", "probability": 0.542236328125}, {"start": 898.02, "end": 898.16, "word": " خد", "probability": 0.810546875}, {"start": 898.16, "end": 898.36, "word": " الآن", "probability": 0.53778076171875}, {"start": 898.36, "end": 898.5, "word": " من", "probability": 0.94580078125}, {"start": 898.5, "end": 898.88, "word": " وين؟", "probability": 0.7643229166666666}, {"start": 898.88, "end": 898.96, "word": " من", "probability": 0.97265625}, {"start": 898.96, "end": 899.42, "word": " اليسار", "probability": 0.9921875}, {"start": 899.42, "end": 900.3, "word": " خد", "probability": 0.906494140625}, {"start": 900.3, "end": 900.56, "word": " لأن", "probability": 0.763427734375}, {"start": 900.56, "end": 900.98, "word": " احسب", "probability": 0.8865559895833334}, {"start": 900.98, "end": 901.78, "word": " similarly", "probability": 0.5146484375}, {"start": 901.78, "end": 902.7, "word": " عندي", "probability": 0.5999755859375}, {"start": 902.7, "end": 903.52, "word": " سفر", "probability": 0.6846923828125}, {"start": 903.52, "end": 904.06, "word": " بساوي", "probability": 0.8065185546875}, {"start": 904.06, "end": 904.62, "word": " absolute", "probability": 0.55029296875}, {"start": 904.62, "end": 905.1, "word": " value", "probability": 0.986328125}, {"start": 905.1, "end": 905.22, "word": " of", "probability": 0.32763671875}, {"start": 905.22, "end": 905.72, "word": " limit", "probability": 0.78515625}, {"start": 905.72, "end": 906.6, "word": " f", "probability": 0.2342529296875}, {"start": 906.6, "end": 906.8, "word": " of", "probability": 0.36962890625}, {"start": 906.8, "end": 907.22, "word": " x", "probability": 0.66162109375}, {"start": 907.22, "end": 907.96, "word": " على", "probability": 0.5625}, {"start": 907.96, "end": 908.22, "word": " x", "probability": 0.82177734375}, {"start": 908.22, "end": 908.54, "word": " minus", "probability": 0.75634765625}, {"start": 908.54, "end": 908.84, "word": " c", "probability": 0.8994140625}, {"start": 908.84, "end": 909.12, "word": " لما", "probability": 0.8759765625}, {"start": 909.12, "end": 909.36, "word": " x", "probability": 0.861328125}, {"start": 909.36, "end": 909.66, "word": " تروح", "probability": 0.9881184895833334}, {"start": 909.66, "end": 909.8, "word": " ل", "probability": 0.62646484375}, {"start": 909.8, "end": 909.96, "word": " c", "probability": 0.5986328125}, {"start": 909.96, "end": 910.18, "word": " من", "probability": 0.98486328125}, {"start": 910.18, "end": 911.48, "word": " وين؟", "probability": 0.9677734375}, {"start": 911.48, "end": 911.7, "word": " من", "probability": 0.9794921875}, {"start": 911.7, "end": 912.76, "word": " اليسار", "probability": 0.9978841145833334}, {"start": 912.76, "end": 913.72, "word": " ويساوي", "probability": 0.8728515625}, {"start": 913.72, "end": 914.84, "word": " عبارة", "probability": 0.9930419921875}, {"start": 914.84, "end": 915.1, "word": " عن", "probability": 0.9951171875}, {"start": 915.1, "end": 915.9, "word": " limit", "probability": 0.98486328125}, {"start": 915.9, "end": 917.02, "word": " absolute", "probability": 0.951171875}, {"start": 917.02, "end": 917.46, "word": " value", "probability": 0.98876953125}, {"start": 917.46, "end": 917.62, "word": " of", "probability": 0.64501953125}, {"start": 917.62, "end": 917.82, "word": " f", "probability": 0.939453125}, {"start": 917.82, "end": 918.02, "word": " of", "probability": 0.91455078125}, {"start": 918.02, "end": 918.44, "word": " x", "probability": 0.9912109375}, {"start": 918.44, "end": 919.16, "word": " على", "probability": 0.7431640625}, {"start": 919.16, "end": 919.6, "word": " absolute", "probability": 0.94580078125}, {"start": 919.6, "end": 919.96, "word": " value", "probability": 0.98583984375}, {"start": 919.96, "end": 920.04, "word": " of", "probability": 0.875}, {"start": 920.04, "end": 920.2, "word": " x", "probability": 0.9892578125}, {"start": 920.2, "end": 920.44, "word": " minus", "probability": 0.986328125}, {"start": 920.44, "end": 920.94, "word": " c", "probability": 0.98681640625}, {"start": 920.94, "end": 921.7, "word": " لما", "probability": 0.97802734375}, {"start": 921.7, "end": 921.96, "word": " x", "probability": 0.96923828125}, {"start": 921.96, "end": 922.28, "word": " تروح", "probability": 0.9952799479166666}, {"start": 922.28, "end": 922.42, "word": " ل", "probability": 0.8642578125}, {"start": 922.42, "end": 922.6, "word": " c", "probability": 0.9384765625}, {"start": 922.6, "end": 922.8, "word": " من", "probability": 0.99267578125}, {"start": 922.8, "end": 923.62, "word": " وين؟", "probability": 0.98974609375}, {"start": 923.62, "end": 924.18, "word": " من", "probability": 0.9912109375}, {"start": 924.18, "end": 924.72, "word": " اليسار", "probability": 0.9983723958333334}], "temperature": 1.0}, {"id": 37, "seek": 94102, "start": 925.52, "end": 941.02, "text": "هذه نفسها بساوي limit أو بساوي سالب limit f of x absolute value على x minus c لما x تروح", "tokens": [3224, 24192, 8717, 36178, 11296, 4724, 3794, 995, 45865, 4948, 34051, 4724, 3794, 995, 45865, 8608, 6027, 3555, 4948, 283, 295, 2031, 8236, 2158, 15844, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016], "avg_logprob": -0.1620535739830562, "compression_ratio": 1.1401869158878504, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 925.52, "end": 925.9, "word": "هذه", "probability": 0.818115234375}, {"start": 925.9, "end": 926.64, "word": " نفسها", "probability": 0.9835611979166666}, {"start": 926.64, "end": 927.44, "word": " بساوي", "probability": 0.760498046875}, {"start": 927.44, "end": 928.56, "word": " limit", "probability": 0.83740234375}, {"start": 928.56, "end": 929.92, "word": " أو", "probability": 0.6162109375}, {"start": 929.92, "end": 930.42, "word": " بساوي", "probability": 0.957275390625}, {"start": 930.42, "end": 931.38, "word": " سالب", "probability": 0.9080403645833334}, {"start": 931.38, "end": 932.8, "word": " limit", "probability": 0.9296875}, {"start": 932.8, "end": 934.02, "word": " f", "probability": 0.23681640625}, {"start": 934.02, "end": 934.28, "word": " of", "probability": 0.55859375}, {"start": 934.28, "end": 934.58, "word": " x", "probability": 0.794921875}, {"start": 934.58, "end": 934.96, "word": " absolute", "probability": 0.88427734375}, {"start": 934.96, "end": 935.64, "word": " value", "probability": 0.99267578125}, {"start": 935.64, "end": 936.64, "word": " على", "probability": 0.67578125}, {"start": 936.64, "end": 937.58, "word": " x", "probability": 0.83642578125}, {"start": 937.58, "end": 938.1, "word": " minus", "probability": 0.7470703125}, {"start": 938.1, "end": 938.6, "word": " c", "probability": 0.8095703125}, {"start": 938.6, "end": 940.08, "word": " لما", "probability": 0.830810546875}, {"start": 940.08, "end": 940.4, "word": " x", "probability": 0.84765625}, {"start": 940.4, "end": 941.02, "word": " تروح", "probability": 0.9894205729166666}], "temperature": 1.0}, {"id": 38, "seek": 96921, "start": 941.69, "end": 969.21, "text": "للـ C من اليسار، ليش؟ لأن X أصغر من C، إذا X minus C سالبة إذا الـ absolute value سالب إليها واخدت السالب برا هذا الآن المخضر بيساوي سفر، إذا هذا لحاله برضه إيش ماله؟ سفر، إذا limit absolute 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20193, 5016, 19913, 36145, 2423, 4948, 9154, 45595, 2304, 9957], "avg_logprob": -0.2059563770390197, "compression_ratio": 2.059071729957806, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 941.69, "end": 942.03, "word": "للـ", "probability": 0.6399739583333334}, {"start": 942.03, "end": 942.15, "word": " C", "probability": 0.5087890625}, {"start": 942.15, "end": 942.27, "word": " من", "probability": 0.95751953125}, {"start": 942.27, "end": 942.77, "word": " اليسار،", "probability": 0.82489013671875}, {"start": 942.77, "end": 943.73, "word": " ليش؟", "probability": 0.755126953125}, {"start": 943.73, "end": 944.07, "word": " لأن", "probability": 0.8916015625}, {"start": 944.07, "end": 944.59, "word": " X", "probability": 0.89013671875}, {"start": 944.59, "end": 944.99, "word": " أصغر", "probability": 0.9705810546875}, {"start": 944.99, "end": 945.17, "word": " من", "probability": 0.9931640625}, {"start": 945.17, "end": 945.61, "word": " C،", "probability": 0.669921875}, 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955.79, "word": " ماله؟", "probability": 0.82879638671875}, {"start": 955.79, "end": 956.23, "word": " سفر،", "probability": 0.9503173828125}, {"start": 956.23, "end": 956.53, "word": " إذا", "probability": 0.938720703125}, {"start": 956.53, "end": 957.87, "word": " limit", "probability": 0.91552734375}, {"start": 957.87, "end": 958.91, "word": " absolute", "probability": 0.92236328125}, {"start": 958.91, "end": 959.39, "word": " value", "probability": 0.9892578125}, {"start": 959.39, "end": 959.61, "word": " للـ", "probability": 0.5020751953125}, {"start": 959.61, "end": 959.77, "word": " F", "probability": 0.61474609375}, {"start": 959.77, "end": 959.93, "word": " of", "probability": 0.93115234375}, {"start": 959.93, "end": 960.37, "word": " X", "probability": 0.99658203125}, {"start": 960.37, "end": 961.27, "word": " على", "probability": 0.73779296875}, {"start": 961.27, "end": 961.63, "word": " X", "probability": 0.986328125}, {"start": 961.63, "end": 961.95, "word": " minus", "probability": 0.9794921875}, {"start": 961.95, "end": 962.37, "word": " C،", "probability": 0.752197265625}, {"start": 962.37, "end": 962.53, "word": " لما", "probability": 0.955322265625}, {"start": 962.53, "end": 962.77, "word": " X", "probability": 0.9677734375}, {"start": 962.77, "end": 963.05, "word": " تروح", "probability": 0.9830729166666666}, {"start": 963.05, "end": 963.29, "word": " للـ", "probability": 0.748291015625}, {"start": 963.29, "end": 963.39, "word": " C", "probability": 0.82958984375}, {"start": 963.39, "end": 963.53, "word": " من", "probability": 0.9892578125}, {"start": 963.53, "end": 964.39, "word": " اليسار،", "probability": 0.8795166015625}, {"start": 964.39, "end": 964.67, "word": " برضه", "probability": 0.9876302083333334}, {"start": 964.67, "end": 964.87, "word": " إيش", "probability": 0.9547526041666666}, {"start": 964.87, "end": 965.73, "word": " بيساوي؟", "probability": 0.9657389322916666}, {"start": 965.73, "end": 966.13, "word": " بيساوي", 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996.91, "word": " of", "probability": 0.95263671875}, {"start": 996.91, "end": 997.31, "word": " c", "probability": 0.93017578125}, {"start": 997.31, "end": 998.03, "word": " على", "probability": 0.7041015625}, {"start": 998.03, "end": 998.31, "word": " x", "probability": 0.95849609375}, {"start": 998.31, "end": 998.61, "word": " minus", "probability": 0.91259765625}, {"start": 998.61, "end": 999.03, "word": " c", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 40, "seek": 102393, "start": 999.39, "end": 1023.93, "text": "as x → c بساوي حسب اللي عندى من هنا و من هنا و من هنا هيساوي سفر الان conversely بتأفترض طبعا ان ال conversely هيكون الخطوات كثير مشابهه لللي هنا يعني كثير اللي استخدمته هنا هستخدمه في اللي بعدها", "tokens": [296, 2031, 41600, 269, 4724, 3794, 995, 45865, 11331, 35457, 13672, 1829, 43242, 7578, 9154, 34105, 4032, 9154, 34105, 4032, 9154, 34105, 39896, 3794, 995, 45865, 8608, 5172, 2288, 2423, 7649, 2615, 736, 39894, 10721, 5172, 2655, 43042, 23032, 3555, 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1003.31, "end": 1004.53, "word": " عندى", "probability": 0.594482421875}, {"start": 1004.53, "end": 1006.19, "word": " من", "probability": 0.7734375}, {"start": 1006.19, "end": 1006.45, "word": " هنا", "probability": 0.5595703125}, {"start": 1006.45, "end": 1006.69, "word": " و", "probability": 0.826171875}, {"start": 1006.69, "end": 1006.87, "word": " من", "probability": 0.732421875}, {"start": 1006.87, "end": 1007.15, "word": " هنا", "probability": 0.98974609375}, {"start": 1007.15, "end": 1007.33, "word": " و", "probability": 0.95458984375}, {"start": 1007.33, "end": 1007.47, "word": " من", "probability": 0.96875}, {"start": 1007.47, "end": 1007.79, "word": " هنا", "probability": 0.9912109375}, {"start": 1007.79, "end": 1008.99, "word": " هيساوي", "probability": 0.6663818359375}, {"start": 1008.99, "end": 1009.89, "word": " سفر", "probability": 0.85546875}, {"start": 1009.89, "end": 1011.45, "word": " الان", "probability": 0.65771484375}, {"start": 1011.45, "end": 1012.27, "word": " conversely", "probability": 0.82080078125}, {"start": 1012.27, "end": 1015.31, "word": " بتأفترض", "probability": 0.46146240234375}, {"start": 1015.31, "end": 1015.67, "word": " طبعا", "probability": 0.8831787109375}, {"start": 1015.67, "end": 1015.79, "word": " ان", "probability": 0.3798828125}, {"start": 1015.79, "end": 1015.97, "word": " ال", "probability": 0.74267578125}, {"start": 1015.97, "end": 1016.33, "word": " conversely", "probability": 0.5279541015625}, {"start": 1016.33, "end": 1016.73, "word": " هيكون", "probability": 0.859130859375}, {"start": 1016.73, "end": 1017.19, "word": " الخطوات", "probability": 0.9783935546875}, {"start": 1017.19, "end": 1017.53, "word": " كثير", "probability": 0.7532552083333334}, {"start": 1017.53, "end": 1018.09, "word": " مشابهه", "probability": 0.83551025390625}, {"start": 1018.09, "end": 1018.41, "word": " لللي", "probability": 0.7587890625}, {"start": 1018.41, "end": 1018.63, "word": " هنا", "probability": 0.2490234375}, {"start": 1018.63, "end": 1019.77, "word": " يعني", "probability": 0.881591796875}, {"start": 1019.77, "end": 1020.09, "word": " كثير", "probability": 0.88427734375}, {"start": 1020.09, "end": 1020.17, "word": " اللي", "probability": 0.84326171875}, {"start": 1020.17, "end": 1020.71, "word": " استخدمته", "probability": 0.9327392578125}, {"start": 1020.71, "end": 1020.87, "word": " هنا", "probability": 0.9052734375}, {"start": 1020.87, "end": 1021.81, "word": " هستخدمه", "probability": 0.89150390625}, {"start": 1021.81, "end": 1023.35, "word": " في", "probability": 0.75341796875}, {"start": 1023.35, "end": 1023.47, "word": " اللي", "probability": 0.963623046875}, {"start": 1023.47, "end": 1023.93, "word": " بعدها", "probability": 0.70556640625}], "temperature": 1.0}, {"id": 41, "seek": 105991, "start": 1032.67, "end": 1059.91, "text": "Conversely suppose that g of x سواء absolute value او f of x اللي هو is differentiable at c بدا وجدلك الان اثبتلك ان f prime of c ايش ما لها بتساوي سفر يعني بدا اثبت limit", "tokens": [9838, 4308, 356, 7297, 300, 290, 295, 2031, 8608, 2407, 16606, 8236, 2158, 1975, 2407, 283, 295, 2031, 13672, 1829, 31439, 307, 819, 9364, 412, 269, 4724, 28259, 49610, 3215, 23275, 2423, 7649, 1975, 12984, 3555, 2655, 23275, 16472, 283, 5835, 295, 269, 1975, 1829, 8592, 19446, 5296, 11296, 39894, 3794, 995, 45865, 8608, 5172, 2288, 37495, 22653, 4724, 28259, 1975, 12984, 3555, 2655, 4948], "avg_logprob": -0.41477272456342523, "compression_ratio": 1.3275862068965518, "no_speech_prob": 0.0, "words": [{"start": 1032.6699999999998, "end": 1033.55, "word": "Conversely", "probability": 0.5113525390625}, {"start": 1033.55, "end": 1034.43, "word": " suppose", "probability": 0.2186279296875}, {"start": 1034.43, "end": 1037.79, "word": " that", "probability": 0.88525390625}, {"start": 1037.79, "end": 1039.37, "word": " g", "probability": 0.45751953125}, {"start": 1039.37, "end": 1039.59, "word": " of", "probability": 0.405517578125}, {"start": 1039.59, "end": 1040.05, "word": " x", "probability": 0.869140625}, {"start": 1040.05, "end": 1040.97, "word": " سواء", "probability": 0.4903157552083333}, {"start": 1040.97, "end": 1041.29, "word": " absolute", "probability": 0.213623046875}, {"start": 1041.29, "end": 1041.75, "word": " value", "probability": 0.97705078125}, {"start": 1041.75, "end": 1041.89, "word": " او", "probability": 0.71484375}, {"start": 1041.89, "end": 1042.07, "word": " f", "probability": 0.414306640625}, {"start": 1042.07, "end": 1042.23, "word": " of", "probability": 0.85693359375}, {"start": 1042.23, "end": 1042.71, "word": " x", "probability": 0.90478515625}, {"start": 1042.71, "end": 1045.89, "word": " اللي", "probability": 0.5924072265625}, {"start": 1045.89, "end": 1046.13, "word": " هو", "probability": 0.9931640625}, {"start": 1046.13, "end": 1046.63, "word": " is", "probability": 0.74609375}, {"start": 1046.63, "end": 1048.85, "word": " differentiable", "probability": 0.962646484375}, {"start": 1048.85, "end": 1050.19, "word": " 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"start": 1446.41, "end": 1474.97, "text": "بتكون الـ function الـ G prime إيه شمالها is even انحل واحدة من هنا والتانية similarly زيها الآن لنفترض F من عند R لعند R be an odd differentiable function ماشي الحال show that", "tokens": [3555, 2655, 30544, 2423, 39184, 2445, 2423, 39184, 460, 5835, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 307, 754, 16472, 5016, 1211, 36764, 24401, 3660, 9154, 34105, 16070, 2655, 7649, 10632, 1034, 2202, 356, 30767, 1829, 11296, 6024, 48506, 5296, 1863, 5172, 2655, 43042, 479, 9154, 43242, 497, 5296, 3615, 41260, 497, 312, 364, 7401, 819, 9364, 2445, 3714, 33599, 1829, 21542, 6027, 855, 300], "avg_logprob": -0.2904829473206491, "compression_ratio": 1.358695652173913, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1446.41, "end": 1447.01, "word": "بتكون", "probability": 0.67919921875}, {"start": 1447.01, "end": 1447.19, "word": " الـ", "probability": 0.821533203125}, {"start": 1447.19, "end": 1447.51, "word": " function", "probability": 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limit f of xₙ as n goes to infinity بساوي برضه الـ", "tokens": [3555, 30544, 43242, 7578, 36632, 8310, 2031, 37781, 247, 39894, 32887, 5016, 24976, 39184, 383, 5296, 31377, 2304, 7251, 2655, 5016, 4587, 4587, 5296, 11296, 4948, 283, 295, 2031, 37781, 247, 382, 297, 1709, 281, 13202, 4724, 3794, 995, 45865, 4724, 43042, 3224, 2423, 39184], "avg_logprob": -0.26460598344388214, "compression_ratio": 1.1044776119402986, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1845.7, "end": 1846.14, "word": "بكون", "probability": 0.7431640625}, {"start": 1846.14, "end": 1846.94, "word": " عندى", "probability": 0.75390625}, {"start": 1846.94, "end": 1847.32, "word": " أي", "probability": 0.443603515625}, {"start": 1847.32, "end": 1848.24, "word": " sequence", "probability": 0.7919921875}, {"start": 1848.24, "end": 1849.42, "word": " xₙ", "probability": 0.4777933756510417}, {"start": 1849.42, "end": 1850.62, "word": " بتروح", "probability": 0.9111328125}, {"start": 1850.62, "end": 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"word": " to", "probability": 0.953125}, {"start": 1858.34, "end": 1859.02, "word": " infinity", "probability": 0.8505859375}, {"start": 1859.02, "end": 1860.04, "word": " بساوي", "probability": 0.7733154296875}, {"start": 1860.04, "end": 1860.42, "word": " برضه", "probability": 0.9654947916666666}, {"start": 1860.42, "end": 1861.9, "word": " الـ", "probability": 0.41357421875}], "temperature": 1.0}, {"id": 73, "seek": 188539, "start": 1861.93, "end": 1885.39, "text": "كنا نتحدث بالحديث، باستبداء الحديث عن الـ limit العادية للـ function S X بتروح للـ C إلى limit لمين للـ sequence أو limit للـ sequences الآن بنستخل هذه اللي هو المعلومة في إثبات اللي بدنايا عند الآن since F prime of C exist بما أنه ال derivative عند C موجودة", "tokens": [4117, 8315, 8717, 2655, 24401, 12984, 20666, 5016, 16254, 12984, 12399, 4724, 995, 14851, 44510, 16606, 21542, 16254, 12984, 18871, 2423, 39184, 4948, 18863, 18513, 10632, 24976, 39184, 2445, 318, 1783, 39894, 32887, 5016, 24976, 39184, 383, 30731, 4948, 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1880.99, "end": 1881.79, "word": " exist", "probability": 0.6103515625}, {"start": 1881.79, "end": 1882.23, "word": " بما", "probability": 0.908935546875}, {"start": 1882.23, "end": 1882.63, "word": " أنه", "probability": 0.610595703125}, {"start": 1882.63, "end": 1883.03, "word": " ال", "probability": 0.97265625}, {"start": 1883.03, "end": 1883.51, "word": " derivative", "probability": 0.63916015625}, {"start": 1883.51, "end": 1884.01, "word": " عند", "probability": 0.986328125}, {"start": 1884.01, "end": 1884.41, "word": " C", "probability": 0.93310546875}, {"start": 1884.41, "end": 1885.39, "word": " موجودة", "probability": 0.992431640625}], "temperature": 1.0}, {"id": 74, "seek": 189701, "start": 1886.03, "end": 1897.01, "text": "إذا أكيد عندي صار f prime of c بسهولمة f of x أو اللي هي الـ x عند c", "tokens": [28814, 15730, 5551, 4117, 25708, 18871, 16254, 20328, 9640, 283, 5835, 295, 269, 4724, 3794, 3224, 12610, 46007, 283, 295, 2031, 34051, 13672, 1829, 39896, 2423, 39184, 2031, 43242, 269], "avg_logprob": -0.4697580779752424, "compression_ratio": 1.0957446808510638, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1886.03, "end": 1886.45, "word": "إذا", "probability": 0.44818115234375}, {"start": 1886.45, "end": 1887.09, "word": " أكيد", "probability": 0.7860514322916666}, {"start": 1887.09, "end": 1887.77, "word": " عندي", "probability": 0.6884765625}, {"start": 1887.77, "end": 1888.97, "word": " صار", "probability": 0.6317138671875}, {"start": 1888.97, "end": 1889.25, "word": " f", "probability": 0.3076171875}, {"start": 1889.25, "end": 1889.89, "word": " prime", "probability": 0.379150390625}, {"start": 1889.89, "end": 1890.11, "word": " of", "probability": 0.908203125}, {"start": 1890.11, "end": 1890.53, "word": " c", "probability": 0.69580078125}, {"start": 1890.53, "end": 1891.97, "word": " بسهولمة", "probability": 0.6477783203125}, {"start": 1891.97, "end": 1893.21, "word": " f", "probability": 0.85595703125}, {"start": 1893.21, "end": 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mean to zero ماشي الحل ال L بما أنه اللي هو ال 1 على N sequence بتروح للسفر", "tokens": [11622, 16373, 3215, 276, 8717, 995, 4587, 9381, 283, 295, 269, 15844, 276, 382, 276, 1709, 281, 914, 281, 4018, 13672, 1829, 31439, 16712, 3615, 16572, 5172, 16712, 3615, 16572, 5172, 2423, 13760, 34051, 25124, 28820, 6024, 95, 34740, 24976, 2655, 3615, 16572, 5172, 2423, 13760, 283, 295, 269, 30767, 16373, 3215, 2423, 26200, 8717, 995, 4587, 9381, 283, 295, 269, 15844, 2423, 26200, 382, 2423, 26200, 1709, 281, 914, 281, 4018, 3714, 33599, 1829, 21542, 1211, 2423, 441, 4724, 15042, 14739, 3224, 13672, 1829, 31439, 2423, 502, 15844, 426, 8310, 39894, 32887, 5016, 24976, 3794, 5172, 2288], "avg_logprob": -0.1991792938323936, "compression_ratio": 1.9447236180904524, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 1898.08, "end": 1898.78, "word": "زائد", "probability": 0.6513671875}, {"start": 1898.78, "end": 1899.4, "word": " h", "probability": 0.31591796875}, {"start": 1899.4, "end": 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{"start": 1920.08, "end": 1920.4, "word": " L", "probability": 0.57421875}, {"start": 1920.4, "end": 1921.6, "word": " بما", "probability": 0.94482421875}, {"start": 1921.6, "end": 1922.16, "word": " أنه", "probability": 0.656494140625}, {"start": 1922.16, "end": 1922.98, "word": " اللي", "probability": 0.978271484375}, {"start": 1922.98, "end": 1923.24, "word": " هو", "probability": 0.99267578125}, {"start": 1923.24, "end": 1923.46, "word": " ال", "probability": 0.9765625}, {"start": 1923.46, "end": 1923.76, "word": " 1", "probability": 0.47607421875}, {"start": 1923.76, "end": 1924.08, "word": " على", "probability": 0.8564453125}, {"start": 1924.08, "end": 1924.36, "word": " N", "probability": 0.5458984375}, {"start": 1924.36, "end": 1925.24, "word": " sequence", "probability": 0.916015625}, {"start": 1925.24, "end": 1925.68, "word": " بتروح", "probability": 0.9581705729166666}, {"start": 1925.68, "end": 1926.38, "word": " للسفر", "probability": 0.796142578125}], "temperature": 1.0}, {"id": 76, "seek": 195258, "start": 1927.04, "end": 1952.58, "text": "وهذا الـ limit exist لأن حسب النظرية اللي حكيتها قبل بشوية بكون عندي لأن but كذا then F prime of C can be اللي هو إعادة اللي هي rewritten as a limit of a sequence F of اللي هو limit limit", "tokens": [2407, 3224, 15730, 2423, 39184, 4948, 2514, 5296, 33456, 11331, 35457, 28239, 19913, 2288, 10632, 13672, 1829, 11331, 4117, 36081, 11296, 12174, 36150, 4724, 8592, 2407, 10632, 4724, 30544, 18871, 16254, 5296, 33456, 457, 9122, 15730, 550, 479, 5835, 295, 383, 393, 312, 13672, 1829, 31439, 11933, 3615, 18513, 3660, 13672, 1829, 39896, 319, 26859, 382, 257, 4948, 295, 257, 8310, 479, 295, 13672, 1829, 31439, 4948, 4948], "avg_logprob": -0.27513587129288825, "compression_ratio": 1.4719101123595506, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1927.04, "end": 1927.48, "word": "وهذا", "probability": 0.7101236979166666}, {"start": 1927.48, "end": 1927.6, "word": " الـ", "probability": 0.42626953125}, 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0.9724934895833334}, {"start": 2031.51, "end": 2031.63, "word": " ل", "probability": 0.974609375}, {"start": 2031.63, "end": 2031.95, "word": " n", "probability": 0.4501953125}, {"start": 2031.95, "end": 2032.85, "word": " ناقص", "probability": 0.9140625}, {"start": 2032.85, "end": 2033.09, "word": " f", "probability": 0.89892578125}, {"start": 2033.09, "end": 2033.29, "word": " of", "probability": 0.94140625}, {"start": 2033.29, "end": 2033.67, "word": " c", "probability": 0.98193359375}, {"start": 2033.67, "end": 2034.69, "word": " الكل", "probability": 0.6812744140625}, {"start": 2034.69, "end": 2035.17, "word": " مضروف", "probability": 0.88818359375}, {"start": 2035.17, "end": 2035.35, "word": " في", "probability": 0.90478515625}, {"start": 2035.35, "end": 2035.65, "word": " n", "probability": 0.8427734375}, {"start": 2035.65, "end": 2036.33, "word": " as", "probability": 0.88427734375}, {"start": 2036.33, "end": 2036.51, "word": " n", "probability": 0.939453125}, {"start": 2036.51, "end": 2036.73, "word": " goes", "probability": 0.91650390625}, {"start": 2036.73, "end": 2036.87, "word": " to", "probability": 0.91162109375}, {"start": 2036.87, "end": 2037.35, "word": " infinity", "probability": 0.892578125}, {"start": 2037.35, "end": 2038.69, "word": " exist", "probability": 0.495361328125}, {"start": 2038.69, "end": 2041.13, "word": " if", "probability": 0.7333984375}, {"start": 2041.13, "end": 2041.61, "word": " كده", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 80, "seek": 206992, "start": 2042.5, "end": 2069.92, "text": "then f prime at c need not be exist اصلا مش انه يكون بيسوي هذا او لا need not to be اشمله exist لان لو كان exist على طول بيسوي اما need not to be exist ومااخد مثال جالي consider consider consider f of x", "tokens": [19096, 283, 5835, 412, 269, 643, 406, 312, 2514, 1975, 9381, 15040, 37893, 16472, 3224, 7251, 30544, 4724, 1829, 3794, 45865, 23758, 1975, 2407, 20193, 643, 406, 281, 312, 1975, 8592, 2304, 43761, 2514, 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"probability": 0.8857421875}], "temperature": 1.0}, {"id": 81, "seek": 209973, "start": 2070.66, "end": 2099.74, "text": "بساوي ال absolute value لل X وخد عند ال C أش بتساوي سفر واضح F prime of 0 does not exist لأنها عبارة عن corner point، انتوا عارفين احنا اللي هو ال F prime عند ال zero لل absolute value does not exist لكن هذه متحققة، ليش؟ but limit", "tokens": [3555, 3794, 995, 45865, 2423, 8236, 2158, 24976, 1783, 4032, 9778, 3215, 43242, 2423, 383, 5551, 8592, 39894, 3794, 995, 45865, 8608, 5172, 2288, 4032, 46958, 5016, 479, 5835, 295, 1958, 775, 406, 2514, 5296, 33456, 11296, 6225, 3555, 9640, 3660, 18871, 4538, 935, 12399, 16472, 2655, 14407, 6225, 9640, 5172, 9957, 1975, 5016, 8315, 13672, 1829, 31439, 2423, 479, 5835, 43242, 2423, 4018, 24976, 8236, 2158, 775, 406, 2514, 44381, 29538, 44650, 5016, 4587, 28671, 12399, 32239, 8592, 22807, 457, 4948], "avg_logprob": -0.2682605292423662, "compression_ratio": 1.4703196347031964, "no_speech_prob": 2.682209014892578e-06, "words": 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2090.64, "word": " zero", "probability": 0.438232421875}, {"start": 2090.64, "end": 2090.86, "word": " لل", "probability": 0.65673828125}, {"start": 2090.86, "end": 2091.64, "word": " absolute", "probability": 0.89501953125}, {"start": 2091.64, "end": 2092.06, "word": " value", "probability": 0.990234375}, {"start": 2092.06, "end": 2092.26, "word": " does", "probability": 0.5595703125}, {"start": 2092.26, "end": 2092.48, "word": " not", "probability": 0.96875}, {"start": 2092.48, "end": 2092.96, "word": " exist", "probability": 0.9736328125}, {"start": 2092.96, "end": 2094.62, "word": " لكن", "probability": 0.93603515625}, {"start": 2094.62, "end": 2095.16, "word": " هذه", "probability": 0.837890625}, {"start": 2095.16, "end": 2096.66, "word": " متحققة،", "probability": 0.866015625}, {"start": 2096.66, "end": 2097.34, "word": " ليش؟", "probability": 0.8447265625}, {"start": 2097.34, "end": 2097.76, "word": " but", "probability": 0.62939453125}, {"start": 2097.76, "end": 2099.74, "word": " limit", "probability": 0.78955078125}], "temperature": 1.0}, {"id": 82, "seek": 212896, "start": 2101.28, "end": 2128.96, "text": "N في F of 0 زائد 1 على N نقص F of 0 as N goes to infinity بساوي limit N F of 0 زائد 1 على N يعني F of 1 على N F of X بساوي absolute value X ف1 على N مظبوط أه as N goes to infinity طبعا الـ N بتروح", "tokens": [45, 8978, 479, 295, 1958, 30767, 16373, 3215, 502, 15844, 426, 8717, 4587, 9381, 479, 295, 1958, 382, 426, 1709, 281, 13202, 4724, 3794, 995, 45865, 4948, 426, 479, 295, 1958, 30767, 16373, 3215, 502, 15844, 426, 37495, 22653, 479, 295, 502, 15844, 426, 479, 295, 1783, 4724, 3794, 995, 45865, 8236, 2158, 1783, 6156, 16, 15844, 426, 3714, 19913, 3555, 2407, 9566, 5551, 3224, 382, 426, 1709, 281, 13202, 23032, 3555, 3615, 995, 2423, 39184, 426, 39894, 32887, 5016], "avg_logprob": -0.1947337904094178, "compression_ratio": 1.59375, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 2101.28, "end": 2101.92, "word": "N", "probability": 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{"start": 2120.54, "end": 2120.8, "word": " absolute", "probability": 0.81103515625}, {"start": 2120.8, "end": 2121.12, "word": " value", "probability": 0.99169921875}, {"start": 2121.12, "end": 2121.38, "word": " X", "probability": 0.87744140625}, {"start": 2121.38, "end": 2122.1, "word": " ف1", "probability": 0.5560302734375}, {"start": 2122.1, "end": 2123.2, "word": " على", "probability": 0.890625}, {"start": 2123.2, "end": 2123.56, "word": " N", "probability": 0.982421875}, {"start": 2123.56, "end": 2124.34, "word": " مظبوط", "probability": 0.90498046875}, {"start": 2124.34, "end": 2124.88, "word": " أه", "probability": 0.621337890625}, {"start": 2124.88, "end": 2125.56, "word": " as", "probability": 0.46826171875}, {"start": 2125.56, "end": 2125.76, "word": " N", "probability": 0.98095703125}, {"start": 2125.76, "end": 2126.0, "word": " goes", "probability": 0.95263671875}, {"start": 2126.0, "end": 2126.18, "word": " to", "probability": 0.96484375}, {"start": 2126.18, "end": 2126.62, "word": " infinity", "probability": 0.89697265625}, {"start": 2126.62, "end": 2127.96, "word": " طبعا", "probability": 0.9835205078125}, {"start": 2127.96, "end": 2128.18, "word": " الـ", "probability": 0.7005615234375}, {"start": 2128.18, "end": 2128.3, "word": " N", "probability": 0.8740234375}, {"start": 2128.3, "end": 2128.96, "word": " بتروح", "probability": 0.9820963541666666}], "temperature": 1.0}, {"id": 83, "seek": 214900, "start": 2129.22, "end": 2149.0, "text": "يصير عبارة عن ash واحد إذا فعلا جبنا مثال أن ال limit هذه تكون exist و سوى واحد but ال F prime عند هذا النقطة C اللي هي 00 في هذه الحالة does not exist بيكون هيك احنا انتهينا من الجزء الأول من المحاضرة الخامسة", "tokens": [1829, 9381, 13546, 6225, 3555, 9640, 3660, 18871, 12588, 36764, 24401, 11933, 15730, 6156, 3615, 15040, 10874, 3555, 8315, 50113, 6027, 14739, 2423, 4948, 29538, 6055, 30544, 2514, 4032, 8608, 2407, 7578, 36764, 24401, 457, 2423, 479, 5835, 43242, 23758, 28239, 47432, 3660, 383, 13672, 1829, 39896, 7143, 8978, 29538, 21542, 6027, 3660, 775, 406, 2514, 4724, 1829, 30544, 39896, 4117, 1975, 5016, 8315, 16472, 47395, 1829, 8315, 9154, 25724, 11622, 38207, 16247, 12610, 9154, 9673, 5016, 46958, 25720, 33962, 10943, 3794, 3660], "avg_logprob": -0.2736235009062858, "compression_ratio": 1.5896226415094339, "no_speech_prob": 2.4259090423583984e-05, "words": [{"start": 2129.22, "end": 2129.7, "word": "يصير", "probability": 0.8001302083333334}, {"start": 2129.7, "end": 2130.6, "word": " عبارة", "probability": 0.986083984375}, {"start": 2130.6, "end": 2130.86, "word": " عن", "probability": 0.96044921875}, {"start": 2130.86, "end": 2131.4, "word": " ash", "probability": 0.177734375}, {"start": 2131.4, "end": 2132.62, "word": " واحد", "probability": 0.573486328125}, {"start": 2132.62, "end": 2133.48, "word": " إذا", "probability": 0.5986328125}, {"start": 2133.48, "end": 2133.9, "word": " فعلا", "probability": 0.9117838541666666}, {"start": 2133.9, "end": 2134.22, "word": " جبنا", "probability": 0.8313802083333334}, {"start": 2134.22, "end": 2134.74, "word": " مثال", "probability": 0.989990234375}, {"start": 2134.74, "end": 2134.94, "word": " أن", "probability": 0.40966796875}, {"start": 2134.94, "end": 2135.1, "word": " ال", "probability": 0.58203125}, {"start": 2135.1, "end": 2135.36, "word": " limit", "probability": 0.7470703125}, {"start": 2135.36, "end": 2135.6, "word": " هذه", "probability": 0.40478515625}, {"start": 2135.6, "end": 2135.9, "word": " تكون", "probability": 0.875244140625}, {"start": 2135.9, "end": 2136.28, "word": " exist", "probability": 0.75341796875}, {"start": 2136.28, "end": 2136.48, "word": " و", "probability": 0.81982421875}, {"start": 2136.48, "end": 2136.72, "word": " سوى", "probability": 0.464111328125}, {"start": 2136.72, "end": 2137.22, "word": " واحد", "probability": 0.9765625}, {"start": 2137.22, "end": 2138.02, "word": " but", "probability": 0.6240234375}, {"start": 2138.02, "end": 2138.2, "word": " ال", "probability": 0.77587890625}, {"start": 2138.2, "end": 2138.42, "word": " F", "probability": 0.5244140625}, {"start": 2138.42, "end": 2138.98, "word": " prime", "probability": 0.5380859375}, {"start": 2138.98, "end": 2139.72, "word": " عند", "probability": 0.97998046875}, {"start": 2139.72, "end": 2139.96, "word": " هذا", "probability": 0.408935546875}, {"start": 2139.96, "end": 2140.38, "word": " النقطة", "probability": 0.9733072916666666}, {"start": 2140.38, "end": 2140.5, "word": " C", "probability": 0.62255859375}, {"start": 2140.5, "end": 2140.62, "word": " اللي", "probability": 0.8740234375}, {"start": 2140.62, "end": 2140.78, "word": " هي", "probability": 0.82666015625}, {"start": 2140.78, "end": 2141.2, "word": " 00", "probability": 0.188232421875}, {"start": 2141.2, "end": 2141.5, "word": " في", "probability": 0.76220703125}, {"start": 2141.5, "end": 2141.66, "word": " هذه", "probability": 0.77001953125}, {"start": 2141.66, "end": 2142.04, "word": " الحالة", "probability": 0.9759114583333334}, {"start": 2142.04, "end": 2142.26, "word": " does", "probability": 0.63916015625}, {"start": 2142.26, "end": 2142.64, "word": " not", "probability": 0.96826171875}, {"start": 2142.64, "end": 2143.58, "word": " exist", "probability": 0.97265625}, {"start": 2143.58, "end": 2144.28, "word": " بيكون", "probability": 0.583251953125}, {"start": 2144.28, "end": 2144.52, "word": " هيك", "probability": 0.82275390625}, {"start": 2144.52, "end": 2144.74, "word": " احنا", "probability": 0.771728515625}, {"start": 2144.74, "end": 2145.5, "word": " انتهينا", "probability": 0.972412109375}, {"start": 2145.5, "end": 2146.06, "word": " من", "probability": 0.9921875}, {"start": 2146.06, "end": 2146.48, "word": " الجزء", "probability": 0.96435546875}, {"start": 2146.48, "end": 2147.02, "word": " الأول", "probability": 0.92822265625}, {"start": 2147.02, "end": 2147.32, "word": " من", "probability": 0.9443359375}, {"start": 2147.32, "end": 2148.12, "word": " المحاضرة", "probability": 0.9747314453125}, {"start": 2148.12, "end": 2149.0, "word": " الخامسة", "probability": 0.990966796875}], "temperature": 1.0}, {"id": 84, "seek": 217203, "start": 2150.43, "end": 2172.03, "text": "اللي هو discussion لأو مناقشة ل section 6-1 اللي هو the derivative والآن سنكمل الحديث في الجزء الثاني من المحاضرة اللي هو عن اللي هو the mean value theorem أو اللي هي نكمل applications على mean value theorem وناخد اللي هو ال", "tokens": [6027, 20292, 31439, 5017, 5296, 10721, 2407, 3714, 8315, 4587, 8592, 3660, 5296, 3541, 1386, 12, 16, 13672, 1829, 31439, 264, 13760, 16070, 148, 48506, 8608, 1863, 24793, 1211, 21542, 16254, 12984, 8978, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 9673, 5016, 46958, 25720, 13672, 1829, 31439, 18871, 13672, 1829, 31439, 264, 914, 2158, 20904, 34051, 13672, 1829, 39896, 8717, 24793, 1211, 5821, 15844, 914, 2158, 20904, 4032, 1863, 47283, 3215, 13672, 1829, 31439, 2423], "avg_logprob": -0.21266233534007878, "compression_ratio": 1.6683673469387754, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 2150.4300000000003, "end": 2151.15, "word": "اللي", "probability": 0.753173828125}, {"start": 2151.15, "end": 2151.51, "word": " هو", "probability": 0.9287109375}, {"start": 2151.51, "end": 2152.81, "word": " discussion", "probability": 0.88818359375}, {"start": 2152.81, "end": 2153.89, "word": " لأو", "probability": 0.6074625651041666}, {"start": 2153.89, "end": 2154.65, "word": " مناقشة", "probability": 0.948046875}, {"start": 2154.65, "end": 2154.87, "word": " ل", "probability": 0.88916015625}, {"start": 2154.87, "end": 2155.27, "word": " section", "probability": 0.271240234375}, {"start": 2155.27, "end": 2155.59, "word": " 6", "probability": 0.587890625}, {"start": 2155.59, "end": 2155.85, "word": "-1", "probability": 0.6712646484375}, {"start": 2155.85, "end": 2156.03, "word": " اللي", "probability": 0.73388671875}, {"start": 2156.03, "end": 2156.17, "word": " هو", "probability": 0.9755859375}, {"start": 2156.17, "end": 2156.29, "word": " the", "probability": 0.42041015625}, {"start": 2156.29, "end": 2157.47, "word": " derivative", "probability": 0.853515625}, {"start": 2157.47, "end": 2158.57, "word": " والآن", "probability": 0.7032877604166666}, {"start": 2158.57, "end": 2159.91, "word": " سنكمل", "probability": 0.985595703125}, {"start": 2159.91, "end": 2160.83, "word": " الحديث", "probability": 0.9915364583333334}, {"start": 2160.83, "end": 2160.99, "word": " في", "probability": 0.91357421875}, {"start": 2160.99, "end": 2161.29, "word": " الجزء", "probability": 0.9462890625}, {"start": 2161.29, "end": 2161.65, "word": " الثاني", "probability": 0.9615478515625}, {"start": 2161.65, "end": 2161.81, "word": " من", "probability": 0.970703125}, {"start": 2161.81, "end": 2162.55, "word": " المحاضرة", "probability": 0.9903564453125}, {"start": 2162.55, "end": 2163.81, "word": " اللي", "probability": 0.9267578125}, {"start": 2163.81, "end": 2164.15, "word": " هو", "probability": 0.9775390625}, {"start": 2164.15, "end": 2164.75, "word": " عن", "probability": 0.96630859375}, {"start": 2164.75, "end": 2165.69, "word": " اللي", "probability": 0.7099609375}, {"start": 2165.69, "end": 2166.01, "word": " هو", "probability": 0.9833984375}, {"start": 2166.01, "end": 2166.35, "word": " the", "probability": 0.74462890625}, {"start": 2166.35, "end": 2166.59, "word": " mean", "probability": 0.73193359375}, {"start": 2166.59, "end": 2166.91, "word": " value", "probability": 0.9765625}, {"start": 2166.91, "end": 2167.41, "word": " theorem", "probability": 0.87939453125}, {"start": 2167.41, "end": 2167.79, "word": " أو", "probability": 0.73193359375}, {"start": 2167.79, "end": 2168.41, "word": " اللي", "probability": 0.943603515625}, {"start": 2168.41, "end": 2168.67, "word": " هي", "probability": 0.92578125}, {"start": 2168.67, "end": 2169.25, "word": " نكمل", "probability": 0.9290364583333334}, {"start": 2169.25, "end": 2169.95, "word": " applications", "probability": 0.58984375}, {"start": 2169.95, "end": 2170.31, "word": " على", "probability": 0.7041015625}, {"start": 2170.31, "end": 2170.49, "word": " mean", "probability": 0.685546875}, {"start": 2170.49, "end": 2170.81, "word": " value", "probability": 0.98876953125}, {"start": 2170.81, "end": 2171.17, "word": " theorem", "probability": 0.8916015625}, {"start": 2171.17, "end": 2171.65, "word": " وناخد", "probability": 0.9600830078125}, {"start": 2171.65, "end": 2171.75, "word": " اللي", "probability": 0.975341796875}, {"start": 2171.75, "end": 2171.91, "word": " هو", "probability": 0.98095703125}, {"start": 2171.91, "end": 2172.03, "word": " ال", "probability": 0.311767578125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2173.5270625, "duration_after_vad": 2117.446874999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0fe1e77efbcbf108e3fabf9108b97f46e2f98add
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Apc0JvRJbDQ_raw.srt
@@ -0,0 +1,1500 @@
+1
+00:00:04,910 --> 00:00:09,510
+بسم الله الرحمن الرحيم هذه المحاضرة الخامسة في
+
+2
+00:00:09,510 --> 00:00:15,630
+مساق تحليل حقيقه اتنين لطلبة كلية العلوم تخصص
+
+3
+00:00:15,630 --> 00:00:22,110
+رياضيات في الجامعة الإسلامية بغزا المحاضرة
+
+4
+00:00:22,110 --> 00:00:26,550
+اليوم هي جزئين الجزء الاول اللي هو عبارة عن
+
+5
+00:00:26,550 --> 00:00:31,350
+discussion لست واحد اللي هو مناقشة لموضوع اللي هو
+
+6
+00:00:31,350 --> 00:00:37,410
+derivative او الاشتقاءالجزء الثاني هنكمل اللي هو
+
+7
+00:00:37,410 --> 00:00:43,210
+الحديث عن 6.2 اللي هو الـ Mean Value Theorem أو
+
+8
+00:00:43,210 --> 00:00:47,730
+نظرية القيمة المتوسطة هناخذ بعض التطبيقات لنبدأ
+
+9
+00:00:47,730 --> 00:00:51,750
+الآن اللي هي بالأسئلة اللي احنا طلبناها منكم
+
+10
+00:00:51,750 --> 00:00:57,230
+تحلوها كواجب المرة الماضية أو التي قبلها وكانت
+
+11
+00:00:57,230 --> 00:01:01,210
+الأسئلة هي عبارة عن السؤال الرابع والسؤال السابع
+
+12
+00:01:02,000 --> 00:01:07,420
+والسؤال التاسع و السؤال تلتاشر بالنسبة للسؤال
+
+13
+00:01:07,420 --> 00:01:13,600
+الثالث اللي هو عبارة عن اللي هي برهان نظرية 613A
+
+14
+00:01:13,600 --> 00:01:19,200
+وB وهذه البرهين براهين سهلة اللي كانت ال F
+
+15
+00:01:19,200 --> 00:01:22,960
+differentiableالـ F differentiable والـ Alpha
+
+16
+00:01:22,960 --> 00:01:26,560
+عبارة عن constant بيعطينا الـ Alpha F برضه is
+
+17
+00:01:26,560 --> 00:01:30,200
+differentiable و لو كانت الـ F والـ G
+
+18
+00:01:30,200 --> 00:01:32,700
+differentiable بيعطينا الـ F زائد G is
+
+19
+00:01:32,700 --> 00:01:35,660
+differentiable و احنا برهننا حالة الضرب و حالة
+
+20
+00:01:35,660 --> 00:01:41,500
+القسمة و هدول حالات تعتبر سهلة مباشرة على التعريف
+
+21
+00:01:41,500 --> 00:01:45,900
+لذلك هنبدأ ان شاء الله في الحديث او في حل الأسئلة
+
+22
+00:01:45,900 --> 00:01:52,540
+على السؤال الرابع اللي هو ببول ماليعندي معطيني F
+
+23
+00:01:52,540 --> 00:02:01,760
+من R لـ R بي defined by F of X بساوي اللي هو X
+
+24
+00:02:01,760 --> 00:02:06,420
+تربيع إذا كانت X rational وبساوي سفر إذا كانت X
+
+25
+00:02:06,420 --> 00:02:09,700
+irrational اثبت إن الـ F الـ differential بالقدر X
+
+26
+00:02:09,700 --> 00:02:15,550
+بتساوي سفر أو جد اللي هي F prime of 0لاحظ أن الـ
+
+27
+00:02:15,550 --> 00:02:16,610
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+28
+00:02:16,610 --> 00:02:17,090
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+29
+00:02:17,090 --> 00:02:17,910
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+30
+00:02:17,910 --> 00:02:20,450
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+31
+00:02:20,450 --> 00:02:27,990
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+32
+00:02:27,990 --> 00:02:28,350
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+33
+00:02:28,350 --> 00:02:29,630
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+34
+00:02:29,630 --> 00:02:29,690
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+35
+00:02:29,690 --> 00:02:41,470
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+36
+00:02:41,470 --> 00:02:52,150
+الـ الـ الـFind this value a proof الآن عشان نوجد
+
+37
+00:02:52,150 --> 00:02:56,730
+اللي هي نثبت أن F prime of 0 موجودة خلّيني ألاحظ
+
+38
+00:02:56,730 --> 00:03:00,950
+مالي عند ال function اللي هي X تربيع لما X
+
+39
+00:03:00,950 --> 00:03:07,150
+rational و Zero لما Xاش is irrationalالان بدنا
+
+40
+00:03:07,150 --> 00:03:11,770
+نتوقع اول اشي اللي هو لانه هتلزمني جاي اللي بعدين
+
+41
+00:03:11,770 --> 00:03:15,890
+find this value بدنا نتوقع ايش قيمة اللي هو ال
+
+42
+00:03:15,890 --> 00:03:20,950
+derivative عند الصفر لاحظ انه اللي هو .. اللي ..
+
+43
+00:03:20,950 --> 00:03:25,630
+اللي لو بدنا نقول انه ال derivative ممكن تكون zero
+
+44
+00:03:25,630 --> 00:03:30,510
+كون ان off of x صفر او لو بدها تكون و ال
+
+45
+00:03:30,510 --> 00:03:36,560
+derivative هنا لو قولنا رفل 2xبدو يكون اللي هو لو
+
+46
+00:03:36,560 --> 00:03:40,820
+بدو يكون اللي عند الـ zero اللي هي F prime بدو في
+
+47
+00:03:40,820 --> 00:03:47,220
+النهاية تروح ل اللي هيكون برضه قريبة من انه نقول
+
+48
+00:03:47,220 --> 00:03:52,580
+او نأكد انها صفر عشان هي كالظن الغالب ان F prime
+
+49
+00:03:52,580 --> 00:03:58,660
+هتكون ايش صفر هذه مجرد تفكيرات الانبدي أثبت لك إنه
+
+50
+00:03:58,660 --> 00:04:03,080
+فعلًا هي الـ derivative بتساوي 0 كيف بدي أثبتها؟
+
+51
+00:04:03,080 --> 00:04:11,280
+بدي أثبت لك إنه الـ limit لـ F of X نقص F of 0 على
+
+52
+00:04:11,280 --> 00:04:17,600
+X minus 0 لما X تروح لـ 0 بتساوي 0 بدي أثبت لك
+
+53
+00:04:17,600 --> 00:04:24,240
+هيهاالان واضح ان X تقول الى الصفر X تقول الى الصفر
+
+54
+00:04:24,240 --> 00:04:29,200
+هتمر بال rational وال rational عشان هيك صعب ان انا
+
+55
+00:04:29,200 --> 00:04:32,600
+اتحدث عن اللي هو ايجاد ال derivative مباشرة من
+
+56
+00:04:32,600 --> 00:04:36,130
+الان او من ال two branches اللي عندىلا بقدر أخد من
+
+57
+00:04:36,130 --> 00:04:40,030
+اليمين ولا أخد من اليسار لإنه عندي من اليمين أو من
+
+58
+00:04:40,030 --> 00:04:44,130
+اليسار هيكون عندي اللي هو قابلت اللي هي الأعداد ال
+
+59
+00:04:44,130 --> 00:04:48,110
+rational لل rational فعشانك أسلم إشي إنه نستخدم
+
+60
+00:04:48,110 --> 00:04:52,650
+التعريف في إثبات هذا يعني الآن بدي أثبت هذا الكلام
+
+61
+00:04:53,270 --> 00:04:58,090
+كيف بدي أثبته؟ بدي أثبت ما يعني بدي أصل لكل إبسلون
+
+62
+00:04:58,090 --> 00:05:03,190
+أكبر من 0 بدلاج دلتا أكبر من 0 بدلاجية حاجيلك دلتا
+
+63
+00:05:03,190 --> 00:05:08,350
+بحيث أنه لما يكون ال absolute value ل F of X ناقص
+
+64
+00:05:08,350 --> 00:05:14,630
+F of Zero على X minus Zero يكون ناقص Zero طبعا
+
+65
+00:05:14,630 --> 00:05:19,790
+Zero هذي أصغر من إبسلون هذا متى؟ whenever
+
+66
+00:05:22,670 --> 00:05:28,470
+x-0 أكبر من 0 وأصغر من مين من دلتا هذا اللي بده
+
+67
+00:05:28,470 --> 00:05:33,150
+أصله أو هذا اللي بده أثبته خلّينا نشوف إذا خلّينا
+
+68
+00:05:33,150 --> 00:05:36,530
+نشوف كيف بدنا نوجده عشان أثبت إن ال limit هذا
+
+69
+00:05:36,530 --> 00:05:43,110
+بساوي 0 لاحظ القيمة اللي عندي أول إشي ال absolute
+
+70
+00:05:43,110 --> 00:05:50,530
+value of f of x ناقص f of 0 على x-0 إيش هتساوي؟
+
+71
+00:05:51,590 --> 00:05:57,390
+هتساوي اللي هو ال absolute value of of X عندى يا X
+
+72
+00:05:57,390 --> 00:06:01,070
+تربيع يمين يا سفر خلّينها زي ما هي أول إشي of of X
+
+73
+00:06:01,070 --> 00:06:06,010
+ناقص of of Zero اللي هو جداش بيساوي Zero لإنه of
+
+74
+00:06:06,010 --> 00:06:10,130
+of Zero بيساوي Zero لإنه Zero rational على إذن هذا
+
+75
+00:06:10,130 --> 00:06:16,230
+سفر على X ناقص سفر اللي هو X absolute value هذا
+
+76
+00:06:16,230 --> 00:06:22,790
+القيمة الآن لاحظ بتساوييا إما اللي هو x تربيع على
+
+77
+00:06:22,790 --> 00:06:30,750
+x absolute value في حالة x is rational أو بتساوي
+
+78
+00:06:30,750 --> 00:06:37,450
+اللي هو سفر في حالة x أشمالها is irrational لأن
+
+79
+00:06:37,450 --> 00:06:42,030
+مقيمة f of x يا x تربيع يا سفر حسب اللي هو كتبناه
+
+80
+00:06:42,030 --> 00:06:46,790
+حاليًاالآن هذا بالظبط هو عبارة عن الـ absolute
+
+81
+00:06:46,790 --> 00:06:57,590
+value لل X if X is rational Zero if X is
+
+82
+00:06:57,590 --> 00:07:03,950
+irrational الآن الصورة وضحت خلّينا نسمي هذا اللي
+
+83
+00:07:03,950 --> 00:07:09,900
+هو واحدالان حضرت عشان اصل للنهاية اللى هاني كاتبها
+
+84
+00:07:09,900 --> 00:07:13,800
+هنا واشوف ايش ال delta اللى بتطلع عندى الان بتدعي
+
+85
+00:07:13,800 --> 00:07:17,380
+مالي for every epsilon أكبر من سفر انا بقول there
+
+86
+00:07:17,380 --> 00:07:21,800
+exists delta هتساوي من ال epsilon هتجد تشوفوا ليش
+
+87
+00:07:21,800 --> 00:07:26,980
+there exists delta بساوي epsilon such that if x
+
+88
+00:07:26,980 --> 00:07:35,210
+minus 0 أكبر من سفره أصغر من delta thenهذا معناته
+
+89
+00:07:35,210 --> 00:07:37,870
+إيش أن أبسل يوت فيها ال X أكبر من صفر وأصغر من
+
+90
+00:07:37,870 --> 00:07:41,870
+مين؟ من دلتا إذا اخترت دلتا إيش بتساوي و هي اللي
+
+91
+00:07:41,870 --> 00:07:47,850
+هتخلص من الموضوع then اللي هو F of X نقص F of Zero
+
+92
+00:07:47,850 --> 00:07:50,970
+على
+
+93
+00:07:50,970 --> 00:07:57,790
+X minus Zero هو طبعا نقص الصفر اللي قلنا عنها ال
+
+94
+00:07:57,790 --> 00:08:01,520
+derivative المتوقع عليا هذه بالظبطاللي فوق هذا هو
+
+95
+00:08:01,520 --> 00:08:05,920
+اللي فوق طلع إيش عندي هذا بساوي هذا المقدار إذا
+
+96
+00:08:05,920 --> 00:08:09,760
+كانت X rational و 0 إذا كانت X irrational يعني
+
+97
+00:08:09,760 --> 00:08:15,400
+بمعنى أخر بساوي absolute value ل X if X is
+
+98
+00:08:15,400 --> 00:08:23,530
+rational و 0 if X is irrational in both casesاللي
+
+99
+00:08:23,530 --> 00:08:27,590
+هي إذا كان بساوي absolute value للـ X هيكون أصغر
+
+100
+00:08:27,590 --> 00:08:31,250
+من Delta اللي انا اخترتها أشملها Epsilon هيكون
+
+101
+00:08:31,250 --> 00:08:34,570
+أصغر من Epsilon و أيضا هذه متحققة لإن الـ Epsilon
+
+102
+00:08:34,570 --> 00:08:38,850
+دائما أشملها أكبر من 0 إذا اللي حصلته أنه لكل
+
+103
+00:08:38,850 --> 00:08:42,490
+Epsilon أكبر من 0 اللي جيت Delta لما يكون هذا أصغر
+
+104
+00:08:42,490 --> 00:08:47,130
+من Delta بيعطيني هذا أصغر من Epsilon وهذا يعني
+
+105
+00:08:47,130 --> 00:08:54,370
+hence limitهذا المقدار اللي هو f of x ناقص f of 0
+
+106
+00:08:54,370 --> 00:09:01,690
+على x minus 0 لما x تروح للصفر بساوية اللي هو
+
+107
+00:09:01,690 --> 00:09:12,870
+الصفر وهذا هو تعريف من ال f prime عند 0 that is f
+
+108
+00:09:12,870 --> 00:09:18,740
+prime at 0 بساوية 0 وفي نفس الواجب طبعا أثبتناالـ
+
+109
+00:09:18,740 --> 00:09:25,960
+existence للـ F prime عند الـ zero أي سؤال طيب
+
+110
+00:09:25,960 --> 00:09:30,840
+نيجي الآن نشوف السؤال الثاني خلّال السؤال الأربعة
+
+111
+00:09:30,840 --> 00:09:44,220
+نيجي لسؤال سبعة الان
+
+112
+00:09:44,220 --> 00:09:48,100
+سؤال سبعة اش اللي بقوله سؤال سبعةاللي بيقوله سؤال
+
+113
+00:09:48,100 --> 00:09:52,420
+سبعة مالي عندي
+
+114
+00:09:52,420 --> 00:09:55,740
+suppose
+
+115
+00:09:55,740 --> 00:09:59,320
+that F من R لR is differentiable at C يعني نفترض
+
+116
+00:09:59,320 --> 00:10:04,520
+أنه F قبل الاشتقاق عند Cونفترض ان f of c قيمة الـ
+
+117
+00:10:04,520 --> 00:10:07,920
+function عند c بساوة 0 لان بقول لشهدات ال absolute
+
+118
+00:10:07,920 --> 00:10:10,960
+value لل f of x اللي هي نسميها d of x is
+
+119
+00:10:10,960 --> 00:10:14,080
+differentiable at c if and only if a شمالها f
+
+120
+00:10:14,080 --> 00:10:21,740
+prime of c بتساوة 0 إذا ناخد لك f من R لعند R و
+
+121
+00:10:21,740 --> 00:10:30,810
+جايلك أن f prime عند c exist معطيكي إياهاأو ومعطيك
+
+122
+00:10:30,810 --> 00:10:37,390
+اللي هو f of c بتساوي سفر وبقول لي prove that أنه
+
+123
+00:10:37,390 --> 00:10:42,370
+g of x بساوي ال absolute value لل f of x is
+
+124
+00:10:42,370 --> 00:10:49,810
+differentiable at c if and only if f prime عند ال
+
+125
+00:10:49,810 --> 00:10:57,880
+c ايش بتساوي بساوي سفر، مظبوط؟ طيب شوفالان خلينا
+
+126
+00:10:57,880 --> 00:11:03,380
+افترض اول اشي ان f prime عند c ايش بتساوي سفر نقول
+
+127
+00:11:03,380 --> 00:11:09,320
+suppose proof suppose
+
+128
+00:11:09,320 --> 00:11:15,580
+suppose
+
+129
+00:11:15,580 --> 00:11:23,120
+that f prime at c بتساوي سفر ايش هذا بيعني ان then
+
+130
+00:11:23,120 --> 00:11:25,940
+limit
+
+131
+00:11:27,220 --> 00:11:36,680
+F of X ناقص F of C على X minus C لما X تروح للـ C
+
+132
+00:11:36,680 --> 00:11:40,240
+اللي هو بيساوي سفر لأن هذا تعريف مين F براين
+
+133
+00:11:40,240 --> 00:11:46,000
+بيساوي سفر و F of C إيش معطنية هو بيساوي سفر لأن
+
+134
+00:11:46,000 --> 00:11:53,260
+بيساوي limit F of X على X minus C لما X تروح لمين
+
+135
+00:11:53,260 --> 00:11:58,730
+للـ C مدامة ال limit هذه موجودةإذا ال limit من
+
+136
+00:11:58,730 --> 00:12:02,270
+اليمين وال limit من اليسار أيش برضه مالها موجودة
+
+137
+00:12:02,270 --> 00:12:06,710
+ماشي الحال انا الآن غرضي ان او اثبت ان g of x بسبب
+
+138
+00:12:06,710 --> 00:12:09,190
+absolute value of f of x أيش مالها is
+
+139
+00:12:09,190 --> 00:12:14,110
+differentiable at c ماشي الان ايش اللي بدي اثبته
+
+140
+00:12:14,110 --> 00:12:22,370
+بمعنى اخر بدي اثبتلك انه limitالـ G of X ناقص G of
+
+141
+00:12:22,370 --> 00:12:29,430
+C على X minus C لما X تروح للـ C exist باشي إذا
+
+142
+00:12:29,430 --> 00:12:31,930
+أثبتوا معناته أثبتتوا إن الـ G is differentiable
+
+143
+00:12:31,930 --> 00:12:36,970
+at C أو بمعنى آخر بالدثبت limit لـ absolute value
+
+144
+00:12:36,970 --> 00:12:42,660
+لل F of Xمدلة g of x ناقص ال absolute value of f
+
+145
+00:12:42,660 --> 00:12:48,960
+of c على x minus c لما x بتروح لل c exist بدي أشوف
+
+146
+00:12:48,960 --> 00:12:53,240
+هدا لسه exist ولا لأ يعني بدي أثبت اللي هو limit
+
+147
+00:12:53,240 --> 00:12:58,900
+absolute value of f of x على x minus c as x بتروح
+
+148
+00:12:58,900 --> 00:13:07,520
+لل c أشماله exist ماشي الحال طيب الآن واضح
+
+149
+00:13:08,360 --> 00:13:13,000
+عندي من اللي فوق ال limit لل f of x على x minus c
+
+150
+00:13:13,000 --> 00:13:19,160
+as x بتروح لل c انه ايش بيساوي بيساوي صفر، مظبوط؟
+
+151
+00:13:19,160 --> 00:13:27,160
+اذا هيكون عندي limit اللي هو limit absolute value
+
+152
+00:13:27,160 --> 00:13:33,400
+لل limit خليني اكتبها بس في طريقة أخرى الصفر هذا
+
+153
+00:13:33,400 --> 00:13:43,200
+اللي بدأتبته اه انه existعندي ال absolute value ل
+
+154
+00:13:43,200 --> 00:13:52,020
+limit f of x على x minus c لما x تروح لل c اللي هو
+
+155
+00:13:52,020 --> 00:13:58,020
+من اليمين و من اليسار exist، مظبوط؟ واضحة و يساوي
+
+156
+00:13:58,020 --> 00:14:05,160
+اللي هو limit absolute value لل f of x على x minus
+
+157
+00:14:05,160 --> 00:14:12,420
+c as absolute valueas X بتروح لمين؟ للـ C باشي
+
+158
+00:14:12,420 --> 00:14:16,820
+الحال الآن من اليمين ومن اليسار كله هيكون موجود
+
+159
+00:14:16,820 --> 00:14:20,480
+بناء على هذا أنه موجود خلّيني أخد من اليمين وهنا
+
+160
+00:14:20,480 --> 00:14:25,860
+من اليمين فبصير هذا عبارة عن limit absolute value
+
+161
+00:14:25,860 --> 00:14:32,140
+ل F of X على X minus C لما X بتروح ل C من وين؟ من
+
+162
+00:14:32,140 --> 00:14:38,330
+اليمين يعني هذا المقدارصار موجود وإيش بساوي بساوي
+
+163
+00:14:38,330 --> 00:14:42,350
+سفر هذا خلّيه لإنه هذا اللي بدنا نصلّه لأن limit
+
+164
+00:14:42,350 --> 00:14:47,310
+صار عندي معنى آخر limit absolute value of f of x
+
+165
+00:14:47,310 --> 00:14:53,850
+على x minus c لما x تروح لل c من اليمين بساوي سفر
+
+166
+00:14:53,850 --> 00:14:58,360
+existلاحظا قاعد رايح لأثبت أن هذا exist ده خد الآن
+
+167
+00:14:58,360 --> 00:15:03,520
+من وين؟ من اليسار خد لأن احسب similarly عندي سفر
+
+168
+00:15:03,520 --> 00:15:08,840
+بساوي absolute value of limit f of x على x minus c
+
+169
+00:15:08,840 --> 00:15:15,100
+لما x تروح ل c من وين؟ من اليسار ويساوي عبارة عن
+
+170
+00:15:15,100 --> 00:15:19,960
+limit absolute value of f of x على absolute value
+
+171
+00:15:19,960 --> 00:15:25,900
+of x minus c لما x تروح ل c من وين؟ من اليسارهذه
+
+172
+00:15:25,900 --> 00:15:34,580
+نفسها بساوي limit أو بساوي سالب limit f of x
+
+173
+00:15:34,580 --> 00:15:42,270
+absolute value على x minus c لما x تروحللـ C من
+
+174
+00:15:42,270 --> 00:15:47,030
+اليسار، ليش؟ لأن X أصغر من C، إذا X minus C سالبة
+
+175
+00:15:47,030 --> 00:15:50,230
+إذا الـ absolute value سالب إليها واخدت السالب برا
+
+176
+00:15:50,230 --> 00:15:54,990
+هذا الآن المخضر بيساوي سفر، إذا هذا لحاله برضه إيش
+
+177
+00:15:54,990 --> 00:16:01,270
+ماله؟ سفر، إذا limit absolute value للـ F of X على
+
+178
+00:16:01,270 --> 00:16:04,870
+X minus C، لما X تروح للـ C من اليسار، برضه إيش
+
+179
+00:16:04,870 --> 00:16:10,450
+بيساوي؟ بيساوي سفر، لاحظ إن ال limit من اليمينوالـ
+
+180
+00:16:10,450 --> 00:16:15,890
+limit من اليسار موجود وبساوي 0 متساويين يعني الآن
+
+181
+00:16:15,890 --> 00:16:23,130
+ال limit هذا صار ايش بساوي بساوي 0 إذا الان هذا
+
+182
+00:16:23,130 --> 00:16:29,870
+الآن بنقوله كله تحت هذا وبقول hence اللي هو g
+
+183
+00:16:29,870 --> 00:16:38,310
+prime of c بساوي limit of g of x نقص g of c على x
+
+184
+00:16:38,310 --> 00:16:46,870
+minus cas x → c بساوي حسب اللي عندى من هنا و من
+
+185
+00:16:46,870 --> 00:16:55,310
+هنا و من هنا هيساوي سفر الان conversely بتأفترض
+
+186
+00:16:55,310 --> 00:16:58,090
+طبعا ان ال conversely هيكون الخطوات كثير مشابهه
+
+187
+00:16:58,090 --> 00:17:03,350
+لللي هنا يعني كثير اللي استخدمته هنا هستخدمه في
+
+188
+00:17:03,350 --> 00:17:03,930
+اللي بعدها
+
+189
+00:17:12,670 --> 00:17:17,790
+Conversely suppose that
+
+190
+00:17:17,790 --> 00:17:25,890
+g of x سواء absolute value او f of x اللي
+
+191
+00:17:25,890 --> 00:17:33,550
+هو is differentiable at c بدا وجدلك الان اثبتلك ان
+
+192
+00:17:33,550 --> 00:17:39,650
+f prime of c ايش ما لها بتساوي سفر يعني بدا اثبت
+
+193
+00:17:39,650 --> 00:17:46,880
+limitf of x ناقص f of c اللي هي سفر على x minus c
+
+194
+00:17:46,880 --> 00:17:51,160
+لما x تروح لل c ايش بيساوي بساوي سفر بكون خلصت
+
+195
+00:17:51,160 --> 00:17:58,500
+الان issue مشابه عند الان limit
+
+196
+00:17:58,500 --> 00:18:05,180
+هذا exist عند ال c اذا عندي صار g prime of c exist
+
+197
+00:18:05,180 --> 00:18:10,430
+ويساوي حسب الحديث اللي هنا limitabsolute value of
+
+198
+00:18:10,430 --> 00:18:18,570
+f of x ناقص ال absolute value of f of c صفر على x
+
+199
+00:18:18,570 --> 00:18:26,310
+minus c لما x تروح ل c اشماله exist معايا؟ طيب شوف
+
+200
+00:18:26,310 --> 00:18:34,960
+الآن عندى اذا احسبلي limitf of x اللي حسبناها قبل
+
+201
+00:18:34,960 --> 00:18:39,660
+بشوية بنفس الأسلوب على x minus c لما x تروح ل c من
+
+202
+00:18:39,660 --> 00:18:47,020
+وين؟ من اليمين بساوي limit لل absolute value ل f
+
+203
+00:18:47,020 --> 00:18:53,780
+of x على x minus c لما x تروح ل c من اليمين لأن ال
+
+204
+00:18:53,780 --> 00:19:01,840
+x أكبر من ال c واضحالآن من جهة أخرى احسبلي الـ
+
+205
+00:19:01,840 --> 00:19:08,060
+absolute value لل limit لل F of X طبعا هذا ايش
+
+206
+00:19:08,060 --> 00:19:15,620
+هيساوي بسوى G prime of C، مظبوط؟ بسوى G prime of
+
+207
+00:19:15,620 --> 00:19:23,290
+C، موجود، limit F of Xعلى x minus c لما x تروح ل c
+
+208
+00:19:23,290 --> 00:19:28,570
+من وين؟ من اليسار بساوي زي ما عملنا قبل شوية سالب
+
+209
+00:19:28,570 --> 00:19:33,530
+limit absolute value of f of x على x minus c لما x
+
+210
+00:19:33,530 --> 00:19:41,050
+تروح ل c من وين؟ من اليسار الآن واضح بما أن هذه
+
+211
+00:19:41,050 --> 00:19:51,470
+exist إذا هذا المقدار و هذا المقدار زي بعضالان هذا
+
+212
+00:19:51,470 --> 00:19:56,590
+بيساوي ناقص هذا او بمعنى اخر نشيل الناقص من هنا و
+
+213
+00:19:56,590 --> 00:20:03,390
+نضربه هنا صار عندى المقدرين هدولة بما انه متساويين
+
+214
+00:20:03,390 --> 00:20:10,310
+لإن الاتنين ايش بيساوين ال G prime of C مظبوط اذا
+
+215
+00:20:10,310 --> 00:20:13,390
+صار عندى هذا المقدار بيساوي هذا المقدار اذا صار
+
+216
+00:20:13,390 --> 00:20:20,940
+عندى ال limitF of X على X minus C لما X تروح للـ C
+
+217
+00:20:20,940 --> 00:20:29,560
+من اليمين absolute value بساوي ناقص limit F of X
+
+218
+00:20:29,560 --> 00:20:34,600
+على X minus C لما X تروح للـ C من وين؟ من اليسار
+
+219
+00:20:34,600 --> 00:20:41,500
+واضحة؟ لكن أصلا عندى هذا
+
+220
+00:20:43,370 --> 00:20:49,010
+بساوي اللي هو التنين بساوي نفس القيمة ماشي الحال
+
+221
+00:20:49,010 --> 00:20:55,850
+إذا لازم عندي من هنا جي برايم و جي برايم اللي هو
+
+222
+00:20:55,850 --> 00:21:00,210
+صار بنساوي نفس القيمة إذا هيطلع الجي برايم إيش
+
+223
+00:21:00,210 --> 00:21:05,530
+ماله بساوي سفرإذا صار المقدار هذا كله إش بده يساوي
+
+224
+00:21:05,530 --> 00:21:08,650
+صفر وهذا بيساوي صفر يعني ال limit من اليمين و
+
+225
+00:21:08,650 --> 00:21:12,070
+limit من اليسار متساويين إذا صارت limit F of X على
+
+226
+00:21:12,070 --> 00:21:23,310
+X minus C لما X تروح للـC بدها تساوي صفر أي سؤال؟
+
+227
+00:21:23,310 --> 00:21:31,130
+زي ما حكينا، الآن إحنا قلنا إنه لو كانت D بدينا D
+
+228
+00:21:31,130 --> 00:21:34,600
+بيساوي F of X ال differential بالأد Cجيبنا g prime
+
+229
+00:21:34,600 --> 00:21:37,500
+و كتبناها بالصورة اللي أمامنا بعدين أخدنا ال
+
+230
+00:21:37,500 --> 00:21:40,120
+absolute value لlimit f of x علي x minus c لم x
+
+231
+00:21:40,120 --> 00:21:45,200
+تروح ل c positive طلعت عندي بساوي g prime of c و
+
+232
+00:21:45,200 --> 00:21:48,680
+أخدنا اللي هي ناقص هذه طلعت عندي برضه g prime
+
+233
+00:21:48,680 --> 00:21:53,920
+الاتنين ال c إذا صار هذا بساوي هذا المقدار و احنا
+
+234
+00:21:53,920 --> 00:21:57,640
+بنعرف في الأصل ان f prime of c exist يعني
+
+235
+00:21:57,640 --> 00:22:01,900
+differentiable يعني ال limit هذا اللي هو موجودو من
+
+236
+00:22:01,900 --> 00:22:05,100
+اليمين و من اليسار زي بعض يعني يعني هذا بده يساوي
+
+237
+00:22:05,100 --> 00:22:07,500
+هذا من اليمين و هذا من اليسار يعني في الواقع هذا
+
+238
+00:22:07,500 --> 00:22:10,960
+اللي جوا هو نفسه اللي جوا بساوي limit of of X يعني
+
+239
+00:22:10,960 --> 00:22:15,780
+بمعنى أخر absolute value ل limit of of X على X
+
+240
+00:22:15,780 --> 00:22:22,100
+minus C لما X تروح لل C هو نفسه سالب limit لل of
+
+241
+00:22:22,100 --> 00:22:27,400
+of X على X minus C لما X تروح لل C من وين من
+
+242
+00:22:27,400 --> 00:22:31,540
+اليسار هو نفسه لل C من وين تبت هذالأنه احنا بنقول
+
+243
+00:22:31,540 --> 00:22:34,560
+f prime of c exist يعني ال limit هذا موجود و من
+
+244
+00:22:34,560 --> 00:22:37,360
+اليمين و من اليسار زي بعر إذا صار هذا المقدر نفس
+
+245
+00:22:37,360 --> 00:22:41,200
+هذا المقدر زي ما قلنا إذا صار عند هذا المقدر بساوة
+
+246
+00:22:41,200 --> 00:22:46,800
+سفر لإن التنين بسينا بساوة سفر إذا صار عنده limitF
+
+247
+00:22:46,800 --> 00:22:50,880
+of X على X minus C اللي هو الـ absolute value as X
+
+248
+00:22:50,880 --> 00:22:56,100
+بتروح للـ C بساوة صفر ومن ثم اللي جوا بساوة صفر هو
+
+249
+00:22:56,100 --> 00:22:58,740
+مين هو اللي جوا هذا اللي كنا بدنا نصله من الأول
+
+250
+00:22:58,740 --> 00:23:04,260
+اللي هو F prime of C بتساوة صفر وهو المطلوب هذا
+
+251
+00:23:04,260 --> 00:23:10,300
+توضيح بشكل كامل ل اللي صار في اللي هو الاتجاه
+
+252
+00:23:10,300 --> 00:23:16,200
+الثاني نيجينا سؤال بعد ما خلصنا السؤال سبعةنجي
+
+253
+00:23:16,200 --> 00:23:23,420
+لسؤال تسعة تسعة ايش اللي بقوله تسعة نشوف ايش سؤال
+
+254
+00:23:23,420 --> 00:23:31,360
+تسعة بقول ونحل سؤال تسعة سؤال تسعة بقول ليه
+
+255
+00:23:31,360 --> 00:23:39,110
+باختصار انه لو كان عنده ال function ofعبارة عن من
+
+256
+00:23:39,110 --> 00:23:43,130
+R لـ R even function طبعا عارفين ايش ال even اللي
+
+257
+00:23:43,130 --> 00:23:49,130
+هو F ناقص X بيساوي F X لكل X موجودة في الـ R and
+
+258
+00:23:49,130 --> 00:23:54,310
+has a derivative at every point then F prime is an
+
+259
+00:23:54,310 --> 00:23:58,190
+odd function يعني بيقول لي لو كانت باختصار يعني لو
+
+260
+00:23:58,190 --> 00:24:01,730
+كانت ال F even و ال derivative موجودة بتكون ال
+
+261
+00:24:01,730 --> 00:24:07,010
+derivative odd و لو كانت ال derivative oddبتكون
+
+262
+00:24:07,010 --> 00:24:11,350
+الـ function الـ G prime إيه شمالها is even انحل
+
+263
+00:24:11,350 --> 00:24:16,970
+واحدة من هنا والتانية similarly زيها الآن لنفترض F
+
+264
+00:24:16,970 --> 00:24:29,890
+من عند R لعند R be an odd differentiable function
+
+265
+00:24:29,890 --> 00:24:34,970
+ماشي الحال show that
+
+266
+00:24:36,040 --> 00:24:44,360
+F' is even a proof بدنا نثبت أنه لو كانت الـ F
+
+267
+00:24:44,360 --> 00:24:49,940
+اللي هي odd function بدو يكون عنده و
+
+268
+00:24:49,940 --> 00:24:52,320
+differentiable بدو يكون عنده derivative إلها إيه
+
+269
+00:24:52,320 --> 00:25:03,000
+إيش even لأن let C element in R be arbitrary and
+
+270
+00:25:03,000 --> 00:25:04,180
+fixed
+
+271
+00:25:06,310 --> 00:25:15,930
+NR ناخد الـ R ناخد الـ C أي اللي هو real number in
+
+272
+00:25:15,930 --> 00:25:23,360
+R لكن نحكي عن اي شي محدد الان F prime of Cبدأ
+
+273
+00:25:23,360 --> 00:25:29,060
+أثبتلك أنه هو بسوء F prime of ناقص C يعني F prime
+
+274
+00:25:29,060 --> 00:25:34,920
+is even إذا خد F prime ناقص C وابدأ حسب وواصلك في
+
+275
+00:25:34,920 --> 00:25:39,140
+النهاية بسوء F prime of C إذا F prime is even بسوء
+
+276
+00:25:39,140 --> 00:25:49,380
+limit اللي هي F of X ناقص F of minus C على X minus
+
+277
+00:25:50,570 --> 00:25:57,070
+اللي هو minus C لما X تروح لمين لـ minus C مظبوط
+
+278
+00:25:57,070 --> 00:26:05,550
+طيب و يساوي limit ال F إيش معتنيها عبارة عن odd
+
+279
+00:26:05,550 --> 00:26:12,250
+إيش يعني odd يعني F of ناقص X بيساوي ناقص F of X
+
+280
+00:26:12,250 --> 00:26:16,590
+مظبوط هذه اللي هي إيش ما لها odd function اللي هو
+
+281
+00:26:16,590 --> 00:26:28,550
+بيساوي limit F ofالان اللي هي ناقص f of ناقص x
+
+282
+00:26:28,550 --> 00:26:34,150
+واضح أه؟
+
+283
+00:26:34,150 --> 00:26:37,150
+f of ناقص x بيساوي ناقص f of x يعني f of x بيساوي
+
+284
+00:26:37,150 --> 00:26:41,230
+ناقص f of ناقص x فالجد تعرفوا ليش بعملت هيك لأن
+
+285
+00:26:41,230 --> 00:26:48,570
+ناقص f of ناقص c الان f is odd مظبوط بيصير زائد f
+
+286
+00:26:48,570 --> 00:26:49,330
+of c
+
+287
+00:26:52,220 --> 00:26:58,060
+على خد الان ناقص من هنا عامل مشترك بيصير عبارة عن
+
+288
+00:26:58,060 --> 00:27:08,220
+ناقص X الان ناقص ال C لما X تروح لمين لسالب ال C
+
+289
+00:27:08,220 --> 00:27:14,040
+ال X بتروح لسالب ال C إذا و فقط إذا سالب ال X
+
+290
+00:27:14,040 --> 00:27:22,160
+بتروح لمين إلى ال C الان خد لي Yبساوي سالب ال X
+
+291
+00:27:22,160 --> 00:27:29,240
+واستبدل عشان نضح لك إياه بساوي limit الان خد الان
+
+292
+00:27:29,240 --> 00:27:38,320
+عندي F حكما كان نقص اكسميا ال Y limit ناقص F of Y
+
+293
+00:27:38,320 --> 00:27:49,390
+زائد F of C على اللي هو Y بتروح إلى ال Cوهنا y
+
+294
+00:27:49,390 --> 00:27:57,430
+ناقص ال c وهنا في عندي ايش برضه ناقص برا لان خد من
+
+295
+00:27:57,430 --> 00:28:01,670
+هنا ناقص عام المشترك او ضيعه مع الناقص اللي هنا
+
+296
+00:28:01,670 --> 00:28:11,160
+ماضح اه بيصير عندي y ساوي limit f of yنقص f of c
+
+297
+00:28:11,160 --> 00:28:16,800
+على y minus c لما y تروح لل c وهذا عبارة عن f
+
+298
+00:28:16,800 --> 00:28:22,440
+prime لمين لل c بدأنا ب f prime نقص c وانتهينا ب f
+
+299
+00:28:22,440 --> 00:28:31,520
+prime لل c لذا therefore f prime is even whenever
+
+300
+00:28:31,520 --> 00:28:37,160
+f is odd and f is differentiable
+
+301
+00:28:40,710 --> 00:28:56,810
+السؤال الأخير السؤال 13 السؤال
+
+302
+00:28:56,810 --> 00:29:03,990
+13 هو كما يلي اش
+
+303
+00:29:03,990 --> 00:29:09,200
+اللي بقول السؤال 13سؤال 13 بيقول إذا كانت F من R
+
+304
+00:29:09,200 --> 00:29:12,380
+لـ R is differentiable at C element in R show that
+
+305
+00:29:12,380 --> 00:29:16,840
+F prime of C سوى limit N في F of C زائد 1 لأن ناقص
+
+306
+00:29:16,840 --> 00:29:20,620
+F of C as N goes to infinity يعني لو كانت F
+
+307
+00:29:20,620 --> 00:29:24,900
+differentiable عند الـ C element in R بنقدر نكتب
+
+308
+00:29:24,900 --> 00:29:27,920
+ال derivative اللي هي F prime of C على سورة limit
+
+309
+00:29:27,920 --> 00:29:32,320
+N F of C زائد 1 لأن ناقص F of C as N goes to
+
+310
+00:29:32,320 --> 00:29:38,120
+infinityلكن بيقول لي by example show that the
+
+311
+00:29:38,120 --> 00:29:44,000
+existence of this limit this limit need not اللي
+
+312
+00:29:44,000 --> 00:29:52,300
+هو imply the existence of the derivative نيجي
+
+313
+00:29:52,300 --> 00:30:03,960
+الآن للجزء الأول عندي F من R لRو F prime of C
+
+314
+00:30:03,960 --> 00:30:12,120
+exist لانه يقول لي prove that F prime of C can be
+
+315
+00:30:12,120 --> 00:30:20,760
+written as limit on F of C زائد واحدة لان ناقص F
+
+316
+00:30:20,760 --> 00:30:26,180
+of C as N goes to infinity هذا الجزء الأول الجزء
+
+317
+00:30:26,180 --> 00:30:32,400
+الثاني حنجي الان نقول prove للجزء الأولقبل ما نقول
+
+318
+00:30:32,400 --> 00:30:37,700
+الـ proof نذكركم بس بنظرية سابقة في الـ real واحد
+
+319
+00:30:37,700 --> 00:30:43,840
+إنه لو عندي limit f of x لما x تروح لل c لو كانت
+
+320
+00:30:43,840 --> 00:30:52,780
+بتساوي Lبكون عندى أي sequence xₙ بتروح للـ C لازم
+
+321
+00:30:52,780 --> 00:30:59,020
+يتحقق لها limit f of xₙ as n goes to infinity
+
+322
+00:30:59,020 --> 00:31:05,530
+بساوي برضه الـكنا نتحدث بالحديث، باستبداء الحديث
+
+323
+00:31:05,530 --> 00:31:08,670
+عن الـ limit العادية للـ function S X بتروح للـ C
+
+324
+00:31:08,670 --> 00:31:13,470
+إلى limit لمين للـ sequence أو limit للـ sequences
+
+325
+00:31:13,470 --> 00:31:17,290
+الآن بنستخل هذه اللي هو المعلومة في إثبات اللي
+
+326
+00:31:17,290 --> 00:31:22,630
+بدنايا عند الآن since F prime of C exist بما أنه
+
+327
+00:31:22,630 --> 00:31:29,250
+ال derivative عند C موجودةإذا أكيد عندي صار f
+
+328
+00:31:29,250 --> 00:31:37,010
+prime of c بسهولمة f of x أو اللي هي الـ x عند c
+
+329
+00:31:38,080 --> 00:31:46,140
+زائد h ناقص f of c على h as h goes to mean to zero
+
+330
+00:31:46,140 --> 00:31:49,860
+اللي هو التعريف التعريف ال derivative أو الشكل
+
+331
+00:31:49,860 --> 00:31:52,980
+الآخر للتعريف ال derivative f of c زائد ال
+
+332
+00:31:52,980 --> 00:31:55,560
+increment ناقص f of c على ال increment as ال
+
+333
+00:31:55,560 --> 00:32:01,600
+increment goes to mean to zero ماشي الحل ال L بما
+
+334
+00:32:01,600 --> 00:32:07,480
+أنه اللي هو ال 1 على N sequence بتروح للسفروهذا
+
+335
+00:32:07,480 --> 00:32:11,440
+الـ limit exist لأن حسب النظرية اللي حكيتها قبل
+
+336
+00:32:11,440 --> 00:32:21,100
+بشوية بكون عندي لأن but كذا then F prime of C can
+
+337
+00:32:21,100 --> 00:32:26,580
+be اللي هو إعادة اللي هي rewritten as a limit of a
+
+338
+00:32:26,580 --> 00:32:36,800
+sequence F of اللي هو limit limitF of C زائد but
+
+339
+00:32:36,800 --> 00:32:40,000
+الـ H اللي هي تروح للصفر صارت mean ال sequence
+
+340
+00:32:40,000 --> 00:32:46,380
+واحدة ل N تروح للصفر واحدة ل N ناقص F of C على
+
+341
+00:32:46,380 --> 00:32:52,640
+واحدة ل N as N goes to infinity مدامت ال sequence
+
+342
+00:32:52,640 --> 00:32:57,100
+واحدة ل N بتروح للصفر صارت ال F of واحدة ل N اللي
+
+343
+00:32:57,100 --> 00:33:00,900
+هي عبارة عن F of C زائد واحدة ل N لإن الـ C عبارة
+
+344
+00:33:00,900 --> 00:33:07,740
+عن إياش فالتةواضح أه؟ الان هذا بيساوي اللي هو
+
+345
+00:33:07,740 --> 00:33:14,600
+limit الان as n goes to infinity اللي هو أكيد اللي
+
+346
+00:33:14,600 --> 00:33:21,920
+هو بيصير عندي f n في الجوس f of c زائد واحدة ل n
+
+347
+00:33:21,920 --> 00:33:28,260
+ناقص f of c اللي هو as n goes to infinity هو هذا
+
+348
+00:33:28,260 --> 00:33:35,150
+صار f prime of c وهو المطلوبالان conversely the
+
+349
+00:33:35,150 --> 00:33:37,890
+converse need not to be true in general هيك بيقول
+
+350
+00:33:37,890 --> 00:33:45,390
+ليه يعني بيقوللي if if بيقوللي او اللي بيقول if f
+
+351
+00:33:45,390 --> 00:33:53,670
+برا اللي هو limit f of c زاد واحدة ل n ناقص f of c
+
+352
+00:33:53,670 --> 00:34:01,610
+الكل مضروف في n as n goes to infinity exist if كده
+
+353
+00:34:02,500 --> 00:34:12,640
+then f prime at c need not be exist اصلا مش انه
+
+354
+00:34:12,640 --> 00:34:16,180
+يكون بيسوي هذا او لا need not to be اشمله exist
+
+355
+00:34:16,180 --> 00:34:19,640
+لان لو كان exist على طول بيسوي اما need not to be
+
+356
+00:34:19,640 --> 00:34:28,200
+exist ومااخد مثال جالي consider consider consider
+
+357
+00:34:28,200 --> 00:34:37,000
+f of xبساوي ال absolute value لل X وخد عند ال C أش
+
+358
+00:34:37,000 --> 00:34:46,440
+بتساوي سفر واضح F prime of 0 does not exist لأنها
+
+359
+00:34:46,440 --> 00:34:48,780
+عبارة عن corner point، انتوا عارفين احنا اللي هو
+
+360
+00:34:48,780 --> 00:34:52,480
+ال F prime عند ال zero لل absolute value does not
+
+361
+00:34:52,480 --> 00:34:59,740
+exist لكن هذه متحققة، ليش؟ but limit
+
+362
+00:35:01,280 --> 00:35:10,900
+N في F of 0 زائد 1 على N نقص F of 0 as N goes to
+
+363
+00:35:10,900 --> 00:35:18,840
+infinity بساوي limit N F of 0 زائد 1 على N يعني F
+
+364
+00:35:18,840 --> 00:35:23,560
+of 1 على N F of X بساوي absolute value X ف1 على N
+
+365
+00:35:23,560 --> 00:35:28,960
+مظبوط أه as N goes to infinity طبعا الـ N بتروح
+
+366
+00:35:29,220 --> 00:35:35,100
+يصير عبارة عن ash واحد إذا فعلا جبنا مثال أن ال
+
+367
+00:35:35,100 --> 00:35:39,720
+limit هذه تكون exist و سوى واحد but ال F prime عند
+
+368
+00:35:39,720 --> 00:35:42,640
+هذا النقطة C اللي هي 00 في هذه الحالة does not
+
+369
+00:35:42,640 --> 00:35:47,320
+exist بيكون هيك احنا انتهينا من الجزء الأول من
+
+370
+00:35:47,320 --> 00:35:54,870
+المحاضرة الخامسةاللي هو discussion لأو مناقشة ل
+
+371
+00:35:54,870 --> 00:35:59,910
+section 6-1 اللي هو the derivative والآن سنكمل
+
+372
+00:35:59,910 --> 00:36:05,690
+الحديث في الجزء الثاني من المحاضرة اللي هو عن اللي
+
+373
+00:36:05,690 --> 00:36:09,250
+هو the mean value theorem أو اللي هي نكمل
+
+374
+00:36:09,250 --> 00:36:11,910
+applications على mean value theorem وناخد اللي هو
+
+375
+00:36:11,910 --> 00:36:12,030
+ال
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..71375412a167696490a55b8e7d724c5a15def915
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY.srt
@@ -0,0 +1,3571 @@
+1
+00:00:04,720 --> 00:00:09,780
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 11 في
+
+2
+00:00:09,780 --> 00:00:16,040
+مساق تحليل حقيقي 2 لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:16,040 --> 00:00:24,760
+كلية العلوم وهي المحاضرة الأولى بعد إعلان الطوارئ 
+
+4
+00:00:24,760 --> 00:00:32,580
+بخصوص أو بمواجهة فيروس كورونا المنتشر  اتحدتنا
+
+5
+00:00:32,580 --> 00:00:37,960
+المرة الماضية بدأنا في اللي هو chapter 7 اللي كان 
+
+6
+00:00:37,960 --> 00:00:41,280
+الحديث عن ال riman integral أو تكامل ال riman
+
+7
+00:00:41,280 --> 00:00:45,860
+بدأنا في ال section الأول اللي هو تحت عنوان riman 
+
+8
+00:00:45,860 --> 00:00:50,740
+integrability عرفنا شغلتين حاجة اسمها ال upper sum
+
+9
+00:00:50,740 --> 00:00:55,960
+و حاجة اسمها ال lower sum و قلنا اللي هو ال lower
+
+10
+00:00:55,960 --> 00:01:00,290
+sum هو عبارة عن الـ summation للـ mk الـ mk هذه
+
+11
+00:01:00,290 --> 00:01:06,410
+تمثل في xk minus xk minus 1 حيث mk كانت تمثل أو m
+
+12
+00:01:06,410 --> 00:01:10,910
+small k كانت تمثل عبارة عن الـ infimum للدالة على
+
+13
+00:01:10,910 --> 00:01:15,520
+الفترة اللي هي المذكورة الآن ال .. ال .. ال other
+
+14
+00:01:15,520 --> 00:01:19,380
+sum هو عبارة عن ال summation لنفس ال sum العلوي
+
+15
+00:01:19,380 --> 00:01:24,520
+ولكن بدلا منها اللي هي M K capital اللي كانت تمثل
+
+16
+00:01:24,520 --> 00:01:28,280
+ال supremum ل ال F of X وال X على اللي هي في
+
+17
+00:01:28,280 --> 00:01:34,110
+الفترة المذكورة اللي عندي الآن أخدنا أول لمّة المرة
+
+18
+00:01:34,110 --> 00:01:38,190
+الماضية وقلنا إذا كانت F من I لR bounded و B any
+
+19
+00:01:38,190 --> 00:01:43,230
+partition of I بدي يكون ال lower اللي هو sum لأي
+
+20
+00:01:43,230 --> 00:01:47,810
+partition B و function F أصغر أو يساوي ال upper
+
+21
+00:01:47,810 --> 00:01:52,470
+sum لنفس ال partition و لنفس اللي هي ال function F
+
+22
+00:01:52,470 --> 00:01:58,710
+بعد هي طبعا خطينا خطوة أخرى و جينا عرفنا اللي هو شو
+
+23
+00:01:58,710 --> 00:02:03,110
+معناته انها تكون اللي هو ال partition Q refinement
+
+24
+00:02:03,110 --> 00:02:08,610
+لل partition B قلنا Q اللي هو تحسين ل B إذا كانت B
+
+25
+00:02:08,610 --> 00:02:13,940
+بي عبارة عن مجموعة جزئية من Q و بناء عليه اللي هو
+
+26
+00:02:13,940 --> 00:02:19,440
+قلنا ان اي اللي هو sub interval xk-1xk من ال
+
+27
+00:02:19,440 --> 00:02:23,520
+partition B يمكن كتابتها على صورة union of sub
+
+28
+00:02:23,520 --> 00:02:27,680
+intervals من اللي هو التحسين اللي هو EQ
+
+29
+00:02:31,060 --> 00:02:36,380
+الآن جينا اللي هو بناء على هذا التعريف جينا قولنا
+
+30
+00:02:36,380 --> 00:02:40,480
+لو كانت F is من I لعند R is bounded و B is any
+
+31
+00:02:40,480 --> 00:02:45,780
+partition of I و Q refinement لل B مدام اللي هو Q
+
+32
+00:02:45,780 --> 00:02:50,420
+refinement إذا ال lower sum هيعلى و ال upper sum
+
+33
+00:02:50,420 --> 00:02:54,820
+هينزل على أساس انه اللي هو في النهاية يلتقي ال
+
+34
+00:02:54,820 --> 00:02:58,740
+upper مع ال lower و نصل لاللي هو ال integrability
+
+35
+00:02:58,740 --> 00:03:02,800
+أو معنى ال integrability كما سنرى لاحقا على الأقل
+
+36
+00:03:02,800 --> 00:03:06,560
+في اللي هو يكون واضح من خلال الرسم في اللي هي
+
+37
+00:03:06,560 --> 00:03:13,890
+الدوال الموجبة كما ذكرنا سابقا اللي بحكيه إنه لو
+
+38
+00:03:13,890 --> 00:03:17,330
+كانت عندي اللي هو F من I ل R bounded وB partition
+
+39
+00:03:17,330 --> 00:03:22,750
+وQ وrefinement للـ B هيكون عندي lower sum لل
+
+40
+00:03:22,750 --> 00:03:28,570
+partition B أصغر أو يساوي lower sum للتحسين عماله
+
+41
+00:03:28,570 --> 00:03:32,850
+التحسين بكبر لما بده يصل لفعلا المساحة تحت المنحنة
+
+42
+00:03:32,850 --> 00:03:39,470
+في حالة الدوال الموجبة القبر صم لـ Q و F سيبدأ يصغر
+
+43
+00:03:39,470 --> 00:03:42,850
+ويكون أصغر من الساوي اللي هو القبر صم لـ P و F
+
+44
+00:03:42,850 --> 00:03:47,310
+التحسين يعني سيصغره بمعنى آخر سيبدأ يلتقوا إلى
+
+45
+00:03:47,310 --> 00:03:51,770
+أسفل لما نصل إلى اللي هو مساواة في حالة الـ
+
+46
+00:03:51,770 --> 00:03:55,730
+Integrability لما نكون عندنا أخدنا الـ Supremum
+
+47
+00:03:55,730 --> 00:04:01,340
+لكل L و F الـ L والـ infimum لكل الـ U بيصير بنسمي
+
+48
+00:04:01,340 --> 00:04:04,800
+بعد شوية حاجة اسمها ال lower integral وال upper
+
+49
+00:04:04,800 --> 00:04:08,980
+integral وبرهننا هذه النظرية و بعدين جينا لللمة و
+
+50
+00:04:08,980 --> 00:04:13,520
+بعدين جينا لللمة أخرى اللي هو لو كانت F من I ل R
+
+51
+00:04:13,520 --> 00:04:17,600
+bounded وB1 وB2 اي partitions الآن لأي partitions
+
+52
+00:04:17,600 --> 00:04:22,480
+هيكون الlower دايما بغض النظر عن ال partition اللي
+
+53
+00:04:22,480 --> 00:04:26,120
+هو هيكون أصغر أو يساوي الأبر بغض النظر عن ال
+
+54
+00:04:26,120 --> 00:04:28,660
+partition B2 يعني مش لنفس ال partition زي ما قلنا
+
+55
+00:04:28,660 --> 00:04:33,180
+في اللمبة 7 1 1 لأ لأي two partitions دايما
+
+56
+00:04:33,180 --> 00:04:37,170
+الlower ما هو هيكون تحت أسفل المنحنى والـ Upper
+
+57
+00:04:37,170 --> 00:04:41,350
+هيكون أعلى المنحنى بغض النظر عن ال partitions اللي
+
+58
+00:04:41,350 --> 00:04:45,690
+عندي طبعا التمثيل هذا في حال اللي هو ال F is a
+
+59
+00:04:45,690 --> 00:04:49,130
+positive function على ال interval المذكورة الآن
+
+60
+00:04:49,130 --> 00:04:52,730
+بعد هيكة اجينا وعرفنا شو معناه ال lower integral
+
+61
+00:04:52,730 --> 00:04:55,510
+وشو معناه ال upper integral قولنا ال lower
+
+62
+00:04:55,510 --> 00:05:00,050
+integral كما هو متوقع سميناه الف F هو عبارة عن ال
+
+63
+00:05:00,050 --> 00:05:05,660
+supremum لل lowers وال .. و ال .. و ال .. و ال
+
+64
+00:05:05,660 --> 00:05:10,440
+upper هو عبارة عن الـ infimum لل uppers حتى لو
+
+65
+00:05:10,440 --> 00:05:14,300
+التقت الالو أف مع الالو أف اللي هو من أعلى مع
+
+66
+00:05:14,300 --> 00:05:17,940
+الأسفل هيكونوا التقوا بالظبط عند .. من مساحة تحت
+
+67
+00:05:17,940 --> 00:05:20,960
+المنحنى في حالة الدالة الموجبة وهذه .. في هذه
+
+68
+00:05:20,960 --> 00:05:24,300
+الحالة بنسمي إذا كانت ال upper تساوي ال lower
+
+69
+00:05:24,300 --> 00:05:27,920
+بنسمي ال function على هذه الفترة is integral و هذا
+
+70
+00:05:27,920 --> 00:05:31,900
+الكلام كله تحدثنا فيه عشان هيك أنا مسرع شوية هو
+
+71
+00:05:31,900 --> 00:05:37,160
+حكينا إنه اللي هو دايما ال lower sum لل F أخدنا
+
+72
+00:05:37,160 --> 00:05:40,760
+نظرية قولنا ال lower integral أسف ال lower
+
+73
+00:05:40,760 --> 00:05:45,100
+integral دايما أصغر يساوي مين ال upper integral
+
+74
+00:05:45,100 --> 00:05:46,860
+إذن الآن النظرية 
+
+75
+00:05:49,600 --> 00:05:52,760
+الإعلان المهم اللي هو لو كانت F من I لعند R
+
+76
+00:05:52,760 --> 00:05:56,000
+bounded function على closed bounded interval A وB
+
+77
+00:05:56,000 --> 00:05:59,720
+بدي يكون ال lower integral L of F أصغر أو ساوي ال
+
+78
+00:05:59,720 --> 00:06:04,930
+upper integral U of F بصورة عامة هذه هي الـ
+
+79
+00:06:04,930 --> 00:06:08,050
+definition اللي ذكرته قبل و شوية نقول عن الـ
+
+80
+00:06:08,050 --> 00:06:15,150
+function F على bounded sub interval A و B أو
+
+81
+00:06:15,150 --> 00:06:18,650
+closed bounded interval A و B و كانت الـ F عبارة
+
+82
+00:06:18,650 --> 00:06:22,080
+عن bounded function بنعرف أن الـ F is remain
+
+83
+00:06:22,080 --> 00:06:26,840
+integrable on I إذا كانت ال lower of F بساوي ال
+
+84
+00:06:26,840 --> 00:06:30,080
+upper of F معناته صارت اللي هي ال F is remain
+
+85
+00:06:30,080 --> 00:06:34,460
+integrable if and only if ال lower sum يساوي ال
+
+86
+00:06:34,460 --> 00:06:39,240
+upper sum هذا كله ذكرناه المرة الماضية و أيضا
+
+87
+00:06:39,240 --> 00:06:42,520
+عرفنا .. قلنا في هذا الحلقة أن كل integration من A
+
+88
+00:06:42,520 --> 00:06:47,890
+ل B هو ال lower أو ال upper المتساويين وعرفنا ايضا
+
+89
+00:06:47,890 --> 00:06:50,610
+تعريف آخر قولنا ال integration من a ل b بساوي ناقص
+
+90
+00:06:50,610 --> 00:06:53,830
+ال integration من b ل a وعرفنا ال integration من a
+
+91
+00:06:53,830 --> 00:06:59,410
+ل a بساوي صفر هذا كله حكينا المرة الماضية ومش هيك
+
+92
+00:06:59,410 --> 00:07:03,820
+كمان واخدنا المثال اللي هو أثبتنا إنه اللي هو g of
+
+93
+00:07:03,820 --> 00:07:07,880
+x بيساوي x is integrable on i استنادًا على إنه
+
+94
+00:07:07,880 --> 00:07:11,020
+أوجدنا ال lower sum ال lower integral و ال upper
+
+95
+00:07:11,020 --> 00:07:13,300
+integral أثبتنا إن ال lower integral و ال upper
+
+96
+00:07:13,300 --> 00:07:16,300
+integral are equal و من ثم أثبتنا إنه ال
+
+97
+00:07:16,300 --> 00:07:19,940
+integration exist لل function x على الفترة 0 و 1
+
+98
+00:07:19,940 --> 00:07:26,810
+وأوجدنا قيمة ال integration في حينه وصلنا إلى اللي
+
+99
+00:07:26,810 --> 00:07:33,290
+هو مثالنا التالي أنه لو كانت F من I لعند .. F من I
+
+100
+00:07:33,290 --> 00:07:40,090
+اللي هي 01 لعند ال .. ال R be defined by أخدنا
+
+101
+00:07:40,090 --> 00:07:45,990
+الدالة كما يلي اللي هو قولنا أن F of X F of X
+
+102
+00:07:45,990 --> 00:07:53,040
+بساوي واحد إذا كانت x rational number element in Q
+
+103
+00:07:53,040 --> 00:08:00,100
+وبساوي 0 إذا كانت x element in IQ أو element in Q
+
+104
+00:08:00,100 --> 00:08:04,660
+complement اللي هي ال rational numbers الآن بدنا
+
+105
+00:08:04,660 --> 00:08:11,200
+نثبت بقول show that this function F طبعا أنا method
+
+106
+00:08:11,200 --> 00:08:17,340
+F على اللي هي الـ Q تقاطع طبعا الـ 0 و 1 اللي هي
+
+107
+00:08:17,340 --> 00:08:19,920
+الـ interval اللي بدأ عليها التقاطع الـ 0 و 1
+
+108
+00:08:19,920 --> 00:08:25,160
+بمعنى إن دالت F صارت من I اللي هي عبارة عن 0 و 1
+
+109
+00:08:26,040 --> 00:08:29,380
+اللي عند R واضح ان الدالة هذه is a bounded
+
+110
+00:08:29,380 --> 00:08:33,560
+function الآن بدأ أثبت لكم ان هذا الدالة is not
+
+111
+00:08:33,560 --> 00:08:38,120
+integrable on this interval is not integrable on
+
+112
+00:08:38,120 --> 00:08:44,100
+this interval الآن علشان أصل اللي هو اللي هي ان
+
+113
+00:08:44,100 --> 00:08:48,180
+هذا الدالة غير قابلة تكامل بالنسبة لتكامل بالنسبة
+
+114
+00:08:48,180 --> 00:08:55,650
+لتكامل الريمان بدي اخد الان B أخدوا أي partition X0
+
+115
+00:08:55,650 --> 00:09:02,550
+X1 لعند Xn هذا any partition لإيه ال interval اللي
+
+116
+00:09:02,550 --> 00:09:06,790
+هي الفترة مين Zero و واحد يعني بمعنى أتيت للفترة
+
+117
+00:09:06,790 --> 00:09:14,030
+Zero و واحد و جزقتها X0 X1 لعند مؤصل لعند مين لعند
+
+118
+00:09:14,030 --> 00:09:18,610
+Xn اللي هي إيش بتساوي بتساوي واحد الآن هذا ال
+
+119
+00:09:18,610 --> 00:09:22,130
+partition اخدته arbitrarily اللي هو partition
+
+120
+00:09:22,130 --> 00:09:31,790
+لفترة L عندي الآن بدي احسب ال Lof B و F لهذا ال
+
+121
+00:09:31,790 --> 00:09:34,990
+partition أيش بتساوي حسب اللي عرفناها سابقا بتساوي
+
+122
+00:09:34,990 --> 00:09:40,610
+ال summation لل M K في X K minus X K minus واحد K
+
+123
+00:09:40,610 --> 00:09:46,330
+من عند واحد لعند مين لعند اللي هي N ويساوي الآن ال
+
+124
+00:09:46,330 --> 00:09:52,450
+M K عرفناها ال M K هي عبارة عن ال infimum لقيمة ال
+
+125
+00:09:52,450 --> 00:09:56,470
+function F of X حيث X تنتمي إلى الفترة X K minus
+
+126
+00:09:56,470 --> 00:10:02,210
+واحد لعند X K طبعا اللي هي F of X معرفة على
+
+127
+00:10:02,210 --> 00:10:05,130
+أساسيها يا إما واحد يا إما سفر حسب إنها تكون
+
+128
+00:10:05,130 --> 00:10:08,030
+rational أو إيش ال rational يعني ال function F
+
+129
+00:10:08,030 --> 00:10:11,910
+أصلا اللي هي قيمتين بس إذا الآن ال infimum لل F of
+
+130
+00:10:11,910 --> 00:10:16,630
+X عندها يا هيكون واحد يا هيكون سفر ليش؟ لأن أصلا
+
+131
+00:10:16,630 --> 00:10:23,340
+الفترة هذه فيها أي فترة subinterval xk-1xk فيها
+
+132
+00:10:23,340 --> 00:10:27,620
+rational وirrational إذا قيمة ال up of x في الفترة
+
+133
+00:10:27,620 --> 00:10:31,260
+هتلاقي عند قيم واحد هتلاقي أكيد عند قيم أش بتساوي
+
+134
+00:10:31,260 --> 00:10:35,000
+بساوي سفر إذا ال infimum في هذه الحالة هو عبارة عن
+
+135
+00:10:35,000 --> 00:10:42,320
+إيش يساوي سفر إذا ال summation ل 0 في xk-xk-1 كامل
+
+136
+00:10:42,320 --> 00:10:46,120
+عند واحد عند أنه طبيعي هذا بديهي إيش هيساوي بساوي
+
+137
+00:10:46,120 --> 00:10:52,410
+سفر إذن الآن L of F بي و F ساوة سفر فور أي بورتيشن
+
+138
+00:10:52,410 --> 00:10:59,370
+بيه إذا ال L of F اللي هي عبارة عن الأو الـ
+
+139
+00:10:59,370 --> 00:11:06,070
+Supremum الـ Supremum لكل الـ L of B و F Such that
+
+140
+00:11:06,070 --> 00:11:09,890
+B element in the set of all partitions اللي هو B 
+
+141
+00:11:09,890 --> 00:11:14,090
+هو هيكون الـ .. الـ Supremum اللي هيكون صفر لأن كل
+
+142
+00:11:14,090 --> 00:11:18,350
+اللي هيكون أصلا إيش بتنطلع .. بتنطلع بساوي صفر إذا
+
+143
+00:11:18,350 --> 00:11:23,070
+هذا إيش هيساوي يا شباب؟ هو يساوي Zero إذا طلع عندي
+
+144
+00:11:23,070 --> 00:11:28,150
+الـ lower sum بساوي 0 الآن بدي أحسب لكم مين أحسب لكم
+
+145
+00:11:28,150 --> 00:11:31,390
+الـ upper sum سامحوني أكتب هنا بس عشان اللي يبقى
+
+146
+00:11:31,390 --> 00:11:39,670
+كله مكتوب عندي نوجد الـ upper sum الـ upper sum اللي
+
+147
+00:11:39,670 --> 00:11:45,510
+هي الـ UPUF بساوي summation للـ n K capital في XK
+
+148
+00:11:45,510 --> 00:11:51,740
+minus XK minus واحد K من عند واحد لعند الـ n الآن
+
+149
+00:11:51,740 --> 00:11:55,900
+هذا بيساوي الـ Mk زي ما قلنا قبل هيك الـ Mk بدل ما
+
+150
+00:11:55,900 --> 00:11:59,400
+هي الـ M في مميزة استعريفها الـ Mk بتساوي الـ
+
+151
+00:11:59,400 --> 00:12:03,780
+supremum لهذه الـ 6 وزي ما قلنا الـ 6 هذه في داخلها
+
+152
+00:12:03,780 --> 00:12:08,400
+يا واحد يا زيرو نظرا لأن اللي هو أي sub interval
+
+153
+00:12:08,400 --> 00:12:11,820
+هيكون فيها rational و irrational وتبعا لها هيكون
+
+154
+00:12:11,820 --> 00:12:16,060
+قيمة الـ function في داخلها واحد أو صفر واحنا بنبحث
+
+155
+00:12:16,060 --> 00:12:19,280
+عن الـ supremum إذا هيكون الـ supremum في كل الأحوال
+
+156
+00:12:19,280 --> 00:12:25,600
+الـ Mk بتساوي واحد مضروبة في xk-xk-1 k من عند 1 لعند
+
+157
+00:12:25,600 --> 00:12:30,700
+n نفردها هذه ويساوي اللي هنبصير k من عند 1 يعني x1
+
+158
+00:12:30,700 --> 00:12:39,570
+-x0 زائد x2-x1 زائد إلى آخر لما أصل لعند xn-1 ناقص xn
+
+159
+00:12:39,570 --> 00:12:44,550
+ناقص واحد طبعا واضح إنه عندي الـ x واحد هت cancel مع
+
+160
+00:12:44,550 --> 00:12:48,270
+ناقص x واحد و الـ x اتنين مع ناقص x اتنين لما نصل
+
+161
+00:12:48,270 --> 00:12:52,450
+للاخر هيكون في عندي ات cancel الجميع بس ضل عندي
+
+162
+00:12:52,450 --> 00:12:58,170
+الـ xn و الـ x note و هد بتساوي xn ناقص x note و
+
+163
+00:12:58,170 --> 00:13:01,750
+يساوي الـ xn طبعا إيش هي عبارة عن واحد و الـ x note
+
+164
+00:13:01,750 --> 00:13:07,190
+إيش هي شبه صفر و يساوي واحد ناقص صفر و يساوي واحد
+
+165
+00:13:07,570 --> 00:13:12,930
+إذا طلع عندي الـ Upper Sum لأي Bar تشمل به، هيتلع
+
+166
+00:13:12,930 --> 00:13:18,510
+إيش بساوي؟ بساوي واحدة إذا الآن لما بدي أخد الـ U
+
+167
+00:13:18,510 --> 00:13:23,510
+of F اللي هو Upper Integral هيساوي عبارة عن الـ
+
+168
+00:13:23,510 --> 00:13:30,220
+Infimum لمين؟ للـ U, B وF such that B element in
+
+169
+00:13:30,220 --> 00:13:34,580
+the set of all partitions B of I والـ U, B وF
+
+170
+00:13:34,580 --> 00:13:38,840
+قيمته ثابتة for أي partition بيساوي واحد إذا الـ
+
+171
+00:13:38,840 --> 00:13:43,300
+infimum لكل اللي هنا عبارة عن برضه إيش بيساوي واحد
+
+172
+00:13:43,300 --> 00:13:47,410
+صار عندي الآن lower integral و الـ upper integral
+
+173
+00:13:47,410 --> 00:13:51,110
+have different values واحد بيساوي صفر واحد بيساوي
+
+174
+00:13:51,110 --> 00:13:56,890
+واحد وبناء عليه بتكون عند اللي هو الـ F is not
+
+175
+00:13:56,890 --> 00:14:03,150
+Riemann integrable أي سؤال؟ طيب ماشي الحاجة
+
+176
+00:14:03,150 --> 00:14:10,930
+الآنصار عندي أخذنا مثالين المثال الأول اللي هو
+
+177
+00:14:10,930 --> 00:14:16,770
+أثبتنا إن off of x بيساوي x is integrable على
+
+178
+00:14:16,770 --> 00:14:22,010
+الفترة 0 و1 وأثبتناها بواسطة التعريف وأيضا أثبتنا
+
+179
+00:14:22,010 --> 00:14:26,190
+مثال آخر لـ bounded function أيضا وكانت is not
+
+180
+00:14:26,190 --> 00:14:31,250
+Riemann integrable اللي هي off of x بيساوي 1 إذا
+
+181
+00:14:31,250 --> 00:14:36,090
+كانت x rational ويساوي 0 إذا كانت x irrational هذا
+
+182
+00:14:36,090 --> 00:14:43,040
+اللي هو المثال الثاني الآن نيجي للي هو criterion
+
+183
+00:14:43,040 --> 00:14:49,280
+مهمة اللي احنا بنسميها اللي هي عبارة عن Riemann
+
+184
+00:14:49,280 --> 00:14:54,800
+criterion for
+
+185
+00:14:54,800 --> 00:15:01,490
+integrability احنا طبعا تحدثنا عن الـ Riemann
+
+186
+00:15:01,490 --> 00:15:05,330
+Integrability كيف نثبت أنه Riemann Integrable عن
+
+187
+00:15:05,330 --> 00:15:09,470
+طريق التعريف طبعا الآن مش دائما بدنا نثبت عن طريق
+
+188
+00:15:09,470 --> 00:15:14,350
+التعريف إذا بدنا اللي هو طرق أخرى نحاول اللي هو
+
+189
+00:15:14,350 --> 00:15:21,780
+نوسع اللي هي إمكانياتنا في الحكم على الدالة إنها
+
+190
+00:15:21,780 --> 00:15:26,860
+integrable أو مش integrable وهذه الإمكانية الأخرى
+
+191
+00:15:26,860 --> 00:15:31,400
+غير التعريف هي اللي بنسميها اللي هو الـ Riemann
+
+192
+00:15:31,400 --> 00:15:36,500
+integrability criterion أو criterion for
+
+193
+00:15:36,500 --> 00:15:41,340
+integrability نشوف إيش بيقول النظرية
+
+194
+00:15:43,700 --> 00:15:48,060
+لت I بساوي A وB ولت F من I لـ R بيـ bounded نفترض
+
+195
+00:15:48,060 --> 00:15:51,360
+أن F عبارة عن إيه إيش مالها يا جماعة؟ bounded function
+
+196
+00:15:51,360 --> 00:15:57,500
+then F is integrable on I if and only if for each
+
+197
+00:15:57,500 --> 00:16:00,340
+epsilon أكبر من 0 there exists a partition B
+
+198
+00:16:00,340 --> 00:16:04,660
+epsilon of I such that U B epsilon ناقص الـ L B
+
+199
+00:16:04,660 --> 00:16:10,730
+epsilon إيش إيش ماله أصغر من اللي هو إبسلون إذن اللي
+
+200
+00:16:10,730 --> 00:16:16,410
+هو واضح إنه عندي فصار فيه test لل integrability أو
+
+201
+00:16:16,410 --> 00:16:20,150
+اللي هو طريقة للحكم على ال integrability أخرى غير
+
+202
+00:16:20,150 --> 00:16:26,430
+التعريف اللي هو بتقول F is integrable
+
+203
+00:16:28,870 --> 00:16:32,890
+if and only if طبعا هذه لمين الـ F؟ F عبارة عن زي
+
+204
+00:16:32,890 --> 00:16:36,190
+ما أنتم عارفين bounded function لأن كل شغلنا
+
+205
+00:16:36,190 --> 00:16:40,010
+أصلا على اللي هو Riemann integrability أنه نفترض
+
+206
+00:16:40,010 --> 00:16:43,210
+أنه الـ F bounded عشان اللي هو تكون الـ supremum و
+
+207
+00:16:43,210 --> 00:16:46,330
+الـ infimum اللي مبني عليها التعريف تكون مضمون إنها
+
+208
+00:16:46,330 --> 00:16:49,870
+موجودة عشان هيك بنحكي أن F is bounded function طيب
+
+209
+00:16:49,870 --> 00:16:56,140
+إذا الـ F is integrable if and only if اللي هي لكل
+
+210
+00:16:56,140 --> 00:17:00,620
+إبسلون أكبر من 0 there exists a partition P إبسلون
+
+211
+00:17:00,620 --> 00:17:04,240
+هذا الـ P اللي هو الـ partition يعتمد عالميا على
+
+212
+00:17:04,240 --> 00:17:07,820
+إبسلون لكل إبسلون بالله دي partition P إبسلون لمين
+
+213
+00:17:07,820 --> 00:17:11,840
+الـ partition طبعا للـ interval اللي عندنا اللي هي I
+
+214
+00:17:11,840 --> 00:17:17,040
+there exists P إبسلون a partition of I such that
+
+215
+00:17:17,040 --> 00:17:25,210
+الـ U P إبسلون و الـ F ناقص الـ L بي إبسلون و
+
+216
+00:17:25,210 --> 00:17:31,050
+F يكون أصغر من مين من إبسلون الآن إذا كان لجينا
+
+217
+00:17:31,050 --> 00:17:34,190
+لكل إبسلون لجينا بي إبسلون بحيث هذا يتحقق معناته F
+
+218
+00:17:34,190 --> 00:17:37,590
+is integrable and conversely if F is integrable
+
+219
+00:17:37,590 --> 00:17:42,550
+أكيد لكل إبسلون هلجي بي إبسلون بحيث أن هذا يتحقق
+
+220
+00:17:42,550 --> 00:17:48,170
+خلونا نيجي الآن نبرهن و نشوف كيف بدنا نبرهن
+
+221
+00:17:48,170 --> 00:17:53,880
+نظريتنا الآن بدنا نفترض أن F إيش ماله is
+
+222
+00:17:53,880 --> 00:18:00,240
+integrable ونصل منها للي عايزينه اللي هي الـ partition
+
+223
+00:18:00,240 --> 00:18:07,040
+اللي مذكور مدام F is integrable إذا كانت .. الآن
+
+224
+00:18:07,040 --> 00:18:16,100
+بنقول suppose that F is integrable مدام integrable
+
+225
+00:18:16,100 --> 00:18:22,090
+يا شباب أكيد عند اللي هو الـ U of F بساوي L of
+
+226
+00:18:22,090 --> 00:18:29,490
+إيش؟ Of F، مظبوط؟ أكيد الـ L of .. الـ U of F
+
+227
+00:18:29,490 --> 00:18:33,410
+بساوي الـ L of F إيش اللي بيدل عليه؟ بيدل عليه لأي
+
+228
+00:18:33,410 --> 00:18:35,810
+إبسلون أكبر من صفر بدلجي بإبسلون، شوفوا كيف
+
+229
+00:18:35,810 --> 00:18:41,090
+بنلجيه، الآن نفترض إن إبسلون let إبسلون أكبر من
+
+230
+00:18:41,090 --> 00:18:47,810
+صفر be given، ماشي الحال عندي الـ U of F هو إيش يا
+
+231
+00:18:47,810 --> 00:18:54,910
+شباب؟ هو عبارة عن الـ infimum للـ L of B و F such
+
+232
+00:18:54,910 --> 00:19:01,170
+that B element in B of I، مظبوط؟ إذا الـ U of F
+
+233
+00:19:01,170 --> 00:19:05,830
+عبارة عن infimum يعني هو عبارة عن greatest lower
+
+234
+00:19:05,830 --> 00:19:11,630
+bound لو هذا الـ greatest lower bound ضفنا إليه أي
+
+235
+00:19:11,630 --> 00:19:17,230
+كمية هيبطل الـ lower bound لأن هو أصلا إيش اسمه
+
+236
+00:19:17,230 --> 00:19:23,510
+greatest lower bound إذا لو الـU of F ضفت له Y على
+
+237
+00:19:23,510 --> 00:19:28,610
+2 مثلا طبعا هذا المقدار هيبطل الـ lower bound إيش
+
+238
+00:19:28,610 --> 00:19:33,690
+معناته بطل الـ lower bound؟ يعني بمعنى آخر هيكون في
+
+239
+00:19:33,690 --> 00:19:44,080
+عندي إشي أصغر منه هيكون عندي أصغر من الـ U of F أو بي
+
+240
+00:19:44,080 --> 00:19:49,740
+واحد مثلا و F for some B واحد إذا لما نشيل
+
+241
+00:19:49,740 --> 00:19:54,600
+من الـ infimum إبسلون
+
+242
+00:19:54,600 --> 00:19:57,740
+على اتنين هيبطل هذا lower bound يعني بمعنى آخر
+
+243
+00:19:57,740 --> 00:20:03,280
+هلاقي اللي هو lower bound
+
+244
+00:20:07,660 --> 00:20:12,140
+عند الـ Y أكبر من 0 خلّيني أبدأ لت Y أكبر من 0 بي
+
+245
+00:20:12,140 --> 00:20:17,940
+given إذا عندي الآن بدي أثبت لك بدي أجيب لك
+
+246
+00:20:17,940 --> 00:20:21,440
+partition بيبسلون بحيث إنه هذا ناقص هذا يكون أصغر
+
+247
+00:20:21,440 --> 00:20:26,070
+من مين من إبسلون شوف كيف بدي أعمل الآن أنا عندي الـ
+
+248
+00:20:26,070 --> 00:20:30,710
+U of F إيش بيساوي يا جماعة الـ U of F بيساوي الـ
+
+249
+00:20:30,710 --> 00:20:39,590
+infimum للـ L بيقف ب element I طيب الـ U of F آسف يا
+
+250
+00:20:39,590 --> 00:20:43,010
+جماعة الـ U of F بيساوي الـ infimum لمين للـ U بيقف
+
+251
+00:20:43,720 --> 00:20:49,780
+ماشي الحال الآن إيش معناه إنه هذا infimum معناته
+
+252
+00:20:49,780 --> 00:20:55,100
+هذا هو عبارة عن الـ greatest lower bound مدام الـ
+
+253
+00:20:55,100 --> 00:20:59,450
+greatest lower bound إذا الـ lower bound هذا أو الـ
+
+254
+00:20:59,450 --> 00:21:03,330
+Greatest Lower Bound لو ضفت له أي رقم إبسلون على
+
+255
+00:21:03,330 --> 00:21:06,370
+اتنين مثلا بالذنب إبسلون على اتنين الـ game
+
+256
+00:21:06,370 --> 00:21:09,670
+بتعرفوا ليش إبسلون على اتنين يعني لو ضفت له أي رقم
+
+257
+00:21:09,670 --> 00:21:14,730
+بيبطل Lower Bound إيش معناته بيبطل Lower Bound
+
+258
+00:21:14,730 --> 00:21:21,830
+يعني هيصير هذا أكبر من الـ UB 1 of F for some B
+
+259
+00:21:21,830 --> 00:21:27,510
+واحدة لأنه بطل إيش ماله هذا بطل lower bound بطل يكون
+
+260
+00:21:27,510 --> 00:21:32,670
+أصغر من الكل من هان يعني هلاجي واحد من هان هو مش
+
+261
+00:21:32,670 --> 00:21:36,830
+أصغر منه أو بمعنى آخر U, P, 1 و F أصغر من اللي هو
+
+262
+00:21:36,830 --> 00:21:44,850
+هذا المقدر طيب similarly الـ L of F هي عبارة عن الـ
+
+263
+00:21:44,850 --> 00:21:52,050
+supremum للـ L, P و F such that P elemented P of I
+
+264
+00:21:53,040 --> 00:21:57,780
+بنفس الطريقة يا جماعة الـ L of F هي عبارة عن إيش الـ
+
+265
+00:21:57,780 --> 00:22:04,040
+least upper bound يعني هذا لو least upper bound
+
+266
+00:22:04,040 --> 00:22:07,200
+Upper bound لو كان أصغر و أحد لو هذا least upper
+
+267
+00:22:07,200 --> 00:22:11,000
+bound راحت منه عدد ولو صغير جدا وليكن إبسلون على
+
+268
+00:22:11,000 --> 00:22:16,800
+اتنين هيبطل هذا عبارة عن upper bound يعني هلاقي
+
+269
+00:22:16,800 --> 00:22:24,280
+واحد من اللي هان اللي هو L of B2 وF مثلا أكبر منه
+
+270
+00:22:24,280 --> 00:22:30,560
+لأنه هيبطل هذا إيش ماله upper bound لأنه هو الـ least
+
+271
+00:22:30,560 --> 00:22:35,780
+لما طلعت منه بطل من الـ upper bounds يعني لجيت واحد
+
+272
+00:22:35,780 --> 00:22:43,120
+من هذول أكبر منه إذا صار في عندي اللي هو لجيت بي
+
+273
+00:22:43,120 --> 00:22:53,960
+واحد بحقق الأولى و بيتنين بحقق التانية لأن خذ الآن
+
+274
+00:22:53,960 --> 00:22:58,840
+خذ لي بي إبسلون هذا اللي بديها هذا يحقق اللي اللي
+
+275
+00:22:58,840 --> 00:23:03,600
+بديها خذ بي إبسلون إيش بيساوي الـ بي واحد اللي لجيته
+
+276
+00:23:03,600 --> 00:23:12,050
+هنا اتحاد الـ B2 اللي لجيته هان اتحاد مين؟ B2 صار
+
+277
+00:23:12,050 --> 00:23:18,510
+عندي .. صار عندي الآن مع بعض خليني أمسح فأقوم،
+
+278
+00:23:18,510 --> 00:23:22,170
+مهمش؟
+
+279
+00:23:22,170 --> 00:23:31,670
+صار
+
+280
+00:23:31,670 --> 00:23:41,110
+عندي ما يليه؟ صار عندي الآن L of F ناقص 
+
+281
+00:23:41,110 --> 00:23:53,490
+Y على 2 أصغر من L of B2 F، اللي هو أكيد أصغر أو 
+
+282
+00:23:53,490 --> 00:23:59,750
+يساوي L of By، قُطف، ليش؟ لأن الـBy يا جماعة عبارة
+
+283
+00:23:59,750 --> 00:24:04,570
+عن refinement للـB2 والـlower لما يصير فيه تحسين
+
+284
+00:24:04,570 --> 00:24:08,510
+بكبُر، بروح نحو اتجاه نيل اللي هو المنحنة التالية
+
+285
+00:24:08,510 --> 00:24:14,010
+مساحة تحت المنحنة الكلية لأن أيضا لو جيت قولت الـU
+
+286
+00:24:14,010 --> 00:24:24,400
+of F زاد إبسلون على اتنين هتلاقيها أكبر من ال U B
+
+287
+00:24:24,400 --> 00:24:30,410
+واحد و F، وأكيد عندي الـ U of F زائد إبسلون عدنان
+
+288
+00:24:30,410 --> 00:24:34,490
+أكبر من الـ U B1 of F، هيكون هذا أكبر أو يساوي الـ
+
+289
+00:24:34,490 --> 00:24:39,610
+U B epsilon of F، لأن الـ B epsilon refinement لمين
+
+290
+00:24:39,610 --> 00:24:44,790
+برضه؟ للـ B1، بزام refinement، إذن اللي هو التحسين
+
+291
+00:24:44,790 --> 00:24:50,270
+بيزغَر القبُر وبروح ناحية اللي هو المنحنة، إذن الآن
+
+292
+00:24:50,270 --> 00:24:55,480
+من الـ tip 2 هذولة، واجدنا طبعا احنا تنسوش ان احنا
+
+293
+00:24:55,480 --> 00:24:59,100
+مفترضين من رأس الدول ان U of F is integrable، يعني
+
+294
+00:24:59,100 --> 00:25:05,340
+مفترضين ان ال L of F ايش بتساوي U of F، تنسواش هذه
+
+295
+00:25:05,340 --> 00:25:12,540
+ليه جيت تنتر مع بعض دول بيصير عندى، الحصل على L of F
+
+296
+00:25:12,540 --> 00:25:22,970
+ناقص Y على 2، اللي هو اصغر من Lof B, Epsilon و F
+
+297
+00:25:22,970 --> 00:25:30,110
+والـ L والـ U of F زائد Epsilon على 2 أكبر من U,
+
+298
+00:25:30,190 --> 00:25:35,290
+B, Epsilon و F، أنا إيش غرضي؟ غرضي أثبت إن U, B,
+
+299
+00:25:35,350 --> 00:25:39,130
+Epsilon و F ناقص L, B, Epsilon و F أصغر من Epsilon
+
+300
+00:25:39,130 --> 00:25:42,890
+يلا إترحل من بعض، إذا بيصير عندي، بتحصل البدكية
+
+301
+00:25:42,890 --> 00:25:48,570
+بيصير عندي الآن، بطرح حياة دي، بقول U, B, Epsilon و
+
+302
+00:25:48,570 --> 00:25:53,240
+F، ناقص لأنه لما نضرب هذا في ناقص هتنعكس يعني هتصير
+
+303
+00:25:53,240 --> 00:25:57,100
+هذه يا جماعة ناقص وهذه زائد وهذه هتنعكس هيك وهيصير
+
+304
+00:25:57,100 --> 00:26:05,600
+الاش ناقص بيصير عندي U B و F ناقص ال L B و F، هيصير
+
+305
+00:26:05,600 --> 00:26:11,820
+أصغر من مين؟ من ناقص L of F، ناخد هذا قبل زي ما احنا
+
+306
+00:26:11,820 --> 00:26:20,690
+مرتبينها، U of F زائد ي على 2 ناقص L of F زي إبسلون
+
+307
+00:26:20,690 --> 00:26:24,790
+على 2 وطبعا إحنا جايلين إن F is integrable يعني
+
+308
+00:26:24,790 --> 00:26:28,770
+الـ U of F بيساوي L of F، إذا هذي بتروح مع هذي بظل
+
+309
+00:26:28,770 --> 00:26:33,610
+ايه شماله؟ بظل إبسلون، إذا إحنا لكل إبسلون أكبر من
+
+310
+00:26:33,610 --> 00:26:36,950
+صفر لجينا بـ بي إبسلون، هي في الواقع بي إبسلون اللي
+
+311
+00:26:36,950 --> 00:26:39,970
+لجيناها بـ بي واحد اتحاد بي اتنين، حيث بي واحد اللي
+
+312
+00:26:39,970 --> 00:26:44,120
+لجيناها هان، والـ بي اتنين اللي لجيناها هان such that U
+
+313
+00:26:44,120 --> 00:26:49,120
+P Y of F نقص L P Y of F أصغر من اللي هو Epsilon
+
+314
+00:26:49,120 --> 00:26:57,480
+وهو المطلوب، أي سؤال؟ طيب، ماشي يا شباب، الآن خلصنا
+
+315
+00:26:57,480 --> 00:27:04,420
+الجزء الأول من النظرية، أثبتنا اللي بدنا يا انه اللي
+
+316
+00:27:04,420 --> 00:27:08,860
+هو هذه العلاقة صحيحة، لأننا نفترض انه suppose that
+
+317
+00:27:08,860 --> 00:27:12,380
+star holds، اللي هي star، ليه هذه؟ نفترض ان لكل
+
+318
+00:27:12,380 --> 00:27:15,380
+epsilon أكبر من 0 there exists B of epsilon such
+
+319
+00:27:15,380 --> 00:27:18,680
+that U B Epsilon و F نقصها دي أصغر من Epsilon و
+
+320
+00:27:18,680 --> 00:27:24,280
+بدنا نصل من خلالها لإيش؟ لأن ال F is integrable
+
+321
+00:27:24,280 --> 00:27:25,760
+فنشوف
+
+322
+00:27:40,480 --> 00:27:47,440
+البرهان بسيط، لو طلعنا عليه مباشرة على اللوح الآن
+
+323
+00:27:47,440 --> 00:27:52,140
+بدنا نفترض أن هذه تتحقق، اللي هو نفترض أنه لكل ي
+
+324
+00:27:52,140 --> 00:27:57,020
+أكبر من 0 يوجد بي إبسلون بحيث أن هذا اللي هي تتحقق
+
+325
+00:27:57,020 --> 00:28:01,620
+عشان أصل بدي أصلكم في النهاية أن L of F هي إيش
+
+326
+00:28:01,620 --> 00:28:05,810
+بتساوي U of F، شوف كيف بده يصلها، اللي هبدأ أقوللك اللي
+
+327
+00:28:05,810 --> 00:28:08,650
+هو نفترض انه زي ما قلنا انه star holds اللي حكينا
+
+328
+00:28:08,650 --> 00:28:12,990
+عنها، لأن for any partition B هيكون ال L B of F
+
+329
+00:28:12,990 --> 00:28:17,970
+أصغر أو يساوي L of F، و ال U of F أصغر أو يساوي مين؟ ال U
+
+330
+00:28:17,970 --> 00:28:25,970
+B of F، واضح؟ إذا أصار عيدي الآن L، يمكن أوضحلكم على
+
+331
+00:28:25,970 --> 00:28:35,790
+اللوح، L of B of F ده ال B أي partition أصغر، مظبوط؟
+
+332
+00:28:35,790 --> 00:28:40,910
+أو يساوي ال L of F، لانه ال L of F يا جماعة
+
+333
+00:28:40,910 --> 00:28:47,330
+هو ال supremum اللي هنا، و ال U بيقف
+
+334
+00:28:47,330 --> 00:28:53,130
+أكبر أو يساوي ال U of F، لانه ال U of F يا جماعة
+
+335
+00:28:53,130 --> 00:28:57,950
+هو عبارة عن مين؟ عبارة عن ال infimum، إترحولي الجهة
+
+336
+00:28:57,950 --> 00:29:01,410
+التانية، هذا طبعا لكل مين؟ لكل ال partitions اللي في
+
+337
+00:29:01,410 --> 00:29:06,750
+الدنيا، من ضمنهم ال P Epsilon اللي احنا ما عطينايا
+
+338
+00:29:06,750 --> 00:29:12,250
+في الـ .. اللي هو نص النظرية، إذا بسيري عندى لأن لو
+
+339
+00:29:12,250 --> 00:29:19,990
+اجيب طرحة ال U F ناقص L F، ال U F ناقص L F هيصير إيش
+
+340
+00:29:19,990 --> 00:29:23,850
+ماله يا جماعة؟ يعني طريقة رحلة من هذه بيصير أصغر
+
+341
+00:29:23,850 --> 00:29:28,510
+أو يساوي لإن هذه بتضربها في ناقص و هذه ناقص و
+
+342
+00:29:28,510 --> 00:29:32,750
+بتنقلب زي ما عملنا قبل و شوية بيصير أصغر أو يساوي
+
+343
+00:29:32,750 --> 00:29:43,640
+U P of F ناقص ال L B of F، هذا الكلام صحيح لإيش؟ لكل
+
+344
+00:29:43,640 --> 00:29:48,200
+partition في الدنيا من ضمنها المين؟ ال partition
+
+345
+00:29:48,200 --> 00:29:52,580
+المواطع لنا، يعني حيصير عند هذا ينطبق برضه على ال
+
+346
+00:29:52,580 --> 00:29:57,500
+بي إبسلون، إذا صار هذا أصغر يسوي بي إبسلون نقص ال
+
+347
+00:29:57,500 --> 00:30:01,740
+بي إبسلون of F، طيب هم يعطيين إن هذا المقدار إيش
+
+348
+00:30:01,740 --> 00:30:06,260
+ماله؟ أصغر من إبسلون لأي إبسلون في الدنياهو أنا
+
+349
+00:30:06,260 --> 00:30:10,580
+بعرف أن هذا المقدار نفسه أكبر أو يساوي إيش؟ صفر، صار
+
+350
+00:30:10,580 --> 00:30:17,720
+عندي الآن ال U of F ناقص ال L of F دايما أصغر من
+
+351
+00:30:17,720 --> 00:30:23,420
+إبسلون و أكبر أو يساوي صفر لكل إبسلون أكبر من صفر
+
+352
+00:30:23,420 --> 00:30:28,260
+إذا على طول من نظرية في تحليل واحد هيكون هذا اللى
+
+353
+00:30:28,260 --> 00:30:36,250
+عندي إذا U of F ناقص L of F بيساوي صفر، إذا U of F
+
+354
+00:30:36,250 --> 00:30:44,850
+بيساوي L of F وهذا يعني F is a Riemann Integral هو
+
+355
+00:30:44,850 --> 00:30:52,110
+المطلوب بيكون احنا هيك أثبتنا اللي هو Integrable
+
+356
+00:30:52,110 --> 00:30:58,350
+criterion أو اللي هو طريقة لتحديد اللي هو ال
+
+357
+00:30:58,350 --> 00:31:02,270
+function is integrable أو لا، غير اللي هو طريقة
+
+358
+00:31:02,270 --> 00:31:07,110
+التعريف، الآن في عند كورولاري بعدها، كورولاري
+
+359
+00:31:07,110 --> 00:31:11,530
+الكورولاري
+
+360
+00:31:11,530 --> 00:31:16,230
+هي تقول كما يلي الآن، بدنا نترجم الحديث بدل ما كان
+
+361
+00:31:16,230 --> 00:31:22,710
+بإبسلون نحكي عن مين؟ عن اللي هو sequence of
+
+362
+00:31:22,710 --> 00:31:29,870
+partitions، طبعا هو هذا معهود التحويل في نظريات
+
+363
+00:31:29,870 --> 00:31:34,590
+مشابهة في حتى في كورسات أخرى، خلّينا نشوف عندنا
+
+364
+00:31:34,590 --> 00:31:38,790
+اللي هو النظرية ايش بـ .. أو الكورلري ايش بتقول
+
+365
+00:31:38,790 --> 00:31:43,350
+بتقول let I بساوة A و B and let F من I لR be a
+
+366
+00:31:43,350 --> 00:31:48,600
+bounded function، لأن لو فرضنا بي أن أن element none
+
+367
+00:31:48,600 --> 00:31:52,300
+is a sequence of partitions of I بحيث أن ال limit
+
+368
+00:31:52,300 --> 00:31:55,920
+هذا بيساوي صفر، then f is integrable and ال limit
+
+369
+00:31:55,920 --> 00:31:58,040
+لل integration بيساوي ال integration، بيساوي ال
+
+370
+00:31:58,040 --> 00:32:04,480
+limit، ال أسف، ال limit لل lower p and f بيساوي ال
+
+371
+00:32:04,480 --> 00:32:07,020
+limit لل upper p and f اللي هو بيساوي قيمة ال
+
+372
+00:32:07,020 --> 00:32:13,000
+integration، حتى ال converse يا جماعة اللي هو اللي قبل
+
+373
+00:32:13,000 --> 00:32:16,820
+بشوية اللي كان .. اللي هي كانت F اندولي F لأن لو
+
+374
+00:32:16,820 --> 00:32:21,520
+كانت F is integrable، أكيد هلاقي sequence من
+
+375
+00:32:21,520 --> 00:32:25,380
+partitions بحيث أنه ال limit اللي حاصل الطرح بساوي
+
+376
+00:32:25,380 --> 00:32:29,760
+صفر، اللي هو البرهان مشابه لإي اللي حكيناه فيه اللي
+
+377
+00:32:29,760 --> 00:32:34,500
+هو برهان إيجاد الـ B epsilon ولكن هنا بنجد اللي هو
+
+378
+00:32:34,500 --> 00:32:37,380
+الـ Epsilon بساوية واحد، لأن فبنلاقي اللي هو ال
+
+379
+00:32:37,380 --> 00:32:42,380
+sequence هذه في ال corollary .. في من مشابه .. شيء
+
+380
+00:32:42,380 --> 00:32:45,900
+مشابه في برهان النظرية الأولى اللي قبل بشوية و
+
+381
+00:32:45,900 --> 00:32:49,360
+ياريت تجربوها عندكم، خلينا ناخد اللي .. اللي موجود
+
+382
+00:32:49,360 --> 00:32:54,160
+حاليا اللي هو الاتجاه هذا، إن لو لجينا sequence of
+
+383
+00:32:54,160 --> 00:32:59,430
+partitions وكان ال limit لل U P N و F نقص ال L P N و
+
+384
+00:32:59,430 --> 00:33:02,870
+F بساوة صفر، إذا هتكون F is integrable و هتكون ال
+
+385
+00:33:02,870 --> 00:33:07,990
+limit للأولى بساوة limit للثانية بساوة قيمة ال
+
+386
+00:33:07,990 --> 00:33:08,970
+integration
+
+387
+00:33:12,900 --> 00:33:17,500
+عندما أعطيني limit هذا إيش بساوي؟ صفر، خلّينا ندخل
+
+388
+00:33:17,500 --> 00:33:20,580
+على التعريف مباشرة، تعريف ال limit، بتعرفوا تعريف ال
+
+389
+00:33:20,580 --> 00:33:23,140
+limit يا شباب؟ اللي هو لكل إبسلون أكبر من صفر
+
+390
+00:33:23,140 --> 00:33:26,160
+there exist k such that لكل أن أكبر سوى k بيصير
+
+391
+00:33:26,160 --> 00:33:33,200
+هذا ناقص هذا أصغر من مين؟ من اللي هو إبسلون، وهذا
+
+392
+00:33:33,200 --> 00:33:35,980
+على طول يعطينا as integral، خلّيش تشوف أيش اللي
+
+393
+00:33:35,980 --> 00:33:43,000
+بيقوله، لأن since عند ما أعطيني limit U P N و F ناقص
+
+394
+00:33:43,000 --> 00:33:51,240
+ال L P N و F as N goes to infinity بساوة صفر، مظبوط؟
+
+395
+00:33:51,240 --> 00:33:56,220
+هي كل ما أعطينيها نجي للتعريف، إذا تعريف ال
+
+396
+00:33:56,220 --> 00:33:58,880
+sequence عادية for every epsilon أكبر من صفر there
+
+397
+00:33:58,880 --> 00:34:02,680
+exists K element in N such that for every N أكبر
+
+398
+00:34:02,680 --> 00:34:13,090
+سوى K اللي هو عندي ال U P N و F ناقص L P N و F أصغر من
+
+399
+00:34:13,090 --> 00:34:19,010
+إبسلون، إذا مش لجينا بارتشن واحد لجينا بارتشن بك و
+
+400
+00:34:19,010 --> 00:34:22,710
+بك زائد واحد و بك زائد اتنين و بك زائد تلاتة كلهم
+
+401
+00:34:22,710 --> 00:34:29,110
+بسبب إن ال UBK أو ال UBK زائد واحد أو الاخره ناقص
+
+402
+00:34:29,110 --> 00:34:32,590
+القللها أصغر من 100 من إبسلون، إذا ال criterion
+
+403
+00:34:32,590 --> 00:34:36,550
+اللي في الكورولاريت حققت، إذا صارت عندي هذه إذا F
+
+404
+00:34:36,550 --> 00:34:41,830
+is integrable، يعني مش بي إبسلون واحد اللي جينا لأ
+
+405
+00:34:41,830 --> 00:34:46,550
+من عند بك وطالع كل ال partitions هذه اللي هي بك و
+
+406
+00:34:46,550 --> 00:34:49,950
+بك زائد واحد و بك زائد اتنين بتعمل عمل ال بي
+
+407
+00:34:49,950 --> 00:34:53,510
+إبسلون اللي في وين؟ في النظرية، إذا ال F أشمالها
+
+408
+00:34:53,510 --> 00:34:58,750
+صارت ال F عبارة عن Integrable من النظرية السابقة
+
+409
+00:34:58,750 --> 00:35:05,200
+الآن الدور دل ان نثبت مين؟ ان ال limit لل اللي هو
+
+410
+00:35:05,200 --> 00:35:09,260
+هذا المقدار هو limit لهذا المقدار، بساوي إيش؟ اللي
+
+411
+00:35:09,260 --> 00:35:12,540
+جوا طبعا، هو لو كانت يا جماعة limit هذا نقص هذا صفر
+
+412
+00:35:12,540 --> 00:35:15,920
+مش معناته ال limit الأول و limit الثاني exist، هاي
+
+413
+00:35:15,920 --> 00:35:20,610
+مثلا هذه لو كانت هذه un تربيع وهذه un، unterm .. آسف
+
+414
+00:35:20,610 --> 00:35:24,610
+un تربيع و un تربيع أو un و un، limit un نقص un على
+
+415
+00:35:24,610 --> 00:35:27,850
+طول صفر، لكن لا limit الأولى عدد ولا limit الثاني
+
+416
+00:35:27,850 --> 00:35:33,270
+عدد، اتنين اتين بيروحين إلى مالا نهاية، فالان لكن في
+
+417
+00:35:33,270 --> 00:35:37,390
+هذه الحالة نظرا للمعطيات اللي موجودة و اللي هي
+
+418
+00:35:37,390 --> 00:35:40,930
+طبيعي اللي هو اللي بنحكي فيه NuF is bounded و ببو
+
+419
+00:35:40,930 --> 00:35:45,550
+و الاخره، هو استخدام السابق هيطلع عندي فعلا ال
+
+420
+00:35:45,550 --> 00:35:50,840
+limit لل lower بيساوي limit للأبر بيساوي قيمة ال
+
+421
+00:35:50,840 --> 00:36:08,200
+integration ماشي اطلعوا يا جماعة عندي الآن خليني
+
+422
+00:36:08,200 --> 00:36:15,240
+أطلع .. نحط البرهان أمامنا، بدي الآن خلصت اللي هو F
+
+423
+00:36:15,240 --> 00:36:21,500
+is integrable بدي أستخدم زي جابل بشوية بالظبط اللي 
+
+424
+00:36:21,500 --> 00:36:28,570
+هو تعريف الـ L of F و U of F وإيش تعريفها ذا ما
+
+425
+00:36:28,570 --> 00:36:32,250
+بديش أعيد اللي حكيته قبل بشوية، الآن بما أن الـ L of
+
+426
+00:36:32,250 --> 00:36:42,370
+F عبارة عن اللي هي supremum للـ L B of F، إذا لكل
+
+427
+00:36:42,370 --> 00:36:46,610
+ي ساوي واحدة لأن there exists B N partition of I
+
+428
+00:36:46,610 --> 00:36:50,390
+such that L of F ناقص 1 لأن أصغر من مين؟ من الـ L B
+
+429
+00:36:50,390 --> 00:36:54,070
+N of F زي ما قلت قبل شوية، لو الـ Supremum طرحنا 
+
+430
+00:36:54,070 --> 00:36:57,270
+اللي هي الـ Least Upper Bound، طرحنا منه أي عدد، 1
+
+431
+00:36:57,270 --> 00:37:01,330
+على N، إذا هلاجي، هي بطل إيش ماله؟ Upper Bound، إيش
+
+432
+00:37:01,330 --> 00:37:04,190
+معناه يبطل Upper Bound؟ هيلاجي واحد من المجموعة
+
+433
+00:37:04,190 --> 00:37:08,230
+أكبر منه، وهذا فعلا اللي لاجينا BN بحيث أن الـ BN
+
+434
+00:37:08,230 --> 00:37:13,910
+و F أكبر من الـ F ناقص 1 لأن، الآن من هذا .. من 
+
+435
+00:37:13,910 --> 00:37:16,670
+.. من .. من ال .. ال .. ال .. ناخذ هذا على الطرف 
+
+436
+00:37:16,670 --> 00:37:19,970
+الثاني على الطرف هنا، و ناخذ هذا على الطرف هذا بصير
+
+437
+00:37:19,970 --> 00:37:23,890
+عندي L of F ناقص Lb of F أصغر من 1 الآن وأنا
+
+438
+00:37:23,890 --> 00:37:28,670
+بعرف أن هذا دايما أكبر يساوي هذا لأن هذا الـ
+
+439
+00:37:28,670 --> 00:37:32,410
+supremum منهم، إذا أنا هيكون أكبر يساوي صفر، الآن
+
+440
+00:37:32,410 --> 00:37:38,440
+خدوا الـ limit للجهتين as n goes to infinity بيصير
+
+441
+00:37:38,440 --> 00:37:43,160
+عندي هذا اللي هي limit
+
+442
+00:37:43,160 --> 00:37:48,060
+لـ L بيقل نوف أف، حيث الـ L أوف أف لإنه حيثير الـ
+
+443
+00:37:48,060 --> 00:37:53,720
+limit هذا أيش بيساوي؟ بيساوي صفر، واضحالان يا جماعة
+
+444
+00:37:53,720 --> 00:37:58,400
+عندي الـ L of F ناقص الـ P L of F أصغر من 1 لأنه
+
+445
+00:37:58,400 --> 00:38:03,660
+أكبر يساوي صفر لأن معله، الآن هذا لكل إبسلون اللي هو
+
+446
+00:38:03,660 --> 00:38:07,300
+1 لأن لجينا partition يعني للإبسلون بيساوي
+
+447
+00:38:07,300 --> 00:38:09,360
+1، لجينا بيه 1، للإبسلون بيساوي 2 بيه 
+
+448
+00:38:09,360 --> 00:38:12,160
+2، للإبسلون 3 بيه 3 إذا صار عندي
+
+449
+00:38:12,160 --> 00:38:16,580
+sequence of اللي هي إيش partitions الآن طلع عندي
+
+450
+00:38:16,580 --> 00:38:20,460
+دائما دائما دائما L of F ناقص الـ PN of F أصغر من
+
+451
+00:38:20,460 --> 00:38:25,440
+1 على N لكل N، الآن as N goes to infinity هذا الـ
+
+452
+00:38:25,440 --> 00:38:30,620
+limit هيصير صفر، وهذا صفر، إذا هيصير limit هذا as N
+
+453
+00:38:30,620 --> 00:38:33,200
+goes to infinity بيساوي صفر لكن الـ L of F أصلا
+
+454
+00:38:33,200 --> 00:38:37,860
+independent of N إذا هيصير limit PN of F as N goes
+
+455
+00:38:37,860 --> 00:38:43,720
+to infinity بيساوي L of F لأن المواضحات لوش يا شباب
+
+456
+00:38:43,720 --> 00:38:52,360
+limit L of F ناقص L B N و F هيساوي 0 as N goes to
+
+457
+00:38:52,360 --> 00:38:56,920
+infinity وهذا المقدار عبارة عن مقدار ثابت
+
+458
+00:38:56,920 --> 00:39:04,740
+independent of N إذا هيصير عندي limit L B N و F
+
+459
+00:39:04,740 --> 00:39:10,540
+بتساوي limit L of F ناقص
+
+460
+00:39:17,660 --> 00:39:27,170
+L of P L و F زائد L of F مظبوط؟ طيب هذا الآن
+
+461
+00:39:27,170 --> 00:39:33,590
+المقدار معروف أنه بيساوي 0 وهذا ثابت إذا بقدر أوزع
+
+462
+00:39:33,590 --> 00:39:37,210
+الـ limit على الجهتين وأنا مرتاح، إذا بيساوي limit
+
+463
+00:39:37,210 --> 00:39:42,950
+الأول اللي هو 0 زائد limit الثاني نفسه لأنه ثابت
+
+464
+00:39:42,950 --> 00:39:46,450
+إذا صار عندي limit L P N of F as N goes to
+
+465
+00:39:46,450 --> 00:39:54,710
+infinity بيساوي L of F كما هو حكينا عنه حقا، من جهة
+
+466
+00:39:54,710 --> 00:39:58,650
+أخرى limit الـ U ناقص limit الـ L المعطيلة هي بيساوي
+
+467
+00:39:58,650 --> 00:40:03,490
+0، إذا صار عندي سهل أن أوجد mean برضه limit الـ U
+
+468
+00:40:03,490 --> 00:40:08,990
+اللي هو limit الـ U إيش هيساوي؟ ناقص اللي هو .. الـ
+
+469
+00:40:08,990 --> 00:40:12,670
+.. ال .. هيساوي limit الـ L of F، يساوي الـ U of F
+
+470
+00:40:12,670 --> 00:40:17,270
+يساوي ال integration أكثر توضيحاً، and بيهاجدى
+
+471
+00:40:17,270 --> 00:40:22,420
+أعتقد أنه واضح، لكن خلينا نوضحه بشكل أكبر عشان
+
+472
+00:40:22,420 --> 00:40:34,100
+ما يضلش مشي عندي limit U P N of F إيش هيساوي؟ هيساوي
+
+473
+00:40:34,100 --> 00:40:44,560
+اللي هو limit U
+
+474
+00:40:44,560 --> 00:40:49,740
+P N of F
+
+475
+00:40:52,490 --> 00:40:58,090
+limit U P N و F ناقص
+
+476
+00:40:58,090 --> 00:41:07,810
+L of P N of F زائد L P N of F واضحة يا شباب أه؟
+
+477
+00:41:07,810 --> 00:41:12,690
+الآن هذا مضمون أنه موجود وصفر وهذا مضمون و
+
+478
+00:41:12,690 --> 00:41:18,350
+أثبتناه، إيش بيساوي؟ L of F إذا إيش صار بيساوي؟
+
+479
+00:41:18,350 --> 00:41:21,810
+بيساوي اللي هو هذا صفر، إذا صار بيساوي أقل و فأف
+
+480
+00:41:21,810 --> 00:41:25,510
+إذا صار هذا برضه بيساوي أقل و فأف، لكن أنا مثبت قبل
+
+481
+00:41:25,510 --> 00:41:29,610
+بشوية أن الـ F is integrable يعني الـ U في F إيش
+
+482
+00:41:29,610 --> 00:41:34,550
+هتساوي؟ اللي أقل و فأف، وهذه أثبتناها إيش بتساوي؟
+
+483
+00:41:34,550 --> 00:41:39,350
+limit U P N و F وهذه نفسها أثبتناها قبل بشوية إيش
+
+484
+00:41:39,350 --> 00:41:46,070
+بتساوي؟ limit L P N و F وهو المطلوب طبعاً، مدام
+
+485
+00:41:46,070 --> 00:41:49,370
+integration هذه، وهذه هي عبارة عن ال integration
+
+486
+00:41:49,370 --> 00:41:55,410
+على الفترة اللي بنحكي عنها، الإنقلا بيه لقيمة الـ F
+
+487
+00:41:55,410 --> 00:42:01,710
+لأن صار عندي كل القيام هذه متساوية، وصار عندي إيجاد
+
+488
+00:42:01,710 --> 00:42:07,610
+الـ limit للـ U P N و F أو limit للـ L P N و F يكفي
+
+489
+00:42:07,610 --> 00:42:11,330
+أنه نوجد فيه قيمة الـ integration بعد ما أثبتناه أو
+
+490
+00:42:11,330 --> 00:42:16,260
+تحت الظروف اللي هي في الكورو الأخرى، لأ نيجي بدنا
+
+491
+00:42:16,260 --> 00:42:22,660
+نبرهن اللي هو المثال اللي برهناه المرة الماضية
+
+492
+00:42:22,660 --> 00:42:27,660
+بالتعريف بدنا نبرهنه بواسطة اللي هي الـ corollary
+
+493
+00:42:27,660 --> 00:42:33,060
+اللي عندنا بدنا نبرهن اللي هو اللي هي نثبت أنه
+
+494
+00:42:36,170 --> 00:42:42,070
+نثبت أن F of X بساوة X يا شباب عبارة عن Integrable
+
+495
+00:42:42,070 --> 00:42:45,770
+أو اللي سمناها G of X بساوة X is Integrable على
+
+496
+00:42:45,770 --> 00:42:48,830
+الفترة Zero واحد، المرة الماضية أثبتناها كيف؟
+
+497
+00:42:48,830 --> 00:42:54,230
+أثبتناها زي ما أنتم متذكرين بواسط التعريف، مظبوط؟
+
+498
+00:42:54,230 --> 00:42:58,610
+طيب جيبنا اللي هو الـ upper sum والـ lower sum و
+
+499
+00:42:58,610 --> 00:43:02,930
+بعدين جيبنا الـ upper integral والـ lower integral
+
+500
+00:43:02,930 --> 00:43:04,750
+و أثبتنا أن الـ upper integral بساوي الـ lower
+
+501
+00:43:04,750 --> 00:43:08,760
+integral وخلصناه، الآن بدنا نثبتها بطريقتنا اللي هي 
+
+502
+00:43:08,760 --> 00:43:12,540
+على الكورولر اللي جابل بشوية عند g of x ساوة x على
+
+503
+00:43:12,540 --> 00:43:16,600
+الفترة 0 بواحد، هي المطلوب إثباتها show that g is
+
+504
+00:43:16,600 --> 00:43:20,940
+integrable على هذه الفترة، الآن بديش أعيد اللي
+
+505
+00:43:20,940 --> 00:43:23,850
+حكيته المرة الماضية، اللي حكيناه المرة الماضية، من
+
+506
+00:43:23,850 --> 00:43:26,910
+الـ Example اللي أثبتنا فيه إنها Integra بالبواسطة
+
+507
+00:43:26,910 --> 00:43:31,470
+اللي هي التعريف أخدنا P N اللي هو صفر واحد على N
+
+508
+00:43:31,470 --> 00:43:34,910
+واثنين على N، وان ناقص 1 على N لعند الواحد، أخدنا
+
+509
+00:43:34,910 --> 00:43:39,290
+اللي هو عبارة عن Any Partition اللي هو بالطريقة
+
+510
+00:43:39,290 --> 00:43:43,710
+اللي أمامي، يعني حسب N بيصير بختلف الـ Partition أما
+
+511
+00:43:43,710 --> 00:43:46,730
+إيش فكرة الـ Partition زي ما قلنا المرة الفائتة من
+
+512
+00:43:46,730 --> 00:43:51,350
+0 لعند 1 جزأناها إلى أجزاء متساوية إلى N من
+
+513
+00:43:51,350 --> 00:43:55,350
+الأجزاء المتساوية صار طول كل sub integral عبارة عن
+
+514
+00:43:55,350 --> 00:44:00,850
+إيه؟ إيش عبارة عن 1 على N، وأوجدنا في حينه اللي هو
+
+515
+00:44:00,850 --> 00:44:08,470
+الـ U P N O G ولاجناها بتساوي إيه ده؟ بتتذكروا نص في
+
+516
+00:44:08,470 --> 00:44:13,710
+1 زائد 1 على N، وأوجدنا برضه الـ P N O G
+
+517
+00:44:13,710 --> 00:44:18,910
+ولاجناها عبارة عن نص في 1 ناقص 1 على N كما
+
+518
+00:44:18,910 --> 00:44:26,960
+أذكر ماشي الحال فعلاً طيب، الآن صار عندي الـ PN في
+
+519
+00:44:26,960 --> 00:44:29,780
+الواقع عبارة عن sequence of partitions
+
+520
+00:44:35,190 --> 00:44:39,110
+هذه صارت sequence of partitions، بواحد بتعود عن أنا
+
+521
+00:44:39,110 --> 00:44:42,750
+بواحد، باتنين كده، بتلاتة كده، بأربعة كده، وفي كل
+
+522
+00:44:42,750 --> 00:44:47,270
+الأحوال الـ U, B, N و G انحروا لهيها، والـ L, B, N
+
+523
+00:44:47,270 --> 00:44:51,490
+و G بساوي إيش المقدار الأمامي؟ الآن عشان أثبت إنها
+
+524
+00:44:51,490 --> 00:44:56,590
+integrable يكفي من النظرية الكورولاري إن قاعد أقول
+
+525
+00:44:56,590 --> 00:45:03,290
+طب خلينا نشوف limit الـ U, B, N و G ناقص الـ L, B, 
+
+526
+00:45:03,450 --> 00:45:09,840
+N و G as n goes to infinity بساوة إيه يا عشان بساوة
+
+527
+00:45:09,840 --> 00:45:16,360
+صفر نشوفها صح ولا لأ؟ طبعاً أكيد مع حسبة بسيطة
+
+528
+00:45:16,360 --> 00:45:24,580
+احسبليها بساوة limit نص في 1 زيادة 1 لأن زيادة 
+
+529
+00:45:24,580 --> 00:45:28,600
+نص في 1 ناقص 1 لأن as n goes to infinity
+
+530
+00:45:28,600 --> 00:45:32,260
+هذه صفر وهذه صفر وهذه نص وهذه نص وهذه نص وهذه نص
+
+531
+00:45:32,260 --> 00:45:32,340
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+532
+00:45:32,340 --> 00:45:32,920
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+533
+00:45:32,920 --> 00:45:38,340
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+534
+00:45:38,340 --> 00:45:45,580
+وهذه اللي هو y ساوي نص ناقص النص، y ساوي صفر واضح أهي
+
+535
+00:45:45,580 --> 00:45:50,120
+عندي اللي هو هاد صفر وهاد صفر ونص ناقص النص، y
+
+536
+00:45:50,120 --> 00:45:54,920
+ساوي صفر، مادام صفر إذا إيه شمالها؟ إذا the function
+
+537
+00:45:54,920 --> 00:46:02,720
+d of x ساوي x is integrable on zero واحد هذا by
+
+538
+00:46:02,720 --> 00:46:06,560
+mean by الـ corollary اللي قبل بشوية
+
+539
+00:46:15,600 --> 00:46:19,420
+الآن قيمة الـ integration إيش هيكون؟ قيمة الـ limit
+
+540
+00:46:19,420 --> 00:46:24,280
+limit u, b, n, g هيقدر الغرض، و limit l of n of g
+
+541
+00:46:24,280 --> 00:46:29,320
+هيقدر الغرض ليش؟ لأن limit هذا أصلاً هيطلع لك limit
+
+542
+00:46:29,320 --> 00:46:35,710
+الـ u, b, n و g هو عبارة عن قيمة integration من A لـ
+
+543
+00:46:35,710 --> 00:46:42,370
+B حسب النظرية الـ Corollary ويساوي limit 2.5 في 1
+
+544
+00:46:42,370 --> 00:46:48,600
+زائد 1 ل N ويساوي هذا تروح لـ 0، ويساوي نص، وأيضاً
+
+545
+00:46:48,600 --> 00:46:54,080
+لو جربت حسب تاب limit الـ b, n و g طبعاً هيطلع نفس
+
+546
+00:46:54,080 --> 00:46:58,200
+الجواب، وإلا إن كان هناك مشكلة لدينا limit نص في
+
+547
+00:46:58,200 --> 00:47:02,340
+1 ناقص 1 على n ويساوي برضه جدياش نص؟ إذن
+
+548
+00:47:02,340 --> 00:47:06,700
+قيمة الـ integration بساوة نص، إذن هذه طريقة أخرى
+
+549
+00:47:06,700 --> 00:47:11,780
+لحساب اللي هو أو لإثبات أن g of x بساوة x is
+
+550
+00:47:11,780 --> 00:47:17,560
+integrable الآن بدنا ندخل على أمر آخر، الأمر هو في
+
+551
+00:47:17,560 --> 00:47:24,500
+الواقع يا شباب أنه بدنا نشوف إيش في من عائلات
+
+552
+00:47:24,500 --> 00:47:28,400
+الدوال، عائلات الدوال إنها تكون Integrable الآن
+
+553
+00:47:28,400 --> 00:47:31,720
+بدنا نيجي نحوش الدوال الـ Integrable إحنا عرفنا بس
+
+554
+00:47:31,720 --> 00:47:36,500
+ده لأ D of X سو X is Integrable وهنلاقي زيها لكن
+
+555
+00:47:36,500 --> 00:47:40,960
+الآن بدنا نيجي نحكي عن دوال اللي هو عائلات من
+
+556
+00:47:40,960 --> 00:47:45,480
+الدوال، الأول عائلة من العائلات المهمة اللي هي الـ
+
+557
+00:47:45,480 --> 00:47:48,960
+monotone functions يعني الدوال اللي بتكون يا
+
+558
+00:47:48,960 --> 00:47:52,360
+increasing على كل الفترة يا decreasing على كل
+
+559
+00:47:52,360 --> 00:47:59,320
+الفترة، بقول لكم هذا على اللي هي F من F الـ function
+
+560
+00:47:59,320 --> 00:48:04,000
+لو كانت bounded لو كانت monotone على اللي هي 
+
+561
+00:48:04,000 --> 00:48:09,660
+على طول integrable إذن closed bounded interval I 
+
+562
+00:48:09,660 --> 00:48:16,700
+عيلة كبيرة عيلة الدوال اللي بتكون يا increasing يا
+
+563
+00:48:16,700 --> 00:48:22,380
+decreasing على كل الفترة a و b هذه مضمون أن تكون
+
+564
+00:48:22,380 --> 00:48:26,980
+الدوال ايه شمالها عبارة عن integrable functions
+
+565
+00:48:26,980 --> 00:48:35,090
+إذا أول إعلان الآن اللي هو any monotone function on
+
+566
+00:48:35,090 --> 00:48:40,850
+a closed bounded interval is integrable وهذا اللي
+
+567
+00:48:40,850 --> 00:48:47,090
+هو عنواننا integrability of monotone functions لـ I
+
+568
+00:48:47,090 --> 00:48:51,650
+بتساوي A و B و لـ F من I لـ R بيكون مونوتون فانكشن
+
+569
+00:48:51,650 --> 00:48:57,370
+on I ثم F أشمالها is integrable on I نفترض أن F
+
+570
+00:48:57,370 --> 00:49:03,110
+انتقل هو مونوتور نصل إليها integrable نفترض أن F
+
+571
+00:49:03,110 --> 00:49:09,440
+مثلا increasing ونصل إنها integrable و similarly
+
+572
+00:49:09,440 --> 00:49:14,560
+وفعلا similarly لو كانت f is decreasing هتكون برضه
+
+573
+00:49:14,560 --> 00:49:21,500
+is integrable خلينا مع بعض شباب نفترض suppose
+
+574
+00:49:21,500 --> 00:49:31,240
+that f is increasing يعني الدالة على الفترة هي a
+
+575
+00:49:31,240 --> 00:49:37,760
+و b مثلا والدالة هتكون أشمالها تزايدية يا هيك يا هيك
+
+576
+00:49:37,760 --> 00:49:41,620
+طبعا حسب مش مشكلة بتفرج أشمالها ماشي الحال اللي هي
+
+577
+00:49:41,620 --> 00:49:47,060
+الدالة أشمالها is increasing is increasing بتدخل
+
+578
+00:49:47,060 --> 00:49:53,500
+الآن بي أن اللي هو عبارة عن any partition اللي هو
+
+579
+00:49:55,970 --> 00:50:00,970
+بس بدي أجزه زي منهج اللي عملته معه اللي هو f of x
+
+580
+00:50:00,970 --> 00:50:05,370
+بساوي x اللي قبله شوية بدي أجزه إلى أجزاء متساوية
+
+581
+00:50:05,370 --> 00:50:11,130
+يعني بدي أجز الفقرة a و b إلى أجزاء متساوية الأولى
+
+582
+00:50:11,130 --> 00:50:15,730
+بدي أسميها x note اللي بعدها x1 اللي بعدها x2 لما
+
+583
+00:50:15,730 --> 00:50:21,780
+أصل لآخر 11 أسميها xn ونكون طول كل واحدة متساوية
+
+584
+00:50:21,780 --> 00:50:26,340
+للثانية إذا الآن إذا بدي أجزئها إلى N إلى N من ال
+
+585
+00:50:26,340 --> 00:50:30,240
+sub intervals بيصير طول كل فترة عبارة عن B minus A
+
+586
+00:50:30,240 --> 00:50:35,080
+على مين؟ على N طول الفترة على عدد الفترات اللي
+
+587
+00:50:35,080 --> 00:50:39,400
+بتديها أنا بدّي الفترات إيش عددها؟ N فبيصير عند بي
+
+588
+00:50:39,400 --> 00:50:43,320
+ماينس إيه على مين على N هذا طول الفترة يعني الفترة
+
+589
+00:50:43,320 --> 00:50:47,740
+النموذجية لأي K X K minus X K minus واحد هيتمكن
+
+590
+00:50:47,740 --> 00:50:52,560
+طولها عبارة عن بي ماينس إيه على N for every K كيه
+
+591
+00:50:52,560 --> 00:50:56,000
+طبعا إيه أشمالها؟ يا ما بيساوي Zero يا واحد، لعند
+
+592
+00:50:56,000 --> 00:51:01,100
+ماصل، لعند مين؟ لعند N أو K بيساوي واحد لعند N
+
+593
+00:51:04,810 --> 00:51:10,230
+xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+594
+00:51:10,230 --> 00:51:14,230
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+595
+00:51:14,230 --> 00:51:14,590
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+596
+00:51:14,590 --> 00:51:17,070
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+597
+00:51:17,070 --> 00:51:25,770
+-xn-n-xn-n-xn-n-xn-n-xn-n لأ لو جينا هذا increasing
+
+598
+00:51:25,770 --> 00:51:30,170
+مدام increasing إذن الـ Mk اللي هي عبارة عن ال
+
+599
+00:51:30,170 --> 00:51:35,510
+supremum اللي هنا supremum لهذه Mk ال supremum
+
+600
+00:51:35,510 --> 00:51:39,910
+اللي هنا هيكون على أخر واحدة لأن أجملها ده لا is
+
+601
+00:51:39,910 --> 00:51:45,510
+increasing إذن هيكون ال Mk هو F of XK رسم عنها
+
+602
+00:51:45,990 --> 00:51:51,210
+بساوي F of X K طيب ال M K Small أكيد هيقولنا كلكم
+
+603
+00:51:51,210 --> 00:51:54,010
+هتقوله بتساوي ال M في معمع الفترة مدام ال M في
+
+604
+00:51:54,010 --> 00:51:57,370
+معمع الفترة إذا أول واحدة فيهم إذا هو F of X K
+
+605
+00:51:57,370 --> 00:52:04,530
+minus واحد، مظبوط شباب؟ طيب، مظبوط هذه اللي هي
+
+606
+00:52:04,530 --> 00:52:10,750
+مالها الدالة اللي بتكون monotone عندي،
+
+607
+00:52:10,750 --> 00:52:21,840
+احسبلي الآن ال U P N و F نقص الـ BNOF إيش هيساوي؟
+
+608
+00:52:21,840 --> 00:52:26,840
+جهزة الأمور بساوي الـ summation لمين؟ للـ MK
+
+609
+00:52:26,840 --> 00:52:36,190
+Capital في XK نقص XK minus واحدك من عند 1 لعند n
+
+610
+00:52:36,190 --> 00:52:44,370
+نقص summation mk في xk minus xk minus 1 k من عند 1
+
+611
+00:52:44,370 --> 00:52:49,440
+لعند n ويساوي الـ Mk وجدناها، اللي هي عبارة عن مين؟
+
+612
+00:52:49,440 --> 00:52:55,420
+F of Xk ويساوي الـ summation للـ F of Xk في مين
+
+613
+00:52:55,420 --> 00:53:00,200
+مضروبة؟ في هذه، هذه كده طولها ثابت، ما احنا هيك
+
+614
+00:53:00,200 --> 00:53:02,540
+على هذا الأساس إذا اخترنا الـ sequence of
+
+615
+00:53:02,540 --> 00:53:05,320
+partitions اللي عندنا، اللي هو طوالث في
+
+616
+00:53:05,320 --> 00:53:09,580
+subintervals ثابتة، كل واحد اسمه يشمله B minus A
+
+617
+00:53:09,580 --> 00:53:14,250
+على N، هذا K من واحد إن عندنا ناقص خليني أضعه في
+
+618
+00:53:14,250 --> 00:53:18,550
+summation 1 ناقص نفس القصة اللي هي m k small إيش
+
+619
+00:53:18,550 --> 00:53:23,710
+هي يا جماعة اتفاقنا عبارة عن f of x k minus 1 في
+
+620
+00:53:23,710 --> 00:53:27,610
+هذه خليني أخدها عامل مشترك بعد إذنكم لإن هو
+
+621
+00:53:27,610 --> 00:53:31,070
+موجودة هنا وموجودة هنا خليني أطلّحها برا واضحة
+
+622
+00:53:31,070 --> 00:53:36,070
+أشيل هذه برا بيصير اللي هو مضروبة في b minus a على
+
+623
+00:53:36,910 --> 00:53:42,350
+و أصلا هذه ثابتة بالنسبة لل summation ليش؟ لأن ال
+
+624
+00:53:42,350 --> 00:53:46,110
+summation العداد K من واحد عندنا أن هذه N ثابتة
+
+625
+00:53:46,110 --> 00:53:52,870
+بالنسبة لل K لذلك بتساوي B minus A على N مضروبة في
+
+626
+00:53:52,870 --> 00:53:59,280
+مين في ال summation للـ f of x k minus f of x k
+
+627
+00:53:59,280 --> 00:54:03,840
+minus واحد k من عند واحد لعند مين يا جماعة لعند ان
+
+628
+00:54:03,840 --> 00:54:07,920
+بعدين the is and could بدي أفرطها هذه بيصير عندي y
+
+629
+00:54:07,920 --> 00:54:14,880
+ساوي هذا اللي هو مين كله اللي جاعت بحسبه ال u,b,n
+
+630
+00:54:14,880 --> 00:54:19,320
+و f ناقص ال b,n و f هيسوي هذا المقدار اللي هو b
+
+631
+00:54:19,320 --> 00:54:25,970
+minus a على المضروب فيه الآن ال summation عبارة عن
+
+632
+00:54:25,970 --> 00:54:32,630
+k ب 1 بصير f of x 1 ناقص f of x naught اللي بعدها
+
+633
+00:54:32,630 --> 00:54:40,170
+k ب 2 زائد f of x 2 ناقص f of x 1 اللي بعدها زائد
+
+634
+00:54:40,170 --> 00:54:46,130
+f of x 3 ناقص f of x 2 لما نقضى اللي ماشي لأخر
+
+635
+00:54:46,130 --> 00:54:53,140
+واحد بكون عندي f of x n ناقص f of x n ناقص واحد
+
+636
+00:54:57,360 --> 00:55:04,840
+F of X1 بيطير مع سالب F of X1 و F of X2 بيطير مع
+
+637
+00:55:04,840 --> 00:55:09,840
+سالب F of X2 و هكذا بظل ماشي لما كله يروح مع كله
+
+638
+00:55:09,840 --> 00:55:16,640
+ما عدا بظل عندي اللي هو أول قيمة اللي هي F of X
+
+639
+00:55:16,640 --> 00:55:22,660
+note بالسالب مع F of Xn الأخيرة بالموجب بيصير عندي
+
+640
+00:55:22,660 --> 00:55:34,740
+Y ساوي B minus A على N في F of Xn ناقص F of X0 طبعا
+
+641
+00:55:34,740 --> 00:55:39,420
+Xn آخر واحدة اللي هي B و X0 أول واحدة اللي هي A
+
+642
+00:55:39,420 --> 00:55:46,580
+إذن هيساوي هذا عبارة عن B minus A في F of B minus
+
+643
+00:55:46,580 --> 00:55:53,150
+F of A الكل هذا مجسوم على مين يا جماعة؟ على N هذا
+
+644
+00:55:53,150 --> 00:55:58,090
+عبارة عن ثابت وهذا عبارة عن ثابت وهذا الآن هي اللي
+
+645
+00:55:58,090 --> 00:56:03,670
+بدلالتها كُتِب ال partitions إذا صار عندي الآن بعد
+
+646
+00:56:03,670 --> 00:56:07,230
+كل اللي حكيته هنا أخدت ال بي أن بالشكل اللي أمامي
+
+647
+00:56:07,230 --> 00:56:12,190
+عبارة عن sequence of partitions ووصلنا إلى ما
+
+648
+00:56:12,190 --> 00:56:17,890
+لاقيا ليه يا جماعة اللي هو وصلنا أن ال you بي أن و
+
+649
+00:56:17,890 --> 00:56:26,260
+أف ناقص ال بي أن و أف أصغر أو يساوي طبعا أكيد أكبر
+
+650
+00:56:26,260 --> 00:56:29,600
+يساوي صفر لأن هذا دايما أكبر يساوي هذا أصغر يساوي
+
+651
+00:56:29,600 --> 00:56:36,140
+B minus A ف F of B أكيد عرفت أشهد أساوي نقص F of A
+
+652
+00:56:36,140 --> 00:56:41,720
+على اللي هو N الـ N خد ال limit للجهتين as N goes
+
+653
+00:56:41,720 --> 00:56:45,160
+to infinity as N goes to infinity هذا goes to zero
+
+654
+00:56:45,160 --> 00:56:51,730
+وهذا أصلا صفر فبيصير عندي limit إذا .. إذا limit ال
+
+655
+00:56:51,730 --> 00:56:59,290
+U P N و F ناقص الـ L P N و F as N goes to infinity
+
+656
+00:56:59,290 --> 00:57:04,210
+بساوي سفر إذا صار عندي sequence of partitions تحقق
+
+657
+00:57:04,210 --> 00:57:07,730
+لهذا إذا حسب الـ Corollary اللي حكيتها قبل بشوية
+
+658
+00:57:07,730 --> 00:57:17,130
+إذا F is integrable وهو المطلوب إذا صار عندي أي
+
+659
+00:57:17,130 --> 00:57:21,850
+increasing function is integrable similarly for
+
+660
+00:57:21,850 --> 00:57:26,170
+decreasing لماذا similarly لأنه تصبح الدالة بدل ما
+
+661
+00:57:26,170 --> 00:57:30,950
+هي طالع هيك تصبح أشمالها نازلة نزول الدالة فبصير
+
+662
+00:57:30,950 --> 00:57:35,430
+عندك اللي هو ال maximum هي الأولى أو ال supremum
+
+663
+00:57:35,430 --> 00:57:41,920
+هي أف بصير الـ MK بسوء F of XK minus واحد و الـ MK
+
+664
+00:57:41,920 --> 00:57:46,760
+بسوء F of XK و بيتكاملوا البرهان بنفس الطريقة، هيطلع
+
+665
+00:57:46,760 --> 00:57:52,040
+عندكم البرهان automatic وبشكل سهل وبشكل سلس،
+
+666
+00:57:52,040 --> 00:57:58,500
+similar أي سؤال؟ إذن الإعلان اللي أعلنناه قبل
+
+667
+00:57:58,500 --> 00:58:04,800
+بشوية أنه any monotone function يعني any increasing
+
+668
+00:58:04,800 --> 00:58:08,780
+function on a closed bounded interval must be
+
+669
+00:58:08,780 --> 00:58:15,740
+integrable and any decreasing function on a closed
+
+670
+00:58:15,740 --> 00:58:20,420
+bounded interval برضه must be integrable إذا صار
+
+671
+00:58:20,420 --> 00:58:26,060
+في عنا عائلة كاملة من الدوال القابلة للتكامل بواسط
+
+672
+00:58:26,060 --> 00:58:32,160
+التكامل remand الآن بدنا ننتقل إلى عائلة أخرى
+
+673
+00:58:32,160 --> 00:58:38,300
+وعائلة لا تقل أهمية عن هذه العائلة وعائلة يعني
+
+674
+00:58:38,300 --> 00:58:45,560
+محبوبة عنها اللي هي اللي
+
+675
+00:58:45,560 --> 00:58:53,960
+هي عائلة الدوال المتصلة اللي هي integrable of
+
+676
+00:58:53,960 --> 00:58:56,140
+continuous functions
+
+677
+00:59:00,850 --> 00:59:06,130
+اللي هي integrability of continuous functions
+
+678
+00:59:06,130 --> 00:59:12,210
+النظرية بتقول ما يلي لـ أ .. طبعا عندي ال function
+
+679
+00:59:12,210 --> 00:59:16,410
+على closed bounded interval لـ F من I لـ R be
+
+680
+00:59:16,410 --> 00:59:20,750
+continuous on I then F is integrable on I إذا الآن
+
+681
+00:59:20,750 --> 00:59:24,230
+any continuous function on a closed bounded
+
+682
+00:59:24,230 --> 00:59:29,600
+interval must be integrable كمان مرة any continuous
+
+683
+00:59:29,600 --> 00:59:33,840
+function on a closed bounded interval must be
+
+684
+00:59:33,840 --> 00:59:38,920
+integrable طبعا حيزنا في البرهان شغلة اللي هي
+
+685
+00:59:38,920 --> 00:59:45,080
+أخدناها سابقا أنه Any continuous function on a
+
+686
+00:59:45,080 --> 00:59:49,840
+closed bounded interval must attain its maximum
+
+687
+00:59:49,840 --> 00:59:57,800
+and minimum on this interval بمعنى
+
+688
+00:59:57,800 --> 01:00:01,970
+آخر هنلاقيلو كانت F is continuous على اللي هو الـ
+
+689
+01:00:01,970 --> 01:00:05,990
+A و الـ B هنلاقي نقطة في داخل الفترة A و B بحيث
+
+690
+01:00:05,990 --> 01:00:09,570
+أنها تكون الـ F عندها نقطة maximum و هنلاقي نقطة
+
+691
+01:00:09,570 --> 01:00:12,750
+أخرى في داخل هذه الفترة هنلاقي اللي هي الـ
+
+692
+01:00:12,750 --> 01:00:15,930
+function عندها أشمالها is minimum طبعا absolute و
+
+693
+01:00:15,930 --> 01:00:24,180
+absolute نيجي نشوف .. نيجي للبرهان الآن .. نظرية
+
+694
+01:00:24,180 --> 01:00:28,540
+أخرى أيضا .. برضه خلينا نقولها أن لو كانت F is
+
+695
+01:00:28,540 --> 01:00:32,580
+continuous على closed bounded interval then F is
+
+696
+01:00:32,580 --> 01:00:43,820
+uniformly continuous الآن F .. عند F من A و B لعند
+
+697
+01:00:43,820 --> 01:00:51,090
+R is continuous on A و B continuous عالمين على
+
+698
+01:00:51,090 --> 01:00:54,450
+closed bounded interval في عندنا نظرية اللي بتقول
+
+699
+01:00:54,450 --> 01:00:58,270
+any continuous function في الواحد on a closed
+
+700
+01:00:58,270 --> 01:01:02,230
+bounded interval must be uniformly continuous إذا 
+
+701
+01:01:02,230 --> 01:01:10,030
+then f is uniformly continuous
+
+702
+01:01:10,730 --> 01:01:15,290
+on a و b ايش يعني uniformly continuous يعني لكل 
+
+703
+01:01:15,290 --> 01:01:18,810
+ابسلون أكبر من صفر there exist دلتا أكبر من صفر
+
+704
+01:01:18,810 --> 01:01:22,990
+دلتا بس بتعتمد عالميا على ابسلون بتنفع لكل ال X و
+
+705
+01:01:22,990 --> 01:01:30,810
+ال Y such that if X minus Y أو U ناقص V زي ما هو
+
+706
+01:01:30,810 --> 01:01:40,200
+مسميها U minus V أصغر من دلتا then F of U ناقص F of 
+
+707
+01:01:40,200 --> 01:01:49,800
+V أصغر من إبسلون لكل UV element in A أو B إذن لكل y
+
+708
+01:01:49,800 --> 01:01:52,900
+أكبر من 0 there exists Delta دلتا لا بتعتمد
+
+709
+01:01:52,900 --> 01:01:56,280
+على مين بس على إبسلون في حالة ال continuity
+
+710
+01:01:56,280 --> 01:02:01,560
+العادية بنقول إحنا limit f of x as x بتروح لل a
+
+711
+01:02:01,560 --> 01:02:07,260
+بساوي ايش f of a بنقول الآن إنه limit f of x بساوي
+
+712
+01:02:07,260 --> 01:02:13,450
+f of a as x بتروح لل a لكل إبسلون أكبر من 0  هصب مين
+
+713
+01:02:13,450 --> 01:02:18,070
+بالـ a هذه there exist دي و لكل a element in a
+
+714
+01:02:18,070 --> 01:02:23,270
+there exist delta such that اللي لما يكون x minus
+
+715
+01:02:23,270 --> 01:02:27,190
+a أصغر من delta بيعطينا f of x ناقص f of a أصغر من
+
+716
+01:02:27,190 --> 01:02:32,550
+إبسلون يعني بيكون الـ delta هنا تعتمد على الإبسلون
+
+717
+01:02:32,550 --> 01:02:37,550
+وتعتمد على ال a اللي عندها ال continuity لكن في الـ
+
+718
+01:02:37,550 --> 01:02:41,890
+Uniform Continuous الـ Delta اللي اللي جيت هنا
+
+719
+01:02:41,890 --> 01:02:47,510
+بتنفع لكل اللي هو ال .. ال .. ال .. ال .. ال .. ال
+
+720
+01:02:47,510 --> 01:02:47,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+721
+01:02:47,890 --> 01:02:47,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+722
+01:02:47,910 --> 01:02:48,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+723
+01:02:48,290 --> 01:02:48,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+724
+01:02:48,530 --> 01:02:50,270
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+725
+01:02:50,270 --> 01:02:50,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+726
+01:02:50,330 --> 01:02:50,410
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+727
+01:02:50,410 --> 01:02:54,250
+.. ال .. ال .. ال .. ال .. ال ..
+
+728
+01:02:54,250 --> 01:02:59,970
+ال .. ال ..F is continuous، إذن يُنفرم الـ
+
+729
+01:02:59,970 --> 01:03:02,650
+continuous، إيش معناته؟ كل إبسلون أكبر من صفر،
+
+730
+01:03:02,650 --> 01:03:05,490
+there exists دلتا، بحيث إن U minus V أصغر من دلتا
+
+731
+01:03:05,490 --> 01:03:08,690
+يعطيني F of U ناقص F of V أصغر من إيش، من إبسلون،
+
+732
+01:03:08,690 --> 01:03:11,870
+وخلّي هذه إيش مالها في الذاكرة، أنا عشان الحسابات
+
+733
+01:03:11,870 --> 01:03:15,890
+بدي أخليها إبسلون على مين، على B minus A، طول
+
+734
+01:03:15,890 --> 01:03:19,070
+الفترة اللي أنا بشتغل عليها، هتشوفوا ليش كتبت هيك،
+
+735
+01:03:19,070 --> 01:03:22,720
+بس لا الحسابات بقدر أه بقدر لإن هو أصغر .. أه بقدر
+
+736
+01:03:22,720 --> 01:03:25,140
+خليه أصغر من الـ Epsilon في الدنيا من ضمن إن كل
+
+737
+01:03:25,140 --> 01:03:27,520
+الـ Epsilon عن الـ B minus A لكل الـ Epsilonات
+
+738
+01:03:27,520 --> 01:03:34,040
+اللي في الدنيا طيب لأن شوف وين بده أروح، بده أروح
+
+739
+01:03:34,040 --> 01:03:39,250
+لـ Integrability لـ الـ function F الآن خُد n الآن
+
+740
+01:03:39,250 --> 01:03:42,190
+بدنا نعمل partitions بدنا نجيب sequence of
+
+741
+01:03:42,190 --> 01:03:45,890
+partitions Bn ال sequence of partitions هذه هي
+
+742
+01:03:45,890 --> 01:03:50,010
+اللي هتخدمني هتخدمني متى؟ بعد شوية بتشوفوا ليش
+
+743
+01:03:50,010 --> 01:03:54,110
+هتخدمني لكل الأنات اللي وين ما لإن اللي أكبر من ال
+
+744
+01:03:54,110 --> 01:03:59,370
+B minus A على مين؟ على ال delta اللي لجيتها إذا
+
+745
+01:03:59,370 --> 01:04:04,130
+اللي صارت ال delta بين إيديا إذا بقولك الآن choose
+
+746
+01:04:05,140 --> 01:04:12,320
+N element in N such that ما لها N أكبر من B minus
+
+747
+01:04:12,320 --> 01:04:17,620
+A على مين على دلتا برضه B minus A عشان الحسبان N
+
+748
+01:04:17,620 --> 01:04:21,240
+أكبر من B minus A على مين على دلتا يعني الآن أنا
+
+749
+01:04:21,240 --> 01:04:26,920
+بحكي بحكي عن الأنات اللي بكون أكبر من B minus A
+
+750
+01:04:26,920 --> 01:04:31,460
+على مين على الدلتا اللي لجيتها فوق عندي في اللي هو
+
+751
+01:04:31,460 --> 01:04:37,080
+هذا واحد ماشي الحالة الآن بتبدأ أكوّن partitions من
+
+752
+01:04:37,080 --> 01:04:42,480
+مين؟ من الأمنات هذه الآن بتاخد بيئا اني partitions
+
+753
+01:04:42,480 --> 01:04:47,220
+اني partitions برضه أشماله with equal اللي هي إيش
+
+754
+01:04:47,220 --> 01:04:54,240
+sub intervals يعني X نوت و X واحد لعند X ان يعني
+
+755
+01:04:54,240 --> 01:04:58,540
+طول كل فترة منهم برضه طول .. بتاخد اللي هي كلهم
+
+756
+01:04:58,540 --> 01:05:03,590
+أشمالين من عند A لعند B يكون إن كل ال sub intervals
+
+757
+01:05:03,590 --> 01:05:08,530
+جت بعض يعني بمعنى آخر هيكون ال XK minus XK minus
+
+758
+01:05:08,530 --> 01:05:12,970
+واحد بيساوي B minus A على N طول كل فترة ايش بيساوي
+
+759
+01:05:12,970 --> 01:05:16,950
+B minus A على عدد الفترات اللي هي N فبكون B minus
+
+760
+01:05:16,950 --> 01:05:21,250
+A عالميا على N أنا حرّن إنهم ألاقي في النهاية
+
+761
+01:05:21,250 --> 01:05:25,630
+sequence of partitions BN limit الـ U B N و F ناقص
+
+762
+01:05:25,630 --> 01:05:29,290
+الـ L B N و F بساوي 0 بيكون F is integrable خلصنا
+
+763
+01:05:29,290 --> 01:05:32,950
+أنا قاعد اخترت اللي هي sequence of partitions بناء
+
+764
+01:05:32,950 --> 01:05:36,390
+على الـ Delta اللي لجيتها في ال uniformity و
+
+765
+01:05:36,390 --> 01:05:39,830
+الأنات اللي أكبر منها و حطيت ال partition اللي هو
+
+766
+01:05:39,830 --> 01:05:44,710
+بشكل اللي هو تكون ال subintervals كلها لها نفس
+
+767
+01:05:44,710 --> 01:05:46,230
+الطول طيب
+
+768
+01:05:48,470 --> 01:05:56,170
+الآن زي ما قلت قبل بشوية negation على الفترة xk و
+
+769
+01:05:56,170 --> 01:06:01,710
+minus 1 و xk هذا ال sub interval ال function is
+
+770
+01:06:01,710 --> 01:06:03,550
+continuous عليها لأنها continuous على كل ال
+
+771
+01:06:03,550 --> 01:06:06,970
+interval a و b مدام continuous عليها إذا it
+
+772
+01:06:06,970 --> 01:06:10,310
+attains its maximum and its minimum on this
+
+773
+01:06:10,310 --> 01:06:16,100
+interval أكيد؟ لقد حد كده قبل بشوية إذن بما أن الـ
+
+774
+01:06:16,100 --> 01:06:18,480
+F is continuously not closed bound in الـ interval
+
+775
+01:06:18,480 --> 01:06:26,800
+هذه إذن there exist سميها U K و V K element in X K
+
+776
+01:06:26,800 --> 01:06:33,720
+minus واحد و X K such that F of U K هي ال maximum
+
+777
+01:06:33,720 --> 01:06:41,190
+على كل هذه ال maximum معناته هي ال supremum of K أو
+
+778
+01:06:41,190 --> 01:06:47,110
+أيضًا عند الـ VK F of VK هي الـ Minimum على هذه
+
+779
+01:06:47,110 --> 01:06:52,310
+مضمون موجود قلناها هي طبعًا مدامة Minimum على كل
+
+780
+01:06:52,310 --> 01:06:56,150
+الفترة إذًا هي الـ Infimum اللي ببحث عنها اليمين
+
+781
+01:06:56,150 --> 01:07:00,850
+MK على هذه الفترة وها المفتاح أصلا في استخدام الـ
+
+782
+01:07:00,850 --> 01:07:06,120
+Continuity إن ضمن لوجود نقطة عندها ال maximum في
+
+783
+01:07:06,120 --> 01:07:10,540
+هذه المنطقة وضمن اللي وجود نقطة هنا ضمن اللي وجود
+
+784
+01:07:10,540 --> 01:07:13,680
+ال minimum عندها و ال minimum و ال maximum مدام
+
+785
+01:07:13,680 --> 01:07:18,100
+عند نقاط محددة في الفترة هي هتتلاقى و تنقل هي
+
+786
+01:07:18,100 --> 01:07:21,780
+عبارة عن ال supremum و ال infimum على ال sub
+
+787
+01:07:21,780 --> 01:07:29,160
+interval أي سؤال طيب الآن ضال علينا إيش نسوي إن
+
+788
+01:07:29,160 --> 01:07:35,610
+نحسب الحسابات اللي هو نبدأ في حساباتنا اللي هو نحسب
+
+789
+01:07:35,610 --> 01:07:44,230
+الـ U و نحسب مين يا جماعة أو نحسب اللي هو ال ال ال
+
+790
+01:07:44,230 --> 01:07:44,930
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+791
+01:07:44,930 --> 01:07:44,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+792
+01:07:44,950 --> 01:07:45,050
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+793
+01:07:45,050 --> 01:07:45,070
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+794
+01:07:45,070 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+795
+01:07:45,130 --> 01:07:53,950
+ال ال الت حسبولي
+
+796
+01:07:54,430 --> 01:07:59,790
+ناقص L, P, N و F طبعا أكيد هذا أكبر يساوي صفر حفظنا
+
+797
+01:07:59,790 --> 01:08:04,050
+عن غيره هذا أنه أكبر أو يساوي صفر معروف ضل بدي
+
+798
+01:08:04,050 --> 01:08:08,850
+أحسبهم مع بعض ال summation عبارة عن بساوي
+
+799
+01:08:08,850 --> 01:08:13,610
+summation اللي هو ال M K صارت من ال M K capital
+
+800
+01:08:13,610 --> 01:08:19,950
+اللي هي F of U K صح ولا لأ يا جماعة أه صح و ال U K
+
+801
+01:08:19,950 --> 01:08:26,220
+وين موجودة في هذه الآن في مين؟ في xk minus xk minus
+
+802
+01:08:26,220 --> 01:08:31,520
+واحد xk minus xk minus واحد كامل عند واحد اللي
+
+803
+01:08:31,520 --> 01:08:37,020
+عندها انهدمين هي الـ U الآن زيها مين ال L ناقص
+
+804
+01:08:37,020 --> 01:08:42,600
+summation الآن مين عند ال MK small ال F of VK ال
+
+805
+01:08:42,600 --> 01:08:48,920
+VK اللي لاجيناها برضه هان اللي هي F of VK مضروبة في
+
+806
+01:08:48,920 --> 01:08:54,380
+طول الفترة xk-xk-1 كامل عند واحد لعند مين يا جماعة
+
+807
+01:08:54,380 --> 01:09:00,000
+لعندنا خدولي الآن xk-xk-1 عامل مشترك وطبعا أنا
+
+808
+01:09:00,000 --> 01:09:03,220
+مفترضها اللي هو وماخدها إلا طول ال intervals أو
+
+809
+01:09:03,220 --> 01:09:07,080
+sub intervals متساوي يعني طول هذه وطول هذه هو
+
+810
+01:09:07,080 --> 01:09:10,600
+عبارة عن b-a على n زي النظرية السابقة ويساوي ال
+
+811
+01:09:10,600 --> 01:09:17,850
+summation لل F of uk ناقص F of vk الكل مضروب في مين
+
+812
+01:09:17,850 --> 01:09:26,030
+يا جماعة في B-A على N N أو K من عند واحد لعند إيش
+
+813
+01:09:26,030 --> 01:09:36,830
+لعند N أي سؤال طيب شوفوا الآن اسمحولي بس هنا أشتغل
+
+814
+01:09:36,830 --> 01:09:39,730
+شوية طيب
+
+815
+01:09:42,370 --> 01:09:47,490
+طولوا روحكم عندنا خلصنا يعني جربنا إذا صار عندي ال
+
+816
+01:09:47,490 --> 01:09:51,870
+U, P, N و F عشان تعرفوا أين رايح أنا هي ال U, P, N
+
+817
+01:09:51,870 --> 01:09:55,550
+و F ناقص ال P, N و F أكبر يساوي الصفر اللي جيته
+
+818
+01:09:55,550 --> 01:10:00,610
+أصغر يساوي المقدار اللي أمامي الآن خلوني أطلع حد
+
+819
+01:10:00,610 --> 01:10:06,400
+برا بعد اسمكم هي B- a على n لأنها عبارة عن ثابت في
+
+820
+01:10:06,400 --> 01:10:13,020
+ال summation f of u,k ناقص f of v,k كامنة عند واحد
+
+821
+01:10:13,020 --> 01:10:20,340
+لأنك لاحظوا ما يلي يا جماعة عند ال u,k و ال v,k
+
+822
+01:10:20,340 --> 01:10:27,480
+وين موجودة في ال x,k minus واحد و ال x,k اه مظبوط
+
+823
+01:10:27,480 --> 01:10:32,540
+يعني الآن اللي هي طول
+
+824
+01:10:34,610 --> 01:10:41,150
+طول الفترة طول الفترة xk على جهة دي بس يا شباب
+
+825
+01:10:41,150 --> 01:10:46,850
+ناقص xk minus واحد طول الفترة لإن هاد صارت هي xk
+
+826
+01:10:46,850 --> 01:10:53,480
+minus واحد وهي xk ماشي جوات هنا ال mean ال UKو الـ
+
+827
+01:10:53,480 --> 01:10:56,860
+VK في مكان الماد، التنتين المهم جوا التنتين يعني
+
+828
+01:10:56,860 --> 01:10:59,840
+المسافة بين اللي برا هدول، حتى لو كان التنتين
+
+829
+01:10:59,840 --> 01:11:04,120
+زيهن، بكون أصغر أو يساوي المسافة بين التنتين هدول
+
+830
+01:11:04,120 --> 01:11:11,560
+أصغر أو يساوي المسافة هذه، اللي هو UK ناقص VK،
+
+831
+01:11:11,560 --> 01:11:17,010
+مظبوط؟ آسف، العكس، أكبر شكرا سامحونا أكبر إيش أو
+
+832
+01:11:17,010 --> 01:11:21,310
+يساوي صارت المسافة بين الجهتين هدولة أكيد أصغر
+
+833
+01:11:21,310 --> 01:11:24,970
+أشهر من المسافة الكلية اللي هنا بينهم طيب المسافة
+
+834
+01:11:24,970 --> 01:11:28,890
+بين هذه وهذه احنا ماخدينها أصلا طول ال interval
+
+835
+01:11:28,890 --> 01:11:29,670
+إيش بتساوي
+
+836
+01:11:33,030 --> 01:11:39,710
+على N إذا المسافة هذه أصلا عبارة عن B-A عالمين على
+
+837
+01:11:39,710 --> 01:11:43,890
+N سامحوني أني بنكتبها هنا إذا صار عندي اللي هو ال
+
+838
+01:11:43,890 --> 01:11:50,230
+U K ناقص ال V K أصغر أو يساوي B-A عالمين على N إذا
+
+839
+01:11:50,230 --> 01:11:58,530
+يا شباب راحظولي هنا U K ناقص V K صارت أصغر أو
+
+840
+01:11:58,530 --> 01:12:06,440
+يساوي B-A عالمين على n واضحة طيب نشوف ايش معناه هذا
+
+841
+01:12:06,440 --> 01:12:08,700
+الكلام وإيش اللي بتقوله؟ ليش بتقولنا هذا الكلام؟
+
+842
+01:12:08,700 --> 01:12:13,620
+بقوله عشان الكلام مهم، هذا هو، شوفوا فهمتوه، أنا مختار
+
+843
+01:12:13,620 --> 01:12:19,260
+الـ n أكبر من مين؟ من b minus a على delta، يعني بمعنى
+
+844
+01:12:19,260 --> 01:12:24,280
+آخر إيش معنى هذا؟ يعني b minus a على n أصغر من مين؟
+
+845
+01:12:24,280 --> 01:12:29,640
+من delta، يعني هذا المقدار أصغر من إيش يا جماعة؟ من
+
+846
+01:12:29,640 --> 01:12:35,160
+delta، صارت الـ U k ناقص الـ V k أصغر من مين؟ من delta
+
+847
+01:12:35,160 --> 01:12:40,800
+واحنا بنقول أن المقاطع اللي بتحقق فيها الـ U ناقص V
+
+848
+01:12:40,800 --> 01:12:44,560
+أصغر من delta بكون عندي F of U ناقص F of V أصغر من
+
+849
+01:12:44,560 --> 01:12:50,240
+مين يا جماعة؟ من Epsilon على B minus A، إذا صارت
+
+850
+01:12:50,240 --> 01:12:55,100
+عندي المقاطعين هذولة الـ U k ناقص الـ V k اللي أصغر من
+
+851
+01:12:55,100 --> 01:13:04,770
+delta، إذا أكيد من واحد هيكون عندي F of U k ناقص F of 
+
+852
+01:13:04,770 --> 01:13:12,670
+V k إيش هيكون؟ هيكون عبارة عن أصغر من Epsilon على B
+
+853
+01:13:12,670 --> 01:13:20,410
+minus A، إذا الآن بيحملني أني أقول أن هذا المقدار
+
+854
+01:13:20,410 --> 01:13:24,400
+اللي عندي، اللي هو طبعا هذا الكبير وهذا الصغير طبعا
+
+855
+01:13:24,400 --> 01:13:27,800
+على absolute value نفسه بيحملني إن أقول هذا أصغر أو
+
+856
+01:13:27,800 --> 01:13:34,680
+يساوي B minus A على N مضروب في مين؟ في الـ summation
+
+857
+01:13:34,680 --> 01:13:42,480
+للـ Epsilon على B minus A، كامن عند واحد لعند مين؟
+
+858
+01:13:42,480 --> 01:13:50,100
+لعند N، واضح
+
+859
+01:13:52,720 --> 01:13:58,440
+إذا صار عندي الآن اللي هو اللي أثبته أنه U P N و F
+
+860
+01:13:58,440 --> 01:14:04,220
+ناقص L P N و F أصغر أو يساوي B minus A على N في
+
+861
+01:14:04,220 --> 01:14:10,300
+.. خلّيني أوقف وأقولها.. أه.. انتظر.. أعمل لي..
+
+862
+01:14:13,410 --> 01:14:18,250
+إذا اللي وصلنا له يا جماعة اللي هو أن الـ U P N و F
+
+863
+01:14:18,250 --> 01:14:21,650
+ناقص الـ L P N و F أكبر يساوي صفر وفي نفس الوقت أصغر
+
+864
+01:14:21,650 --> 01:14:24,430
+يساوي B Minus A على N في الـ summation للـ Epsilon على
+
+865
+01:14:24,430 --> 01:14:28,630
+B Minus A اللي هو كامن عند واحد لـ N، يعني هذه قاعدة
+
+866
+01:14:28,630 --> 01:14:34,050
+عمالها كل مرة بتعد Epsilon على B Minus A كم مرة؟
+
+867
+01:14:34,050 --> 01:14:37,670
+بتعد N من المرات، إذا حيصير عندي هذا عبارة عن B
+
+868
+01:14:37,670 --> 01:14:43,170
+Minus A على N واللي بنعد هنا N من القيمة اللي هذه
+
+869
+01:14:43,170 --> 01:14:47,630
+يعني N في Epsilon على B minus A، الآن B minus A مع
+
+870
+01:14:47,630 --> 01:14:51,970
+الـ B minus A والـ N مع الـ N، فبيصير أوصلنا احنا إلى
+
+871
+01:14:51,970 --> 01:14:55,950
+ما يلي، انتبهوا للنتيجة النهائية اللي بتوصّل لي
+
+872
+01:14:55,950 --> 01:15:04,310
+اللي هو المطلوب، النتيجة اللي وصلت لها إنه إذا U P N
+
+873
+01:15:04,310 --> 01:15:12,430
+و F ناقص L P N و F أكبر أو يساوي صفر وأصغر من مين؟
+
+874
+01:15:12,430 --> 01:15:19,190
+من Epsilon لكل Epsilon أكبر من صفر، إذا اللي جوا غصب
+
+875
+01:15:19,190 --> 01:15:24,310
+عنه، إذا لازم يكون اللي هو لو أخذت الـ limit هيظل
+
+876
+01:15:24,310 --> 01:15:30,220
+limit الـ U بن لأن هذا أصلا صحيح علميا للإنات
+
+877
+01:15:30,220 --> 01:15:34,200
+الكبيرة، فلما أخد الـ limit أزنه جوزه infinity بيضل
+
+878
+01:15:34,200 --> 01:15:38,280
+في الـ safe side، يعني بيضل في اللي بتحقق فيه هذا، إذا
+
+879
+01:15:38,280 --> 01:15:45,630
+الـ limit U, B, N و F ناقص L, B, N و F هيكون أكبر أو
+
+880
+01:15:45,630 --> 01:15:50,490
+يساوي صفر وأصغر أو يساوي Epsilon، وهذا الكلام as
+
+881
+01:15:50,490 --> 01:15:53,530
+n goes to infinity، وهذا الكلام صحيح برضه لمين؟
+
+882
+01:15:53,530 --> 01:15:58,790
+لكل Epsilon أكبر من صفر، إذا غصب عنها هيكون اللي جوا
+
+883
+01:15:58,790 --> 01:16:08,780
+limit U P N و F-L P N و F لازم يساوي إيش؟ صفر، as N نقص
+
+884
+01:16:08,780 --> 01:16:14,780
+infinity، وهذا by corollary اللي قبل بشوية، هيعني إن
+
+885
+01:16:14,780 --> 01:16:23,310
+F is integrable، Hence, F is integrable، وهكذا
+
+886
+01:16:23,310 --> 01:16:27,610
+أثبتنا العائلة الثانية من الدوال الـ continuous
+
+887
+01:16:27,610 --> 01:16:31,170
+function على closed bounded interval is a
+
+888
+01:16:31,170 --> 01:16:34,210
+continuous function is an integrable function
+
+889
+01:16:34,210 --> 01:16:40,790
+وهكذا خلصنا الـ section الأول والـ homework هي
+
+890
+01:16:40,790 --> 01:16:46,750
+اللي موجودة في التلخيص، والمرة القادمة إن شاء الله
+
+891
+01:16:47,630 --> 01:16:57,970
+إن شاء الله بكون احنا بنبدأ في اللي هي الـ section
+
+892
+01:16:57,970 --> 01:17:03,510
+اللي بعده اللي هو properties of the Riemann
+
+893
+01:17:03,510 --> 01:17:04,470
+Integral
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..615cab0444a228171429cbca4aa8e393f68d4efc
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_postprocess.srt
@@ -0,0 +1,3572 @@
+1
+00:00:04,720 --> 00:00:09,780
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 11 في
+
+2
+00:00:09,780 --> 00:00:16,040
+مساق تحليل حقيقي 2 لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:16,040 --> 00:00:24,760
+كلية العلوم وهي المحاضرة الأولى بعد إعلان الطوارئ
+
+4
+00:00:24,760 --> 00:00:32,580
+بخصوص أو بمواجهة فيروس كورونا المنتشر اتحدتنا
+
+5
+00:00:32,580 --> 00:00:37,960
+المرة الماضيةبدأنا في اللي هو chapter 7 اللي كان
+
+6
+00:00:37,960 --> 00:00:41,280
+الحديث عن ال riman integral أو تكامل ال riman
+
+7
+00:00:41,280 --> 00:00:45,860
+بدأنا في ال section الأول اللي هو تحت عنوان riman
+
+8
+00:00:45,860 --> 00:00:50,740
+integrability عرفنا شغلتين حاجة اسمها ال upper sum
+
+9
+00:00:50,740 --> 00:00:55,960
+و حاجة اسمها ال lower sum و قلنا اللي هو ال lower
+
+10
+00:00:55,960 --> 00:01:00,290
+sumهو عبارة عن الـ summation للـ mk الـ mk هذه
+
+11
+00:01:00,290 --> 00:01:06,410
+تمثل في xk minus xk minus 1 حيث mk كانت تمثل أو m
+
+12
+00:01:06,410 --> 00:01:10,910
+small k كانت تمثل عبارة عن الـ infimum للدالة على
+
+13
+00:01:10,910 --> 00:01:15,520
+الفترة اللي هي المذكورةالان ال .. ال .. ال other
+
+14
+00:01:15,520 --> 00:01:19,380
+sum هو عبارة عن ال summation لنفس ال sum العلوي
+
+15
+00:01:19,380 --> 00:01:24,520
+ولكن بدلا منها اللي هي M K capital اللي كانت تمثل
+
+16
+00:01:24,520 --> 00:01:28,280
+ال supremum ل ال F of X وال X على اللي هي في
+
+17
+00:01:28,280 --> 00:01:34,110
+الفترة المذكورة اللي عنديالآن أخدنا أول لمّة المرة
+
+18
+00:01:34,110 --> 00:01:38,190
+الماضية وقلنا إذا كانت F من I لR bounded و B any
+
+19
+00:01:38,190 --> 00:01:43,230
+partition of I بدي يكون ال lower اللي هو sum لأي
+
+20
+00:01:43,230 --> 00:01:47,810
+partition B و function F أصغر أو يساوي ال upper
+
+21
+00:01:47,810 --> 00:01:52,470
+sum لنفس ال partition و لنفس اللي هي ال function F
+
+22
+00:01:52,470 --> 00:01:58,710
+بعد هي طبعا خطينا خطوة أخرىو جينا عرفنا اللي هو شو
+
+23
+00:01:58,710 --> 00:02:03,110
+معناته انها تكون اللي هو ال partition Q refinement
+
+24
+00:02:03,110 --> 00:02:08,610
+لل partition B قلنا Q اللي هو تحسين ل B إذا كانت B
+
+25
+00:02:08,610 --> 00:02:13,940
+بي عبارة عن مجموعة جزئية من Qو بناء عليه اللي هو
+
+26
+00:02:13,940 --> 00:02:19,440
+قلنا ان اي اللي هو sub interval xk-1xk من ال
+
+27
+00:02:19,440 --> 00:02:23,520
+partition B يمكن كتابتها على صورة union of sub
+
+28
+00:02:23,520 --> 00:02:27,680
+intervals من اللي هو التحسين اللي هو EQ
+
+29
+00:02:31,060 --> 00:02:36,380
+الان جينا اللي هو بناء على هذا التعريف جينا قولنا
+
+30
+00:02:36,380 --> 00:02:40,480
+لو كانت F is من I لعند R is bounded و B is any
+
+31
+00:02:40,480 --> 00:02:45,780
+partition of I و Q refinement لل Bمدام اللي هو Q
+
+32
+00:02:45,780 --> 00:02:50,420
+-refinement إذا ال lower sum هيعلى و ال upper sum
+
+33
+00:02:50,420 --> 00:02:54,820
+هينزل على أساس انه اللي هو في النهاية يلتقي ال
+
+34
+00:02:54,820 --> 00:02:58,740
+upper مع ال lower و نصل لاللي هو ال integrability
+
+35
+00:02:58,740 --> 00:03:02,800
+أو معنى ال integrability كما سنرى لاحقا على الأقل
+
+36
+00:03:02,800 --> 00:03:06,560
+في اللي هو يكون واضح من خلال الرسم في اللي هي
+
+37
+00:03:06,560 --> 00:03:13,890
+الدوال الموجبة كما ذكرنا سابقااللي بحكيه إنه لو
+
+38
+00:03:13,890 --> 00:03:17,330
+كانت عندي اللي هو F من I ل R bounded وB partition
+
+39
+00:03:17,330 --> 00:03:22,750
+وQ وrefinement للـ B هيكون عندي lower sum لل
+
+40
+00:03:22,750 --> 00:03:28,570
+partition B أصغر أو يساوي lower sum للتحسين عماله
+
+41
+00:03:28,570 --> 00:03:32,850
+التحسين بكبر لما بده يصل لفعلا المساحة تحت المنحنة
+
+42
+00:03:32,850 --> 00:03:39,470
+في حالة الدوال الموجبةالقبر صم لـ Q و F سيبدأ يصغر
+
+43
+00:03:39,470 --> 00:03:42,850
+ويكون أصغر من الساوي اللي هو القبر صم لـ P و F
+
+44
+00:03:42,850 --> 00:03:47,310
+التحسين يعني سيصغره بمعنى آخر سيبدأ يلتقوا إلى
+
+45
+00:03:47,310 --> 00:03:51,770
+أسفل لما نصل إلى اللي هو مساواة في حالة الـ
+
+46
+00:03:51,770 --> 00:03:55,730
+Integrability لما نكون عندنا أخدنا الـ Supremum
+
+47
+00:03:55,730 --> 00:04:01,340
+لكل L و Fالـ L والـ infimum لكل الـ U بيصير بنسمي
+
+48
+00:04:01,340 --> 00:04:04,800
+بعد شوية حاجة اسمها ال lower integral وال upper
+
+49
+00:04:04,800 --> 00:04:08,980
+integral وبرهننا هذه النظرية و بعدين جينا لللمة و
+
+50
+00:04:08,980 --> 00:04:13,520
+بعدين جينا لللمة أخرىاللي هو لو كانت F من I ل R
+
+51
+00:04:13,520 --> 00:04:17,600
+bounded وB1 وB2 اي partitions الآن لأي partitions
+
+52
+00:04:17,600 --> 00:04:22,480
+هيكون الlower دايما بغض النظر عن ال partition اللي
+
+53
+00:04:22,480 --> 00:04:26,120
+هو هيكون أصغر أو يساوي الأبر بغض النظر عن ال
+
+54
+00:04:26,120 --> 00:04:28,660
+partition B2 يعني مش لنفس ال partition زي ما قلنا
+
+55
+00:04:28,660 --> 00:04:33,180
+في اللمبة 7 1 1 لأ لأي two partitions دايما
+
+56
+00:04:33,180 --> 00:04:37,170
+الlower ما هو هيكون تحتأسفل المنحنى والـ Upper
+
+57
+00:04:37,170 --> 00:04:41,350
+هيكون أعلى المنحنى بغض النظر عن ال partitions اللي
+
+58
+00:04:41,350 --> 00:04:45,690
+عندى طبعا التمثيل هذا في حال اللي هو ال F is a
+
+59
+00:04:45,690 --> 00:04:49,130
+positive function على ال interval المذكورة الآن
+
+60
+00:04:49,130 --> 00:04:52,730
+بعد هيكة اجينا وعرفنا شو معناه ال lower integral
+
+61
+00:04:52,730 --> 00:04:55,510
+وشو معناه ال upper integral قولنا ال lower
+
+62
+00:04:55,510 --> 00:05:00,050
+integral كما هو متوقع سميناه الف F هو عبارة عن ال
+
+63
+00:05:00,050 --> 00:05:05,660
+supremum لل lowersوال .. و ال .. و ال .. و ال
+
+64
+00:05:05,660 --> 00:05:10,440
+upper هو عبارة عن الـ infimum لل uppers حتى لو
+
+65
+00:05:10,440 --> 00:05:14,300
+التقت الالو أف مع الالو أف اللي هو من أعلى مع
+
+66
+00:05:14,300 --> 00:05:17,940
+الأسفل هيكونوا التقوا بالظبط عند .. من مساحة تحت
+
+67
+00:05:17,940 --> 00:05:20,960
+المنحنى في حالة الدالة الموجبة وهذه .. في هذه
+
+68
+00:05:20,960 --> 00:05:24,300
+الحالة بنسمي إذا كانت ال upper تساوي ال lower
+
+69
+00:05:24,300 --> 00:05:27,920
+بنسمي ال function على هذه الفترة is integral و هذا
+
+70
+00:05:27,920 --> 00:05:31,900
+الكلام كله تحدثنا فيه عشان هيك أنا مسرع شويةهو
+
+71
+00:05:31,900 --> 00:05:37,160
+حكينا إنه اللي هو دايما ال lower sum لل F أخدنا
+
+72
+00:05:37,160 --> 00:05:40,760
+نظرية قولنا ال lower integral أسف ال lower
+
+73
+00:05:40,760 --> 00:05:45,100
+integral دايما أصغر يساوي مين ال upper integral
+
+74
+00:05:45,100 --> 00:05:46,860
+إذن الآن النظرية
+
+75
+00:05:49,600 --> 00:05:52,760
+الإعلان المهم اللي هو لو كانت F من I لعند R
+
+76
+00:05:52,760 --> 00:05:56,000
+bounded function على closed bounded interval A وB
+
+77
+00:05:56,000 --> 00:05:59,720
+بدي يكون ال lower integral L of F أصغر أو ساوي ال
+
+78
+00:05:59,720 --> 00:06:04,930
+upper integral U of F بصورة عامةهذه هي الـ
+
+79
+00:06:04,930 --> 00:06:08,050
+definition اللي ذكرته قبل و شوية نقول عن الـ
+
+80
+00:06:08,050 --> 00:06:15,150
+function F على bounded sub interval A و B أو
+
+81
+00:06:15,150 --> 00:06:18,650
+closed bounded interval A و B و كانت الـ F عبارة
+
+82
+00:06:18,650 --> 00:06:22,080
+عن bounded functionبنعرف أن الـ F is remain
+
+83
+00:06:22,080 --> 00:06:26,840
+integrable on I إذا كانت ال lower of F بساوي ال
+
+84
+00:06:26,840 --> 00:06:30,080
+upper of F معناته صارت اللي هي ال F is remain
+
+85
+00:06:30,080 --> 00:06:34,460
+integrable if and only if ال lower sum يساوي ال
+
+86
+00:06:34,460 --> 00:06:39,240
+upper sum هذا كله ذكرناه المرة الماضية و أيضا
+
+87
+00:06:39,240 --> 00:06:42,520
+عرفنا .. قلنا في هذا الحلقة أن كل integration من A
+
+88
+00:06:42,520 --> 00:06:47,890
+ل B هو ال lower أو ال upper المتساويينوعرفنا ايضا
+
+89
+00:06:47,890 --> 00:06:50,610
+تعريف اخر قولنا ال integration من a ل b بساوي ناقص
+
+90
+00:06:50,610 --> 00:06:53,830
+ال integration من b ل a وعرفنا ال integration من a
+
+91
+00:06:53,830 --> 00:06:59,410
+ل a بساوي صفر هذا كله حكينا المرة الماضية ومش هيك
+
+92
+00:06:59,410 --> 00:07:03,820
+كمان واخدنا المثالاللي هو أثبتنا إنه اللي هو g of
+
+93
+00:07:03,820 --> 00:07:07,880
+x بيساوي x is integrable on i استنادًا على إنه
+
+94
+00:07:07,880 --> 00:07:11,020
+أوجدنا ال lower sum ال lower integral و ال upper
+
+95
+00:07:11,020 --> 00:07:13,300
+integral أثبتنا إن ال lower integral و ال upper
+
+96
+00:07:13,300 --> 00:07:16,300
+integral are equal و من ثم أثبتنا إنه ال
+
+97
+00:07:16,300 --> 00:07:19,940
+integration exist لل function x على الفترة 0 و 1
+
+98
+00:07:19,940 --> 00:07:26,810
+وأوجدنا قيمة ال integration في حينهوصلنا إلى اللي
+
+99
+00:07:26,810 --> 00:07:33,290
+هو مثالنا التالي أنه لو كانت F من I لعند .. F من I
+
+100
+00:07:33,290 --> 00:07:40,090
+اللي هي 01 لعند ال .. ال R be defined by أخدنا
+
+101
+00:07:40,090 --> 00:07:45,990
+الدالة كما يلي اللي هو قولنا أن F of X F of X
+
+102
+00:07:45,990 --> 00:07:53,040
+بساوي واحدإذا كانت x rational number element in Q
+
+103
+00:07:53,040 --> 00:08:00,100
+وبساوي 0 إذا كانت x element in IQ أو element in Q
+
+104
+00:08:00,100 --> 00:08:04,660
+complement اللي هي ال rational numbers الآن بدنا
+
+105
+00:08:04,660 --> 00:08:11,200
+نثبت بقول show that this function Fطبعا أنا method
+
+106
+00:08:11,200 --> 00:08:17,340
+F على اللي هي الـ Q تقاطع طبعا الـ 0 و 1 اللي هي
+
+107
+00:08:17,340 --> 00:08:19,920
+الـ interval اللي بدأ عليها التقاطع الـ 0 و 1
+
+108
+00:08:19,920 --> 00:08:25,160
+بمعنى إن دالت F صارت من I اللي هي عبارة عن 0 و 1
+
+109
+00:08:26,040 --> 00:08:29,380
+اللي عند R واضح ان الدالة هذه is a bounded
+
+110
+00:08:29,380 --> 00:08:33,560
+function الان بدأ أثبت لكم ان هذا الدالة is not
+
+111
+00:08:33,560 --> 00:08:38,120
+integrable on this interval is not integrable on
+
+112
+00:08:38,120 --> 00:08:44,100
+this interval الان علشان أصل اللي هو اللي هي ان
+
+113
+00:08:44,100 --> 00:08:48,180
+هذا الدالة غير قابلة تكامل بالنسبة لتكامل بالنسبة
+
+114
+00:08:48,180 --> 00:08:55,650
+لتكامل الريمان بدي اخد الان Bأخدوا أي partition X0
+
+115
+00:08:55,650 --> 00:09:02,550
+X1 لعند Xn هذا any partition لإيه ال interval اللي
+
+116
+00:09:02,550 --> 00:09:06,790
+هي الفترة مين Zero و واحد يعني بمعنى أتيت للفترة
+
+117
+00:09:06,790 --> 00:09:14,030
+Zero و واحد و جزقتها X0 X1 لعند مؤصل لعند مين لعند
+
+118
+00:09:14,030 --> 00:09:18,610
+Xn اللي هي إيش بتساوي بتساوي واحدالان هذا ال
+
+119
+00:09:18,610 --> 00:09:22,130
+partition اخدته arbitrarily اللى هو partition
+
+120
+00:09:22,130 --> 00:09:31,790
+لفترة L عندى الان بدى احسب ال Lof B و F لهذا ال
+
+121
+00:09:31,790 --> 00:09:34,990
+partition أيش بتساوي حسب اللي عرفناها سابقا بتساوي
+
+122
+00:09:34,990 --> 00:09:40,610
+ال summation لل M K في X K minus X K minus واحد K
+
+123
+00:09:40,610 --> 00:09:46,330
+من عند واحد لعند مين لعند اللي هي N ويساوي الآن ال
+
+124
+00:09:46,330 --> 00:09:52,450
+M K عرفناها ال M K هي عبارة عن ال infimum لقيمة ال
+
+125
+00:09:52,450 --> 00:09:56,470
+function F of X حيث X تنتمي إلى الفترة X K minus
+
+126
+00:09:56,470 --> 00:10:02,210
+واحد لعند X Kطبعاً اللي هي F of X معرفة على
+
+127
+00:10:02,210 --> 00:10:05,130
+أساسيها يا إما واحد يا إما سفر حسب إنها تكون
+
+128
+00:10:05,130 --> 00:10:08,030
+rational أو إيش ال rational يعني ال function F
+
+129
+00:10:08,030 --> 00:10:11,910
+أصلا اللي هي قيمتين بس إذا الأن ال infimum لل F of
+
+130
+00:10:11,910 --> 00:10:16,630
+X عندها يا هيكون واحد يا هيكون سفر ليش؟ لأن أصلا
+
+131
+00:10:16,630 --> 00:10:23,340
+الفترة هذهفيها أي فترة subinterval xk-1xk فيها
+
+132
+00:10:23,340 --> 00:10:27,620
+rational وirrational إذا قيمة ال up of x في الفترة
+
+133
+00:10:27,620 --> 00:10:31,260
+هتلاقي عند قيم واحد هتلاقي أكيد عند قيم أش بتساوي
+
+134
+00:10:31,260 --> 00:10:35,000
+بساوي سفر إذا ال infimum في هذه الحالة هو عبارة عن
+
+135
+00:10:35,000 --> 00:10:42,320
+إيش يساوي سفر إذا ال summation ل 0 في xk-xk-1 كامل
+
+136
+00:10:42,320 --> 00:10:46,120
+عند واحد عند أنه طبيعي هذا بديهي إيش هيساوي بساوي
+
+137
+00:10:46,120 --> 00:10:52,410
+سفرأذن الان L of F بي و F ساوة سفر فور أي بورتيشن
+
+138
+00:10:52,410 --> 00:10:59,370
+بيه إذا ال L of F اللي هي عبارة عن الأو الـ
+
+139
+00:10:59,370 --> 00:11:06,070
+Supremum الـ Supremum لكل الـ L of B و F Such that
+
+140
+00:11:06,070 --> 00:11:09,890
+B element in the set of all partitions اللي هو B
+
+141
+00:11:09,890 --> 00:11:14,090
+of I هيكون ال .. ال Supremum اللي هين صفر لإن كل
+
+142
+00:11:14,090 --> 00:11:18,350
+اللي هين أصلا إشق بتنطلع .. تنطلع بساوي صفر إذا
+
+143
+00:11:18,350 --> 00:11:23,070
+هذا إيش هيساوي يا شباب؟ هو يساوي Zeroإذا طلع عندى
+
+144
+00:11:23,070 --> 00:11:28,150
+ال lower sum بساوة 0 الان بدي أحسبلكم مين أحسبلكم
+
+145
+00:11:28,150 --> 00:11:31,390
+ال upper sum سامحوني أكتب هنا بس عساس اللي يبقى
+
+146
+00:11:31,390 --> 00:11:39,670
+كله مكتوب عندى نوجد ال upper sum ال upper sum اللي
+
+147
+00:11:39,670 --> 00:11:45,510
+هي ال UPUF بساوة summation للان K capital في XK
+
+148
+00:11:45,510 --> 00:11:51,740
+minus XK minus واحد K من عند واحد لعند الانالان
+
+149
+00:11:51,740 --> 00:11:55,900
+هذا بيساوي ال Mk زي ما قلنا قبل هيك ال Mk بدل ما
+
+150
+00:11:55,900 --> 00:11:59,400
+هي ال M في مميزة استعريفها ال Mk بتساوي ال
+
+151
+00:11:59,400 --> 00:12:03,780
+supremum لهذه ال 6 وزي ما قلنا ال 6 هذه في داخلها
+
+152
+00:12:03,780 --> 00:12:08,400
+يا واحد يا زيرو نظرا لإن اللي هو أي sub interval
+
+153
+00:12:08,400 --> 00:12:11,820
+هيكون فيها rational و irrational وتبعا إلها هيكون
+
+154
+00:12:11,820 --> 00:12:16,060
+قيمة ال function في داخلها واحد أو سفر واحنا بنبحث
+
+155
+00:12:16,060 --> 00:12:19,280
+عن ال supremum إذا هيكون ال supremum في كل الأحوال
+
+156
+00:12:19,280 --> 00:12:25,600
+ال Mk بتساوي واحدمضروبة في xk-xk-1 k من عند 1 لعند
+
+157
+00:12:25,600 --> 00:12:30,700
+n نفردها هذه ويساوي اللي هنبصير k من عند 1 يعني x1
+
+158
+00:12:30,700 --> 00:12:39,570
+-x0 زاد x2-x1 زاد إلى أخير لما أصل لعند xn-1نقص xn
+
+159
+00:12:39,570 --> 00:12:44,550
+نقص واحد طبعا واضح انه عندي ال x واحد هت cancel مع
+
+160
+00:12:44,550 --> 00:12:48,270
+ناقص x واحد و ال x اتنين مع ناقص x اتنين لما نصل
+
+161
+00:12:48,270 --> 00:12:52,450
+للاخر هيكون في عندي ات cancel الجميع بس ضال عندي
+
+162
+00:12:52,450 --> 00:12:58,170
+ال xn و ال x note و هد بتساوي xn ناقص x note و
+
+163
+00:12:58,170 --> 00:13:01,750
+يساوي ال xn طبعا ايش هي عبارة عن واحد و ال x note
+
+164
+00:13:01,750 --> 00:13:07,190
+ايش هي شبه سفر و يساوي واحد ناقص سفر و يساوي واحد
+
+165
+00:13:07,570 --> 00:13:12,930
+إذا طلع عندي الـ Upper Sum لأي Bar تشهم بيه، هيتلع
+
+166
+00:13:12,930 --> 00:13:18,510
+ايش بساوة؟ بساوة واحدة إذا الان لما بدي أخد ال U
+
+167
+00:13:18,510 --> 00:13:23,510
+of F اللي هو Upper Integral هيساوة عبارة عن ال
+
+168
+00:13:23,510 --> 00:13:30,220
+Infimumلمين؟ للـ U, B وF such that B element in
+
+169
+00:13:30,220 --> 00:13:34,580
+the set of all partitions B of I والـ U, B وF
+
+170
+00:13:34,580 --> 00:13:38,840
+قيمته ثابتة for أي partition بيساوي واحد إذا الـ
+
+171
+00:13:38,840 --> 00:13:43,300
+infimum لكل اللي هنا عبارة عن برضه إيش بيساوي واحد
+
+172
+00:13:43,300 --> 00:13:47,410
+صار عندي الآنlower integral و ال upper integral
+
+173
+00:13:47,410 --> 00:13:51,110
+have different values واحد بيساوي صفر واحد بيساوي
+
+174
+00:13:51,110 --> 00:13:56,890
+واحد وبناء عليه بتكون عنده اللي هو ال F is not
+
+175
+00:13:56,890 --> 00:14:03,150
+Riemann integrable اي سؤال؟ طيب ماشي الحاجة
+
+176
+00:14:03,150 --> 00:14:10,930
+الانصار عندى اخدنا مثلين المثال الأولاللي هو
+
+177
+00:14:10,930 --> 00:14:16,770
+أثبتنا إن off of x بيساوي x is integrable على
+
+178
+00:14:16,770 --> 00:14:22,010
+الفترة 0 و1 و أثبتناها بواسطة التعريف وأيضا أثبتنا
+
+179
+00:14:22,010 --> 00:14:26,190
+مثال آخر لbounded function أيضا وكانت is not
+
+180
+00:14:26,190 --> 00:14:31,250
+remain integrable اللي هي off of x بيساوي 1 إذا
+
+181
+00:14:31,250 --> 00:14:36,090
+كانت x rational ويساوي 0 إذا كانت x irrational هذا
+
+182
+00:14:36,090 --> 00:14:43,040
+اللي هو المثال الثانيالان نيجي لاللي هو criterion
+
+183
+00:14:43,040 --> 00:14:49,280
+مهمة اللي احنا بنسميها اللي هي عبارة عن remain
+
+184
+00:14:49,280 --> 00:14:54,800
+criterion for
+
+185
+00:14:54,800 --> 00:15:01,490
+integrabilityأحنا طبعا اتحدثنا عن الـ Remain
+
+186
+00:15:01,490 --> 00:15:05,330
+Integrability كيف نثبت أنه Remain Integrable عن
+
+187
+00:15:05,330 --> 00:15:09,470
+طريق التعريف طبعا الآن مش دايما بدنا نثبت عن طريق
+
+188
+00:15:09,470 --> 00:15:14,350
+التعريف إذا بدنا اللي هو طرق أخرى نحاول اللي هو
+
+189
+00:15:14,350 --> 00:15:21,780
+نوسع اللي هيإمكانياتنا في الحكم على الدالة إنها
+
+190
+00:15:21,780 --> 00:15:26,860
+integrable أو مش integrable وهذه الإمكانية الأخرى
+
+191
+00:15:26,860 --> 00:15:31,400
+غير التعريف هي اللي بنسميها اللي هو الريمان
+
+192
+00:15:31,400 --> 00:15:36,500
+integrability criterion أو criterion for
+
+193
+00:15:36,500 --> 00:15:41,340
+integrability نشوف أيش بيقول النظرية
+
+194
+00:15:43,700 --> 00:15:48,060
+لت I بساوة A وB و لت F من I لـ R بيـ bounded نفترض
+
+195
+00:15:48,060 --> 00:15:51,360
+أن F عبارة عن إيه اشمال يا جماعة؟ bounded function
+
+196
+00:15:51,360 --> 00:15:57,500
+then F is integrable on I if and only if for each
+
+197
+00:15:57,500 --> 00:16:00,340
+epsilon أكبر من 0 there exists a partition B
+
+198
+00:16:00,340 --> 00:16:04,660
+epsilon of I such that U B epsilon نقص الـ B
+
+199
+00:16:04,660 --> 00:16:10,730
+epsilon إيه إشماله أصغر من اللي هو إبسلونإذن اللي
+
+200
+00:16:10,730 --> 00:16:16,410
+هو واضح إنه عندي فصار فيه test لل integrability أو
+
+201
+00:16:16,410 --> 00:16:20,150
+اللي هو طريقة للحكم على ال integrability أخرى غير
+
+202
+00:16:20,150 --> 00:16:26,430
+التعريف اللي هو بتقول F is integrable
+
+203
+00:16:28,870 --> 00:16:32,890
+if and only if طبعاً هذه لمين الـ F؟ F عبارة عن زي
+
+204
+00:16:32,890 --> 00:16:36,190
+ما انتوا عارفين bounded function لإنه كل شغلنا
+
+205
+00:16:36,190 --> 00:16:40,010
+أصلا على اللي هو remaining integrability أنه نفترض
+
+206
+00:16:40,010 --> 00:16:43,210
+أنه الـ F bounded عشان اللي هو تكون ال supremum و
+
+207
+00:16:43,210 --> 00:16:46,330
+ال infimum اللي مبني عليها التعريف تكون مضمون إنها
+
+208
+00:16:46,330 --> 00:16:49,870
+موجودة عشان هيك بنحكي أن F is bounded function طيب
+
+209
+00:16:49,870 --> 00:16:56,140
+إذا الـ F is integrable if and only ifاللي هي لكل
+
+210
+00:16:56,140 --> 00:17:00,620
+إبسلون أكبر من 0 there exists a partition P إبسلون
+
+211
+00:17:00,620 --> 00:17:04,240
+هذا ال P اللي هو ال partition يعتمد عالميا على
+
+212
+00:17:04,240 --> 00:17:07,820
+إبسلون لكل إبسلون بالله دي partition P إبسلون لمين
+
+213
+00:17:07,820 --> 00:17:11,840
+ال partition طبعا لل interval اللي عندنا اللي هي R
+
+214
+00:17:11,840 --> 00:17:17,040
+there exists P إبسلون a partition of I such that
+
+215
+00:17:17,040 --> 00:17:25,210
+ال P ال U ال P إبسلونوالـ F ناقص الـ L بي إبسلون و
+
+216
+00:17:25,210 --> 00:17:31,050
+F يكون أصغر من مين من إبسلون الآن إذا كان لجينا
+
+217
+00:17:31,050 --> 00:17:34,190
+لكل إبسلون لجينا بي إبسلون بحيث هذا يتحقق معناته F
+
+218
+00:17:34,190 --> 00:17:37,590
+is integrable and conversely if F is integrable
+
+219
+00:17:37,590 --> 00:17:42,550
+أكيد لكل إبسلون هلجي بي إبسلون بحيث أن هذا يتحقق
+
+220
+00:17:42,550 --> 00:17:48,170
+خلونا نيجي الآن نبرهم و نشوف كيف بدنا نبرهم
+
+221
+00:17:48,170 --> 00:17:53,880
+نظريتناالان بدنا نفترض ان F اي شمالها is
+
+222
+00:17:53,880 --> 00:18:00,240
+integrable ونصل منها للي عيدي اللي هي ال partition
+
+223
+00:18:00,240 --> 00:18:07,040
+اللي مذكور مدام F is integrable اذا كانت ..الان
+
+224
+00:18:07,040 --> 00:18:16,100
+بنقول suppose that F is integrable مدام integrable
+
+225
+00:18:16,100 --> 00:18:22,090
+يا شبابأكيد عنده اللي هو الـ U of F بساوي L of
+
+226
+00:18:22,090 --> 00:18:29,490
+إيش؟ Of F، مظبوط؟ أكيد الـ L of .. الـ U of F
+
+227
+00:18:29,490 --> 00:18:33,410
+بساوي الـ L of F إيش اللي بيدثبته؟ بيدثبته لأي
+
+228
+00:18:33,410 --> 00:18:35,810
+إبسلون أكبر من سفر بدلاجي بإبسلون، شوفوا كيف
+
+229
+00:18:35,810 --> 00:18:41,090
+بنلاجيه، الآن نفترض إن إبسلون let إبسلون أكبر من
+
+230
+00:18:41,090 --> 00:18:47,810
+سفر be given، ماشي الحالةعندي الـ U of F هو إيش يا
+
+231
+00:18:47,810 --> 00:18:54,910
+شباب؟ هو عبارة عن الـ infimum للـ L of B و F such
+
+232
+00:18:54,910 --> 00:19:01,170
+that B element in B of I، مظبوط؟ إذا الـ U of F
+
+233
+00:19:01,170 --> 00:19:05,830
+عبارة عن infimum يعني هو عبارة عن greatest lower
+
+234
+00:19:05,830 --> 00:19:11,630
+boundلو هذا الـ greatest lower bound ضفنا إليه أي
+
+235
+00:19:11,630 --> 00:19:17,230
+كمية هيبط اللاور باوند لأن هو أصلا إيش اسمه
+
+236
+00:19:17,230 --> 00:19:23,510
+greatest lower bound إذا لو الـU of F ضفتله Y على
+
+237
+00:19:23,510 --> 00:19:28,610
+2 مثلا طبعا هذا المقدار هيبط اللاور باوند إيش
+
+238
+00:19:28,610 --> 00:19:33,690
+معناته بط اللاور باوند؟ يعني بمعنى آخر هيكون في
+
+239
+00:19:33,690 --> 00:19:44,080
+عند إشي أصغر منههيكون عندى أصغر من ال U of F أو بي
+
+240
+00:19:44,080 --> 00:19:49,740
+واحد مثلا و F for some mean بي واحد إذا لما نشيل
+
+241
+00:19:49,740 --> 00:19:54,600
+من ال infimum إبسلون
+
+242
+00:19:54,600 --> 00:19:57,740
+على اتنين هيبطل هذا lower bound يعني بمعنى أخر
+
+243
+00:19:57,740 --> 00:20:03,280
+هلاقي اللي هو lower bound
+
+244
+00:20:07,660 --> 00:20:12,140
+عند الـ Y أكبر من 0 خلّيني أبدأ لت Y أكبر من 0 بي
+
+245
+00:20:12,140 --> 00:20:17,940
+given إذا عندي الآن بدي أثبت لك بدي أجيب لك
+
+246
+00:20:17,940 --> 00:20:21,440
+partition بيبسلون بحيث أنه هذا ناقص هذا يكون أصغر
+
+247
+00:20:21,440 --> 00:20:26,070
+من مين من ابسلون شوف كيف بدي أعملالان انا عندي ال
+
+248
+00:20:26,070 --> 00:20:30,710
+U of F ايش بيساوي يا جماعة ال U of F بيساوي ال
+
+249
+00:20:30,710 --> 00:20:39,590
+infimum لل L بيقف ب element I طيب ال U of F اسف يا
+
+250
+00:20:39,590 --> 00:20:43,010
+جماعة ال U of F بيساوي ال infimum لمين لل U بيقف
+
+251
+00:20:43,720 --> 00:20:49,780
+ماشي الحال الان ايش معناه انه هذا infimum معناته
+
+252
+00:20:49,780 --> 00:20:55,100
+هذا هو عبارة عن ال greatest lower bound مدام ال
+
+253
+00:20:55,100 --> 00:20:59,450
+greatest lower bound اذا ال lower bound هذاأو الـ
+
+254
+00:20:59,450 --> 00:21:03,330
+Greatest Lower Bound لو ضفتله أي رقم يابسون على
+
+255
+00:21:03,330 --> 00:21:06,370
+اتنين مثلا بالذنب يابسون على اتنين الـ game
+
+256
+00:21:06,370 --> 00:21:09,670
+بتعرفوا ليش يابسون على اتنين يعني لو ضفتله أي رقم
+
+257
+00:21:09,670 --> 00:21:14,730
+بيبطل Lower Bound إيش معناته بيبطل Lower Bound
+
+258
+00:21:14,730 --> 00:21:21,830
+يعني هيصير هذا أكبر من ال UB 1 of F for some B
+
+259
+00:21:21,830 --> 00:21:27,510
+وحدهالأنه بطل أش ماله هذا بطل lower bound بطل يكون
+
+260
+00:21:27,510 --> 00:21:32,670
+أصغر من الكل من هان يعني هلاجي واحد من هان هو مش
+
+261
+00:21:32,670 --> 00:21:36,830
+أصغر منه أو بمعنى أخر U, P, 1 و F أصغر من اللي هو
+
+262
+00:21:36,830 --> 00:21:44,850
+هذا المقدر طيب similarly ال L of F هي عبارة عن ال
+
+263
+00:21:44,850 --> 00:21:52,050
+supremum لل L, P و F such that P elemented P of I
+
+264
+00:21:53,040 --> 00:21:57,780
+بنفس الطريقة يا جماعة ال L of F هي عبارة عن إيش ال
+
+265
+00:21:57,780 --> 00:22:04,040
+least upper bound يعني هذا لو least upper bound
+
+266
+00:22:04,040 --> 00:22:07,200
+Upper bound لو كان أصغر و أحد لو هذا least upper
+
+267
+00:22:07,200 --> 00:22:11,000
+bound راحت منه عدد ولو صغير جدا و ليكن يبسلون على
+
+268
+00:22:11,000 --> 00:22:16,800
+اتنينهيبطل هذا عبارة عن upper bound يعني هلاقي
+
+269
+00:22:16,800 --> 00:22:24,280
+واحد من اللي هان اللي هو L of B2 وF مثلا أكبر منه
+
+270
+00:22:24,280 --> 00:22:30,560
+لأنه هيبطل هذا أشماله upper bound لأنه هو ال least
+
+271
+00:22:30,560 --> 00:22:35,780
+لما طلعت منه بطل من ال upper bounds يعني لجيت واحد
+
+272
+00:22:35,780 --> 00:22:43,120
+من هذول أكبر منه إذا صار في عندي اللي هولجيت بي
+
+273
+00:22:43,120 --> 00:22:53,960
+واحد بحقق الأولى و بيتنين بحقق التانية لأن خد الآن
+
+274
+00:22:53,960 --> 00:22:58,840
+خدلي بي إبسلون هذا اللي بديها هذا الحقق اللي اللي
+
+275
+00:22:58,840 --> 00:23:03,600
+بديها خد بي إبسلون إيش بساوي ال بي واحد اللي لجيته
+
+276
+00:23:03,600 --> 00:23:12,050
+هنااتحاد الـ B2 اللي لجيته هان اتحاد مين؟ B2 صار
+
+277
+00:23:12,050 --> 00:23:18,510
+عندى .. صار عندى الآن مع بعض خليني أمسح فأقوم،
+
+278
+00:23:18,510 --> 00:23:22,170
+مهمش؟
+
+279
+00:23:22,170 --> 00:23:31,670
+صار
+
+280
+00:23:31,670 --> 00:23:41,110
+عندى ما يليه؟ صار عندى الآنL of F نقص
+
+281
+00:23:41,110 --> 00:23:53,490
+Y على 2 أصغر من L of B2 Fاللي هو أكيد أصغر أو
+
+282
+00:23:53,490 --> 00:23:59,750
+يساوي L of By قُقَف، ليش؟ لأن الـBy يا جماعة عبارة
+
+283
+00:23:59,750 --> 00:24:04,570
+عن refinement للـB2 والlower لما يصير فيه تحسين
+
+284
+00:24:04,570 --> 00:24:08,510
+بكبر، بروح نحو اتجاه نيل اللي هو المنحنة التالية
+
+285
+00:24:08,510 --> 00:24:14,010
+مساحة تحت المنحنة الكلية لأن أيضا لو جيت قولة الـU
+
+286
+00:24:14,010 --> 00:24:24,400
+of Fزاد إبسلون على اتنين هتلاقيها أكبر من ال U بي
+
+287
+00:24:24,400 --> 00:24:30,410
+واحد و Fوأكيد عندي الـ U of F زائد إبسلون عدنان
+
+288
+00:24:30,410 --> 00:24:34,490
+أكبر من الـ U B1 of F هيكون هذا أكبر أو يساوي الـ
+
+289
+00:24:34,490 --> 00:24:39,610
+U B epsilon of F لأن الـ B epsilon refinement لمين
+
+290
+00:24:39,610 --> 00:24:44,790
+برضه؟ للـ B1 بزام refinement إذن اللي هو التحسين
+
+291
+00:24:44,790 --> 00:24:50,270
+بيزغر القبر وبروح ناحية اللي هو المنحنة إذن الآن
+
+292
+00:24:50,270 --> 00:24:55,480
+من الـ tip 2 هذولةواجدنا طبعا احنا تنسوش ان احنا
+
+293
+00:24:55,480 --> 00:24:59,100
+مفترضين من رأس الدول ان U of F is integrable يعني
+
+294
+00:24:59,100 --> 00:25:05,340
+مفترضين ان ال L of F ايش بتساوي U of F تنسواش هذه
+
+295
+00:25:05,340 --> 00:25:12,540
+ليه جيت تنتر مع بعض دول بصير عندى الحصل على L of F
+
+296
+00:25:12,540 --> 00:25:22,970
+ناقص Y على 2 اللي هو اصغر من Lof B, Epsilon و F
+
+297
+00:25:22,970 --> 00:25:30,110
+والـ L و الـ U of F زائد Epsilon على 2 أكبر من U,
+
+298
+00:25:30,190 --> 00:25:35,290
+B, Epsilon و F أنا إيش غرضي؟ غرضي أثبت إن U, B,
+
+299
+00:25:35,350 --> 00:25:39,130
+Epsilon و F ناقص L, B, Epsilon و F أصغر من Epsilon
+
+300
+00:25:39,130 --> 00:25:42,890
+يلّا اترحل من بعض، إذا بصير عندي، بتحصل البدكية
+
+301
+00:25:42,890 --> 00:25:48,570
+بصير عندي الآن، بطرح حياة دي، بقول U, B, Epsilon و
+
+302
+00:25:48,570 --> 00:25:53,240
+Fناقص لأنه لما نضرب هذا في ناقص هتنعكس يعني هتصير
+
+303
+00:25:53,240 --> 00:25:57,100
+هذه جماعة ناقص وهذه زائد وهذه هتنعكس هيك وهيصير
+
+304
+00:25:57,100 --> 00:26:05,600
+الاش ناقص بيصير عندي U بي و F ناقص ال بي و F هيصير
+
+305
+00:26:05,600 --> 00:26:11,820
+أصغر من مين من ناقص L of F ناخد هذا قبل زي ما احنا
+
+306
+00:26:11,820 --> 00:26:20,690
+مرتبينها U of F زائد ي على 2 ناقصL of F زي إبسلون
+
+307
+00:26:20,690 --> 00:26:24,790
+على 2 وطبعا إحنا جايلين إن F is integrable يعني
+
+308
+00:26:24,790 --> 00:26:28,770
+الـ U of F بسوء L of F إذا هذي بتروح مع هذي بظل
+
+309
+00:26:28,770 --> 00:26:33,610
+إيه شماله؟ بظل إبسلون إذا إحنا لكل إبسلون أكبر من
+
+310
+00:26:33,610 --> 00:26:36,950
+سفر لجينا بي إبسلون هي في الواقع بي إبسلون اللي
+
+311
+00:26:36,950 --> 00:26:39,970
+لجيناها بي واحد اتحاد بي اتنين حيث بي واحد اللي
+
+312
+00:26:39,970 --> 00:26:44,120
+لجيناه هان وال بي اتنين اللي لجيناه هانsuch that U
+
+313
+00:26:44,120 --> 00:26:49,120
+P Y of F نقص L P Y of F أصغر من اللي هو Epsilon
+
+314
+00:26:49,120 --> 00:26:57,480
+وهو المطلوب أي سؤال؟ طيب، ماشي يا شباب، الآن خلصنا
+
+315
+00:26:57,480 --> 00:27:04,420
+الجزء الأول من النظريةأثبتنا اللي بدنا يا انه اللي
+
+316
+00:27:04,420 --> 00:27:08,860
+هو هذه العلاقة صحيحة لأننا نفترض انه suppose that
+
+317
+00:27:08,860 --> 00:27:12,380
+star holds اللي هي star ليه هذه نفترض ان لكل
+
+318
+00:27:12,380 --> 00:27:15,380
+epsilon أكبر من 0 there exists B of epsilon such
+
+319
+00:27:15,380 --> 00:27:18,680
+that U B Epsilon و F نقصها دي أصغر من Epsilon و
+
+320
+00:27:18,680 --> 00:27:24,280
+بدنا نصل من خلالها لإيش لأن ال F is integrable
+
+321
+00:27:24,280 --> 00:27:25,760
+فنشوف
+
+322
+00:27:40,480 --> 00:27:47,440
+البرهام بسيط لو طلعنا عليه مباشرة على اللوح الآن
+
+323
+00:27:47,440 --> 00:27:52,140
+بدنا نفترض أن هذه تتحقق اللي هو نفترض أنه لكل ي
+
+324
+00:27:52,140 --> 00:27:57,020
+أكبر من 0 يوجد بي إبسلون بحيث أن هذا اللي هي تتحقق
+
+325
+00:27:57,020 --> 00:28:01,620
+علشان أصل بدي أصلكم في النهاية أن L of F هي إيش
+
+326
+00:28:01,620 --> 00:28:05,810
+بتساوي U of F شوف كيف ده صلهااللي هبدأ أقوللك اللي
+
+327
+00:28:05,810 --> 00:28:08,650
+هو نفترض انه زي ما قلنا انه star holds اللي حكينا
+
+328
+00:28:08,650 --> 00:28:12,990
+عنها لأن for any partition B هيكون ال L B of F
+
+329
+00:28:12,990 --> 00:28:17,970
+أصغر أساوي L of F و ال U of F أصغر أساوي مين ال U
+
+330
+00:28:17,970 --> 00:28:25,970
+B of F واضح؟ إذا أصار عيدي الآن L يمكن أوضحلكم على
+
+331
+00:28:25,970 --> 00:28:35,790
+اللوح L of B of F ده ال B أي partition أصغرمظبوط
+
+332
+00:28:35,790 --> 00:28:40,910
+أو يساوي ال L of A H of F لانه ال L of F يا جماعة
+
+333
+00:28:40,910 --> 00:28:47,330
+هو ال supremum اللي هنا و ال U بيقف
+
+334
+00:28:47,330 --> 00:28:53,130
+أكبر أو يساوي ال U of F لانه ال U of F H يا جماعة
+
+335
+00:28:53,130 --> 00:28:57,950
+هو عبارة عن مين عبارة عن ال infimumأترحولي الجهة
+
+336
+00:28:57,950 --> 00:29:01,410
+تانية هذا طبعا لكل مين لكل ال partitions اللي في
+
+337
+00:29:01,410 --> 00:29:06,750
+الدنيا من ضمنهم ال P Epsilon اللي احنا ماعطينايا
+
+338
+00:29:06,750 --> 00:29:12,250
+في ال .. اللي هو نص النظرية اذا بسيري عندى لأن لو
+
+339
+00:29:12,250 --> 00:29:19,990
+اجيب طرحة ال U F ناقص L F ال U F ناقص L Fهيصير ايش
+
+340
+00:29:19,990 --> 00:29:23,850
+ماله يا جماعة؟ يعني طريقة رحلة من هذه بيصير أصغر
+
+341
+00:29:23,850 --> 00:29:28,510
+أو يساوي لإن هذه بتضربها في ناقص و هذه ناقص و
+
+342
+00:29:28,510 --> 00:29:32,750
+بتنقلب زي ما عملنا قبل و شوية بيصير أصغر أو يساوي
+
+343
+00:29:32,750 --> 00:29:43,640
+U P of Fنقص ال B of F هذا الكلام صحيح لإيش لكل
+
+344
+00:29:43,640 --> 00:29:48,200
+partition في الدنيا من ضمنها المين ال partition
+
+345
+00:29:48,200 --> 00:29:52,580
+المواطع لنا يعني حيصير عند هذا ينطبق برضه على ال
+
+346
+00:29:52,580 --> 00:29:57,500
+بي إبسلون إذا صار هذا أصغر يسوي بي إبسلون نقص ال
+
+347
+00:29:57,500 --> 00:30:01,740
+بي إبسلون of F طيب هم يعطيين إن هذا المقدار إيش
+
+348
+00:30:01,740 --> 00:30:06,260
+ماله أصغر من إبسلون لأي إبسلون في الدنياهو أنا
+
+349
+00:30:06,260 --> 00:30:10,580
+بعرف أن هذا المقدار نفسه أكبر أو يساوي إيش سفر صار
+
+350
+00:30:10,580 --> 00:30:17,720
+عندى الآن ال U of F ناقص ال L of F دايما أصغر من
+
+351
+00:30:17,720 --> 00:30:23,420
+إبسلون و أكبر أو يساوي سفر لكل إبسلون أكبر من سفر
+
+352
+00:30:23,420 --> 00:30:28,260
+إذا على طول من نظرية في تحليل واحد هيكون هذا اللى
+
+353
+00:30:28,260 --> 00:30:36,250
+عندى إذا U of Fنقص L of F بيساوي سفر إذا U of F
+
+354
+00:30:36,250 --> 00:30:44,850
+بيساوي L of F وهذا يعني F is a Riemann Integral هو
+
+355
+00:30:44,850 --> 00:30:52,110
+المطلوب بيكون احنا هيك أثبتنا اللي هوIntegrable
+
+356
+00:30:52,110 --> 00:30:58,350
+criterion أو اللي هو طريقة لتحديد اللي هو ال
+
+357
+00:30:58,350 --> 00:31:02,270
+function is integrable أو لا غير اللي هو طريقة
+
+358
+00:31:02,270 --> 00:31:07,110
+التعريف الآن في عند كورولاري بعدها كورولاري
+
+359
+00:31:07,110 --> 00:31:11,530
+الكورولاري
+
+360
+00:31:11,530 --> 00:31:16,230
+هي تقول كما يليه الآن بدنا نترجم الحديث بدل ما كان
+
+361
+00:31:16,230 --> 00:31:22,710
+بإبسلون نحكي عن مين؟ عن اللي هوsequence of
+
+362
+00:31:22,710 --> 00:31:29,870
+partitions طبعاً هو هذا معهود التحويل في نظريات
+
+363
+00:31:29,870 --> 00:31:34,590
+مشابهة في حتى في كورسات أخرى خلّينا نشوف عندنا
+
+364
+00:31:34,590 --> 00:31:38,790
+اللي هو النظرية ايش ب .. او الكورلري ايش بتقول
+
+365
+00:31:38,790 --> 00:31:43,350
+بتقول let I بساوة A و B and let F من I لR be a
+
+366
+00:31:43,350 --> 00:31:48,600
+bounded functionلأن لو فرضنا بي أن أن element none
+
+367
+00:31:48,600 --> 00:31:52,300
+is a sequence of partitions of I بحيث أن ال limit
+
+368
+00:31:52,300 --> 00:31:55,920
+هذا بيساوي سفر then f is integrable and ال limit
+
+369
+00:31:55,920 --> 00:31:58,040
+لل integration بيساوي ال integration بيساوي ال
+
+370
+00:31:58,040 --> 00:32:04,480
+limit ال أسف ال limit لل lower p and f بيساوي ال
+
+371
+00:32:04,480 --> 00:32:07,020
+limit لل upper p and f اللي هو بيساوي قيمة ال
+
+372
+00:32:07,020 --> 00:32:13,000
+integration حتى ال converse جماعة اللي هواللي قبل
+
+373
+00:32:13,000 --> 00:32:16,820
+بشوية اللي كان .. اللي هي كانت F أندولي F لأن لو
+
+374
+00:32:16,820 --> 00:32:21,520
+كانت F is integrable أكيد هلاقي sequence من
+
+375
+00:32:21,520 --> 00:32:25,380
+partitions بحيث أنه ال limit اللي حاصل الطرح بساوي
+
+376
+00:32:25,380 --> 00:32:29,760
+سفر اللي هو البرهان مشابه لإي اللي حكيناه فيه اللي
+
+377
+00:32:29,760 --> 00:32:34,500
+هو برهان إيجاد الـ B epsilon ولكن هنا بنجداللي هو
+
+378
+00:32:34,500 --> 00:32:37,380
+الـ Epsilon بساوية واحدة لان فبنلاقي اللي هو ال
+
+379
+00:32:37,380 --> 00:32:42,380
+sequence هذه في ال corollary .. في من مشابه .. شيء
+
+380
+00:32:42,380 --> 00:32:45,900
+مشابه في برهان النظرية الأولى اللي قبل بشوية و
+
+381
+00:32:45,900 --> 00:32:49,360
+ياريت تجربوها عندكم خلينا ناخد اللي .. اللي موجود
+
+382
+00:32:49,360 --> 00:32:54,160
+حاليا اللي هو الاتجاه هذا ان لو لجينا sequence of
+
+383
+00:32:54,160 --> 00:32:59,430
+partitionsوكان ال limit لل U P N و F نقص ال P N و
+
+384
+00:32:59,430 --> 00:33:02,870
+F بساوة سفر إذا هتكون F is integrable و هتكون ال
+
+385
+00:33:02,870 --> 00:33:07,990
+limit للأولى بساوة limit للثانية بساوة قيمة ال
+
+386
+00:33:07,990 --> 00:33:08,970
+integration
+
+387
+00:33:12,900 --> 00:33:17,500
+عند ما أعطيني limit هذا إيش بساوي؟ سفر خلّينا ندخل
+
+388
+00:33:17,500 --> 00:33:20,580
+على التعريف مباشرة تعريف ال limit بتعرفوا تعريف ال
+
+389
+00:33:20,580 --> 00:33:23,140
+limit يا شباب؟ اللي هو لكل إبسلون أكبر من سفر
+
+390
+00:33:23,140 --> 00:33:26,160
+there exist k such that لكل أن أكبر سوى k بيصير
+
+391
+00:33:26,160 --> 00:33:33,200
+هذا ناقص هذا أصغر من مين؟ من اللي هو إبسلون وهذا
+
+392
+00:33:33,200 --> 00:33:35,980
+على طول يعطينا as integral خلّيش تشوف أيش اللي
+
+393
+00:33:35,980 --> 00:33:43,000
+بيقوله لأن since عند ما أعطيني limitU P N و F ناقص
+
+394
+00:33:43,000 --> 00:33:51,240
+ال P N و F as N goes to infinity بساوة سفر، مظبوط؟
+
+395
+00:33:51,240 --> 00:33:56,220
+هي كل ما أعطينيها نجي للتعريف، إذا تعريف ال
+
+396
+00:33:56,220 --> 00:33:58,880
+sequence عادية for every epsilon أكبر من سفر there
+
+397
+00:33:58,880 --> 00:34:02,680
+exists K element in N such that for every N أكبر
+
+398
+00:34:02,680 --> 00:34:13,090
+سوا K اللي هو عندي ال U P N و F ناقصبن و F أصغر من
+
+399
+00:34:13,090 --> 00:34:19,010
+إبسلون إذا مش لجينا بارتشن واحد لجينا بارتشن بك و
+
+400
+00:34:19,010 --> 00:34:22,710
+بك زاد واحد و بك زاد اتنين و بك زاد تلاتة كلهم
+
+401
+00:34:22,710 --> 00:34:29,110
+بسبب إن ال UBK أو ال UBK زاد واحد أو الاخره ناقص
+
+402
+00:34:29,110 --> 00:34:32,590
+القللها أصغر من 100 من إبسلون إذا ال criterion
+
+403
+00:34:32,590 --> 00:34:36,550
+اللي في الكورولاريت حققت إذا صارت عندي هذه إذا F
+
+404
+00:34:36,550 --> 00:34:41,830
+is integrableيعني مش بي إبسلون واحد اللي جينا لأ
+
+405
+00:34:41,830 --> 00:34:46,550
+من عند بك وطالع كل ال partitions هذه اللي هي بك و
+
+406
+00:34:46,550 --> 00:34:49,950
+بك زائد واحد و بك زائد اتنين بتعمل عمل ال بي
+
+407
+00:34:49,950 --> 00:34:53,510
+إبسلون اللي في وين في النظرية إذا ال F أشمالها
+
+408
+00:34:53,510 --> 00:34:58,750
+صارت ال F عبارة عن Integrable من النظرية السابقة
+
+409
+00:34:58,750 --> 00:35:05,200
+الآن الدور دل أن نثبت مين أن ال limitلأ اللي هو
+
+410
+00:35:05,200 --> 00:35:09,260
+هذا المقدار هو limit لهذا المقدار بساوي إيش اللي
+
+411
+00:35:09,260 --> 00:35:12,540
+جوا طبعا هو لو كانت يا جماعة limit هذا نقص هذا سفر
+
+412
+00:35:12,540 --> 00:35:15,920
+مش معناته ال limit الأول و limit الثاني exist هاي
+
+413
+00:35:15,920 --> 00:35:20,610
+مثلا هذه لو كانت هذه un تربيع وهذه unUnterm .. آسف
+
+414
+00:35:20,610 --> 00:35:24,610
+Unتربيع و Unتربيع أو Un و Un limit Un نقص Un على
+
+415
+00:35:24,610 --> 00:35:27,850
+طول سفر لكن لا limit الأولى عدد ولا limit الثاني
+
+416
+00:35:27,850 --> 00:35:33,270
+عدد اتنين اتين بروحين إلى مالا نهاية فالان لكن في
+
+417
+00:35:33,270 --> 00:35:37,390
+هذه الحالة نظرا للمعطيات اللي موجودة و اللي هي
+
+418
+00:35:37,390 --> 00:35:40,930
+طبيعي اللي هو اللي بنحكي فيه NuF is bounded و ببو
+
+419
+00:35:40,930 --> 00:35:45,550
+و الاخره هو استخدام السابق هيطلع عندي فعلا ال
+
+420
+00:35:45,550 --> 00:35:50,840
+limitللأل بيساوي limit للأبر بيساوي قيمة ال
+
+421
+00:35:50,840 --> 00:36:08,200
+integration ماشي اطلعوا يا جماعة عندي الآن خليني
+
+422
+00:36:08,200 --> 00:36:15,240
+أطلع .. نحط البرهان أمامنابدي الآن خلصت اللي هو F
+
+423
+00:36:15,240 --> 00:36:21,500
+is integrable بدي أستخدم زي جابل بشوية بالظبط اللي
+
+424
+00:36:21,500 --> 00:36:28,570
+هو تعريف ال L of F و U of F و إيش تعريفهاذا ما
+
+425
+00:36:28,570 --> 00:36:32,250
+بديش اعيد اللي حكيته قبل بشوية الان بما ان ال L of
+
+426
+00:36:32,250 --> 00:36:42,370
+F عبارة عن اللي هي supremum لل L B of F اذا لكل
+
+427
+00:36:42,370 --> 00:36:46,610
+ي ساوي واحدة لان there exists B N partition of I
+
+428
+00:36:46,610 --> 00:36:50,390
+such that L of F نقص واحدة لان اصغر من مين من L B
+
+429
+00:36:50,390 --> 00:36:54,070
+N of Fزي ما قلت قبل شوية، لو الـ Supremum طرحنا
+
+430
+00:36:54,070 --> 00:36:57,270
+اللي هي الـ Least Upper Bound، طرحنا منه أي عدد، 1
+
+431
+00:36:57,270 --> 00:37:01,330
+على N، إذا هلاجي، هيبطل إيش ماله Upper Bound، إيش
+
+432
+00:37:01,330 --> 00:37:04,190
+معناه يبطل Upper Bound؟ هيلاجي واحد من المجموعة
+
+433
+00:37:04,190 --> 00:37:08,230
+أكبر منه، وهذا فعلا اللي لاجينا BN، بحيث أن الـ BN
+
+434
+00:37:08,230 --> 00:37:13,910
+و F أكبر من الـ F ناقص واحدة لأنالان من هذا .. من
+
+435
+00:37:13,910 --> 00:37:16,670
+.. من .. من ال .. ال .. ال .. ناخد هذا على الطرف
+
+436
+00:37:16,670 --> 00:37:19,970
+الثاني على الطرف هنا و ناخد هذا على الطرف هذا بصير
+
+437
+00:37:19,970 --> 00:37:23,890
+عندي L of F نقص Lb of F أصغر من واحدة الآن و أنا
+
+438
+00:37:23,890 --> 00:37:28,670
+بعرف أن هذا دايما أكبر يساوي هذا لأن هذا ال
+
+439
+00:37:28,670 --> 00:37:32,410
+supremum منهم إذا انا هيكون أكبر يساوي سفر الان
+
+440
+00:37:32,410 --> 00:37:38,440
+خدوا ال limit للجهتينas n goes to infinity بيصير
+
+441
+00:37:38,440 --> 00:37:43,160
+عندي هذا اللي هي limit
+
+442
+00:37:43,160 --> 00:37:48,060
+لL بيقل نوف أف حيثالوي لL أوف أف لإنه حيثير ال
+
+443
+00:37:48,060 --> 00:37:53,720
+limit هذا أيش بيساوي بيساوي سفر واضحالان يا جماعة
+
+444
+00:37:53,720 --> 00:37:58,400
+عندي ال L of F ناقص ال P L of F أصغر من واحدة لأنه
+
+445
+00:37:58,400 --> 00:38:03,660
+أكبر سوى سفر لان معله الان هذا لكل إبسلون اللي هو
+
+446
+00:38:03,660 --> 00:38:07,300
+واحدة لان لجينا partition يعني للإبسلون بيساوي
+
+447
+00:38:07,300 --> 00:38:09,360
+واحد لجينا بيه واحد للإبسلون بيساوي اتنين بيه
+
+448
+00:38:09,360 --> 00:38:12,160
+اتنين للإبسلون تلاتة بيه تلاتة إذا صار عندي
+
+449
+00:38:12,160 --> 00:38:16,580
+sequence of اللي هي إياش partitionsالأن طلع عندي
+
+450
+00:38:16,580 --> 00:38:20,460
+دائما دائما دائما L of F نقص ال PN of F أصغر من
+
+451
+00:38:20,460 --> 00:38:25,440
+واحد على N لكل N الأن as N goes to infinity هذا ال
+
+452
+00:38:25,440 --> 00:38:30,620
+limit هيصير سفر وهذا سفر إذا هيصير limit هذا as N
+
+453
+00:38:30,620 --> 00:38:33,200
+goes to infinity بساوي سفر لكن ال L of F أصلا
+
+454
+00:38:33,200 --> 00:38:37,860
+independent of N إذا هيصير limit PN of F as N goes
+
+455
+00:38:37,860 --> 00:38:43,720
+to infinity بساوي L of F لأن المواضحات لوش يا شباب
+
+456
+00:38:43,720 --> 00:38:52,360
+limitL of F ناقص L B N و F هيساوي 0 as N goes to
+
+457
+00:38:52,360 --> 00:38:56,920
+infinity و هذا المقدار عبارة عن مقدار ثابت
+
+458
+00:38:56,920 --> 00:39:04,740
+independent of N إذا هيصير عندي limit L B N و F
+
+459
+00:39:04,740 --> 00:39:10,540
+بتساوي limit L of F ناقص
+
+460
+00:39:17,660 --> 00:39:27,170
+L of P L و F زائد L of Fمظبوط؟ طيب هذا الأن
+
+461
+00:39:27,170 --> 00:39:33,590
+المقدار معروف أنه بساوي 0 و هذا ثابت إذا بقدر أوزع
+
+462
+00:39:33,590 --> 00:39:37,210
+ال limit على الجهتيين و أنا مرتاح إذا بساوي limit
+
+463
+00:39:37,210 --> 00:39:42,950
+الأول اللي هو 0 زائد limit الثاني نفسه لأنه ثابت
+
+464
+00:39:42,950 --> 00:39:46,450
+إذا صار عندي limit L P N of F as N goes to
+
+465
+00:39:46,450 --> 00:39:54,710
+infinity بساوي L of F كما هو حكينا عنه حقامن جهة
+
+466
+00:39:54,710 --> 00:39:58,650
+أخرى limit الـU ناقص limit الـL المعطيلة هي بيساوي
+
+467
+00:39:58,650 --> 00:40:03,490
+0 إذا صار عندى سهل أن أوجد mean برضه limit الـU
+
+468
+00:40:03,490 --> 00:40:08,990
+اللي هو limit الـU إيش هيساوي ناقص اللي هو .. ال
+
+469
+00:40:08,990 --> 00:40:12,670
+.. ال .. هيساوي limit الـL of F يساوي الـU of F
+
+470
+00:40:12,670 --> 00:40:17,270
+يساوي ال integration أكثر توضيحاً and بيهاجدى
+
+471
+00:40:17,270 --> 00:40:22,420
+أعتقد أنه واضح لكن خلّينا نوضحه بشكل أكبرعشان
+
+472
+00:40:22,420 --> 00:40:34,100
+مايضلش مشي عندى limit U P N of F ايش هيساوي هيساوي
+
+473
+00:40:34,100 --> 00:40:44,560
+اللي هو limit U
+
+474
+00:40:44,560 --> 00:40:49,740
+P N of F
+
+475
+00:40:52,490 --> 00:40:58,090
+limit U P N و F ناقص
+
+476
+00:40:58,090 --> 00:41:07,810
+L of P N of F زائد L P N of F واضحة يا شباب أه؟
+
+477
+00:41:07,810 --> 00:41:12,690
+الآن هذا مضمون أنه موجود و سفر وهذا مضمون و
+
+478
+00:41:12,690 --> 00:41:18,350
+أثبتناه إيش بيساوي L of Fإذا إيش صار بيساوي؟
+
+479
+00:41:18,350 --> 00:41:21,810
+بيساوي اللي هو هذا صفر إذا صار بيساوي أقل و فأف
+
+480
+00:41:21,810 --> 00:41:25,510
+إذا صار هذا برضه بيساوي أقل و فأف لكن أنا مثبت قبل
+
+481
+00:41:25,510 --> 00:41:29,610
+بشوية أن ال F is integrable يعني ال U في F إيش
+
+482
+00:41:29,610 --> 00:41:34,550
+هتساوي؟ اللي أقل و فأف وهذه أثبتناها إيش بتساوي؟
+
+483
+00:41:34,550 --> 00:41:39,350
+limit U P N و F وهذه نفسها أثبتناها قبل بشوية إيش
+
+484
+00:41:39,350 --> 00:41:46,070
+بتساوي؟ limit L P N و Fوهو المطلوب طبعاً مدام
+
+485
+00:41:46,070 --> 00:41:49,370
+integration هذه وهذه هي عبارة عن ال integration
+
+486
+00:41:49,370 --> 00:41:55,410
+على الفترة اللي بنحكي عنها الإنقلا بيه لقيمة ال F
+
+487
+00:41:55,410 --> 00:42:01,710
+لأن صار عندي كل القيام هذه متساوية وصار عندي إيجاد
+
+488
+00:42:01,710 --> 00:42:07,610
+ال limit لل U P N و F أو limit لل L P N و F يكفي
+
+489
+00:42:07,610 --> 00:42:11,330
+أنه نوجد فيه قيمة ال integration بعد ما أثبتناه أو
+
+490
+00:42:11,330 --> 00:42:16,260
+تحت الظروف اللي هي في الكورو الأخرىلأ نيجي بدنا
+
+491
+00:42:16,260 --> 00:42:22,660
+نبرهن اللي هو المثال اللي برهناه المرة الماضية
+
+492
+00:42:22,660 --> 00:42:27,660
+بالتعريف بدنا نبرهنه بواسطة اللي هي ال corollary
+
+493
+00:42:27,660 --> 00:42:33,060
+اللي عندنا بدنا نبرهن اللي هو اللي هي نثبت أنه
+
+494
+00:42:36,170 --> 00:42:42,070
+نثبت أن F of X بساوة X يا شباب عبارة عن Integrable
+
+495
+00:42:42,070 --> 00:42:45,770
+أو اللي سمناها G of X بساوة X is Integrable على
+
+496
+00:42:45,770 --> 00:42:48,830
+الفترة Zero واحد المرة الماضية أثبتناها كيف
+
+497
+00:42:48,830 --> 00:42:54,230
+أثبتناها زي ما أنتم متذكرين بواسط التعريفمظبوط؟
+
+498
+00:42:54,230 --> 00:42:58,610
+طيب جيبنا اللي هو ال upper sum و ال lower sum و
+
+499
+00:42:58,610 --> 00:43:02,930
+بعدين جيبنا ال upper integral و ال lower integral
+
+500
+00:43:02,930 --> 00:43:04,750
+و أثبتنا ان ال upper integral بساوي ال lower
+
+501
+00:43:04,750 --> 00:43:08,760
+integral و خلصناهالآن بدنا نثبتها بطريقتنا اللي هي
+
+502
+00:43:08,760 --> 00:43:12,540
+على الكورولر اللي جابل بشوية عند g of x ساوة x على
+
+503
+00:43:12,540 --> 00:43:16,600
+الفترة 0 بواحد هي المطلوب اثباتها show that g is
+
+504
+00:43:16,600 --> 00:43:20,940
+integrable على هذه الفترة الآن بديش اعيد اللي
+
+505
+00:43:20,940 --> 00:43:23,850
+حكيته المرة الماضية اللي حكيناه المرة الماضيةمن
+
+506
+00:43:23,850 --> 00:43:26,910
+الـ Example اللي أثبتنا فيه انها Integra بالبواسطة
+
+507
+00:43:26,910 --> 00:43:31,470
+اللي هي التعريف أخدنا P N اللي هو Zero واحد على N
+
+508
+00:43:31,470 --> 00:43:34,910
+واثنين على N وان نقص واحد على N لعند الواحد أخدنا
+
+509
+00:43:34,910 --> 00:43:39,290
+اللي هو عبارة عن Any Partition اللي هو بالطريقة
+
+510
+00:43:39,290 --> 00:43:43,710
+اللي أمامي يعني حسب N بيصير بختلف ال Partition أما
+
+511
+00:43:43,710 --> 00:43:46,730
+إيش فكرة ال Partition زي ما قلنا المرة الفائتة من
+
+512
+00:43:46,730 --> 00:43:51,350
+0 لعند 1 جزأناها إلى أجزاء متساوية إلى N من
+
+513
+00:43:51,350 --> 00:43:55,350
+الأجزاء المتساويةصار طول كل sub integral عبارة عن
+
+514
+00:43:55,350 --> 00:44:00,850
+إيهاش عبارة عن واحد على N وأوجدنا في حينه اللي هو
+
+515
+00:44:00,850 --> 00:44:08,470
+ال U P N O G ولاجناها بتساوي إيه ده بتتذكروا نص في
+
+516
+00:44:08,470 --> 00:44:13,710
+واحد زائد واحد على N وأوجدنا برضه ال P N O G
+
+517
+00:44:13,710 --> 00:44:18,910
+ولاجناها عبارة عن نص في واحد ناقص واحد على N كما
+
+518
+00:44:18,910 --> 00:44:26,960
+أذكر ماشي الحال فعلا طيبالان صار عندى الـ PN في
+
+519
+00:44:26,960 --> 00:44:29,780
+الواقع عبارة عن sequence of partitions
+
+520
+00:44:35,190 --> 00:44:39,110
+هذه صارت sequence of partitions بواحد بتعود عن انا
+
+521
+00:44:39,110 --> 00:44:42,750
+بواحد باتنين كده بتلاتة كده باربعة كده وفي كل
+
+522
+00:44:42,750 --> 00:44:47,270
+الأحوال الـ U, B, N و G انجروا لهيها و الـ L, B, N
+
+523
+00:44:47,270 --> 00:44:51,490
+و G بساوي إيش المقدار الأمامي الآن عشان أثبت إنها
+
+524
+00:44:51,490 --> 00:44:56,590
+integrable يكفي من النظرية الكورولاري إن قاعد أقول
+
+525
+00:44:56,590 --> 00:45:03,290
+طب خلينا نشوف limit الـ U, B, N و G ناقص الـ L, B,
+
+526
+00:45:03,450 --> 00:45:09,840
+N و Gas n goes to infinity بساوة إيه يا عشان بساوة
+
+527
+00:45:09,840 --> 00:45:16,360
+سفر نشوفها صح ولا لأ طبعا أكيد مع حسبة بسيطة
+
+528
+00:45:16,360 --> 00:45:24,580
+احسبليها بساوة limit نصفي واحد زياد واحدة لان زياد
+
+529
+00:45:24,580 --> 00:45:28,600
+نص في واحد ناقص واحدة لان as n goes to infinity
+
+530
+00:45:28,600 --> 00:45:32,260
+هذه سفر وهذه سفر وهذه نص وهذه نص وهذه نص وهذه نص
+
+531
+00:45:32,260 --> 00:45:32,340
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+532
+00:45:32,340 --> 00:45:32,920
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+533
+00:45:32,920 --> 00:45:38,340
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+534
+00:45:38,340 --> 00:45:45,580
+وهذهاللي هو y ساوي نص نقص النص y ساوي سفر واضح أهي
+
+535
+00:45:45,580 --> 00:45:50,120
+عندي اللي هو هاد سفر و هاد سفر و نص نقص النص y
+
+536
+00:45:50,120 --> 00:45:54,920
+ساوي سفر مادام سفر إذا إيه شمالها إذا the function
+
+537
+00:45:54,920 --> 00:46:02,720
+d of x ساوي x is integrable on zero واحد هذا by
+
+538
+00:46:02,720 --> 00:46:06,560
+mean by ال corollary اللي قبل بشوية
+
+539
+00:46:15,600 --> 00:46:19,420
+الان بقيمة ال integration ايش هيكون قيمة ال limit
+
+540
+00:46:19,420 --> 00:46:24,280
+limit u, b, n, g هيقدر الغرض و limit l of n of g
+
+541
+00:46:24,280 --> 00:46:29,320
+هيقدر الغرض ليش لأن limit هذا اصلا هيطلع لك limit
+
+542
+00:46:29,320 --> 00:46:35,710
+ال u, b, n و gهو عبارة عن قيمة integration من A ل
+
+543
+00:46:35,710 --> 00:46:42,370
+B حسب النظرية الـ Corollary و يساوي limit 2.5 في 1
+
+544
+00:46:42,370 --> 00:46:48,600
+زائد 1 ل N و يساوي هذا تروح ل 0و يساوى نص و أيضا
+
+545
+00:46:48,600 --> 00:46:54,080
+لو جربت حسب تاب limit ال b, n و g طبعا هيطلع نفس
+
+546
+00:46:54,080 --> 00:46:58,200
+الجواب و إلا إن كان هناك مشكلة لدينا limit نص في
+
+547
+00:46:58,200 --> 00:47:02,340
+واحد ناقص واحد على n و يساوى برضه جدياش نص إذن
+
+548
+00:47:02,340 --> 00:47:06,700
+قيمة ال integration بساوة نص إذن هذه طريقة أخرى
+
+549
+00:47:06,700 --> 00:47:11,780
+لحساب اللي هو أو لإثبات أن g of x بساوة x is
+
+550
+00:47:11,780 --> 00:47:17,560
+integrableالآن بدنا ندخل على أمر آخر الأمر هو في
+
+551
+00:47:17,560 --> 00:47:24,500
+الواقع يا شباب أنه بدنا نشوف إيش في من عائلات
+
+552
+00:47:24,500 --> 00:47:28,400
+الدوال عائلات الدوال إنها تكون Integrable الآن
+
+553
+00:47:28,400 --> 00:47:31,720
+بدنا نيجي نحوش الدوال الـ Integrable إحنا عرفنا بس
+
+554
+00:47:31,720 --> 00:47:36,500
+ده لأ D of X سو X is Integrable و هنلاقي زيها لكن
+
+555
+00:47:36,500 --> 00:47:40,960
+الآن بدنا نيجي نحكي عن دوال اللي هو عائلات من
+
+556
+00:47:40,960 --> 00:47:45,480
+الدوالأول عائلة من العائلات المهمة اللي هي الـ
+
+557
+00:47:45,480 --> 00:47:48,960
+monotone functions يعني الدوال اللي بتكون يا
+
+558
+00:47:48,960 --> 00:47:52,360
+increasing على كل الفترة يا decreasing على كل
+
+559
+00:47:52,360 --> 00:47:59,320
+الفترة بقولكم هذا على اللي هي F من F ال function
+
+560
+00:47:59,320 --> 00:48:04,000
+لو كانت bounded لو كانت monotone على اللي هي
+
+561
+00:48:04,000 --> 00:48:09,660
+closed bounded interval I على طول integrable إذن
+
+562
+00:48:09,660 --> 00:48:16,700
+عيلة كبيرةعيلة الدوال اللي بتكون يا increasing يا
+
+563
+00:48:16,700 --> 00:48:22,380
+decreasing على كل الفترة a و b هذه مضمون انها تكون
+
+564
+00:48:22,380 --> 00:48:26,980
+الدوال ايه شمالها عبارة عن integrable functions
+
+565
+00:48:26,980 --> 00:48:35,090
+اذا اول اعلان الان اللي هو any monotone functionon
+
+566
+00:48:35,090 --> 00:48:40,850
+a closed bounded interval is integrable وهذا اللي
+
+567
+00:48:40,850 --> 00:48:47,090
+هو عنواننا integrability of monotone functionsلت I
+
+568
+00:48:47,090 --> 00:48:51,650
+بتساوي A و B و لت F من I لR بيكون مونوتون فانكشن
+
+569
+00:48:51,650 --> 00:48:57,370
+on I ثم F أشمالها is integrable on I نفترض أن F
+
+570
+00:48:57,370 --> 00:49:03,110
+انتقل هو مونوتور نصل إليها integrable نفترض أن F
+
+571
+00:49:03,110 --> 00:49:09,440
+مثلا increasingونصل إنها integrable وsimilarly
+
+572
+00:49:09,440 --> 00:49:14,560
+وفعلا similarly لو كانت f is decreasing هتكون برضه
+
+573
+00:49:14,560 --> 00:49:21,500
+is integrable خلّينا مع بعض شباب نفترض suppose
+
+574
+00:49:21,500 --> 00:49:31,240
+that f is increasing يعني الدالة على الفترة هي a
+
+575
+00:49:31,240 --> 00:49:37,760
+وb مثلاوالدالة هتكون أشمالها تزايدية يا هيك يا هيك
+
+576
+00:49:37,760 --> 00:49:41,620
+طبعا حسب مش مشكلة بتفرج أشمالها ماشي الحال اللي هي
+
+577
+00:49:41,620 --> 00:49:47,060
+الدالة أشمالها is increasing is increasing بتدخل
+
+578
+00:49:47,060 --> 00:49:53,500
+الآن بي أن اللي هو عبارة عن any partition اللي هو
+
+579
+00:49:55,970 --> 00:50:00,970
+بس بدي أجزه زي منهج اللي عملته معه اللي هو f of x
+
+580
+00:50:00,970 --> 00:50:05,370
+بساوة x اللي قبله شوية بدي أجزه إلى أجزاء متساوية
+
+581
+00:50:05,370 --> 00:50:11,130
+يعني بدي أجز الفقرة a و b إلى أجزاء متساوية الأولى
+
+582
+00:50:11,130 --> 00:50:15,730
+بدي أسميها x note اللي بعدها x1 اللي بعدها x2 لما
+
+583
+00:50:15,730 --> 00:50:21,780
+أصل لآخر 11 أسميها xnونكون طول كل واحدة متساوية
+
+584
+00:50:21,780 --> 00:50:26,340
+للثانية إذا الان إذا بدي أجزئها إلى N إلى N من ال
+
+585
+00:50:26,340 --> 00:50:30,240
+sub intervals بيصير طول كل فترة عبارة عن B minus A
+
+586
+00:50:30,240 --> 00:50:35,080
+على مين؟ على N طول الفترة على عدد الفترات اللي
+
+587
+00:50:35,080 --> 00:50:39,400
+بتديهاأنا بدّي الفترات إيش عددها؟ N فبيصير عند بي
+
+588
+00:50:39,400 --> 00:50:43,320
+ماينس إيه على مين على N هذا طول الفترة يعني الفترة
+
+589
+00:50:43,320 --> 00:50:47,740
+النموذجية لأي K X K minus X K minus واحد هيتمكن
+
+590
+00:50:47,740 --> 00:50:52,560
+طولها عبارة عن بي ماينس إيه على N for every K كيه
+
+591
+00:50:52,560 --> 00:50:56,000
+طبعا إيه اشمالها؟ يا ما بيساوي Zero يا واحد، لعند
+
+592
+00:50:56,000 --> 00:51:01,100
+ماصل، لعند مين؟ لعند N أو K بيساوي واحد لعند N
+
+593
+00:51:04,810 --> 00:51:10,230
+xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+594
+00:51:10,230 --> 00:51:14,230
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+595
+00:51:14,230 --> 00:51:14,590
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+596
+00:51:14,590 --> 00:51:17,070
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+597
+00:51:17,070 --> 00:51:25,770
+-xn-n-xn-n-xn-n-xn-n-xn-nلأ لو جينا هذا increasing
+
+598
+00:51:25,770 --> 00:51:30,170
+مدام increasing إذن الـ Mk اللي هي عبارة عن ال
+
+599
+00:51:30,170 --> 00:51:35,510
+supremum اللي هنا supremum لهذه Mk ال supremum
+
+600
+00:51:35,510 --> 00:51:39,910
+اللي هنا هيكون على أخر واحدة لأن أجملها ده لا is
+
+601
+00:51:39,910 --> 00:51:45,510
+increasing إذن هيكون ال Mk هو F of XK رسم عنها
+
+602
+00:51:45,990 --> 00:51:51,210
+بساوة F of X K طيب ال M K Small أكيد هيقولنا كلكم
+
+603
+00:51:51,210 --> 00:51:54,010
+هتقوله بتساوة ال M في معمع الفترة مدام ال M في
+
+604
+00:51:54,010 --> 00:51:57,370
+معمع الفترة إذا أول واحدة فيهم إذا هو F of X K
+
+605
+00:51:57,370 --> 00:52:04,530
+minus واحد، مظبوط شباب؟ طيب، مظبوط هذه اللي هي
+
+606
+00:52:04,530 --> 00:52:10,750
+مالها الدالة اللي بتكون monotone عندي،
+
+607
+00:52:10,750 --> 00:52:21,840
+احسبلي الآن ال U P N و Fنقص الـ BNOF إيش هيساوي؟
+
+608
+00:52:21,840 --> 00:52:26,840
+جهزة الأمور بساوي الـ summation لمين؟ للـ MK
+
+609
+00:52:26,840 --> 00:52:36,190
+Capital في XK نقص XK minus واحدك من عند 1 لعند n
+
+610
+00:52:36,190 --> 00:52:44,370
+نقص summation mk في xk minus xk minus 1 k من عند 1
+
+611
+00:52:44,370 --> 00:52:49,440
+لعند n ويساويالـ Mk وجدناها، اللي هي عبارة عن مين؟
+
+612
+00:52:49,440 --> 00:52:55,420
+F of Xk ويساوي الـ summation للـ F of Xk في مين
+
+613
+00:52:55,420 --> 00:53:00,200
+مضروبة؟ في هذه، هذه كده طولها ثابت، ما احنا هيك
+
+614
+00:53:00,200 --> 00:53:02,540
+على هذا الأساس اذا اخترنا الـ sequence of
+
+615
+00:53:02,540 --> 00:53:05,320
+partitions اللي عندنا، اللي هو طوالث في
+
+616
+00:53:05,320 --> 00:53:09,580
+subintervals ثابتة، كل واحد اسمه يشمله B minus A
+
+617
+00:53:09,580 --> 00:53:14,250
+على N، هذا K من واحدإن عندنا ناقص خلّيني أضعه في
+
+618
+00:53:14,250 --> 00:53:18,550
+summation 1 ناقص نفس القصة اللي هي m k small إيش
+
+619
+00:53:18,550 --> 00:53:23,710
+هي يا جماعة اتفاقنا عبارة عن f of x k minus 1 في
+
+620
+00:53:23,710 --> 00:53:27,610
+هذه خلّيني أخدها عامل مشترك بعد إذنكم لإن هو
+
+621
+00:53:27,610 --> 00:53:31,070
+موجودة هنا وموجودة هنا خلّيني أطلّحها برا واضحة
+
+622
+00:53:31,070 --> 00:53:36,070
+أشيل هذه برا بيصير اللي هو مضروبة في b minus a على
+
+623
+00:53:36,910 --> 00:53:42,350
+وأصلا هذه ثابتة بالنسبة لل summation ليش؟ لأن ال
+
+624
+00:53:42,350 --> 00:53:46,110
+summation العداد K من واحد عندنا أن هذه N ثابتة
+
+625
+00:53:46,110 --> 00:53:52,870
+بالنسبة لل K لذلك بتساوي B minus A على N مضروبة في
+
+626
+00:53:52,870 --> 00:53:59,280
+مين في ال summationللـ f of x k minus f of x k
+
+627
+00:53:59,280 --> 00:54:03,840
+minus واحد k من عند واحد لعند مين يا جماعة لعند ان
+
+628
+00:54:03,840 --> 00:54:07,920
+بعدين the is and could بدي افرطها هذه بيصير عندي y
+
+629
+00:54:07,920 --> 00:54:14,880
+ساوي هذا اللي هو مين كله اللي جاعت بحسبه ال u,b,n
+
+630
+00:54:14,880 --> 00:54:19,320
+وf ناقص ال b,n وf هيسوي هذا المقدار اللي هو b
+
+631
+00:54:19,320 --> 00:54:25,970
+minus a على المضروب فيهالان ال summation عبارة عن
+
+632
+00:54:25,970 --> 00:54:32,630
+k ب 1 بصير f of x 1 ناقص f of x naught اللي بعدها
+
+633
+00:54:32,630 --> 00:54:40,170
+k ب 2 زائد f of x 2 ناقص f of x 1 اللي بعدها زائد
+
+634
+00:54:40,170 --> 00:54:46,130
+f of x 3 ناقص f of x 2 لما نقضى اللي ماشي لأخر
+
+635
+00:54:46,130 --> 00:54:53,140
+واحد بكون عندى f of x nناقص f of x n ناقص واحد
+
+636
+00:54:57,360 --> 00:55:04,840
+F of X1 بيطير مع سالب F of X1 و F of X2 بيطير مع
+
+637
+00:55:04,840 --> 00:55:09,840
+سالب F of X2 و هكذا بظل ماشي لما كله يروح مع كله
+
+638
+00:55:09,840 --> 00:55:16,640
+ما عدا بظل عندي اللي هو أول قيمة اللي هي F of X
+
+639
+00:55:16,640 --> 00:55:22,660
+note بالسالب مع F of Xn الأخيرة بالموجب بيصير عندي
+
+640
+00:55:22,660 --> 00:55:34,740
+Y ساوي B minus A على Nفي F of Xn ناقص F of X0 طبعا
+
+641
+00:55:34,740 --> 00:55:39,420
+Xn آخر واحدة اللي هي B و X0 أول واحدة اللي هي A
+
+642
+00:55:39,420 --> 00:55:46,580
+إذن هيساوي هذا عبارة عن B minus A في F of B minus
+
+643
+00:55:46,580 --> 00:55:53,150
+F of A الكل هذا مجسوم على مين يا جماعة؟ على Nهذا
+
+644
+00:55:53,150 --> 00:55:58,090
+عبارة عن ثابت وهذا عبارة عن ثابت وهذا الان هي اللي
+
+645
+00:55:58,090 --> 00:56:03,670
+بدلالتها كُتِب ال partitions إذا صار عندى الآن بعد
+
+646
+00:56:03,670 --> 00:56:07,230
+كل اللي حكيته هان أخدت ال بي أن بالشكل اللي أمامي
+
+647
+00:56:07,230 --> 00:56:12,190
+عبارة عن sequence of partitions ووصلنا إلى ما
+
+648
+00:56:12,190 --> 00:56:17,890
+لاقيا ليه يا جماعة اللي هو وصلنا ان ال you بي أن و
+
+649
+00:56:17,890 --> 00:56:26,260
+أف ناقص ال بي أن و أفأصغر أو يساوي طبعا أكيد أكبر
+
+650
+00:56:26,260 --> 00:56:29,600
+يساوي صفر لأن هذا دايما أكبر يساوي هذا أصغر يساوي
+
+651
+00:56:29,600 --> 00:56:36,140
+B minus A ف F of B أكيد عرفت أشهد أساوي نقص F of A
+
+652
+00:56:36,140 --> 00:56:41,720
+على اللي هو N الـ N خد ال limit للجهتين as N goes
+
+653
+00:56:41,720 --> 00:56:45,160
+to infinity as N goes to infinity هذا goes to zero
+
+654
+00:56:45,160 --> 00:56:51,730
+وهذا أصلا صفر فبصير عندي limit إذا .. إذا limitالـ
+
+655
+00:56:51,730 --> 00:56:59,290
+U P N و F ناقص الـ L P N و F as N goes to infinity
+
+656
+00:56:59,290 --> 00:57:04,210
+بساوي سفر إذا صار عندي sequence of partitions تحقق
+
+657
+00:57:04,210 --> 00:57:07,730
+لهذا إذا حسب الـ Corollary اللي حكيتها قبل بشوية
+
+658
+00:57:07,730 --> 00:57:17,130
+إذا F is integrable وهو المطلوب إذا صار عندي أي
+
+659
+00:57:17,130 --> 00:57:21,850
+increasing function is integrablesimilarly for
+
+660
+00:57:21,850 --> 00:57:26,170
+decreasing لماذا similarly لأنه تصبح الدالة بدل ما
+
+661
+00:57:26,170 --> 00:57:30,950
+هي طالع هيك تصبح أشمالها نازلة نزول الدالة فبصير
+
+662
+00:57:30,950 --> 00:57:35,430
+عندك اللي هو ال maximum هي الأولى أو ال supremum
+
+663
+00:57:35,430 --> 00:57:41,920
+هي أفبصير الـ MK بسوء F of XK minus واحد والـ MK
+
+664
+00:57:41,920 --> 00:57:46,760
+بسوء F of XK وبيتكملوا البرهان بنفس الطريقة، هيطلع
+
+665
+00:57:46,760 --> 00:57:52,040
+عندكم البرهان automatic وبشكل سهل وبشكل سلس،
+
+666
+00:57:52,040 --> 00:57:58,500
+similar أي سؤال؟ إذن الإعلان اللي أعلنناه قبل
+
+667
+00:57:58,500 --> 00:58:04,800
+بشوية أنه any monotone functionيعني any increasing
+
+668
+00:58:04,800 --> 00:58:08,780
+function on a closed bounded interval must be
+
+669
+00:58:08,780 --> 00:58:15,740
+integrable and any decreasing function on a closed
+
+670
+00:58:15,740 --> 00:58:20,420
+bounded interval برضه must be integrable إذا صار
+
+671
+00:58:20,420 --> 00:58:26,060
+في عنا عائلة كاملة من الدوال القابلة للتكامل بواسط
+
+672
+00:58:26,060 --> 00:58:32,160
+التكامل remandالآن بدنا ننتقل إلى عائلة أخرى
+
+673
+00:58:32,160 --> 00:58:38,300
+وعائلة لا تقل أهمية عن هذه العائلة وعائلة يعني
+
+674
+00:58:38,300 --> 00:58:45,560
+محبوبة عنها اللي هي اللي
+
+675
+00:58:45,560 --> 00:58:53,960
+هي عائلة الدوال المتصلة اللي هي integrable of
+
+676
+00:58:53,960 --> 00:58:56,140
+continuous functions
+
+677
+00:59:00,850 --> 00:59:06,130
+اللي هي integrability of continuous functions
+
+678
+00:59:06,130 --> 00:59:12,210
+النظرية بتقول ما يلي لت أ .. طبعا عندي ال function
+
+679
+00:59:12,210 --> 00:59:16,410
+على closed bounded interval لت F من I لR be
+
+680
+00:59:16,410 --> 00:59:20,750
+continuous on I then F is integrable on I إذا الآن
+
+681
+00:59:20,750 --> 00:59:24,230
+any continuous function on a closed bounded
+
+682
+00:59:24,230 --> 00:59:29,600
+interval must be integrableكمان مرة any continuous
+
+683
+00:59:29,600 --> 00:59:33,840
+function on a closed bounded interval must be
+
+684
+00:59:33,840 --> 00:59:38,920
+integrable طبعا حيزنا في البرهان شغلة اللي هي
+
+685
+00:59:38,920 --> 00:59:45,080
+أخدناها سابقا انهAny continuous function on a
+
+686
+00:59:45,080 --> 00:59:49,840
+closed bounded interval must attain its maximum
+
+687
+00:59:49,840 --> 00:59:57,800
+and minimum on this interval بمعنى
+
+688
+00:59:57,800 --> 01:00:01,970
+آخر هنلاقيلو كانت F is continuous على اللي هو الـ
+
+689
+01:00:01,970 --> 01:00:05,990
+A و الـ B هنلاقي نقطة في داخل الفترة A و B بحيث
+
+690
+01:00:05,990 --> 01:00:09,570
+انها تكون الـ F عندها نقطة maximum و هنلاقي نقطة
+
+691
+01:00:09,570 --> 01:00:12,750
+أخرى في داخل هذه الفترة هنلاقي اللي هي الـ
+
+692
+01:00:12,750 --> 01:00:15,930
+function عندها إشمالها is minimum طبعا absolute و
+
+693
+01:00:15,930 --> 01:00:24,180
+absolute نيجي نشوف .. نيجي للبرهانالان .. نظرية
+
+694
+01:00:24,180 --> 01:00:28,540
+أخرى أيضا .. برضه خلينا نقولها أن لو كانت F is
+
+695
+01:00:28,540 --> 01:00:32,580
+continuous على closed bounded interval then F is
+
+696
+01:00:32,580 --> 01:00:43,820
+uniformly continuous الان F .. عند F من A و B لعند
+
+697
+01:00:43,820 --> 01:00:51,090
+R is continuous on A و Bcontinuous عالمين على
+
+698
+01:00:51,090 --> 01:00:54,450
+closed bounded interval في عندنا نظرية اللي بتقول
+
+699
+01:00:54,450 --> 01:00:58,270
+any continuous function في الواحد on a closed
+
+700
+01:00:58,270 --> 01:01:02,230
+bounded interval must be uniformly continuous إذا
+
+701
+01:01:02,230 --> 01:01:10,030
+then f is uniformly continuous
+
+702
+01:01:10,730 --> 01:01:15,290
+on a و b ايش يعني uniformly continuous يعني لكل
+
+703
+01:01:15,290 --> 01:01:18,810
+ابسلون اكبر من سفر there exist دلتا اكبر من سفر
+
+704
+01:01:18,810 --> 01:01:22,990
+دلتا بس بتعتمد عالميا على ابسلون بتنفع لكل ال X و
+
+705
+01:01:22,990 --> 01:01:30,810
+ال Y such that if X minus Y او U ناقص V زي ما هو
+
+706
+01:01:30,810 --> 01:01:40,200
+مسميها U minus Vأصغر من دلتا then F of U ناقص F of
+
+707
+01:01:40,200 --> 01:01:49,800
+V أصغر من إبسلون لكل UV element in A أو Bإذن لكل y
+
+708
+01:01:49,800 --> 01:01:52,900
+أكبر من 0 there exists Delta دلتا أشمة لا بتعتمد
+
+709
+01:01:52,900 --> 01:01:56,280
+على مين بس على إبسلون في حالة ال continuity
+
+710
+01:01:56,280 --> 01:02:01,560
+العادية بنقول إحنا limit f of x as x بتروح لل a
+
+711
+01:02:01,560 --> 01:02:07,260
+بساوي ايش f of a بنقول الآن إنه limit f of x بساوي
+
+712
+01:02:07,260 --> 01:02:13,450
+f of a as x بتروح لل a لكل إبسلون أكبر من 0هصب مين
+
+713
+01:02:13,450 --> 01:02:18,070
+بالـ a هذه there exist دي و لكل a element in a
+
+714
+01:02:18,070 --> 01:02:23,270
+there exist delta such that اللي لما يكون x minus
+
+715
+01:02:23,270 --> 01:02:27,190
+a أصغر من delta بيعطينا f of x نقص f of a أصغر من
+
+716
+01:02:27,190 --> 01:02:32,550
+إبسلون يعني بيكون الـ delta هنا تعتمد على الإبسلون
+
+717
+01:02:32,550 --> 01:02:37,550
+وتعتمد على ال a اللي عندها ال continuityلكن في الـ
+
+718
+01:02:37,550 --> 01:02:41,890
+Uniform Continuous الـ Delta اللي اللي جيت هنا
+
+719
+01:02:41,890 --> 01:02:47,510
+بتنفع لكل اللي هو ال .. ال .. ال .. ال .. ال .. ال
+
+720
+01:02:47,510 --> 01:02:47,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+721
+01:02:47,890 --> 01:02:47,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+722
+01:02:47,910 --> 01:02:48,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+723
+01:02:48,290 --> 01:02:48,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+724
+01:02:48,530 --> 01:02:50,270
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+725
+01:02:50,270 --> 01:02:50,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+726
+01:02:50,330 --> 01:02:50,410
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+727
+01:02:50,410 --> 01:02:54,250
+.. ال .. ال .. ال .. ال .. ال ..
+
+728
+01:02:54,250 --> 01:02:59,970
+ال .. ال ..F is continuous، إذن يُنفرم الـ
+
+729
+01:02:59,970 --> 01:03:02,650
+continuous، إيش معناته؟ كل إبسلون أكبر من صفر،
+
+730
+01:03:02,650 --> 01:03:05,490
+there exists دلتا، بحيث إن U minus V أصغر من دلتا
+
+731
+01:03:05,490 --> 01:03:08,690
+يعطيني F of U ناقص F of V أصغر من إياش، من إبسلون،
+
+732
+01:03:08,690 --> 01:03:11,870
+وخلّي هذه إيش مالها في الذاكرة، أنا عشان الحسابات
+
+733
+01:03:11,870 --> 01:03:15,890
+بدي أخليها إبسلون على مين، على B minus A، طول
+
+734
+01:03:15,890 --> 01:03:19,070
+الفترة اللي أنا بشتغل عليها، هتشوفوا ليش كتبت هيك،
+
+735
+01:03:19,070 --> 01:03:22,720
+بس لا الحساباتبقدر أه بقدر لإن هو أصغر .. أه بقدر
+
+736
+01:03:22,720 --> 01:03:25,140
+خليه أصغر من الـ Epsilon في الدنيا من ضمن إن كل
+
+737
+01:03:25,140 --> 01:03:27,520
+الـ Epsilon عن الـ B minus A لكل الـ Epsilonات
+
+738
+01:03:27,520 --> 01:03:34,040
+اللي في الدنيا طيب لأن شوف وين بده أروح، بده أروح
+
+739
+01:03:34,040 --> 01:03:39,250
+لـ Integrability لـ الـ function Fالأن خُد n الان
+
+740
+01:03:39,250 --> 01:03:42,190
+بدنا نعمل partitions بدنا نجيب sequence of
+
+741
+01:03:42,190 --> 01:03:45,890
+partitions Bn ال sequence of partitions هذه هي
+
+742
+01:03:45,890 --> 01:03:50,010
+اللي هتخدمني هتخدمني متى؟ بعد شوية بتشوفوا ليش
+
+743
+01:03:50,010 --> 01:03:54,110
+هتخدمني لكل الأنات اللي وين ما لإن اللي أكبر من ال
+
+744
+01:03:54,110 --> 01:03:59,370
+B minus A على مين؟ على ال delta اللي لجيتها إذا
+
+745
+01:03:59,370 --> 01:04:04,130
+اللي صارت ال delta بين إيديا إذا بقولك الآن choose
+
+746
+01:04:05,140 --> 01:04:12,320
+N element in N such that ما لها N أكبر من B minus
+
+747
+01:04:12,320 --> 01:04:17,620
+A على مين على دلتا برضه B minus A عشان الحسبان N
+
+748
+01:04:17,620 --> 01:04:21,240
+أكبر من B minus A على مين على دلتا يعني الآن أنا
+
+749
+01:04:21,240 --> 01:04:26,920
+بحكي بحكي عن الأنات اللي بكون أكبر من B minus A
+
+750
+01:04:26,920 --> 01:04:31,460
+على مين على الدلتا اللي لجيتها فوق عندي في اللي هو
+
+751
+01:04:31,460 --> 01:04:37,080
+هذا واحدماشي الحالة الان بتبدأ اكوّن partitions من
+
+752
+01:04:37,080 --> 01:04:42,480
+مين؟ من الأمنات هذه الان بتاخد بيئا اني partitions
+
+753
+01:04:42,480 --> 01:04:47,220
+اني partitions برضه أشماله with equal اللي هي إيش
+
+754
+01:04:47,220 --> 01:04:54,240
+sub intervals يعني X نوت و X واحد لعند X ان يعني
+
+755
+01:04:54,240 --> 01:04:58,540
+طول كل فترة منهم برضه طول .. بتاخد اللي هي كلهم
+
+756
+01:04:58,540 --> 01:05:03,590
+أشمالينمن عند A لعند B يكون ان كل ال sub intervals
+
+757
+01:05:03,590 --> 01:05:08,530
+جت بعض يعني بمعنى أخر هيكون ال XK minus XK minus
+
+758
+01:05:08,530 --> 01:05:12,970
+واحد بيساوي B minus A على N طول كل فترة ايش بيساوي
+
+759
+01:05:12,970 --> 01:05:16,950
+B minus A على عدد الفترات اللي هي N فبكون B minus
+
+760
+01:05:16,950 --> 01:05:21,250
+A عالميا على Nأنا حرّن انهم ألاقي في النهاية
+
+761
+01:05:21,250 --> 01:05:25,630
+sequence of partitions BN limit الـ U B N و F نقص
+
+762
+01:05:25,630 --> 01:05:29,290
+الـ L B N و F بساوي 0 بيكون F is integrable خلصنا
+
+763
+01:05:29,290 --> 01:05:32,950
+أنا قاعد اخترت اللي هي sequence of partitions بناء
+
+764
+01:05:32,950 --> 01:05:36,390
+على الـ Delta اللي لجيتها في ال uniformity و
+
+765
+01:05:36,390 --> 01:05:39,830
+الأنات اللي أكبر منها و حطيت ال partition اللي هو
+
+766
+01:05:39,830 --> 01:05:44,710
+بشكل اللي هو تكون ال subintervals كلها لها نفس
+
+767
+01:05:44,710 --> 01:05:46,230
+الطول طيب
+
+768
+01:05:48,470 --> 01:05:56,170
+الآن زي ما قلت قبل بشوية negation على الفترة xk و
+
+769
+01:05:56,170 --> 01:06:01,710
+minus 1 و xk هذا ال sub interval ال function is
+
+770
+01:06:01,710 --> 01:06:03,550
+continuous عليها لأنها continuous على كل ال
+
+771
+01:06:03,550 --> 01:06:06,970
+interval a و b مدام continuous عليها إذا it
+
+772
+01:06:06,970 --> 01:06:10,310
+attains its maximum and its minimum on this
+
+773
+01:06:10,310 --> 01:06:16,100
+intervalأكيد؟ لقد حد كده قبل مشوية إذن بما أن الـ
+
+774
+01:06:16,100 --> 01:06:18,480
+F is continuously not closed bound in الـ interval
+
+775
+01:06:18,480 --> 01:06:26,800
+هذه إذن there exist سميها U K و V K element in X K
+
+776
+01:06:26,800 --> 01:06:33,720
+minus واحد و X K such that F of U K هي ال maximum
+
+777
+01:06:33,720 --> 01:06:41,190
+على كل هذه ال maximum معناته هي ال supremum of Kأو
+
+778
+01:06:41,190 --> 01:06:47,110
+أيضًا عند الـ VK F of VK هي الـ Minimum على هذه
+
+779
+01:06:47,110 --> 01:06:52,310
+مضمون موجود قلناها هي طبعًا مدامة Minimum على كل
+
+780
+01:06:52,310 --> 01:06:56,150
+الفترة إذًا هي الـ Infimum اللي ببحث عنها اليمين
+
+781
+01:06:56,150 --> 01:07:00,850
+MK على هذه الفترة وها المفتاح أصلا في استخدام الـ
+
+782
+01:07:00,850 --> 01:07:06,120
+Continuity إن ضمن لوجود نقطةعندها ال maximum في
+
+783
+01:07:06,120 --> 01:07:10,540
+هذه المنطقة وضمن اللي وجود نقطة هنا ضمن اللي وجود
+
+784
+01:07:10,540 --> 01:07:13,680
+ال minimum عندها و ال minimum و ال maximum مدام
+
+785
+01:07:13,680 --> 01:07:18,100
+عند نقاط محددة في الفترة هي هتتلاقى و تنقل هي
+
+786
+01:07:18,100 --> 01:07:21,780
+عبارة عن ال supremum و ال infimum على ال sub
+
+787
+01:07:21,780 --> 01:07:29,160
+interval أي سؤال طيب الآن ضال علينا إيش نسوي إن
+
+788
+01:07:29,160 --> 01:07:35,610
+نحسب الحسابات اللي هو نبدأ في حساباتنااللي هو نحسب
+
+789
+01:07:35,610 --> 01:07:44,230
+الـ U و نحسب مين يا جماعة أو نحسب اللي هو ال ال ال
+
+790
+01:07:44,230 --> 01:07:44,930
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+791
+01:07:44,930 --> 01:07:44,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+792
+01:07:44,950 --> 01:07:45,050
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+793
+01:07:45,050 --> 01:07:45,070
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+794
+01:07:45,070 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+795
+01:07:45,130 --> 01:07:53,950
+ال ال الت حسبولي
+
+796
+01:07:54,430 --> 01:07:59,790
+نقص L, P, N و F طبعا أكيد هذا أكبر يساوي سفر حفظنا
+
+797
+01:07:59,790 --> 01:08:04,050
+عن غيره هذا أنه أكبر أو يساوي سفر معروف ضل بدي
+
+798
+01:08:04,050 --> 01:08:08,850
+أحسبهم مع بعض ال summation عبارة عن بساوي
+
+799
+01:08:08,850 --> 01:08:13,610
+summation اللي هو ال M K صارت من ال M K capital
+
+800
+01:08:13,610 --> 01:08:19,950
+اللي هي F of U K صح ولا لأ يا جماعة أه صح و ال U K
+
+801
+01:08:19,950 --> 01:08:26,220
+وين موجودة في هذهالان في مين؟ في xk minus xk minus
+
+802
+01:08:26,220 --> 01:08:31,520
+واحد xk minus xk minus واحد كامل عند واحد اللي
+
+803
+01:08:31,520 --> 01:08:37,020
+عندها انهدمين هي الـ U الان زيها مين ال L ناقص
+
+804
+01:08:37,020 --> 01:08:42,600
+summation الان مين عند ال MK small ال F of VK ال
+
+805
+01:08:42,600 --> 01:08:48,920
+VK اللي لاجيناها برضه هان اللي هي F of VKمضروبة في
+
+806
+01:08:48,920 --> 01:08:54,380
+طول الفترة xk-xk-1 كامل عند واحد لعند مين يا جماعة
+
+807
+01:08:54,380 --> 01:09:00,000
+لعندنا خدولي الآن xk-xk-1 عامل مشترك وطبعا أنا
+
+808
+01:09:00,000 --> 01:09:03,220
+مفترضها اللي هو وماخدها إلا طول ال intervals أو
+
+809
+01:09:03,220 --> 01:09:07,080
+sub intervals متساوي يعني طول هذه وطول هذه هو
+
+810
+01:09:07,080 --> 01:09:10,600
+عبارة عن b-a على n زي النظرية السابقة ويساوي ال
+
+811
+01:09:10,600 --> 01:09:17,850
+summation لل F of uk ناقص F of vkالكل مضروب في مين
+
+812
+01:09:17,850 --> 01:09:26,030
+يا جماعة في B-A على N N أو K من عند واحد لعند إيش
+
+813
+01:09:26,030 --> 01:09:36,830
+لعند N أي سؤال طيب شوفوا الآن اسمحولي بس هنا أشتغل
+
+814
+01:09:36,830 --> 01:09:39,730
+شوية طيب
+
+815
+01:09:42,370 --> 01:09:47,490
+طولوا روحكم عندنا خلصنا يعني جربنا اذا صار عندي ال
+
+816
+01:09:47,490 --> 01:09:51,870
+U, P, N و F عشان تعرفوا أين رايح أنا هي ال U, P, N
+
+817
+01:09:51,870 --> 01:09:55,550
+و F ناقص ال P, N و F أكبر يساوي الصفر اللي جيته
+
+818
+01:09:55,550 --> 01:10:00,610
+أصغر يساوي المقدار اللي أمامي الان خلوني أطلع حد
+
+819
+01:10:00,610 --> 01:10:06,400
+برا بعد اسمكم هي B- a على n لأنها عبارة عن ثابت في
+
+820
+01:10:06,400 --> 01:10:13,020
+ال summation f of u,k ناقص f of v,k كامنة عند واحد
+
+821
+01:10:13,020 --> 01:10:20,340
+لأنك لاحظوا ما يلي يا جماعة عند ال u,k و ال v,k
+
+822
+01:10:20,340 --> 01:10:27,480
+وين موجودة في ال x,k minus واحد و ال x,k اه مظبوط
+
+823
+01:10:27,480 --> 01:10:32,540
+يعني الآن اللي هي طول
+
+824
+01:10:34,610 --> 01:10:41,150
+طول الفترة طول الفترة xk على جهة دي بس يا شباب
+
+825
+01:10:41,150 --> 01:10:46,850
+ناقص xk minus واحد طول الفترة لإن هاد صارت هي xk
+
+826
+01:10:46,850 --> 01:10:53,480
+minus واحد وهي xk ماشي جوات هنا ال mean ال UKو الـ
+
+827
+01:10:53,480 --> 01:10:56,860
+VK في مكان الماد، التنتين المهم جوا التنتين يعني
+
+828
+01:10:56,860 --> 01:10:59,840
+المسافة بين اللي برا هدول، حتى لو كان التنتين
+
+829
+01:10:59,840 --> 01:11:04,120
+زيهن، بكون أصغر أو يساوي المسافة بين التنتين هدول
+
+830
+01:11:04,120 --> 01:11:11,560
+أصغر أو يساوي المسافة هذه، اللي هو UK ناقص VK،
+
+831
+01:11:11,560 --> 01:11:17,010
+مظبوط؟ آسف، العكس، أكبر شكراسامحونا أكبر اياش أو
+
+832
+01:11:17,010 --> 01:11:21,310
+يساوي صارت المسافة بين الجهتين هدولة أكيد أصغر
+
+833
+01:11:21,310 --> 01:11:24,970
+أشهر من المسافة الكلية اللي هنا بينهم طيب المسافة
+
+834
+01:11:24,970 --> 01:11:28,890
+بين هذه وهذه احنا ماخدينها أصلا طول ال interval
+
+835
+01:11:28,890 --> 01:11:29,670
+ايش بتساوي
+
+836
+01:11:33,030 --> 01:11:39,710
+على N إذا المسافة هذه أصلا عبارة عن B-A عالمين على
+
+837
+01:11:39,710 --> 01:11:43,890
+N سامحوني أني بنكتبها هنا إذا صار عندي اللي هو ال
+
+838
+01:11:43,890 --> 01:11:50,230
+U K ناقص ال V K أصغر أو يساوي B-A عالمين على N إذا
+
+839
+01:11:50,230 --> 01:11:58,530
+يا شباب راحظولي هنا U K ناقص V K صارت أصغر أو
+
+840
+01:11:58,530 --> 01:12:06,440
+يساوي B-A عالمينعلى n واضحة طيب نشوف ايش معناه هذا
+
+841
+01:12:06,440 --> 01:12:08,700
+الكلام واش اللي بتقوله ليش بتقولنا هذا الكلام
+
+842
+01:12:08,700 --> 01:12:13,620
+بقوله عشان كلام مهم هذا هو شوفوا فهميته انا مختار
+
+843
+01:12:13,620 --> 01:12:19,260
+ال n اكبر من مين من b minus a على delta يعني بمعنى
+
+844
+01:12:19,260 --> 01:12:24,280
+اخر ايش معنات هذا يعني b minus a على n اصغر من مين
+
+845
+01:12:24,280 --> 01:12:29,640
+من دلتا يعني هذا المقدارأصغر من إيش يا جماعة؟ من
+
+846
+01:12:29,640 --> 01:12:35,160
+دلتا صارت ال U K ناقص ال V K أصغر من مين؟ من دلتا
+
+847
+01:12:35,160 --> 01:12:40,800
+واحنا بنقول أن المقاطع اللي بتحقق فيها ال U ناقص V
+
+848
+01:12:40,800 --> 01:12:44,560
+أصغر من دلتا بكون عندي F of U ناقص F of V أصغر من
+
+849
+01:12:44,560 --> 01:12:50,240
+مين يا جماعة؟ من Epsilon على B minus A إذا صارت
+
+850
+01:12:50,240 --> 01:12:55,100
+عندي المقاطين هذولة ال U K ناقص V K اللي أصغر من
+
+851
+01:12:55,100 --> 01:13:04,770
+دلتاإذا أكيد من واحد هيكون عندي F of U K ناقص F of
+
+852
+01:13:04,770 --> 01:13:12,670
+V K إيش هيكون؟ هيكون عبارة عن أصغر من Y على B
+
+853
+01:13:12,670 --> 01:13:20,410
+minus A إذا الآن بحجلني أني أقول أن هذا المقدار
+
+854
+01:13:20,410 --> 01:13:24,400
+اللي عندياللي هو طبعا هذا الكبير وهذا الصغير طبعا
+
+855
+01:13:24,400 --> 01:13:27,800
+على absolute value نفسه بحجل إن أقول هذا أصغر أو
+
+856
+01:13:27,800 --> 01:13:34,680
+ساوي B minus A على N مضروب في مين في ال summation
+
+857
+01:13:34,680 --> 01:13:42,480
+لل Epsilon على B minus A كامن عند واحد لعند مين
+
+858
+01:13:42,480 --> 01:13:50,100
+لعند N واضح
+
+859
+01:13:52,720 --> 01:13:58,440
+إذا صار عندى الآن اللى هو اللى أثبته أنه U P N و F
+
+860
+01:13:58,440 --> 01:14:04,220
+ناطق سؤال P N و F أصغر أو ساوى P minus A على N في
+
+861
+01:14:04,220 --> 01:14:10,300
+.. خلّيني أجف و أقولها .. أه .. انتظر .. أعملنى ..
+
+862
+01:14:13,410 --> 01:14:18,250
+إذا اللي وصلنا له يا جماعة اللي هو أن ال U P N و F
+
+863
+01:14:18,250 --> 01:14:21,650
+نقص ال P N و F أكبر يساوي سفر و في نفس الوقت أصغر
+
+864
+01:14:21,650 --> 01:14:24,430
+يساوي P Minus A على N في ال summation لل Epsilon ع
+
+865
+01:14:24,430 --> 01:14:28,630
+P Minus A اللي هو كامن عند واحد ل N يعني هذه قاعدة
+
+866
+01:14:28,630 --> 01:14:34,050
+عمالها كل مرة بتعد Epsilon ع P Minus A أكم مرة
+
+867
+01:14:34,050 --> 01:14:37,670
+بتعد N من المرات إذا حيصير عندي هذا عبارة عن P
+
+868
+01:14:37,670 --> 01:14:43,170
+Minus A على N و اللي نعد هناN من القمية اللي هذه
+
+869
+01:14:43,170 --> 01:14:47,630
+يعني N في epsilon على B minus A الان B minus A مع
+
+870
+01:14:47,630 --> 01:14:51,970
+ال B minus A و ال N مع ال N فبصير أوصلنا احنا إلى
+
+871
+01:14:51,970 --> 01:14:55,950
+ما يلي انتبهوا للنتيجة النهائية اللي بتوصلي لي
+
+872
+01:14:55,950 --> 01:15:04,310
+اللي هو المطلوب النتيجة اللي وصلت لها انه اذاU P N
+
+873
+01:15:04,310 --> 01:15:12,430
+و F نقص L P N و F أكبر أو يساوي سفر وأصغر من مين
+
+874
+01:15:12,430 --> 01:15:19,190
+من إبسلون لكل إبسلون أكبر من سفر إذا اللي جوا غصب
+
+875
+01:15:19,190 --> 01:15:24,310
+عنه إذا لازم يكون اللي هو لو أخدت ال limit هيظل
+
+876
+01:15:24,310 --> 01:15:30,220
+limit ال Uبن لأن هذا أصلا صحيح علميا للأنات
+
+877
+01:15:30,220 --> 01:15:34,200
+الكبيرة فلما أخد ال limit أزنه جوزه infinity بضل
+
+878
+01:15:34,200 --> 01:15:38,280
+في ال safe side يعني بضل في اللي بتحقق فيه هذا إذا
+
+879
+01:15:38,280 --> 01:15:45,630
+ال limit U, B, N و F ماقص L, B, N و Fهيكون أكبر أو
+
+880
+01:15:45,630 --> 01:15:50,490
+يساوي سفر و أصغر أو يساوي إبسلون و هذا الكلام as
+
+881
+01:15:50,490 --> 01:15:53,530
+and goes to infinity و هذا الكلام صحيح برضه لمين
+
+882
+01:15:53,530 --> 01:15:58,790
+لكل إبسلون أكبر من سفر إذا غصب عنها هيكون اللي جوا
+
+883
+01:15:58,790 --> 01:16:08,780
+limit UPN و F-Lبان و اف لازم يساوي ايش سفر از انقص
+
+884
+01:16:08,780 --> 01:16:14,780
+انفينيتي وهذا by corollary اللي قبل بشوية هيعني ان
+
+885
+01:16:14,780 --> 01:16:23,310
+اف is integrableHence, F is integrable وهكذا
+
+886
+01:16:23,310 --> 01:16:27,610
+أثبتنا العائلة الثانية من الدوال الـ continuous
+
+887
+01:16:27,610 --> 01:16:31,170
+function على closed bounded interval is a
+
+888
+01:16:31,170 --> 01:16:34,210
+continuous function is an integrable function
+
+889
+01:16:34,210 --> 01:16:40,790
+وهكذا خلصنا الـ section الأول و الـ homework هيا
+
+890
+01:16:40,790 --> 01:16:46,750
+اللي موجودة في التلخيص و المرة القادمة ان شاء الله
+
+891
+01:16:47,630 --> 01:16:57,970
+إن شاء الله بكون احنا بنبدأ في اللي هي ال section
+
+892
+01:16:57,970 --> 01:17:03,510
+اللي بعده اللي هو properties of the Riemann
+
+893
+01:17:03,510 --> 01:17:04,470
+Integral
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f417a739af19a6a40a72d5a3a13b8e122386dbda
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3361, "start": 4.72, "end": 33.62, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 11 في مساق تحليل حقيقي 2 لطلاب وطالبات الجامعة الإسلامية كلية العلوم وهي المحاضرة الأولى بعد إعلان الطوارئ بخصوص أو بمواجهة فيروس كورونا المنتشر اتحدتنا المرة الماضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 2975, 8978, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11331, 38436, 38436, 568, 5296, 9566, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 9122, 20292, 3660, 18863, 1211, 20498, 37037, 1829, 9673, 5016, 46958, 25720, 16247, 12610, 7578, 39182, 11933, 30241, 7649, 41950, 2407, 9640, 19986, 4724, 9778, 9381, 2407, 9381, 34051, 4724, 2304, 2407, 26108, 3224, 3660, 8978, 32887, 3794, 9122, 13063, 2407, 8315, 9673, 29399, 46309, 1975, 2655, 24401, 2655, 8315, 9673, 25720, 9673, 46958, 10632], "avg_logprob": -0.07702517986876294, 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"word": " X", "probability": 0.9716796875}, {"start": 86.44, "end": 86.96, "word": " وال", "probability": 0.60400390625}, {"start": 86.96, "end": 87.3, "word": " X", "probability": 0.55908203125}, {"start": 87.3, "end": 87.64, "word": " على", "probability": 0.75048828125}, {"start": 87.64, "end": 87.98, "word": " اللي", "probability": 0.981689453125}, {"start": 87.98, "end": 88.14, "word": " هي", "probability": 0.83642578125}, {"start": 88.14, "end": 88.28, "word": " في", "probability": 0.72265625}, {"start": 88.28, "end": 88.78, "word": " الفترة", "probability": 0.9890950520833334}, {"start": 88.78, "end": 89.86, "word": " المذكورة", "probability": 0.99111328125}, {"start": 89.86, "end": 90.42, "word": " اللي", "probability": 0.986083984375}, {"start": 90.42, "end": 90.76, "word": " عندي", "probability": 0.7822265625}], "temperature": 1.0}, {"id": 5, "seek": 11595, "start": 91.05, "end": 115.95, "text": "الآن أخدنا أول لمّة المرة الماضية وقلنا إذا كانت F من I لR bounded و B any partition of I بدي يكون ال lower اللي هو sum لأي partition B و function F أصغر أو يساوي ال upper sum لنفس ال partition و لنفس اللي هي ال function F بعد هي طبعا خطينا خطوة أخرى", "tokens": [6027, 148, 48506, 5551, 9778, 3215, 8315, 5551, 12610, 32767, 11703, 3660, 9673, 25720, 9673, 46958, 10632, 4032, 4587, 1211, 8315, 11933, 15730, 25961, 2655, 479, 9154, 286, 5296, 49, 37498, 4032, 363, 604, 24808, 295, 286, 4724, 16254, 7251, 30544, 2423, 3126, 13672, 1829, 31439, 2408, 5296, 10721, 1829, 24808, 363, 4032, 2445, 479, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2423, 6597, 2408, 5296, 1863, 36178, 2423, 24808, 4032, 5296, 1863, 36178, 13672, 1829, 39896, 2423, 2445, 479, 39182, 39896, 23032, 3555, 3615, 995, 16490, 9566, 1829, 8315, 16490, 9566, 2407, 3660, 5551, 34740, 7578], "avg_logprob": -0.2101562462747097, "compression_ratio": 1.6457399103139014, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 91.05, "end": 91.61, "word": "الآن", "probability": 0.6083984375}, {"start": 91.61, "end": 92.15, "word": " أخدنا", "probability": 0.881103515625}, {"start": 92.15, "end": 92.49, "word": " أول", "probability": 0.976318359375}, {"start": 92.49, "end": 93.09, "word": " لمّة", "probability": 0.71630859375}, {"start": 93.09, "end": 94.11, "word": " المرة", "probability": 0.947021484375}, {"start": 94.11, "end": 94.75, "word": " الماضية", "probability": 0.9939778645833334}, {"start": 94.75, "end": 95.27, "word": " وقلنا", "probability": 0.8489990234375}, {"start": 95.27, "end": 95.45, "word": " إذا", "probability": 0.893798828125}, {"start": 95.45, "end": 95.77, "word": " كانت", "probability": 0.8896484375}, {"start": 95.77, "end": 95.93, "word": " F", "probability": 0.477783203125}, {"start": 95.93, "end": 96.07, "word": " من", "probability": 0.95947265625}, {"start": 96.07, "end": 96.25, "word": " I", "probability": 0.97705078125}, {"start": 96.25, "end": 96.57, "word": " لR", "probability": 0.6402587890625}, {"start": 96.57, "end": 97.17, "word": " bounded", "probability": 0.71826171875}, {"start": 97.17, "end": 97.65, "word": " و", "probability": 0.76025390625}, {"start": 97.65, "end": 97.85, "word": " B", "probability": 0.19482421875}, {"start": 97.85, "end": 98.19, "word": " any", "probability": 0.52490234375}, {"start": 98.19, "end": 98.63, "word": " partition", "probability": 0.9208984375}, {"start": 98.63, "end": 98.93, "word": " of", "probability": 0.97119140625}, {"start": 98.93, "end": 99.27, "word": " I", "probability": 0.98876953125}, {"start": 99.27, "end": 99.55, "word": " بدي", "probability": 0.5367431640625}, {"start": 99.55, "end": 99.87, "word": " يكون", "probability": 0.6761474609375}, {"start": 99.87, "end": 100.15, "word": " ال", "probability": 0.93359375}, {"start": 100.15, "end": 100.65, "word": " lower", "probability": 0.6025390625}, {"start": 100.65, "end": 101.31, "word": " اللي", "probability": 0.854248046875}, {"start": 101.31, "end": 101.59, "word": " هو", "probability": 0.98046875}, {"start": 101.59, "end": 102.05, "word": " sum", "probability": 0.81689453125}, {"start": 102.05, "end": 103.23, "word": " لأي", "probability": 0.8489583333333334}, {"start": 103.23, "end": 104.33, "word": " partition", "probability": 0.6484375}, {"start": 104.33, "end": 104.95, "word": " B", "probability": 0.70166015625}, {"start": 104.95, "end": 105.31, "word": " و", "probability": 0.9833984375}, {"start": 105.31, "end": 105.75, "word": " function", "probability": 0.490234375}, {"start": 105.75, "end": 106.31, "word": " F", "probability": 0.97509765625}, {"start": 106.31, "end": 107.07, "word": " أصغر", "probability": 0.9805908203125}, {"start": 107.07, "end": 107.19, "word": " أو", "probability": 0.869140625}, {"start": 107.19, "end": 107.47, "word": " يساوي", "probability": 0.6431884765625}, {"start": 107.47, "end": 107.59, "word": " ال", "probability": 0.8681640625}, {"start": 107.59, "end": 107.81, "word": " upper", "probability": 0.59716796875}, {"start": 107.81, "end": 108.19, "word": " sum", "probability": 0.921875}, {"start": 108.19, "end": 108.69, "word": " لنفس", "probability": 0.9850260416666666}, {"start": 108.69, "end": 108.83, "word": " ال", "probability": 0.9609375}, {"start": 108.83, "end": 109.29, "word": " partition", "probability": 0.87548828125}, {"start": 109.29, "end": 109.99, "word": " و", "probability": 0.83935546875}, {"start": 109.99, "end": 110.53, "word": " لنفس", "probability": 0.9345703125}, {"start": 110.53, "end": 110.79, "word": " اللي", "probability": 0.7308349609375}, {"start": 110.79, "end": 111.19, "word": " هي", "probability": 0.93408203125}, {"start": 111.19, "end": 111.45, "word": " ال", "probability": 0.943359375}, {"start": 111.45, "end": 111.85, "word": " function", "probability": 0.95654296875}, {"start": 111.85, "end": 112.47, "word": " F", "probability": 0.9755859375}, {"start": 112.47, "end": 113.35, "word": " بعد", "probability": 0.9033203125}, {"start": 113.35, "end": 113.57, "word": " هي", "probability": 0.95556640625}, {"start": 113.57, "end": 114.03, "word": " طبعا", "probability": 0.8714599609375}, {"start": 114.03, "end": 115.03, "word": " خطينا", "probability": 0.894287109375}, {"start": 115.03, "end": 115.43, "word": " خطوة", "probability": 0.991455078125}, {"start": 115.43, "end": 115.95, "word": " أخرى", "probability": 0.9890950520833334}], "temperature": 1.0}, {"id": 6, "seek": 13141, "start": 116.45, "end": 131.41, "text": "و جينا عرفنا اللي هو شو معناته انها تكون اللي هو ال partition Q refinement لل partition B قلنا Q اللي هو تحسين ل B إذا كانت B بي عبارة عن مجموعة جزئية من Q", "tokens": [2407, 10874, 1829, 8315, 6225, 28480, 8315, 13672, 1829, 31439, 13412, 2407, 20449, 8315, 47395, 16472, 11296, 6055, 30544, 13672, 1829, 31439, 2423, 24808, 1249, 1895, 30229, 24976, 24808, 363, 12174, 1211, 8315, 1249, 13672, 1829, 31439, 6055, 5016, 3794, 9957, 5296, 363, 11933, 15730, 25961, 2655, 363, 4724, 1829, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 2407, 27884, 10874, 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"word": " هو", "probability": 0.9638671875}, {"start": 120.89, "end": 121.31, "word": " ال", "probability": 0.6318359375}, {"start": 121.31, "end": 121.89, "word": " partition", "probability": 0.386474609375}, {"start": 121.89, "end": 122.35, "word": " Q", "probability": 0.1663818359375}, {"start": 122.35, "end": 123.11, "word": " refinement", "probability": 0.63232421875}, {"start": 123.11, "end": 123.39, "word": " لل", "probability": 0.720703125}, {"start": 123.39, "end": 123.85, "word": " partition", "probability": 0.70263671875}, {"start": 123.85, "end": 124.21, "word": " B", "probability": 0.8115234375}, {"start": 124.21, "end": 125.07, "word": " قلنا", "probability": 0.7986653645833334}, {"start": 125.07, "end": 125.51, "word": " Q", "probability": 0.373046875}, {"start": 125.51, "end": 125.81, "word": " اللي", "probability": 0.96044921875}, {"start": 125.81, "end": 125.95, "word": " هو", "probability": 0.96240234375}, {"start": 125.95, "end": 126.55, "word": " تحسين", "probability": 0.9896240234375}, {"start": 126.55, "end": 126.73, "word": " ل", "probability": 0.84423828125}, {"start": 126.73, "end": 127.01, "word": " B", "probability": 0.5771484375}, {"start": 127.01, "end": 127.85, "word": " إذا", "probability": 0.8515625}, {"start": 127.85, "end": 128.31, "word": " كانت", "probability": 0.9716796875}, {"start": 128.31, "end": 128.61, "word": " B", "probability": 0.7841796875}, {"start": 128.61, "end": 128.93, "word": " بي", "probability": 0.631591796875}, {"start": 128.93, "end": 129.35, "word": " عبارة", "probability": 0.9488525390625}, {"start": 129.35, "end": 129.49, "word": " عن", "probability": 0.98876953125}, {"start": 129.49, "end": 130.01, "word": " مجموعة", "probability": 0.96728515625}, {"start": 130.01, "end": 130.67, "word": " جزئية", "probability": 0.9501953125}, {"start": 130.67, "end": 131.13, "word": " من", "probability": 0.99267578125}, {"start": 131.13, "end": 131.41, "word": " Q", "probability": 0.806640625}], "temperature": 1.0}, {"id": 7, "seek": 14768, "start": 131.66, "end": 147.68, "text": "و بناء عليه اللي هو قلنا ان اي اللي هو sub interval xk-1xk من ال partition B يمكن كتابتها على صورة union of sub intervals من اللي هو التحسين اللي هو EQ", "tokens": [2407, 44945, 16606, 47356, 13672, 1829, 31439, 12174, 1211, 8315, 16472, 1975, 1829, 13672, 1829, 31439, 1422, 15035, 2031, 74, 12, 16, 87, 74, 9154, 2423, 24808, 363, 7251, 43020, 9122, 2655, 16758, 2655, 11296, 15844, 20328, 13063, 3660, 11671, 295, 1422, 26651, 9154, 13672, 1829, 31439, 16712, 5016, 3794, 9957, 13672, 1829, 31439, 33580], "avg_logprob": -0.23353794323546545, "compression_ratio": 1.457516339869281, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 131.66, "end": 132.0, "word": "و", "probability": 0.54638671875}, {"start": 132.0, "end": 132.4, "word": " بناء", "probability": 0.884521484375}, {"start": 132.4, "end": 132.98, "word": " عليه", "probability": 0.479248046875}, {"start": 132.98, "end": 133.82, "word": " اللي", "probability": 0.8271484375}, {"start": 133.82, "end": 133.94, "word": " هو", "probability": 0.8984375}, {"start": 133.94, "end": 134.32, "word": " قلنا", "probability": 0.8639322916666666}, {"start": 134.32, "end": 134.52, "word": " ان", "probability": 0.41845703125}, {"start": 134.52, "end": 135.08, "word": " اي", "probability": 0.6907958984375}, {"start": 135.08, "end": 135.4, "word": " اللي", "probability": 0.85595703125}, {"start": 135.4, "end": 135.68, "word": " هو", "probability": 0.96044921875}, {"start": 135.68, "end": 136.18, "word": " sub", "probability": 0.9130859375}, {"start": 136.18, "end": 136.98, "word": " interval", "probability": 0.60400390625}, {"start": 136.98, "end": 137.88, "word": " xk", "probability": 0.4771728515625}, {"start": 137.88, "end": 139.18, "word": "-1xk", "probability": 0.644805908203125}, {"start": 139.18, "end": 139.3, "word": " من", "probability": 0.94970703125}, {"start": 139.3, "end": 139.44, "word": " ال", "probability": 0.86572265625}, {"start": 139.44, "end": 139.86, "word": " partition", "probability": 0.5791015625}, {"start": 139.86, "end": 140.34, "word": " B", "probability": 0.59423828125}, {"start": 140.34, "end": 141.14, "word": " يمكن", "probability": 0.968017578125}, {"start": 141.14, "end": 141.7, "word": " كتابتها", "probability": 0.96669921875}, {"start": 141.7, "end": 141.9, "word": " على", "probability": 0.9033203125}, {"start": 141.9, "end": 142.3, "word": " صورة", "probability": 0.9835611979166666}, {"start": 142.3, "end": 142.74, "word": " union", "probability": 0.5654296875}, {"start": 142.74, "end": 143.22, "word": " of", "probability": 0.96240234375}, {"start": 143.22, "end": 143.52, "word": " sub", "probability": 0.9697265625}, {"start": 143.52, "end": 144.2, "word": " intervals", "probability": 0.81640625}, {"start": 144.2, "end": 144.48, "word": " من", "probability": 0.90283203125}, {"start": 144.48, "end": 145.08, "word": " اللي", "probability": 0.7861328125}, {"start": 145.08, "end": 145.58, "word": " هو", "probability": 0.86865234375}, {"start": 145.58, "end": 146.64, "word": " التحسين", "probability": 0.9815673828125}, {"start": 146.64, "end": 146.92, "word": " اللي", "probability": 0.76708984375}, {"start": 146.92, "end": 147.32, "word": " هو", "probability": 0.97900390625}, {"start": 147.32, "end": 147.68, "word": " EQ", "probability": 0.1844482421875}], "temperature": 1.0}, {"id": 8, "seek": 16410, "start": 151.06, "end": 164.1, "text": "الان جينا اللي هو بناء على هذا التعريف جينا قولنا لو كانت F is من I لعند R is bounded و B is any partition of I و Q refinement لل B", "tokens": [6027, 7649, 10874, 1829, 8315, 13672, 1829, 31439, 44945, 16606, 15844, 23758, 16712, 3615, 16572, 5172, 10874, 1829, 8315, 12174, 12610, 8315, 45164, 25961, 2655, 479, 307, 9154, 286, 5296, 3615, 41260, 497, 307, 37498, 4032, 363, 307, 604, 24808, 295, 286, 4032, 1249, 1895, 30229, 24976, 363], "avg_logprob": -0.2375637706445188, "compression_ratio": 1.2466666666666666, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 151.06, "end": 151.6, "word": "الان", "probability": 0.746826171875}, {"start": 151.6, "end": 152.12, "word": " جينا", "probability": 0.7722981770833334}, {"start": 152.12, "end": 152.44, "word": " اللي", "probability": 0.791015625}, {"start": 152.44, "end": 152.7, "word": " هو", "probability": 0.9873046875}, {"start": 152.7, "end": 153.46, "word": " بناء", "probability": 0.880615234375}, {"start": 153.46, "end": 153.78, "word": " على", "probability": 0.72412109375}, {"start": 153.78, "end": 154.54, "word": " هذا", "probability": 0.8056640625}, {"start": 154.54, "end": 155.28, "word": " التعريف", "probability": 0.9935302734375}, {"start": 155.28, "end": 156.02, "word": " جينا", "probability": 0.9347330729166666}, {"start": 156.02, "end": 156.38, "word": " قولنا", "probability": 0.7432454427083334}, {"start": 156.38, "end": 156.54, "word": " لو", "probability": 0.88623046875}, {"start": 156.54, "end": 156.88, "word": " كانت", "probability": 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"start": 421.48, "end": 443.32, "text": "اللي هو أثبتنا إنه اللي هو g of x بيساوي x is integrable on i استنادًا على إنه أوجدنا ال lower sum ال lower integral و ال upper integral أثبتنا إن ال lower integral و ال upper integral are equal و من ثم أثبتنا إنه ال integration exist لل function x على الفترة 0 و 1 وأوجدنا قيمة ال integration في حينه", "tokens": [6027, 20292, 31439, 5551, 12984, 3555, 2655, 8315, 36145, 3224, 13672, 1829, 31439, 290, 295, 2031, 4724, 1829, 3794, 995, 45865, 2031, 307, 16200, 424, 638, 322, 741, 44713, 8315, 3215, 14111, 995, 15844, 36145, 3224, 5551, 29245, 3215, 8315, 2423, 3126, 2408, 2423, 3126, 11573, 4032, 2423, 6597, 11573, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 3126, 11573, 4032, 2423, 6597, 11573, 366, 2681, 4032, 9154, 38637, 2304, 5551, 12984, 3555, 2655, 8315, 36145, 3224, 2423, 10980, 2514, 24976, 2445, 2031, 15844, 27188, 2655, 25720, 1958, 4032, 502, 36725, 29245, 3215, 8315, 12174, 32640, 3660, 2423, 10980, 8978, 11331, 9957, 3224], 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F من I اللي هي 01 لعند ال .. ال R be defined by أخدنا الدالة كما يلي اللي هو قولنا أن F of X F of X بساوي واحد", "tokens": [2407, 36520, 8315, 30731, 13672, 1829, 31439, 50113, 6027, 8315, 16712, 6027, 1829, 14739, 3224, 45164, 25961, 2655, 479, 9154, 286, 5296, 3615, 41260, 4386, 479, 9154, 286, 13672, 1829, 39896, 23185, 5296, 3615, 41260, 2423, 4386, 2423, 497, 312, 7642, 538, 5551, 9778, 3215, 8315, 32748, 6027, 3660, 9122, 15042, 7251, 20292, 13672, 1829, 31439, 12174, 12610, 8315, 14739, 479, 295, 1783, 479, 295, 1783, 4724, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.20783389757757317, "compression_ratio": 1.6158536585365855, "no_speech_prob": 5.185604095458984e-06, "words": [{"start": 444.9100000000001, "end": 445.69000000000005, "word": "وصلنا", "probability": 0.8396809895833334}, {"start": 445.69000000000005, "end": 446.47, "word": " إلى", "probability": 0.491455078125}, {"start": 446.47, "end": 446.81, "word": " اللي", "probability": 0.766845703125}, {"start": 446.81, 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"probability": 0.99072265625}, {"start": 452.85, "end": 453.29, "word": " I", "probability": 0.9853515625}, {"start": 453.29, "end": 454.27, "word": " اللي", "probability": 0.94580078125}, {"start": 454.27, "end": 454.45, "word": " هي", "probability": 0.955078125}, {"start": 454.45, "end": 454.87, "word": " 01", "probability": 0.2744140625}, {"start": 454.87, "end": 456.75, "word": " لعند", "probability": 0.9521484375}, {"start": 456.75, "end": 457.13, "word": " ال", "probability": 0.97119140625}, {"start": 457.13, "end": 457.35, "word": " ..", "probability": 0.5380859375}, {"start": 457.35, "end": 457.61, "word": " ال", "probability": 0.9599609375}, {"start": 457.61, "end": 457.93, "word": " R", "probability": 0.79296875}, {"start": 457.93, "end": 458.25, "word": " be", "probability": 0.11431884765625}, {"start": 458.25, "end": 458.81, "word": " defined", "probability": 0.9091796875}, {"start": 458.81, "end": 459.13, "word": " by", "probability": 0.96240234375}, {"start": 459.13, "end": 460.09, "word": " أخدنا", "probability": 0.939453125}, {"start": 460.09, "end": 460.77, "word": " الدالة", "probability": 0.98681640625}, {"start": 460.77, "end": 461.39, "word": " كما", "probability": 0.945068359375}, {"start": 461.39, "end": 461.73, "word": " يلي", "probability": 0.845703125}, {"start": 461.73, "end": 462.55, "word": " اللي", "probability": 0.806640625}, {"start": 462.55, "end": 462.67, "word": " هو", "probability": 0.98974609375}, {"start": 462.67, "end": 463.09, "word": " قولنا", "probability": 0.8362630208333334}, {"start": 463.09, "end": 463.29, "word": " أن", "probability": 0.74072265625}, {"start": 463.29, "end": 463.51, "word": " F", "probability": 0.88623046875}, {"start": 463.51, "end": 463.69, "word": " of", "probability": 0.8701171875}, {"start": 463.69, "end": 464.11, "word": " X", "probability": 0.984375}, {"start": 464.11, "end": 465.41, "word": " F", "probability": 0.67919921875}, {"start": 465.41, "end": 465.59, "word": " of", "probability": 0.970703125}, {"start": 465.59, "end": 465.99, "word": " X", "probability": 0.99462890625}, {"start": 465.99, "end": 467.23, "word": " بساوي", "probability": 0.8560791015625}, {"start": 467.23, "end": 469.25, "word": " واحد", "probability": 0.830810546875}], "temperature": 1.0}, {"id": 23, "seek": 48876, "start": 469.9, "end": 488.76, "text": "إذا كانت x rational number element in Q وبساوي 0 إذا كانت x element in IQ أو element in Q complement اللي هي ال rational numbers الآن بدنا نثبت بقول show that this function F", "tokens": [28814, 15730, 25961, 2655, 2031, 15090, 1230, 4478, 294, 1249, 4032, 3555, 3794, 995, 45865, 1958, 11933, 15730, 25961, 2655, 2031, 4478, 294, 28921, 34051, 4478, 294, 1249, 17103, 13672, 1829, 39896, 2423, 15090, 3547, 6024, 48506, 47525, 8315, 8717, 12984, 3555, 2655, 4724, 39648, 855, 300, 341, 2445, 479], "avg_logprob": -0.3014705929101682, "compression_ratio": 1.4569536423841059, "no_speech_prob": 1.5020370483398438e-05, "words": [{"start": 469.9, "end": 470.2, "word": "إذا", "probability": 0.7236328125}, {"start": 470.2, "end": 470.64, "word": " كانت", "probability": 0.944580078125}, {"start": 470.64, "end": 470.9, "word": " x", "probability": 0.339111328125}, {"start": 470.9, "end": 471.52, "word": " rational", "probability": 0.10888671875}, {"start": 471.52, "end": 472.14, "word": " number", "probability": 0.96435546875}, {"start": 472.14, "end": 472.46, "word": " element", "probability": 0.5439453125}, {"start": 472.46, "end": 472.72, "word": " in", "probability": 0.94921875}, {"start": 472.72, "end": 473.04, "word": " Q", "probability": 0.51611328125}, {"start": 473.04, "end": 474.36, "word": " وبساوي", "probability": 0.661962890625}, {"start": 474.36, "end": 475.08, "word": " 0", "probability": 0.626953125}, {"start": 475.08, "end": 475.82, "word": " إذا", "probability": 0.94482421875}, {"start": 475.82, "end": 476.26, "word": " كانت", "probability": 0.97900390625}, {"start": 476.26, "end": 476.54, "word": " x", "probability": 0.81640625}, {"start": 476.54, "end": 477.06, "word": " element", "probability": 0.8740234375}, {"start": 477.06, "end": 477.32, "word": " in", "probability": 0.92236328125}, {"start": 477.32, "end": 477.82, "word": " IQ", "probability": 0.80029296875}, {"start": 477.82, "end": 478.36, "word": " أو", "probability": 0.865234375}, {"start": 478.36, "end": 479.1, "word": " element", "probability": 0.91259765625}, {"start": 479.1, "end": 479.5, "word": " in", "probability": 0.9560546875}, {"start": 479.5, "end": 480.1, "word": " Q", "probability": 0.94970703125}, {"start": 480.1, "end": 480.64, "word": " complement", "probability": 0.544921875}, {"start": 480.64, "end": 480.88, "word": " اللي", "probability": 0.86669921875}, {"start": 480.88, "end": 481.1, "word": " هي", "probability": 0.94775390625}, {"start": 481.1, "end": 481.28, "word": " ال", "probability": 0.8857421875}, {"start": 481.28, "end": 481.6, "word": " rational", "probability": 0.521484375}, {"start": 481.6, "end": 482.52, "word": " numbers", "probability": 0.39794921875}, {"start": 482.52, "end": 483.76, "word": " الآن", "probability": 0.6888427734375}, {"start": 483.76, "end": 484.66, "word": " بدنا", "probability": 0.756103515625}, {"start": 484.66, "end": 485.14, "word": " نثبت", "probability": 0.9949951171875}, {"start": 485.14, "end": 485.46, "word": " بقول", "probability": 0.670654296875}, {"start": 485.46, "end": 485.7, "word": " show", "probability": 0.75634765625}, {"start": 485.7, "end": 486.26, "word": " that", "probability": 0.9375}, {"start": 486.26, "end": 487.06, "word": " this", "probability": 0.94677734375}, {"start": 487.06, "end": 487.72, "word": " function", "probability": 0.96630859375}, {"start": 487.72, "end": 488.76, "word": " F", "probability": 0.5966796875}], "temperature": 1.0}, {"id": 24, "seek": 50516, "start": 490.3, "end": 505.16, "text": "طبعا أنا method F على اللي هي الـ Q تقاطع طبعا الـ 0 و 1 اللي هي الـ interval اللي بدأ عليها التقاطع الـ 0 و 1 بمعنى إن دالت F صارت من I اللي هي عبارة عن 0 و 1", "tokens": [9566, 3555, 3615, 995, 41850, 3170, 479, 15844, 13672, 1829, 39896, 2423, 39184, 1249, 6055, 4587, 41193, 3615, 23032, 3555, 3615, 995, 2423, 39184, 1958, 4032, 502, 13672, 1829, 39896, 2423, 39184, 15035, 13672, 1829, 47525, 10721, 25894, 11296, 16712, 4587, 41193, 3615, 2423, 39184, 1958, 4032, 502, 4724, 2304, 3615, 1863, 7578, 36145, 11778, 6027, 2655, 479, 20328, 9640, 2655, 9154, 286, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 1958, 4032, 502], "avg_logprob": -0.22541667381922403, "compression_ratio": 1.6601307189542485, "no_speech_prob": 1.5139579772949219e-05, "words": [{"start": 490.3, "end": 490.68, "word": "طبعا", "probability": 0.8153076171875}, {"start": 490.68, "end": 490.88, "word": " أنا", "probability": 0.286865234375}, {"start": 490.88, "end": 491.2, "word": " method", "probability": 0.935546875}, {"start": 491.2, "end": 491.56, "word": " F", "probability": 0.65771484375}, {"start": 491.56, "end": 492.48, "word": " على", 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"end": 497.46, "word": " الـ", "probability": 0.7230224609375}, {"start": 497.46, "end": 497.78, "word": " interval", "probability": 0.748046875}, {"start": 497.78, "end": 497.92, "word": " اللي", "probability": 0.971435546875}, {"start": 497.92, "end": 498.12, "word": " بدأ", "probability": 0.4183349609375}, {"start": 498.12, "end": 498.5, "word": " عليها", "probability": 0.98046875}, {"start": 498.5, "end": 499.18, "word": " التقاطع", "probability": 0.78466796875}, {"start": 499.18, "end": 499.32, "word": " الـ", "probability": 0.896484375}, {"start": 499.32, "end": 499.5, "word": " 0", "probability": 0.869140625}, {"start": 499.5, "end": 499.64, "word": " و", "probability": 0.89208984375}, {"start": 499.64, "end": 499.92, "word": " 1", "probability": 0.333251953125}, {"start": 499.92, "end": 500.86, "word": " بمعنى", "probability": 0.97265625}, {"start": 500.86, "end": 501.02, "word": " إن", "probability": 0.39501953125}, {"start": 501.02, "end": 501.58, "word": " دالت", "probability": 0.652099609375}, {"start": 501.58, "end": 501.84, "word": " F", "probability": 0.947265625}, {"start": 501.84, "end": 502.7, "word": " صارت", "probability": 0.9733072916666666}, {"start": 502.7, "end": 503.12, "word": " من", "probability": 0.98876953125}, {"start": 503.12, "end": 503.56, "word": " I", "probability": 0.9638671875}, {"start": 503.56, "end": 503.78, "word": " اللي", "probability": 0.948974609375}, {"start": 503.78, "end": 503.92, "word": " هي", "probability": 0.6162109375}, {"start": 503.92, "end": 504.22, "word": " عبارة", "probability": 0.9930419921875}, {"start": 504.22, "end": 504.4, "word": " عن", "probability": 0.990234375}, {"start": 504.4, "end": 504.7, "word": " 0", "probability": 0.85595703125}, {"start": 504.7, "end": 504.82, "word": " و", "probability": 0.85302734375}, {"start": 504.82, "end": 505.16, "word": " 1", "probability": 0.93994140625}], "temperature": 1.0}, {"id": 25, "seek": 53216, "start": 506.04, "end": 532.16, "text": "اللي عند R واضح ان الدالة هذه is a bounded function الان بدأ أثبت لكم ان هذا الدالة is not integrable on this interval is not integrable on this interval الان علشان أصل اللي هو اللي هي ان هذا الدالة غير قابلة تكامل بالنسبة لتكامل بالنسبة لتكامل الريمان بدي اخد الان B", "tokens": [6027, 20292, 43242, 497, 4032, 46958, 5016, 16472, 32748, 6027, 3660, 29538, 307, 257, 37498, 2445, 2423, 7649, 47525, 10721, 5551, 12984, 3555, 2655, 5296, 24793, 16472, 23758, 32748, 6027, 3660, 307, 406, 16200, 424, 638, 322, 341, 15035, 307, 406, 16200, 424, 638, 322, 341, 15035, 2423, 7649, 11203, 8592, 7649, 5551, 36520, 13672, 1829, 31439, 13672, 1829, 39896, 16472, 23758, 32748, 6027, 3660, 32771, 13546, 12174, 16758, 37977, 6055, 4117, 10943, 1211, 20666, 1863, 35457, 3660, 5296, 2655, 4117, 10943, 1211, 20666, 1863, 35457, 3660, 5296, 2655, 4117, 10943, 1211, 2423, 16572, 2304, 7649, 4724, 16254, 1975, 9778, 3215, 2423, 7649, 363], "avg_logprob": -0.25803570974440804, "compression_ratio": 1.975609756097561, 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"end": 523.86, "word": " هي", "probability": 0.89013671875}, {"start": 523.86, "end": 524.1, "word": " ان", "probability": 0.8271484375}, {"start": 524.1, "end": 524.38, "word": " هذا", "probability": 0.60546875}, {"start": 524.38, "end": 524.76, "word": " الدالة", "probability": 0.9822591145833334}, {"start": 524.76, "end": 525.02, "word": " غير", "probability": 0.988525390625}, {"start": 525.02, "end": 525.56, "word": " قابلة", "probability": 0.9327799479166666}, {"start": 525.56, "end": 526.3, "word": " تكامل", "probability": 0.79241943359375}, {"start": 526.3, "end": 526.9, "word": " بالنسبة", "probability": 0.980224609375}, {"start": 526.9, "end": 527.54, "word": " لتكامل", "probability": 0.8990234375}, {"start": 527.54, "end": 528.18, "word": " بالنسبة", "probability": 0.9180908203125}, {"start": 528.18, "end": 529.18, "word": " لتكامل", "probability": 0.96396484375}, {"start": 529.18, "end": 529.74, "word": " الريمان", "probability": 0.6346435546875}, {"start": 529.74, "end": 530.78, "word": " بدي", "probability": 0.68212890625}, {"start": 530.78, "end": 531.28, "word": " اخد", "probability": 0.7665201822916666}, {"start": 531.28, "end": 531.7, "word": " الان", "probability": 0.765869140625}, {"start": 531.7, "end": 532.16, "word": " B", "probability": 0.326416015625}], "temperature": 1.0}, {"id": 26, "seek": 55680, "start": 532.83, "end": 556.81, "text": "أخدوا أي partition X0 X1 لعند Xn هذا any partition لإيه ال interval اللي هي الفترة مين Zero و واحد يعني بمعنى أتيت للفترة Zero و واحد و جزقتها X0 X1 لعند مؤصل لعند مين لعند Xn اللي هي إيش بتساوي بتساوي واحد", "tokens": [10721, 9778, 3215, 14407, 36632, 24808, 1783, 15, 1783, 16, 5296, 3615, 41260, 1783, 77, 23758, 604, 24808, 5296, 28814, 1829, 3224, 2423, 15035, 13672, 1829, 39896, 27188, 2655, 25720, 3714, 9957, 17182, 4032, 36764, 24401, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 31371, 2655, 24976, 5172, 2655, 25720, 17182, 4032, 36764, 24401, 4032, 10874, 11622, 38149, 11296, 1783, 15, 1783, 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L عندى الان بدى احسب ال L", "tokens": [6027, 7649, 23758, 2423, 24808, 1975, 9778, 3215, 47395, 19071, 3289, 13672, 7578, 31439, 24808, 5296, 5172, 2655, 25720, 441, 43242, 7578, 2423, 7649, 47525, 7578, 1975, 5016, 35457, 2423, 441], "avg_logprob": -0.39892579056322575, "compression_ratio": 1.201834862385321, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 557.35, "end": 557.79, "word": "الان", "probability": 0.759521484375}, {"start": 557.79, "end": 558.51, "word": " هذا", "probability": 0.69677734375}, {"start": 558.51, "end": 558.61, "word": " ال", "probability": 0.78515625}, {"start": 558.61, "end": 558.95, "word": " partition", "probability": 0.357177734375}, {"start": 558.95, "end": 559.55, "word": " اخدته", "probability": 0.7041015625}, {"start": 559.55, "end": 560.31, "word": " arbitrarily", "probability": 0.9189453125}, {"start": 560.31, "end": 561.21, "word": " اللى", "probability": 0.663330078125}, {"start": 561.21, "end": 561.49, "word": " هو", "probability": 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" X", "probability": 0.9580078125}, {"start": 595.93, "end": 596.13, "word": " K", "probability": 0.92919921875}, {"start": 596.13, "end": 596.47, "word": " minus", "probability": 0.91943359375}, {"start": 596.47, "end": 597.07, "word": " واحد", "probability": 0.965576171875}, {"start": 597.07, "end": 597.93, "word": " لعند", "probability": 0.9742838541666666}, {"start": 597.93, "end": 598.43, "word": " X", "probability": 0.99267578125}, {"start": 598.43, "end": 598.99, "word": " K", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 29, "seek": 61759, "start": 599.95, "end": 617.59, "text": "طبعاً اللي هي F of X معرفة على أساسيها يا إما واحد يا إما سفر حسب إنها تكون rational أو إيش ال rational يعني ال function F أصلا اللي هي قيمتين بس إذا الأن ال infimum لل F of X عندها يا هيكون واحد يا هيكون سفر ليش؟ لأن أصلا الفترة هذه", "tokens": [9566, 3555, 3615, 995, 14111, 13672, 1829, 39896, 479, 295, 1783, 20449, 28480, 3660, 15844, 5551, 3794, 32277, 1829, 11296, 35186, 11933, 15042, 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partitions اللي هو B of I هيكون ال .. ال Supremum اللي هين صفر لإن كل اللي هين أصلا إشق بتنطلع .. تنطلع بساوي صفر إذا هذا إيش هيساوي يا شباب؟ هو يساوي Zero", "tokens": [10721, 2407, 2423, 39184, 9141, 2579, 449, 2423, 39184, 9141, 2579, 449, 5296, 28820, 2423, 39184, 441, 295, 363, 4032, 479, 9653, 300, 363, 4478, 294, 264, 992, 295, 439, 644, 2451, 13672, 1829, 31439, 363, 295, 286, 39896, 30544, 2423, 4386, 2423, 9141, 2579, 449, 13672, 1829, 8032, 9957, 20328, 5172, 2288, 5296, 28814, 1863, 28242, 13672, 1829, 8032, 9957, 5551, 9381, 15040, 11933, 8592, 4587, 39894, 1863, 9566, 1211, 3615, 4386, 6055, 1863, 9566, 1211, 3615, 4724, 3794, 995, 45865, 20328, 5172, 2288, 11933, 15730, 23758, 11933, 1829, 8592, 39896, 3794, 995, 45865, 35186, 13412, 3555, 16758, 22807, 31439, 7251, 3794, 995, 45865, 17182], "avg_logprob": -0.271466108126061, "compression_ratio": 1.6893203883495145, "no_speech_prob": 2.9802322387695312e-06, "words": [{"start": 658.53, "end": 659.15, "word": "أو", 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"tokens": [6027, 7649, 8717, 1829, 7435, 1829, 5296, 6027, 20292, 31439, 46691, 3714, 16095, 3660, 13672, 1829, 1975, 5016, 8315, 44945, 38251, 1829, 11296, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 6222, 46691, 337, 16200, 5305, 1140], "avg_logprob": -0.28556742087790843, "compression_ratio": 1.2820512820512822, "no_speech_prob": 0.0, "words": [{"start": 879.0, "end": 879.52, "word": "الان", "probability": 0.708984375}, {"start": 879.52, "end": 880.14, "word": " نيجي", "probability": 0.82025146484375}, {"start": 880.14, "end": 880.86, "word": " لاللي", "probability": 0.530029296875}, {"start": 880.86, "end": 881.4, "word": " هو", "probability": 0.91650390625}, {"start": 881.4, "end": 883.04, "word": " criterion", "probability": 0.85302734375}, {"start": 883.04, "end": 884.36, "word": " مهمة", "probability": 0.94482421875}, {"start": 884.36, "end": 884.78, "word": " اللي", "probability": 0.896484375}, {"start": 884.78, "end": 885.6, "word": " احنا", "probability": 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طرق أخرى نحاول اللي هو نوسع اللي هي", "tokens": [10721, 5016, 8315, 23032, 3555, 3615, 995, 1975, 2655, 24401, 12984, 8315, 18871, 2423, 39184, 4080, 491, 5681, 1146, 5305, 1140, 9122, 33911, 8717, 12984, 3555, 2655, 14739, 3224, 4080, 491, 5681, 1146, 424, 638, 18871, 23032, 16572, 4587, 16712, 3615, 16572, 5172, 23032, 3555, 3615, 995, 6024, 48506, 37893, 11778, 47302, 15042, 47525, 8315, 8717, 12984, 3555, 2655, 18871, 23032, 16572, 4587, 16712, 3615, 16572, 5172, 11933, 15730, 47525, 8315, 13672, 1829, 31439, 23032, 2288, 4587, 5551, 34740, 7578, 8717, 5016, 995, 12610, 13672, 1829, 31439, 8717, 41779, 3615, 13672, 1829, 39896], "avg_logprob": -0.13264628277814133, "compression_ratio": 1.7714285714285714, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 896.63, "end": 897.29, "word": "أحنا", "probability": 0.744140625}, {"start": 897.29, "end": 897.77, "word": " طبعا", "probability": 0.943603515625}, {"start": 897.77, "end": 898.97, "word": " اتحدثنا", "probability": 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there exists P إبسلون a partition of I such that ال P ال U ال P إبسلون", "tokens": [6027, 20292, 39896, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 1958, 456, 8198, 257, 24808, 430, 11933, 3555, 3794, 1211, 11536, 23758, 2423, 430, 13672, 1829, 31439, 2423, 24808, 7251, 34268, 2304, 3215, 6225, 45340, 25528, 15844, 11933, 3555, 3794, 1211, 11536, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 20666, 43761, 11778, 1829, 24808, 430, 11933, 3555, 3794, 1211, 11536, 5296, 2304, 9957, 2423, 24808, 23032, 3555, 3615, 995, 24976, 15035, 13672, 1829, 43242, 8315, 13672, 1829, 39896, 497, 456, 8198, 430, 11933, 3555, 3794, 1211, 11536, 257, 24808, 295, 286, 1270, 300, 2423, 430, 2423, 624, 2423, 430, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.18133601136163835, "compression_ratio": 2.0656565656565657, "no_speech_prob": 3.0994415283203125e-05, "words": [{"start": 1014.76, "end": 1015.14, "word": "اللي", "probability": 0.7353515625}, {"start": 1015.14, "end": 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integrable أكيد لكل إبسلون هلجي بي إبسلون بحيث أن هذا يتحقق خلونا نيجي الآن نبرهم و نشوف كيف بدنا نبرهم نظريتنا", "tokens": [2407, 6027, 39184, 479, 8717, 995, 4587, 9381, 2423, 39184, 441, 4724, 1829, 11933, 3555, 3794, 1211, 11536, 4032, 479, 7251, 30544, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 11933, 3555, 3794, 1211, 11536, 6024, 48506, 11933, 15730, 25961, 5296, 7435, 1829, 8315, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 5296, 7435, 1829, 8315, 4724, 1829, 11933, 3555, 3794, 1211, 11536, 4724, 5016, 1829, 12984, 23758, 7251, 2655, 5016, 4587, 4587, 20449, 8315, 47395, 479, 307, 16200, 424, 638, 293, 2615, 736, 498, 479, 307, 16200, 424, 638, 5551, 4117, 25708, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 8032, 1211, 7435, 1829, 4724, 1829, 11933, 3555, 3794, 1211, 11536, 4724, 5016, 1829, 12984, 14739, 23758, 7251, 2655, 5016, 4587, 4587, 16490, 1211, 2407, 8315, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 26890, 16095, 4032, 8717, 8592, 38688, 9122, 33911, 47525, 8315, 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"start": 1069.54, "end": 1096.8, "text": "الان بدنا نفترض ان F اي شمالها is integrable ونصل منها للي عيدي اللي هي ال partition اللي مذكور مدام F is integrable اذا كانت ..الان بنقول suppose that F is integrable مدام integrable يا شباب", "tokens": [6027, 7649, 47525, 8315, 8717, 5172, 2655, 43042, 16472, 479, 1975, 1829, 13412, 2304, 6027, 11296, 307, 16200, 424, 638, 4032, 1863, 36520, 9154, 11296, 5296, 20292, 6225, 1829, 16254, 13672, 1829, 39896, 2423, 24808, 13672, 1829, 3714, 8848, 4117, 13063, 3714, 3215, 10943, 479, 307, 16200, 424, 638, 1975, 15730, 25961, 2655, 4386, 6027, 7649, 44945, 39648, 7297, 300, 479, 307, 16200, 424, 638, 3714, 3215, 10943, 3572, 712, 35186, 13412, 3555, 16758], "avg_logprob": -0.2714583396911621, "compression_ratio": 1.5862068965517242, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1069.54, "end": 1070.02, "word": "الان", "probability": 0.7315673828125}, {"start": 1070.02, "end": 1070.9, "word": " بدنا", "probability": 0.8486328125}, 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of F هو إيش يا شباب؟ هو عبارة عن الـ infimum للـ L of B و F such that B element in B of I، مظبوط؟ إذا الـ U of F عبارة عن infimum يعني هو عبارة عن greatest lower bound", "tokens": [3615, 1863, 16254, 2423, 39184, 624, 295, 479, 31439, 11933, 1829, 8592, 35186, 13412, 3555, 16758, 22807, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 1536, 332, 449, 24976, 39184, 441, 295, 363, 4032, 479, 1270, 300, 363, 4478, 294, 363, 295, 286, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 2423, 39184, 624, 295, 479, 6225, 3555, 9640, 3660, 18871, 1536, 332, 449, 37495, 22653, 31439, 6225, 3555, 9640, 3660, 18871, 6636, 3126, 5472], "avg_logprob": -0.15858360931470797, "compression_ratio": 1.455621301775148, "no_speech_prob": 0.0, "words": [{"start": 1125.19, "end": 1125.73, "word": "عندي", "probability": 0.767578125}, {"start": 1125.73, "end": 1126.01, "word": " الـ", "probability": 0.83349609375}, {"start": 1126.01, "end": 1126.13, "word": " U", "probability": 0.56787109375}, 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1258.54, "text": "ماشي الحال الان ايش معناه انه هذا infimum معناته هذا هو عبارة عن ال greatest lower bound مدام ال greatest lower bound اذا ال lower bound هذا", "tokens": [2304, 33599, 1829, 21542, 6027, 2423, 7649, 1975, 1829, 8592, 20449, 8315, 3224, 16472, 3224, 23758, 1536, 332, 449, 20449, 8315, 47395, 23758, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 6636, 3126, 5472, 3714, 3215, 10943, 2423, 6636, 3126, 5472, 1975, 15730, 2423, 3126, 5472, 23758], "avg_logprob": -0.3124999911227125, "compression_ratio": 1.558139534883721, "no_speech_prob": 9.953975677490234e-06, "words": [{"start": 1243.72, "end": 1244.04, "word": "ماشي", "probability": 0.8440755208333334}, {"start": 1244.04, "end": 1244.4, "word": " الحال", "probability": 0.959716796875}, {"start": 1244.4, "end": 1245.38, "word": " الان", "probability": 0.581298828125}, {"start": 1245.38, "end": 1245.74, "word": " ايش", "probability": 0.7503255208333334}, {"start": 1245.74, "end": 1246.38, "word": " معناه", "probability": 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مثلا بالذنب يابسون على اتنين الـ game بتعرفوا ليش يابسون على اتنين يعني لو ضفتله أي رقم بيبطل Lower Bound إيش معناته بيبطل Lower Bound يعني هيصير هذا أكبر من ال UB 1 of F for some B وحدها", "tokens": [10721, 2407, 2423, 39184, 3769, 377, 25523, 363, 554, 45164, 48812, 5172, 2655, 43761, 36632, 12602, 4587, 2304, 7251, 16758, 3794, 11536, 15844, 1975, 2655, 1863, 9957, 50113, 15040, 20666, 8848, 1863, 3555, 7251, 16758, 3794, 11536, 15844, 1975, 2655, 1863, 9957, 2423, 39184, 1216, 39894, 3615, 28480, 14407, 32239, 8592, 7251, 16758, 3794, 11536, 15844, 1975, 2655, 1863, 9957, 37495, 22653, 45164, 48812, 5172, 2655, 43761, 36632, 12602, 4587, 2304, 4724, 1829, 3555, 9566, 1211, 25523, 363, 554, 11933, 1829, 8592, 20449, 8315, 47395, 4724, 1829, 3555, 9566, 1211, 25523, 363, 554, 37495, 22653, 39896, 9381, 13546, 23758, 5551, 4117, 26890, 9154, 2423, 624, 33, 502, 295, 479, 337, 512, 363, 4032, 24401, 11296], "avg_logprob": -0.23343210590296778, "compression_ratio": 1.875, 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لأن الـBy يا جماعة عبارة عن refinement للـB2 والlower لما يصير فيه تحسين بكبر، بروح نحو اتجاه نيل اللي هو المنحنة التالية مساحة تحت المنحنة الكلية لأن أيضا لو جيت قولة الـU of F", "tokens": [6027, 20292, 31439, 5551, 4117, 25708, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 441, 295, 3146, 12174, 10859, 4587, 6808, 5172, 12399, 32239, 8592, 22807, 5296, 33456, 2423, 39184, 33, 88, 35186, 10874, 15042, 27884, 6225, 3555, 9640, 3660, 18871, 1895, 30229, 24976, 39184, 33, 17, 16070, 34598, 5296, 15042, 7251, 9381, 13546, 8978, 3224, 6055, 5016, 3794, 9957, 4724, 4117, 26890, 12399, 4724, 32887, 5016, 8717, 5016, 2407, 1975, 2655, 7435, 40294, 8717, 26895, 13672, 1829, 31439, 9673, 1863, 5016, 1863, 3660, 16712, 6027, 10632, 47524, 39319, 3660, 6055, 33753, 9673, 1863, 5016, 1863, 3660, 33251, 1211, 10632, 5296, 33456, 36632, 11242, 995, 45164, 10874, 36081, 12174, 12610, 3660, 2423, 39184, 52, 295, 479], "avg_logprob": -0.2223252161579617, "compression_ratio": 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U بي واحد و F", "tokens": [11622, 18513, 11933, 3555, 3794, 1211, 11536, 15844, 1975, 2655, 1863, 9957, 8032, 2655, 15040, 38436, 11296, 5551, 4117, 26890, 9154, 2423, 624, 4724, 1829, 36764, 24401, 4032, 479], "avg_logprob": -0.3830729047457377, "compression_ratio": 1.119047619047619, "no_speech_prob": 3.337860107421875e-06, "words": [{"start": 1455.4, "end": 1455.9, "word": "زاد", "probability": 0.600341796875}, {"start": 1455.9, "end": 1456.38, "word": " إبسلون", "probability": 0.71796875}, {"start": 1456.38, "end": 1456.54, "word": " على", "probability": 0.69189453125}, {"start": 1456.54, "end": 1456.86, "word": " اتنين", "probability": 0.81903076171875}, {"start": 1456.86, "end": 1457.84, "word": " هتلاقيها", "probability": 0.869140625}, {"start": 1457.84, "end": 1459.86, "word": " أكبر", "probability": 0.7158610026041666}, {"start": 1459.86, "end": 1460.12, "word": " من", "probability": 0.91943359375}, {"start": 1460.12, "end": 1460.32, "word": " ال", "probability": 0.57080078125}, {"start": 1460.32, "end": 1460.66, "word": " U", "probability": 0.58544921875}, {"start": 1460.66, "end": 1464.4, "word": " بي", "probability": 0.461181640625}, {"start": 1464.4, "end": 1465.0, "word": " واحد", "probability": 0.85986328125}, {"start": 1465.0, "end": 1466.28, "word": " و", "probability": 0.8388671875}, {"start": 1466.28, "end": 1466.64, "word": " F", "probability": 0.63232421875}], "temperature": 1.0}, {"id": 66, "seek": 149167, "start": 1467.51, "end": 1491.67, "text": "وأكيد عندي الـ U of F زائد إبسلون عدنان أكبر من الـ U B1 of F هيكون هذا أكبر أو يساوي الـ U B epsilon of F لأن الـ B epsilon refinement لمين برضه؟ للـ B1 بزام refinement إذن اللي هو التحسين بيزغر القبر وبروح ناحية اللي هو المنحنة إذن الآن من الـ tip 2 هذولة", "tokens": [2407, 10721, 4117, 25708, 43242, 1829, 2423, 39184, 624, 295, 479, 30767, 16373, 3215, 11933, 3555, 3794, 1211, 11536, 6225, 3215, 1863, 7649, 5551, 4117, 26890, 9154, 2423, 39184, 624, 363, 16, 295, 479, 39896, 30544, 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"probability": 0.87197265625}, {"start": 1597.55, "end": 1598.11, "word": " بي", "probability": 0.757568359375}, {"start": 1598.11, "end": 1598.35, "word": " واحد", "probability": 0.95947265625}, {"start": 1598.35, "end": 1598.77, "word": " اتحاد", "probability": 0.89111328125}, {"start": 1598.77, "end": 1598.95, "word": " بي", "probability": 0.919921875}, {"start": 1598.95, "end": 1599.19, "word": " اتنين", "probability": 0.911376953125}, {"start": 1599.19, "end": 1599.41, "word": " حيث", "probability": 0.8756510416666666}, {"start": 1599.41, "end": 1599.61, "word": " بي", "probability": 0.829345703125}, {"start": 1599.61, "end": 1599.83, "word": " واحد", "probability": 0.975830078125}, {"start": 1599.83, "end": 1599.97, "word": " اللي", "probability": 0.994384765625}, {"start": 1599.97, "end": 1600.35, "word": " لجيناه", "probability": 0.84716796875}, {"start": 1600.35, "end": 1600.63, "word": " هان", "probability": 0.60546875}, {"start": 1600.63, "end": 1601.05, "word": " وال", "probability": 0.4052734375}, {"start": 1601.05, "end": 1601.25, "word": " بي", "probability": 0.677490234375}, {"start": 1601.25, "end": 1601.49, "word": " اتنين", "probability": 0.948974609375}, {"start": 1601.49, "end": 1601.65, "word": " اللي", "probability": 0.99560546875}, {"start": 1601.65, "end": 1602.11, "word": " لجيناه", "probability": 0.97880859375}, {"start": 1602.11, "end": 1602.41, "word": " هان", "probability": 0.952880859375}], "temperature": 1.0}, {"id": 71, "seek": 161986, "start": 1602.62, "end": 1619.86, "text": "such that U P Y of F نقص L P Y of F أصغر من اللي هو Epsilon وهو المطلوب أي سؤال؟ طيب، ماشي يا شباب، الآن خلصنا الجزء الأول من النظرية", "tokens": [39974, 300, 624, 430, 398, 295, 479, 8717, 4587, 9381, 441, 430, 398, 295, 479, 5551, 9381, 17082, 2288, 9154, 13672, 1829, 31439, 462, 16592, 37037, 2407, 9673, 9566, 1211, 37746, 36632, 8608, 33604, 6027, 22807, 23032, 1829, 3555, 12399, 3714, 33599, 1829, 35186, 13412, 3555, 16758, 12399, 6024, 48506, 16490, 1211, 9381, 8315, 25724, 11622, 38207, 16247, 12610, 9154, 28239, 19913, 2288, 10632], "avg_logprob": -0.25048076923076923, "compression_ratio": 1.3164556962025316, "no_speech_prob": 1.3887882232666016e-05, "words": [{"start": 1602.62, "end": 1603.24, "word": "such", "probability": 0.603515625}, {"start": 1603.24, "end": 1603.72, "word": " that", "probability": 0.95654296875}, {"start": 1603.72, "end": 1604.12, "word": " U", "probability": 0.2481689453125}, {"start": 1604.12, "end": 1604.3, "word": " P", "probability": 0.2509765625}, {"start": 1604.3, "end": 1604.62, "word": " Y", "probability": 0.5654296875}, {"start": 1604.62, "end": 1604.86, "word": " of", "probability": 0.215576171875}, {"start": 1604.86, "end": 1605.12, "word": " F", "probability": 0.9775390625}, {"start": 1605.12, "end": 1605.54, "word": " نقص", "probability": 0.7513834635416666}, {"start": 1605.54, "end": 1605.72, "word": " L", "probability": 0.150146484375}, {"start": 1605.72, "end": 1605.84, "word": " P", "probability": 0.95166015625}, {"start": 1605.84, "end": 1606.16, "word": " Y", "probability": 0.8681640625}, {"start": 1606.16, "end": 1606.28, "word": " of", "probability": 0.470458984375}, {"start": 1606.28, "end": 1606.5, "word": " F", "probability": 0.99658203125}, {"start": 1606.5, "end": 1607.1, "word": " أصغر", "probability": 0.95556640625}, {"start": 1607.1, "end": 1607.62, "word": " من", "probability": 0.97216796875}, {"start": 1607.62, "end": 1607.82, "word": " اللي", "probability": 0.62060546875}, {"start": 1607.82, "end": 1608.16, "word": " هو", "probability": 0.95947265625}, {"start": 1608.16, "end": 1609.12, "word": " Epsilon", "probability": 0.598388671875}, {"start": 1609.12, "end": 1609.96, "word": " وهو", "probability": 0.760498046875}, {"start": 1609.96, "end": 1611.3, "word": " المطلوب", "probability": 0.9892578125}, {"start": 1611.3, "end": 1612.48, "word": " أي", "probability": 0.5947265625}, {"start": 1612.48, "end": 1614.04, "word": " سؤال؟", "probability": 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انه suppose that star holds اللي هي star ليه هذه نفترض ان لكل epsilon أكبر من 0 there exists B of epsilon such that U B Epsilon و F نقصها دي أصغر من Epsilon و بدنا نصل من خلالها لإيش لأن ال F is integrable فنشوف", "tokens": [10721, 12984, 3555, 2655, 8315, 13672, 1829, 47525, 8315, 35186, 16472, 3224, 13672, 1829, 31439, 29538, 18863, 15040, 28671, 20328, 5016, 1829, 5016, 3660, 5296, 33456, 8315, 8717, 5172, 2655, 43042, 16472, 3224, 7297, 300, 3543, 9190, 13672, 1829, 39896, 3543, 32239, 3224, 29538, 8717, 5172, 2655, 43042, 16472, 5296, 28820, 17889, 5551, 4117, 26890, 9154, 1958, 456, 8198, 363, 295, 17889, 1270, 300, 624, 363, 462, 16592, 4032, 479, 8717, 4587, 9381, 11296, 11778, 1829, 5551, 9381, 17082, 2288, 9154, 462, 16592, 4032, 47525, 8315, 8717, 36520, 9154, 16490, 1211, 6027, 11296, 5296, 28814, 1829, 8592, 5296, 33456, 2423, 479, 307, 16200, 424, 638, 6156, 1863, 8592, 38688], "avg_logprob": -0.2977272862737829, "compression_ratio": 1.6514522821576763, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1622.18, "end": 1622.88, "word": "أثبتنا", "probability": 0.840576171875}, {"start": 1622.88, "end": 1623.1, "word": " اللي", "probability": 0.627197265625}, {"start": 1623.1, "end": 1623.46, "word": " بدنا", "probability": 0.9169921875}, {"start": 1623.46, "end": 1623.72, "word": " يا", "probability": 0.194091796875}, {"start": 1623.72, "end": 1624.16, "word": " انه", "probability": 0.4786376953125}, {"start": 1624.16, "end": 1624.42, "word": " اللي", "probability": 0.71923828125}, {"start": 1624.42, "end": 1624.6, "word": " هو", "probability": 0.94970703125}, {"start": 1624.6, "end": 1624.8, "word": " هذه", "probability": 0.63671875}, {"start": 1624.8, "end": 1625.16, "word": " العلاقة", "probability": 0.9578450520833334}, {"start": 1625.16, "end": 1626.08, "word": " صحيحة", "probability": 0.901171875}, {"start": 1626.08, "end": 1626.6, "word": " لأننا", "probability": 0.590576171875}, {"start": 1626.6, "end": 1627.1, "word": " نفترض", "probability": 0.9346923828125}, {"start": 1627.1, "end": 1627.62, "word": " انه", "probability": 0.4951171875}, {"start": 1627.62, "end": 1628.4, "word": " suppose", "probability": 0.6474609375}, {"start": 1628.4, "end": 1628.86, "word": " that", "probability": 0.8828125}, {"start": 1628.86, "end": 1629.3, "word": " star", "probability": 0.50830078125}, {"start": 1629.3, "end": 1629.76, "word": " holds", "probability": 0.82373046875}, {"start": 1629.76, "end": 1629.96, "word": " اللي", "probability": 0.95361328125}, {"start": 1629.96, "end": 1630.12, "word": " هي", "probability": 0.8671875}, {"start": 1630.12, "end": 1630.4, "word": " star", "probability": 0.410400390625}, {"start": 1630.4, "end": 1630.72, "word": " ليه", "probability": 0.611328125}, {"start": 1630.72, "end": 1631.02, "word": " هذه", "probability": 0.607421875}, {"start": 1631.02, "end": 1631.9, "word": " نفترض", "probability": 0.9337158203125}, {"start": 1631.9, "end": 1632.04, "word": " ان", "probability": 0.69189453125}, {"start": 1632.04, "end": 1632.38, "word": " لكل", "probability": 0.869384765625}, {"start": 1632.38, "end": 1632.82, "word": " epsilon", "probability": 0.1429443359375}, {"start": 1632.82, "end": 1633.12, "word": " أكبر", "probability": 0.9319661458333334}, {"start": 1633.12, "end": 1633.24, "word": " من", "probability": 0.88818359375}, {"start": 1633.24, "end": 1633.44, "word": " 0", "probability": 0.499267578125}, {"start": 1633.44, "end": 1633.66, "word": " there", "probability": 0.74462890625}, {"start": 1633.66, "end": 1633.96, "word": " exists", "probability": 0.6494140625}, {"start": 1633.96, "end": 1634.16, "word": " B", "probability": 0.363037109375}, {"start": 1634.16, "end": 1634.36, "word": " of", "probability": 0.8115234375}, {"start": 1634.36, "end": 1634.8, "word": " epsilon", "probability": 0.86328125}, {"start": 1634.8, "end": 1635.38, "word": " such", "probability": 0.88818359375}, {"start": 1635.38, "end": 1635.74, "word": " that", "probability": 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ال limit هذا بيساوي سفر then f is integrable and ال limit لل integration بيساوي ال integration بيساوي ال limit ال أسف ال limit لل lower p and f بيساوي ال limit لل upper p and f اللي هو بيساوي قيمة ال integration حتى ال converse جماعة اللي هو", "tokens": [1211, 33456, 45164, 6156, 43042, 8315, 4724, 1829, 14739, 14739, 4478, 6022, 307, 257, 8310, 295, 644, 2451, 295, 286, 4724, 5016, 1829, 12984, 14739, 2423, 4948, 23758, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 550, 283, 307, 16200, 424, 638, 293, 2423, 4948, 24976, 10980, 4724, 1829, 3794, 995, 45865, 2423, 10980, 4724, 1829, 3794, 995, 45865, 2423, 4948, 2423, 5551, 3794, 5172, 2423, 4948, 24976, 3126, 280, 293, 283, 4724, 1829, 3794, 995, 45865, 2423, 4948, 24976, 6597, 280, 293, 283, 13672, 1829, 31439, 4724, 1829, 3794, 995, 45865, 12174, 32640, 3660, 2423, 10980, 11331, 49975, 2423, 416, 4308, 10874, 15042, 27884, 13672, 1829, 31439], "avg_logprob": -0.30877293906080616, "compression_ratio": 1.9631336405529953, 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"probability": 0.69580078125}, {"start": 1924.48, "end": 1924.7, "word": " limit", "probability": 0.98583984375}, {"start": 1924.7, "end": 1924.9, "word": " لل", "probability": 0.96826171875}, {"start": 1924.9, "end": 1925.18, "word": " upper", "probability": 0.78955078125}, {"start": 1925.18, "end": 1925.42, "word": " p", "probability": 0.81787109375}, {"start": 1925.42, "end": 1925.62, "word": " and", "probability": 0.94482421875}, {"start": 1925.62, "end": 1925.86, "word": " f", "probability": 0.9755859375}, {"start": 1925.86, "end": 1926.0, "word": " اللي", "probability": 0.927734375}, {"start": 1926.0, "end": 1926.1, "word": " هو", "probability": 0.90869140625}, {"start": 1926.1, "end": 1926.4, "word": " بيساوي", "probability": 0.97470703125}, {"start": 1926.4, "end": 1926.88, "word": " قيمة", "probability": 0.9860026041666666}, {"start": 1926.88, "end": 1927.02, "word": " ال", "probability": 0.98583984375}, {"start": 1927.02, "end": 1927.56, "word": " integration", "probability": 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"probability": 0.752685546875}, {"start": 1933.6, "end": 1933.82, "word": " كان", "probability": 0.94921875}, {"start": 1933.82, "end": 1933.96, "word": " ..", "probability": 0.13916015625}, {"start": 1933.96, "end": 1934.08, "word": " اللي", "probability": 0.917724609375}, {"start": 1934.08, "end": 1934.2, "word": " هي", "probability": 0.64794921875}, {"start": 1934.2, "end": 1934.56, "word": " كانت", "probability": 0.953369140625}, {"start": 1934.56, "end": 1934.7, "word": " F", "probability": 0.71875}, {"start": 1934.7, "end": 1935.2, "word": " أندولي", "probability": 0.4805145263671875}, {"start": 1935.2, "end": 1935.52, "word": " F", "probability": 0.951171875}, {"start": 1935.52, "end": 1936.46, "word": " لأن", "probability": 0.85400390625}, {"start": 1936.46, "end": 1936.82, "word": " لو", "probability": 0.9892578125}, {"start": 1936.82, "end": 1937.3, "word": " كانت", "probability": 0.98388671875}, {"start": 1937.3, "end": 1937.56, "word": " F", "probability": 0.92919921875}, 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"probability": 0.75927734375}, {"start": 1949.58, "end": 1949.76, "word": " اللي", "probability": 0.985595703125}, {"start": 1949.76, "end": 1949.96, "word": " هو", "probability": 0.99462890625}, {"start": 1949.96, "end": 1950.5, "word": " برهان", "probability": 0.9271240234375}, {"start": 1950.5, "end": 1950.96, "word": " إيجاد", "probability": 0.9779052734375}, {"start": 1950.96, "end": 1951.28, "word": " الـ", "probability": 0.6883544921875}, {"start": 1951.28, "end": 1951.38, "word": " B", "probability": 0.252685546875}, {"start": 1951.38, "end": 1952.06, "word": " epsilon", "probability": 0.165771484375}, {"start": 1952.06, "end": 1952.74, "word": " ولكن", "probability": 0.84375}, {"start": 1952.74, "end": 1952.92, "word": " هنا", "probability": 0.7412109375}, {"start": 1952.92, "end": 1953.38, "word": " بنجد", "probability": 0.7364908854166666}], "temperature": 1.0}, {"id": 85, "seek": 197478, "start": 1953.78, "end": 1974.78, "text": "اللي هو الـ Epsilon بساوية واحدة لان فبنلاقي اللي هو ال sequence هذه في ال corollary .. في من مشابه .. شيء مشابه في برهان النظرية الأولى اللي قبل بشوية و ياريت تجربوها عندكم خلينا ناخد اللي .. اللي موجود حاليا اللي هو الاتجاه هذا ان لو لجينا sequence of partitions", "tokens": [6027, 20292, 31439, 2423, 39184, 462, 16592, 4724, 3794, 995, 2407, 10632, 36764, 24401, 3660, 5296, 7649, 6156, 3555, 1863, 15040, 38436, 13672, 1829, 31439, 2423, 8310, 29538, 8978, 2423, 1181, 1833, 822, 4386, 8978, 9154, 37893, 16758, 3224, 4386, 44049, 38207, 37893, 16758, 3224, 8978, 4724, 2288, 3224, 7649, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 4032, 7251, 9640, 36081, 6055, 7435, 25513, 2407, 11296, 43242, 24793, 16490, 20292, 8315, 8717, 47283, 3215, 13672, 1829, 4386, 13672, 1829, 3714, 29245, 23328, 11331, 6027, 25528, 13672, 1829, 31439, 2423, 9307, 7435, 40294, 23758, 16472, 45164, 5296, 7435, 1829, 8315, 8310, 295, 644, 2451], "avg_logprob": -0.27525111261223045, "compression_ratio": 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"end": 1957.66, "word": " sequence", "probability": 0.611328125}, {"start": 1957.66, "end": 1958.24, "word": " هذه", "probability": 0.481201171875}, {"start": 1958.24, "end": 1958.92, "word": " في", "probability": 0.6611328125}, {"start": 1958.92, "end": 1959.14, "word": " ال", "probability": 0.677734375}, {"start": 1959.14, "end": 1959.72, "word": " corollary", "probability": 0.6469930013020834}, {"start": 1959.72, "end": 1959.82, "word": " ..", "probability": 0.4609375}, {"start": 1959.82, "end": 1959.96, "word": " في", "probability": 0.75244140625}, {"start": 1959.96, "end": 1960.36, "word": " من", "probability": 0.69287109375}, {"start": 1960.36, "end": 1961.8, "word": " مشابه", "probability": 0.6602376302083334}, {"start": 1961.8, "end": 1961.8, "word": " ..", "probability": 0.7939453125}, {"start": 1961.8, "end": 1962.38, "word": " شيء", "probability": 0.666015625}, {"start": 1962.38, "end": 1962.9, "word": " مشابه", "probability": 0.98876953125}, {"start": 1962.9, "end": 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"word": " ناخد", "probability": 0.9523111979166666}, {"start": 1968.6, "end": 1968.8, "word": " اللي", "probability": 0.968994140625}, {"start": 1968.8, "end": 1968.8, "word": " ..", "probability": 0.39990234375}, {"start": 1968.8, "end": 1968.96, "word": " اللي", "probability": 0.994384765625}, {"start": 1968.96, "end": 1969.36, "word": " موجود", "probability": 0.9890950520833334}, {"start": 1969.36, "end": 1969.88, "word": " حاليا", "probability": 0.70849609375}, {"start": 1969.88, "end": 1970.9, "word": " اللي", "probability": 0.6544189453125}, {"start": 1970.9, "end": 1971.12, "word": " هو", "probability": 0.91064453125}, {"start": 1971.12, "end": 1971.8, "word": " الاتجاه", "probability": 0.9072265625}, {"start": 1971.8, "end": 1972.02, "word": " هذا", "probability": 0.95654296875}, {"start": 1972.02, "end": 1972.16, "word": " ان", "probability": 0.27392578125}, {"start": 1972.16, "end": 1972.34, "word": " لو", "probability": 0.703125}, {"start": 1972.34, "end": 1972.88, "word": " 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2578.01, "word": " ال", "probability": 0.46240234375}, {"start": 2578.01, "end": 2578.21, "word": " lower", "probability": 0.83935546875}, {"start": 2578.21, "end": 2578.51, "word": " sum", "probability": 0.978515625}, {"start": 2578.51, "end": 2578.61, "word": " و", "probability": 0.8349609375}, {"start": 2578.61, "end": 2578.89, "word": " بعدين", "probability": 0.93798828125}, {"start": 2578.89, "end": 2579.15, "word": " جيبنا", "probability": 0.990234375}, {"start": 2579.15, "end": 2579.25, "word": " ال", "probability": 0.9228515625}, {"start": 2579.25, "end": 2579.49, "word": " upper", "probability": 0.90087890625}, {"start": 2579.49, "end": 2581.87, "word": " integral", "probability": 0.4345703125}, {"start": 2581.87, "end": 2582.17, "word": " و", "probability": 0.97509765625}, {"start": 2582.17, "end": 2582.25, "word": " ال", "probability": 0.44921875}, {"start": 2582.25, "end": 2582.43, "word": " lower", "probability": 0.90625}, {"start": 2582.43, "end": 2582.93, "word": " 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عبارة عن Any Partition اللي هو بالطريقة اللي أمامي يعني حسب N بيصير بختلف ال Partition أما إيش فكرة ال Partition زي ما قلنا المرة الفائتة من 0 لعند 1 جزأناها إلى أجزاء متساوية إلى N من الأجزاء المتساوية", "tokens": [27842, 2423, 39184, 24755, 781, 13672, 1829, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 16472, 11296, 5681, 1146, 424, 20666, 3555, 14407, 3794, 9566, 3660, 13672, 1829, 39896, 16712, 3615, 16572, 5172, 5551, 9778, 3215, 8315, 430, 426, 13672, 1829, 31439, 17182, 36764, 24401, 15844, 426, 4032, 5718, 104, 1863, 9957, 15844, 426, 4032, 7649, 8717, 4587, 9381, 36764, 24401, 15844, 426, 5296, 3615, 41260, 2423, 14407, 24401, 5551, 9778, 3215, 8315, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 2639, 4100, 849, 13672, 1829, 31439, 20666, 9566, 16572, 28671, 13672, 1829, 5551, 2304, 10943, 1829, 37495, 22653, 11331, 35457, 426, 4724, 1829, 9381, 13546, 4724, 46456, 46538, 2423, 4100, 849, 5551, 15042, 11933, 1829, 8592, 6156, 4117, 25720, 2423, 4100, 849, 30767, 1829, 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integration ايش هيكون قيمة ال limit limit u, b, n, g هيقدر الغرض و limit l of n of g هيقدر الغرض ليش لأن limit هذا اصلا هيطلع لك limit ال u, b, n و g", "tokens": [6027, 7649, 4724, 4587, 32640, 3660, 2423, 10980, 1975, 1829, 8592, 39896, 30544, 12174, 32640, 3660, 2423, 4948, 4948, 344, 11, 272, 11, 297, 11, 290, 39896, 28543, 2288, 6024, 118, 43042, 4032, 4948, 287, 295, 297, 295, 290, 39896, 28543, 2288, 6024, 118, 43042, 32239, 8592, 5296, 33456, 4948, 23758, 1975, 9381, 15040, 39896, 9566, 1211, 3615, 5296, 4117, 4948, 2423, 344, 11, 272, 11, 297, 4032, 290], "avg_logprob": -0.3066964362348829, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 2775.6000000000004, "end": 2776.2000000000003, "word": "الان", "probability": 0.715576171875}, {"start": 2776.2000000000003, "end": 2776.8, "word": " بقيمة", "probability": 0.675537109375}, {"start": 2776.8, "end": 2776.88, "word": " ال", "probability": 0.89892578125}, {"start": 2776.88, "end": 2777.38, "word": " 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2904.64, "word": " عبارة", "probability": 0.9227294921875}, {"start": 2904.64, "end": 2905.02, "word": " عن", "probability": 0.98876953125}, {"start": 2905.02, "end": 2906.12, "word": " integrable", "probability": 0.7100830078125}, {"start": 2906.12, "end": 2906.98, "word": " functions", "probability": 0.84912109375}, {"start": 2906.98, "end": 2907.64, "word": " اذا", "probability": 0.681884765625}, {"start": 2907.64, "end": 2908.2, "word": " اول", "probability": 0.785400390625}, {"start": 2908.2, "end": 2908.8, "word": " اعلان", "probability": 0.9150390625}, {"start": 2908.8, "end": 2909.38, "word": " الان", "probability": 0.6268310546875}, {"start": 2909.38, "end": 2910.5, "word": " اللي", "probability": 0.949951171875}, {"start": 2910.5, "end": 2910.84, "word": " هو", "probability": 0.94775390625}, {"start": 2910.84, "end": 2912.0, "word": " any", "probability": 0.428955078125}, {"start": 2912.0, "end": 2912.62, "word": " monotone", "probability": 0.88916015625}, {"start": 2912.62, "end": 2913.32, "word": " function", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 126, "seek": 292529, "start": 2914.67, "end": 2925.29, "text": "on a closed bounded interval is integrable وهذا اللي هو عنواننا integrability of monotone functions", "tokens": [266, 257, 5395, 37498, 15035, 307, 16200, 424, 638, 37037, 15730, 13672, 1829, 31439, 18871, 2407, 7649, 8315, 3572, 2310, 295, 1108, 310, 546, 6828], "avg_logprob": -0.3587740258528636, "compression_ratio": 1.1262135922330097, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2914.67, "end": 2915.09, "word": "on", "probability": 0.02874755859375}, {"start": 2915.09, "end": 2915.73, "word": " a", "probability": 0.97216796875}, {"start": 2915.73, "end": 2916.29, "word": " closed", "probability": 0.75439453125}, {"start": 2916.29, "end": 2916.81, "word": " bounded", "probability": 0.890625}, {"start": 2916.81, "end": 2917.77, "word": " interval", "probability": 0.95751953125}, {"start": 2917.77, "end": 2918.83, "word": " is", "probability": 0.83251953125}, {"start": 2918.83, "end": 2920.13, "word": " integrable", "probability": 0.7224934895833334}, {"start": 2920.13, "end": 2920.71, "word": " وهذا", "probability": 0.6890869140625}, {"start": 2920.71, "end": 2920.85, "word": " اللي", "probability": 0.818603515625}, {"start": 2920.85, "end": 2921.09, "word": " هو", "probability": 0.98046875}, {"start": 2921.09, "end": 2921.83, "word": " عنواننا", "probability": 0.83203125}, {"start": 2921.83, "end": 2923.27, "word": " integrability", "probability": 0.55914306640625}, {"start": 2923.27, "end": 2923.57, "word": " of", "probability": 0.9560546875}, {"start": 2923.57, "end": 2924.49, "word": " monotone", "probability": 0.9488932291666666}, {"start": 2924.49, "end": 2925.29, "word": " functions", "probability": 0.833984375}], "temperature": 1.0}, {"id": 127, "seek": 294413, "start": 2926.29, "end": 2944.13, "text": "لت I بتساوي A و B و لت F من I لR بيكون مونوتون فانكشن on I ثم F أشمالها is integrable on I نفترض أن F انتقل هو مونوتور نصل إليها integrable نفترض أن F مثلا increasing", "tokens": [1211, 2655, 286, 39894, 3794, 995, 45865, 316, 4032, 363, 4032, 5296, 2655, 479, 9154, 286, 5296, 49, 4724, 1829, 30544, 3714, 11536, 35473, 11536, 6156, 7649, 4117, 8592, 1863, 322, 286, 38637, 2304, 479, 5551, 8592, 2304, 6027, 11296, 307, 16200, 424, 638, 322, 286, 8717, 5172, 2655, 43042, 14739, 479, 16472, 2655, 4587, 1211, 31439, 3714, 11536, 35473, 13063, 8717, 36520, 11933, 20292, 11296, 16200, 424, 638, 8717, 5172, 2655, 43042, 14739, 479, 50113, 15040, 5662], "avg_logprob": -0.4005142382428616, "compression_ratio": 1.4850299401197604, "no_speech_prob": 3.0994415283203125e-06, "words": [{"start": 2926.29, "end": 2926.75, "word": "لت", "probability": 0.4788055419921875}, {"start": 2926.75, "end": 2927.09, "word": " I", "probability": 0.62939453125}, {"start": 2927.09, "end": 2927.99, "word": " بتساوي", "probability": 0.669525146484375}, {"start": 2927.99, "end": 2928.17, 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وsimilarly وفعلا similarly لو كانت f is decreasing هتكون برضه is integrable خلّينا مع بعض شباب نفترض suppose that f is increasing يعني الدالة على الفترة هي a وb مثلا", "tokens": [2407, 1863, 36520, 36145, 11296, 16200, 424, 638, 4032, 30937, 2202, 356, 4032, 5172, 3615, 15040, 14138, 45164, 25961, 2655, 283, 307, 23223, 8032, 2655, 30544, 4724, 43042, 3224, 307, 16200, 424, 638, 16490, 1211, 11703, 1829, 8315, 20449, 45030, 11242, 13412, 3555, 16758, 8717, 5172, 2655, 43042, 7297, 300, 283, 307, 5662, 37495, 22653, 32748, 6027, 3660, 15844, 27188, 2655, 25720, 39896, 257, 4032, 65, 50113, 15040], "avg_logprob": -0.25226449102595233, "compression_ratio": 1.4184782608695652, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2945.06, "end": 2945.64, "word": "ونصل", "probability": 0.5909830729166666}, {"start": 2945.64, "end": 2946.34, "word": " إنها", "probability": 0.713134765625}, {"start": 2946.34, "end": 2947.7, "word": " integrable", "probability": 0.690673828125}, 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0.8484700520833334}, {"start": 2956.3, "end": 2956.64, "word": " خلّينا", "probability": 0.7337890625}, {"start": 2956.64, "end": 2956.76, "word": " مع", "probability": 0.99169921875}, {"start": 2956.76, "end": 2957.04, "word": " بعض", "probability": 0.9970703125}, {"start": 2957.04, "end": 2957.46, "word": " شباب", "probability": 0.8163248697916666}, {"start": 2957.46, "end": 2959.92, "word": " نفترض", "probability": 0.824462890625}, {"start": 2959.92, "end": 2961.5, "word": " suppose", "probability": 0.4501953125}, {"start": 2961.5, "end": 2964.26, "word": " that", "probability": 0.92431640625}, {"start": 2964.26, "end": 2966.06, "word": " f", "probability": 0.85205078125}, {"start": 2966.06, "end": 2967.08, "word": " is", "probability": 0.9638671875}, {"start": 2967.08, "end": 2969.02, "word": " increasing", "probability": 0.9658203125}, {"start": 2969.02, "end": 2969.9, "word": " يعني", "probability": 0.956298828125}, {"start": 2969.9, "end": 2970.4, "word": " الدالة", 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"word": " هيك", "probability": 0.6492919921875}, {"start": 3447.03, "end": 3447.33, "word": " تصبح", "probability": 0.8414713541666666}, {"start": 3447.33, "end": 3448.07, "word": " أشمالها", "probability": 0.93193359375}, {"start": 3448.07, "end": 3448.91, "word": " نازلة", "probability": 0.6817220052083334}, {"start": 3448.91, "end": 3449.35, "word": " نزول", "probability": 0.85107421875}, {"start": 3449.35, "end": 3450.07, "word": " الدالة", "probability": 0.9638671875}, {"start": 3450.07, "end": 3450.95, "word": " فبصير", "probability": 0.73687744140625}, {"start": 3450.95, "end": 3451.61, "word": " عندك", "probability": 0.906005859375}, {"start": 3451.61, "end": 3452.17, "word": " اللي", "probability": 0.888916015625}, {"start": 3452.17, "end": 3452.49, "word": " هو", "probability": 0.98974609375}, {"start": 3452.49, "end": 3452.77, "word": " ال", "probability": 0.83544921875}, {"start": 3452.77, "end": 3453.25, "word": " maximum", "probability": 0.9638671875}, {"start": 3453.25, 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" البرهان", "probability": 0.9169921875}, {"start": 3465.2, "end": 3465.58, "word": " بنفس", "probability": 0.98876953125}, {"start": 3465.58, "end": 3466.22, "word": " الطريقة،", "probability": 0.8271484375}, {"start": 3466.22, "end": 3466.76, "word": " هيطلع", "probability": 0.86114501953125}, {"start": 3466.76, "end": 3467.44, "word": " عندكم", "probability": 0.958251953125}, {"start": 3467.44, "end": 3468.7, "word": " البرهان", "probability": 0.9713134765625}, {"start": 3468.7, "end": 3469.3, "word": " automatic", "probability": 0.361328125}, {"start": 3469.3, "end": 3470.0, "word": " وبشكل", "probability": 0.9265950520833334}, {"start": 3470.0, "end": 3470.44, "word": " سهل", "probability": 0.9943033854166666}, {"start": 3470.44, "end": 3471.06, "word": " وبشكل", "probability": 0.935546875}, {"start": 3471.06, "end": 3472.04, "word": " سلس،", "probability": 0.84130859375}, {"start": 3472.04, "end": 3472.5, "word": " similar", "probability": 0.791015625}, {"start": 3472.5, "end": 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"word": " إذا", "probability": 0.611083984375}, {"start": 3500.14, "end": 3500.42, "word": " صار", "probability": 0.93212890625}, {"start": 3500.42, "end": 3500.56, "word": " في", "probability": 0.7041015625}, {"start": 3500.56, "end": 3500.78, "word": " عنا", "probability": 0.6578369140625}, {"start": 3500.78, "end": 3501.48, "word": " عائلة", "probability": 0.9933268229166666}, {"start": 3501.48, "end": 3502.5, "word": " كاملة", "probability": 0.9931640625}, {"start": 3502.5, "end": 3502.7, "word": " من", "probability": 0.99365234375}, {"start": 3502.7, "end": 3503.34, "word": " الدوال", "probability": 0.93212890625}, {"start": 3503.34, "end": 3504.14, "word": " القابلة", "probability": 0.9798177083333334}, {"start": 3504.14, "end": 3505.04, "word": " للتكامل", "probability": 0.96845703125}, {"start": 3505.04, "end": 3506.06, "word": " بواسط", "probability": 0.9505615234375}, {"start": 3506.06, "end": 3506.92, "word": " التكامل", "probability": 0.9677734375}, {"start": 3506.92, 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{"start": 4554.77, "end": 4555.31, "word": " من", "probability": 0.99365234375}, {"start": 4555.31, "end": 4555.61, "word": " سفر", "probability": 0.9840494791666666}, {"start": 4555.61, "end": 4555.83, "word": " إذا", "probability": 0.618408203125}, {"start": 4555.83, "end": 4556.63, "word": " غصب", "probability": 0.9295247395833334}, {"start": 4556.63, "end": 4557.07, "word": " عنها", "probability": 0.5478515625}, {"start": 4557.07, "end": 4557.71, "word": " هيكون", "probability": 0.6708984375}, {"start": 4557.71, "end": 4558.33, "word": " اللي", "probability": 0.922607421875}, {"start": 4558.33, "end": 4558.79, "word": " جوا", "probability": 0.885986328125}, {"start": 4558.79, "end": 4559.61, "word": " limit", "probability": 0.64453125}, {"start": 4559.61, "end": 4560.95, "word": " UPN", "probability": 0.446044921875}, {"start": 4560.95, "end": 4561.71, "word": " و", "probability": 0.8623046875}, {"start": 4561.71, "end": 4562.13, "word": " F", "probability": 0.7216796875}, {"start": 4562.13, "end": 4563.19, "word": "-L", "probability": 0.53143310546875}], "temperature": 1.0}, {"id": 196, "seek": 457706, "start": 4563.52, "end": 4577.06, "text": "بان و اف لازم يساوي ايش سفر از انقص انفينيتي وهذا by corollary اللي قبل بشوية هيعني ان اف is integrable", "tokens": [3555, 7649, 4032, 1975, 5172, 5296, 31377, 2304, 7251, 3794, 995, 45865, 1975, 1829, 8592, 8608, 5172, 2288, 1975, 11622, 16472, 4587, 9381, 16472, 5172, 9957, 1829, 31371, 37037, 15730, 538, 1181, 1833, 822, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 39896, 3615, 22653, 16472, 1975, 5172, 307, 16200, 424, 638], "avg_logprob": -0.36969340297411074, "compression_ratio": 1.2635658914728682, "no_speech_prob": 1.1742115020751953e-05, "words": [{"start": 4563.52, "end": 4564.22, "word": "بان", "probability": 0.40869140625}, {"start": 4564.22, "end": 4564.58, "word": " و", "probability": 0.8427734375}, {"start": 4564.58, "end": 4565.04, "word": " اف", "probability": 0.58502197265625}, {"start": 4565.04, "end": 4566.1, "word": " لازم", "probability": 0.8336588541666666}, {"start": 4566.1, "end": 4566.56, "word": " يساوي", "probability": 0.9423828125}, {"start": 4566.56, "end": 4567.16, "word": " ايش", "probability": 0.5628255208333334}, {"start": 4567.16, "end": 4568.0, "word": " سفر", "probability": 0.7197265625}, {"start": 4568.0, "end": 4568.3, "word": " از", "probability": 0.5137939453125}, {"start": 4568.3, "end": 4568.78, "word": " انقص", "probability": 0.7032063802083334}, {"start": 4568.78, "end": 4569.42, "word": " انفينيتي", "probability": 0.6779296875}, {"start": 4569.42, "end": 4570.84, "word": " وهذا", "probability": 0.881591796875}, {"start": 4570.84, "end": 4571.3, "word": " by", "probability": 0.55029296875}, {"start": 4571.3, "end": 4572.04, "word": " corollary", "probability": 0.8015950520833334}, {"start": 4572.04, "end": 4572.28, "word": " اللي", "probability": 0.90478515625}, {"start": 4572.28, "end": 4572.54, "word": " قبل", "probability": 0.906982421875}, {"start": 4572.54, "end": 4573.26, "word": " بشوية", "probability": 0.915283203125}, {"start": 4573.26, "end": 4574.5, "word": " هيعني", "probability": 0.7845052083333334}, {"start": 4574.5, "end": 4574.78, "word": " ان", "probability": 0.93310546875}, {"start": 4574.78, "end": 4575.4, "word": " اف", "probability": 0.6392822265625}, {"start": 4575.4, "end": 4575.86, "word": " is", "probability": 0.8349609375}, {"start": 4575.86, "end": 4577.06, "word": " integrable", "probability": 0.777587890625}], "temperature": 1.0}, {"id": 197, "seek": 460675, "start": 4578.37, "end": 4606.75, "text": "Hence, F is integrable وهكذا أثبتنا العائلة الثانية من الدوال الـ continuous function على closed bounded interval is a continuous function is an integrable function وهكذا خلصنا الـ section الأول و الـ homework هيا اللي موجودة في التلخيص و المرة القادمة ان شاء الله", "tokens": [39, 655, 11, 479, 307, 16200, 424, 638, 4032, 3224, 4117, 15730, 5551, 12984, 3555, 2655, 8315, 18863, 16373, 37977, 6024, 104, 7649, 10632, 9154, 32748, 2407, 6027, 2423, 39184, 10957, 2445, 15844, 5395, 37498, 15035, 307, 257, 10957, 2445, 307, 364, 16200, 424, 638, 2445, 4032, 3224, 4117, 15730, 16490, 1211, 9381, 8315, 2423, 39184, 3541, 16247, 12610, 4032, 2423, 39184, 14578, 8032, 25528, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 16712, 1211, 9778, 1829, 9381, 4032, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984], "avg_logprob": -0.34588067707690323, "compression_ratio": 1.654708520179372, "no_speech_prob": 9.715557098388672e-06, "words": [{"start": 4578.37, "end": 4579.05, "word": "Hence,", "probability": 0.5777587890625}, {"start": 4579.61, "end": 4580.33, "word": " F", "probability": 0.548828125}, {"start": 4580.33, "end": 4581.39, "word": " is", "probability": 0.94091796875}, {"start": 4581.39, "end": 4582.39, "word": " integrable", "probability": 0.79296875}, {"start": 4582.39, "end": 4583.31, "word": " وهكذا", "probability": 0.52410888671875}, {"start": 4583.31, "end": 4584.43, "word": " أثبتنا", "probability": 0.88486328125}, {"start": 4584.43, "end": 4584.99, "word": " العائلة", "probability": 0.9601236979166666}, {"start": 4584.99, "end": 4585.75, "word": " الثانية", "probability": 0.849853515625}, {"start": 4585.75, "end": 4586.25, "word": " من", "probability": 0.94580078125}, {"start": 4586.25, "end": 4586.85, "word": " الدوال", "probability": 0.92724609375}, {"start": 4586.85, "end": 4587.13, "word": " الـ", "probability": 0.2310791015625}, {"start": 4587.13, "end": 4587.61, "word": " continuous", "probability": 0.66845703125}, {"start": 4587.61, "end": 4588.33, "word": " function", "probability": 0.9033203125}, {"start": 4588.33, "end": 4588.83, "word": " على", "probability": 0.724609375}, {"start": 4588.83, "end": 4589.17, "word": " closed", "probability": 0.55224609375}, {"start": 4589.17, "end": 4589.53, "word": " bounded", "probability": 0.87890625}, {"start": 4589.53, "end": 4590.25, "word": " interval", "probability": 0.9560546875}, {"start": 4590.25, "end": 4590.91, "word": " is", "probability": 0.43212890625}, {"start": 4590.91, "end": 4591.17, "word": " a", "probability": 0.78271484375}, {"start": 4591.17, "end": 4591.59, "word": " continuous", "probability": 0.87158203125}, {"start": 4591.59, "end": 4592.37, "word": " function", "probability": 0.95361328125}, {"start": 4592.37, "end": 4592.77, "word": " is", "probability": 0.54833984375}, {"start": 4592.77, "end": 4593.11, "word": " an", "probability": 0.8486328125}, {"start": 4593.11, "end": 4593.65, "word": " integrable", "probability": 0.9156901041666666}, {"start": 4593.65, "end": 4594.21, "word": " function", "probability": 0.962890625}, {"start": 4594.21, "end": 4594.97, "word": " وهكذا", "probability": 0.8243408203125}, {"start": 4594.97, "end": 4597.73, "word": " خلصنا", "probability": 0.8372802734375}, {"start": 4597.73, "end": 4598.27, "word": " الـ", "probability": 0.423828125}, {"start": 4598.27, "end": 4598.99, "word": " section", "probability": 0.371826171875}, {"start": 4598.99, "end": 4599.69, "word": " الأول", "probability": 0.96533203125}, {"start": 4599.69, "end": 4599.91, "word": " و", "probability": 0.384765625}, {"start": 4599.91, "end": 4600.05, "word": " الـ", "probability": 0.32379150390625}, {"start": 4600.05, "end": 4600.45, "word": " homework", "probability": 0.8388671875}, {"start": 4600.45, "end": 4600.79, "word": " هيا", "probability": 0.207550048828125}, {"start": 4600.79, "end": 4601.65, "word": " اللي", "probability": 0.5518798828125}, {"start": 4601.65, "end": 4602.41, "word": " موجودة", "probability": 0.9193115234375}, {"start": 4602.41, "end": 4602.73, "word": " في", "probability": 0.87744140625}, {"start": 4602.73, "end": 4604.03, "word": " التلخيص", "probability": 0.97509765625}, {"start": 4604.03, "end": 4604.75, "word": " و", "probability": 0.6494140625}, {"start": 4604.75, "end": 4605.11, "word": " المرة", "probability": 0.936279296875}, {"start": 4605.11, "end": 4605.71, "word": " القادمة", "probability": 0.9931640625}, {"start": 4605.71, "end": 4606.05, "word": " ان", "probability": 0.474365234375}, {"start": 4606.05, "end": 4606.43, "word": " شاء", "probability": 0.98681640625}, {"start": 4606.43, "end": 4606.75, "word": " الله", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 198, "seek": 462447, "start": 4607.63, "end": 4624.47, "text": "إن شاء الله بكون احنا بنبدأ في اللي هي ال section اللي بعده اللي هو properties of the Riemann Integral", "tokens": [28814, 1863, 13412, 16606, 21984, 4724, 30544, 1975, 5016, 8315, 44945, 44510, 10721, 8978, 13672, 1829, 39896, 2423, 3541, 13672, 1829, 39182, 3224, 13672, 1829, 31439, 7221, 295, 264, 497, 4907, 969, 23894, 304], "avg_logprob": -0.30937499829701015, "compression_ratio": 1.2231404958677685, "no_speech_prob": 0.0, "words": [{"start": 4607.63, "end": 4607.91, "word": "إن", "probability": 0.50543212890625}, {"start": 4607.91, "end": 4608.15, "word": " شاء", "probability": 0.988037109375}, {"start": 4608.15, "end": 4608.49, "word": " الله", "probability": 0.95654296875}, {"start": 4608.49, "end": 4609.71, "word": " بكون", "probability": 0.4173583984375}, {"start": 4609.71, "end": 4610.15, "word": " احنا", "probability": 0.8141276041666666}, {"start": 4610.15, "end": 4611.23, "word": " بنبدأ", "probability": 0.8792317708333334}, {"start": 4611.23, "end": 4612.15, "word": " في", "probability": 0.7529296875}, {"start": 4612.15, "end": 4612.53, "word": " اللي", "probability": 0.900634765625}, {"start": 4612.53, "end": 4612.99, "word": " هي", "probability": 0.9072265625}, {"start": 4612.99, "end": 4614.57, "word": " ال", "probability": 0.79833984375}, {"start": 4614.57, "end": 4617.97, "word": " section", "probability": 0.5}, {"start": 4617.97, "end": 4620.51, "word": " اللي", "probability": 0.932373046875}, {"start": 4620.51, "end": 4620.91, "word": " بعده", "probability": 0.9111328125}, {"start": 4620.91, "end": 4621.09, "word": " اللي", "probability": 0.93994140625}, {"start": 4621.09, "end": 4621.25, "word": " هو", "probability": 0.96923828125}, {"start": 4621.25, "end": 4621.77, "word": " properties", "probability": 0.4912109375}, {"start": 4621.77, "end": 4622.87, "word": " of", "probability": 0.9755859375}, {"start": 4622.87, "end": 4623.05, "word": " the", "probability": 0.87890625}, {"start": 4623.05, "end": 4623.51, "word": " Riemann", "probability": 0.6896565755208334}, {"start": 4623.51, "end": 4624.47, "word": " Integral", "probability": 0.717041015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4625.4381875, "duration_after_vad": 4507.979374999997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..29d2a6a6cb2fa8bc7d19473ba071d23011b4af51
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EHWkgcDuyyY_raw.srt
@@ -0,0 +1,3624 @@
+1
+00:00:04,720 --> 00:00:09,780
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 11 في
+
+2
+00:00:09,780 --> 00:00:16,040
+مساق تحليل حقيقي 2 لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:16,040 --> 00:00:24,760
+كلية العلوم وهي المحاضرة الأولى بعد إعلان الطوارئ
+
+4
+00:00:24,760 --> 00:00:32,580
+بخصوص أو بمواجهة فيروس كورونا المنتشر اتحدتنا
+
+5
+00:00:32,580 --> 00:00:37,960
+المرة الماضيةبدأنا في اللي هو chapter 7 اللي كان
+
+6
+00:00:37,960 --> 00:00:41,280
+الحديث عن ال riman integral أو تكامل ال riman
+
+7
+00:00:41,280 --> 00:00:45,860
+بدأنا في ال section الأول اللي هو تحت عنوان riman
+
+8
+00:00:45,860 --> 00:00:50,740
+integrability عرفنا شغلتين حاجة اسمها ال upper sum
+
+9
+00:00:50,740 --> 00:00:55,960
+و حاجة اسمها ال lower sum و قلنا اللي هو ال lower
+
+10
+00:00:55,960 --> 00:01:00,290
+sumهو عبارة عن الـ summation للـ mk الـ mk هذه
+
+11
+00:01:00,290 --> 00:01:06,410
+تمثل في xk minus xk minus 1 حيث mk كانت تمثل أو m
+
+12
+00:01:06,410 --> 00:01:10,910
+small k كانت تمثل عبارة عن الـ infimum للدالة على
+
+13
+00:01:10,910 --> 00:01:15,520
+الفترة اللي هي المذكورةالان ال .. ال .. ال other
+
+14
+00:01:15,520 --> 00:01:19,380
+sum هو عبارة عن ال summation لنفس ال sum العلوي
+
+15
+00:01:19,380 --> 00:01:24,520
+ولكن بدلا منها اللي هي M K capital اللي كانت تمثل
+
+16
+00:01:24,520 --> 00:01:28,280
+ال supremum ل ال F of X وال X على اللي هي في
+
+17
+00:01:28,280 --> 00:01:34,110
+الفترة المذكورة اللي عنديالآن أخدنا أول لمّة المرة
+
+18
+00:01:34,110 --> 00:01:38,190
+الماضية وقلنا إذا كانت F من I لR bounded و B any
+
+19
+00:01:38,190 --> 00:01:43,230
+partition of I بدي يكون ال lower اللي هو sum لأي
+
+20
+00:01:43,230 --> 00:01:47,810
+partition B و function F أصغر أو يساوي ال upper
+
+21
+00:01:47,810 --> 00:01:52,470
+sum لنفس ال partition و لنفس اللي هي ال function F
+
+22
+00:01:52,470 --> 00:01:58,710
+بعد هي طبعا خطينا خطوة أخرىو جينا عرفنا اللي هو شو
+
+23
+00:01:58,710 --> 00:02:03,110
+معناته انها تكون اللي هو ال partition Q refinement
+
+24
+00:02:03,110 --> 00:02:08,610
+لل partition B قلنا Q اللي هو تحسين ل B إذا كانت B
+
+25
+00:02:08,610 --> 00:02:13,940
+بي عبارة عن مجموعة جزئية من Qو بناء عليه اللي هو
+
+26
+00:02:13,940 --> 00:02:19,440
+قلنا ان اي اللي هو sub interval xk-1xk من ال
+
+27
+00:02:19,440 --> 00:02:23,520
+partition B يمكن كتابتها على صورة union of sub
+
+28
+00:02:23,520 --> 00:02:27,680
+intervals من اللي هو التحسين اللي هو EQ
+
+29
+00:02:31,060 --> 00:02:36,380
+الان جينا اللي هو بناء على هذا التعريف جينا قولنا
+
+30
+00:02:36,380 --> 00:02:40,480
+لو كانت F is من I لعند R is bounded و B is any
+
+31
+00:02:40,480 --> 00:02:45,780
+partition of I و Q refinement لل Bمدام اللي هو Q
+
+32
+00:02:45,780 --> 00:02:50,420
+-refinement إذا ال lower sum هيعلى و ال upper sum
+
+33
+00:02:50,420 --> 00:02:54,820
+هينزل على أساس انه اللي هو في النهاية يلتقي ال
+
+34
+00:02:54,820 --> 00:02:58,740
+upper مع ال lower و نصل لاللي هو ال integrability
+
+35
+00:02:58,740 --> 00:03:02,800
+أو معنى ال integrability كما سنرى لاحقا على الأقل
+
+36
+00:03:02,800 --> 00:03:06,560
+في اللي هو يكون واضح من خلال الرسم في اللي هي
+
+37
+00:03:06,560 --> 00:03:13,890
+الدوال الموجبة كما ذكرنا سابقااللي بحكيه إنه لو
+
+38
+00:03:13,890 --> 00:03:17,330
+كانت عندي اللي هو F من I ل R bounded وB partition
+
+39
+00:03:17,330 --> 00:03:22,750
+وQ وrefinement للـ B هيكون عندي lower sum لل
+
+40
+00:03:22,750 --> 00:03:28,570
+partition B أصغر أو يساوي lower sum للتحسين عماله
+
+41
+00:03:28,570 --> 00:03:32,850
+التحسين بكبر لما بده يصل لفعلا المساحة تحت المنحنة
+
+42
+00:03:32,850 --> 00:03:39,470
+في حالة الدوال الموجبةالقبر صم لـ Q و F سيبدأ يصغر
+
+43
+00:03:39,470 --> 00:03:42,850
+ويكون أصغر من الساوي اللي هو القبر صم لـ P و F
+
+44
+00:03:42,850 --> 00:03:47,310
+التحسين يعني سيصغره بمعنى آخر سيبدأ يلتقوا إلى
+
+45
+00:03:47,310 --> 00:03:51,770
+أسفل لما نصل إلى اللي هو مساواة في حالة الـ
+
+46
+00:03:51,770 --> 00:03:55,730
+Integrability لما نكون عندنا أخدنا الـ Supremum
+
+47
+00:03:55,730 --> 00:04:01,340
+لكل L و Fالـ L والـ infimum لكل الـ U بيصير بنسمي
+
+48
+00:04:01,340 --> 00:04:04,800
+بعد شوية حاجة اسمها ال lower integral وال upper
+
+49
+00:04:04,800 --> 00:04:08,980
+integral وبرهننا هذه النظرية و بعدين جينا لللمة و
+
+50
+00:04:08,980 --> 00:04:13,520
+بعدين جينا لللمة أخرىاللي هو لو كانت F من I ل R
+
+51
+00:04:13,520 --> 00:04:17,600
+bounded وB1 وB2 اي partitions الآن لأي partitions
+
+52
+00:04:17,600 --> 00:04:22,480
+هيكون الlower دايما بغض النظر عن ال partition اللي
+
+53
+00:04:22,480 --> 00:04:26,120
+هو هيكون أصغر أو يساوي الأبر بغض النظر عن ال
+
+54
+00:04:26,120 --> 00:04:28,660
+partition B2 يعني مش لنفس ال partition زي ما قلنا
+
+55
+00:04:28,660 --> 00:04:33,180
+في اللمبة 7 1 1 لأ لأي two partitions دايما
+
+56
+00:04:33,180 --> 00:04:37,170
+الlower ما هو هيكون تحتأسفل المنحنى والـ Upper
+
+57
+00:04:37,170 --> 00:04:41,350
+هيكون أعلى المنحنى بغض النظر عن ال partitions اللي
+
+58
+00:04:41,350 --> 00:04:45,690
+عندى طبعا التمثيل هذا في حال اللي هو ال F is a
+
+59
+00:04:45,690 --> 00:04:49,130
+positive function على ال interval المذكورة الآن
+
+60
+00:04:49,130 --> 00:04:52,730
+بعد هيكة اجينا وعرفنا شو معناه ال lower integral
+
+61
+00:04:52,730 --> 00:04:55,510
+وشو معناه ال upper integral قولنا ال lower
+
+62
+00:04:55,510 --> 00:05:00,050
+integral كما هو متوقع سميناه الف F هو عبارة عن ال
+
+63
+00:05:00,050 --> 00:05:05,660
+supremum لل lowersوال .. و ال .. و ال .. و ال
+
+64
+00:05:05,660 --> 00:05:10,440
+upper هو عبارة عن الـ infimum لل uppers حتى لو
+
+65
+00:05:10,440 --> 00:05:14,300
+التقت الالو أف مع الالو أف اللي هو من أعلى مع
+
+66
+00:05:14,300 --> 00:05:17,940
+الأسفل هيكونوا التقوا بالظبط عند .. من مساحة تحت
+
+67
+00:05:17,940 --> 00:05:20,960
+المنحنى في حالة الدالة الموجبة وهذه .. في هذه
+
+68
+00:05:20,960 --> 00:05:24,300
+الحالة بنسمي إذا كانت ال upper تساوي ال lower
+
+69
+00:05:24,300 --> 00:05:27,920
+بنسمي ال function على هذه الفترة is integral و هذا
+
+70
+00:05:27,920 --> 00:05:31,900
+الكلام كله تحدثنا فيه عشان هيك أنا مسرع شويةهو
+
+71
+00:05:31,900 --> 00:05:37,160
+حكينا إنه اللي هو دايما ال lower sum لل F أخدنا
+
+72
+00:05:37,160 --> 00:05:40,760
+نظرية قولنا ال lower integral أسف ال lower
+
+73
+00:05:40,760 --> 00:05:45,100
+integral دايما أصغر يساوي مين ال upper integral
+
+74
+00:05:45,100 --> 00:05:46,860
+إذن الآن النظرية
+
+75
+00:05:49,600 --> 00:05:52,760
+الإعلان المهم اللي هو لو كانت F من I لعند R
+
+76
+00:05:52,760 --> 00:05:56,000
+bounded function على closed bounded interval A وB
+
+77
+00:05:56,000 --> 00:05:59,720
+بدي يكون ال lower integral L of F أصغر أو ساوي ال
+
+78
+00:05:59,720 --> 00:06:04,930
+upper integral U of F بصورة عامةهذه هي الـ
+
+79
+00:06:04,930 --> 00:06:08,050
+definition اللي ذكرته قبل و شوية نقول عن الـ
+
+80
+00:06:08,050 --> 00:06:15,150
+function F على bounded sub interval A و B أو
+
+81
+00:06:15,150 --> 00:06:18,650
+closed bounded interval A و B و كانت الـ F عبارة
+
+82
+00:06:18,650 --> 00:06:22,080
+عن bounded functionبنعرف أن الـ F is remain
+
+83
+00:06:22,080 --> 00:06:26,840
+integrable on I إذا كانت ال lower of F بساوي ال
+
+84
+00:06:26,840 --> 00:06:30,080
+upper of F معناته صارت اللي هي ال F is remain
+
+85
+00:06:30,080 --> 00:06:34,460
+integrable if and only if ال lower sum يساوي ال
+
+86
+00:06:34,460 --> 00:06:39,240
+upper sum هذا كله ذكرناه المرة الماضية و أيضا
+
+87
+00:06:39,240 --> 00:06:42,520
+عرفنا .. قلنا في هذا الحلقة أن كل integration من A
+
+88
+00:06:42,520 --> 00:06:47,890
+ل B هو ال lower أو ال upper المتساويينوعرفنا ايضا
+
+89
+00:06:47,890 --> 00:06:50,610
+تعريف اخر قولنا ال integration من a ل b بساوي ناقص
+
+90
+00:06:50,610 --> 00:06:53,830
+ال integration من b ل a وعرفنا ال integration من a
+
+91
+00:06:53,830 --> 00:06:59,410
+ل a بساوي صفر هذا كله حكينا المرة الماضية ومش هيك
+
+92
+00:06:59,410 --> 00:07:03,820
+كمان واخدنا المثالاللي هو أثبتنا إنه اللي هو g of
+
+93
+00:07:03,820 --> 00:07:07,880
+x بيساوي x is integrable on i استنادًا على إنه
+
+94
+00:07:07,880 --> 00:07:11,020
+أوجدنا ال lower sum ال lower integral و ال upper
+
+95
+00:07:11,020 --> 00:07:13,300
+integral أثبتنا إن ال lower integral و ال upper
+
+96
+00:07:13,300 --> 00:07:16,300
+integral are equal و من ثم أثبتنا إنه ال
+
+97
+00:07:16,300 --> 00:07:19,940
+integration exist لل function x على الفترة 0 و 1
+
+98
+00:07:19,940 --> 00:07:26,810
+وأوجدنا قيمة ال integration في حينهوصلنا إلى اللي
+
+99
+00:07:26,810 --> 00:07:33,290
+هو مثالنا التالي أنه لو كانت F من I لعند .. F من I
+
+100
+00:07:33,290 --> 00:07:40,090
+اللي هي 01 لعند ال .. ال R be defined by أخدنا
+
+101
+00:07:40,090 --> 00:07:45,990
+الدالة كما يلي اللي هو قولنا أن F of X F of X
+
+102
+00:07:45,990 --> 00:07:53,040
+بساوي واحدإذا كانت x rational number element in Q
+
+103
+00:07:53,040 --> 00:08:00,100
+وبساوي 0 إذا كانت x element in IQ أو element in Q
+
+104
+00:08:00,100 --> 00:08:04,660
+complement اللي هي ال rational numbers الآن بدنا
+
+105
+00:08:04,660 --> 00:08:11,200
+نثبت بقول show that this function Fطبعا أنا method
+
+106
+00:08:11,200 --> 00:08:17,340
+F على اللي هي الـ Q تقاطع طبعا الـ 0 و 1 اللي هي
+
+107
+00:08:17,340 --> 00:08:19,920
+الـ interval اللي بدأ عليها التقاطع الـ 0 و 1
+
+108
+00:08:19,920 --> 00:08:25,160
+بمعنى إن دالت F صارت من I اللي هي عبارة عن 0 و 1
+
+109
+00:08:26,040 --> 00:08:29,380
+اللي عند R واضح ان الدالة هذه is a bounded
+
+110
+00:08:29,380 --> 00:08:33,560
+function الان بدأ أثبت لكم ان هذا الدالة is not
+
+111
+00:08:33,560 --> 00:08:38,120
+integrable on this interval is not integrable on
+
+112
+00:08:38,120 --> 00:08:44,100
+this interval الان علشان أصل اللي هو اللي هي ان
+
+113
+00:08:44,100 --> 00:08:48,180
+هذا الدالة غير قابلة تكامل بالنسبة لتكامل بالنسبة
+
+114
+00:08:48,180 --> 00:08:55,650
+لتكامل الريمان بدي اخد الان Bأخدوا أي partition X0
+
+115
+00:08:55,650 --> 00:09:02,550
+X1 لعند Xn هذا any partition لإيه ال interval اللي
+
+116
+00:09:02,550 --> 00:09:06,790
+هي الفترة مين Zero و واحد يعني بمعنى أتيت للفترة
+
+117
+00:09:06,790 --> 00:09:14,030
+Zero و واحد و جزقتها X0 X1 لعند مؤصل لعند مين لعند
+
+118
+00:09:14,030 --> 00:09:18,610
+Xn اللي هي إيش بتساوي بتساوي واحدالان هذا ال
+
+119
+00:09:18,610 --> 00:09:22,130
+partition اخدته arbitrarily اللى هو partition
+
+120
+00:09:22,130 --> 00:09:31,790
+لفترة L عندى الان بدى احسب ال Lof B و F لهذا ال
+
+121
+00:09:31,790 --> 00:09:34,990
+partition أيش بتساوي حسب اللي عرفناها سابقا بتساوي
+
+122
+00:09:34,990 --> 00:09:40,610
+ال summation لل M K في X K minus X K minus واحد K
+
+123
+00:09:40,610 --> 00:09:46,330
+من عند واحد لعند مين لعند اللي هي N ويساوي الآن ال
+
+124
+00:09:46,330 --> 00:09:52,450
+M K عرفناها ال M K هي عبارة عن ال infimum لقيمة ال
+
+125
+00:09:52,450 --> 00:09:56,470
+function F of X حيث X تنتمي إلى الفترة X K minus
+
+126
+00:09:56,470 --> 00:10:02,210
+واحد لعند X Kطبعاً اللي هي F of X معرفة على
+
+127
+00:10:02,210 --> 00:10:05,130
+أساسيها يا إما واحد يا إما سفر حسب إنها تكون
+
+128
+00:10:05,130 --> 00:10:08,030
+rational أو إيش ال rational يعني ال function F
+
+129
+00:10:08,030 --> 00:10:11,910
+أصلا اللي هي قيمتين بس إذا الأن ال infimum لل F of
+
+130
+00:10:11,910 --> 00:10:16,630
+X عندها يا هيكون واحد يا هيكون سفر ليش؟ لأن أصلا
+
+131
+00:10:16,630 --> 00:10:23,340
+الفترة هذهفيها أي فترة subinterval xk-1xk فيها
+
+132
+00:10:23,340 --> 00:10:27,620
+rational وirrational إذا قيمة ال up of x في الفترة
+
+133
+00:10:27,620 --> 00:10:31,260
+هتلاقي عند قيم واحد هتلاقي أكيد عند قيم أش بتساوي
+
+134
+00:10:31,260 --> 00:10:35,000
+بساوي سفر إذا ال infimum في هذه الحالة هو عبارة عن
+
+135
+00:10:35,000 --> 00:10:42,320
+إيش يساوي سفر إذا ال summation ل 0 في xk-xk-1 كامل
+
+136
+00:10:42,320 --> 00:10:46,120
+عند واحد عند أنه طبيعي هذا بديهي إيش هيساوي بساوي
+
+137
+00:10:46,120 --> 00:10:52,410
+سفرأذن الان L of F بي و F ساوة سفر فور أي بورتيشن
+
+138
+00:10:52,410 --> 00:10:59,370
+بيه إذا ال L of F اللي هي عبارة عن الأو الـ
+
+139
+00:10:59,370 --> 00:11:06,070
+Supremum الـ Supremum لكل الـ L of B و F Such that
+
+140
+00:11:06,070 --> 00:11:09,890
+B element in the set of all partitions اللي هو B
+
+141
+00:11:09,890 --> 00:11:14,090
+of I هيكون ال .. ال Supremum اللي هين صفر لإن كل
+
+142
+00:11:14,090 --> 00:11:18,350
+اللي هين أصلا إشق بتنطلع .. تنطلع بساوي صفر إذا
+
+143
+00:11:18,350 --> 00:11:23,070
+هذا إيش هيساوي يا شباب؟ هو يساوي Zeroإذا طلع عندى
+
+144
+00:11:23,070 --> 00:11:28,150
+ال lower sum بساوة 0 الان بدي أحسبلكم مين أحسبلكم
+
+145
+00:11:28,150 --> 00:11:31,390
+ال upper sum سامحوني أكتب هنا بس عساس اللي يبقى
+
+146
+00:11:31,390 --> 00:11:39,670
+كله مكتوب عندى نوجد ال upper sum ال upper sum اللي
+
+147
+00:11:39,670 --> 00:11:45,510
+هي ال UPUF بساوة summation للان K capital في XK
+
+148
+00:11:45,510 --> 00:11:51,740
+minus XK minus واحد K من عند واحد لعند الانالان
+
+149
+00:11:51,740 --> 00:11:55,900
+هذا بيساوي ال Mk زي ما قلنا قبل هيك ال Mk بدل ما
+
+150
+00:11:55,900 --> 00:11:59,400
+هي ال M في مميزة استعريفها ال Mk بتساوي ال
+
+151
+00:11:59,400 --> 00:12:03,780
+supremum لهذه ال 6 وزي ما قلنا ال 6 هذه في داخلها
+
+152
+00:12:03,780 --> 00:12:08,400
+يا واحد يا زيرو نظرا لإن اللي هو أي sub interval
+
+153
+00:12:08,400 --> 00:12:11,820
+هيكون فيها rational و irrational وتبعا إلها هيكون
+
+154
+00:12:11,820 --> 00:12:16,060
+قيمة ال function في داخلها واحد أو سفر واحنا بنبحث
+
+155
+00:12:16,060 --> 00:12:19,280
+عن ال supremum إذا هيكون ال supremum في كل الأحوال
+
+156
+00:12:19,280 --> 00:12:25,600
+ال Mk بتساوي واحدمضروبة في xk-xk-1 k من عند 1 لعند
+
+157
+00:12:25,600 --> 00:12:30,700
+n نفردها هذه ويساوي اللي هنبصير k من عند 1 يعني x1
+
+158
+00:12:30,700 --> 00:12:39,570
+-x0 زاد x2-x1 زاد إلى أخير لما أصل لعند xn-1نقص xn
+
+159
+00:12:39,570 --> 00:12:44,550
+نقص واحد طبعا واضح انه عندي ال x واحد هت cancel مع
+
+160
+00:12:44,550 --> 00:12:48,270
+ناقص x واحد و ال x اتنين مع ناقص x اتنين لما نصل
+
+161
+00:12:48,270 --> 00:12:52,450
+للاخر هيكون في عندي ات cancel الجميع بس ضال عندي
+
+162
+00:12:52,450 --> 00:12:58,170
+ال xn و ال x note و هد بتساوي xn ناقص x note و
+
+163
+00:12:58,170 --> 00:13:01,750
+يساوي ال xn طبعا ايش هي عبارة عن واحد و ال x note
+
+164
+00:13:01,750 --> 00:13:07,190
+ايش هي شبه سفر و يساوي واحد ناقص سفر و يساوي واحد
+
+165
+00:13:07,570 --> 00:13:12,930
+إذا طلع عندي الـ Upper Sum لأي Bar تشهم بيه، هيتلع
+
+166
+00:13:12,930 --> 00:13:18,510
+ايش بساوة؟ بساوة واحدة إذا الان لما بدي أخد ال U
+
+167
+00:13:18,510 --> 00:13:23,510
+of F اللي هو Upper Integral هيساوة عبارة عن ال
+
+168
+00:13:23,510 --> 00:13:30,220
+Infimumلمين؟ للـ U, B وF such that B element in
+
+169
+00:13:30,220 --> 00:13:34,580
+the set of all partitions B of I والـ U, B وF
+
+170
+00:13:34,580 --> 00:13:38,840
+قيمته ثابتة for أي partition بيساوي واحد إذا الـ
+
+171
+00:13:38,840 --> 00:13:43,300
+infimum لكل اللي هنا عبارة عن برضه إيش بيساوي واحد
+
+172
+00:13:43,300 --> 00:13:47,410
+صار عندي الآنlower integral و ال upper integral
+
+173
+00:13:47,410 --> 00:13:51,110
+have different values واحد بيساوي صفر واحد بيساوي
+
+174
+00:13:51,110 --> 00:13:56,890
+واحد وبناء عليه بتكون عنده اللي هو ال F is not
+
+175
+00:13:56,890 --> 00:14:03,150
+Riemann integrable اي سؤال؟ طيب ماشي الحاجة
+
+176
+00:14:03,150 --> 00:14:10,930
+الانصار عندى اخدنا مثلين المثال الأولاللي هو
+
+177
+00:14:10,930 --> 00:14:16,770
+أثبتنا إن off of x بيساوي x is integrable على
+
+178
+00:14:16,770 --> 00:14:22,010
+الفترة 0 و1 و أثبتناها بواسطة التعريف وأيضا أثبتنا
+
+179
+00:14:22,010 --> 00:14:26,190
+مثال آخر لbounded function أيضا وكانت is not
+
+180
+00:14:26,190 --> 00:14:31,250
+remain integrable اللي هي off of x بيساوي 1 إذا
+
+181
+00:14:31,250 --> 00:14:36,090
+كانت x rational ويساوي 0 إذا كانت x irrational هذا
+
+182
+00:14:36,090 --> 00:14:43,040
+اللي هو المثال الثانيالان نيجي لاللي هو criterion
+
+183
+00:14:43,040 --> 00:14:49,280
+مهمة اللي احنا بنسميها اللي هي عبارة عن remain
+
+184
+00:14:49,280 --> 00:14:54,800
+criterion for
+
+185
+00:14:54,800 --> 00:15:01,490
+integrabilityأحنا طبعا اتحدثنا عن الـ Remain
+
+186
+00:15:01,490 --> 00:15:05,330
+Integrability كيف نثبت أنه Remain Integrable عن
+
+187
+00:15:05,330 --> 00:15:09,470
+طريق التعريف طبعا الآن مش دايما بدنا نثبت عن طريق
+
+188
+00:15:09,470 --> 00:15:14,350
+التعريف إذا بدنا اللي هو طرق أخرى نحاول اللي هو
+
+189
+00:15:14,350 --> 00:15:21,780
+نوسع اللي هيإمكانياتنا في الحكم على الدالة إنها
+
+190
+00:15:21,780 --> 00:15:26,860
+integrable أو مش integrable وهذه الإمكانية الأخرى
+
+191
+00:15:26,860 --> 00:15:31,400
+غير التعريف هي اللي بنسميها اللي هو الريمان
+
+192
+00:15:31,400 --> 00:15:36,500
+integrability criterion أو criterion for
+
+193
+00:15:36,500 --> 00:15:41,340
+integrability نشوف أيش بيقول النظرية
+
+194
+00:15:43,700 --> 00:15:48,060
+لت I بساوة A وB و لت F من I لـ R بيـ bounded نفترض
+
+195
+00:15:48,060 --> 00:15:51,360
+أن F عبارة عن إيه اشمال يا جماعة؟ bounded function
+
+196
+00:15:51,360 --> 00:15:57,500
+then F is integrable on I if and only if for each
+
+197
+00:15:57,500 --> 00:16:00,340
+epsilon أكبر من 0 there exists a partition B
+
+198
+00:16:00,340 --> 00:16:04,660
+epsilon of I such that U B epsilon نقص الـ B
+
+199
+00:16:04,660 --> 00:16:10,730
+epsilon إيه إشماله أصغر من اللي هو إبسلونإذن اللي
+
+200
+00:16:10,730 --> 00:16:16,410
+هو واضح إنه عندي فصار فيه test لل integrability أو
+
+201
+00:16:16,410 --> 00:16:20,150
+اللي هو طريقة للحكم على ال integrability أخرى غير
+
+202
+00:16:20,150 --> 00:16:26,430
+التعريف اللي هو بتقول F is integrable
+
+203
+00:16:28,870 --> 00:16:32,890
+if and only if طبعاً هذه لمين الـ F؟ F عبارة عن زي
+
+204
+00:16:32,890 --> 00:16:36,190
+ما انتوا عارفين bounded function لإنه كل شغلنا
+
+205
+00:16:36,190 --> 00:16:40,010
+أصلا على اللي هو remaining integrability أنه نفترض
+
+206
+00:16:40,010 --> 00:16:43,210
+أنه الـ F bounded عشان اللي هو تكون ال supremum و
+
+207
+00:16:43,210 --> 00:16:46,330
+ال infimum اللي مبني عليها التعريف تكون مضمون إنها
+
+208
+00:16:46,330 --> 00:16:49,870
+موجودة عشان هيك بنحكي أن F is bounded function طيب
+
+209
+00:16:49,870 --> 00:16:56,140
+إذا الـ F is integrable if and only ifاللي هي لكل
+
+210
+00:16:56,140 --> 00:17:00,620
+إبسلون أكبر من 0 there exists a partition P إبسلون
+
+211
+00:17:00,620 --> 00:17:04,240
+هذا ال P اللي هو ال partition يعتمد عالميا على
+
+212
+00:17:04,240 --> 00:17:07,820
+إبسلون لكل إبسلون بالله دي partition P إبسلون لمين
+
+213
+00:17:07,820 --> 00:17:11,840
+ال partition طبعا لل interval اللي عندنا اللي هي R
+
+214
+00:17:11,840 --> 00:17:17,040
+there exists P إبسلون a partition of I such that
+
+215
+00:17:17,040 --> 00:17:25,210
+ال P ال U ال P إبسلونوالـ F ناقص الـ L بي إبسلون و
+
+216
+00:17:25,210 --> 00:17:31,050
+F يكون أصغر من مين من إبسلون الآن إذا كان لجينا
+
+217
+00:17:31,050 --> 00:17:34,190
+لكل إبسلون لجينا بي إبسلون بحيث هذا يتحقق معناته F
+
+218
+00:17:34,190 --> 00:17:37,590
+is integrable and conversely if F is integrable
+
+219
+00:17:37,590 --> 00:17:42,550
+أكيد لكل إبسلون هلجي بي إبسلون بحيث أن هذا يتحقق
+
+220
+00:17:42,550 --> 00:17:48,170
+خلونا نيجي الآن نبرهم و نشوف كيف بدنا نبرهم
+
+221
+00:17:48,170 --> 00:17:53,880
+نظريتناالان بدنا نفترض ان F اي شمالها is
+
+222
+00:17:53,880 --> 00:18:00,240
+integrable ونصل منها للي عيدي اللي هي ال partition
+
+223
+00:18:00,240 --> 00:18:07,040
+اللي مذكور مدام F is integrable اذا كانت ..الان
+
+224
+00:18:07,040 --> 00:18:16,100
+بنقول suppose that F is integrable مدام integrable
+
+225
+00:18:16,100 --> 00:18:22,090
+يا شبابأكيد عنده اللي هو الـ U of F بساوي L of
+
+226
+00:18:22,090 --> 00:18:29,490
+إيش؟ Of F، مظبوط؟ أكيد الـ L of .. الـ U of F
+
+227
+00:18:29,490 --> 00:18:33,410
+بساوي الـ L of F إيش اللي بيدثبته؟ بيدثبته لأي
+
+228
+00:18:33,410 --> 00:18:35,810
+إبسلون أكبر من سفر بدلاجي بإبسلون، شوفوا كيف
+
+229
+00:18:35,810 --> 00:18:41,090
+بنلاجيه، الآن نفترض إن إبسلون let إبسلون أكبر من
+
+230
+00:18:41,090 --> 00:18:47,810
+سفر be given، ماشي الحالةعندي الـ U of F هو إيش يا
+
+231
+00:18:47,810 --> 00:18:54,910
+شباب؟ هو عبارة عن الـ infimum للـ L of B و F such
+
+232
+00:18:54,910 --> 00:19:01,170
+that B element in B of I، مظبوط؟ إذا الـ U of F
+
+233
+00:19:01,170 --> 00:19:05,830
+عبارة عن infimum يعني هو عبارة عن greatest lower
+
+234
+00:19:05,830 --> 00:19:11,630
+boundلو هذا الـ greatest lower bound ضفنا إليه أي
+
+235
+00:19:11,630 --> 00:19:17,230
+كمية هيبط اللاور باوند لأن هو أصلا إيش اسمه
+
+236
+00:19:17,230 --> 00:19:23,510
+greatest lower bound إذا لو الـU of F ضفتله Y على
+
+237
+00:19:23,510 --> 00:19:28,610
+2 مثلا طبعا هذا المقدار هيبط اللاور باوند إيش
+
+238
+00:19:28,610 --> 00:19:33,690
+معناته بط اللاور باوند؟ يعني بمعنى آخر هيكون في
+
+239
+00:19:33,690 --> 00:19:44,080
+عند إشي أصغر منههيكون عندى أصغر من ال U of F أو بي
+
+240
+00:19:44,080 --> 00:19:49,740
+واحد مثلا و F for some mean بي واحد إذا لما نشيل
+
+241
+00:19:49,740 --> 00:19:54,600
+من ال infimum إبسلون
+
+242
+00:19:54,600 --> 00:19:57,740
+على اتنين هيبطل هذا lower bound يعني بمعنى أخر
+
+243
+00:19:57,740 --> 00:20:03,280
+هلاقي اللي هو lower bound
+
+244
+00:20:07,660 --> 00:20:12,140
+عند الـ Y أكبر من 0 خلّيني أبدأ لت Y أكبر من 0 بي
+
+245
+00:20:12,140 --> 00:20:17,940
+given إذا عندي الآن بدي أثبت لك بدي أجيب لك
+
+246
+00:20:17,940 --> 00:20:21,440
+partition بيبسلون بحيث أنه هذا ناقص هذا يكون أصغر
+
+247
+00:20:21,440 --> 00:20:26,070
+من مين من ابسلون شوف كيف بدي أعملالان انا عندي ال
+
+248
+00:20:26,070 --> 00:20:30,710
+U of F ايش بيساوي يا جماعة ال U of F بيساوي ال
+
+249
+00:20:30,710 --> 00:20:39,590
+infimum لل L بيقف ب element I طيب ال U of F اسف يا
+
+250
+00:20:39,590 --> 00:20:43,010
+جماعة ال U of F بيساوي ال infimum لمين لل U بيقف
+
+251
+00:20:43,720 --> 00:20:49,780
+ماشي الحال الان ايش معناه انه هذا infimum معناته
+
+252
+00:20:49,780 --> 00:20:55,100
+هذا هو عبارة عن ال greatest lower bound مدام ال
+
+253
+00:20:55,100 --> 00:20:59,450
+greatest lower bound اذا ال lower bound هذاأو الـ
+
+254
+00:20:59,450 --> 00:21:03,330
+Greatest Lower Bound لو ضفتله أي رقم يابسون على
+
+255
+00:21:03,330 --> 00:21:06,370
+اتنين مثلا بالذنب يابسون على اتنين الـ game
+
+256
+00:21:06,370 --> 00:21:09,670
+بتعرفوا ليش يابسون على اتنين يعني لو ضفتله أي رقم
+
+257
+00:21:09,670 --> 00:21:14,730
+بيبطل Lower Bound إيش معناته بيبطل Lower Bound
+
+258
+00:21:14,730 --> 00:21:21,830
+يعني هيصير هذا أكبر من ال UB 1 of F for some B
+
+259
+00:21:21,830 --> 00:21:27,510
+وحدهالأنه بطل أش ماله هذا بطل lower bound بطل يكون
+
+260
+00:21:27,510 --> 00:21:32,670
+أصغر من الكل من هان يعني هلاجي واحد من هان هو مش
+
+261
+00:21:32,670 --> 00:21:36,830
+أصغر منه أو بمعنى أخر U, P, 1 و F أصغر من اللي هو
+
+262
+00:21:36,830 --> 00:21:44,850
+هذا المقدر طيب similarly ال L of F هي عبارة عن ال
+
+263
+00:21:44,850 --> 00:21:52,050
+supremum لل L, P و F such that P elemented P of I
+
+264
+00:21:53,040 --> 00:21:57,780
+بنفس الطريقة يا جماعة ال L of F هي عبارة عن إيش ال
+
+265
+00:21:57,780 --> 00:22:04,040
+least upper bound يعني هذا لو least upper bound
+
+266
+00:22:04,040 --> 00:22:07,200
+Upper bound لو كان أصغر و أحد لو هذا least upper
+
+267
+00:22:07,200 --> 00:22:11,000
+bound راحت منه عدد ولو صغير جدا و ليكن يبسلون على
+
+268
+00:22:11,000 --> 00:22:16,800
+اتنينهيبطل هذا عبارة عن upper bound يعني هلاقي
+
+269
+00:22:16,800 --> 00:22:24,280
+واحد من اللي هان اللي هو L of B2 وF مثلا أكبر منه
+
+270
+00:22:24,280 --> 00:22:30,560
+لأنه هيبطل هذا أشماله upper bound لأنه هو ال least
+
+271
+00:22:30,560 --> 00:22:35,780
+لما طلعت منه بطل من ال upper bounds يعني لجيت واحد
+
+272
+00:22:35,780 --> 00:22:43,120
+من هذول أكبر منه إذا صار في عندي اللي هولجيت بي
+
+273
+00:22:43,120 --> 00:22:53,960
+واحد بحقق الأولى و بيتنين بحقق التانية لأن خد الآن
+
+274
+00:22:53,960 --> 00:22:58,840
+خدلي بي إبسلون هذا اللي بديها هذا الحقق اللي اللي
+
+275
+00:22:58,840 --> 00:23:03,600
+بديها خد بي إبسلون إيش بساوي ال بي واحد اللي لجيته
+
+276
+00:23:03,600 --> 00:23:12,050
+هنااتحاد الـ B2 اللي لجيته هان اتحاد مين؟ B2 صار
+
+277
+00:23:12,050 --> 00:23:18,510
+عندى .. صار عندى الآن مع بعض خليني أمسح فأقوم،
+
+278
+00:23:18,510 --> 00:23:22,170
+مهمش؟
+
+279
+00:23:22,170 --> 00:23:31,670
+صار
+
+280
+00:23:31,670 --> 00:23:41,110
+عندى ما يليه؟ صار عندى الآنL of F نقص
+
+281
+00:23:41,110 --> 00:23:53,490
+Y على 2 أصغر من L of B2 Fاللي هو أكيد أصغر أو
+
+282
+00:23:53,490 --> 00:23:59,750
+يساوي L of By قُقَف، ليش؟ لأن الـBy يا جماعة عبارة
+
+283
+00:23:59,750 --> 00:24:04,570
+عن refinement للـB2 والlower لما يصير فيه تحسين
+
+284
+00:24:04,570 --> 00:24:08,510
+بكبر، بروح نحو اتجاه نيل اللي هو المنحنة التالية
+
+285
+00:24:08,510 --> 00:24:14,010
+مساحة تحت المنحنة الكلية لأن أيضا لو جيت قولة الـU
+
+286
+00:24:14,010 --> 00:24:24,400
+of Fزاد إبسلون على اتنين هتلاقيها أكبر من ال U بي
+
+287
+00:24:24,400 --> 00:24:30,410
+واحد و Fوأكيد عندي الـ U of F زائد إبسلون عدنان
+
+288
+00:24:30,410 --> 00:24:34,490
+أكبر من الـ U B1 of F هيكون هذا أكبر أو يساوي الـ
+
+289
+00:24:34,490 --> 00:24:39,610
+U B epsilon of F لأن الـ B epsilon refinement لمين
+
+290
+00:24:39,610 --> 00:24:44,790
+برضه؟ للـ B1 بزام refinement إذن اللي هو التحسين
+
+291
+00:24:44,790 --> 00:24:50,270
+بيزغر القبر وبروح ناحية اللي هو المنحنة إذن الآن
+
+292
+00:24:50,270 --> 00:24:55,480
+من الـ tip 2 هذولةواجدنا طبعا احنا تنسوش ان احنا
+
+293
+00:24:55,480 --> 00:24:59,100
+مفترضين من رأس الدول ان U of F is integrable يعني
+
+294
+00:24:59,100 --> 00:25:05,340
+مفترضين ان ال L of F ايش بتساوي U of F تنسواش هذه
+
+295
+00:25:05,340 --> 00:25:12,540
+ليه جيت تنتر مع بعض دول بصير عندى الحصل على L of F
+
+296
+00:25:12,540 --> 00:25:22,970
+ناقص Y على 2 اللي هو اصغر من Lof B, Epsilon و F
+
+297
+00:25:22,970 --> 00:25:30,110
+والـ L و الـ U of F زائد Epsilon على 2 أكبر من U,
+
+298
+00:25:30,190 --> 00:25:35,290
+B, Epsilon و F أنا إيش غرضي؟ غرضي أثبت إن U, B,
+
+299
+00:25:35,350 --> 00:25:39,130
+Epsilon و F ناقص L, B, Epsilon و F أصغر من Epsilon
+
+300
+00:25:39,130 --> 00:25:42,890
+يلّا اترحل من بعض، إذا بصير عندي، بتحصل البدكية
+
+301
+00:25:42,890 --> 00:25:48,570
+بصير عندي الآن، بطرح حياة دي، بقول U, B, Epsilon و
+
+302
+00:25:48,570 --> 00:25:53,240
+Fناقص لأنه لما نضرب هذا في ناقص هتنعكس يعني هتصير
+
+303
+00:25:53,240 --> 00:25:57,100
+هذه جماعة ناقص وهذه زائد وهذه هتنعكس هيك وهيصير
+
+304
+00:25:57,100 --> 00:26:05,600
+الاش ناقص بيصير عندي U بي و F ناقص ال بي و F هيصير
+
+305
+00:26:05,600 --> 00:26:11,820
+أصغر من مين من ناقص L of F ناخد هذا قبل زي ما احنا
+
+306
+00:26:11,820 --> 00:26:20,690
+مرتبينها U of F زائد ي على 2 ناقصL of F زي إبسلون
+
+307
+00:26:20,690 --> 00:26:24,790
+على 2 وطبعا إحنا جايلين إن F is integrable يعني
+
+308
+00:26:24,790 --> 00:26:28,770
+الـ U of F بسوء L of F إذا هذي بتروح مع هذي بظل
+
+309
+00:26:28,770 --> 00:26:33,610
+إيه شماله؟ بظل إبسلون إذا إحنا لكل إبسلون أكبر من
+
+310
+00:26:33,610 --> 00:26:36,950
+سفر لجينا بي إبسلون هي في الواقع بي إبسلون اللي
+
+311
+00:26:36,950 --> 00:26:39,970
+لجيناها بي واحد اتحاد بي اتنين حيث بي واحد اللي
+
+312
+00:26:39,970 --> 00:26:44,120
+لجيناه هان وال بي اتنين اللي لجيناه هانsuch that U
+
+313
+00:26:44,120 --> 00:26:49,120
+P Y of F نقص L P Y of F أصغر من اللي هو Epsilon
+
+314
+00:26:49,120 --> 00:26:57,480
+وهو المطلوب أي سؤال؟ طيب، ماشي يا شباب، الآن خلصنا
+
+315
+00:26:57,480 --> 00:27:04,420
+الجزء الأول من النظريةأثبتنا اللي بدنا يا انه اللي
+
+316
+00:27:04,420 --> 00:27:08,860
+هو هذه العلاقة صحيحة لأننا نفترض انه suppose that
+
+317
+00:27:08,860 --> 00:27:12,380
+star holds اللي هي star ليه هذه نفترض ان لكل
+
+318
+00:27:12,380 --> 00:27:15,380
+epsilon أكبر من 0 there exists B of epsilon such
+
+319
+00:27:15,380 --> 00:27:18,680
+that U B Epsilon و F نقصها دي أصغر من Epsilon و
+
+320
+00:27:18,680 --> 00:27:24,280
+بدنا نصل من خلالها لإيش لأن ال F is integrable
+
+321
+00:27:24,280 --> 00:27:25,760
+فنشوف
+
+322
+00:27:40,480 --> 00:27:47,440
+البرهام بسيط لو طلعنا عليه مباشرة على اللوح الآن
+
+323
+00:27:47,440 --> 00:27:52,140
+بدنا نفترض أن هذه تتحقق اللي هو نفترض أنه لكل ي
+
+324
+00:27:52,140 --> 00:27:57,020
+أكبر من 0 يوجد بي إبسلون بحيث أن هذا اللي هي تتحقق
+
+325
+00:27:57,020 --> 00:28:01,620
+علشان أصل بدي أصلكم في النهاية أن L of F هي إيش
+
+326
+00:28:01,620 --> 00:28:05,810
+بتساوي U of F شوف كيف ده صلهااللي هبدأ أقوللك اللي
+
+327
+00:28:05,810 --> 00:28:08,650
+هو نفترض انه زي ما قلنا انه star holds اللي حكينا
+
+328
+00:28:08,650 --> 00:28:12,990
+عنها لأن for any partition B هيكون ال L B of F
+
+329
+00:28:12,990 --> 00:28:17,970
+أصغر أساوي L of F و ال U of F أصغر أساوي مين ال U
+
+330
+00:28:17,970 --> 00:28:25,970
+B of F واضح؟ إذا أصار عيدي الآن L يمكن أوضحلكم على
+
+331
+00:28:25,970 --> 00:28:35,790
+اللوح L of B of F ده ال B أي partition أصغرمظبوط
+
+332
+00:28:35,790 --> 00:28:40,910
+أو يساوي ال L of A H of F لانه ال L of F يا جماعة
+
+333
+00:28:40,910 --> 00:28:47,330
+هو ال supremum اللي هنا و ال U بيقف
+
+334
+00:28:47,330 --> 00:28:53,130
+أكبر أو يساوي ال U of F لانه ال U of F H يا جماعة
+
+335
+00:28:53,130 --> 00:28:57,950
+هو عبارة عن مين عبارة عن ال infimumأترحولي الجهة
+
+336
+00:28:57,950 --> 00:29:01,410
+تانية هذا طبعا لكل مين لكل ال partitions اللي في
+
+337
+00:29:01,410 --> 00:29:06,750
+الدنيا من ضمنهم ال P Epsilon اللي احنا ماعطينايا
+
+338
+00:29:06,750 --> 00:29:12,250
+في ال .. اللي هو نص النظرية اذا بسيري عندى لأن لو
+
+339
+00:29:12,250 --> 00:29:19,990
+اجيب طرحة ال U F ناقص L F ال U F ناقص L Fهيصير ايش
+
+340
+00:29:19,990 --> 00:29:23,850
+ماله يا جماعة؟ يعني طريقة رحلة من هذه بيصير أصغر
+
+341
+00:29:23,850 --> 00:29:28,510
+أو يساوي لإن هذه بتضربها في ناقص و هذه ناقص و
+
+342
+00:29:28,510 --> 00:29:32,750
+بتنقلب زي ما عملنا قبل و شوية بيصير أصغر أو يساوي
+
+343
+00:29:32,750 --> 00:29:43,640
+U P of Fنقص ال B of F هذا الكلام صحيح لإيش لكل
+
+344
+00:29:43,640 --> 00:29:48,200
+partition في الدنيا من ضمنها المين ال partition
+
+345
+00:29:48,200 --> 00:29:52,580
+المواطع لنا يعني حيصير عند هذا ينطبق برضه على ال
+
+346
+00:29:52,580 --> 00:29:57,500
+بي إبسلون إذا صار هذا أصغر يسوي بي إبسلون نقص ال
+
+347
+00:29:57,500 --> 00:30:01,740
+بي إبسلون of F طيب هم يعطيين إن هذا المقدار إيش
+
+348
+00:30:01,740 --> 00:30:06,260
+ماله أصغر من إبسلون لأي إبسلون في الدنياهو أنا
+
+349
+00:30:06,260 --> 00:30:10,580
+بعرف أن هذا المقدار نفسه أكبر أو يساوي إيش سفر صار
+
+350
+00:30:10,580 --> 00:30:17,720
+عندى الآن ال U of F ناقص ال L of F دايما أصغر من
+
+351
+00:30:17,720 --> 00:30:23,420
+إبسلون و أكبر أو يساوي سفر لكل إبسلون أكبر من سفر
+
+352
+00:30:23,420 --> 00:30:28,260
+إذا على طول من نظرية في تحليل واحد هيكون هذا اللى
+
+353
+00:30:28,260 --> 00:30:36,250
+عندى إذا U of Fنقص L of F بيساوي سفر إذا U of F
+
+354
+00:30:36,250 --> 00:30:44,850
+بيساوي L of F وهذا يعني F is a Riemann Integral هو
+
+355
+00:30:44,850 --> 00:30:52,110
+المطلوب بيكون احنا هيك أثبتنا اللي هوIntegrable
+
+356
+00:30:52,110 --> 00:30:58,350
+criterion أو اللي هو طريقة لتحديد اللي هو ال
+
+357
+00:30:58,350 --> 00:31:02,270
+function is integrable أو لا غير اللي هو طريقة
+
+358
+00:31:02,270 --> 00:31:07,110
+التعريف الآن في عند كورولاري بعدها كورولاري
+
+359
+00:31:07,110 --> 00:31:11,530
+الكورولاري
+
+360
+00:31:11,530 --> 00:31:16,230
+هي تقول كما يليه الآن بدنا نترجم الحديث بدل ما كان
+
+361
+00:31:16,230 --> 00:31:22,710
+بإبسلون نحكي عن مين؟ عن اللي هوsequence of
+
+362
+00:31:22,710 --> 00:31:29,870
+partitions طبعاً هو هذا معهود التحويل في نظريات
+
+363
+00:31:29,870 --> 00:31:34,590
+مشابهة في حتى في كورسات أخرى خلّينا نشوف عندنا
+
+364
+00:31:34,590 --> 00:31:38,790
+اللي هو النظرية ايش ب .. او الكورلري ايش بتقول
+
+365
+00:31:38,790 --> 00:31:43,350
+بتقول let I بساوة A و B and let F من I لR be a
+
+366
+00:31:43,350 --> 00:31:48,600
+bounded functionلأن لو فرضنا بي أن أن element none
+
+367
+00:31:48,600 --> 00:31:52,300
+is a sequence of partitions of I بحيث أن ال limit
+
+368
+00:31:52,300 --> 00:31:55,920
+هذا بيساوي سفر then f is integrable and ال limit
+
+369
+00:31:55,920 --> 00:31:58,040
+لل integration بيساوي ال integration بيساوي ال
+
+370
+00:31:58,040 --> 00:32:04,480
+limit ال أسف ال limit لل lower p and f بيساوي ال
+
+371
+00:32:04,480 --> 00:32:07,020
+limit لل upper p and f اللي هو بيساوي قيمة ال
+
+372
+00:32:07,020 --> 00:32:13,000
+integration حتى ال converse جماعة اللي هواللي قبل
+
+373
+00:32:13,000 --> 00:32:16,820
+بشوية اللي كان .. اللي هي كانت F أندولي F لأن لو
+
+374
+00:32:16,820 --> 00:32:21,520
+كانت F is integrable أكيد هلاقي sequence من
+
+375
+00:32:21,520 --> 00:32:25,380
+partitions بحيث أنه ال limit اللي حاصل الطرح بساوي
+
+376
+00:32:25,380 --> 00:32:29,760
+سفر اللي هو البرهان مشابه لإي اللي حكيناه فيه اللي
+
+377
+00:32:29,760 --> 00:32:34,500
+هو برهان إيجاد الـ B epsilon ولكن هنا بنجداللي هو
+
+378
+00:32:34,500 --> 00:32:37,380
+الـ Epsilon بساوية واحدة لان فبنلاقي اللي هو ال
+
+379
+00:32:37,380 --> 00:32:42,380
+sequence هذه في ال corollary .. في من مشابه .. شيء
+
+380
+00:32:42,380 --> 00:32:45,900
+مشابه في برهان النظرية الأولى اللي قبل بشوية و
+
+381
+00:32:45,900 --> 00:32:49,360
+ياريت تجربوها عندكم خلينا ناخد اللي .. اللي موجود
+
+382
+00:32:49,360 --> 00:32:54,160
+حاليا اللي هو الاتجاه هذا ان لو لجينا sequence of
+
+383
+00:32:54,160 --> 00:32:59,430
+partitionsوكان ال limit لل U P N و F نقص ال P N و
+
+384
+00:32:59,430 --> 00:33:02,870
+F بساوة سفر إذا هتكون F is integrable و هتكون ال
+
+385
+00:33:02,870 --> 00:33:07,990
+limit للأولى بساوة limit للثانية بساوة قيمة ال
+
+386
+00:33:07,990 --> 00:33:08,970
+integration
+
+387
+00:33:12,900 --> 00:33:17,500
+عند ما أعطيني limit هذا إيش بساوي؟ سفر خلّينا ندخل
+
+388
+00:33:17,500 --> 00:33:20,580
+على التعريف مباشرة تعريف ال limit بتعرفوا تعريف ال
+
+389
+00:33:20,580 --> 00:33:23,140
+limit يا شباب؟ اللي هو لكل إبسلون أكبر من سفر
+
+390
+00:33:23,140 --> 00:33:26,160
+there exist k such that لكل أن أكبر سوى k بيصير
+
+391
+00:33:26,160 --> 00:33:33,200
+هذا ناقص هذا أصغر من مين؟ من اللي هو إبسلون وهذا
+
+392
+00:33:33,200 --> 00:33:35,980
+على طول يعطينا as integral خلّيش تشوف أيش اللي
+
+393
+00:33:35,980 --> 00:33:43,000
+بيقوله لأن since عند ما أعطيني limitU P N و F ناقص
+
+394
+00:33:43,000 --> 00:33:51,240
+ال P N و F as N goes to infinity بساوة سفر، مظبوط؟
+
+395
+00:33:51,240 --> 00:33:56,220
+هي كل ما أعطينيها نجي للتعريف، إذا تعريف ال
+
+396
+00:33:56,220 --> 00:33:58,880
+sequence عادية for every epsilon أكبر من سفر there
+
+397
+00:33:58,880 --> 00:34:02,680
+exists K element in N such that for every N أكبر
+
+398
+00:34:02,680 --> 00:34:13,090
+سوا K اللي هو عندي ال U P N و F ناقصبن و F أصغر من
+
+399
+00:34:13,090 --> 00:34:19,010
+إبسلون إذا مش لجينا بارتشن واحد لجينا بارتشن بك و
+
+400
+00:34:19,010 --> 00:34:22,710
+بك زاد واحد و بك زاد اتنين و بك زاد تلاتة كلهم
+
+401
+00:34:22,710 --> 00:34:29,110
+بسبب إن ال UBK أو ال UBK زاد واحد أو الاخره ناقص
+
+402
+00:34:29,110 --> 00:34:32,590
+القللها أصغر من 100 من إبسلون إذا ال criterion
+
+403
+00:34:32,590 --> 00:34:36,550
+اللي في الكورولاريت حققت إذا صارت عندي هذه إذا F
+
+404
+00:34:36,550 --> 00:34:41,830
+is integrableيعني مش بي إبسلون واحد اللي جينا لأ
+
+405
+00:34:41,830 --> 00:34:46,550
+من عند بك وطالع كل ال partitions هذه اللي هي بك و
+
+406
+00:34:46,550 --> 00:34:49,950
+بك زائد واحد و بك زائد اتنين بتعمل عمل ال بي
+
+407
+00:34:49,950 --> 00:34:53,510
+إبسلون اللي في وين في النظرية إذا ال F أشمالها
+
+408
+00:34:53,510 --> 00:34:58,750
+صارت ال F عبارة عن Integrable من النظرية السابقة
+
+409
+00:34:58,750 --> 00:35:05,200
+الآن الدور دل أن نثبت مين أن ال limitلأ اللي هو
+
+410
+00:35:05,200 --> 00:35:09,260
+هذا المقدار هو limit لهذا المقدار بساوي إيش اللي
+
+411
+00:35:09,260 --> 00:35:12,540
+جوا طبعا هو لو كانت يا جماعة limit هذا نقص هذا سفر
+
+412
+00:35:12,540 --> 00:35:15,920
+مش معناته ال limit الأول و limit الثاني exist هاي
+
+413
+00:35:15,920 --> 00:35:20,610
+مثلا هذه لو كانت هذه un تربيع وهذه unUnterm .. آسف
+
+414
+00:35:20,610 --> 00:35:24,610
+Unتربيع و Unتربيع أو Un و Un limit Un نقص Un على
+
+415
+00:35:24,610 --> 00:35:27,850
+طول سفر لكن لا limit الأولى عدد ولا limit الثاني
+
+416
+00:35:27,850 --> 00:35:33,270
+عدد اتنين اتين بروحين إلى مالا نهاية فالان لكن في
+
+417
+00:35:33,270 --> 00:35:37,390
+هذه الحالة نظرا للمعطيات اللي موجودة و اللي هي
+
+418
+00:35:37,390 --> 00:35:40,930
+طبيعي اللي هو اللي بنحكي فيه NuF is bounded و ببو
+
+419
+00:35:40,930 --> 00:35:45,550
+و الاخره هو استخدام السابق هيطلع عندي فعلا ال
+
+420
+00:35:45,550 --> 00:35:50,840
+limitللأل بيساوي limit للأبر بيساوي قيمة ال
+
+421
+00:35:50,840 --> 00:36:08,200
+integration ماشي اطلعوا يا جماعة عندي الآن خليني
+
+422
+00:36:08,200 --> 00:36:15,240
+أطلع .. نحط البرهان أمامنابدي الآن خلصت اللي هو F
+
+423
+00:36:15,240 --> 00:36:21,500
+is integrable بدي أستخدم زي جابل بشوية بالظبط اللي
+
+424
+00:36:21,500 --> 00:36:28,570
+هو تعريف ال L of F و U of F و إيش تعريفهاذا ما
+
+425
+00:36:28,570 --> 00:36:32,250
+بديش اعيد اللي حكيته قبل بشوية الان بما ان ال L of
+
+426
+00:36:32,250 --> 00:36:42,370
+F عبارة عن اللي هي supremum لل L B of F اذا لكل
+
+427
+00:36:42,370 --> 00:36:46,610
+ي ساوي واحدة لان there exists B N partition of I
+
+428
+00:36:46,610 --> 00:36:50,390
+such that L of F نقص واحدة لان اصغر من مين من L B
+
+429
+00:36:50,390 --> 00:36:54,070
+N of Fزي ما قلت قبل شوية، لو الـ Supremum طرحنا
+
+430
+00:36:54,070 --> 00:36:57,270
+اللي هي الـ Least Upper Bound، طرحنا منه أي عدد، 1
+
+431
+00:36:57,270 --> 00:37:01,330
+على N، إذا هلاجي، هيبطل إيش ماله Upper Bound، إيش
+
+432
+00:37:01,330 --> 00:37:04,190
+معناه يبطل Upper Bound؟ هيلاجي واحد من المجموعة
+
+433
+00:37:04,190 --> 00:37:08,230
+أكبر منه، وهذا فعلا اللي لاجينا BN، بحيث أن الـ BN
+
+434
+00:37:08,230 --> 00:37:13,910
+و F أكبر من الـ F ناقص واحدة لأنالان من هذا .. من
+
+435
+00:37:13,910 --> 00:37:16,670
+.. من .. من ال .. ال .. ال .. ناخد هذا على الطرف
+
+436
+00:37:16,670 --> 00:37:19,970
+الثاني على الطرف هنا و ناخد هذا على الطرف هذا بصير
+
+437
+00:37:19,970 --> 00:37:23,890
+عندي L of F نقص Lb of F أصغر من واحدة الآن و أنا
+
+438
+00:37:23,890 --> 00:37:28,670
+بعرف أن هذا دايما أكبر يساوي هذا لأن هذا ال
+
+439
+00:37:28,670 --> 00:37:32,410
+supremum منهم إذا انا هيكون أكبر يساوي سفر الان
+
+440
+00:37:32,410 --> 00:37:38,440
+خدوا ال limit للجهتينas n goes to infinity بيصير
+
+441
+00:37:38,440 --> 00:37:43,160
+عندي هذا اللي هي limit
+
+442
+00:37:43,160 --> 00:37:48,060
+لL بيقل نوف أف حيثالوي لL أوف أف لإنه حيثير ال
+
+443
+00:37:48,060 --> 00:37:53,720
+limit هذا أيش بيساوي بيساوي سفر واضحالان يا جماعة
+
+444
+00:37:53,720 --> 00:37:58,400
+عندي ال L of F ناقص ال P L of F أصغر من واحدة لأنه
+
+445
+00:37:58,400 --> 00:38:03,660
+أكبر سوى سفر لان معله الان هذا لكل إبسلون اللي هو
+
+446
+00:38:03,660 --> 00:38:07,300
+واحدة لان لجينا partition يعني للإبسلون بيساوي
+
+447
+00:38:07,300 --> 00:38:09,360
+واحد لجينا بيه واحد للإبسلون بيساوي اتنين بيه
+
+448
+00:38:09,360 --> 00:38:12,160
+اتنين للإبسلون تلاتة بيه تلاتة إذا صار عندي
+
+449
+00:38:12,160 --> 00:38:16,580
+sequence of اللي هي إياش partitionsالأن طلع عندي
+
+450
+00:38:16,580 --> 00:38:20,460
+دائما دائما دائما L of F نقص ال PN of F أصغر من
+
+451
+00:38:20,460 --> 00:38:25,440
+واحد على N لكل N الأن as N goes to infinity هذا ال
+
+452
+00:38:25,440 --> 00:38:30,620
+limit هيصير سفر وهذا سفر إذا هيصير limit هذا as N
+
+453
+00:38:30,620 --> 00:38:33,200
+goes to infinity بساوي سفر لكن ال L of F أصلا
+
+454
+00:38:33,200 --> 00:38:37,860
+independent of N إذا هيصير limit PN of F as N goes
+
+455
+00:38:37,860 --> 00:38:43,720
+to infinity بساوي L of F لأن المواضحات لوش يا شباب
+
+456
+00:38:43,720 --> 00:38:52,360
+limitL of F ناقص L B N و F هيساوي 0 as N goes to
+
+457
+00:38:52,360 --> 00:38:56,920
+infinity و هذا المقدار عبارة عن مقدار ثابت
+
+458
+00:38:56,920 --> 00:39:04,740
+independent of N إذا هيصير عندي limit L B N و F
+
+459
+00:39:04,740 --> 00:39:10,540
+بتساوي limit L of F ناقص
+
+460
+00:39:17,660 --> 00:39:27,170
+L of P L و F زائد L of Fمظبوط؟ طيب هذا الأن
+
+461
+00:39:27,170 --> 00:39:33,590
+المقدار معروف أنه بساوي 0 و هذا ثابت إذا بقدر أوزع
+
+462
+00:39:33,590 --> 00:39:37,210
+ال limit على الجهتيين و أنا مرتاح إذا بساوي limit
+
+463
+00:39:37,210 --> 00:39:42,950
+الأول اللي هو 0 زائد limit الثاني نفسه لأنه ثابت
+
+464
+00:39:42,950 --> 00:39:46,450
+إذا صار عندي limit L P N of F as N goes to
+
+465
+00:39:46,450 --> 00:39:54,710
+infinity بساوي L of F كما هو حكينا عنه حقامن جهة
+
+466
+00:39:54,710 --> 00:39:58,650
+أخرى limit الـU ناقص limit الـL المعطيلة هي بيساوي
+
+467
+00:39:58,650 --> 00:40:03,490
+0 إذا صار عندى سهل أن أوجد mean برضه limit الـU
+
+468
+00:40:03,490 --> 00:40:08,990
+اللي هو limit الـU إيش هيساوي ناقص اللي هو .. ال
+
+469
+00:40:08,990 --> 00:40:12,670
+.. ال .. هيساوي limit الـL of F يساوي الـU of F
+
+470
+00:40:12,670 --> 00:40:17,270
+يساوي ال integration أكثر توضيحاً and بيهاجدى
+
+471
+00:40:17,270 --> 00:40:22,420
+أعتقد أنه واضح لكن خلّينا نوضحه بشكل أكبرعشان
+
+472
+00:40:22,420 --> 00:40:34,100
+مايضلش مشي عندى limit U P N of F ايش هيساوي هيساوي
+
+473
+00:40:34,100 --> 00:40:44,560
+اللي هو limit U
+
+474
+00:40:44,560 --> 00:40:49,740
+P N of F
+
+475
+00:40:52,490 --> 00:40:58,090
+limit U P N و F ناقص
+
+476
+00:40:58,090 --> 00:41:07,810
+L of P N of F زائد L P N of F واضحة يا شباب أه؟
+
+477
+00:41:07,810 --> 00:41:12,690
+الآن هذا مضمون أنه موجود و سفر وهذا مضمون و
+
+478
+00:41:12,690 --> 00:41:18,350
+أثبتناه إيش بيساوي L of Fإذا إيش صار بيساوي؟
+
+479
+00:41:18,350 --> 00:41:21,810
+بيساوي اللي هو هذا صفر إذا صار بيساوي أقل و فأف
+
+480
+00:41:21,810 --> 00:41:25,510
+إذا صار هذا برضه بيساوي أقل و فأف لكن أنا مثبت قبل
+
+481
+00:41:25,510 --> 00:41:29,610
+بشوية أن ال F is integrable يعني ال U في F إيش
+
+482
+00:41:29,610 --> 00:41:34,550
+هتساوي؟ اللي أقل و فأف وهذه أثبتناها إيش بتساوي؟
+
+483
+00:41:34,550 --> 00:41:39,350
+limit U P N و F وهذه نفسها أثبتناها قبل بشوية إيش
+
+484
+00:41:39,350 --> 00:41:46,070
+بتساوي؟ limit L P N و Fوهو المطلوب طبعاً مدام
+
+485
+00:41:46,070 --> 00:41:49,370
+integration هذه وهذه هي عبارة عن ال integration
+
+486
+00:41:49,370 --> 00:41:55,410
+على الفترة اللي بنحكي عنها الإنقلا بيه لقيمة ال F
+
+487
+00:41:55,410 --> 00:42:01,710
+لأن صار عندي كل القيام هذه متساوية وصار عندي إيجاد
+
+488
+00:42:01,710 --> 00:42:07,610
+ال limit لل U P N و F أو limit لل L P N و F يكفي
+
+489
+00:42:07,610 --> 00:42:11,330
+أنه نوجد فيه قيمة ال integration بعد ما أثبتناه أو
+
+490
+00:42:11,330 --> 00:42:16,260
+تحت الظروف اللي هي في الكورو الأخرىلأ نيجي بدنا
+
+491
+00:42:16,260 --> 00:42:22,660
+نبرهن اللي هو المثال اللي برهناه المرة الماضية
+
+492
+00:42:22,660 --> 00:42:27,660
+بالتعريف بدنا نبرهنه بواسطة اللي هي ال corollary
+
+493
+00:42:27,660 --> 00:42:33,060
+اللي عندنا بدنا نبرهن اللي هو اللي هي نثبت أنه
+
+494
+00:42:36,170 --> 00:42:42,070
+نثبت أن F of X بساوة X يا شباب عبارة عن Integrable
+
+495
+00:42:42,070 --> 00:42:45,770
+أو اللي سمناها G of X بساوة X is Integrable على
+
+496
+00:42:45,770 --> 00:42:48,830
+الفترة Zero واحد المرة الماضية أثبتناها كيف
+
+497
+00:42:48,830 --> 00:42:54,230
+أثبتناها زي ما أنتم متذكرين بواسط التعريفمظبوط؟
+
+498
+00:42:54,230 --> 00:42:58,610
+طيب جيبنا اللي هو ال upper sum و ال lower sum و
+
+499
+00:42:58,610 --> 00:43:02,930
+بعدين جيبنا ال upper integral و ال lower integral
+
+500
+00:43:02,930 --> 00:43:04,750
+و أثبتنا ان ال upper integral بساوي ال lower
+
+501
+00:43:04,750 --> 00:43:08,760
+integral و خلصناهالآن بدنا نثبتها بطريقتنا اللي هي
+
+502
+00:43:08,760 --> 00:43:12,540
+على الكورولر اللي جابل بشوية عند g of x ساوة x على
+
+503
+00:43:12,540 --> 00:43:16,600
+الفترة 0 بواحد هي المطلوب اثباتها show that g is
+
+504
+00:43:16,600 --> 00:43:20,940
+integrable على هذه الفترة الآن بديش اعيد اللي
+
+505
+00:43:20,940 --> 00:43:23,850
+حكيته المرة الماضية اللي حكيناه المرة الماضيةمن
+
+506
+00:43:23,850 --> 00:43:26,910
+الـ Example اللي أثبتنا فيه انها Integra بالبواسطة
+
+507
+00:43:26,910 --> 00:43:31,470
+اللي هي التعريف أخدنا P N اللي هو Zero واحد على N
+
+508
+00:43:31,470 --> 00:43:34,910
+واثنين على N وان نقص واحد على N لعند الواحد أخدنا
+
+509
+00:43:34,910 --> 00:43:39,290
+اللي هو عبارة عن Any Partition اللي هو بالطريقة
+
+510
+00:43:39,290 --> 00:43:43,710
+اللي أمامي يعني حسب N بيصير بختلف ال Partition أما
+
+511
+00:43:43,710 --> 00:43:46,730
+إيش فكرة ال Partition زي ما قلنا المرة الفائتة من
+
+512
+00:43:46,730 --> 00:43:51,350
+0 لعند 1 جزأناها إلى أجزاء متساوية إلى N من
+
+513
+00:43:51,350 --> 00:43:55,350
+الأجزاء المتساويةصار طول كل sub integral عبارة عن
+
+514
+00:43:55,350 --> 00:44:00,850
+إيهاش عبارة عن واحد على N وأوجدنا في حينه اللي هو
+
+515
+00:44:00,850 --> 00:44:08,470
+ال U P N O G ولاجناها بتساوي إيه ده بتتذكروا نص في
+
+516
+00:44:08,470 --> 00:44:13,710
+واحد زائد واحد على N وأوجدنا برضه ال P N O G
+
+517
+00:44:13,710 --> 00:44:18,910
+ولاجناها عبارة عن نص في واحد ناقص واحد على N كما
+
+518
+00:44:18,910 --> 00:44:26,960
+أذكر ماشي الحال فعلا طيبالان صار عندى الـ PN في
+
+519
+00:44:26,960 --> 00:44:29,780
+الواقع عبارة عن sequence of partitions
+
+520
+00:44:35,190 --> 00:44:39,110
+هذه صارت sequence of partitions بواحد بتعود عن انا
+
+521
+00:44:39,110 --> 00:44:42,750
+بواحد باتنين كده بتلاتة كده باربعة كده وفي كل
+
+522
+00:44:42,750 --> 00:44:47,270
+الأحوال الـ U, B, N و G انجروا لهيها و الـ L, B, N
+
+523
+00:44:47,270 --> 00:44:51,490
+و G بساوي إيش المقدار الأمامي الآن عشان أثبت إنها
+
+524
+00:44:51,490 --> 00:44:56,590
+integrable يكفي من النظرية الكورولاري إن قاعد أقول
+
+525
+00:44:56,590 --> 00:45:03,290
+طب خلينا نشوف limit الـ U, B, N و G ناقص الـ L, B,
+
+526
+00:45:03,450 --> 00:45:09,840
+N و Gas n goes to infinity بساوة إيه يا عشان بساوة
+
+527
+00:45:09,840 --> 00:45:16,360
+سفر نشوفها صح ولا لأ طبعا أكيد مع حسبة بسيطة
+
+528
+00:45:16,360 --> 00:45:24,580
+احسبليها بساوة limit نصفي واحد زياد واحدة لان زياد
+
+529
+00:45:24,580 --> 00:45:28,600
+نص في واحد ناقص واحدة لان as n goes to infinity
+
+530
+00:45:28,600 --> 00:45:32,260
+هذه سفر وهذه سفر وهذه نص وهذه نص وهذه نص وهذه نص
+
+531
+00:45:32,260 --> 00:45:32,260
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+532
+00:45:32,260 --> 00:45:32,260
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+533
+00:45:32,260 --> 00:45:32,260
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+534
+00:45:32,260 --> 00:45:32,260
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+535
+00:45:32,260 --> 00:45:32,340
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+536
+00:45:32,340 --> 00:45:32,920
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+537
+00:45:32,920 --> 00:45:38,340
+وهذه نص وهذه نص وهذه نص وهذه نص وهذه نص
+
+538
+00:45:38,340 --> 00:45:45,580
+وهذهاللي هو y ساوي نص نقص النص y ساوي سفر واضح أهي
+
+539
+00:45:45,580 --> 00:45:50,120
+عندي اللي هو هاد سفر و هاد سفر و نص نقص النص y
+
+540
+00:45:50,120 --> 00:45:54,920
+ساوي سفر مادام سفر إذا إيه شمالها إذا the function
+
+541
+00:45:54,920 --> 00:46:02,720
+d of x ساوي x is integrable on zero واحد هذا by
+
+542
+00:46:02,720 --> 00:46:06,560
+mean by ال corollary اللي قبل بشوية
+
+543
+00:46:15,600 --> 00:46:19,420
+الان بقيمة ال integration ايش هيكون قيمة ال limit
+
+544
+00:46:19,420 --> 00:46:24,280
+limit u, b, n, g هيقدر الغرض و limit l of n of g
+
+545
+00:46:24,280 --> 00:46:29,320
+هيقدر الغرض ليش لأن limit هذا اصلا هيطلع لك limit
+
+546
+00:46:29,320 --> 00:46:35,710
+ال u, b, n و gهو عبارة عن قيمة integration من A ل
+
+547
+00:46:35,710 --> 00:46:42,370
+B حسب النظرية الـ Corollary و يساوي limit 2.5 في 1
+
+548
+00:46:42,370 --> 00:46:48,600
+زائد 1 ل N و يساوي هذا تروح ل 0و يساوى نص و أيضا
+
+549
+00:46:48,600 --> 00:46:54,080
+لو جربت حسب تاب limit ال b, n و g طبعا هيطلع نفس
+
+550
+00:46:54,080 --> 00:46:58,200
+الجواب و إلا إن كان هناك مشكلة لدينا limit نص في
+
+551
+00:46:58,200 --> 00:47:02,340
+واحد ناقص واحد على n و يساوى برضه جدياش نص إذن
+
+552
+00:47:02,340 --> 00:47:06,700
+قيمة ال integration بساوة نص إذن هذه طريقة أخرى
+
+553
+00:47:06,700 --> 00:47:11,780
+لحساب اللي هو أو لإثبات أن g of x بساوة x is
+
+554
+00:47:11,780 --> 00:47:17,560
+integrableالآن بدنا ندخل على أمر آخر الأمر هو في
+
+555
+00:47:17,560 --> 00:47:24,500
+الواقع يا شباب أنه بدنا نشوف إيش في من عائلات
+
+556
+00:47:24,500 --> 00:47:28,400
+الدوال عائلات الدوال إنها تكون Integrable الآن
+
+557
+00:47:28,400 --> 00:47:31,720
+بدنا نيجي نحوش الدوال الـ Integrable إحنا عرفنا بس
+
+558
+00:47:31,720 --> 00:47:36,500
+ده لأ D of X سو X is Integrable و هنلاقي زيها لكن
+
+559
+00:47:36,500 --> 00:47:40,960
+الآن بدنا نيجي نحكي عن دوال اللي هو عائلات من
+
+560
+00:47:40,960 --> 00:47:45,480
+الدوالأول عائلة من العائلات المهمة اللي هي الـ
+
+561
+00:47:45,480 --> 00:47:48,960
+monotone functions يعني الدوال اللي بتكون يا
+
+562
+00:47:48,960 --> 00:47:52,360
+increasing على كل الفترة يا decreasing على كل
+
+563
+00:47:52,360 --> 00:47:59,320
+الفترة بقولكم هذا على اللي هي F من F ال function
+
+564
+00:47:59,320 --> 00:48:04,000
+لو كانت bounded لو كانت monotone على اللي هي
+
+565
+00:48:04,000 --> 00:48:09,660
+closed bounded interval I على طول integrable إذن
+
+566
+00:48:09,660 --> 00:48:16,700
+عيلة كبيرةعيلة الدوال اللي بتكون يا increasing يا
+
+567
+00:48:16,700 --> 00:48:22,380
+decreasing على كل الفترة a و b هذه مضمون انها تكون
+
+568
+00:48:22,380 --> 00:48:26,980
+الدوال ايه شمالها عبارة عن integrable functions
+
+569
+00:48:26,980 --> 00:48:35,090
+اذا اول اعلان الان اللي هو any monotone functionon
+
+570
+00:48:35,090 --> 00:48:40,850
+a closed bounded interval is integrable وهذا اللي
+
+571
+00:48:40,850 --> 00:48:47,090
+هو عنواننا integrability of monotone functionsلت I
+
+572
+00:48:47,090 --> 00:48:51,650
+بتساوي A و B و لت F من I لR بيكون مونوتون فانكشن
+
+573
+00:48:51,650 --> 00:48:57,370
+on I ثم F أشمالها is integrable on I نفترض أن F
+
+574
+00:48:57,370 --> 00:49:03,110
+انتقل هو مونوتور نصل إليها integrable نفترض أن F
+
+575
+00:49:03,110 --> 00:49:09,440
+مثلا increasingونصل إنها integrable وsimilarly
+
+576
+00:49:09,440 --> 00:49:14,560
+وفعلا similarly لو كانت f is decreasing هتكون برضه
+
+577
+00:49:14,560 --> 00:49:21,500
+is integrable خلّينا مع بعض شباب نفترض suppose
+
+578
+00:49:21,500 --> 00:49:31,240
+that f is increasing يعني الدالة على الفترة هي a
+
+579
+00:49:31,240 --> 00:49:37,760
+وb مثلاوالدالة هتكون أشمالها تزايدية يا هيك يا هيك
+
+580
+00:49:37,760 --> 00:49:41,620
+طبعا حسب مش مشكلة بتفرج أشمالها ماشي الحال اللي هي
+
+581
+00:49:41,620 --> 00:49:47,060
+الدالة أشمالها is increasing is increasing بتدخل
+
+582
+00:49:47,060 --> 00:49:53,500
+الآن بي أن اللي هو عبارة عن any partition اللي هو
+
+583
+00:49:55,970 --> 00:50:00,970
+بس بدي أجزه زي منهج اللي عملته معه اللي هو f of x
+
+584
+00:50:00,970 --> 00:50:05,370
+بساوة x اللي قبله شوية بدي أجزه إلى أجزاء متساوية
+
+585
+00:50:05,370 --> 00:50:11,130
+يعني بدي أجز الفقرة a و b إلى أجزاء متساوية الأولى
+
+586
+00:50:11,130 --> 00:50:15,730
+بدي أسميها x note اللي بعدها x1 اللي بعدها x2 لما
+
+587
+00:50:15,730 --> 00:50:21,780
+أصل لآخر 11 أسميها xnونكون طول كل واحدة متساوية
+
+588
+00:50:21,780 --> 00:50:26,340
+للثانية إذا الان إذا بدي أجزئها إلى N إلى N من ال
+
+589
+00:50:26,340 --> 00:50:30,240
+sub intervals بيصير طول كل فترة عبارة عن B minus A
+
+590
+00:50:30,240 --> 00:50:35,080
+على مين؟ على N طول الفترة على عدد الفترات اللي
+
+591
+00:50:35,080 --> 00:50:39,400
+بتديهاأنا بدّي الفترات إيش عددها؟ N فبيصير عند بي
+
+592
+00:50:39,400 --> 00:50:43,320
+ماينس إيه على مين على N هذا طول الفترة يعني الفترة
+
+593
+00:50:43,320 --> 00:50:47,740
+النموذجية لأي K X K minus X K minus واحد هيتمكن
+
+594
+00:50:47,740 --> 00:50:52,560
+طولها عبارة عن بي ماينس إيه على N for every K كيه
+
+595
+00:50:52,560 --> 00:50:56,000
+طبعا إيه اشمالها؟ يا ما بيساوي Zero يا واحد، لعند
+
+596
+00:50:56,000 --> 00:51:01,100
+ماصل، لعند مين؟ لعند N أو K بيساوي واحد لعند N
+
+597
+00:51:04,810 --> 00:51:10,230
+xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+598
+00:51:10,230 --> 00:51:14,230
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+599
+00:51:14,230 --> 00:51:14,590
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+600
+00:51:14,590 --> 00:51:17,070
+-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n-xn-n
+
+601
+00:51:17,070 --> 00:51:25,770
+-xn-n-xn-n-xn-n-xn-n-xn-nلأ لو جينا هذا increasing
+
+602
+00:51:25,770 --> 00:51:30,170
+مدام increasing إذن الـ Mk اللي هي عبارة عن ال
+
+603
+00:51:30,170 --> 00:51:35,510
+supremum اللي هنا supremum لهذه Mk ال supremum
+
+604
+00:51:35,510 --> 00:51:39,910
+اللي هنا هيكون على أخر واحدة لأن أجملها ده لا is
+
+605
+00:51:39,910 --> 00:51:45,510
+increasing إذن هيكون ال Mk هو F of XK رسم عنها
+
+606
+00:51:45,990 --> 00:51:51,210
+بساوة F of X K طيب ال M K Small أكيد هيقولنا كلكم
+
+607
+00:51:51,210 --> 00:51:54,010
+هتقوله بتساوة ال M في معمع الفترة مدام ال M في
+
+608
+00:51:54,010 --> 00:51:57,370
+معمع الفترة إذا أول واحدة فيهم إذا هو F of X K
+
+609
+00:51:57,370 --> 00:52:04,530
+minus واحد، مظبوط شباب؟ طيب، مظبوط هذه اللي هي
+
+610
+00:52:04,530 --> 00:52:10,750
+مالها الدالة اللي بتكون monotone عندي،
+
+611
+00:52:10,750 --> 00:52:21,840
+احسبلي الآن ال U P N و Fنقص الـ BNOF إيش هيساوي؟
+
+612
+00:52:21,840 --> 00:52:26,840
+جهزة الأمور بساوي الـ summation لمين؟ للـ MK
+
+613
+00:52:26,840 --> 00:52:36,190
+Capital في XK نقص XK minus واحدك من عند 1 لعند n
+
+614
+00:52:36,190 --> 00:52:44,370
+نقص summation mk في xk minus xk minus 1 k من عند 1
+
+615
+00:52:44,370 --> 00:52:49,440
+لعند n ويساويالـ Mk وجدناها، اللي هي عبارة عن مين؟
+
+616
+00:52:49,440 --> 00:52:55,420
+F of Xk ويساوي الـ summation للـ F of Xk في مين
+
+617
+00:52:55,420 --> 00:53:00,200
+مضروبة؟ في هذه، هذه كده طولها ثابت، ما احنا هيك
+
+618
+00:53:00,200 --> 00:53:02,540
+على هذا الأساس اذا اخترنا الـ sequence of
+
+619
+00:53:02,540 --> 00:53:05,320
+partitions اللي عندنا، اللي هو طوالث في
+
+620
+00:53:05,320 --> 00:53:09,580
+subintervals ثابتة، كل واحد اسمه يشمله B minus A
+
+621
+00:53:09,580 --> 00:53:14,250
+على N، هذا K من واحدإن عندنا ناقص خلّيني أضعه في
+
+622
+00:53:14,250 --> 00:53:18,550
+summation 1 ناقص نفس القصة اللي هي m k small إيش
+
+623
+00:53:18,550 --> 00:53:23,710
+هي يا جماعة اتفاقنا عبارة عن f of x k minus 1 في
+
+624
+00:53:23,710 --> 00:53:27,610
+هذه خلّيني أخدها عامل مشترك بعد إذنكم لإن هو
+
+625
+00:53:27,610 --> 00:53:31,070
+موجودة هنا وموجودة هنا خلّيني أطلّحها برا واضحة
+
+626
+00:53:31,070 --> 00:53:36,070
+أشيل هذه برا بيصير اللي هو مضروبة في b minus a على
+
+627
+00:53:36,910 --> 00:53:42,350
+وأصلا هذه ثابتة بالنسبة لل summation ليش؟ لأن ال
+
+628
+00:53:42,350 --> 00:53:46,110
+summation العداد K من واحد عندنا أن هذه N ثابتة
+
+629
+00:53:46,110 --> 00:53:52,870
+بالنسبة لل K لذلك بتساوي B minus A على N مضروبة في
+
+630
+00:53:52,870 --> 00:53:59,280
+مين في ال summationللـ f of x k minus f of x k
+
+631
+00:53:59,280 --> 00:54:03,840
+minus واحد k من عند واحد لعند مين يا جماعة لعند ان
+
+632
+00:54:03,840 --> 00:54:07,920
+بعدين the is and could بدي افرطها هذه بيصير عندي y
+
+633
+00:54:07,920 --> 00:54:14,880
+ساوي هذا اللي هو مين كله اللي جاعت بحسبه ال u,b,n
+
+634
+00:54:14,880 --> 00:54:19,320
+وf ناقص ال b,n وf هيسوي هذا المقدار اللي هو b
+
+635
+00:54:19,320 --> 00:54:25,970
+minus a على المضروب فيهالان ال summation عبارة عن
+
+636
+00:54:25,970 --> 00:54:32,630
+k ب 1 بصير f of x 1 ناقص f of x naught اللي بعدها
+
+637
+00:54:32,630 --> 00:54:40,170
+k ب 2 زائد f of x 2 ناقص f of x 1 اللي بعدها زائد
+
+638
+00:54:40,170 --> 00:54:46,130
+f of x 3 ناقص f of x 2 لما نقضى اللي ماشي لأخر
+
+639
+00:54:46,130 --> 00:54:53,140
+واحد بكون عندى f of x nناقص f of x n ناقص واحد
+
+640
+00:54:57,360 --> 00:55:04,840
+F of X1 بيطير مع سالب F of X1 و F of X2 بيطير مع
+
+641
+00:55:04,840 --> 00:55:09,840
+سالب F of X2 و هكذا بظل ماشي لما كله يروح مع كله
+
+642
+00:55:09,840 --> 00:55:16,640
+ما عدا بظل عندي اللي هو أول قيمة اللي هي F of X
+
+643
+00:55:16,640 --> 00:55:22,660
+note بالسالب مع F of Xn الأخيرة بالموجب بيصير عندي
+
+644
+00:55:22,660 --> 00:55:34,740
+Y ساوي B minus A على Nفي F of Xn ناقص F of X0 طبعا
+
+645
+00:55:34,740 --> 00:55:39,420
+Xn آخر واحدة اللي هي B و X0 أول واحدة اللي هي A
+
+646
+00:55:39,420 --> 00:55:46,580
+إذن هيساوي هذا عبارة عن B minus A في F of B minus
+
+647
+00:55:46,580 --> 00:55:53,150
+F of A الكل هذا مجسوم على مين يا جماعة؟ على Nهذا
+
+648
+00:55:53,150 --> 00:55:58,090
+عبارة عن ثابت وهذا عبارة عن ثابت وهذا الان هي اللي
+
+649
+00:55:58,090 --> 00:56:03,670
+بدلالتها كُتِب ال partitions إذا صار عندى الآن بعد
+
+650
+00:56:03,670 --> 00:56:07,230
+كل اللي حكيته هان أخدت ال بي أن بالشكل اللي أمامي
+
+651
+00:56:07,230 --> 00:56:12,190
+عبارة عن sequence of partitions ووصلنا إلى ما
+
+652
+00:56:12,190 --> 00:56:17,890
+لاقيا ليه يا جماعة اللي هو وصلنا ان ال you بي أن و
+
+653
+00:56:17,890 --> 00:56:26,260
+أف ناقص ال بي أن و أفأصغر أو يساوي طبعا أكيد أكبر
+
+654
+00:56:26,260 --> 00:56:29,600
+يساوي صفر لأن هذا دايما أكبر يساوي هذا أصغر يساوي
+
+655
+00:56:29,600 --> 00:56:36,140
+B minus A ف F of B أكيد عرفت أشهد أساوي نقص F of A
+
+656
+00:56:36,140 --> 00:56:41,720
+على اللي هو N الـ N خد ال limit للجهتين as N goes
+
+657
+00:56:41,720 --> 00:56:45,160
+to infinity as N goes to infinity هذا goes to zero
+
+658
+00:56:45,160 --> 00:56:51,730
+وهذا أصلا صفر فبصير عندي limit إذا .. إذا limitالـ
+
+659
+00:56:51,730 --> 00:56:59,290
+U P N و F ناقص الـ L P N و F as N goes to infinity
+
+660
+00:56:59,290 --> 00:57:04,210
+بساوي سفر إذا صار عندي sequence of partitions تحقق
+
+661
+00:57:04,210 --> 00:57:07,730
+لهذا إذا حسب الـ Corollary اللي حكيتها قبل بشوية
+
+662
+00:57:07,730 --> 00:57:17,130
+إذا F is integrable وهو المطلوب إذا صار عندي أي
+
+663
+00:57:17,130 --> 00:57:21,850
+increasing function is integrablesimilarly for
+
+664
+00:57:21,850 --> 00:57:26,170
+decreasing لماذا similarly لأنه تصبح الدالة بدل ما
+
+665
+00:57:26,170 --> 00:57:30,950
+هي طالع هيك تصبح أشمالها نازلة نزول الدالة فبصير
+
+666
+00:57:30,950 --> 00:57:35,430
+عندك اللي هو ال maximum هي الأولى أو ال supremum
+
+667
+00:57:35,430 --> 00:57:41,920
+هي أفبصير الـ MK بسوء F of XK minus واحد والـ MK
+
+668
+00:57:41,920 --> 00:57:46,760
+بسوء F of XK وبيتكملوا البرهان بنفس الطريقة، هيطلع
+
+669
+00:57:46,760 --> 00:57:52,040
+عندكم البرهان automatic وبشكل سهل وبشكل سلس،
+
+670
+00:57:52,040 --> 00:57:58,500
+similar أي سؤال؟ إذن الإعلان اللي أعلنناه قبل
+
+671
+00:57:58,500 --> 00:58:04,800
+بشوية أنه any monotone functionيعني any increasing
+
+672
+00:58:04,800 --> 00:58:08,780
+function on a closed bounded interval must be
+
+673
+00:58:08,780 --> 00:58:15,740
+integrable and any decreasing function on a closed
+
+674
+00:58:15,740 --> 00:58:20,420
+bounded interval برضه must be integrable إذا صار
+
+675
+00:58:20,420 --> 00:58:26,060
+في عنا عائلة كاملة من الدوال القابلة للتكامل بواسط
+
+676
+00:58:26,060 --> 00:58:32,160
+التكامل remandالآن بدنا ننتقل إلى عائلة أخرى
+
+677
+00:58:32,160 --> 00:58:38,300
+وعائلة لا تقل أهمية عن هذه العائلة وعائلة يعني
+
+678
+00:58:38,300 --> 00:58:45,560
+محبوبة عنها اللي هي اللي
+
+679
+00:58:45,560 --> 00:58:53,960
+هي عائلة الدوال المتصلة اللي هي integrable of
+
+680
+00:58:53,960 --> 00:58:56,140
+continuous functions
+
+681
+00:59:00,850 --> 00:59:06,130
+اللي هي integrability of continuous functions
+
+682
+00:59:06,130 --> 00:59:12,210
+النظرية بتقول ما يلي لت أ .. طبعا عندي ال function
+
+683
+00:59:12,210 --> 00:59:16,410
+على closed bounded interval لت F من I لR be
+
+684
+00:59:16,410 --> 00:59:20,750
+continuous on I then F is integrable on I إذا الآن
+
+685
+00:59:20,750 --> 00:59:24,230
+any continuous function on a closed bounded
+
+686
+00:59:24,230 --> 00:59:29,600
+interval must be integrableكمان مرة any continuous
+
+687
+00:59:29,600 --> 00:59:33,840
+function on a closed bounded interval must be
+
+688
+00:59:33,840 --> 00:59:38,920
+integrable طبعا حيزنا في البرهان شغلة اللي هي
+
+689
+00:59:38,920 --> 00:59:45,080
+أخدناها سابقا انهAny continuous function on a
+
+690
+00:59:45,080 --> 00:59:49,840
+closed bounded interval must attain its maximum
+
+691
+00:59:49,840 --> 00:59:57,800
+and minimum on this interval بمعنى
+
+692
+00:59:57,800 --> 01:00:01,970
+آخر هنلاقيلو كانت F is continuous على اللي هو الـ
+
+693
+01:00:01,970 --> 01:00:05,990
+A و الـ B هنلاقي نقطة في داخل الفترة A و B بحيث
+
+694
+01:00:05,990 --> 01:00:09,570
+انها تكون الـ F عندها نقطة maximum و هنلاقي نقطة
+
+695
+01:00:09,570 --> 01:00:12,750
+أخرى في داخل هذه الفترة هنلاقي اللي هي الـ
+
+696
+01:00:12,750 --> 01:00:15,930
+function عندها إشمالها is minimum طبعا absolute و
+
+697
+01:00:15,930 --> 01:00:24,180
+absolute نيجي نشوف .. نيجي للبرهانالان .. نظرية
+
+698
+01:00:24,180 --> 01:00:28,540
+أخرى أيضا .. برضه خلينا نقولها أن لو كانت F is
+
+699
+01:00:28,540 --> 01:00:32,580
+continuous على closed bounded interval then F is
+
+700
+01:00:32,580 --> 01:00:43,820
+uniformly continuous الان F .. عند F من A و B لعند
+
+701
+01:00:43,820 --> 01:00:51,090
+R is continuous on A و Bcontinuous عالمين على
+
+702
+01:00:51,090 --> 01:00:54,450
+closed bounded interval في عندنا نظرية اللي بتقول
+
+703
+01:00:54,450 --> 01:00:58,270
+any continuous function في الواحد on a closed
+
+704
+01:00:58,270 --> 01:01:02,230
+bounded interval must be uniformly continuous إذا
+
+705
+01:01:02,230 --> 01:01:10,030
+then f is uniformly continuous
+
+706
+01:01:10,730 --> 01:01:15,290
+on a و b ايش يعني uniformly continuous يعني لكل
+
+707
+01:01:15,290 --> 01:01:18,810
+ابسلون اكبر من سفر there exist دلتا اكبر من سفر
+
+708
+01:01:18,810 --> 01:01:22,990
+دلتا بس بتعتمد عالميا على ابسلون بتنفع لكل ال X و
+
+709
+01:01:22,990 --> 01:01:30,810
+ال Y such that if X minus Y او U ناقص V زي ما هو
+
+710
+01:01:30,810 --> 01:01:40,200
+مسميها U minus Vأصغر من دلتا then F of U ناقص F of
+
+711
+01:01:40,200 --> 01:01:49,800
+V أصغر من إبسلون لكل UV element in A أو Bإذن لكل y
+
+712
+01:01:49,800 --> 01:01:52,900
+أكبر من 0 there exists Delta دلتا أشمة لا بتعتمد
+
+713
+01:01:52,900 --> 01:01:56,280
+على مين بس على إبسلون في حالة ال continuity
+
+714
+01:01:56,280 --> 01:02:01,560
+العادية بنقول إحنا limit f of x as x بتروح لل a
+
+715
+01:02:01,560 --> 01:02:07,260
+بساوي ايش f of a بنقول الآن إنه limit f of x بساوي
+
+716
+01:02:07,260 --> 01:02:13,450
+f of a as x بتروح لل a لكل إبسلون أكبر من 0هصب مين
+
+717
+01:02:13,450 --> 01:02:18,070
+بالـ a هذه there exist دي و لكل a element in a
+
+718
+01:02:18,070 --> 01:02:23,270
+there exist delta such that اللي لما يكون x minus
+
+719
+01:02:23,270 --> 01:02:27,190
+a أصغر من delta بيعطينا f of x نقص f of a أصغر من
+
+720
+01:02:27,190 --> 01:02:32,550
+إبسلون يعني بيكون الـ delta هنا تعتمد على الإبسلون
+
+721
+01:02:32,550 --> 01:02:37,550
+وتعتمد على ال a اللي عندها ال continuityلكن في الـ
+
+722
+01:02:37,550 --> 01:02:41,890
+Uniform Continuous الـ Delta اللي اللي جيت هنا
+
+723
+01:02:41,890 --> 01:02:47,510
+بتنفع لكل اللي هو ال .. ال .. ال .. ال .. ال .. ال
+
+724
+01:02:47,510 --> 01:02:47,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+725
+01:02:47,890 --> 01:02:47,910
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+726
+01:02:47,910 --> 01:02:48,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+727
+01:02:48,290 --> 01:02:48,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+728
+01:02:48,530 --> 01:02:48,530
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+729
+01:02:48,530 --> 01:02:50,270
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+730
+01:02:50,270 --> 01:02:50,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+731
+01:02:50,330 --> 01:02:50,330
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+732
+01:02:50,330 --> 01:02:50,410
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+733
+01:02:50,410 --> 01:02:50,410
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+734
+01:02:50,410 --> 01:02:54,250
+.. ال .. ال .. ال .. ال .. ال ..
+
+735
+01:02:54,250 --> 01:02:59,970
+ال .. ال ..F is continuous، إذن يُنفرم الـ
+
+736
+01:02:59,970 --> 01:03:02,650
+continuous، إيش معناته؟ كل إبسلون أكبر من صفر،
+
+737
+01:03:02,650 --> 01:03:05,490
+there exists دلتا، بحيث إن U minus V أصغر من دلتا
+
+738
+01:03:05,490 --> 01:03:08,690
+يعطيني F of U ناقص F of V أصغر من إياش، من إبسلون،
+
+739
+01:03:08,690 --> 01:03:11,870
+وخلّي هذه إيش مالها في الذاكرة، أنا عشان الحسابات
+
+740
+01:03:11,870 --> 01:03:15,890
+بدي أخليها إبسلون على مين، على B minus A، طول
+
+741
+01:03:15,890 --> 01:03:19,070
+الفترة اللي أنا بشتغل عليها، هتشوفوا ليش كتبت هيك،
+
+742
+01:03:19,070 --> 01:03:22,720
+بس لا الحساباتبقدر أه بقدر لإن هو أصغر .. أه بقدر
+
+743
+01:03:22,720 --> 01:03:25,140
+خليه أصغر من الـ Epsilon في الدنيا من ضمن إن كل
+
+744
+01:03:25,140 --> 01:03:27,520
+الـ Epsilon عن الـ B minus A لكل الـ Epsilonات
+
+745
+01:03:27,520 --> 01:03:34,040
+اللي في الدنيا طيب لأن شوف وين بده أروح، بده أروح
+
+746
+01:03:34,040 --> 01:03:39,250
+لـ Integrability لـ الـ function Fالأن خُد n الان
+
+747
+01:03:39,250 --> 01:03:42,190
+بدنا نعمل partitions بدنا نجيب sequence of
+
+748
+01:03:42,190 --> 01:03:45,890
+partitions Bn ال sequence of partitions هذه هي
+
+749
+01:03:45,890 --> 01:03:50,010
+اللي هتخدمني هتخدمني متى؟ بعد شوية بتشوفوا ليش
+
+750
+01:03:50,010 --> 01:03:54,110
+هتخدمني لكل الأنات اللي وين ما لإن اللي أكبر من ال
+
+751
+01:03:54,110 --> 01:03:59,370
+B minus A على مين؟ على ال delta اللي لجيتها إذا
+
+752
+01:03:59,370 --> 01:04:04,130
+اللي صارت ال delta بين إيديا إذا بقولك الآن choose
+
+753
+01:04:05,140 --> 01:04:12,320
+N element in N such that ما لها N أكبر من B minus
+
+754
+01:04:12,320 --> 01:04:17,620
+A على مين على دلتا برضه B minus A عشان الحسبان N
+
+755
+01:04:17,620 --> 01:04:21,240
+أكبر من B minus A على مين على دلتا يعني الآن أنا
+
+756
+01:04:21,240 --> 01:04:26,920
+بحكي بحكي عن الأنات اللي بكون أكبر من B minus A
+
+757
+01:04:26,920 --> 01:04:31,460
+على مين على الدلتا اللي لجيتها فوق عندي في اللي هو
+
+758
+01:04:31,460 --> 01:04:37,080
+هذا واحدماشي الحالة الان بتبدأ اكوّن partitions من
+
+759
+01:04:37,080 --> 01:04:42,480
+مين؟ من الأمنات هذه الان بتاخد بيئا اني partitions
+
+760
+01:04:42,480 --> 01:04:47,220
+اني partitions برضه أشماله with equal اللي هي إيش
+
+761
+01:04:47,220 --> 01:04:54,240
+sub intervals يعني X نوت و X واحد لعند X ان يعني
+
+762
+01:04:54,240 --> 01:04:58,540
+طول كل فترة منهم برضه طول .. بتاخد اللي هي كلهم
+
+763
+01:04:58,540 --> 01:05:03,590
+أشمالينمن عند A لعند B يكون ان كل ال sub intervals
+
+764
+01:05:03,590 --> 01:05:08,530
+جت بعض يعني بمعنى أخر هيكون ال XK minus XK minus
+
+765
+01:05:08,530 --> 01:05:12,970
+واحد بيساوي B minus A على N طول كل فترة ايش بيساوي
+
+766
+01:05:12,970 --> 01:05:16,950
+B minus A على عدد الفترات اللي هي N فبكون B minus
+
+767
+01:05:16,950 --> 01:05:21,250
+A عالميا على Nأنا حرّن انهم ألاقي في النهاية
+
+768
+01:05:21,250 --> 01:05:25,630
+sequence of partitions BN limit الـ U B N و F نقص
+
+769
+01:05:25,630 --> 01:05:29,290
+الـ L B N و F بساوي 0 بيكون F is integrable خلصنا
+
+770
+01:05:29,290 --> 01:05:32,950
+أنا قاعد اخترت اللي هي sequence of partitions بناء
+
+771
+01:05:32,950 --> 01:05:36,390
+على الـ Delta اللي لجيتها في ال uniformity و
+
+772
+01:05:36,390 --> 01:05:39,830
+الأنات اللي أكبر منها و حطيت ال partition اللي هو
+
+773
+01:05:39,830 --> 01:05:44,710
+بشكل اللي هو تكون ال subintervals كلها لها نفس
+
+774
+01:05:44,710 --> 01:05:46,230
+الطول طيب
+
+775
+01:05:48,470 --> 01:05:56,170
+الآن زي ما قلت قبل بشوية negation على الفترة xk و
+
+776
+01:05:56,170 --> 01:06:01,710
+minus 1 و xk هذا ال sub interval ال function is
+
+777
+01:06:01,710 --> 01:06:03,550
+continuous عليها لأنها continuous على كل ال
+
+778
+01:06:03,550 --> 01:06:06,970
+interval a و b مدام continuous عليها إذا it
+
+779
+01:06:06,970 --> 01:06:10,310
+attains its maximum and its minimum on this
+
+780
+01:06:10,310 --> 01:06:16,100
+intervalأكيد؟ لقد حد كده قبل مشوية إذن بما أن الـ
+
+781
+01:06:16,100 --> 01:06:18,480
+F is continuously not closed bound in الـ interval
+
+782
+01:06:18,480 --> 01:06:26,800
+هذه إذن there exist سميها U K و V K element in X K
+
+783
+01:06:26,800 --> 01:06:33,720
+minus واحد و X K such that F of U K هي ال maximum
+
+784
+01:06:33,720 --> 01:06:41,190
+على كل هذه ال maximum معناته هي ال supremum of Kأو
+
+785
+01:06:41,190 --> 01:06:47,110
+أيضًا عند الـ VK F of VK هي الـ Minimum على هذه
+
+786
+01:06:47,110 --> 01:06:52,310
+مضمون موجود قلناها هي طبعًا مدامة Minimum على كل
+
+787
+01:06:52,310 --> 01:06:56,150
+الفترة إذًا هي الـ Infimum اللي ببحث عنها اليمين
+
+788
+01:06:56,150 --> 01:07:00,850
+MK على هذه الفترة وها المفتاح أصلا في استخدام الـ
+
+789
+01:07:00,850 --> 01:07:06,120
+Continuity إن ضمن لوجود نقطةعندها ال maximum في
+
+790
+01:07:06,120 --> 01:07:10,540
+هذه المنطقة وضمن اللي وجود نقطة هنا ضمن اللي وجود
+
+791
+01:07:10,540 --> 01:07:13,680
+ال minimum عندها و ال minimum و ال maximum مدام
+
+792
+01:07:13,680 --> 01:07:18,100
+عند نقاط محددة في الفترة هي هتتلاقى و تنقل هي
+
+793
+01:07:18,100 --> 01:07:21,780
+عبارة عن ال supremum و ال infimum على ال sub
+
+794
+01:07:21,780 --> 01:07:29,160
+interval أي سؤال طيب الآن ضال علينا إيش نسوي إن
+
+795
+01:07:29,160 --> 01:07:35,610
+نحسب الحسابات اللي هو نبدأ في حساباتنااللي هو نحسب
+
+796
+01:07:35,610 --> 01:07:44,230
+الـ U و نحسب مين يا جماعة أو نحسب اللي هو ال ال ال
+
+797
+01:07:44,230 --> 01:07:44,230
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+798
+01:07:44,230 --> 01:07:44,930
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+799
+01:07:44,930 --> 01:07:44,930
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+800
+01:07:44,930 --> 01:07:44,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+801
+01:07:44,950 --> 01:07:45,050
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+802
+01:07:45,050 --> 01:07:45,070
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+803
+01:07:45,070 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+804
+01:07:45,130 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+805
+01:07:45,130 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+806
+01:07:45,130 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+807
+01:07:45,130 --> 01:07:45,130
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+808
+01:07:45,130 --> 01:07:53,950
+ال ال الت حسبولي
+
+809
+01:07:54,430 --> 01:07:59,790
+نقص L, P, N و F طبعا أكيد هذا أكبر يساوي سفر حفظنا
+
+810
+01:07:59,790 --> 01:08:04,050
+عن غيره هذا أنه أكبر أو يساوي سفر معروف ضل بدي
+
+811
+01:08:04,050 --> 01:08:08,850
+أحسبهم مع بعض ال summation عبارة عن بساوي
+
+812
+01:08:08,850 --> 01:08:13,610
+summation اللي هو ال M K صارت من ال M K capital
+
+813
+01:08:13,610 --> 01:08:19,950
+اللي هي F of U K صح ولا لأ يا جماعة أه صح و ال U K
+
+814
+01:08:19,950 --> 01:08:26,220
+وين موجودة في هذهالان في مين؟ في xk minus xk minus
+
+815
+01:08:26,220 --> 01:08:31,520
+واحد xk minus xk minus واحد كامل عند واحد اللي
+
+816
+01:08:31,520 --> 01:08:37,020
+عندها انهدمين هي الـ U الان زيها مين ال L ناقص
+
+817
+01:08:37,020 --> 01:08:42,600
+summation الان مين عند ال MK small ال F of VK ال
+
+818
+01:08:42,600 --> 01:08:48,920
+VK اللي لاجيناها برضه هان اللي هي F of VKمضروبة في
+
+819
+01:08:48,920 --> 01:08:54,380
+طول الفترة xk-xk-1 كامل عند واحد لعند مين يا جماعة
+
+820
+01:08:54,380 --> 01:09:00,000
+لعندنا خدولي الآن xk-xk-1 عامل مشترك وطبعا أنا
+
+821
+01:09:00,000 --> 01:09:03,220
+مفترضها اللي هو وماخدها إلا طول ال intervals أو
+
+822
+01:09:03,220 --> 01:09:07,080
+sub intervals متساوي يعني طول هذه وطول هذه هو
+
+823
+01:09:07,080 --> 01:09:10,600
+عبارة عن b-a على n زي النظرية السابقة ويساوي ال
+
+824
+01:09:10,600 --> 01:09:17,850
+summation لل F of uk ناقص F of vkالكل مضروب في مين
+
+825
+01:09:17,850 --> 01:09:26,030
+يا جماعة في B-A على N N أو K من عند واحد لعند إيش
+
+826
+01:09:26,030 --> 01:09:36,830
+لعند N أي سؤال طيب شوفوا الآن اسمحولي بس هنا أشتغل
+
+827
+01:09:36,830 --> 01:09:39,730
+شوية طيب
+
+828
+01:09:42,370 --> 01:09:47,490
+طولوا روحكم عندنا خلصنا يعني جربنا اذا صار عندي ال
+
+829
+01:09:47,490 --> 01:09:51,870
+U, P, N و F عشان تعرفوا أين رايح أنا هي ال U, P, N
+
+830
+01:09:51,870 --> 01:09:55,550
+و F ناقص ال P, N و F أكبر يساوي الصفر اللي جيته
+
+831
+01:09:55,550 --> 01:10:00,610
+أصغر يساوي المقدار اللي أمامي الان خلوني أطلع حد
+
+832
+01:10:00,610 --> 01:10:06,400
+برا بعد اسمكم هي B- a على n لأنها عبارة عن ثابت في
+
+833
+01:10:06,400 --> 01:10:13,020
+ال summation f of u,k ناقص f of v,k كامنة عند واحد
+
+834
+01:10:13,020 --> 01:10:20,340
+لأنك لاحظوا ما يلي يا جماعة عند ال u,k و ال v,k
+
+835
+01:10:20,340 --> 01:10:27,480
+وين موجودة في ال x,k minus واحد و ال x,k اه مظبوط
+
+836
+01:10:27,480 --> 01:10:32,540
+يعني الآن اللي هي طول
+
+837
+01:10:34,610 --> 01:10:41,150
+طول الفترة طول الفترة xk على جهة دي بس يا شباب
+
+838
+01:10:41,150 --> 01:10:46,850
+ناقص xk minus واحد طول الفترة لإن هاد صارت هي xk
+
+839
+01:10:46,850 --> 01:10:53,480
+minus واحد وهي xk ماشي جوات هنا ال mean ال UKو الـ
+
+840
+01:10:53,480 --> 01:10:56,860
+VK في مكان الماد، التنتين المهم جوا التنتين يعني
+
+841
+01:10:56,860 --> 01:10:59,840
+المسافة بين اللي برا هدول، حتى لو كان التنتين
+
+842
+01:10:59,840 --> 01:11:04,120
+زيهن، بكون أصغر أو يساوي المسافة بين التنتين هدول
+
+843
+01:11:04,120 --> 01:11:11,560
+أصغر أو يساوي المسافة هذه، اللي هو UK ناقص VK،
+
+844
+01:11:11,560 --> 01:11:17,010
+مظبوط؟ آسف، العكس، أكبر شكراسامحونا أكبر اياش أو
+
+845
+01:11:17,010 --> 01:11:21,310
+يساوي صارت المسافة بين الجهتين هدولة أكيد أصغر
+
+846
+01:11:21,310 --> 01:11:24,970
+أشهر من المسافة الكلية اللي هنا بينهم طيب المسافة
+
+847
+01:11:24,970 --> 01:11:28,890
+بين هذه وهذه احنا ماخدينها أصلا طول ال interval
+
+848
+01:11:28,890 --> 01:11:29,670
+ايش بتساوي
+
+849
+01:11:33,030 --> 01:11:39,710
+على N إذا المسافة هذه أصلا عبارة عن B-A عالمين على
+
+850
+01:11:39,710 --> 01:11:43,890
+N سامحوني أني بنكتبها هنا إذا صار عندي اللي هو ال
+
+851
+01:11:43,890 --> 01:11:50,230
+U K ناقص ال V K أصغر أو يساوي B-A عالمين على N إذا
+
+852
+01:11:50,230 --> 01:11:58,530
+يا شباب راحظولي هنا U K ناقص V K صارت أصغر أو
+
+853
+01:11:58,530 --> 01:12:06,440
+يساوي B-A عالمينعلى n واضحة طيب نشوف ايش معناه هذا
+
+854
+01:12:06,440 --> 01:12:08,700
+الكلام واش اللي بتقوله ليش بتقولنا هذا الكلام
+
+855
+01:12:08,700 --> 01:12:13,620
+بقوله عشان كلام مهم هذا هو شوفوا فهميته انا مختار
+
+856
+01:12:13,620 --> 01:12:19,260
+ال n اكبر من مين من b minus a على delta يعني بمعنى
+
+857
+01:12:19,260 --> 01:12:24,280
+اخر ايش معنات هذا يعني b minus a على n اصغر من مين
+
+858
+01:12:24,280 --> 01:12:29,640
+من دلتا يعني هذا المقدارأصغر من إيش يا جماعة؟ من
+
+859
+01:12:29,640 --> 01:12:35,160
+دلتا صارت ال U K ناقص ال V K أصغر من مين؟ من دلتا
+
+860
+01:12:35,160 --> 01:12:40,800
+واحنا بنقول أن المقاطع اللي بتحقق فيها ال U ناقص V
+
+861
+01:12:40,800 --> 01:12:44,560
+أصغر من دلتا بكون عندي F of U ناقص F of V أصغر من
+
+862
+01:12:44,560 --> 01:12:50,240
+مين يا جماعة؟ من Epsilon على B minus A إذا صارت
+
+863
+01:12:50,240 --> 01:12:55,100
+عندي المقاطين هذولة ال U K ناقص V K اللي أصغر من
+
+864
+01:12:55,100 --> 01:13:04,770
+دلتاإذا أكيد من واحد هيكون عندي F of U K ناقص F of
+
+865
+01:13:04,770 --> 01:13:12,670
+V K إيش هيكون؟ هيكون عبارة عن أصغر من Y على B
+
+866
+01:13:12,670 --> 01:13:20,410
+minus A إذا الآن بحجلني أني أقول أن هذا المقدار
+
+867
+01:13:20,410 --> 01:13:24,400
+اللي عندياللي هو طبعا هذا الكبير وهذا الصغير طبعا
+
+868
+01:13:24,400 --> 01:13:27,800
+على absolute value نفسه بحجل إن أقول هذا أصغر أو
+
+869
+01:13:27,800 --> 01:13:34,680
+ساوي B minus A على N مضروب في مين في ال summation
+
+870
+01:13:34,680 --> 01:13:42,480
+لل Epsilon على B minus A كامن عند واحد لعند مين
+
+871
+01:13:42,480 --> 01:13:50,100
+لعند N واضح
+
+872
+01:13:52,720 --> 01:13:58,440
+إذا صار عندى الآن اللى هو اللى أثبته أنه U P N و F
+
+873
+01:13:58,440 --> 01:14:04,220
+ناطق سؤال P N و F أصغر أو ساوى P minus A على N في
+
+874
+01:14:04,220 --> 01:14:10,300
+.. خلّيني أجف و أقولها .. أه .. انتظر .. أعملنى ..
+
+875
+01:14:13,410 --> 01:14:18,250
+إذا اللي وصلنا له يا جماعة اللي هو أن ال U P N و F
+
+876
+01:14:18,250 --> 01:14:21,650
+نقص ال P N و F أكبر يساوي سفر و في نفس الوقت أصغر
+
+877
+01:14:21,650 --> 01:14:24,430
+يساوي P Minus A على N في ال summation لل Epsilon ع
+
+878
+01:14:24,430 --> 01:14:28,630
+P Minus A اللي هو كامن عند واحد ل N يعني هذه قاعدة
+
+879
+01:14:28,630 --> 01:14:34,050
+عمالها كل مرة بتعد Epsilon ع P Minus A أكم مرة
+
+880
+01:14:34,050 --> 01:14:37,670
+بتعد N من المرات إذا حيصير عندي هذا عبارة عن P
+
+881
+01:14:37,670 --> 01:14:43,170
+Minus A على N و اللي نعد هناN من القمية اللي هذه
+
+882
+01:14:43,170 --> 01:14:47,630
+يعني N في epsilon على B minus A الان B minus A مع
+
+883
+01:14:47,630 --> 01:14:51,970
+ال B minus A و ال N مع ال N فبصير أوصلنا احنا إلى
+
+884
+01:14:51,970 --> 01:14:55,950
+ما يلي انتبهوا للنتيجة النهائية اللي بتوصلي لي
+
+885
+01:14:55,950 --> 01:15:04,310
+اللي هو المطلوب النتيجة اللي وصلت لها انه اذاU P N
+
+886
+01:15:04,310 --> 01:15:12,430
+و F نقص L P N و F أكبر أو يساوي سفر وأصغر من مين
+
+887
+01:15:12,430 --> 01:15:19,190
+من إبسلون لكل إبسلون أكبر من سفر إذا اللي جوا غصب
+
+888
+01:15:19,190 --> 01:15:24,310
+عنه إذا لازم يكون اللي هو لو أخدت ال limit هيظل
+
+889
+01:15:24,310 --> 01:15:30,220
+limit ال Uبن لأن هذا أصلا صحيح علميا للأنات
+
+890
+01:15:30,220 --> 01:15:34,200
+الكبيرة فلما أخد ال limit أزنه جوزه infinity بضل
+
+891
+01:15:34,200 --> 01:15:38,280
+في ال safe side يعني بضل في اللي بتحقق فيه هذا إذا
+
+892
+01:15:38,280 --> 01:15:45,630
+ال limit U, B, N و F ماقص L, B, N و Fهيكون أكبر أو
+
+893
+01:15:45,630 --> 01:15:50,490
+يساوي سفر و أصغر أو يساوي إبسلون و هذا الكلام as
+
+894
+01:15:50,490 --> 01:15:53,530
+and goes to infinity و هذا الكلام صحيح برضه لمين
+
+895
+01:15:53,530 --> 01:15:58,790
+لكل إبسلون أكبر من سفر إذا غصب عنها هيكون اللي جوا
+
+896
+01:15:58,790 --> 01:16:08,780
+limit UPN و F-Lبان و اف لازم يساوي ايش سفر از انقص
+
+897
+01:16:08,780 --> 01:16:14,780
+انفينيتي وهذا by corollary اللي قبل بشوية هيعني ان
+
+898
+01:16:14,780 --> 01:16:23,310
+اف is integrableHence, F is integrable وهكذا
+
+899
+01:16:23,310 --> 01:16:27,610
+أثبتنا العائلة الثانية من الدوال الـ continuous
+
+900
+01:16:27,610 --> 01:16:31,170
+function على closed bounded interval is a
+
+901
+01:16:31,170 --> 01:16:34,210
+continuous function is an integrable function
+
+902
+01:16:34,210 --> 01:16:40,790
+وهكذا خلصنا الـ section الأول و الـ homework هيا
+
+903
+01:16:40,790 --> 01:16:46,750
+اللي موجودة في التلخيص و المرة القادمة ان شاء الله
+
+904
+01:16:47,630 --> 01:16:57,970
+إن شاء الله بكون احنا بنبدأ في اللي هي ال section
+
+905
+01:16:57,970 --> 01:17:03,510
+اللي بعده اللي هو properties of the Riemann
+
+906
+01:17:03,510 --> 01:17:04,470
+Integral
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EIprZTnXBQc_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EIprZTnXBQc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..90baac16b3028f233d1961917fab7505687be3ae
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EIprZTnXBQc_raw.srt
@@ -0,0 +1,3444 @@
+1
+00:00:05,090 --> 00:00:08,030
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,030 --> 00:00:11,070
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:11,070 --> 00:00:18,250
+أجمعين هذه المحاضرة رقم 24 مساق تحليل حقيقة 2 طلاب
+
+4
+00:00:18,250 --> 00:00:22,650
+وطالبات الجامعة الإسلامية قسم رياضيات كلية العلوم
+
+5
+00:00:23,470 --> 00:00:26,630
+اليوم هنكمل ان شاء الله ال section الأخير في
+
+6
+00:00:26,630 --> 00:00:29,870
+chapter 8 اللي هو 8 أربعة تحت عنوان the
+
+7
+00:00:29,870 --> 00:00:35,170
+trigonometric functions وهو أيضا اللي هو section
+
+8
+00:00:35,170 --> 00:00:42,210
+أو موضوع تطبيق على اللي هوالـ pointwise and
+
+9
+00:00:42,210 --> 00:00:46,030
+uniform convergence للـ sequence of functions وكيف
+
+10
+00:00:46,030 --> 00:00:50,510
+بدنا نعرف بطريقة مشابهة جدا لمعرفناها المرة
+
+11
+00:00:50,510 --> 00:00:53,330
+الماضية أو اللي قبلها بخصوص الـ exponential
+
+12
+00:00:53,330 --> 00:00:58,710
+function هنعرف اليوم اللي هو بنفس الطريقة كيف نعرف
+
+13
+00:00:58,710 --> 00:01:03,510
+اللي هو الـ sine و الـ cosine as a limit اللي هو
+
+14
+00:01:03,510 --> 00:01:07,390
+of a uniformly convergent sequence of functions
+
+15
+00:01:07,950 --> 00:01:11,230
+العنوان is in the trigonometric functions اللي هو
+
+16
+00:01:11,230 --> 00:01:15,450
+section 8 أربعة النظرية
+
+17
+00:01:15,450 --> 00:01:21,950
+الأولى اللى عندنا اللى مشابهة لنظرية سابقة اللى هي
+
+18
+00:01:21,950 --> 00:01:25,870
+ال exponential اللى من خلالها بدنا نصل لاللي هو
+
+19
+00:01:25,870 --> 00:01:31,370
+تعريف اللى هي ال cosine و ال sineالنظرية بتقول
+
+20
+00:01:31,370 --> 00:01:35,190
+مالي there exist functions يوجد دوال الأمنان في
+
+21
+00:01:35,190 --> 00:01:40,570
+بتوجود دوال C من R ل R and S من R ل R such that
+
+22
+00:01:40,570 --> 00:01:44,690
+اللي هي طبعا مستقبلا هنتسمي ال C اللي هي ال cosine
+
+23
+00:01:44,690 --> 00:01:48,910
+ومستقبلا هنتسمي ال S اللي هي ال sine اللي احنا
+
+24
+00:01:48,910 --> 00:01:54,090
+بنعرفهاالان بنقول في ده اللي تاني واحدة اسمها c
+
+25
+00:01:54,090 --> 00:01:59,950
+واحدة s تحقق ما يلي اللي هي cw prime of x بيساوي
+
+26
+00:01:59,950 --> 00:02:04,870
+ناقص c of x s w prime of x بيساوي ناقص s of x ولو
+
+27
+00:02:04,870 --> 00:02:08,730
+استذكرت انت ال sine و ال cosine دي ما سيحدث لاحقا
+
+28
+00:02:08,730 --> 00:02:12,270
+طبعا لو استذكرت ال cosine لما ان .. ان .. ان .. ان
+
+29
+00:02:12,270 --> 00:02:16,130
+فاضلها مرتين هتصير اللي هي ناقص اللي هي نفسها و لو
+
+30
+00:02:16,130 --> 00:02:19,570
+فاضلت ال sine برضه فاضلها مرتين هتلاقيها ايش هي
+
+31
+00:02:19,960 --> 00:02:23,840
+بتطلع سالب S الخاصية التانية اللي هي C of Zero
+
+32
+00:02:23,840 --> 00:02:27,780
+بساوة واحد ولو استذكرت الكوسين كوسين ال Zero بساوة
+
+33
+00:02:27,780 --> 00:02:31,240
+واحد ولو استذكرت الكوسين لما تاخدها ال derivative
+
+34
+00:02:31,240 --> 00:02:35,160
+هتصير عبارة عن سالب Sin عند Zero هتطلع H بساوة
+
+35
+00:02:35,160 --> 00:02:38,960
+Zero and S of Zero بساوة Zero وS prime of Zero
+
+36
+00:02:38,960 --> 00:02:45,330
+بساوة واحد يعني بمعنى أخر يوجد دالتين الآندالتين
+
+37
+00:02:45,330 --> 00:02:49,770
+واحدة من C لـ A اسمها S واحدة اسمها C من R ل R
+
+38
+00:02:49,770 --> 00:02:56,690
+تحقق الشرطين التاليين CW' بسوء ناقص C وSW' بسوء
+
+39
+00:02:56,690 --> 00:03:01,330
+ناقص S على كل R وC عند الـ 0 هي 1 وC' عند الـ 0
+
+40
+00:03:01,330 --> 00:03:05,650
+بسوء 0 وS عند الـ 0 بسوء 0 وS' عند الـ 0 بسوء 1
+
+41
+00:03:05,650 --> 00:03:11,250
+وبعد شوية هقولك لا يوجد في الدنيا دالتين بحقق ان
+
+42
+00:03:11,250 --> 00:03:17,300
+الشروط هذولةإلا هي واحدة اسمها C واحدة اسمها S
+
+43
+00:03:17,300 --> 00:03:22,640
+يعني التنتين واحدات وهذا يجعلنا نسميهم التسمية بعد
+
+44
+00:03:22,640 --> 00:03:26,380
+ذلك واحدة اسمها cosine واحدة اسمها sine ومن ثم
+
+45
+00:03:26,380 --> 00:03:29,320
+بنجيب كل الخواص اللي احنا بنعرفه عن ال sine و ال
+
+46
+00:03:29,320 --> 00:03:34,020
+cosine من هذا البناء إذن الآن أنا ببني ببني ببني
+
+47
+00:03:34,020 --> 00:03:36,980
+وجود ال sine و ال cosine و بعد شوية ببني اللي هو
+
+48
+00:03:36,980 --> 00:03:40,960
+ال uniqueness طبقا لهذه الشروط اللي موجودة عندى
+
+49
+00:03:42,380 --> 00:03:45,860
+الان بكيف بدنا نعمل زي ما عملنا المرة الماضية في
+
+50
+00:03:45,860 --> 00:03:48,340
+ال .. في ال .. اللي هو الـ Exponential عشانك
+
+51
+00:03:48,340 --> 00:03:52,060
+هتلاقوني شوية مسرع لإن اللي بيحضر اللي هي محاضرة
+
+52
+00:03:52,060 --> 00:03:56,620
+الـ Exponential هيلاقي إن هذا في كتير من الحديث في
+
+53
+00:03:56,620 --> 00:04:00,640
+إعادة We define the sequence cn as n of continuous
+
+54
+00:04:00,640 --> 00:04:05,240
+functions inductively as بدنا نعرف اللي هي .. اللي
+
+55
+00:04:05,240 --> 00:04:09,640
+هو two sequences واحدة نسميها cn وواحدة نسميها sn
+
+56
+00:04:10,270 --> 00:04:13,890
+كيف بدنا نعرفها؟ زي ما عرفنا الـ exponential بنعرف
+
+57
+00:04:13,890 --> 00:04:19,250
+C1 of X إيش بتساوي واحد وS1 of X إيش بدنا نسميها
+
+58
+00:04:19,250 --> 00:04:26,490
+بساوي X الآن S2 of X S2 of X هيساوي ال integration
+
+59
+00:04:26,490 --> 00:04:31,990
+من صفر لعند X C2 of T DT طب C2 من وين أجيبها؟ C2
+
+60
+00:04:31,990 --> 00:04:36,050
+بتجيبها من هنا C اللي هي واحد زائد واحد يعني C2
+
+61
+00:04:36,050 --> 00:04:41,470
+بساوي واحد ناقص ال integration من صفر ل Xلـ S1 of
+
+62
+00:04:41,470 --> 00:04:48,870
+T اللي هذا DT فبكون جيبت ال C2 و بتجيبت ال S2 من
+
+63
+00:04:48,870 --> 00:04:55,530
+ال C2 لأن S3 و C3 بنفس الطريقة in general اللي أنا
+
+64
+00:04:55,530 --> 00:04:59,170
+عملت sequence of functions اللي هو بدأت اللي هي ال
+
+65
+00:04:59,170 --> 00:05:05,120
+C1 ب1 S1 ب Xومن ثم S N بتساوي من صفر ل X
+
+66
+00:05:05,120 --> 00:05:10,760
+integration C N of T DT يعني كمالة C N of T DT وC
+
+67
+00:05:10,760 --> 00:05:13,460
+N زائد واحد of X بتساوي واحد نقص integration من
+
+68
+00:05:13,460 --> 00:05:18,700
+صفر ل X S N of T DT الآن هو بيقول اللي هو هذه
+
+69
+00:05:18,700 --> 00:05:21,820
+sequence of continuous functions طب sequence of
+
+70
+00:05:21,820 --> 00:05:25,840
+continuous functions هذا الكلام بده إثباتطيب، الان
+
+71
+00:05:25,840 --> 00:05:29,500
+عندى اللى هو by induction زى ما انتوا عارفين الان
+
+72
+00:05:29,500 --> 00:05:33,600
+عندى الـC1 continuous لان الثابتة S1 continuous
+
+73
+00:05:33,600 --> 00:05:38,880
+لان هى شمالها بتساوي X بناء عليه هتطلع عندى اللى
+
+74
+00:05:38,880 --> 00:05:44,920
+هى C2 continuous ومن ثم C3 وC4 الاخرين الان لو
+
+75
+00:05:44,920 --> 00:05:49,000
+بدنا نثبتها by induction بدنا نفترض انه هذولة
+
+76
+00:05:49,000 --> 00:05:52,560
+الـSn والـCn
+
+77
+00:05:53,920 --> 00:06:00,700
+continuous سنثبت هنا continuous لأن S1 ايش بتساوي
+
+78
+00:06:00,700 --> 00:06:06,860
+X؟ C1 ايش بتساوي 1؟ continuous إذا صارت هذه اللي
+
+79
+00:06:06,860 --> 00:06:12,340
+هي الجملة is true for N بتساوي 1 نفترض الآن
+
+80
+00:06:12,340 --> 00:06:19,900
+supposeby induction بتهدي suppose that الهو star
+
+81
+00:06:19,900 --> 00:06:25,960
+هذي is true for n ايش بتساوي n بتساوي k معناته
+
+82
+00:06:25,960 --> 00:06:33,820
+صارت ال S Kوالـ CK are continuous بتثبت الآن من
+
+83
+00:06:33,820 --> 00:06:38,520
+الصحيحة لـ K زائد واحد يعني بتثبت اللي هو CK زائد
+
+84
+00:06:38,520 --> 00:06:42,700
+واحد و SK زائد واحد ان هنا شمال هنا continuous طيب
+
+85
+00:06:42,700 --> 00:06:48,000
+الآن شوف CK زائد واحد بتساوي حسب اللي هي عندي هان
+
+86
+00:06:48,000 --> 00:06:51,740
+ايش بتساوي اللي هو عبارة عن CK واحد of X بتساوي ال
+
+87
+00:06:51,740 --> 00:06:58,020
+integration واحد نقص ال integration من صفر X Sك ..
+
+88
+00:06:58,020 --> 00:07:03,020
+هذا كز واحد .. هذا ك .. of DT طيب أنا مفترض أن S K
+
+89
+00:07:03,020 --> 00:07:06,600
+من ال hypothesis induction إنها continuous إذا
+
+90
+00:07:06,600 --> 00:07:11,040
+صارت هذه كلها إيش مالها؟ اللي هي S K integrable
+
+91
+00:07:11,040 --> 00:07:15,600
+وصارت هذه كلها على بعض by fundamental theorem of
+
+92
+00:07:15,600 --> 00:07:20,980
+calculus اللي هي ال derivative إلها موجودة إذا
+
+93
+00:07:20,980 --> 00:07:23,440
+صارت هذه كلها ال derivative إلها وموجودة بالنسبة
+
+94
+00:07:23,440 --> 00:07:27,680
+لل Xإذا صارت مدام هيك هاذ is differentiable إذا
+
+95
+00:07:27,680 --> 00:07:30,940
+continuous إذا صارت اللي هي ck زائد واحد
+
+96
+00:07:30,940 --> 00:07:35,200
+continuous اللي ثبت الآن is sk زائد واحد sk زائد
+
+97
+00:07:35,200 --> 00:07:39,280
+واحد of x أيش بتساوي حسب اللي التعريف بتساوي ال
+
+98
+00:07:39,280 --> 00:07:47,660
+integration من صفر العند x ck of tزايد واحد هذا N
+
+99
+00:07:47,660 --> 00:07:52,620
+هذا N K زايد واحد K زايد واحد DT وانا مثبت فوق انه
+
+100
+00:07:52,620 --> 00:07:56,160
+CK زايد واحد is continuous إذا صارت هذه كلها على
+
+101
+00:07:56,160 --> 00:07:59,500
+بعض integrable اللي هي CK زايد واحد صار هذا ال
+
+102
+00:07:59,500 --> 00:08:02,000
+integration exist ومش هيك by fundamental theorem
+
+103
+00:08:02,000 --> 00:08:04,720
+of calculus برضه ال derivative له إيه شمالها
+
+104
+00:08:04,720 --> 00:08:07,700
+موجودة إذا صارت هذه ال differentiable إذا
+
+105
+00:08:07,700 --> 00:08:11,060
+continuous إذا صارت CK زايد واحد وSK زايد واحد are
+
+106
+00:08:11,060 --> 00:08:16,160
+continuous إذا صارت الجملة هذه صحيحةلأ K زائد واحد
+
+107
+00:08:16,160 --> 00:08:21,000
+إذا صارت صحيحة دائما إذا صارت عندي الان مفرغ منه
+
+108
+00:08:21,000 --> 00:08:26,360
+ال CN والSN are continuous functions وبناء عليه
+
+109
+00:08:26,360 --> 00:08:29,860
+مدام continuous functions by fundamental theorem
+
+110
+00:08:29,860 --> 00:08:35,460
+of calculus هتكون هذه ال SN differentiable و ال CN
+
+111
+00:08:35,460 --> 00:08:39,800
+زائد واحد differentiable ومش هيك كمان و هيعطيني ال
+
+112
+00:08:39,800 --> 00:08:43,440
+SN prime of X حسب ال fundamental theorem of
+
+113
+00:08:43,440 --> 00:08:46,820
+calculusالـ differentiation بتضايق ال integration
+
+114
+00:08:46,820 --> 00:08:54,580
+بتضال بساوي cn of x الان و ال derivative لهذه برضه
+
+115
+00:08:54,580 --> 00:08:59,900
+exist cn زائد واحد prime of x اللي هو هي ساوي اللي
+
+116
+00:08:59,900 --> 00:09:10,170
+هو مين هتطلع ناقص snof X إذا صار عندي الآن اللي هي
+
+117
+00:09:10,170 --> 00:09:15,610
+ال sequence اللي عندي صارت well defined كلها و
+
+118
+00:09:15,610 --> 00:09:20,270
+continuous كلها و لأ و differentiable كمان ال SN
+
+119
+00:09:20,270 --> 00:09:25,150
+prime of X بيساوي CN of X و CN زائد واحد prime of
+
+120
+00:09:25,150 --> 00:09:31,730
+X بيساوي ناقص SN of X زي ما أنا أثبتها و أوضحت لكم
+
+121
+00:09:31,730 --> 00:09:38,710
+إياها هناالآن induction arguments برضه induction
+
+122
+00:09:38,710 --> 00:09:42,970
+arguments بقول لي we leave this argument for you
+
+123
+00:09:42,970 --> 00:09:46,890
+خلينا نشوفها مع بعض ماهي اللي بنقصده زي ما عملت
+
+124
+00:09:46,890 --> 00:09:49,870
+بالظبط لو طلعت على الخطوات هتلاقيها مشابه لخطوات
+
+125
+00:09:49,870 --> 00:09:54,970
+تبعات ال exponential عند ال Sn of X زي ما قلنا
+
+126
+00:09:54,970 --> 00:10:02,060
+بسوء ال integration من 0 ل X Cn of T dtC N زائد
+
+127
+00:10:02,060 --> 00:10:06,140
+واحد of X بساوة واحد مقص ال integration من C ل X S
+
+128
+00:10:06,140 --> 00:10:15,360
+N of T DT ومعطينا طبعا احنا اخدنا ال C واحد of X
+
+129
+00:10:15,360 --> 00:10:22,530
+بساوة واحدو الـ c و s1 of x بسوة x هذه اللي هي ال
+
+130
+00:10:22,530 --> 00:10:25,370
+sequence of functions اللي أثبتناها هذه ال
+
+131
+00:10:25,370 --> 00:10:27,990
+sequence of functions ال sn و ال cn زائد واحد
+
+132
+00:10:27,990 --> 00:10:32,230
+التنتين are continuous for every n و همش هي
+
+133
+00:10:32,230 --> 00:10:34,850
+codifferentiable و ال derivative إلها زي ما قلنا
+
+134
+00:10:34,850 --> 00:10:39,430
+sn prime of x بسوة cn of x و ال cn زائد واحد prime
+
+135
+00:10:39,430 --> 00:10:44,190
+of x بسوة ناقص sn of x و خلّينا نسجلها هذه لإنه
+
+136
+00:10:44,190 --> 00:10:52,370
+هنحتاجها بعد شويةاللي هي S N prime of X بساوي
+
+137
+00:10:52,370 --> 00:11:00,310
+C N of X and C N زائد واحد prime of X بساوي ناقص S
+
+138
+00:11:00,310 --> 00:11:09,070
+N of X طيب الآن بدنا اللي هو by induction نثبت
+
+139
+00:11:09,070 --> 00:11:12,570
+اللي هو C N زائد واحد of X بساوي اللي هو اللي
+
+140
+00:11:12,570 --> 00:11:18,460
+أمامي هذا طبعا أكيد اللي هوبعضكم قال ما هي by
+
+141
+00:11:18,460 --> 00:11:24,960
+induction نتطلع على C2 of X C1 في القرآن بتساوي
+
+142
+00:11:24,960 --> 00:11:31,720
+واحد نثبتها يعني الان C2of X ايش بتساوي حسب
+
+143
+00:11:31,720 --> 00:11:35,960
+القانون بساوي واحد ماقص ال integration من صفر ل X
+
+144
+00:11:35,960 --> 00:11:41,020
+أس واحد لأنه بواحد هنا أس واحد اللي هي جدش أس واحد
+
+145
+00:11:41,020 --> 00:11:46,060
+ال X integration اللي هي TDT ويساوي التفاضل اللي
+
+146
+00:11:46,060 --> 00:11:49,820
+هذي بيصير واحد ماقص X تربيع على مين على اتنين إذا
+
+147
+00:11:49,820 --> 00:11:54,410
+فعلا اللي هي Cاللي هي هذه اتنين is true for any
+
+148
+00:11:54,410 --> 00:11:58,870
+ايش بتساوي ان بتساوي واحد بدنا نثبت التانية معها
+
+149
+00:11:58,870 --> 00:12:01,730
+اللي هي true for any بتساوي واحد لإنها دي جملة
+
+150
+00:12:01,730 --> 00:12:05,690
+واحدة بدأ أثبتها انها true for every any الان for
+
+151
+00:12:05,690 --> 00:12:10,590
+any بتساوي واحد بيصير عندي أس اتنين of x بدأ أتأكد
+
+152
+00:12:10,590 --> 00:12:15,990
+انه اللي هي بتحقق اللي هي ال .. اللي .. ايه هذه ال
+
+153
+00:12:15,990 --> 00:12:19,960
+equationS2 of X بيساوي من وين بده اجيبها من
+
+154
+00:12:19,960 --> 00:12:23,480
+التعريف اللي فوق بيساوي ال integration من سفل ل X
+
+155
+00:12:23,480 --> 00:12:29,180
+C2 of X ايش C2 of X هايه اللي هو واحد نقص T تربيع
+
+156
+00:12:29,180 --> 00:12:34,800
+على اتنين لكل ما له DT ويساوي الكملة هذا بيصير
+
+157
+00:12:34,800 --> 00:12:40,200
+عبارة عن Xناقص X تكعيب على تلاتة وفيه اتنين بيصير
+
+158
+00:12:40,200 --> 00:12:44,980
+X تكعيب على مين على تلاتة factorial اللي هي جداش
+
+159
+00:12:44,980 --> 00:12:50,380
+اللي هي ستة إذا فعلا فعلا طلع عندي اللي هو C أس
+
+160
+00:12:50,380 --> 00:12:55,400
+اتنين هي عبارة عن انا بواحد يعني أس اتنين بيساوي X
+
+161
+00:12:55,400 --> 00:12:59,380
+ناقص X تكعيب على تلاتة factorial يعني صارت الجملة
+
+162
+00:12:59,380 --> 00:13:02,900
+هذه برضه صحيحة فور أن بيساوي واحد إذا كلها على بعض
+
+163
+00:13:02,900 --> 00:13:09,650
+هذه صارت صحيحة فور أن بتساوي جداشالان بدنا نفترض
+
+164
+00:13:09,650 --> 00:13:13,430
+انها
+
+165
+00:13:13,430 --> 00:13:19,490
+true for n بتساوي k ونجيب منها مين اللي هو k زائد
+
+166
+00:13:19,490 --> 00:13:25,950
+واحد نفترض suppose that this is true for n بتساوي
+
+167
+00:13:25,950 --> 00:13:30,690
+k يعني بمعنى اخر صار عندى ck زائد واحد بساوي هذا
+
+168
+00:13:30,690 --> 00:13:37,260
+وهنا اتنين k وهنا kوهنا اتنين K وهنا نفس الاشي
+
+169
+00:13:37,260 --> 00:13:41,640
+اللي هو نفترض انها صحيحة for N بتساوي K صارت عبارة
+
+170
+00:13:41,640 --> 00:13:48,460
+عن اتنين K و اتنين K أو اس K ماشي الحال نثبت ان
+
+171
+00:13:48,460 --> 00:13:53,480
+هذه صحيحة for من؟ for K بتساوي .. for N بتساوي
+
+172
+00:13:53,480 --> 00:14:02,020
+كدهش؟ K زائد واحد يعني بدي اديب Cك زائد جداش اتنين
+
+173
+00:14:02,020 --> 00:14:07,480
+لأن في الاصل هي ك زائد واحد في الاصل سن زائد واحد
+
+174
+00:14:07,480 --> 00:14:11,620
+فرضتها صحيحة في القرآن بتساوي ك لأن بتثبتها صحيحة
+
+175
+00:14:11,620 --> 00:14:15,520
+لأن بتساوي ك زائد واحد يعني ك زائد واحد واحد بيصير
+
+176
+00:14:15,520 --> 00:14:22,820
+ك زائد اتنين of Xماذا يعني حساب تعريفها؟ تعريفها 1
+
+177
+00:14:22,820 --> 00:14:29,300
+ناقص الانتجريشن من 0 إلى X هذا K زائد 2 إذا هذا K
+
+178
+00:14:29,300 --> 00:14:34,420
+N زائد 1 وهذا N K زائد 2 ماذا؟ هذا سيصبح SK زائد 1
+
+179
+00:14:34,420 --> 00:14:36,340
+of DT
+
+180
+00:14:38,530 --> 00:14:42,870
+و يساوي واحد ناقص الفكرة انت فاهمت من صفر لمين
+
+181
+00:14:42,870 --> 00:14:47,910
+لإكس مين هكامل هكامل S K زائد واحد انا فرضت ان انا
+
+182
+00:14:47,910 --> 00:14:52,750
+اتروه في القرآن بالساوية K اللي هي عبارة عن T ناقص
+
+183
+00:14:52,750 --> 00:15:00,450
+T تكعيب ع تلاتة factorial لما اصل لآخر واحد زائد
+
+184
+00:15:00,450 --> 00:15:12,390
+ناقص واحد أس K فيهT 2K 1 2 T 1 كل ايه اش مالها
+
+185
+00:15:12,390 --> 00:15:16,110
+factorial الكل دي تي حسابات والله يا جماعة اللي
+
+186
+00:15:16,110 --> 00:15:22,660
+حالكم بتعملوها دي تي و يساويواحد ناقص نفتح جوس هذي
+
+187
+00:15:22,660 --> 00:15:26,700
+T بيصير T تربيع على اتنين factorial هذي ايش بيصير
+
+188
+00:15:26,700 --> 00:15:32,820
+ناقص T أُس أربعة على أربعة فى تلاتة factorial عن
+
+189
+00:15:32,820 --> 00:15:36,980
+أربعة factorial زائد لما أصل الأخر واحد ناقص واحد
+
+190
+00:15:36,980 --> 00:15:43,580
+أُس K زي ما هي لأن إشارة هذي T بيصير اتنين K زائد
+
+191
+00:15:43,580 --> 00:15:49,130
+واحد زائد واحد يعني زائد اتنين علىاللي هو اتنين K
+
+192
+00:15:49,130 --> 00:15:54,490
+زائد اتنين في هذا بتطلع اتنين K زائد اتنين الكل
+
+193
+00:15:54,490 --> 00:15:59,550
+ايه شماله؟ factorial ماشي الحال هذا طبعا كله من
+
+194
+00:15:59,550 --> 00:16:04,630
+صفر ل X إذا بتصير هذا عبارة عن X وهذا X وهذا
+
+195
+00:16:04,630 --> 00:16:09,010
+الأخير برضه ايه؟ X اللي هي هذا عبارة عن ايه؟ هو
+
+196
+00:16:09,010 --> 00:16:16,350
+يساوي1 ناقص x تربيع على 2 factorial زائد x أُس 4
+
+197
+00:16:16,350 --> 00:16:20,310
+على 4 factorial ضربت الناقص جوا لإن أنا لما أصل
+
+198
+00:16:20,310 --> 00:16:24,910
+ناقص لما أصل الأخر واحد زائد ناقص واحد K وناقص أنا
+
+199
+00:16:24,910 --> 00:16:31,050
+بصير K زائد 1 في X أُس 2K
+
+200
+00:16:31,910 --> 00:16:37,130
+زائد اتنين على اتنين K زائد اتنين لكل vector يعني
+
+201
+00:16:37,130 --> 00:16:41,890
+صارت هذه CK زائد واحد زائد اتنين of X بتساوي هذا
+
+202
+00:16:41,890 --> 00:16:49,290
+المقدار هذا المقدار صحيح صار بالظبط هو هذا اللي هو
+
+203
+00:16:49,290 --> 00:16:53,830
+المقدار اللي عندي أثبتت و كإلمي يعني الآن ان هذا
+
+204
+00:16:54,470 --> 00:16:59,490
+اللي عندى is true for mean for k زائد لأ واحد لإنه
+
+205
+00:16:59,490 --> 00:17:03,950
+لما احط مكان n بيساوي k زائد واحد بيصير هذه k زائد
+
+206
+00:17:03,950 --> 00:17:09,030
+اتنين اشوف اللى طلعته صح ولا لأ بيساوي تبحانة واحد
+
+207
+00:17:09,030 --> 00:17:12,990
+ناقص x تربيع على اتنين فيكتوريا لما اثر الاخر واحد
+
+208
+00:17:12,990 --> 00:17:17,790
+اللى هي ناقص واحد قص مين k زائد واحد فكس قص اتنين
+
+209
+00:17:17,790 --> 00:17:20,970
+في k زائد واحد يعني اتنين k زائد اتنين وها اتنين k
+
+210
+00:17:20,970 --> 00:17:25,760
+زائد اتنين كل فيكتورياالان صارت هذه صحيحة for n
+
+211
+00:17:25,760 --> 00:17:30,600
+ايش بتساوي k زائد واحد التاني بنفس الأسلوب بثبتها
+
+212
+00:17:30,600 --> 00:17:35,260
+صحيحة for ايش for k زائد واحد يعني بدي احسب مين يا
+
+213
+00:17:35,260 --> 00:17:42,300
+جماعة بدي احسب Sكزايد اتنين ايش حسب اللي فوق
+
+214
+00:17:42,300 --> 00:17:47,180
+بتساوي بساوي ال integration من سفر ل X ل CK زايد
+
+215
+00:17:47,180 --> 00:17:54,020
+اتنين of T DT و باجي بعوضها هنا و بكملها و بتطلع
+
+216
+00:17:54,020 --> 00:17:57,800
+عندى بالظبط ال formula هذه يعني صح بيصير عندى
+
+217
+00:17:57,800 --> 00:18:01,620
+بتعملها لحالك لان حسابات نفس الأسلوب بتطلع عندى
+
+218
+00:18:01,620 --> 00:18:06,310
+اللي هي هذه صحيحة for mean برضهfor an بتساوي k
+
+219
+00:18:06,310 --> 00:18:11,050
+زائد واحد إذا هذا صار المقدار صحيح دائما for mean
+
+220
+00:18:11,050 --> 00:18:20,430
+for any k for any n element in n الان واضح ان
+
+221
+00:18:20,430 --> 00:18:26,310
+الخطوات مشابهة لخطوات ال exponential نيجي الآن
+
+222
+00:18:26,310 --> 00:18:28,970
+قصّل n prime
+
+223
+00:18:38,770 --> 00:18:45,020
+نجي الآنوين رايح؟ زي اللي بكونت رايحي الأيام الـ
+
+224
+00:18:45,020 --> 00:18:49,060
+exponential هثبتلك أن الـ sequence هذه converged
+
+225
+00:18:49,060 --> 00:18:52,220
+uniformly وهذه طبعا هتصبح converged uniformly
+
+226
+00:18:52,220 --> 00:18:55,000
+automatic فهتصبح اللي هي differentiable لأنه بيصير
+
+227
+00:18:55,000 --> 00:18:57,860
+طبقة النظرية اللي هي تبعها الـ differentiability
+
+228
+00:18:57,860 --> 00:19:01,200
+بيصير عند مادام differentiable اللي هي ال
+
+229
+00:19:01,200 --> 00:19:04,580
+derivative اللي لها exist و هتكون ال derivative
+
+230
+00:19:04,580 --> 00:19:07,960
+متحقق الشروط و بيكون خلاص نعم نشوف أش بقول طيب
+
+231
+00:19:07,960 --> 00:19:12,530
+الآنبعد ما طلعنا هدولة let a أكبر من صفر b given
+
+232
+00:19:12,530 --> 00:19:15,790
+نفس الخطوات تبعت ال exponential then if الabsolute
+
+233
+00:19:15,790 --> 00:19:19,970
+value of x أصغر بسوء a and m أكبر من n أكبر من 2a
+
+234
+00:19:19,970 --> 00:19:25,510
+يعني بتداخد اللي هي الامات لأكبر من n و أكبر من 2a
+
+235
+00:19:25,510 --> 00:19:29,650
+يعني الآن أنا بشتغل عالين يا جماعة الفترة من ناقص
+
+236
+00:19:29,650 --> 00:19:34,570
+a لعند a وأخدت ال a arbitrarily أكبر من صفر لكن
+
+237
+00:19:34,570 --> 00:19:41,850
+fixed الان we haveعندي اللي هو ..عندي اللي هي الـ
+
+238
+00:19:41,850 --> 00:19:50,630
+A الـ A على اللي هي 2N بما أنه N أكبر من 2A اجسم
+
+239
+00:19:50,630 --> 00:19:56,790
+الجهتين على 2N هن على 2N و هن على 2N بيصير عند الـ
+
+240
+00:19:56,790 --> 00:20:07,710
+A على N .. A على N أصغر من النص، صح؟هي a تروح
+
+241
+00:20:07,710 --> 00:20:11,090
+التنين مع التنين وهذه n مع ال n بصير a أعليها أصغر
+
+242
+00:20:11,090 --> 00:20:16,050
+من نص يعني a على 2n أصغر من 1 على 4 جسمت التنين
+
+243
+00:20:16,050 --> 00:20:22,400
+عالميا على 2 إذا لما تكون ال n أكبر من 2aهتطلع
+
+244
+00:20:22,400 --> 00:20:24,640
+عندها get بتعرف ليش هذه لإن بتلزمنا في الحسابات
+
+245
+00:20:24,640 --> 00:20:28,580
+بعد شوية هتكون اللي هي لما الاتنين a أصغر من n
+
+246
+00:20:28,580 --> 00:20:31,960
+بتكون عند a على اتنين n أصغر من مين من ربع المرة
+
+247
+00:20:31,960 --> 00:20:35,460
+اللي فاتت كان لازمنا a على n أصغر من نص وكملنا ال
+
+248
+00:20:35,460 --> 00:20:40,650
+series اللي متذكر اللي عملنا في اللي هيالـ
+
+249
+00:20:40,650 --> 00:20:43,330
+Exponential أنا بحكيش تفاصيله و مفترض ان انتوا
+
+250
+00:20:43,330 --> 00:20:47,570
+فاهمين حسب حكينا اللي هو في الـ Exponential الان
+
+251
+00:20:47,570 --> 00:20:52,290
+للأمات اللي أكبر من M أكبر من 2A بدي احسب الـCM
+
+252
+00:20:52,290 --> 00:20:59,870
+ناقص 2 الـSN عشان تظلها جدامكم اللي فوق هذه عندى
+
+253
+00:20:59,870 --> 00:21:06,960
+الان الـCMالـ C M الـ C M شايفينها؟ بتظلها ماشية
+
+254
+00:21:06,960 --> 00:21:10,940
+واحد لو ف .. الآن هذه M بدأ الـ N زاد واحد ايش
+
+255
+00:21:10,940 --> 00:21:14,880
+اسمها؟ M بتظلها ماشية واحد ناقص X أربع على اتنين
+
+256
+00:21:14,880 --> 00:21:18,820
+فيكتوريال X أربع على أربع فيكتوريال والـ M أكبر من
+
+257
+00:21:18,820 --> 00:21:23,160
+الـ N هتجيه يقبل في طريقها من الـ N الـ N بيصير
+
+258
+00:21:23,160 --> 00:21:27,540
+الـ N طبعا إيه شمالها؟ الـ N عبارة عن في جبل ال
+
+259
+00:21:27,540 --> 00:21:33,590
+term هذا اللي هو الـ N ناقص واحدأه فبصير زائد اللي
+
+260
+00:21:33,590 --> 00:21:39,350
+هو ناقص واحد أس ان ناقص واحد في X أس اتنين ام ناقص
+
+261
+00:21:39,350 --> 00:21:44,050
+اتنين على اتنين ام ناقص اتنين الكل factorial و
+
+262
+00:21:44,050 --> 00:21:48,390
+بتكمل هذا و بتبقى مكمل ايه انت لما اتصل لعند X أس
+
+263
+00:21:48,390 --> 00:21:54,670
+اتنين ام ناقص اتنين لأن هذا لل ام مش لل ان زائد
+
+264
+00:21:54,670 --> 00:21:59,730
+واحد على اتنين ام ناقص اتنين الكل اشماله factorial
+
+265
+00:22:00,420 --> 00:22:08,320
+لما تطرح ال CM نقص ال CN اللي هو لها بيصير المتبقى
+
+266
+00:22:08,320 --> 00:22:12,600
+هيه زي ما عملنا بالظبط قبل هيك فبيصير ال CM نقص ال
+
+267
+00:22:12,600 --> 00:22:18,080
+CN بساوي النقص واحد طبعا في absolute value عند X2N
+
+268
+00:22:18,080 --> 00:22:21,200
+عشان هيك طيرنا مش فارقة كتير نقص و سالب أخدنا له
+
+269
+00:22:21,200 --> 00:22:25,900
+absolute value مش هتفرج معنا ال X2N على 2N
+
+270
+00:22:25,900 --> 00:22:32,490
+vectorialناقص X أس 2 M زائد 2 اللي بعيدها على 2 M
+
+271
+00:22:32,490 --> 00:22:35,990
+زائد 2 كله factorial لما أصل لآخر term اللي هو X
+
+272
+00:22:35,990 --> 00:22:41,170
+أس 2 M ناقص 2 على 2 M ناقص 2 كله factorial هذا
+
+273
+00:22:41,170 --> 00:22:46,670
+الأن هذا نفسه أخدنا احنا ال absolute value لل X
+
+274
+00:22:46,670 --> 00:22:50,350
+أصغر من A في هذه الفترة احنا شغالين في الفترة ال
+
+275
+00:22:50,350 --> 00:22:54,430
+absolute value X أصغر من A الآن بيصير عند ال X
+
+276
+00:22:54,430 --> 00:23:05,180
+نفسهاأُس 2n أصغر أو يساوي هذه اللي هي a أُس 2n على
+
+277
+00:23:05,180 --> 00:23:09,240
+2n الكل factorial الأولى زائد استخدمت triangle
+
+278
+00:23:09,240 --> 00:23:13,440
+inequality هذه زائد هذه زائد هذه زائد هذه الآن
+
+279
+00:23:13,440 --> 00:23:18,240
+زائد اللي بعيدها لما أصل لآخر واحدة x أو اللي جاب
+
+280
+00:23:18,240 --> 00:23:23,420
+اللي خليني اكتبها عشان x اللي هي بصير aأس اتنين ان
+
+281
+00:23:23,420 --> 00:23:28,060
+زائد اتنين على اتنين ان زائد اتنين لكل factorial
+
+282
+00:23:28,060 --> 00:23:37,020
+زائد لما أصل لآخر term عندي هنا لما أصل لآخر term
+
+283
+00:23:37,020 --> 00:23:43,160
+اللي هو زائد
+
+284
+00:23:43,160 --> 00:23:57,230
+هذا ال term اللي هو زائدA 2M-2 2M-2 كل A شماله
+
+285
+00:23:57,230 --> 00:24:03,930
+فكتوريا خلّيني أخد هذا A 2N 2N كل فكتوريا العام
+
+286
+00:24:03,930 --> 00:24:11,460
+المشتركبظل عندى 1 زائد a تربيع لأنه بيصير a يسوى 2
+
+287
+00:24:11,460 --> 00:24:17,960
+a تربيع على مين على 2n زائد 2 أكيد ال 1 على 2n
+
+288
+00:24:17,960 --> 00:24:23,280
+زائد 2 أصغر من 1 على 2n لأنه 2n أصغر من هذه
+
+289
+00:24:23,280 --> 00:24:27,240
+فمقلوبها بيصير أكبرماشي و بضل زي ما عملته المرة
+
+290
+00:24:27,240 --> 00:24:32,700
+الفاتة أسحب منه A أس 2 على N و في الآخر أستبدل
+
+291
+00:24:32,700 --> 00:24:37,680
+اللي هو 2N هذه عن الرقم اللي أكبر منه N فبصير هي
+
+292
+00:24:37,680 --> 00:24:41,400
+مقلوبها أكبر فبتضلها اللي هي ال inequality زي هيك
+
+293
+00:24:41,400 --> 00:24:45,840
+و بكون سحبتي 2 من هذه بيصير 2 ام نقص 2 ام نقص ايش
+
+294
+00:24:45,840 --> 00:24:53,350
+نقص 2 وصلنا لعند ال inequality هذه الآنأحنا قلنا a
+
+295
+00:24:53,350 --> 00:24:58,950
+على 2n أصغر من مين من ربعه يعني بيصير هذا المقدار
+
+296
+00:24:58,950 --> 00:25:05,310
+كله أصغر أو يساوي a أس 2n على 2n لكل factorial
+
+297
+00:25:05,310 --> 00:25:09,550
+مضروب في مين أصغر أو يساوي لأن الربع أكبر منهم بس
+
+298
+00:25:09,550 --> 00:25:14,930
+تبدأ كل واحد وقت ما كانوا إيهاش ربع واحد زاد واحد
+
+299
+00:25:14,930 --> 00:25:23,510
+على أربعة تربيعزائد لما أصل لآخر واحد a اللي هو
+
+300
+00:25:23,510 --> 00:25:31,370
+عبارة عن واحد على أربعة الكل أس اتنين ام ناقص
+
+301
+00:25:31,370 --> 00:25:36,590
+اتنين ام ناقص ايش اتنين هذه الان ال ال ال ال
+
+302
+00:25:36,590 --> 00:25:39,710
+finite geometric series أصغر أو يساوي ال infinite
+
+303
+00:25:39,710 --> 00:25:45,770
+اللي هي a أس اتنين ان على اتنين ان لكل factorial
+
+304
+00:25:45,770 --> 00:25:53,570
+في اللي هوالـ summation ده واحد زائد ربع تربيع
+
+305
+00:25:53,570 --> 00:26:00,310
+زائد ربع تكعيب زائد لمّا أصل ربع أس أربعة زائد إلى
+
+306
+00:26:00,310 --> 00:26:05,070
+ما لا نهاية هذه الأن أساسها جداش وكأنه أساسها كل
+
+307
+00:26:05,070 --> 00:26:11,750
+مرة تمد واحد على ست عشر فبتصير هذه المجموحة اللي
+
+308
+00:26:11,750 --> 00:26:16,470
+هي واحد مجموحة بتعرفوها واحد ناقص واحد على ست عشر
+
+309
+00:26:17,250 --> 00:26:21,750
+Passive واحد على واحد ناقص واحد على ست عشر ويساوي
+
+310
+00:26:21,750 --> 00:26:27,810
+جداش خمست عشر او ست عشر على خمست عشر لأن هذه واحد
+
+311
+00:26:27,810 --> 00:26:29,870
+ناقص واحد على ست عشر تطلع خمست عشر على ست عشر
+
+312
+00:26:29,870 --> 00:26:34,830
+مجلوبة بيصير ست عشر على خمست عشرالمفهوم المقصود هو
+
+313
+00:26:34,830 --> 00:26:38,670
+بسمحها Geometric Series بضل بقول هذه أصغر أو ساوي
+
+314
+00:26:38,670 --> 00:26:41,930
+الصماشن إلى ماله نهاية و بزدبدل هذا باللي أكبر
+
+315
+00:26:41,930 --> 00:26:46,070
+منها فبتظل هذه أكبر الان مجموحها بيصير عبارة عن 16
+
+316
+00:26:46,070 --> 00:26:51,010
+في المقدار هذا اللي دله موخود عام المشترك فبيصير
+
+317
+00:26:51,010 --> 00:26:58,940
+عندى الآن يا جماعة اللي هو ال CMنقص الـCN زي ما
+
+318
+00:26:58,940 --> 00:27:04,460
+حكينا قبل ذلك بالظبط أصغر من هذا المقدار اللي هذا
+
+319
+00:27:04,460 --> 00:27:09,000
+limit و اين بيروح as N goes to infinity بيروح لـ 0
+
+320
+00:27:09,000 --> 00:27:13,760
+إذا بيصير هذا المقدار زي ما قلنا المرة الماضية CM
+
+321
+00:27:13,760 --> 00:27:20,800
+of X نقص CN of X اللي هو أصغر أو يسوء Y for very
+
+322
+00:27:20,800 --> 00:27:28,700
+large M and NM and N لأنه لما تكبر M كثير N كثير
+
+323
+00:27:28,700 --> 00:27:33,100
+تروح لنا لنهاية لأنه limit بروح لها سفر as N goes
+
+324
+00:27:33,100 --> 00:27:37,080
+to infinity ال M برضه بتكبر إذا for very large M
+
+325
+00:27:37,080 --> 00:27:40,800
+هيكون هذا أصغر أو يساوي إبسلون لأي إبسلون في
+
+326
+00:27:40,800 --> 00:27:44,480
+الدنيا لأنه هذا بيقدي للسفر فبيصير صغير صغير صغير
+
+327
+00:27:44,480 --> 00:27:48,720
+صغير لدرجة إنه مضروب في هذا يكون أصغر من إبسلون
+
+328
+00:27:48,720 --> 00:27:53,360
+وهذه اللي قلنا عنهااللي هي الـ Cauchy criterion
+
+329
+00:27:53,360 --> 00:28:00,040
+for uniform continuity هذا الكلام كله لمين؟ صحيح
+
+330
+00:28:00,040 --> 00:28:06,880
+لأي X وين على الفترة اللي هو absolute value X أصغر
+
+331
+00:28:06,880 --> 00:28:11,220
+أو يساوي A يعني على الفترة المولقة من ناقص A لعند
+
+332
+00:28:11,220 --> 00:28:19,110
+A وهذا بيعطيني أن الـis uniformly continuous على
+
+333
+00:28:19,110 --> 00:28:24,150
+الفترة من نفس A لعند A is as if is uniformly is
+
+334
+00:28:24,150 --> 00:28:28,330
+uniformly convergence على الفترة من نفس A ل A يعني
+
+335
+00:28:28,330 --> 00:28:35,790
+بمعنى آخر صارت عندي ال sequence هذه اللي هي CNN
+
+336
+00:28:35,790 --> 00:28:43,150
+converts uniformly to some function عالميا على
+
+337
+00:28:43,150 --> 00:28:50,730
+الفترةمن ناقص a لعند مين لعند a الآن طب ما هو اللي
+
+338
+00:28:50,730 --> 00:28:53,930
+عملناها أنا على الفترة هذه نقدر نعمله على أي شيء
+
+339
+00:28:53,930 --> 00:28:58,310
+ثاني يعني بمعنى أخر لو جيت أخدت x element in R
+
+340
+00:28:58,310 --> 00:29:04,400
+هلاجي number aبحيث أن هذا ال number a هي ال x في
+
+341
+00:29:04,400 --> 00:29:10,180
+ال R بقدر ألاقي a بحيث أن ناقص a و a تكون ال x في
+
+342
+00:29:10,180 --> 00:29:15,340
+الفترة بين ناقص a و a يعني بمعنى آخر هعمل نفس اللي
+
+343
+00:29:15,340 --> 00:29:18,100
+عملته في الأول و هحصر على c أن uniformly
+
+344
+00:29:18,100 --> 00:29:23,030
+convergence على هذه الفترةيعني بمعنى آخر الآن صار
+
+345
+00:29:23,030 --> 00:29:29,450
+عندي limit cn of x for any x exist بده أسميها هذه
+
+346
+00:29:29,450 --> 00:29:35,190
+limit c of x وبناء عليه بدي أعرف الآن in
+
+347
+00:29:35,190 --> 00:29:38,710
+particular this means that cn of x converge for
+
+348
+00:29:38,710 --> 00:29:42,710
+each x element in R we define c من R لR by c of x
+
+349
+00:29:42,710 --> 00:29:45,650
+بسواية limit cn of x for x element in R
+
+350
+00:29:53,570 --> 00:29:59,630
+الان .. بما انه الان الـCn مرتبط بشكل مرتبط لـC زي
+
+351
+00:29:59,630 --> 00:30:04,690
+ما قلنا أو الـCn of X كلهم مرتبط حسب اللي هو
+
+352
+00:30:04,690 --> 00:30:08,030
+النظرية في الـpointwise .. الـuniform convergence
+
+353
+00:30:08,030 --> 00:30:12,360
+اللي هو the limit .. the uniform .. limitأو الـ
+
+354
+00:30:12,360 --> 00:30:15,220
+Form convergence of a sequence of continuous
+
+355
+00:30:15,220 --> 00:30:18,480
+functions مصمد كونتنيواس الـ limit تبعتها يعني
+
+356
+00:30:18,480 --> 00:30:21,160
+هتطلع عندي C of X continuous مثلاً C of X
+
+357
+00:30:21,160 --> 00:30:25,000
+continuous إذا عندي .. اللي هو صار عندي الـ
+
+358
+00:30:25,000 --> 00:30:28,160
+function هذه continuous اللي هي الـ C اللي إحنا
+
+359
+00:30:28,160 --> 00:30:33,730
+بدنا إياها ومش هيك و limitCn of 0 as n goes to
+
+360
+00:30:33,730 --> 00:30:37,270
+infinity بساوة limit اللي هي Cn of 0 ايش بتساوي
+
+361
+00:30:37,270 --> 00:30:41,910
+واحد وهي ساوية واحد اللي هي عبارة عن مين الـC of
+
+362
+00:30:41,910 --> 00:30:47,370
+ايش of 0 لأن احنا متفجين الـC of X بساوية limit Cn
+
+363
+00:30:47,370 --> 00:30:51,310
+of X و in particular for X بتساوية سفر بسيرة limit
+
+364
+00:30:51,310 --> 00:30:55,430
+Cn of 0 بساوية C of 0 وCn of 0 كلها واحد ايضا
+
+365
+00:30:55,430 --> 00:30:57,730
+limit الواحد اللي هو بساوية واحد يعني الـC of 0
+
+366
+00:30:57,730 --> 00:31:05,970
+ايش هتساوي؟ هتساوي واحدخصّلت كمان شغلة انه حصلت
+
+367
+00:31:05,970 --> 00:31:10,070
+عندي ان الـ c of zero بيساوي واحد
+
+368
+00:31:13,750 --> 00:31:19,670
+لأ اللي هو الـS الـCN بعمل اشي مشابه له لمين للـSN
+
+369
+00:31:19,670 --> 00:31:25,250
+عشان نثبت الآن اللي أثبتناه انه صار في عندى ده
+
+370
+00:31:25,250 --> 00:31:31,730
+اللي عرفناها اسمها الـC of X اللي عبارة عن limit
+
+371
+00:31:31,730 --> 00:31:38,970
+CN of X حيث الـC من R إلى R طيب
+
+372
+00:31:41,560 --> 00:31:45,380
+الان ناخد ايضا ال absolute value X أصغر من مين من
+
+373
+00:31:45,380 --> 00:31:49,960
+ايه وال M أكبر او يساوي N و أصغر من مين من اتنين
+
+374
+00:31:49,960 --> 00:32:00,360
+ايه الان نحسب ل SM ناقص SN SM ايه قيمتهاDT من صفر
+
+375
+00:32:00,360 --> 00:32:05,400
+الاندكس SN وهي SM
+
+376
+00:32:05,400 --> 00:32:11,240
+ناقص هذه هي قيمتها إذا صار هذه ناقص هذه هي قيمتها
+
+377
+00:32:11,240 --> 00:32:19,680
+الان هذه سهل إثباتها أنها تتعامل ال absolute value
+
+378
+00:32:19,680 --> 00:32:24,200
+لهذهأصغر أو يساوي الـ absolute value لهذه أصغر أو
+
+379
+00:32:24,200 --> 00:32:27,700
+يساوي ال integration من 0 ل X ل absolute value CM
+
+380
+00:32:27,700 --> 00:32:35,600
+of T نقص CN of T اشماله DT ماشي الحال أو بنكمل
+
+381
+00:32:35,600 --> 00:32:39,580
+اللي هو بنستخدم هذه الخاصية اللي هو بيكون أصغر أو
+
+382
+00:32:39,580 --> 00:32:42,820
+يساوي من الحسابات اللي حسبناها قبل شوية هذا
+
+383
+00:32:42,820 --> 00:32:45,380
+حسبناها أصغر من مين الحسابات اللي قبل شوية أصغر أو
+
+384
+00:32:45,380 --> 00:32:52,510
+ساوي A أس 2N على 2N الكل factorialمضروبة في اللي
+
+385
+00:32:52,510 --> 00:32:58,130
+هو ست عشر على مين على خمسة في ال integration من
+
+386
+00:32:58,130 --> 00:33:02,750
+صفر لل X ل DT هذا ال integration ايش بيساوي بيساوي
+
+387
+00:33:02,750 --> 00:33:08,230
+X ماشي و ال X عندي احنا ماخدينها اصغر او يساوي مين
+
+388
+00:33:08,230 --> 00:33:13,010
+ايه اصغر او يساوي ايه فبصير عندي هذا المقدار بيكون
+
+389
+00:33:13,680 --> 00:33:18,020
+لما نبعد مكانه بيطلع X قيمته أصغر أو يساوي A
+
+390
+00:33:18,020 --> 00:33:22,040
+فبيصير هذا مضروب في مين في ايه اللي هو هاي المقدار
+
+391
+00:33:22,040 --> 00:33:26,680
+وهي 16 على 5 وهي ايش ال A صار هذا أصغر أو يساوي
+
+392
+00:33:26,680 --> 00:33:31,600
+هذا المقدار نفس ما عملنا قبل بشوية الان as N goes
+
+393
+00:33:31,600 --> 00:33:36,690
+to infinityهذه قيمتها بيساوي 0 إذا هذا المقدار for
+
+394
+00:33:36,690 --> 00:33:41,470
+very large M و N هيكون أصغر أوي يساوي Y و بالكوشي
+
+395
+00:33:41,470 --> 00:33:45,350
+criterion بيصير عندي اللي هي ال S N converts
+
+396
+00:33:45,350 --> 00:33:49,470
+uniformly و الآن على الفترة نقص A و A و ال A كانت
+
+397
+00:33:49,470 --> 00:33:53,730
+arbitrary إذا S من R ل R بنقدر نعرفها بحيث إنه
+
+398
+00:33:53,730 --> 00:33:57,880
+limit S N of X اللي صارت موجودة على هذهوبناء على
+
+399
+00:33:57,880 --> 00:34:00,460
+الـ A-arbitrary صارت موجودة على كل الـ R زي ما
+
+400
+00:34:00,460 --> 00:34:04,340
+قلنا كيف هذا الكلام بسمي limit S N of X اليمين S
+
+401
+00:34:04,340 --> 00:34:08,980
+of X وهذه اللي هي ال function الثانية بنفس الأسلوب
+
+402
+00:34:08,980 --> 00:34:13,380
+وبنفس اللي هو المنطق وبنفس الأسباب بما أن ال S N
+
+403
+00:34:13,380 --> 00:34:16,860
+conversion formally to S وS N continuous إذا حد
+
+404
+00:34:16,860 --> 00:34:22,340
+طلع ال S برضه نفس إشمالها continuousوأيضًا limit
+
+405
+00:34:22,340 --> 00:34:28,540
+of S of 0 هو عبارة عن S of 0 وبما أن S of 0 دايماً
+
+406
+00:34:28,540 --> 00:34:31,640
+0 إذًا limitها سيكون as N goes to infinity 0 يعني
+
+407
+00:34:31,640 --> 00:34:35,300
+ستظهر لدي S of 0 إيش بالساوة 0 إذًا الآن طلعنا
+
+408
+00:34:35,300 --> 00:34:45,840
+كمان شغلة أثبتناها أن S of 0بساوة 0 و C of 0 بساوة
+
+409
+00:34:45,840 --> 00:34:54,400
+1 وعرفنا هذولة الدالتين أسي و أس من اللي هي R لعند
+
+410
+00:34:54,400 --> 00:34:59,680
+مين لعند R إذن الآن احنا الدالتين اللي أثبتنا لان
+
+411
+00:34:59,680 --> 00:35:05,430
+وجود هنا الآن اللي بحكي عنهم هذولة الدالتيناللي هي
+
+412
+00:35:05,430 --> 00:35:10,190
+الدالة الأولى سميتها أسوة تانية C ولاقيت انه C of
+
+413
+00:35:10,190 --> 00:35:15,790
+0 بساوة واحد و S of 0 بساوة H0 وظل أثبت هذه و أثبت
+
+414
+00:35:15,790 --> 00:35:22,910
+هذه و أثبت هذولة اللي أستبعتنا بتحققهم فخلينا نشوف
+
+415
+00:35:22,910 --> 00:35:29,670
+كيف نثبتها طيب الآن أوصلنا لعند اللي هو المنطقة
+
+416
+00:35:29,670 --> 00:35:39,670
+هذه لأن احنا اتفجنا على ما يليهاتفجنا ان الـ S N
+
+417
+00:35:39,670 --> 00:35:47,170
+تتعامل بشكل عام لتعمل S و الـ C N تتعامل بشكل عام
+
+418
+00:35:47,170 --> 00:35:54,280
+لتعمل Cلكن الان احنا اثبتنا في الأول هي ان ما
+
+419
+00:35:54,280 --> 00:36:00,880
+محتاش ال S N برايم بسوء ال C N، مظبوط؟ يعني و كأنه
+
+420
+00:36:00,880 --> 00:36:04,860
+بناء على هذا مزام ال S N برايم بسوء ال C N فبصير
+
+421
+00:36:04,860 --> 00:36:09,520
+ال S N برايم، هذه، مكانها دي S N برايم بصير ال S N
+
+422
+00:36:09,520 --> 00:36:15,340
+برايم converges uniformly to some function mean C
+
+423
+00:36:15,340 --> 00:36:22,060
+الان بما ان S N برايم converges uniformly to Cالان
+
+424
+00:36:22,060 --> 00:36:28,900
+و الاسن converged to us uniformly برضهحسب نظرية
+
+425
+00:36:28,900 --> 00:36:32,360
+بتطلع عندى بما ان s n prime differentiable هتكون
+
+426
+00:36:32,360 --> 00:36:37,140
+ال limit ه differentiable و ال c prime اللي هي ال
+
+427
+00:36:37,140 --> 00:36:42,340
+s prime هدى هي مين ال c اللي طلعت هن يعني s n
+
+428
+00:36:42,340 --> 00:36:45,960
+prime differentiable او s n differentiable و
+
+429
+00:36:45,960 --> 00:36:48,560
+converts to some function اذا بتتذكر كنا نسميها g
+
+430
+00:36:48,560 --> 00:36:52,520
+و هد كنا نسميها f فكنا نقول بما ان s n بتروح لل f
+
+431
+00:36:52,520 --> 00:36:56,740
+و ال s n prime بتروح لل g إذا نتيجة النظرية هتكون
+
+432
+00:36:56,740 --> 00:37:00,000
+اللي هيالـ F هي الـ Differentiable والـ Derivative
+
+433
+00:37:00,000 --> 00:37:04,940
+لها إيش بتطلع D يعني الـ Derivative للـ S' إيش
+
+434
+00:37:04,940 --> 00:37:12,260
+هتطلع عبارة عن مين C' أسف C هتطلع مين اللي هي الـ
+
+435
+00:37:12,260 --> 00:37:21,000
+C إذا أثبتت أنا الآن S' of X بتساوي C of X هاي
+
+436
+00:37:21,000 --> 00:37:28,190
+اللي أثبتته هنا الآن من جهة أخرى من جهة أخرىإحنا
+
+437
+00:37:28,190 --> 00:37:35,850
+أثبتنا اللي هي قبل هيك أن الـCN برايم بسوء ناقص SN
+
+438
+00:37:35,850 --> 00:37:42,450
+ناقص واحد الـCN برايم بسوء ناقص SN of واحد يعني
+
+439
+00:37:42,450 --> 00:37:47,790
+بمعنى آخر الـCN برايم of X أثبتنا بسوء ناقص SN
+
+440
+00:37:47,790 --> 00:37:54,640
+ناقص واحد of Xالان بما ان ال S Unconverted زي ال S
+
+441
+00:37:54,640 --> 00:38:00,260
+خلصنا هذه اه خلصنا هذه المنطقة خليني اشرح بلغة
+
+442
+00:38:00,260 --> 00:38:05,060
+تانية عشان اميز بين الكلامين عندي الان انتبهوا
+
+443
+00:38:05,060 --> 00:38:08,860
+بتعمل نفسي اشي بس بالنسبة لمن الان بالنسبة عشان
+
+444
+00:38:08,860 --> 00:38:13,780
+اجيب ال derivative لل S لل C primeعندى الان الـCN
+
+445
+00:38:13,780 --> 00:38:19,740
+prime of X بسوء نقص SN نقص واحد of X بما أن SN
+
+446
+00:38:19,740 --> 00:38:23,500
+راحت للـS إذا اللى هى ال derivative هى اللى
+
+447
+00:38:23,500 --> 00:38:30,280
+بتسويها اللى هى CNN زائد واحد prime of X هتروح
+
+448
+00:38:30,280 --> 00:38:36,770
+لمين؟اللي هي مش هي ناقصها لأن S N ناقص واحد اللي
+
+449
+00:38:36,770 --> 00:38:40,730
+هي بساوي ناقص هذه أنجل ناقصها بعد أذنكم يعني بدي
+
+450
+00:38:40,730 --> 00:38:44,810
+أستبدل الـ S N بمين بقيمتها هذه صارت ناقص الـ C N
+
+451
+00:38:44,810 --> 00:38:50,330
+prime of X أيش بتساوي بتروح للـ S أو بمعنى آخر صار
+
+452
+00:38:50,330 --> 00:38:56,620
+عندي من هنا من هنا اللي بتطلع عندي هناصار عندى
+
+453
+00:38:56,620 --> 00:39:03,640
+الان من هنا اللى هو cn زائد واحد prime of x بتروح
+
+454
+00:39:03,640 --> 00:39:08,080
+لناقص طبعا uniformly بتروح لمين ناقص s لأنه ناقصها
+
+455
+00:39:08,080 --> 00:39:13,040
+بتروح لل s إذا هي بتروح لناقص ال sوفي نفس الوقت
+
+456
+00:39:13,040 --> 00:39:19,840
+أنا بقول الـCN نفسها بتروح uniform لمين؟ للـC بنفس
+
+457
+00:39:19,840 --> 00:39:24,740
+الإسلوب اللي قبل بشوية اللي هي بما أنه هذه اللي هي
+
+458
+00:39:24,740 --> 00:39:27,580
+differentiable sequence of functions و converge
+
+459
+00:39:27,580 --> 00:39:31,260
+uniform to some function إذا هذه هتكون اللي هي
+
+460
+00:39:31,260 --> 00:39:35,600
+عبارة عن اللي هي الـC الأصلية differentiable و ال
+
+461
+00:39:35,600 --> 00:39:40,070
+derivative فيه لها مين؟ الناقص Sفبصير عندي الـ C'
+
+462
+00:39:40,530 --> 00:39:45,970
+of X بسوء ناقص S of X بكون هذه اللي هي النتيجة
+
+463
+00:39:45,970 --> 00:39:50,330
+الثانية اللي طبقنا عليها طلعت عندي اللي هو هذه
+
+464
+00:39:50,330 --> 00:39:54,050
+الخاصية و هذه الخاصية متحققة يعني الآن صار عندي
+
+465
+00:39:54,050 --> 00:40:02,590
+اللي هو تحقق ما يليه أنه تبعتنا هذه الـ C'of X
+
+466
+00:40:02,590 --> 00:40:08,530
+بيساوي ناقص S of X وطلع عندي اللي هي S prime of X
+
+467
+00:40:08,530 --> 00:40:16,290
+بيساوي C of X ماشي الحال بيكون هيك احنا ضال علينا
+
+468
+00:40:16,290 --> 00:40:21,230
+شغل اخرى لحاول نثبتها بيكون اثبتنا اللي هو كل
+
+469
+00:40:21,230 --> 00:40:27,630
+الصفات المطلوبة اللي تتحقق في ال S وحددت هوية ال S
+
+470
+00:40:27,630 --> 00:40:28,050
+و ال C
+
+471
+00:40:38,700 --> 00:40:48,060
+الجزء الثاني سهل فضل الـ cw prime of x
+
+472
+00:41:00,590 --> 00:41:05,470
+بتصير c double prime هيها و هذه فضلها بنفعلها
+
+473
+00:41:05,470 --> 00:41:09,550
+لأنها قبل التفاضل اللي فضلناها وبتصير ناقص اللي هي
+
+474
+00:41:09,550 --> 00:41:15,030
+s prime of x اللي هي s prime of x هيش بتساوي c of
+
+475
+00:41:15,030 --> 00:41:20,350
+x فبصير ناقص مين؟ c of xوالآن S W' of X من أين بدي
+
+476
+00:41:20,350 --> 00:41:23,650
+أجيبها من هنا S W' بيساوي اللي هو هذه ال
+
+477
+00:41:23,650 --> 00:41:26,050
+derivative اللي هي ال derivative اللي هي عبارة عن
+
+478
+00:41:26,050 --> 00:41:31,530
+ناقص S of X فبصير عبارة عن ناقص S of X فبصير عندي
+
+479
+00:41:31,530 --> 00:41:38,910
+هذا برضه ايش تحقق اخر اشي اللي هي C' of Zero C' of
+
+480
+00:41:38,910 --> 00:41:42,410
+Zero بيساوي ناقص S of Zero وS of Zero بيساوي صفر
+
+481
+00:41:42,410 --> 00:41:47,030
+اذا C' of Zero بيساوي Zero ال S' of Zero
+
+482
+00:41:52,540 --> 00:41:56,800
+وهكذا اثبتنا وجود دالة
+
+483
+00:41:59,570 --> 00:42:04,970
+اللي هي حققتلي اللي هي الشرط الأول هذا والدالتين
+
+484
+00:42:04,970 --> 00:42:09,710
+اسف والشرط الثاني اه اللي بعده هذه بتكون أثبتنا
+
+485
+00:42:09,710 --> 00:42:15,290
+وجود الـC والـS لأن بعض النتائج الأخرى على اللي هي
+
+486
+00:42:15,290 --> 00:42:18,830
+الدالتين
+
+487
+00:42:18,830 --> 00:42:19,790
+اللي أوجدناهم
+
+488
+00:42:24,500 --> 00:42:28,960
+نشوف ايش الـ Corollary الأولى بقول لي if C and S
+
+489
+00:42:28,960 --> 00:42:33,680
+are the functions in 3x,8x,4x,1 then C' of X
+
+490
+00:42:33,680 --> 00:42:39,560
+بيساوي نقص S of X أثبتناها هيها and طبعا في طريقنا
+
+491
+00:42:39,560 --> 00:42:44,020
+في البرهان S' of X بيساوي C of X هيها اللي هي خواص
+
+492
+00:42:44,020 --> 00:42:50,340
+اللي هي أثبتناها طيب الآن بقول لي moreover these
+
+493
+00:42:50,340 --> 00:42:54,630
+functions have derivatives of all orderيعني بأي
+
+494
+00:42:54,630 --> 00:42:57,710
+order ال derivative موجودة طبعاً هذا by induction
+
+495
+00:42:57,710 --> 00:43:01,550
+by induction اللي هو بدك تثبت انه اللي هو اللي هو
+
+496
+00:43:01,550 --> 00:43:06,670
+cn هتكون موجودة و بيساوي ناقص a of x او زاد a of x
+
+497
+00:43:06,670 --> 00:43:11,450
+حسب اللي هي جداش درجة ال n وممكن تساوي c of x او
+
+498
+00:43:11,450 --> 00:43:16,930
+اللي هي ناقص c of x حسب درجة ال n اللي موجودةاذا
+
+499
+00:43:16,930 --> 00:43:19,990
+الان هذه by induction بنقدر نثبت ان ال derivative
+
+500
+00:43:19,990 --> 00:43:26,390
+اللي هو موجودة for any or ضر بناء على اللي حكيناه
+
+501
+00:43:26,390 --> 00:43:32,300
+نيجي الان لـ Corollary اللي بعدهابقول الآن الـ
+
+502
+00:43:32,300 --> 00:43:38,280
+function C and S بحقق اللي هي الـ Pythagorean
+
+503
+00:43:38,280 --> 00:43:42,280
+Identity اللي كنا نعرفها كصين تربيع زات صين تربيع
+
+504
+00:43:42,280 --> 00:43:47,660
+إش بساوي بساوي واحد فكرة البروحان سهلة بسمي هذه
+
+505
+00:43:47,660 --> 00:43:51,520
+كلها بسميها function اسمها F of X بقول سمي هذه
+
+506
+00:43:51,520 --> 00:43:56,080
+اللي هي F of X بساوي هذه فضليها بلّا بتفضليها F
+
+507
+00:43:56,080 --> 00:44:01,200
+prime of X بساوي اتنينفى C of X فى تفاضل اللى جوا
+
+508
+00:44:01,200 --> 00:44:06,300
+اللى هو ناقص S of X والتانية زائد اتنين فS of X
+
+509
+00:44:06,300 --> 00:44:11,880
+فتفاضلها هي C of X هذه هي هذه بس بالسالد اذا حصل
+
+510
+00:44:11,880 --> 00:44:15,100
+طرح حلو اسم ساوى سفر اذا صارت عند ال derivative لل
+
+511
+00:44:15,100 --> 00:44:18,320
+function هذه اشمالها بساوى سفر يعني بمعنى اخر
+
+512
+00:44:18,320 --> 00:44:22,490
+الدالة هي دالة ثابتةيعني F is a constant function
+
+513
+00:44:22,490 --> 00:44:27,210
+يعني قيمة الـ F عند أي قيمة إيش بتساوي مقدار ثابت
+
+514
+00:44:27,210 --> 00:44:31,310
+إذا اتفاج أنها ثابتة أسهل إشي أسهل إشي أوجدلي F of
+
+515
+00:44:31,310 --> 00:44:34,670
+Zero عشان أتعرف إيش ده اللي بالساوية بالظبط C of
+
+516
+00:44:34,670 --> 00:44:38,730
+Zero واحد S of Zero سفر إذا صار عندي F of Zero
+
+517
+00:44:38,730 --> 00:44:42,170
+بساوية واحد وهي ثابتة إذا صارت F of X دايما
+
+518
+00:44:42,170 --> 00:44:46,270
+بالساوية واحد يعني هذا المقدار بساوية واحد دائما
+
+519
+00:44:46,270 --> 00:44:48,690
+طيب نيجي الآن
+
+520
+00:44:51,700 --> 00:44:57,820
+لأ الـ theorem اللي بعدها الـ functions C and S
+
+521
+00:44:57,820 --> 00:45:02,820
+satisfy the properties I and II of theorem 8-4-1
+
+522
+00:45:02,820 --> 00:45:07,020
+are unique لما بقولّي برضه هتلاقي ال uniqueness
+
+523
+00:45:07,020 --> 00:45:13,020
+بشبه ال uniqueness لمن؟ لأ اللي هو ال .. ال ..
+
+524
+00:45:13,020 --> 00:45:18,030
+قولوا معايا ال uniqueness للـ exponentialو سمناها
+
+525
+00:45:18,030 --> 00:45:21,170
+اللي هو let E واحد .. نفترض أنه في E واحد و E
+
+526
+00:45:21,170 --> 00:45:24,070
+اتنين و سمها فرق بيساوي D و في الآخر روحنا لفرق
+
+527
+00:45:24,070 --> 00:45:28,390
+بيساوي إيش؟ بيساوي سفر هنا نفس الاشي هنشتغل و برضه
+
+528
+00:45:28,390 --> 00:45:31,590
+هنستخدم اللي هو ال Taylor's theorem زي ما استخدمنا
+
+529
+00:45:31,590 --> 00:45:34,470
+هناك ال Taylor's theorem يعني هتلاقيه ال sketch
+
+530
+00:45:34,470 --> 00:45:37,470
+للبرهان هو نفس ال sketch الأولاني عشان هيك
+
+531
+00:45:37,470 --> 00:45:43,110
+هتلاقوني سريع فيه بدنا نثبت أن ال C و ال S are
+
+532
+00:45:43,110 --> 00:45:47,930
+unique functionsطبعا الطريقة let c1 and c2 be two
+
+533
+00:45:47,930 --> 00:45:52,290
+functions on R that satisfy it satisfies مين ال
+
+534
+00:45:52,290 --> 00:45:55,850
+conditions اللي احنا بنقول عنهم اللي هي ال I و I I
+
+535
+00:45:55,850 --> 00:46:00,930
+اللي هو بحيث انه c1 double prime of x بساوي c1 of
+
+536
+00:46:00,930 --> 00:46:01,150
+x
+
+537
+00:46:16,750 --> 00:46:18,150
+2�
+
+538
+00:46:18,550 --> 00:46:24,010
+لأن نفترض أن دي بتساوي C1-C2 وبدنا نصل في النهاية
+
+539
+00:46:24,010 --> 00:46:27,410
+أن دي هذي لازم تطلع إيش بتساوي؟ بتساوي 0 مدام دي
+
+540
+00:46:27,410 --> 00:46:32,710
+بتساوي 0 مدام C1 بتساوي إيش؟ C2 لاحظ الآن دي W' of
+
+541
+00:46:32,710 --> 00:46:38,190
+X فاضل هذا مرتين تصير C1W'-C2W'
+
+542
+00:46:39,860 --> 00:46:47,500
+الان بساوي هتطلع ايش بتساوي ناقص اللي هي مين D of
+
+543
+00:46:47,500 --> 00:46:59,700
+X نعملها اللي هي حسابات D of X بساوي D of X بساوي
+
+544
+00:46:59,700 --> 00:47:08,540
+C1 ناقص C2 D prime of X ايش هيساوي اللي هو عبارة
+
+545
+00:47:08,540 --> 00:47:16,670
+عنأس واحد ناقص اس واحد ناقص بيصير اللي هو مين الاس
+
+546
+00:47:16,670 --> 00:47:19,810
+واحد اللي هي بالنسبة لهذه اللي أوجدناها ناقص اس
+
+547
+00:47:19,810 --> 00:47:25,350
+اتنين بيصير زائد لان دي double prime بساوي بتفاضل
+
+548
+00:47:25,350 --> 00:47:30,030
+هذا كمان مرة اللي هي بترجع مين نفسها C واحدوهذه
+
+549
+00:47:30,030 --> 00:47:38,390
+ترجع نفسها C2 التي هي ناقص D التي هي ناقص D طيب
+
+550
+00:47:38,390 --> 00:47:43,410
+إذا ال D لأنه مفترضين ال C1 وC2 أشمالها بتحقق
+
+551
+00:47:43,410 --> 00:47:52,470
+الشروط اللي فوق اللي قلنا عنهاDouble prime بساوة D
+
+552
+00:47:52,470 --> 00:48:02,390
+of X أو D double prime بساوة D double prime بساوة
+
+553
+00:48:06,030 --> 00:48:11,870
+بساوي هد W' ناقص هد W' هد W' ناقص C1 و هد W' اللي
+
+554
+00:48:11,870 --> 00:48:15,870
+هي ناقص ناقص C زائدة سارة D W' بساوي ناقص D و X
+
+555
+00:48:15,870 --> 00:48:21,890
+هيك اللي هو دعنا نقول أسلم طيب الآن بستعجل لإن
+
+556
+00:48:21,890 --> 00:48:29,470
+الكلام معاد يعنيأو الأفكار معادة الآن احطلي D of 0
+
+557
+00:48:29,470 --> 00:48:34,530
+ايش هيساوي؟ Zero لأن D of 0 بيساوي هذي ناقص هذي و
+
+558
+00:48:34,530 --> 00:48:37,630
+هذي عند ال zero واحد و هذي عند ال zero واحد
+
+559
+00:48:37,630 --> 00:48:40,010
+التنتين عند ال zero واحد انحصل طرحي ان ايش هيساوي
+
+560
+00:48:40,010 --> 00:48:47,160
+سفر الان D prime عند ال zeroوDW' عند الـ zero و و
+
+561
+00:48:47,160 --> 00:48:48,760
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+562
+00:48:48,760 --> 00:48:50,140
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+563
+00:48:50,140 --> 00:48:50,140
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+564
+00:48:50,140 --> 00:48:52,320
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+565
+00:48:52,320 --> 00:48:52,380
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+566
+00:48:52,380 --> 00:48:55,440
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+567
+00:48:55,440 --> 00:48:59,220
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+568
+00:48:59,220 --> 00:48:59,240
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+569
+00:48:59,240 --> 00:49:00,380
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+570
+00:49:00,380 --> 00:49:01,520
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+571
+00:49:01,520 --> 00:49:05,260
+.. و
+
+572
+00:49:05,260 --> 00:49:15,970
+.. و .. و .. و .. و .. و .. وبحكي عن الـ
+
+573
+00:49:15,970 --> 00:49:25,410
+derivative الـ dw prime عبارة عن اللي هي ناقص d of
+
+574
+00:49:25,410 --> 00:49:30,410
+0 عند الـ 0 و الـ d عند الـ 00 إذن هذه الـ 0 هذه
+
+575
+00:49:30,410 --> 00:49:34,330
+لمن؟ لـ k اللي هي إتنين و أربعة و ستة و تمانية
+
+576
+00:49:34,330 --> 00:49:37,870
+بنفس السبب هتطلع سفر الفرديات بيجي من مين؟ من هذه
+
+577
+00:49:38,330 --> 00:49:44,430
+فردية الـ Derivative لإيش؟ لأن D' of 0 هتساوي C1'
+
+578
+00:49:44,890 --> 00:49:51,110
+نقص C2' C1' عند الصفر صفر و C2' عند ال 0 0 إذا هذه
+
+579
+00:49:51,110 --> 00:49:56,730
+دي K عند ال 0 بالساوية 0 لكل K سواء زوجية أو إيش
+
+580
+00:49:56,730 --> 00:50:01,230
+أو فردية إذا جهزنا هذا اللي جهزناه قبل هيك يعمل
+
+581
+00:50:01,230 --> 00:50:05,940
+Exponentialوبتنا نطبّك اللي هو مين الـ Taylor's
+
+582
+00:50:05,940 --> 00:50:09,000
+theorem نطبّك الـ Now let x element in R be
+
+583
+00:50:09,000 --> 00:50:12,760
+arbitrary element in R and let I x be the interval
+
+584
+00:50:12,760 --> 00:50:18,940
+within point 0x طبّجنا عليها إذا since D بتساوي C1
+
+585
+00:50:18,940 --> 00:50:25,220
+ناقص C2 وT بتساوي S1 ناقص S2 اللي هي مفترضين S1
+
+586
+00:50:25,220 --> 00:50:28,400
+وS2 اللي هو two functions such that اللي بيحققوا
+
+587
+00:50:28,400 --> 00:50:34,170
+تبعات الـ sineاللي هي بالساوية S1 ايش هي مسميها
+
+588
+00:50:34,170 --> 00:50:39,950
+انا اللي هي بدل C2 prime او هي C2 prime والـ S2
+
+589
+00:50:39,950 --> 00:50:46,510
+اللي هي C2 A prime العكسة
+
+590
+00:50:46,510 --> 00:50:50,530
+ال derivative بيصيح بالنقص are continuous on mean
+
+591
+00:50:50,530 --> 00:50:55,930
+on Ix عارفين continuous انه احنا مفترضين ان نحقق
+
+592
+00:50:55,930 --> 00:51:00,160
+نفس اللي هو اللي قبلمدام continuous الـ D والـ T
+
+593
+00:51:00,160 --> 00:51:07,440
+continuous على closed bounded interval I X إذا في
+
+594
+00:51:07,440 --> 00:51:12,810
+اللي هو K واحد للأولىوK2 للتانية خدوا ال maximum
+
+595
+00:51:12,810 --> 00:51:18,470
+إليها واسموها K إذا في K للجهتين بحيث ان ال D of T
+
+596
+00:51:18,470 --> 00:51:22,930
+bounded علي هذه أصغر شهو T كي على كل الفترة اللي
+
+597
+00:51:22,930 --> 00:51:27,390
+بنحكي عنها IX وT of T أصغر شهو K for all T
+
+598
+00:51:27,390 --> 00:51:30,290
+elements of IX لأنه زي ما أقول continuous function
+
+599
+00:51:30,290 --> 00:51:33,930
+in a closed bounded interval must be boundedالآن
+
+600
+00:51:33,930 --> 00:51:39,170
+جاهزين نطبق مين؟ الـ Taylor's theorem to d من Ix
+
+601
+00:51:39,170 --> 00:51:44,970
+and use the fact دي اللي أثبتناه دي 0 سواء 0 دي K0
+
+602
+00:51:44,970 --> 00:51:50,030
+سواء 0 الآن بنقول for each n unlimited n عملناها
+
+603
+00:51:50,030 --> 00:51:56,510
+عشان هيك بس ماشي عنه بسرعة عملناها قبل هيك there
+
+604
+00:51:56,510 --> 00:51:59,630
+exist a point Cn unlimited Ix such that هذا
+
+605
+00:51:59,630 --> 00:52:03,890
+remainder بتعملي remainderD ب X بيساوي D of 0 زي
+
+606
+00:52:03,890 --> 00:52:06,850
+دي prime of 0 زائد زائد زائد زائد X ان نقص واحد
+
+607
+00:52:06,850 --> 00:52:12,630
+لما أصل لمين لل remainder كل هذول أصفار بسبب مين
+
+608
+00:52:12,630 --> 00:52:16,430
+انه D0 وD prime of 0 وD ان نقص واحد وزير وكلهم إيه
+
+609
+00:52:16,430 --> 00:52:20,090
+شمالهم بيساوي أصفار عند الصفر بيظل هذا المقدار
+
+610
+00:52:20,090 --> 00:52:24,010
+يساوي اللي هو المقدار اللي عندي اللي تحت هذا هذا
+
+611
+00:52:24,010 --> 00:52:27,490
+ال derivative هذا ال derivative أنا بعرفش إيش هي
+
+612
+00:52:27,490 --> 00:52:31,230
+ما أنتوا عارفين ال derivative لل .. لل .. لل C
+
+613
+00:52:34,160 --> 00:52:41,940
+أو ال derivative للـC إذا فضلت مرة واحدة بتطلع
+
+614
+00:52:41,940 --> 00:52:47,120
+الـS أو سلبها فظلت تلت مرات بترجع ليها S بس
+
+615
+00:52:47,120 --> 00:52:53,180
+بالموجة فظلت خمسة بترجع ناقص Sفظلت زوجي بتطلع هي
+
+616
+00:52:53,180 --> 00:52:58,920
+نفسها أو سلبها عشان هي كادل أنا بعرفش طبعا هنا
+
+617
+00:52:58,920 --> 00:53:02,400
+عندك اللي هي بتتوزع على مرة derivative تندين
+
+618
+00:53:02,400 --> 00:53:04,620
+derivative تلاتة derivative أربعة derivative و
+
+619
+00:53:04,620 --> 00:53:08,180
+بترجع الدورة زي ما هي لإنه في الأول بيكون اللي هي
+
+620
+00:53:08,180 --> 00:53:15,520
+تفاضل الـC ناقص S بعدها بتتفاضل بترجع اللي هي ناقص
+
+621
+00:53:15,520 --> 00:53:18,770
+حالهابعدها بترجع اللي هي
+
+622
+00:53:18,770 --> 00:53:36,410
+ببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببب
+
+623
+00:53:36,660 --> 00:53:40,180
+اللي هي الـC ويصير نقص C كمان مرة بترجع اللي هي
+
+624
+00:53:40,180 --> 00:53:45,740
+الـS وكمان مرة بترجع اللي هي الـC بعد هيك بتصير
+
+625
+00:53:45,740 --> 00:53:51,920
+اللي هي تكرر حالها يعني بمعنى آخر جربوها أنتوا
+
+626
+00:53:51,920 --> 00:53:59,920
+هتلاقوا أنه حسب الأُس هنا بتطلع اللي هي عبارة عن
+
+627
+00:53:59,920 --> 00:54:11,180
+هي أو سلبها أو الـS أو سلبهابكل الأحوال بغض النظر
+
+628
+00:54:11,180 --> 00:54:15,600
+اللي هي DN of CN هي حاصل طرح التنتين اللي هي سمنها
+
+629
+00:54:15,600 --> 00:54:23,280
+يا D يا T الـ D تبعت الـ C الفرق طبعا والـ T اللي
+
+630
+00:54:23,280 --> 00:54:29,010
+هي الفرق بين الأسات يعني في الآخرزاد او ناقص و زاد
+
+631
+00:54:29,010 --> 00:54:33,810
+او ناقص سواء هذه او سواء هذه حضرنا من الاصل انها
+
+632
+00:54:33,810 --> 00:54:38,870
+bounded و كله اصغر او يساوي من K اصغر او يساوي ايش
+
+633
+00:54:38,870 --> 00:54:45,860
+K بناء عليه هتطلع هذه هيكabsolute value أصغر أو
+
+634
+00:54:45,860 --> 00:54:51,780
+يساوي هذه أي إن كانت K في X أُس N absolute value
+
+635
+00:54:51,780 --> 00:54:56,880
+على N factorial باشي الحال إذا صلعت عندي هذا
+
+636
+00:54:56,880 --> 00:55:00,860
+المقدار أصغر أو يساوي هذا as N goes to infinity
+
+637
+00:55:00,860 --> 00:55:05,540
+هذا بروح لمن؟ للسفر وهذا independent of N بيصير
+
+638
+00:55:05,540 --> 00:55:08,100
+أكبر أو يساوي السفر يعني هذا اللي جوا بده يصير سفر
+
+639
+00:55:08,100 --> 00:55:12,930
+إذا ال D of X هاشي بدها تساويبتساوي سفر وبكون
+
+640
+00:55:12,930 --> 00:55:21,090
+أثبتنا ان الـ C1 والـ C2 are equivalent الان
+
+641
+00:55:21,090 --> 00:55:27,700
+similar arguments بنفس الاسلوبوخلّيها إليكم إنه
+
+642
+00:55:27,700 --> 00:55:32,120
+اللي هي بنثبت إنه S إذا كان S1 وS2 are two
+
+643
+00:55:32,120 --> 00:55:36,320
+functions such that بيحققوا اللي هما الخواصة اللي
+
+644
+00:55:36,320 --> 00:55:41,700
+بنقولها عنها في النظرية اللي هي S1 double prime
+
+645
+00:55:41,700 --> 00:55:46,400
+بيساوي نفس S1 ونفس ال S2 وهذا عند Zero بيساوي Zero
+
+646
+00:55:46,400 --> 00:55:50,160
+وهذا ال prime عند Zero بيساوي Zero هيتلعلك غصب
+
+647
+00:55:50,160 --> 00:55:52,240
+عنها في الأخر S1 بيساوي S2
+
+648
+00:55:55,620 --> 00:55:59,960
+بس بدل ما تعملوا على ال D يعني ساموا اللي هو T
+
+649
+00:55:59,960 --> 00:56:04,040
+بتساوي S1 نقص S2 وطبقوا الشروط وامشوا نفس اللي
+
+650
+00:56:04,040 --> 00:56:07,580
+امشيناها هتلاقوا حالكم انه لازم تطلع ال S1 بساوي
+
+651
+00:56:07,580 --> 00:56:11,800
+S2 وبناء عليه صار ال ال two functions ال C والS
+
+652
+00:56:11,800 --> 00:56:17,820
+are unique functions طيب
+
+653
+00:56:17,820 --> 00:56:24,720
+ال answer المؤهليننذهب بالاتجاه نثبت أن افترض أن
+
+654
+00:56:24,720 --> 00:56:27,880
+الـ Definition of the unique function C من R لR و
+
+655
+00:56:27,880 --> 00:56:32,400
+أسم الـ R لR اللي يتحقق CW prime of X بساوية نقطة
+
+656
+00:56:32,400 --> 00:56:36,650
+C of Xهو الاصل الـ differential equation التاني S
+
+657
+00:56:36,650 --> 00:56:40,990
+w برامج و X ناقص بساوة ناقص S X لكل X element in R
+
+658
+00:56:40,990 --> 00:56:43,470
+و ال C of Zero اللي هو ال condition ال condition
+
+659
+00:56:43,470 --> 00:56:46,350
+بساوة واحد و C برامج و Zero بساوة Zero و ال S of
+
+660
+00:56:46,350 --> 00:56:49,710
+Zero بساوة Zero و ال S برامج و Zero بساوة Zero
+
+661
+00:56:49,710 --> 00:56:57,150
+الدالتين اللي بحقق إن الكلام هذا اللي أثبتنا إنه
+
+662
+00:56:57,150 --> 00:57:02,740
+uniqueبنسميهم respectively the cosine function and
+
+663
+00:57:02,740 --> 00:57:07,600
+the sine function اللي انتوا بتعرفوها وهي cosine X
+
+664
+00:57:07,600 --> 00:57:12,620
+اللي بتعرفوها وهي sin X اللي انتوا بتعرفوها نيجي
+
+665
+00:57:12,620 --> 00:57:17,930
+الآنلاخد بعض الخواص خلينا ناخد اللي هو الخاصية
+
+666
+00:57:17,930 --> 00:57:23,430
+اللي هي نظرية 4.6 بتقول لي إذا كانت f من R ل R is
+
+667
+00:57:23,430 --> 00:57:27,890
+such that f double prime of x بساعة نقص f of x for
+
+668
+00:57:27,890 --> 00:57:30,370
+x element in R يعني هذه ال differential equation
+
+669
+00:57:30,370 --> 00:57:32,810
+بتقوللي هذه ال differential equation هي حلولها
+
+670
+00:57:32,810 --> 00:57:37,690
+مالي then there exist Alpha و BetaSuch that F of X
+
+671
+00:57:37,690 --> 00:57:41,390
+بيسوء Alpha CX زائد Beta S of X بيقوللي هذه ال
+
+672
+00:57:41,390 --> 00:57:45,110
+differential equation حالة انها عبارة عن linear او
+
+673
+00:57:45,110 --> 00:57:47,870
+خليني اقول combination او linear combination
+
+674
+00:57:47,870 --> 00:57:55,890
+between F C of X S of Xخلّيني أخد نسمي g of x إيش
+
+675
+00:57:55,890 --> 00:57:59,590
+بتساوي اللي هي عبارة عن اللي هي ال c of x و ال a
+
+676
+00:57:59,590 --> 00:58:03,770
+sub x نسمي هذه f of zero و f prime of zero for x
+
+677
+00:58:03,770 --> 00:58:10,330
+element in R الآن لو حسبت ال gw prime of x احسبها
+
+678
+00:58:10,330 --> 00:58:15,270
+فاضل هذه
+
+679
+00:58:15,270 --> 00:58:18,550
+مرتين هدولة ثوابت طبعا و هدولة اللي بتنزلك
+
+680
+00:58:18,550 --> 00:58:23,970
+هتلاقيهم اللي هو بساوي ناقص g of xأه .. و لو حسبت
+
+681
+00:58:23,970 --> 00:58:26,730
+الـ g of zero .. g of zero هتلاقيها بساوي of zero
+
+682
+00:58:26,730 --> 00:58:30,110
+لإن هذا سفر وهذا .. هذا واحد وهذا سفر الان صار
+
+683
+00:58:30,110 --> 00:58:33,850
+عندى gw prime of x بساوي نقص g of x و g of zero
+
+684
+00:58:33,850 --> 00:58:40,410
+بساوي f of zero الان احسب الـ g prime of xصار عندى
+
+685
+00:58:40,410 --> 00:58:43,450
+تلات معلومات معلمتين جي دابل برايم of X بيساوي نقص
+
+686
+00:58:43,450 --> 00:58:45,990
+جي of X و جي of Zero بيساوي أف of Zero خلينا نجيب
+
+687
+00:58:45,990 --> 00:58:50,330
+جي برايم of X جي برايم of X مش بتساوي فاضل اللى هى
+
+688
+00:58:50,330 --> 00:58:55,430
+عبارة عن نقص أس of X و هدا تفضلها اللى هى C of X
+
+689
+00:58:55,430 --> 00:58:58,830
+صار عندى اللى هى جي برايم of X بيساوي هذا الكلام
+
+690
+00:58:58,830 --> 00:59:04,720
+زائد هذا الكلامالان احسبلي g prime of 0 هيصير
+
+691
+00:59:04,720 --> 00:59:08,420
+عبارة عن هذا طبعا سفر وهذا هتصير واحد فبصير F
+
+692
+00:59:08,420 --> 00:59:13,750
+prime of 0 صار عندى الان g prime of 0أيش بيساوي يا
+
+693
+00:59:13,750 --> 00:59:18,090
+جماعة؟ جي برايم اف زيرو خليني أطلعلك إياها لفوق
+
+694
+00:59:18,090 --> 00:59:21,750
+صارت جي برايم اف زيرو بيساوي أف برايم اف زيرو و جي
+
+695
+00:59:21,750 --> 00:59:26,730
+اف زيرو بيساوي أف اف زيرو الآن بديش ناشر نعيد اللي
+
+696
+00:59:26,730 --> 00:59:30,950
+هو therefore الآن the functions h بتساوي f ناقص g
+
+697
+00:59:30,950 --> 00:59:35,990
+is such that يعني عرفلي function h أيش بيساوي؟ f
+
+698
+00:59:35,990 --> 00:59:43,220
+ناقص مين ناقص gالآن الـ H double prime لها لو جيت
+
+699
+00:59:43,220 --> 00:59:46,840
+حسبت الـ H double prime اللي هي هتلاقيها بتساوي
+
+700
+00:59:46,840 --> 00:59:50,260
+ناقص H of X بتحسبوها لحالكم H double prime of X
+
+701
+00:59:50,260 --> 00:59:55,140
+عشان بتساوي ناقص H of X لكل X element in R لو حسبت
+
+702
+00:59:55,140 --> 00:59:59,670
+اللي هي H of Zeroهتساوي اللي هي zero لإنه احنا
+
+703
+00:59:59,670 --> 01:00:03,010
+أثبتنا ان g of zero ساوي f of zero وh prime of
+
+704
+01:00:03,010 --> 01:00:07,110
+zero h prime of zero اللي هي عبارة عن f prime نقص
+
+705
+01:00:07,110 --> 01:00:09,210
+g prime عند ال zero التانية و التساويات إذا إيه مش
+
+706
+01:00:09,210 --> 01:00:15,170
+ساوي سفر الان it then thus it follows as in the
+
+707
+01:00:15,170 --> 01:00:19,430
+proof of the preceding theorem النظرية الماضية إن
+
+708
+01:00:19,430 --> 01:00:22,170
+h of x إيه مش ساوي سفر يعني بدك تعمل نفس اللي
+
+709
+01:00:22,170 --> 01:00:25,180
+عملناها قبل هيك على ال Taylor's theorem و الاخرينو
+
+710
+01:00:25,180 --> 01:00:29,300
+تصل ال H of X بساوية 0 لكل X ومنه هتقول F of X
+
+711
+01:00:29,300 --> 01:00:33,320
+بساوية G of X مدام F of X بساوية G of X إذن هذه
+
+712
+01:00:33,320 --> 01:00:38,580
+اللي هي F of X بتطلع F of X بتساوي اللي هي هذا
+
+713
+01:00:38,580 --> 01:00:42,780
+اسمها Alpha وهذا اسمها Beta وبكون عندي هي اللي هو
+
+714
+01:00:42,780 --> 01:00:46,280
+solution لاللي هي ال differential equation اللي
+
+715
+01:00:46,280 --> 01:00:50,260
+احنا حكينا عنها بديش أعيد نفس الكلام عشان هي كأنا
+
+716
+01:00:50,260 --> 01:00:52,780
+اختصرت لأن الحسابات كلها مشابهة
+
+717
+01:00:58,150 --> 01:01:03,430
+الان بدنا اللي هي 8 4 7 the function C is even and
+
+718
+01:01:03,430 --> 01:01:07,570
+S is odd in the sense that هو بتكون الصحيحة دي
+
+719
+01:01:07,570 --> 01:01:10,610
+الأصل كلها تكون أو معظمها اللي هي عبارة عن
+
+720
+01:01:10,610 --> 01:01:14,430
+exercises لإنها تطبيقات على النظرية اللي قلتها في
+
+721
+01:01:14,430 --> 01:01:19,630
+الأول ال C ناقص X هيسوء C of X يعني عبارة عن even
+
+722
+01:01:19,630 --> 01:01:23,230
+function S ناقص X بيسوء ناقص S of X لكل X element
+
+723
+01:01:23,230 --> 01:01:28,590
+in Rالآن if x,y المتنار then we have the addition
+
+724
+01:01:28,590 --> 01:01:32,230
+formula c of x زي اد y بيسبب c of x في c of y نقص
+
+725
+01:01:32,230 --> 01:01:35,950
+s of x وs of y اللي هي اللي بتعرفوها انتوا sign ال
+
+726
+01:01:35,950 --> 01:01:38,350
+x زي اد y بيسبب sign ال x بكسان ال y زي اد كسان ال
+
+727
+01:01:38,350 --> 01:01:42,090
+y في sign ال x وهكذا هي هذه الخواص اللي احنا
+
+728
+01:01:42,090 --> 01:01:47,570
+عارفينها قبل هيك وبدنا نشوف كيف اللي هي انبرهن
+
+729
+01:01:47,570 --> 01:01:53,660
+النظرية نشوف البرهان تبع النظريةالآن سمّيلي Phi of
+
+730
+01:01:53,660 --> 01:01:59,370
+X بيساوي C of ماقص X لكل X element in Rاحسبلي الـ
+
+731
+01:01:59,370 --> 01:02:05,010
+phi w prime of x لو اتيت فضلت هذه مرتين هتلاقيها
+
+732
+01:02:05,010 --> 01:02:09,950
+ناقص phi of x وهذا الكلام تفضله سهل و بتجيبه لحالك
+
+733
+01:02:09,950 --> 01:02:15,050
+الآن احسبلي ال phi of 0 phi of 0 هتساوي ايش؟
+
+734
+01:02:15,050 --> 01:02:19,350
+بتساوي واحد phi prime of 0 هتطلع اللي هي عبارة عن
+
+735
+01:02:19,350 --> 01:02:24,430
+اللي هي ال sign ال sign ايش معناها؟ بتساوي 0 عند
+
+736
+01:02:24,430 --> 01:02:30,730
+ال zeroالان صار عندى الان الفاى هي مين؟ هي الـC
+
+737
+01:02:30,730 --> 01:02:35,710
+ليش الفاى هي الـC؟ لأن حققت الفاى اللى فرضتها
+
+738
+01:02:35,710 --> 01:02:40,790
+بساوية C-X شروط الـC و الـC is unique إذا الفاى H
+
+739
+01:02:40,790 --> 01:02:47,200
+بتساوي Cإذا صار عندى الان C-X بيساوي C of X الفكرة
+
+740
+01:02:47,200 --> 01:02:52,060
+واضحة أنه أنا جبت سميت الـC-X هي الفاية واتبتت أن
+
+741
+01:02:52,060 --> 01:02:57,060
+هذه الفاية بتحقق الشرطين اللي احنا حكينا عنهم في
+
+742
+01:02:57,060 --> 01:03:01,300
+الأول الدالة اللي بتخلي الـC is unique فصارت
+
+743
+01:03:01,300 --> 01:03:07,080
+الفاية أيش بتساوي الـCالان بمعنى اخر صارت C of X
+
+744
+01:03:07,080 --> 01:03:10,720
+هي C من ناقص X اللي فرضناها الـ Phi in a similar
+
+745
+01:03:10,720 --> 01:03:16,040
+way برضه بدك تعملاش S of ناقص X اللي هو بتسمي اللي
+
+746
+01:03:16,040 --> 01:03:20,480
+هي ال .. الفا .. بتسميها بـ Psi مثلا Psi بتساوي
+
+747
+01:03:20,480 --> 01:03:25,020
+مين؟بتساوي اللي هو ناقص هتجيبها سامي بصي بيساوي
+
+748
+01:03:25,020 --> 01:03:29,540
+ناقص S ناقص X و تجيب الشروط اللي هي تبعها ال sign
+
+749
+01:03:29,540 --> 01:03:33,500
+هتلاقيها متطابق متحققة و بما ان ال S is unique او
+
+750
+01:03:33,500 --> 01:03:37,240
+ال sign is unique اذا اللي هي اللي حققتها اللي
+
+751
+01:03:37,240 --> 01:03:41,500
+كتبتها بتساوي ال S وصارين ايه جهتين متساويات بنفس
+
+752
+01:03:41,500 --> 01:03:47,980
+الأسلوب طيب الآن نيجي نثبت اللي هو مين VI شوفوا
+
+753
+01:03:47,980 --> 01:03:52,850
+صلى على النبي عليه الصلاة والسلامهنفير نبره ان vi
+
+754
+01:03:52,850 --> 01:03:55,830
+let y المتن عار بيجيبنا let f of x بيساوي c of x
+
+755
+01:03:55,830 --> 01:04:00,070
+زي dash زي y for x المتن عار الان a calculation
+
+756
+01:04:00,070 --> 01:04:04,230
+shows that يعني فضلي هذا مرتين التفاضل سهل والله
+
+757
+01:04:04,230 --> 01:04:08,010
+يا جماعة عشانك انا يعني مابديش نضيع واجتنا في
+
+758
+01:04:08,010 --> 01:04:12,190
+التفاضلأو في الحسابات f w prime of x طبعا فاضل
+
+759
+01:04:12,190 --> 01:04:15,430
+بالنسبالي x y ايش ما على f x ثابت أسيبك منها لأن
+
+760
+01:04:15,430 --> 01:04:18,590
+لو فضلت مرتين هتلاقي ناقص f of x for x element in
+
+761
+01:04:18,590 --> 01:04:22,550
+R مدام f w prime بيساوي ناقص f of x بالحصارة اللي
+
+762
+01:04:22,550 --> 01:04:26,850
+هي حل المعادلة القفاضلية هذه اللي هي بالنظرية اللي
+
+763
+01:04:26,850 --> 01:04:32,880
+قبل شويه هي 8 4 6 هتكون اللي هي ال f of xعبارة عن
+
+764
+01:04:32,880 --> 01:04:36,300
+linear combination هذه اللي هو α C of X زي Beta S
+
+765
+01:04:36,300 --> 01:04:39,840
+of X والـ F of X مين هي احنا فرضينا C of XY صارت
+
+766
+01:04:39,840 --> 01:04:43,180
+هذه عبارة عن هذه يعني هذه بتساوي هذه من حال
+
+767
+01:04:43,180 --> 01:04:47,260
+المعادلة التفاضلية هذه بواسطة النظرية هذه وهذه
+
+768
+01:04:47,260 --> 01:04:51,330
+اصلا انا نسميها هيك صارت هذه بتساوي هذا المقطعالان
+
+769
+01:04:51,330 --> 01:04:55,350
+جيبله F prime F prime of X اللي هي هذه التفضيلة
+
+770
+01:04:55,350 --> 01:04:59,070
+بـC ناقص S of X زائد Y وفاضل هذه بيطلع اللي هو
+
+771
+01:04:59,070 --> 01:05:02,910
+عبارة عن ناقص Alpha S of X زائد Beta C of X ثم
+
+772
+01:05:02,910 --> 01:05:09,710
+فضلت ماشي الان خد X بيساوي 0 X بيساوي 0 لما X
+
+773
+01:05:09,710 --> 01:05:18,250
+بتساوي 0بنحصل الآن عندى .. بصير عندى عوض X بتساوي
+
+774
+01:05:18,250 --> 01:05:25,190
+سفر في اللى هى المعادلة اللى عندى هنا بصير عندى S
+
+775
+01:05:25,190 --> 01:05:31,360
+of Zero و C of Zeroبساومين F of Zero F of Zero
+
+776
+01:05:31,360 --> 01:05:40,100
+اللي هي عبارة عن F of Zero هي C of Y هذه فاهمين
+
+777
+01:05:40,100 --> 01:05:44,560
+عليها؟ خليني أقولها واضحة أحسن الآن بدنا ناخد F
+
+778
+01:05:44,560 --> 01:05:52,600
+مين؟ F عند Zero فاشر؟ بيصير هذا C of Y بساومي
+
+779
+01:05:52,600 --> 01:05:58,190
+Alphaفي c of zero واحد وهذه beta s of zero زيرو
+
+780
+01:05:58,190 --> 01:06:03,890
+إذا صارت عندي ال alpha بتساوي c of y هاي واحدة لأن
+
+781
+01:06:03,890 --> 01:06:09,990
+similarly اللي هو ناقص خد عند ال zero عند ال zero
+
+782
+01:06:09,990 --> 01:06:15,570
+بيصير ناقص s of y بساوي هذي بيصير سفر وهذه بيصير
+
+783
+01:06:15,570 --> 01:06:20,070
+beta بساوي beta الآن بنعوض وين في ال formula
+
+784
+01:06:20,070 --> 01:06:26,370
+الأولىبصير عندى الان ال formula اللى عندى اللى هى
+
+785
+01:06:26,370 --> 01:06:30,010
+بتحط مكان C of Y بسوة Alpha و الفورمولة الأولى
+
+786
+01:06:30,010 --> 01:06:35,770
+اللى احنا عملناها بصير عندى اللى هى C
+
+787
+01:06:38,530 --> 01:06:43,570
+Half X زائد Y بساوة Alpha اللي هي اسمها قلنا طلعت
+
+788
+01:06:43,570 --> 01:06:48,310
+عندنا C of Y بصير C of Y في C of X هيها مظبوطة
+
+789
+01:06:48,310 --> 01:06:53,130
+وهذه ناقص S مكان ال Beta بصير ناقص S of Y في S of
+
+790
+01:06:53,130 --> 01:07:01,740
+X صحيحة إذا بكون إحنا خلصنا اللي بدناياه وهذهبتعوض
+
+791
+01:07:01,740 --> 01:07:08,240
+عن اللي هي Alpha C of Y بC نقص C of Y وهذه بتعوضها
+
+792
+01:07:08,240 --> 01:07:13,440
+هنا بتطلع هذه بتساوي نقص هذه اعمل الحساب الأخير
+
+793
+01:07:13,440 --> 01:07:17,400
+وظروف الدقيقتين بنقص بتطلع عندك هذا المخضر يعني
+
+794
+01:07:17,400 --> 01:07:23,840
+هذه التعويض فيها عن قيمة Alpha و Beta بهذه هنا
+
+795
+01:07:23,840 --> 01:07:30,860
+بتطلع هذه وهذه التعويض هذهعن alpha و beta هنا اللي
+
+796
+01:07:30,860 --> 01:07:35,420
+بتطلع الأولى بكون احنا خلصنا اللي هو اثبات هذه
+
+797
+01:07:35,420 --> 01:07:42,800
+اللي هي النظرية وضال عندي اللي هو النظرية هذه
+
+798
+01:07:42,800 --> 01:07:47,350
+الأخيرةوالباقي اللي هو لو اتطلعتوا على اللي هي
+
+799
+01:07:47,350 --> 01:07:52,450
+باقي النظريات اللي هي بس اتطلع لعند الها بيكون
+
+800
+01:07:52,450 --> 01:07:55,990
+احنا بيكون خلصنا chapter اللي هو المطلوب في
+
+801
+01:07:55,990 --> 01:08:00,350
+chapter في تمانية أربعة هذه اللي هي ال theorem
+
+802
+01:08:00,350 --> 01:08:03,530
+خليني أطلعلك عليها على السريع لإن حسابات كلها
+
+803
+01:08:03,530 --> 01:08:07,840
+بتعملها لحالك أكيد بتعرفإذا كان الـ x أكبر أو أقل
+
+804
+01:08:07,840 --> 01:08:12,880
+من 0، فهناك Sx بنقص الـ x والـ x والـ c of x بين
+
+805
+01:08:12,880 --> 01:08:16,780
+الواحد نقصه x أربع عزر تو واحد والـ c of x بقدر
+
+806
+01:08:16,780 --> 01:08:18,820
+أكمل الـ polynomial
+
+807
+01:08:21,810 --> 01:08:25,650
+باللي عملناها اللي هي الـCN of X اللي جابله شوية و
+
+808
+01:08:25,650 --> 01:08:28,430
+الـSN of X لأنه في النهاية limitها ال series
+
+809
+01:08:28,430 --> 01:08:30,790
+الأولى as N goes to infinity ما أنتوا عارفين اللي
+
+810
+01:08:30,790 --> 01:08:34,990
+هي نقدر نكتب الـC of X على صورة ال series اللي في
+
+811
+01:08:34,990 --> 01:08:38,130
+الأول و الS of X عبارة عن limit ال series التانية
+
+812
+01:08:38,130 --> 01:08:43,390
+ال terms إضافة term و طرح term و وجوف عند حدود بال
+
+813
+01:08:43,390 --> 01:08:47,090
+term بتعمل ال inequality اللي عندنا اللي هو كل هذه
+
+814
+01:08:47,090 --> 01:08:49,810
+شغلات اللي أخدناها في ال calculus مافيش داعي
+
+815
+01:08:49,810 --> 01:08:55,650
+للتفصيل فيهاالان الاولىعندي ال .. ال .. احنا قلنا
+
+816
+01:08:55,650 --> 01:08:59,990
+sign تربيع زائد plus sign تربيع بساوي واحد يعني في
+
+817
+01:08:59,990 --> 01:09:02,670
+النهاية ال C of T بين ماقص واحد و واحد ده ممكن
+
+818
+01:09:02,670 --> 01:09:06,710
+هتتجاوزها لأنه بتختل اللي هي ال C .. لو كانت أكبر
+
+819
+01:09:06,710 --> 01:09:10,750
+من واحد معناته بـ C .. C of T تربيع زائد S of T
+
+820
+01:09:10,750 --> 01:09:14,550
+تربيع يتجاوز من واحد لكن مجموح بسوء واحد إذا هدي
+
+821
+01:09:14,550 --> 01:09:18,630
+بين .. يعني هدي اللي وين جاية من C تربيع زائد S
+
+822
+01:09:18,630 --> 01:09:23,030
+تربيع بساوي واحد طيباللي هنعمل integration لجهتين
+
+823
+01:09:23,030 --> 01:09:26,990
+من صفر لعين DX هذه اللي هي بتطلع اللي هي main ال S
+
+824
+01:09:26,990 --> 01:09:30,750
+of X وهذه بتطلع أنخس X وهذه بتطلع X فالمعمل ال
+
+825
+01:09:30,750 --> 01:09:35,990
+integration هدول الان بدي
+
+826
+01:09:35,990 --> 01:09:43,300
+أجيب التانية فضلي ال S of Tهذه وهذه فاضليها هذه
+
+827
+01:09:43,300 --> 01:09:48,460
+فاضليها بنقل صفر عند X بتطلع اللي هي بين هذه وهذه
+
+828
+01:09:48,460 --> 01:09:53,660
+هيتفاضوا لهذه وهذه الان بدنا اللي هو نجيب الواحد
+
+829
+01:09:53,660 --> 01:09:58,280
+ناقص X السربيع اللي هو هذا قيمته اللي هو عبارة عن
+
+830
+01:09:58,280 --> 01:10:02,600
+C في X بالساوية واحد ناقص هذه بنضرب الناقص و بنجمع
+
+831
+01:10:02,600 --> 01:10:08,280
+الجهتين واحد بطلع عندي اللي هي ال inequality اللي
+
+832
+01:10:08,280 --> 01:10:13,190
+عندي هذهزي ما قلنا ضربنا في ناقص و جمعنا واحد طلعت
+
+833
+01:10:13,190 --> 01:10:16,590
+هذه او عوضنا هذه مكان هذه تعويض عادي و بعدين ضربنا
+
+834
+01:10:16,590 --> 01:10:20,690
+في ناقص فبصير عندى هذه المقدار اللى عندى c of x
+
+835
+01:10:20,690 --> 01:10:24,310
+أكبر سواء هذه و ناقص هذه و اللى بتستخدم الثانية
+
+836
+01:10:24,310 --> 01:10:27,670
+بتطلع نفس الاشي الموضوع موضوع حسابات بحت عشان هيك
+
+837
+01:10:27,670 --> 01:10:31,510
+بحت عشان هيك مافي داعي للتكميل و انتوا بتكملوا
+
+838
+01:10:31,510 --> 01:10:35,150
+باقى الحسابات اللى هي المطلوبة في هذا اللى هي
+
+839
+01:10:35,150 --> 01:10:42,700
+النظرية الان الجزء المتبقى هذاحبيته تطلعوا عليه
+
+840
+01:10:42,700 --> 01:10:46,880
+لكن اللي هو مش مطلوب من ضمن حديثنا و هيك ممكن
+
+841
+01:10:46,880 --> 01:10:52,700
+نخلصنااللي هو section تمانية أربعة متسمة سبتر
+
+842
+01:10:52,700 --> 01:10:58,420
+تمانية هذا اللي هو الجزء الثالث من المادة الجزء
+
+843
+01:10:58,420 --> 01:11:00,160
+الأول كان ال differentiation والتاني ال
+
+844
+01:11:00,160 --> 01:11:01,960
+integration والتالت اللي هو point twice
+
+845
+01:11:01,960 --> 01:11:05,700
+convergence المرة الجاية ان شاء الله اللي هو بنبدأ
+
+846
+01:11:05,700 --> 01:11:09,880
+في الجزء الرابع من المادة اللي هو ال series وان
+
+847
+01:11:09,880 --> 01:11:16,590
+شاء الله بقدر الإمكان هأحكي الجزء الخامسفي .. من
+
+848
+01:11:16,590 --> 01:11:20,510
+المادة اللي هو عبارة عن اللي هو Topology in R أو
+
+849
+01:11:20,510 --> 01:11:23,570
+اللي هو اللي هي العلاقة بين اللي هي Topological
+
+850
+01:11:23,570 --> 01:11:27,410
+Spaces وNormed Spaces وHilbert Spaces إلى آخره
+
+851
+01:11:27,410 --> 01:11:33,530
+ويمكن بتكون هي اتجاوزت خلنا نقول حد ال .. ال .. ال
+
+852
+01:11:33,530 --> 01:11:37,150
+.. المطلوب في المادة لكن على أساس إنه لو يكون
+
+853
+01:11:37,150 --> 01:11:42,210
+التصوير كامل للو .. للوصف اللي أنا اقتراحتهأو اللي
+
+854
+01:11:42,210 --> 01:11:47,230
+هو الوصف اللي مقترح في الجسم اللي هو لعين نهاية ال
+
+855
+01:11:47,230 --> 01:11:49,990
+series و طبعا هذا الكلام قلنا احنا فيه له سبب لما
+
+856
+01:11:49,990 --> 01:11:53,450
+بدأنا في الأول انه ال series بتاخدوها في advanced
+
+857
+01:11:53,450 --> 01:11:56,990
+calculus واحد فعشان هيك يمكن اللي هو
+
+858
+01:12:00,350 --> 01:12:03,810
+هيكون منطقي أنه ما ناخدش ال series و ناخد بدلها
+
+859
+01:12:03,810 --> 01:12:07,110
+اللي هو ال topology انار أو اللي هو العلاقة بين ال
+
+860
+01:12:07,110 --> 01:12:10,550
+topological spaces و ال metric spaces و إلى لقاء و
+
+861
+01:12:10,550 --> 01:12:12,650
+السلام آخر والسلام عليكم و رحمه الله وبركاته
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7a4bdd2a02193f6bf8050f260ff1ab767dceaee2
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/EvAUsrqrpFk_postprocess.srt
@@ -0,0 +1,3324 @@
+1
+00:00:04,910 --> 00:00:11,030
+بسم الله الرحمن الرحيم المحاضرة الرابعة بعد حالة
+
+2
+00:00:11,030 --> 00:00:19,410
+الطوارئفي مادة او مساق تحليل لرياضي 2 او تحليل
+
+3
+00:00:19,410 --> 00:00:23,970
+حقيقي 2 لطلبة و طالبات الجامعة الإسلامية كلية
+
+4
+00:00:23,970 --> 00:00:30,110
+العلوم قسم الرياضيات وهي المحاضرة رقم 14 في المادة
+
+5
+00:00:30,110 --> 00:00:35,970
+او في المساق عنوان المحاضرة اليوم اللي هو
+
+6
+00:00:35,970 --> 00:00:43,260
+fundamental theorem ofof calculus بشقيها شق تفاضل
+
+7
+00:00:43,260 --> 00:00:50,640
+التكامل وشق تكامل التفاضل roughly نبدأ اللي هو في
+
+8
+00:00:50,640 --> 00:00:54,960
+النظرية الأولة أو الجزء الأول من النظرية اللي هي
+
+9
+00:00:54,960 --> 00:00:58,760
+ال first form ال fundamental theorem of calculus
+
+10
+00:00:58,760 --> 00:01:04,870
+اللي هي الجزء الأول بتقول ما يليlet f from a و b
+
+11
+00:01:04,870 --> 00:01:08,430
+لعند R be an integrable function on a و b يعني
+
+12
+00:01:08,430 --> 00:01:12,070
+فرضنا أن الـ function f عبارة عن دالة قابلة
+
+13
+00:01:12,070 --> 00:01:17,190
+للتكامل على الفترة المغلقة a و b and let f capital
+
+14
+00:01:17,190 --> 00:01:22,190
+من a و b لعند R تحقق الشروط التاليةتحقق أول شيء
+
+15
+00:01:22,190 --> 00:01:25,110
+أنها تكون الاف كابتنال هادي continuous على الفترة
+
+16
+00:01:25,110 --> 00:01:30,530
+a و b الشرط الثاني f prime exists and f prime of x
+
+17
+00:01:30,530 --> 00:01:34,130
+بساوي الاف small اللي بدأنا فيها دي الفرض منها
+
+18
+00:01:34,130 --> 00:01:39,880
+integrable لكل x element in a و bبنقول الـ
+
+19
+00:01:39,880 --> 00:01:44,900
+integration من A لB للـ F بساوي F of B ناقص F of A
+
+20
+00:01:44,900 --> 00:01:50,400
+إذا الآن و كإني بقول نفترض أنه الـ F small
+
+21
+00:01:50,400 --> 00:01:56,100
+integrable و نفترض F continuous على closed bounded
+
+22
+00:01:56,100 --> 00:02:01,160
+interval A و B و F نفسها differentiable على الـ
+
+23
+00:02:01,160 --> 00:02:05,260
+open اللي هو interval A و B بشرط أنه الـ F prime
+
+24
+00:02:05,260 --> 00:02:07,940
+ال derivative لها الـ F capital طبعا بساوي الـ F
+
+25
+00:02:07,940 --> 00:02:13,240
+small of Xوبناء على كل المعطيات اللي حكيناها بيكون
+
+26
+00:02:13,240 --> 00:02:17,120
+ال integration من a لb لل f small هو عبارة عن fb
+
+27
+00:02:17,120 --> 00:02:21,760
+ناقص f of a او اختصارا واسهلك للحفظ ال integration
+
+28
+00:02:21,760 --> 00:02:29,670
+من a لb لل f prime of x dx هي عبارة عنوكأنه
+
+29
+00:02:29,670 --> 00:02:36,250
+التكامل بلغ التفاضل بيصير اللي هي f of b ناقص f of
+
+30
+00:02:36,250 --> 00:02:40,610
+a هذا فضوء mean يعني هاي هادة باختصار هيك فضوء
+
+31
+00:02:40,610 --> 00:02:44,710
+mean أن f prime of x تكون موجودة على الفترة من a و
+
+32
+00:02:44,710 --> 00:02:51,370
+b و أيضا بتكون انهاش integrable نفسها integrable و
+
+33
+00:02:51,370 --> 00:02:56,110
+تكون ال f نفسها continuous على close من a ل عند b
+
+34
+00:02:56,390 --> 00:03:00,270
+هذه هي النظرية إذا اللي بدنا نثبته الآن أنه قيمة
+
+35
+00:03:00,270 --> 00:03:04,470
+ال integration هذا بساوي اللي هو اللي أمامنا اللي
+
+36
+00:03:04,470 --> 00:03:09,590
+هي f of b ناقص من ناقص f of a خلينا نشوف إيش
+
+37
+00:03:09,590 --> 00:03:15,030
+البكاء في البحران يا جماعةالان اللي واضح انه انا
+
+38
+00:03:15,030 --> 00:03:18,530
+بده اثبت انه ال integration هو عبارة عن f of b
+
+39
+00:03:18,530 --> 00:03:24,990
+ناقص f of a شوف انا كيف بده اوصلك اللي هو ال
+
+40
+00:03:24,990 --> 00:03:28,670
+integration لمنقلة ال b لل f بساوي f of b ناقص f
+
+41
+00:03:28,670 --> 00:03:32,010
+of a انا بعرف اول حاجة هو معطيلي ال f small هذه
+
+42
+00:03:32,010 --> 00:03:35,290
+اللي هي ال f prime اللي هي ال f small سميتها هذه
+
+43
+00:03:35,290 --> 00:03:39,240
+معطينيها integrallyMadame Integrable إذن بواسطة
+
+44
+00:03:39,240 --> 00:03:44,160
+اللي هي .. إذا بتتذكروا Integrable criterion وهي
+
+45
+00:03:44,160 --> 00:03:46,900
+اللي بنستخدمها كثير احنا لإنها .. يعني خلّيني أقول
+
+46
+00:03:46,900 --> 00:03:51,400
+صيغة مهمة في إثبات النظريات اللي هي بما إنه أف
+
+47
+00:03:51,400 --> 00:03:56,380
+Integrable إذن لكل Y أكبر من 0 يوجد there exists a
+
+48
+00:03:56,380 --> 00:04:00,600
+partition B اللي هو X0 X1 عند X ل .. عند ..
+
+49
+00:04:00,600 --> 00:04:03,280
+partition لمين طبعاً للفترة اللي أنتوا عارفينها
+
+50
+00:04:03,280 --> 00:04:06,800
+اللي احنا بنشتغل عليها الفترة من A لعند مين لعند B
+
+51
+00:04:06,960 --> 00:04:12,920
+There exists a partition B X0 X1 XN of A و B such
+
+52
+00:04:12,920 --> 00:04:20,280
+that ال other sum B F'-LB F' أصغر من إبسلون F' من
+
+53
+00:04:20,280 --> 00:04:24,000
+هنا من هي يا جماعة؟ هي ال F لأننا مفترضين ال F
+
+54
+00:04:24,000 --> 00:04:29,940
+small أو ال F' is integrable إذا بواسطة الرماء ال
+
+55
+00:04:29,940 --> 00:04:34,760
+integrable criterion حصلنا على واحد اللي عنده
+
+56
+00:04:34,760 --> 00:04:40,880
+إلحاةأحكي عنها الآن أو أستخدمها للوصول لهدفي طيب
+
+57
+00:04:40,880 --> 00:04:44,040
+because طبعا F prime اللي هي meme زي ما قلنا F of
+
+58
+00:04:44,040 --> 00:04:48,820
+X is integrable on A أو B الآن في شغلة تانية احنا
+
+59
+00:04:48,820 --> 00:04:55,880
+بدأ الآن أستخدم اللي هو أمر آخر خلينا نكتب الآن
+
+60
+00:04:55,880 --> 00:05:00,920
+أول شغلة حصلناها عشان تعرف أين أنا رايح اللي هي
+
+61
+00:05:00,920 --> 00:05:06,550
+قلنا F is integrableF التي بيسمى F' Integrable أيش
+
+62
+00:05:06,550 --> 00:05:12,270
+أعطتنا يا جماعة؟ أعطتنا أن هناك بارتيشن B هناك B
+
+63
+00:05:12,270 --> 00:05:15,830
+طبعا for every epsilon أكبر من سفر هناك بارتيشن B
+
+64
+00:05:15,830 --> 00:05:23,390
+such that U, B و F اللي هي الـ F' طبعا الـ F يمين
+
+65
+00:05:23,390 --> 00:05:29,530
+الـ F' ناقص الـ B و F هي أصغر من Y وهذا سمناها
+
+66
+00:05:29,530 --> 00:05:34,710
+إيش؟ سمناها 1لأن من جهة أخرى يا جماعة بدي أستغل
+
+67
+00:05:34,710 --> 00:05:37,810
+اللي هو اللي معطينيه أن الأفكار بتلقوا continuous
+
+68
+00:05:37,810 --> 00:05:41,490
+أنا الآن زي ما قلنا جزاقنا اللي هي الفترة A و B
+
+69
+00:05:41,490 --> 00:05:52,230
+إلىاللي هي X0 X1 X2 فترة نموذجية Xk-1 لعند Xk لعند
+
+70
+00:05:52,230 --> 00:05:56,010
+مين لعند Xn اللي هي مين الـ B هذا ال partition
+
+71
+00:05:56,010 --> 00:05:59,930
+اللي لجيته أنا الآن أنا بعرف أن ال F capital
+
+72
+00:05:59,930 --> 00:06:03,330
+continuous على ال closed interval كلها من A لعند B
+
+73
+00:06:03,330 --> 00:06:06,870
+إذا الأكيد continuous على كل sub interval موجودة
+
+74
+00:06:06,870 --> 00:06:12,540
+يعني صارت اللي عندي ال F capital continuouson a
+
+75
+00:06:12,540 --> 00:06:18,560
+التي هي xk-1 وعند xk هذه هي ال sub interval اللي
+
+76
+00:06:18,560 --> 00:06:24,080
+ال function f continuous عليها وإحنا مفترضين أيضا
+
+77
+00:06:24,080 --> 00:06:29,220
+أن ال f prime exist على ال open interval كلها إذا
+
+78
+00:06:29,220 --> 00:06:33,860
+أكيد ال fis differentiable لأن f' exist على ال
+
+79
+00:06:33,860 --> 00:06:37,360
+open interval من a لعند b إذا أكيد f is
+
+80
+00:06:37,360 --> 00:06:41,980
+differentiable على الفترة xk minus واحد لعند مين
+
+81
+00:06:41,980 --> 00:06:45,140
+لعند ال xk يعني يا جماعة شروط ال mean value
+
+82
+00:06:45,140 --> 00:06:50,020
+theorem محققة إذا أكيد there existthere exist بما
+
+83
+00:06:50,020 --> 00:06:54,540
+انه اللي هي شروط ال mean value محققة اذا there
+
+84
+00:06:54,540 --> 00:06:59,620
+exist بسميها اللي هو bk او tk there exist tk في
+
+85
+00:06:59,620 --> 00:07:06,440
+الفترة xk minus واحد عند ال xk such that اللي هو F
+
+86
+00:07:06,440 --> 00:07:11,520
+هي الدلل اللي بطبق عليها ال mean value theorem يا
+
+87
+00:07:11,520 --> 00:07:19,320
+جماعة F of xk ناقص F of xk minus واحداللي هو
+
+88
+00:07:19,320 --> 00:07:24,560
+بتساوي اللي هو xk ناقص xk مايلوس واحد طبعا احنا
+
+89
+00:07:24,560 --> 00:07:29,280
+بنكسب عليها اللي هي ايش بتساوي اللي هي ال F prime
+
+90
+00:07:30,370 --> 00:07:35,630
+of الهي main TK هذه اللي هي الـ Main Value Theorem
+
+91
+00:07:35,630 --> 00:07:39,710
+نتجتها مطبق على مين يا جماعة على الفترة اللي هي XK
+
+92
+00:07:39,710 --> 00:07:43,770
+minus واحد لعند XK طبعا هذا الكلام لكل K لأنه لكل
+
+93
+00:07:43,770 --> 00:07:48,170
+مين لكل ال sub intervals بتتحقق نفس الشروط بناء
+
+94
+00:07:48,170 --> 00:07:55,010
+عليه احنا بنعرف قبل هيك خليني أبدأ أشتغلها عند ال
+
+95
+00:07:55,010 --> 00:08:04,450
+MK إبراهيماللي هي أكيد أصغر أو يساوي الـ Fاللي هي
+
+96
+00:08:04,450 --> 00:08:11,370
+ال F عندك ال mk' ايش نذاكركم فيها ايش هي ال mk' ال
+
+97
+00:08:11,370 --> 00:08:15,190
+mk' هي مكتوبة لنكتبها كمان مرة ال mk' هي مين ال
+
+98
+00:08:15,190 --> 00:08:19,610
+infimum لل F' F of X X element of X K minus واحد X
+
+99
+00:08:19,610 --> 00:08:24,950
+K ال F' مين هذه ال F small ماشي الحال طيب ال F او
+
+100
+00:08:24,950 --> 00:08:30,590
+ال mk' هي عبارة عن ال infimum لمين لل F' على ال
+
+101
+00:08:30,590 --> 00:08:37,110
+sub interval هذه اذا اكيدأصغر أو يساوي الـ F of أي
+
+102
+00:08:37,110 --> 00:08:41,630
+مقطوين موجودة في الـ sub-interval والـ TK هدوين
+
+103
+00:08:41,630 --> 00:08:46,410
+موجودة في هذا الـ sub-interval إذن أكيد F of TK
+
+104
+00:08:46,410 --> 00:08:50,670
+أصغر من الـ MK' لأن الـ MK' هي عبارة عن الـ
+
+105
+00:08:50,670 --> 00:08:57,290
+infimum لقيمة الدالة F' of TK عالمياً على الفترة
+
+106
+00:08:57,290 --> 00:09:01,440
+اللي هي ال sub-interval اللي بنحكي عنها ككلوهذه
+
+107
+00:09:01,440 --> 00:09:06,040
+أكيد أصغر أو يساوي من الـ MK Ibrahim مين الـ MK
+
+108
+00:09:06,040 --> 00:09:11,060
+Ibrahim هذه؟ هي عبارة عن الـ Supremum لمين؟ لقيمة
+
+109
+00:09:11,060 --> 00:09:16,990
+اللي هي الدالة هذه على الفترة اللي عندهماشي الحال
+
+110
+00:09:16,990 --> 00:09:23,110
+إذا هذه دائما صحيحة طب لو ضربت جهتي كل الأطراف في
+
+111
+00:09:23,110 --> 00:09:27,650
+طول الفترة اللي هي xk minus xk minus واحد طبعا
+
+112
+00:09:27,650 --> 00:09:31,510
+أكيد هذه xk ناقص xk minus واحد كمية موجبة إذا لما
+
+113
+00:09:31,510 --> 00:09:35,010
+أضربها في الأطراف كلها بتظلها ال inequality صحيحة
+
+114
+00:09:35,010 --> 00:09:40,610
+وزي ما هي في xk ناقص xk minus واحد وهنا في xk ناقص
+
+115
+00:09:40,610 --> 00:09:46,280
+xk minus واحد مظبوط هذا الكلام أكيد صحطيب لكن هذا
+
+116
+00:09:46,280 --> 00:09:52,220
+المقدار هو هذا إذا باجي بحط هذه هان معايا جماعة
+
+117
+00:09:52,220 --> 00:09:57,000
+بحط هذه في المنطقة هذه المكان القيمة هذه اللي هي
+
+118
+00:09:57,000 --> 00:10:05,190
+هذه إذا صار عندي الأن Fof xk ناقص f of xk minus 1
+
+119
+00:10:05,190 --> 00:10:12,070
+أكبر أو يساوي ال Mk' في ال xk minus xk minus 1
+
+120
+00:10:12,070 --> 00:10:18,490
+وهذا أصغر أو يساوي ال Mk' في ال xk minus xk minus
+
+121
+00:10:18,490 --> 00:10:24,290
+1إذا واضح إن أنا حصلت على هذه وهذه صحيحة لكل مين
+
+122
+00:10:24,290 --> 00:10:28,150
+لكل كيه لإنه أخدت أنا هذه فترة عشوائية يعني لكي
+
+123
+00:10:28,150 --> 00:10:33,790
+بتساوي اللي هو واحد واتنين لعند مين لعند الان بناء
+
+124
+00:10:33,790 --> 00:10:38,250
+عليه أنا وصلت الآن إلى ما يليه وصلت إلى هذه
+
+125
+00:10:38,250 --> 00:10:43,670
+النتيجة شايفين يا جماعة وصلت إلى هذه النتيجة اللي
+
+126
+00:10:43,670 --> 00:10:48,860
+أنا وضحتلكم إياها كيف إجتالان و ال mk prime زي ما
+
+127
+00:10:48,860 --> 00:10:55,280
+قلنا ايش هي و ال mk capital prime هيها امامكم نيجي
+
+128
+00:10:55,280 --> 00:10:59,720
+الان ايش اللي بده حصله شوف ال K ايش بده حصل انا
+
+129
+00:10:59,720 --> 00:11:03,020
+عمال بقول انه صحيح على كل K اذا لو أخدت ال
+
+130
+00:11:03,020 --> 00:11:05,900
+summation هنا و أخدت ال summation هنا و أخدت ال
+
+131
+00:11:05,900 --> 00:11:10,440
+summation هنا بظل اللي هي ال inequality صحيحة خد
+
+132
+00:11:10,440 --> 00:11:16,050
+الآن ال summationعلى الفترة الـ summation على
+
+133
+00:11:16,050 --> 00:11:19,530
+الinquality اللي حكينا عنها هيها بيصير ال
+
+134
+00:11:19,530 --> 00:11:23,630
+summation لل M K برايم في X K X K minus واحد K من
+
+135
+00:11:23,630 --> 00:11:26,630
+عند واحد لعند M وهنا هيكون أصغر أو ساوى ال
+
+136
+00:11:26,630 --> 00:11:31,090
+summation لل F of X K ناقص F of X K minus واحد
+
+137
+00:11:31,090 --> 00:11:36,190
+اللي هي احنا هنا حصلناها هان وهذه ال summation
+
+138
+00:11:36,190 --> 00:11:39,490
+عليها وهذه ال summation عليها هي ال summation هذا
+
+139
+00:11:39,850 --> 00:11:43,210
+طيب يا جماعة أكيد أنتم اذكرين هذا ال summation هو
+
+140
+00:11:43,210 --> 00:11:47,770
+عبارة عن مين يا جماعة هو عبارة عن ال lower sum لل
+
+141
+00:11:47,770 --> 00:11:52,370
+partition بي على مين على الدالة اللي بنعمل عليها
+
+142
+00:11:52,370 --> 00:11:56,330
+اللي هي ال F' اللي اشتغلنا عليها اللي أخدنا ال F'
+
+143
+00:11:57,150 --> 00:12:01,270
+ال MK' هي ال infimum لل F' على ال sub interval
+
+144
+00:12:02,160 --> 00:12:07,220
+والان هذه يشبه يا جماعة هي ال upper sum يعني بمعنى
+
+145
+00:12:07,220 --> 00:12:12,960
+آخر صار عندى الآن المقدار هذا هي المقدار هذا اللى
+
+146
+00:12:12,960 --> 00:12:17,680
+محاط بالأزرق هذا المقدار و بالأحمر صار بين اللى هو
+
+147
+00:12:17,680 --> 00:12:22,120
+ال lower sum و بين ال upper sum لكن هذا المقدار
+
+148
+00:12:22,120 --> 00:12:25,860
+الصمشي اللى احنا عملناه قبل ذلك كتير لو فرضناه
+
+149
+00:12:25,860 --> 00:12:33,860
+هيكون عبارة عن F of X واحدناقص F of X Note زائد F
+
+150
+00:12:33,860 --> 00:12:40,360
+of X 2 ناقص F of X 1 زائد F of X 3 ناقص F of X 2
+
+151
+00:12:40,360 --> 00:12:45,460
+زائد لما أصل لآخر إشي F of X N ناقص F of X N ناقص
+
+152
+00:12:45,460 --> 00:12:50,520
+1 حلاجي كله بروح و بظل عندك كل هذا بروح و بظل عندك
+
+153
+00:12:50,520 --> 00:12:54,860
+بس F of X ناقص F of X N ناقص مين F of X Note كل
+
+154
+00:12:54,860 --> 00:13:00,340
+term ب cancel اللي قبله و يساويF of Xn اللي هي
+
+155
+00:13:00,340 --> 00:13:07,420
+مين؟ F of B F of Xnot اللي هي مين؟ F of A إذا صار
+
+156
+00:13:07,420 --> 00:13:10,920
+عندي الآن الـSummation هذا اللي هو بيسوي F of B
+
+157
+00:13:10,920 --> 00:13:16,440
+نقص مين؟ نقص F of A يعني بمعنى آخر بنشيل هذا و
+
+158
+00:13:16,440 --> 00:13:20,580
+بنحط مكانه قيمته اللي هو F of B نقص F of A بيصير F
+
+159
+00:13:20,580 --> 00:13:25,320
+of B minus F of A بين اللي هو L of B و F' و بين
+
+160
+00:13:25,320 --> 00:13:34,230
+الأبقى الـU of B و F'طيب اطلع على فوق شوية خليني
+
+161
+00:13:34,230 --> 00:13:39,830
+اوضحلك هذه النقطة اللي هتوصلي للي بديها انا ايش
+
+162
+00:13:39,830 --> 00:13:44,170
+بدي اثبت انا بدي اثبت ان ال integration خليني بس
+
+163
+00:13:44,170 --> 00:13:51,710
+اشيل هذا بعد اذنكم انا
+
+164
+00:13:51,710 --> 00:13:58,260
+بدي اثبت ان ال integration لل F prime of x dxأو
+
+165
+00:13:58,260 --> 00:14:06,320
+الـ F of X DX بساوي F of B ناقص F of A من A لعند
+
+166
+00:14:06,320 --> 00:14:12,870
+مين؟ لعند B، هيا، بدي أسهلشوف الان كيف انا في
+
+167
+00:14:12,870 --> 00:14:17,590
+الواقع بتوصلكم هذا نقص هذا يكون اكبر او يساوي سفر
+
+168
+00:14:17,590 --> 00:14:20,990
+و اصغر من epsilon لأي اصغر يساوي epsilon لكل
+
+169
+00:14:20,990 --> 00:14:24,110
+epsilon في الدنيا و من ثم هيساوي سفر يعني هتحدث
+
+170
+00:14:24,110 --> 00:14:29,090
+مين المساواة اللي مافهمش عليها هي الان نجلة تفصيل
+
+171
+00:14:29,090 --> 00:14:39,060
+اتفجنا احنا انه احنا حصلنا على اللي هوالـ F of D –
+
+172
+00:14:39,060 --> 00:14:44,520
+F of A بين الـ U و بين الـ L لكن احنا بنقول الـ F
+
+173
+00:14:44,520 --> 00:14:49,420
+نفسها يا جماعة الـ F' هذه is integrable مزام
+
+174
+00:14:49,420 --> 00:14:55,380
+Integrable من A لعند Bأذن الـ U of F و الـ L of F
+
+175
+00:14:55,380 --> 00:14:58,560
+اللي هو الـ Upper Integral و الـ Lower Integral
+
+176
+00:14:58,560 --> 00:15:01,960
+اللي هو هيساوي قيمة الـ Integration عارفينوا هذا
+
+177
+00:15:01,960 --> 00:15:05,760
+الكلام احنا بنتعرف شو معناته Integrable الـ U of F
+
+178
+00:15:05,760 --> 00:15:11,640
+هي عبارة عن مين؟ عن الـ infimum لمين؟ للكبار اللي
+
+179
+00:15:11,640 --> 00:15:19,640
+هي U L أو U P و Fوهذا عبارة عن الـ Supremum لنية
+
+180
+00:15:19,640 --> 00:15:28,200
+للـ L, B و F يعني بيصير عندي اللي هو هذا عبارة عن
+
+181
+00:15:28,200 --> 00:15:32,420
+ال U of F من جهة وهذا عبارة عن ال L of F من جهة
+
+182
+00:15:32,420 --> 00:15:35,900
+أخرى هذا ال integration نقلة بيه ال F' ليش؟ لأن ال
+
+183
+00:15:35,900 --> 00:15:40,630
+F' is integrable زي ما قلناهطيب، إيش علاقة الـ L و
+
+184
+00:15:40,630 --> 00:15:44,130
+F بهذه؟ L و F عبارة عن الـ Supremum لكل هذول، إذا
+
+185
+00:15:44,130 --> 00:15:47,450
+أكيد الـ L و F أكبر أو يساوي هذه، إذا صار ال
+
+186
+00:15:47,450 --> 00:15:51,610
+integration هذا اللي عندى أكبر أو يساوي الـ L و F،
+
+187
+00:15:51,610 --> 00:15:56,070
+خلصنا من هذه، لأن من جهة ثانية ال integration لل F
+
+188
+00:15:56,070 --> 00:15:58,510
+براين هو الـ U of F، لأن الـ F is integrable زي ما
+
+189
+00:15:58,510 --> 00:16:04,770
+قلنا، و الـ U of F مين هو؟هو عبارة عن الـ infimum
+
+190
+00:16:04,770 --> 00:16:08,810
+لها دول إذا الـ U of F أصغر أو يشويها مزام أصغر أو
+
+191
+00:16:08,810 --> 00:16:12,210
+يشويها يعني صار ال integration أصغر أو يشويها يعني
+
+192
+00:16:12,210 --> 00:16:18,050
+بمعنى آخر احنا وصلنا ان ال integration تبعناالـ
+
+193
+00:16:18,050 --> 00:16:23,450
+integration اللي هو من A لعند A بي لل F برايم بين
+
+194
+00:16:23,450 --> 00:16:29,530
+ال L و بين مين و بين ال U ماشي الحالة الآن و هذا
+
+195
+00:16:29,530 --> 00:16:35,390
+برضه بين ال L و بين مين ال U اضربلي الآن اللي تحت
+
+196
+00:16:35,390 --> 00:16:41,820
+اللي هو بسالببتنعكس ال inequality وبعدين اجمعل
+
+197
+00:16:41,820 --> 00:16:46,320
+الجهتين ماشي الحال هذي بيصير سالب وهذي بيصير أكبر
+
+198
+00:16:46,320 --> 00:16:51,220
+أو يساوي سالب وهذي بيصير أكبر أو يساوي سالب اجمعل
+
+199
+00:16:51,220 --> 00:16:56,980
+الجهتين بيصير عند ال integrationأو العكس اضرب اللي
+
+200
+00:16:56,980 --> 00:16:59,720
+فوق بالسالب عساس ان اعمل زي ما عامل هو هان اضرب
+
+201
+00:16:59,720 --> 00:17:02,000
+اسف اللي هو اضرب مين اللي فوق بالسالب يصير هذا
+
+202
+00:17:02,000 --> 00:17:07,640
+ناقص وهذا كله ناقص وهذا عبارة عن ناقص وهذا اكبر او
+
+203
+00:17:07,640 --> 00:17:12,760
+يساوي وهذا اكبر او يساوي واجمح لبعض او بلغة اخرى
+
+204
+00:17:13,150 --> 00:17:16,790
+قول اللي .. اللي .. اللي .. اللي تحت ناقص اللي فوق
+
+205
+00:17:16,790 --> 00:17:20,130
+بطلع عندى ال integration لل F prime من A ل عند B
+
+206
+00:17:20,130 --> 00:17:24,730
+ناقص اللي هي F of B minus F of A أصغر يساوي ال U
+
+207
+00:17:24,730 --> 00:17:30,770
+ناقص ال L و أكبر أوي يساوي ال L ناقص ال U واضح أنه
+
+208
+00:17:30,770 --> 00:17:36,480
+هذهعبارة عن ناقص هذه وهذه كمية موجبة إذا صار عند
+
+209
+00:17:36,480 --> 00:17:41,000
+ال absolute value للقيمة هذه أصغر أو يساوي ال U
+
+210
+00:17:41,000 --> 00:17:49,300
+ناقص مين ال L كمان مرة هذه سالب هذهوهذه موجبة إذاً
+
+211
+00:17:49,300 --> 00:17:53,540
+هذه الـ Inquality صارت هي عبارة عن مفكوك الـ
+
+212
+00:17:53,540 --> 00:17:57,440
+absolute value للـ F prime ال integration ناقص
+
+213
+00:17:57,440 --> 00:18:01,840
+المقدار هذا أصغر أو يساوي هذا القيمة وهذا القيمة
+
+214
+00:18:01,840 --> 00:18:05,700
+لسه ما سحنهاش احنا إيش قلنا عنها أصغر من من إبسلان
+
+215
+00:18:05,700 --> 00:18:09,280
+وانا قاعد باشتغل على ال partition اللي لجيته أعلى
+
+216
+00:18:09,280 --> 00:18:15,390
+إذا صار عندى الآن اللي وصلتلهعبارة عن اللي هو ال
+
+217
+00:18:15,390 --> 00:18:20,150
+absolute value هذا أصغر من إبسلون وطبعا أكبر أوي
+
+218
+00:18:20,150 --> 00:18:24,790
+ساوي سفر والإبسلون واز إيه شمالها arbitrary يعني
+
+219
+00:18:24,790 --> 00:18:29,430
+المقدار هذا لأي إبسلون في الدنيا لأي إبسلون في
+
+220
+00:18:29,430 --> 00:18:33,770
+الدنيا هذا أصغر من مين من الإبسلون هو أكبر أوي سفر
+
+221
+00:18:33,970 --> 00:18:38,510
+إذاً لازم يكون هذا المقدار اللي هو عبارة عن سفر
+
+222
+00:18:38,510 --> 00:18:42,530
+يعني بمعنى آخر ال integration بساوي اللي هو F of B
+
+223
+00:18:42,530 --> 00:18:47,050
+نقص F of A و هيك و نكون حصلنا على المطلوب و أثبتنا
+
+224
+00:18:47,050 --> 00:18:51,470
+النظرية طيب
+
+225
+00:18:51,470 --> 00:18:57,850
+الجماعة الان هذا اللي هو الجزء الأولالجزء الأول من
+
+226
+00:18:57,850 --> 00:19:00,890
+اللي هو الـ Fundamental Theorem of Calculus اللي
+
+227
+00:19:00,890 --> 00:19:05,750
+هو عبارة عن تكامل التفاضل اللي هي عملية التكامل
+
+228
+00:19:05,750 --> 00:19:10,470
+هتلغى عملية التفاضل زي ما شفنا اللي هو قبل بشوية
+
+229
+00:19:10,470 --> 00:19:15,130
+وشفنا إيه اللي جالته الـ Fundamental Theorem طبعا
+
+230
+00:19:15,130 --> 00:19:20,270
+هذا الكلام تحت الشروط المذكورةالآن بقول لي .. يمكن
+
+231
+00:19:20,270 --> 00:19:24,810
+حكيت هادى حتى بقول لي corollary بقول انا أحيانا
+
+232
+00:19:24,810 --> 00:19:29,530
+بحب أريح حالي و نقول خلينا ناخد .. عشان نستذكر ال
+
+233
+00:19:29,530 --> 00:19:32,790
+.. ال .. ال .. ال fundamental theorem الجزء الأول
+
+234
+00:19:32,790 --> 00:19:37,950
+بشكل سريع بس شويه عندنا نعمل .. في الشروط ان هو قف
+
+235
+00:19:37,950 --> 00:19:41,630
+من a ل b لعند R satisfy the conditionsاللي هو F'
+
+236
+00:19:42,150 --> 00:19:45,790
+exists on A وB، مابتدش أجيب سيرة مين الـ F Small؟
+
+237
+00:19:45,790 --> 00:19:49,250
+مابتدش أشغل مين؟ على الـ F Capital لو فرضنا إن الـ
+
+238
+00:19:49,250 --> 00:19:54,010
+F هذه من A وB لعند R إنها الـ F' اللي هي الشمالها
+
+239
+00:19:54,010 --> 00:19:57,890
+exist على الـ A وB يعني فرض إنها، بس هنا زاد شوية
+
+240
+00:19:57,890 --> 00:20:01,130
+على الشروط اللي جابل بشوية إن F is differentiable
+
+241
+00:20:01,130 --> 00:20:03,790
+على الـ closed interval كنا فرضينها إنها F
+
+242
+00:20:03,790 --> 00:20:06,740
+differentiable على الـ Openوفرضين إنها continuous
+
+243
+00:20:06,740 --> 00:20:10,760
+على اللي هي الـ Closed مدام الآن إذا فيها دي سنة
+
+244
+00:20:10,760 --> 00:20:16,680
+زيادة من ال .. من اللي هي الشروط F' exists على الـ
+
+245
+00:20:16,680 --> 00:20:19,820
+A و الـ B يعني continuous و differentiable على الـ
+
+246
+00:20:19,820 --> 00:20:24,350
+closed open .. على ال closed interval A و Bالان هي
+
+247
+00:20:24,350 --> 00:20:29,550
+الشرط والشرط الثاني فرض ان ال F' مش موجودة و بس ال
+
+248
+00:20:29,550 --> 00:20:33,030
+F' انتجر بالعلى ال A و ال B إذا انتجقت شروط ال
+
+249
+00:20:33,030 --> 00:20:36,210
+fundamental theorem إذا حسب ال fundamental theorem
+
+250
+00:20:36,210 --> 00:20:39,410
+اللي قبله شوية بكون عنده ال integration من A لB
+
+251
+00:20:39,410 --> 00:20:44,190
+لمين الآنللـ f prime اللي كنا نسميه في الجبل f
+
+252
+00:20:44,190 --> 00:20:49,310
+small بتساوي f of b ناقص f of a إذا فعلا هي
+
+253
+00:20:49,310 --> 00:20:53,130
+automatic حققت شروط ال fundamental theorem وزيادة
+
+254
+00:20:53,130 --> 00:20:59,850
+سنة إذا أكيد النتيجة بتكون صحيحة يعنيتكامل الدالة
+
+255
+00:20:59,850 --> 00:21:05,210
+المتفاضلة بساوء أصل الدالة اللي هو أصل الدالة عنده
+
+256
+00:21:05,210 --> 00:21:09,070
+النقطة الأولى نقص النقطة مين بنحكي النقطة الثانية
+
+257
+00:21:09,070 --> 00:21:13,950
+اللي هو عبارة عن integration F of B نقص مين F of A
+
+258
+00:21:13,950 --> 00:21:19,210
+طب لو كانت X متغير يعني لو أخذنا أي X بين الفترتين
+
+259
+00:21:19,210 --> 00:21:23,550
+وطبّجنا نظرية على الـA اللي عند الـXفبصير ال
+
+260
+00:21:23,550 --> 00:21:27,130
+integration من إلي إلى عند ال X أف براين بساوي أف
+
+261
+00:21:27,130 --> 00:21:32,490
+of X ناقص أف of A X هذه هتصبح متغيرة والأف of A
+
+262
+00:21:32,490 --> 00:21:39,190
+ثابتة وهذا بيذكرنا انه احنا قيمة التكامل لدالة
+
+263
+00:21:39,190 --> 00:21:43,790
+بساوي اللي هو عبارة عن اللي هي الإجابة اللي هي
+
+264
+00:21:43,790 --> 00:21:47,630
+الدالة اللي بتطلع زائد some constant C اللي هو ال
+
+265
+00:21:47,630 --> 00:21:53,660
+constant طبعا لاللي هيطبيعة الديالي لقداش بيطلعلنا
+
+266
+00:21:53,660 --> 00:21:56,420
+اللي هو ال initial conditions بيسفرلنا إياه ال
+
+267
+00:21:56,420 --> 00:21:59,620
+constant أو بيعطينا إياه خمسة أربعة ستة أو بيظلوا
+
+268
+00:21:59,620 --> 00:22:03,720
+بصورة عامة Constancy طيب شوفوا صلوا على النبي عليه
+
+269
+00:22:03,720 --> 00:22:08,090
+الصلاة والسلامالآن بدنا نيجي للجزء الثاني من الـ
+
+270
+00:22:08,090 --> 00:22:11,470
+Fundamental theorem خلصنا جزء اللي هو تكامل
+
+271
+00:22:11,470 --> 00:22:16,870
+التفاضل، الآن بنتوقع إنه انفاضل التكامل، انفاضل
+
+272
+00:22:16,870 --> 00:22:20,530
+التكامل، تحت شروط، بنشوف اللي هي ال Fundamental
+
+273
+00:22:20,530 --> 00:22:24,650
+theorem of calculus second form أو اللي هو الجزء
+
+274
+00:22:24,650 --> 00:22:27,850
+الثاني من ال Fundamental theorem، إيش اللي بيقوله؟
+
+275
+00:22:27,850 --> 00:22:33,540
+اللي بيقول معايا ليه، نفترض إن F smallمن a و b
+
+276
+00:22:33,540 --> 00:22:38,060
+لعند r اللي هو is integrable in a و b إذا انفرضناه
+
+277
+00:22:38,060 --> 00:22:41,460
+انه integrable ونفرض أن f of x هو بيساوي ال
+
+278
+00:22:41,460 --> 00:22:46,160
+integration من a ل x f for all x element in a و b
+
+279
+00:22:46,160 --> 00:22:52,200
+بس لان نيجي للنتيجة thenهيطلع هذا عبارة عن
+
+280
+00:22:52,200 --> 00:22:55,360
+continuous function في ال .. في ال .. اللي هي main
+
+281
+00:22:55,360 --> 00:23:02,700
+في اللي هي على الفترة a أو b ومش هي كمان ولو كان
+
+282
+00:23:02,700 --> 00:23:09,830
+ال Fsmall continuous عند نقطة C في الفترة من A
+
+283
+00:23:09,830 --> 00:23:14,050
+لعند B أو من A لعند X هتكون ال F هذه نفسها
+
+284
+00:23:14,050 --> 00:23:16,950
+differentiable و ال derivative اللي هي إيش بساوي
+
+285
+00:23:16,950 --> 00:23:22,590
+بساوي قيمة اللي هو ال F اللي جوا يعني باختصار يا
+
+286
+00:23:22,590 --> 00:23:29,450
+جماعة بتتكررها سهل بقولك مفترض FIntegrable ماشي
+
+287
+00:23:29,450 --> 00:23:34,690
+الحال هاي بس الان بقول لو جيت اخدت من A ل X on
+
+288
+00:23:34,690 --> 00:23:44,670
+طبعا A و B لو اخدت الان A و X F small of T DT هاي
+
+289
+00:23:44,670 --> 00:23:51,510
+ده طبعا الان صارت كلها تعتمد على مين على X بقولك
+
+290
+00:23:51,510 --> 00:23:55,370
+هذههذه اللي طلع اللي هو الـ integration للـ
+
+291
+00:23:55,370 --> 00:24:01,130
+integrable function من A ل X F of T DT هتطلع لي
+
+292
+00:24:01,130 --> 00:24:05,210
+continuous function لو سميتها F capital زي ما هو
+
+293
+00:24:05,210 --> 00:24:08,730
+مسميها F of X بتكون الـ F عندها شمالها is
+
+294
+00:24:08,730 --> 00:24:16,430
+continuous الآن بقولك لو اجيت و قلت ان Fis
+
+295
+00:24:16,430 --> 00:24:21,390
+continuous الـ F اللي جوا هذه at C element in A وB
+
+296
+00:24:21,390 --> 00:24:25,650
+لو كانت F is continuous at C element in A وB
+
+297
+00:24:25,650 --> 00:24:31,730
+هيطلعلك بقولك إذا الـ F capital هذه F prime of C
+
+298
+00:24:31,730 --> 00:24:39,870
+existsو مش exist بس و ال F prime of C هتساوي ال F
+
+299
+00:24:39,870 --> 00:24:46,030
+small of إيش؟ of C يعني و كأنه بقولك لما نتفاضل
+
+300
+00:24:46,030 --> 00:24:50,210
+هذه F prime of C اللي هي من إيه اللي عند C يعني
+
+301
+00:24:50,210 --> 00:24:57,370
+تقول F prime of C بساوي تفاضل رفلة by DXعنده
+
+302
+00:24:57,370 --> 00:25:02,630
+النقطة C لل integration من A ل X F of T DT
+
+303
+00:25:27,580 --> 00:25:33,180
+C مثلاً بتساوي F of C اللي هي F small of C هو كون
+
+304
+00:25:33,180 --> 00:25:36,540
+ال F اللي جوا continuous عنده النقطة اللي بنحكي
+
+305
+00:25:36,540 --> 00:25:39,940
+عنها طب لو كانت F اللي جوا هادى continuous وين
+
+306
+00:25:39,940 --> 00:25:43,620
+ماكان على الفترة هادى بصير خلاص وانت مغمض عناك
+
+307
+00:25:43,620 --> 00:25:47,980
+بتيجي بتقول تفاضل هادي بتشيل التكامل و بتحطه اللي
+
+308
+00:25:47,980 --> 00:25:53,540
+جوا بدلالة اللي هي ال X المتغيرواضح المفروض طيب
+
+309
+00:25:53,540 --> 00:25:59,660
+نيجي الآن نثبت اللي هي النظرية نثبت شغلتين أن ال F
+
+310
+00:25:59,660 --> 00:26:02,580
+كابتنال continuous عشان أثبتلك continuous هثبتلك
+
+311
+00:26:02,580 --> 00:26:05,940
+أكثر من continuous هثبتلك uniform ل continuous لأ
+
+312
+00:26:05,940 --> 00:26:09,780
+أقولك هثبتلك أكثر من uniform ل continuous هثبتلك
+
+313
+00:26:09,780 --> 00:26:12,920
+أن ال F is Lipschitz function مثلا من Lipschitz
+
+314
+00:26:12,920 --> 00:26:15,400
+function إذا على طول uniform ل continuous ومن ثم
+
+315
+00:26:15,400 --> 00:26:18,460
+على طول إيش ما لها continuous إيش Lipschitz
+
+316
+00:26:18,460 --> 00:26:25,240
+function يعني هثبتلك أن Fof x-f of y absolute
+
+317
+00:26:25,240 --> 00:26:30,720
+value أصغر أو ساوي k في x-y had there exist k بحيث
+
+318
+00:26:30,720 --> 00:26:35,260
+أن f of x-f of y أصغر من k في xy لكل x و y element
+
+319
+00:26:35,260 --> 00:26:40,020
+in a و b هثبت لك f بتحقق هذا الشرط هثبتها ما ده
+
+320
+00:26:40,020 --> 00:26:42,540
+هثبتها ما ده هتحقق هذا الشرط إذا ما على طول اللي
+
+321
+00:26:42,540 --> 00:26:45,680
+هي هتكون lipschitz يعني بمعنى آخر هتكون is
+
+322
+00:26:45,680 --> 00:26:49,480
+continuous هذا الجزء الأول الجزء الثاني يا شباب و
+
+323
+00:26:49,480 --> 00:26:55,760
+يا بناتلأن if F is continuous at C هنثبت أن F is
+
+324
+00:26:55,760 --> 00:26:59,320
+differentiable عند C يعني بدأ أثبتلك F is
+
+325
+00:26:59,320 --> 00:27:03,460
+differentiable عند C يعني ايش F is differentiable
+
+326
+00:27:03,460 --> 00:27:14,660
+يعني بدأ أثبتلك أن limit F of X زي داتش مثلا او F
+
+327
+00:27:14,660 --> 00:27:21,440
+of C زي داتش ناقص F of Cعلى H اذا H بتروح للصفر
+
+328
+00:27:21,440 --> 00:27:27,380
+بتثبت لك ايه ايش بيساوي F capital طبعا بيساوي F
+
+329
+00:27:27,380 --> 00:27:33,660
+small of Cبدي أثبتلك يعني أو بمعنى آخر هأثبتلك لكل
+
+330
+00:27:33,660 --> 00:27:37,000
+Y أكبر من 0 داريكزيز ديلتا بحيث أنه absolute value
+
+331
+00:27:37,000 --> 00:27:41,320
+أصغر من Delta L على H أصغر من Delta يؤدي إلى F of
+
+332
+00:27:41,320 --> 00:27:48,260
+C زائد H ناقص F of C على H ناقص F of C بدي أثبتلك
+
+333
+00:27:48,260 --> 00:27:53,180
+يه أصغر من 200 من Epsilonبكون اثبتت فعلا انه هذه
+
+334
+00:27:53,180 --> 00:27:56,540
+ال limit بالساوية هذه معناته هذه ال limit طبعا ايش
+
+335
+00:27:56,540 --> 00:28:01,000
+بتعني ان F prime F capital prime of C exist و
+
+336
+00:28:01,000 --> 00:28:06,480
+بتساوية F of C اللي هو اللي هو طالبه انه لما تكون
+
+337
+00:28:06,480 --> 00:28:09,280
+F continuous عند ال C بتكون F capital
+
+338
+00:28:09,280 --> 00:28:12,040
+differentiable عند ال C و ال derivative لل F
+
+339
+00:28:12,040 --> 00:28:15,700
+capital بتساوية ال F اسمه فنشوف
+
+340
+00:28:17,960 --> 00:28:21,380
+Media نثبت الـ Continuity أو نثبت الـ Lipschitz
+
+341
+00:28:21,380 --> 00:28:27,450
+function يعني الأمر سهلأحنا مفترضين يا جماعة أن
+
+342
+00:28:27,450 --> 00:28:31,490
+الـF small هذي is integrable مزام is integrable
+
+343
+00:28:31,490 --> 00:28:37,650
+إذا is bounded S يعني أنه لكل .. نقدر نلاقي K أكبر
+
+344
+00:28:37,650 --> 00:28:41,830
+من 0 بحيث أن ال absolute value ل F of X small أصغر
+
+345
+00:28:41,830 --> 00:28:48,070
+سوى K لكل X موجودة ال A و ال B سبب هذه أن F نفسها
+
+346
+00:28:48,070 --> 00:28:52,350
+is integrable طيب، بدأ اعتمد على هذه للوصول إنها
+
+347
+00:28:52,350 --> 00:28:58,620
+لبشتالان خد اي x و y في ال a و ال b واسمحولي اخد x
+
+348
+00:28:58,620 --> 00:29:01,760
+اقل من y without loss of generality مش عاد باخد y
+
+349
+00:29:01,760 --> 00:29:06,100
+اكبر من .. اصغر من x الان حالة ال x بتساوي
+
+350
+00:29:06,100 --> 00:29:09,660
+هتلاقوها automatic بتتحقق للي بديها نشوف ايش اللي
+
+351
+00:29:09,660 --> 00:29:13,790
+بديهاالان خد x و y في ال a و ال b و نفترض ان x
+
+352
+00:29:13,790 --> 00:29:16,610
+أزرار من y without most of generality زي ما قلنا
+
+353
+00:29:16,610 --> 00:29:22,890
+الان احسبلي f of x f of y نقص مين f of x الكبيرة y
+
+354
+00:29:22,890 --> 00:29:26,630
+و الكبيرة x احسب f of y نقص f of x ايش هيساوي ال
+
+355
+00:29:26,630 --> 00:29:29,470
+integration حسب التعريف f of x بتساوي ال
+
+356
+00:29:29,470 --> 00:29:33,390
+integration من ال x ل ال f smallالأن f of y هي
+
+357
+00:29:33,390 --> 00:29:36,930
+عبارة عن ال integration من a ل y، f small، ناقص، f
+
+358
+00:29:36,930 --> 00:29:40,210
+of x إيش بتساوي؟ ال integration من a ل x ل مين؟ لل
+
+359
+00:29:40,210 --> 00:29:47,290
+F، إذا هذا ناقص هذا، الآن بدي أحول هذه، أجلبها،
+
+360
+00:29:47,290 --> 00:29:52,670
+بيصير زائد ال integration من x لعند مين، لعند ال
+
+361
+00:29:52,670 --> 00:29:57,640
+a، لل Fصار عندى الآن ال integration من X لعند ال A
+
+362
+00:29:57,640 --> 00:30:00,520
+و من A لعند ال Y إذا حيصير هذا عبارة عن ال
+
+363
+00:30:00,520 --> 00:30:05,940
+integration من X لمين من X لعند ال Y عارفين هذه
+
+364
+00:30:05,940 --> 00:30:09,960
+الخاصية إذا صار عند ال F of X F of Y ناقص F of X
+
+365
+00:30:09,960 --> 00:30:15,760
+بسوء ال integration من X ل Y لمين لل F شوف الآن
+
+366
+00:30:15,760 --> 00:30:20,100
+إيش بده أصل؟ بده أصل إنه absolute value F of Y
+
+367
+00:30:20,100 --> 00:30:24,830
+ناقص F of Xأصغر أو سوى K في الـ absolute value X
+
+368
+00:30:24,830 --> 00:30:31,450
+مانس Y يعني صارت لبشت لنشوف كيف نصلها وأكيد بعضكم
+
+369
+00:30:31,450 --> 00:30:36,450
+فهم او اتوقع كيف بتسوي لأن صار ال absolute value
+
+370
+00:30:36,450 --> 00:30:40,250
+لهذه بسوى ال absolute value لهذه هيها لأن ال
+
+371
+00:30:40,250 --> 00:30:43,010
+absolute value ال integration بخاصية احنا عارفينها
+
+372
+00:30:43,010 --> 00:30:46,770
+أصغر أو سوى ال integration لل absolute valueوالـ
+
+373
+00:30:46,770 --> 00:30:50,990
+absolute value للـ F في الفترة X وY أشملها .. هي
+
+374
+00:30:50,990 --> 00:30:53,570
+مش في الفترة X وY بس الـ absolute value للـ F الـ
+
+375
+00:30:53,570 --> 00:30:56,170
+absolute value للـ F أصغر أو سوى K على كل الفترة
+
+376
+00:30:56,170 --> 00:31:01,030
+الكبيرة اللي هي A وB فأكيد برضه هتكون أصغر أو سوى
+
+377
+00:31:01,030 --> 00:31:05,670
+K على الفترة الصغيرة فصار عندي أصغر أو سوى K في
+
+378
+00:31:05,670 --> 00:31:07,890
+مين؟ في ال integration من X لعند Y ال integration
+
+379
+00:31:07,890 --> 00:31:13,080
+من X لعند Y هو إيش بساوي؟ اللي هو Y minus Xالـ
+
+380
+00:31:13,080 --> 00:31:19,400
+integration يعني ال integration لـ DT من X لـ DT
+
+381
+00:31:19,400 --> 00:31:28,660
+ال integration لـ DT من X عند Y ايش بيساوي Y minus
+
+382
+00:31:28,660 --> 00:31:36,240
+X Y minus X فهذا صار Y minus X و اللي جوا أصغر
+
+383
+00:31:36,240 --> 00:31:40,790
+بيساوي Kالان هذا على خطوتين سهلات بتصور ان انتوا
+
+384
+00:31:40,790 --> 00:31:44,370
+فاهمينش بحكي من X لعند Y ال integration لل F فده
+
+385
+00:31:44,370 --> 00:31:47,850
+أصغر أو ساوي اللي هو ال integration من X لعند Y
+
+386
+00:31:47,850 --> 00:31:55,370
+هذه بدلة K لكل DT وهذا بساوي K برة في Y minus X
+
+387
+00:31:55,370 --> 00:31:59,230
+اللي هو أكيد حيصير عند ال absolute value هذه أصغر
+
+388
+00:31:59,230 --> 00:32:03,770
+أو ساوي K في ال absolute value Y minus Xالان هذه
+
+389
+00:32:03,770 --> 00:32:07,570
+ال Xات الأصغر من مين؟ من Y لكن زي ما انتوا عارفين
+
+390
+00:32:07,570 --> 00:32:11,150
+حالة ال X بتساوي Y is trivial لأن لما تكون X
+
+391
+00:32:11,150 --> 00:32:14,450
+بتساوي Y هذا سفر و لما تكون X بتساوي Y هذا سفر إذا
+
+392
+00:32:14,450 --> 00:32:18,610
+ال inequality هذه صحيحة دائما إذا الأن صار عندى
+
+393
+00:32:18,610 --> 00:32:25,590
+هذه ال inequality staris true for all x و y
+
+394
+00:32:25,590 --> 00:32:30,390
+limiting a و b لأنه قلنا ال x أصغر من y ال y أصغر
+
+395
+00:32:30,390 --> 00:32:33,990
+من x أكيد similarly و بنفس الأسلوب أو حتى without
+
+396
+00:32:33,990 --> 00:32:38,170
+loss of generality يعني بدون ما نفقد أي إشي من
+
+397
+00:32:38,170 --> 00:32:44,530
+التعميم بنفترض أن x أصغر من y صار
+
+398
+00:32:44,530 --> 00:32:53,230
+عندي يا جماعةالان F مستمر على A وB لأن F بيصبح
+
+399
+00:32:53,230 --> 00:33:02,750
+عملية Lipschitz اللي هي الآن ضال علي أثبت أن الـ F
+
+400
+00:33:02,750 --> 00:33:11,100
+مستخدم وزي ما قلت بدأ أثبت أن الـ Limitللـ F of C
+
+401
+00:33:11,100 --> 00:33:17,800
+زائد H نقص F of C على H لما H تروح للصفر بساوة F
+
+402
+00:33:17,800 --> 00:33:23,480
+small of C أو أثبت لكم الفرق بين هذولتين أصغر من
+
+403
+00:33:23,480 --> 00:33:28,880
+إبسلون وهذا زي ما قلنا هو اللي هيمثل F' of C ده
+
+404
+00:33:28,880 --> 00:33:34,160
+نشوف كيف طيب الصلاة على النبي صلاة والسلام عليك
+
+405
+00:33:37,390 --> 00:33:42,130
+خلّينا نجف عند .. أيوة نيجي الآن البرهان هتلاقوه
+
+406
+00:33:42,130 --> 00:33:49,730
+برضه سهل وفكرته سهلة شوفوا كيف عندي نفترض الآن
+
+407
+00:33:49,730 --> 00:33:53,550
+suppose that f is continuous at c limiting a وb
+
+408
+00:33:53,550 --> 00:33:58,790
+مدام continuous إذن limit
+
+409
+00:34:01,700 --> 00:34:08,460
+F of X as X بتروح للـ C بساوي F of C مظبوط ولا لأ؟
+
+410
+00:34:08,460 --> 00:34:12,300
+أكيد مظبوط فبقى من جهة أخرى خلينا نكتبها بصورة
+
+411
+00:34:12,300 --> 00:34:18,660
+ثانية X ناقص C بتروح للسفر if and only if اللي هو
+
+412
+00:34:18,660 --> 00:34:23,960
+X بتروح لمين للـ C سمولي هذه X minus C إيش اسمها H
+
+413
+00:34:23,960 --> 00:34:31,410
+بصير هذه اللي فوق مين هي limitF of الـ X minus C
+
+414
+00:34:31,410 --> 00:34:36,490
+بتساوي الـ H يعني الـ X بتساوي H زائد C أو C زائد
+
+415
+00:34:36,490 --> 00:34:41,190
+Hلأن x بتروح للـ c تكافئ أنه .. اللي هو x minus c
+
+416
+00:34:41,190 --> 00:34:44,610
+تروح للصفر، يعني بتكافئ H تروح لمين للصفر، إيش حيث
+
+417
+00:34:44,610 --> 00:34:49,650
+هو هذا؟ F of C، إذا هذه هي تعبير آخر عن ال
+
+418
+00:34:49,650 --> 00:34:56,250
+continuity لل F لما اللي هو اللي هي ال F عند مين،
+
+419
+00:34:56,250 --> 00:34:59,210
+عند ال C، يعني هذه تعبير آخر، ال continuity لل
+
+420
+00:34:59,210 --> 00:35:05,900
+function لما عند النقطة اللي هي Cهذه الآن شو بدي
+
+421
+00:35:05,900 --> 00:35:09,520
+استخدمها للوصول اللي بديها لأن مادام F is
+
+422
+00:35:09,520 --> 00:35:12,600
+continuous ده هذي متحققة هيها مادام F is
+
+423
+00:35:12,600 --> 00:35:15,480
+continuous عن C ده هذي متحققة فمادام هذي متحققة
+
+424
+00:35:15,480 --> 00:35:18,720
+اذا by epsilon delta definition for every epsilon
+
+425
+00:35:18,720 --> 00:35:22,880
+أكبر من 0 there exists delta أكبر من 0 such that
+
+426
+00:35:22,880 --> 00:35:28,950
+لما يكون ال absolute value لل H أصغر من Deltaو
+
+427
+00:35:28,950 --> 00:35:32,230
+طبعا انا وين بشتغل في المنطقة انها تكون C زائد H
+
+428
+00:35:32,230 --> 00:35:36,370
+وين ما لأ في الفترة تبعت من A لعند مين لعند B يعني
+
+429
+00:35:36,370 --> 00:35:41,230
+اخترت ال H صغيرة كفاية بحيث انه C زائد H اضلي وين
+
+430
+00:35:41,230 --> 00:35:45,090
+جاعد في الفترة من A و B لعنده لإن هاي الفترة A وهي
+
+431
+00:35:45,090 --> 00:35:49,330
+Bوالفترة هذه اللي هي I C عندي مثلا في داخلها اللي
+
+432
+00:35:49,330 --> 00:35:55,690
+هي بتختار H دلتتها صغيرة كفاية أنه ضال C زائد H
+
+433
+00:35:55,690 --> 00:36:01,050
+موجودة في الفترة من A لعند B عشان تصير معرفة لإن
+
+434
+00:36:01,050 --> 00:36:05,330
+دالتي أنا عشان تكون معرفة عند C زائد H لازم تكون C
+
+435
+00:36:05,330 --> 00:36:08,490
+زائد H في داخل المنطقة هذه لإن دالتي معرفة على
+
+436
+00:36:08,490 --> 00:36:11,770
+الفترة من A لعند B عشان هيك أقولنا C زائد H لازم
+
+437
+00:36:11,770 --> 00:36:16,630
+تكون في الفترة زائد Bإذن اختيار الـ Delta يعتمد
+
+438
+00:36:16,630 --> 00:36:20,210
+على ال limit ويعتمد على انه أضمن ال C زي داشر ضال
+
+439
+00:36:20,210 --> 00:36:24,510
+هوين في الفترة A وB إذا تعريف ال continuity بيقول
+
+440
+00:36:25,950 --> 00:36:27,530
+لكل y أقوم باستخدام صفر يوجد دلتا لكل y أقوم
+
+441
+00:36:27,530 --> 00:36:28,970
+باستخدام صفر يوجد دلتا لكل y أقوم باستخدام صفر
+
+442
+00:36:28,970 --> 00:36:29,950
+يوجد دلتا لكل y أقوم باستخدام صفر يوجد دلتا لكل y
+
+443
+00:36:29,950 --> 00:36:30,650
+أقوم باستخدام صفر يوجد دلتا لكل y أقوم باستخدام
+
+444
+00:36:30,650 --> 00:36:32,710
+صفر يوجد دلتا لكل y أقوم باستخدام صفر يوجد دلتا
+
+445
+00:36:32,710 --> 00:36:35,050
+لكل y أقوم باستخدام صفر يوجد دلتا لكل y أقوم
+
+446
+00:36:35,050 --> 00:36:41,110
+باستخدام صفر يوجد دلتا
+
+447
+00:36:41,110 --> 00:36:49,400
+لكل y أقوم باستخدام صفر يوجد دلتا لكل y أطيب، الآن
+
+448
+00:36:49,400 --> 00:36:54,020
+وين أنا بدأ أروح؟ بدأ أثبت لكم إنه هذا ناقص هذا
+
+449
+00:36:54,020 --> 00:36:58,240
+أصغر من epsilon عشان ذلك دعنا نحسب F of C زاد H
+
+450
+00:36:58,240 --> 00:37:03,060
+ناقص F of C على H ناقص مين يا جماعة؟ F of C ويساوي
+
+451
+00:37:03,060 --> 00:37:13,170
+الآن F of C زاد H ناقص F of Cخد الآن اللي هي الـ H
+
+452
+00:37:13,170 --> 00:37:16,850
+هدعم المشترك بالـ C الواحدة للـ H ماشي F of C زي
+
+453
+00:37:16,850 --> 00:37:21,910
+دتش تعريفها من A لعند C زي دتش لل F of X DX قلناها
+
+454
+00:37:21,910 --> 00:37:26,090
+هذه اللي ماعطيناها من رأس الدور ناقص ماشي تعريف F
+
+455
+00:37:26,090 --> 00:37:30,230
+of C Capital of C هو ال integration من A لعند C زي
+
+456
+00:37:30,230 --> 00:37:35,630
+دتش الآن دي مش C زي دتش من A لعند مين لعند الـ C
+
+457
+00:37:35,630 --> 00:37:40,110
+واحدة للـ H من A لعند الـ C اللي هي F of C زي دتش
+
+458
+00:37:40,110 --> 00:37:46,360
+هيهاوهي الواحدة الـ H اللي برا ال F of C هيها من A
+
+459
+00:37:46,360 --> 00:37:51,780
+ل C واحدة الـ H ناقص مين F of C هذا من التعريف
+
+460
+00:37:51,780 --> 00:37:55,460
+مباشرة لإنه احنا عرفنا ال F capital of X هي عبارة
+
+461
+00:37:55,460 --> 00:38:01,820
+عن integration من A لعند X F of T DT لأن لما نكون
+
+462
+00:38:01,820 --> 00:38:06,120
+F of C زي دتش بنحطها دي C زي دتش C بنحطها دي عياش
+
+463
+00:38:06,120 --> 00:38:13,460
+C وهي C زي دتش وهي الـ C وهي ساويةالان هذه من ..
+
+464
+00:38:13,460 --> 00:38:18,780
+من .. من عند A لـ C زي ده اتش وهذه من A لعند B
+
+465
+00:38:18,780 --> 00:38:23,980
+لعند C هدولة مع بعض هاي هدولة التنتين بده احسبها
+
+466
+00:38:23,980 --> 00:38:28,120
+مع بعض حسبنا زيين قبل و شوية هو عبارة عن واحد على
+
+467
+00:38:28,120 --> 00:38:32,400
+اتش خدوا عامل مشترك خدوا واحد على اتش عامل مشترك
+
+468
+00:38:32,400 --> 00:38:37,340
+بين الجهتين تصبح واحد على اتش افتح جوس ال
+
+469
+00:38:37,340 --> 00:38:41,660
+integration من A لعند C زي ده اتشلأن بدل الناقص
+
+470
+00:38:41,660 --> 00:38:46,020
+بيصير H اكتب زائد بدل هذا الناقص بيكتب زائد لأن
+
+471
+00:38:46,020 --> 00:38:52,460
+هتنقلب مين الآن من C لعند ال A نظبط اللي هو لنفسها
+
+472
+00:38:52,460 --> 00:38:58,020
+F F هذه الآن من C لعند ال A ومن A لعند ال C زاد H
+
+473
+00:38:58,020 --> 00:39:02,000
+إذا أكيد هذه كلها على بعض يصير ال integration من C
+
+474
+00:39:02,000 --> 00:39:08,930
+ل C زاد H لل F في واحد على H إذا هذه كلهابس
+
+475
+00:39:08,930 --> 00:39:11,350
+ابدلتها بقيمتها اللي قلنا عنها اللي هو ال
+
+476
+00:39:11,350 --> 00:39:15,810
+integration من C ل C زي H اللي اوجدته بدل هذا كله
+
+477
+00:39:15,810 --> 00:39:23,190
+من واحد ال H ل F of X DX ناقص الان هذا هذا اللي هي
+
+478
+00:39:23,190 --> 00:39:28,090
+F of C شوف كيف بده اعملها على جهة تعالي احسب ال
+
+479
+00:39:28,090 --> 00:39:33,660
+integrationالـ integration من C لـ C زائد H للـ
+
+480
+00:39:33,660 --> 00:39:38,180
+constant واحد بعد أذنكم DX إيش هيساوي ال
+
+481
+00:39:38,180 --> 00:39:44,140
+integration هدا عبارة عن C زائد H ناقص C وهيساوي
+
+482
+00:39:44,140 --> 00:39:48,760
+قداش H يعني بمعنى آخر لو جيتها الجد تعرفوا ليش
+
+483
+00:39:48,760 --> 00:39:52,640
+بعمل هيك واحد على H في ال integration من C لـ C
+
+484
+00:39:52,640 --> 00:39:58,720
+زايد H اللي هو الواحد هيساوي إيش؟ واحد، مظبوط ولا
+
+485
+00:39:58,720 --> 00:40:03,450
+لأ؟أكيد مظبوط ماشي هايمل هادي كسمت الديوا تاني
+
+486
+00:40:03,450 --> 00:40:10,570
+علشان تطلع حد واحد الان صار عندى لو ضربت هادي
+
+487
+00:40:11,920 --> 00:40:18,320
+الجهتين في F of C هي F of C بيساوي ايش؟ F of C صار
+
+488
+00:40:18,320 --> 00:40:21,260
+الان F of C بيساوي هذه بدي أشيل F of C تبعتي و أحط
+
+489
+00:40:21,260 --> 00:40:25,360
+مكانها هذه الصورة ليش حطيتها؟ عشان هذه أقدر أتحمل
+
+490
+00:40:25,360 --> 00:40:30,380
+محا محا دي اللي موجودة من الأصل شوف كيف الان شيلت
+
+491
+00:40:30,380 --> 00:40:33,320
+ال F of C و حطيت قيمتها اللي أوجدناها اللي هي
+
+492
+00:40:33,320 --> 00:40:37,660
+عبارة عن F of C على H في ال integration من C لC زي
+
+493
+00:40:37,660 --> 00:40:42,480
+H لمن؟ للواحدماشي لان صار هذا ال integration و هذا
+
+494
+00:40:42,480 --> 00:40:45,920
+ال integration نفس الاشي واحد ل F of X و واحد ل
+
+495
+00:40:45,920 --> 00:40:50,380
+واحد يعني بقدر اشتغل فيهم بيصير عندى خد ال واحد ال
+
+496
+00:40:50,380 --> 00:40:53,960
+H برا عن المشترك خالص بيظل عندى ال integration من
+
+497
+00:40:53,960 --> 00:40:58,720
+C ل C زاد H هذا مين ايش اسمه F of X و هذا F of C
+
+498
+00:40:58,720 --> 00:41:01,580
+دخلتها جوا و مضربتها بالواحد صارت مين بقدر اعلن و
+
+499
+00:41:01,580 --> 00:41:06,520
+ثابت اللي هي ناقص F of C لكل اش ماله DX هذا الكلام
+
+500
+00:41:06,520 --> 00:41:14,340
+كله من C ل C زاد Hصار عندى الآن الصورة هذه هيها اه
+
+501
+00:41:14,340 --> 00:41:20,840
+و هذه الصورة اصلا انا بدياها الان واحد على H أزرع
+
+502
+00:41:20,840 --> 00:41:23,760
+أو ساوي قولنا absolute value of integration أزرع
+
+503
+00:41:23,760 --> 00:41:28,740
+أو ساوي ال integration لل absolute value DX الان
+
+504
+00:41:28,740 --> 00:41:35,320
+هذا المقدار F of X ناقص F of Cقلنا عنها من راس
+
+505
+00:41:35,320 --> 00:41:40,420
+الدور أن F of X ناقص F of C اللي هو أصغر من
+
+506
+00:41:40,420 --> 00:41:44,420
+Epsilon لأن limit F of X لما X تروح للـC أشهر
+
+507
+00:41:44,420 --> 00:41:50,240
+مساوي F of C لأن X الـN هذه في الفترة من C لـC
+
+508
+00:41:50,240 --> 00:41:56,100
+زائداتش يعني بتسمح لي أن أقول limit F of X as X
+
+509
+00:41:56,100 --> 00:42:01,220
+بتروح للـC بتساوي F of C لما X بتروح للـC اللي هي
+
+510
+00:42:01,220 --> 00:42:05,980
+أدش بتروح لمينللسفر مضل في نفس المنطقة لأن قلنا
+
+511
+00:42:05,980 --> 00:42:10,300
+قبل شوية x minus c بتروح للسفر إذا وفقط إذا اللي
+
+512
+00:42:10,300 --> 00:42:13,880
+هي ال H اللي بتروح للسفر اللي هي عبارة عن x minus
+
+513
+00:42:13,880 --> 00:42:18,260
+c يعني هذا المقدار بال continuity لل F عند ال C
+
+514
+00:42:18,260 --> 00:42:21,980
+برضه بكون أصغر من إبسلون على ال absolute value
+
+515
+00:42:21,980 --> 00:42:25,160
+لمين لل H في ال integration من C لC زاد H
+
+516
+00:42:27,990 --> 00:42:33,050
+واضحة اه؟ اكيد هذا الان ايش قيمته؟ C زي داش ناقص C
+
+517
+00:42:33,050 --> 00:42:36,050
+اللي هي عبارة عن H فبصير Y عبارة عن absolute value
+
+518
+00:42:36,050 --> 00:42:42,430
+of H في mean فيه اللي هو الـH الـH اللي هو الـH
+
+519
+00:42:42,430 --> 00:42:42,470
+اللي هو الـH اللي هو الـH الـH اللي هو الـH اللي
+
+520
+00:42:42,470 --> 00:42:42,490
+هو الـH اللي هو الـH اللي هو الـH اللي هو الـH
+
+521
+00:42:42,490 --> 00:42:42,570
+الـH اللي هو الـH اللي هو الـH اللي هو الـH اللي
+
+522
+00:42:42,570 --> 00:42:42,710
+هو الـH اللي هو الـH اللي هو الـH اللي هو الـH
+
+523
+00:42:42,710 --> 00:42:46,490
+الـH اللي هو الـH اللي هو الـH
+
+524
+00:42:46,490 --> 00:42:52,450
+اللي هو الـطيب .. بيصير عندها .. بيصير أكبر من 0
+
+525
+00:42:52,450 --> 00:42:55,790
+أسف هذه بحاجة دي بتطلع أيش بتساوي .. بيساوي بساوي
+
+526
+00:42:55,790 --> 00:42:58,150
+.. بقدر أختار H positive؟ أه بقدر أختار H positive
+
+527
+00:42:58,150 --> 00:43:03,130
+طيب و لو حتى ال H negative بتكون similarly بس
+
+528
+00:43:03,130 --> 00:43:06,950
+بتكون .. كل البرهام بيصير .. بترتب على أنه اللي هي
+
+529
+00:43:06,950 --> 00:43:12,890
+ال .. ال C زائد H أصغر من مين من ال C without loss
+
+530
+00:43:12,890 --> 00:43:17,250
+of generality ال H أكبر من 0بصير عندى لان هذا
+
+531
+00:43:17,250 --> 00:43:24,750
+المقدار أصغر من مين من إبسلون إيش يعني اللى عملنا
+
+532
+00:43:24,750 --> 00:43:28,290
+اللى عملنا لكل إبسلون أكبر من Zero لاجئنا Delta
+
+533
+00:43:28,290 --> 00:43:33,350
+بحيث أنه لما H absolute value أصغر من Deltaيعطيني
+
+534
+00:43:33,350 --> 00:43:39,330
+أن هذا المقدار أصغر من مين؟ من إبسلون يعني صار
+
+535
+00:43:39,330 --> 00:43:43,450
+عندي limit هذا المقدار بسوء f of c و هذا المقدار
+
+536
+00:43:43,450 --> 00:43:46,290
+اللي هو f prime of c يعني اعتبتنا f prime of c
+
+537
+00:43:46,290 --> 00:43:56,410
+بسوء f small of c وهو المطلوب طيب نيجي الآن لاللي
+
+538
+00:43:56,410 --> 00:44:02,210
+هي ال corollaryبرضه الى النظرية اللى جاملة بشوية
+
+539
+00:44:02,210 --> 00:44:10,790
+او خلّيني نقول تلخيصها سريع واستذكرها سريعها اللى
+
+540
+00:44:10,790 --> 00:44:17,830
+هو الأولى كانت تكامل والتفاضل هذه تفاضل التكامل
+
+541
+00:44:17,830 --> 00:44:23,470
+طبعا كل واحدة تحت شروطها المذكورة في نظريتها
+
+542
+00:44:25,860 --> 00:44:30,340
+نجي نشوف يا جماعة ال corollary let f من a و b لعند
+
+543
+00:44:30,340 --> 00:44:34,940
+r بي continuous on a و b and let f of x بي سوى ال
+
+544
+00:44:34,940 --> 00:44:37,720
+integration من ال a ل ال x ل ال f إذا فرض f
+
+545
+00:44:37,720 --> 00:44:40,160
+continuous ال f اسمه ال continuous على كل الفترة
+
+546
+00:44:40,160 --> 00:44:44,980
+ريح حاله طبعا أعطى إشي أكبر من النظرية اللي فاتت
+
+547
+00:44:44,980 --> 00:44:47,640
+يعني فرض ال continuity على ال a و ال b ما زم
+
+548
+00:44:47,640 --> 00:44:49,840
+continuous إذا ما بتزمش تقول integrable لإن و أنا
+
+549
+00:44:49,840 --> 00:44:52,340
+continuous function زي ما قلنا إيش ما لها is
+
+550
+00:44:52,340 --> 00:44:58,190
+integrable إذا مدامة f continuousالان بيصير هذه ال
+
+551
+00:44:58,190 --> 00:45:01,810
+integration اللي هي من a لعند ال x نفسها
+
+552
+00:45:01,810 --> 00:45:06,030
+continuous لأ مش continuous بس is differentiable
+
+553
+00:45:06,030 --> 00:45:09,270
+يعني أجم ال continuous يعني هتكون عندي ال f is
+
+554
+00:45:09,270 --> 00:45:13,670
+differentiable و ال f برامي يمين هي ال f then f is
+
+555
+00:45:13,670 --> 00:45:17,730
+differentiable من a و b عند f برامي بيساوي كده إذن
+
+556
+00:45:17,730 --> 00:45:25,000
+باختصار من a ل x اللي هو fof t dt لو فرضنا هذه
+
+557
+00:45:25,000 --> 00:45:33,060
+continuous على ال a و ال b إذا لكل x element in a
+
+558
+00:45:33,060 --> 00:45:38,080
+و ال b بيصير f of x بالساوي هذا is differentiable
+
+559
+00:45:38,080 --> 00:45:45,500
+و ال f prime of x هتساوي f of اللي هي x يعني بمعنى
+
+560
+00:45:45,500 --> 00:45:52,590
+آخر اللي هوانفضل هذا التكامل و نزيل التفاضل و نحط
+
+561
+00:45:52,590 --> 00:46:00,830
+الـ L جوا يعني بمعنى آخر D by DX للـ integration
+
+562
+00:46:00,830 --> 00:46:08,530
+من A لعند X F of D DT لما تكون F continuous هذا
+
+563
+00:46:08,530 --> 00:46:14,610
+بكون ب cancel هذا أو عملية عكسية لهوبتظللنا F of X
+
+564
+00:46:14,610 --> 00:46:19,070
+يعدى الأحقالها أو F of T والـ T هي المتغير أو الـ
+
+565
+00:46:19,070 --> 00:46:23,370
+X هي المتغير هذه اللي هي الكلرية الآن بدوا يلمّوا
+
+566
+00:46:23,370 --> 00:46:26,610
+النظريتين اللي قبل بشوية في نظرية واحدة يلخصن في
+
+567
+00:46:26,610 --> 00:46:30,910
+نظرية واحدة نشوف كيف بدوا يلخصن في نظرية واحدة
+
+568
+00:46:30,910 --> 00:46:40,630
+يعني بدوا يعيد بس اللي هو صياغة النظريتين صلوا
+
+569
+00:46:40,630 --> 00:46:44,540
+على النبي عليه الصلاة والسلامالان fundamental
+
+570
+00:46:44,540 --> 00:46:48,580
+theorem of calculus combined form يعني التنتين
+
+571
+00:46:48,580 --> 00:46:53,790
+الان موجودات في نفس النظرية شوف ايش بقولكlet
+
+572
+00:46:53,790 --> 00:46:57,610
+Fcapital and Fsmall be continuous on a and b فرض
+
+573
+00:46:57,610 --> 00:47:00,710
+أن Fcapital و Fsmall أشمالهم إتن تان continuous
+
+574
+00:47:00,710 --> 00:47:04,670
+على الفترة a و b و فرضك أن F of a بساوة سفر يعني
+
+575
+00:47:04,670 --> 00:47:07,610
+بدي أحط ال initial condition F of a بساوة سفر عسى
+
+576
+00:47:07,610 --> 00:47:11,070
+أن يجمّل الصورة ماحطه عشان سفر بتطلع F of a في
+
+577
+00:47:11,070 --> 00:47:14,290
+الجواب then the following statements are
+
+578
+00:47:14,290 --> 00:47:18,380
+equivalentيعني لما تكون هذا صحيحة هذا صحيحة و لما
+
+579
+00:47:18,380 --> 00:47:22,640
+تكون هذا صحيحة هذا صحيحة نيجي للجزء الأول لو فرضنا
+
+580
+00:47:22,640 --> 00:47:29,160
+أن F prime of X بيساوي F of X إذا حيصير عندي ال F
+
+581
+00:47:29,160 --> 00:47:33,460
+هذه is differential الماشي هيك مفترض أن F prime of
+
+582
+00:47:33,460 --> 00:47:38,620
+X بيساوي F of X بقول إذاإذاً هذه صحيحة، إيش يعني
+
+583
+00:47:38,620 --> 00:47:43,260
+هذه صحيحة؟ يعني ال integration من ال AX لل F of
+
+584
+00:47:43,260 --> 00:47:48,400
+التي هي T DT، هذه DT يا جماعة، بس .. بس نخلف عن
+
+585
+00:47:48,400 --> 00:47:58,200
+هذه، F of T DT، هذا هيساوي مين؟ هيساوي F of X،
+
+586
+00:47:58,200 --> 00:48:03,070
+ناشي؟الان then the following statements are
+
+587
+00:48:03,070 --> 00:48:06,950
+equivalent يعني لما تكون هذه صحيحة بتعطيها دي اه
+
+588
+00:48:06,950 --> 00:48:11,350
+فرضنا ان f prime of x بيساوي f of x اذا حيكون عند
+
+589
+00:48:11,350 --> 00:48:14,290
+ال integration من a ل x f of t dt بيساوي ايش
+
+590
+00:48:14,290 --> 00:48:20,630
+بالظبط؟ f of x كيف ده تبتها؟ الان فرضنا هذا صحيح
+
+591
+00:48:20,630 --> 00:48:24,710
+اذا ال integration من a ل عند ال x f of t اللي هي
+
+592
+00:48:24,710 --> 00:48:33,010
+مين هتصير؟ f prime of tDT هذه قبل بشوية من نظرية
+
+593
+00:48:33,010 --> 00:48:36,470
+الأولى قلنا كامل التفاوض و ليش بتطلع عندك جواب F
+
+594
+00:48:36,470 --> 00:48:42,210
+of X ناقص مين F of A لإن كل الشروط متحققة ماشي
+
+595
+00:48:42,210 --> 00:48:48,110
+الآن هاي كمان مرة يا جماعة فرضنا إن هذا متحقق بدي
+
+596
+00:48:48,110 --> 00:48:51,250
+أحسب هذه أتبتها بالساوية هذه خد ال integration من
+
+597
+00:48:51,250 --> 00:48:55,510
+X F of T DTهو ماعطيني الـ F small هد مين هي الـ F
+
+598
+00:48:55,510 --> 00:48:58,830
+براهن شفت .. شيلت الـ F small إيش حطيت مكانها؟ F
+
+599
+00:48:58,830 --> 00:49:03,510
+براهن الآن هذه قبل بشوية في الـ Corollary فظلنا ..
+
+600
+00:49:03,510 --> 00:49:07,490
+كملنا التفاضل كيف كملنا التفاضل؟ إنه قولنا شيل
+
+601
+00:49:07,490 --> 00:49:11,230
+التفاضل .. شيل التكامل .. شيل التفاضل بتصير عبارة
+
+602
+00:49:11,230 --> 00:49:15,270
+عن F اللي فوق اللي كانت B ناقص F اللي تحت اللي هي
+
+603
+00:49:15,270 --> 00:49:19,390
+A ويساويأف of X نقص أف of A أف of A ماعطينيها من
+
+604
+00:49:19,390 --> 00:49:24,350
+رأس الدوار صفر إذا إيش هتساوي أف of X إذا هذه اللي
+
+605
+00:49:24,350 --> 00:49:28,290
+بدّينا حساباتها بتساوي هذه طلعت إيش بتساوي أف of X
+
+606
+00:49:28,290 --> 00:49:32,830
+يعني أف of X بتساوي هذا المقدار وهو المطلوب طيب
+
+607
+00:49:32,830 --> 00:49:36,730
+هذا الجزء الأول من النظرية اللي هو نيجي للجزء
+
+608
+00:49:36,730 --> 00:49:42,240
+الثاني نفترض الآن إن هذه صحيحة وده تعطيهاالان برضه
+
+609
+00:49:42,240 --> 00:49:44,760
+الشروط كلها متحققة لأن الـ F في اسمه ليش مالها
+
+610
+00:49:44,760 --> 00:49:47,340
+continuous لسه ان انا ما .. ما .. ما ملاحتوش انا
+
+611
+00:49:47,340 --> 00:49:52,080
+هذا ايه عندي F continuous مدام F continuous ال
+
+612
+00:49:52,080 --> 00:49:57,720
+integration من اعلى عند ال X هذا كلهاللي هو اسمه F
+
+613
+00:49:57,720 --> 00:50:01,320
+of X هيكون differentiable حسب النظرية مزام
+
+614
+00:50:01,320 --> 00:50:04,780
+differentiable حسب هذه النظرية إذا F prime of X
+
+615
+00:50:04,780 --> 00:50:11,100
+إيش هتساوي؟ F of X يعني حققنا مين؟ اللي هي I يعني
+
+616
+00:50:11,100 --> 00:50:20,070
+هذا يؤدي إلى هذانجي الآن بعض التعريفات اللي
+
+617
+00:50:20,070 --> 00:50:26,890
+هنتكرها لكم وانتوا هتكونوا اللي هو اتابعوا الأمثلة
+
+618
+00:50:26,890 --> 00:50:32,130
+من خلال ال homework اللي معاكم هنعطي اللي هي تعريف
+
+619
+00:50:32,130 --> 00:50:36,830
+ممكن انتوا حتى مر عليكم في ال calculus ومن ثم اللي
+
+620
+00:50:36,830 --> 00:50:41,710
+هونعطي بعض ال counter examples اللي هي هنرجعكم
+
+621
+00:50:41,710 --> 00:50:47,370
+فيها للي هي الأسئلة اللي في الكتاب تشوفوا نصوصها
+
+622
+00:50:47,370 --> 00:50:53,530
+على الأقل و اللي مطلوب تحلوها ايه تحلوها و اللي ما
+
+623
+00:50:53,530 --> 00:50:56,910
+بتحلوه يعرفش تحلوهافي عندنا اللي هو في ال homework
+
+624
+00:50:56,910 --> 00:51:01,230
+الحلول الموجودة بتدرسوها لحالكم مادرستوها برضه
+
+625
+00:51:01,230 --> 00:51:04,310
+مافهمتوهاش احنا بنعمل فيها discussion ولو عملناها
+
+626
+00:51:04,310 --> 00:51:07,930
+حتى بشكل صوتي على أساس اللي هو احنا يمكن مانقدرش
+
+627
+00:51:07,930 --> 00:51:12,110
+نصور بشكل كامل اللي هي ال discussions عبر اللي هو
+
+628
+00:51:12,110 --> 00:51:16,270
+التصوير اللي احنا الحالي بنصوره عبر ال power point
+
+629
+00:51:16,270 --> 00:51:22,710
+من البيت ان شاء الله طيب definitionlet I بتساوي A
+
+630
+00:51:22,710 --> 00:51:27,630
+وB subset من مين؟ من R إذا كانت F small من I لR
+
+631
+00:51:30,720 --> 00:51:35,400
+then فرضنا أنه في دالة اسم F من I لعند R then the
+
+632
+00:51:35,400 --> 00:51:42,280
+antiderivative of F يعني وكأنها عكس عملية عكس
+
+633
+00:51:42,280 --> 00:51:45,920
+الدالة اللي بنفضلها roughly antiderivative of F on
+
+634
+00:51:45,920 --> 00:51:50,620
+I is a function F من I لعند R such that F prime of
+
+635
+00:51:50,620 --> 00:51:59,830
+X سوى F of X يعني عندنا دالة Fمن عند I لعند R لو
+
+636
+00:51:59,830 --> 00:52:05,310
+جينا لجينا F تانية من عند I لعند R و لجينا F prime
+
+637
+00:52:05,310 --> 00:52:10,450
+of X للي اللي في الـ I بتساوي mean لـ F small of X
+
+638
+00:52:11,290 --> 00:52:15,490
+في هذه الحالة بنسمي ال F capital هذه عبارة عن
+
+639
+00:52:15,490 --> 00:52:19,850
+antiderivative لل F يعني بمعنى أخر لو فضلناها هذه
+
+640
+00:52:19,850 --> 00:52:25,130
+ال antiderivative هتطلع مين؟ ال F الأصلية يعني
+
+641
+00:52:25,130 --> 00:52:30,890
+بتكون عندي اللي هي ال F capital هي ال
+
+642
+00:52:30,890 --> 00:52:35,210
+antiderivative لل F وال F small هي ال derivative
+
+643
+00:52:35,210 --> 00:52:41,910
+لل F واضح أخدته في ال calculus حتى نيجي الآنلأ
+
+644
+00:52:41,910 --> 00:52:45,650
+اللي هو برضه مفهوم اخدته في الكاركولاس if f من I
+
+645
+00:52:45,650 --> 00:52:49,750
+لعند R small is integrable لو فرضنا هذي integrable
+
+646
+00:52:49,750 --> 00:52:53,950
+و جينا عرفنا
+
+647
+00:52:53,950 --> 00:52:56,910
+ادالة من A لعند X F of X DX قبل شوية قولنا هذا
+
+648
+00:52:56,910 --> 00:53:00,290
+أكيد معرفة مثلا في integrable ومش معرفة ال
+
+649
+00:53:00,290 --> 00:53:04,110
+function F of X هتطلع continuous هذه اللي هي ال
+
+650
+00:53:04,110 --> 00:53:09,930
+function أو هذا هو اللي بنسميه التكامل المحدودهذه
+
+651
+00:53:09,930 --> 00:53:15,110
+بنسميها الـ Indefinite Integral of F يعني هذا
+
+652
+00:53:15,110 --> 00:53:17,790
+بنسميه Indefinite Integral of F أو هذه الدلة
+
+653
+00:53:17,790 --> 00:53:23,030
+بنسميها اللي هي The Indefinite Integral of F on I
+
+654
+00:53:23,030 --> 00:53:28,230
+برضه هذا برضه شغلات اللي هو أخدتوها سابقا في اللي
+
+655
+00:53:28,230 --> 00:53:33,780
+هو ال calculus نيجي بعض الملاحظات بسعلى اللي هو
+
+656
+00:53:33,780 --> 00:53:42,820
+اللي بتعلق بهذه اللي هي المفاهيم نشوفها وهي طبعا
+
+657
+00:53:42,820 --> 00:53:48,760
+هذه المفاهيم في عليها counter examples التمييز
+
+658
+00:53:48,760 --> 00:53:56,400
+بينها نشوف المحبة هذه يا شباب طيب أصلي على النبي
+
+659
+00:53:56,400 --> 00:54:03,640
+عليه الصلاة والسلامالان عندي سؤال سبعة تلاتة اتنين
+
+660
+00:54:03,640 --> 00:54:06,400
+يعني في سبعة تلاتة سؤال اتنين او سبعة تلاتة سؤال
+
+661
+00:54:06,400 --> 00:54:10,660
+خمسة طبعا كله في الطبع التاني هذا اللي هو عندي an
+
+662
+00:54:10,660 --> 00:54:13,540
+integrable function may not have an antiderivative
+
+663
+00:54:13,540 --> 00:54:17,220
+يعني هنلاقي في السؤال هذا integrable function
+
+664
+00:54:17,220 --> 00:54:24,080
+ومالهاش .. ومالهاش antiderivative يعني هنلاقي
+
+665
+00:54:24,080 --> 00:54:30,660
+function Fإنها تكون integrable لكن مالناجيش
+
+666
+00:54:30,660 --> 00:54:34,540
+function F اللي ال derivative تبعي تاش بتساوي
+
+667
+00:54:34,540 --> 00:54:39,860
+بتساوي F هذا اللي هو بتشوفوه في الـ 7 3 2 و 7 3 5
+
+668
+00:54:39,860 --> 00:54:43,340
+الأمثلة أو ال counter examples اللي وجودة هنا طيب
+
+669
+00:54:43,340 --> 00:54:47,710
+الملاحظة التانيةالـ function may have an
+
+670
+00:54:47,710 --> 00:54:52,830
+antiderivative يعني عندي F و بتحقق F و في عندي F
+
+671
+00:54:52,830 --> 00:54:57,310
+كابتال كمان و F برايم إيش بتساوي بسوء F but اللي
+
+672
+00:54:57,310 --> 00:55:02,210
+هي ال integration لل F إيش ماله does not exist لكن
+
+673
+00:55:02,210 --> 00:55:07,370
+but not integrable وهذا بتجاوب عليه برضه سبعة
+
+674
+00:55:07,370 --> 00:55:12,580
+تلاتة خمسة يعني في function Fفي إلها F' بساوة F
+
+675
+00:55:12,580 --> 00:55:17,640
+لكن ال integration للـ F إشماله does not exist
+
+676
+00:55:17,640 --> 00:55:24,900
+تلاتة عندي الملاحظة الثالثة a continuous function
+
+677
+00:55:24,900 --> 00:55:27,800
+always have antiderivative طبعا ال continuous
+
+678
+00:55:27,800 --> 00:55:35,290
+function أصلا من القوة بمكان إنهاتخلّي عندها يكون
+
+679
+00:55:35,290 --> 00:55:39,490
+لها الـ mean antiderivative الان a continuous
+
+680
+00:55:39,490 --> 00:55:44,190
+function always have antiderivative وهذا اللي هو
+
+681
+00:55:44,190 --> 00:55:51,910
+مباشرة من ال corollary 7 3 4 اللي كانت F
+
+682
+00:55:51,910 --> 00:55:56,770
+continuous مدام F continuous إذا ال integration من
+
+683
+00:55:56,770 --> 00:56:07,120
+ال X من A لعند ال XA of T DT بساوة F of X اللي هي
+
+684
+00:56:07,120 --> 00:56:10,900
+is differentiable ومش differentiable كمان و F
+
+685
+00:56:10,900 --> 00:56:14,860
+prime of X بتساوي F small of X يعني مدام أف
+
+686
+00:56:14,860 --> 00:56:17,880
+continuous إذا صار لها antiderivative صارت ال F
+
+687
+00:56:17,880 --> 00:56:20,580
+اللي هي ال derivative لها بساوة F of X إذا صارت
+
+688
+00:56:20,580 --> 00:56:24,620
+إيش antiderivativeهد مين هذا اللي هو عبارة عن الـ
+
+689
+00:56:24,620 --> 00:56:28,980
+Corollary 7 3 4 مدام أن F continuous إذا هذه
+
+690
+00:56:28,980 --> 00:56:33,360
+الدالة اللي سميتها F of X is differentiable ومش هي
+
+691
+00:56:33,360 --> 00:56:35,540
+كمان هذا الجزء الثاني من ال fundamental theorem of
+
+692
+00:56:35,540 --> 00:56:39,200
+calculus و ال F prime of X إيش بيساوي F of X يعني
+
+693
+00:56:39,200 --> 00:56:44,280
+ال F capital is an antiderivative of the F small
+
+694
+00:56:44,280 --> 00:56:50,760
+اللي هو النقطة الرابعة the indefinite integralmay
+
+695
+00:56:50,760 --> 00:56:57,520
+not be an antiderivative of mean of F الآن الـ
+
+696
+00:56:57,520 --> 00:57:02,400
+indefinite integral اللي
+
+697
+00:57:02,400 --> 00:57:12,000
+هو من A لعند X F of T DT لو سميناه F of X هذاهذا
+
+698
+00:57:12,000 --> 00:57:15,480
+the indefinite integral هذا ممكن يكون هذا يعني إيش
+
+699
+00:57:15,480 --> 00:57:18,480
+بمعنى آخر؟ يعني بدنا نفترض إن ال integration من A
+
+700
+00:57:18,480 --> 00:57:22,580
+ل X F of T DT موجود طبعا اللي بقول عنه موجود بس
+
+701
+00:57:22,580 --> 00:57:25,040
+تكون F of T is integrable ماحاجيناش على control U
+
+702
+00:57:25,040 --> 00:57:29,000
+of T ال F of T is integrable إذا ال A لعندي ال X F
+
+703
+00:57:29,000 --> 00:57:35,100
+of T DT لو ممكن يكون هذا موجود و بنسمي F of X
+
+704
+00:57:35,100 --> 00:57:39,830
+بقوللي the indefinite integral هذاmay not have
+
+705
+00:57:39,830 --> 00:57:44,490
+antiderivative of F يعني ممكن مايكونش هذا بالرغم
+
+706
+00:57:44,490 --> 00:57:48,610
+انه هذا موجود مايكونش ال F capital اللي هو هذا
+
+707
+00:57:48,610 --> 00:57:53,530
+مايكونش antiderivative لمين لل F small يعني رغم
+
+708
+00:57:53,530 --> 00:57:58,670
+انه هذا موجود ليس شرطا انه يكون يتفاضل ولمّا
+
+709
+00:57:58,670 --> 00:58:03,290
+يتفاضل يطلع اللي جوا يعني مش شرط انها تكون ال F
+
+710
+00:58:03,890 --> 00:58:07,170
+اللي هي antiderivative اللي هي مين هو الـ
+
+711
+00:58:07,170 --> 00:58:10,110
+indefinite integral هيك بتقول المواحدة طب إيش
+
+712
+00:58:10,110 --> 00:58:14,150
+دليلكم دليلنا هاي في counter examples هاي سبعة
+
+713
+00:58:14,150 --> 00:58:19,390
+تلاتة أربعة وهذا ناتب ناجم ناجم عدم تحقق هذه أو
+
+714
+00:58:19,390 --> 00:58:23,910
+عدم تحقق ال antiderivative أنه it may fail to be
+
+715
+00:58:23,910 --> 00:58:28,050
+differentiable at points at the interval ممكن أصلا
+
+716
+00:58:28,050 --> 00:58:35,440
+أن ال F prime تكونش موجودة بالمرةعند نقطة اللي هو
+
+717
+00:58:35,440 --> 00:58:39,620
+في داخل الـ interval من a إلى x مزام هذي is not
+
+718
+00:58:39,620 --> 00:58:42,720
+differentiable كيف بدنا نلاقي f prime بتساوي f
+
+719
+00:58:42,720 --> 00:58:48,640
+small إذا قد ينشأ عدم وجود الـ antiderivative منه
+
+720
+00:58:48,640 --> 00:58:52,640
+إنه هذي ما تكونش differentiable عند نقطة بين ال a
+
+721
+00:58:52,640 --> 00:58:59,090
+و ال x هاي أولاللي هو سبب ممكن يؤدي إلى عدم تحقق
+
+722
+00:58:59,090 --> 00:59:03,150
+إنه يكون الـ Indefinite Integral ليس Anti
+
+723
+00:59:03,150 --> 00:59:09,650
+-derivative للدالة اللي إحنا بنكملها Or الـ
+
+724
+00:59:09,650 --> 00:59:12,850
+Derivative of Indefinite Integral ممكن يكون موجود
+
+725
+00:59:13,450 --> 00:59:18,310
+لكن يختلف عن مين but different from the value of F
+
+726
+00:59:18,310 --> 00:59:22,410
+at any point of the interval وهذا بيجيبوا سبعة
+
+727
+00:59:22,410 --> 00:59:26,990
+تلاتة تمانية يعني بقولك ممكن تكون يا محلاها و تجيب
+
+728
+00:59:26,990 --> 00:59:32,990
+اللي هو ال F prime of X لكن ما تطلع شاشة تساوي F
+
+729
+00:59:32,990 --> 00:59:38,780
+of Xففي هذه الحالة بيكون الـ Indefinite Integral
+
+730
+00:59:38,780 --> 00:59:46,320
+ليس اللي هو إيه شماله له Antiderivative عارفش
+
+731
+00:59:46,320 --> 00:59:55,080
+لحاله و هاي في مثال طبعا نأتي
+
+732
+00:59:55,080 --> 01:00:01,300
+الآن و نبدأ حديثعن الهو evaluation of integrals
+
+733
+01:00:01,300 --> 01:00:07,780
+evaluation of integrals هناخد اللي هو اللي هي اللي
+
+734
+01:00:07,780 --> 01:00:12,660
+كنا نقول عنها اللي هو integration by parts اللي
+
+735
+01:00:12,660 --> 01:00:17,380
+كنا نقول عنه integration by parts نشوف كيف اللي هو
+
+736
+01:00:17,380 --> 01:00:21,360
+البرهن الأول واحدة يعني هناخد اللي هو النظرية
+
+737
+01:00:21,360 --> 01:00:28,430
+الأولى اللي هي في من ضمن اللي هيكيف يمكن أن نجد
+
+738
+01:00:28,430 --> 01:00:33,770
+طرق لإيجاد التكامل؟ evaluation of integrals أول
+
+739
+01:00:33,770 --> 01:00:39,730
+شيء نحكي عنه هو integral by parts التكامل بالتجزيم
+
+740
+01:00:41,640 --> 01:00:48,040
+نضع الأسس النظرية للتكامل بالتجزئة أو نشرع التكامل
+
+741
+01:00:48,040 --> 01:00:50,920
+بالتجزئة من خلال النظرية اللي أمامنا، أيش بتقول
+
+742
+01:00:50,920 --> 01:00:54,720
+ليه؟ إذا كانت f و g من a و b، f small و g small
+
+743
+01:00:54,720 --> 01:00:58,520
+طبعا، لعند R، R integrable on a و b، نفترض إن
+
+744
+01:00:58,520 --> 01:01:02,040
+التنتين إما اللي هين integrable وبدنا نفترض إنه
+
+745
+01:01:02,040 --> 01:01:06,510
+لهين antiderivativesالان بدأ افرض ان F لها
+
+746
+01:01:06,510 --> 01:01:09,430
+antiderivative اسمها F capital و G لها
+
+747
+01:01:09,430 --> 01:01:13,910
+antiderivative اسمها G capital on A و B اذا الان
+
+748
+01:01:13,910 --> 01:01:22,050
+نظريتنا ترتكز في معطياتها على ان ال F small ل F و
+
+749
+01:01:22,050 --> 01:01:24,210
+G integrable هي واحد
+
+750
+01:01:36,840 --> 01:01:45,420
+ثم عرض علينا الآن نعمل integration ثم بنيجي بقول
+
+751
+01:01:45,420 --> 01:01:52,610
+ليهالـ Integration لحاصل ضرب دالتين F of X في G of
+
+752
+01:01:52,610 --> 01:01:58,890
+X DX من A لعين Bلأن طيب هذه Integrable عارفين طب F
+
+753
+01:01:58,890 --> 01:02:01,090
+capital Integrable اه Integrable لإنها
+
+754
+01:02:01,090 --> 01:02:03,930
+differentiable لإنها differentiable يعني
+
+755
+01:02:03,930 --> 01:02:07,370
+continuous أكتر من continuous يعني يعني أكيد إيش
+
+756
+01:02:07,370 --> 01:02:11,250
+ما لها Integrable إذا معقول كلامه من A لعند B F of
+
+757
+01:02:11,250 --> 01:02:15,590
+X G of X DX إيش بتساوي؟ بقولي عبارة عن F capital
+
+758
+01:02:15,590 --> 01:02:21,750
+of B G capital of B نقص F capital of A G capital
+
+759
+01:02:21,750 --> 01:02:31,040
+of A هذاناقص الـ integration F small of X G
+
+760
+01:02:31,040 --> 01:02:37,520
+capital of X dx من A لعندي هذي اللي هي ال
+
+761
+01:02:37,520 --> 01:02:41,240
+integration by parts اللي عامة اللي بتدخلته أو
+
+762
+01:02:41,240 --> 01:02:45,960
+اللي هي اللي بتقول عنه النظريةإذا if f و g من a
+
+763
+01:02:45,960 --> 01:02:49,260
+لعن بي are integrable on a و b and have
+
+764
+01:02:49,260 --> 01:02:52,140
+antiderivatives f capital and g capital on a و b
+
+765
+01:02:52,140 --> 01:02:56,580
+then ال integration من a لعن بي f of x g x dx
+
+766
+01:02:56,580 --> 01:03:00,080
+بيسوّل f of b g of b نقص f of a g of a طبعاً
+
+767
+01:03:00,080 --> 01:03:06,360
+للcapitals نقص ال integration من a لb f small g
+
+768
+01:03:06,360 --> 01:03:12,200
+capital dx ماشي الحال بدنا الآن اللي هو البرهن
+
+769
+01:03:12,200 --> 01:03:17,750
+النظري البرهن أسهل يا جماعةهو برهانة يعتمد على
+
+770
+01:03:17,750 --> 01:03:22,970
+تفاضل اللي هو حاصل ضرب دلتين ويمكن احنا كنا اصلا
+
+771
+01:03:22,970 --> 01:03:27,110
+في اتناء اول ما بنبدأ في ال integration by bars
+
+772
+01:03:27,110 --> 01:03:31,870
+سنة عارفه للطلاب في ال calculus في الواقع في كل
+
+773
+01:03:31,870 --> 01:03:36,490
+سؤال في الأول يعني و كأننا بنبرهن النظرية و بعد
+
+774
+01:03:36,490 --> 01:03:40,170
+ذلك بنسير اللي هو حافظنا الطريقة و نعملها بشكل
+
+775
+01:03:40,170 --> 01:03:48,220
+سريع طيب نشوف كيفسمّيلي اللي هو F capital of X G
+
+776
+01:03:48,220 --> 01:03:52,060
+of capital of X ايش بتساوي H of X طبعاً F is
+
+777
+01:03:52,060 --> 01:03:53,840
+differentiable و G is differentiable زي ما كنا
+
+778
+01:03:53,840 --> 01:03:56,600
+كاتبين هذه لإنه F antiderivative و G
+
+779
+01:03:56,600 --> 01:03:59,860
+antiderivative يعني F prime لها F small و G prime
+
+780
+01:03:59,860 --> 01:04:03,700
+لها G small يعني إذا صارت الـH عبارة عن
+
+781
+01:04:03,700 --> 01:04:07,160
+differentiable و مدام differentiable إذا أكيد الـH
+
+782
+01:04:07,160 --> 01:04:12,340
+شمالها continuous على الفترة A و B ماشي الحال و مش
+
+783
+01:04:12,340 --> 01:04:18,630
+هيك كمانوبنقدر نفضلها شوفوا كيف
+
+784
+01:04:22,920 --> 01:04:26,280
+واضحة كلها .. اه واضحة كلها .. ماشي زي ما قلنا يا
+
+785
+01:04:26,280 --> 01:04:29,440
+جماعة سمينا F capital of X في G capital of X
+
+786
+01:04:29,440 --> 01:04:32,240
+بالساوية H of X F differentiable و G
+
+787
+01:04:32,240 --> 01:04:35,440
+differentiable ثم H differentiable ومن ثم اكيد
+
+788
+01:04:35,440 --> 01:04:39,780
+continuous فضولي H prime of X لو حاصل ضرب دالتين
+
+789
+01:04:39,780 --> 01:04:44,740
+التفاضل الأول في التاني زي اللي هو التاني الأول في
+
+790
+01:04:44,740 --> 01:04:49,840
+التفاضل التاني ويساويتفاضل الـ F' اللي هي F small
+
+791
+01:04:49,840 --> 01:04:54,440
+وهذه تنزل زي ما هي وتفاضل هذه اللي هي G small لذا
+
+792
+01:04:54,440 --> 01:04:59,020
+صارت الـ H' بالساوية هنا يعني وكأنه صار عنده اللي
+
+793
+01:04:59,020 --> 01:05:04,360
+هي الـH هذه بدون الـPrime antiderivative لمن؟ لهذه
+
+794
+01:05:04,360 --> 01:05:09,520
+صارت يعني الـH capital is an antiderivative of FG
+
+795
+01:05:09,520 --> 01:05:17,320
+زي مين زي FGالان كل شيء نيح F وG Integrable و F
+
+796
+01:05:17,320 --> 01:05:21,560
+capital وG continuous اذا اللي هي اكيد F capital
+
+797
+01:05:21,560 --> 01:05:25,520
+وG capital Integrable ومن ثم هيطلع كل هذا اشماله
+
+798
+01:05:25,520 --> 01:05:31,920
+is integrable ماشي كمان مرة F
+
+799
+01:05:33,190 --> 01:05:36,910
+Integrable و G-Integrable و G-Capital و F-Capital
+
+800
+01:05:36,910 --> 01:05:40,450
+continuous إذا صار الـ Integrable إذا هذا كله على
+
+801
+01:05:40,450 --> 01:05:44,830
+بعض إيش ماله صار Integrable إذا صار عندي الآن اللي
+
+802
+01:05:44,830 --> 01:05:49,550
+هي كل الشروط متحققة إذا من سبعة تلاتة مدامة ال H
+
+803
+01:05:50,390 --> 01:05:53,570
+الـ H وينها الـ H ؟ هي الـ Antiderivative لهذه
+
+804
+01:05:53,570 --> 01:05:57,470
+وهذه Integrable فبصير عندى الان ال integration من
+
+805
+01:05:57,470 --> 01:06:01,770
+هنا ب F في G زايد F capital في G DX بتساوي H of B
+
+806
+01:06:01,770 --> 01:06:11,650
+ناقص مين ناقص H of A طيب صار عندى الان الأمور وضحت
+
+807
+01:06:11,650 --> 01:06:20,490
+وطلعت النتيجة H of B اتطلع عليها وين H of B؟ هيهاH
+
+808
+01:06:20,490 --> 01:06:26,610
+of B بيساوي F capital of B في G
+
+809
+01:06:26,610 --> 01:06:30,930
+of B هايها ماشي F of B في G of B عادلة لو انتوا
+
+810
+01:06:30,930 --> 01:06:36,070
+موجودين لأ على طول قلتولي هايها الان H of A بيساوي
+
+811
+01:06:36,070 --> 01:06:41,980
+F of A في G of A هايها G of A ماشي إذا إيديناهذا
+
+812
+01:06:41,980 --> 01:06:46,060
+المقدار أعوضنا عن H of B هيها وعوضنا عن H دي ها
+
+813
+01:06:46,060 --> 01:06:49,960
+ويها وإيش جينا وهذه فصلناها لإنه Integrable إذا
+
+814
+01:06:49,960 --> 01:06:52,940
+فصلناها بنجيب واحدة على الجهة دي وواحدة على الجهة
+
+815
+01:06:52,940 --> 01:06:57,940
+دي وهو المطلوب اعملكم إياها طيب ال integration من
+
+816
+01:06:57,940 --> 01:07:01,780
+A ل B integration
+
+817
+01:07:01,780 --> 01:07:10,680
+من A ل B FG capital زائد F capital في G بساوي
+
+818
+01:07:11,790 --> 01:07:24,730
+H of B هي H of B H of B سوى F of B G of B نقص H of
+
+819
+01:07:24,730 --> 01:07:31,770
+A هي F of AG of A من الجهة الثانية بيسوي ال
+
+820
+01:07:31,770 --> 01:07:35,890
+integration F في G capital زاد ال integration F
+
+821
+01:07:35,890 --> 01:07:41,070
+capital في G small من A لعند B من A لعند B لأن إن
+
+822
+01:07:41,070 --> 01:07:44,490
+قلولي هذا على الجهة هذه بيصير عند ال integration
+
+823
+01:07:44,490 --> 01:07:51,350
+المطلوب هذاأكيد فهمتم الأصل من a لعن بيه بساوي ال
+
+824
+01:07:51,350 --> 01:07:55,570
+integration f في g capital زي f capital في g small
+
+825
+01:07:55,570 --> 01:08:06,170
+لأ خلصنا منه بساوي f of b في f of a في g of a في b
+
+826
+01:08:06,170 --> 01:08:16,030
+نقص f of a في g of a كل هذاهذا المقدار integration
+
+827
+01:08:16,030 --> 01:08:27,230
+of capital في G من A لـ B وهو المطلوب و هيك احنا
+
+828
+01:08:28,050 --> 01:08:32,490
+بنكون اليوم ان شاء الله وصلنا لعند ال first
+
+829
+01:08:32,490 --> 01:08:36,250
+substitution theorem المرة القادمة ان شاء الله
+
+830
+01:08:36,250 --> 01:08:45,010
+بنكمل المحاضرة او بنكمل المادة و بنكمل هذا ال
+
+831
+01:08:45,010 --> 01:08:49,330
+section في محاضرة قادمة ان شاء الله و إلى لقائنا
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/FLAtGDd1wro.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/FLAtGDd1wro.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1be79713c9411c9634969a70ce87b71202ac9a75
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/FLAtGDd1wro.srt
@@ -0,0 +1,3195 @@
+1
+00:00:04,960 --> 00:00:09,520
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 27 مساق
+
+2
+00:00:09,520 --> 00:00:14,620
+تحليل حقيقي 2 طلاب وطالبات الجامعة الإسلامية كلية
+
+3
+00:00:14,620 --> 00:00:19,740
+العلوم قسم رياضيات اللي هنكمل اليوم إن شاء الله 
+
+4
+00:00:19,740 --> 00:00:23,560
+اللي بدأناها المرة الماضية اللي هو tests for
+
+5
+00:00:23,560 --> 00:00:26,400
+absolute convergence tests for absolute
+
+6
+00:00:26,400 --> 00:00:29,770
+convergence حكينا المرة الماضية على الـ Comparison
+
+7
+00:00:29,770 --> 00:00:33,870
+Test وقلنا إنه الـ Comparison Test بنيجي بنقارن
+
+8
+00:00:33,870 --> 00:00:37,610
+اللي هو Series  الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... 
+
+9
+00:00:37,610 --> 00:00:37,790
+.. الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+10
+00:00:37,790 --> 00:00:39,290
+الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+11
+00:00:39,290 --> 00:00:39,890
+.. الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+12
+00:00:39,890 --> 00:00:40,250
+الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+13
+00:00:40,250 --> 00:00:40,570
+.. الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+14
+00:00:40,570 --> 00:00:42,550
+الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+15
+00:00:42,550 --> 00:00:44,930
+.. الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ ... الـ
+
+16
+00:00:44,930 --> 00:00:49,270
+الـ converges ولو كانت اللي هي الصغيرة diverges من
+
+17
+00:00:49,270 --> 00:00:52,690
+باب أولى هتكون اللي أكبر diverges هذا ال
+
+18
+00:00:52,690 --> 00:00:55,250
+comparison test وبعدين أخذنا ال limit comparison
+
+19
+00:00:55,250 --> 00:00:59,570
+test اللي هو اللي بيقارن بين اللي هو limit XN على
+
+20
+00:00:59,570 --> 00:01:05,070
+YN لو كان عندي لا يساوي صفر معناته يتأكد هي ال then
+
+21
+00:01:05,070 --> 00:01:07,930
+اللي هو summation للـ XN converges  و YN دول ال
+
+22
+00:01:07,930 --> 00:01:10,450
+summation converges يعني التنتين يعني converges
+
+23
+00:01:10,450 --> 00:01:14,980
+التنتين diverges لكن الـ N لو كان ال limit في الـ ..
+
+24
+00:01:14,980 --> 00:01:19,860
+في الـ ... في الـ ... في الـ limit XN على YN بيساوي 0
+
+25
+00:01:19,860 --> 00:01:24,040
+لو ساوي 0 وكانت اللي هي اللي تحت اللي هي is
+
+26
+00:01:24,040 --> 00:01:26,980
+convergent أكيد اللي هي اللي فوق هتكون is
+
+27
+00:01:26,980 --> 00:01:31,950
+convergent الآن اللي هو بعد هيك أخذنا اللي هو الـ
+
+28
+00:01:31,950 --> 00:01:35,350
+Root and Ratio Test الـ Root and Ratio Test قلنا
+
+29
+00:01:35,350 --> 00:01:38,470
+اللي هو اللي بنيجي بنفحص اللي هو Absolute Value لـ
+
+30
+00:01:38,470 --> 00:01:42,030
+XN أصغر من 1 ل N لو من عند N أكبر من أو يساوي K طالع
+
+31
+00:01:42,030 --> 00:01:45,650
+اللي هي عندي XN أصغر من 1 ل N أصغر من R الآن 
+
+32
+00:01:45,650 --> 00:01:48,910
+ال Series اللي عندي هذه بتكون شاملها Absolutely 
+
+33
+00:01:48,910 --> 00:01:53,610
+Convergent لما تكون الـ R أصغر من 1 لو كان اللي هو
+
+34
+00:01:53,610 --> 00:01:58,870
+طلع عندي الـ Xn-1  لأن أكبر من أو يساوي 1 لكل n أكبر 
+
+35
+00:01:58,870 --> 00:02:01,630
+من أو يساوي K بيكون ال series اللي هي summation Xn
+
+36
+00:02:01,630 --> 00:02:06,030
+شاملها is divergent أخذنا كورولري عليها اللي هو
+
+37
+00:02:06,030 --> 00:02:10,150
+بدل ما على ال terms أخذنا ال limit للـ Xn-1 لأن
+
+38
+00:02:10,150 --> 00:02:13,270
+اللي هو لو لجناها بتساوي R بيكون ال summation 
+
+39
+00:02:13,270 --> 00:02:16,770
+absolutely convergent لما R أصغر من 1 و
+
+40
+00:02:16,770 --> 00:02:24,020
+divergent لما R أكبر من 1 أو لما الـ R بتساوي
+
+41
+00:02:24,020 --> 00:02:28,360
+واحد No conclusion بعدين اجينا أخذنا ال ratio test
+
+42
+00:02:28,360 --> 00:02:32,500
+ال ratio test اللي هو مقارنة في داخل ال series
+
+43
+00:02:32,500 --> 00:02:37,060
+نفسها يعني الـ XN زائد واحد على XN اللي هو أصغر من أو يساوي
+
+44
+00:02:37,060 --> 00:02:43,470
+R لجناها لكل N أكبر من أو يساوي K ولاقينا الـ R هنا أصغر من
+
+45
+00:02:43,470 --> 00:02:46,290
+واحد فبصير ال submission للإكسات is absolutely
+
+46
+00:02:46,290 --> 00:02:50,030
+convergent لو كانت اللي طلعت عندي هذه أكبر من أو
+
+47
+00:02:50,030 --> 00:02:54,670
+يساوي واحد بتكون ال series is divergent هذا حكيناه
+
+48
+00:02:54,670 --> 00:02:57,850
+المرة الماضية وقلنا برضه اللي هو في عندي Corollary
+
+49
+00:02:57,850 --> 00:03:01,130
+لو كان أخذنا limit للإكسات زيادة واحد على الإكسات لقيناها
+
+50
+00:03:01,130 --> 00:03:05,090
+بساوى R الآن حسب اللي هي R ده كانت R أكبر من واحد
+
+51
+00:03:05,090 --> 00:03:08,670
+اللي هو عبارة عن Convergent ولو كانت R أكبر من 
+
+52
+00:03:08,670 --> 00:03:11,830
+واحد بتكون Divergent وعند R بيساوى واحد ال test  فعلًا
+
+53
+00:03:12,390 --> 00:03:15,930
+الآن أوصلنا لعند مين لعند الـ Integral Test
+
+54
+00:03:15,930 --> 00:03:19,450
+وخلينا اليوم اللي هو نبحث في اللي هو الـ Integral
+
+55
+00:03:19,450 --> 00:03:23,770
+Test ونشوف كيف نبرهن اللي هو الـ Integral Test
+
+56
+00:03:23,770 --> 00:03:31,720
+ونشوف إيش هو الآن خليكم معنا ال Integral Test الـ
+
+57
+00:03:31,720 --> 00:03:36,740
+927 let F be a positive decreasing function on T,
+
+58
+00:03:36,800 --> 00:03:40,760
+T أكبر من أو يساوي واحد يعني الـ F عبارة عن positive و
+
+59
+00:03:40,760 --> 00:03:44,720
+decreasing function يعني فوق اللي هو الـ X-axis و
+
+60
+00:03:44,720 --> 00:03:48,580
+decreasing عالمين على الفترة من واحد إلى ما لا 
+
+61
+00:03:48,580 --> 00:03:56,530
+نهاية العنوان ثم السيريز summation للأف أن تتعامل إذا
+
+62
+00:03:56,530 --> 00:04:03,170
+انتقلت من واحد إلى ما لا نهاية f of t dt بيساوي limit من
+
+63
+00:04:03,170 --> 00:04:07,010
+واحد عند n as n goes to infinity f of t dt exists
+
+64
+00:04:07,590 --> 00:04:12,570
+إذن الآن وكأنه حولنا الحديث من ال convergence اللي
+
+65
+00:04:12,570 --> 00:04:17,470
+هو series إلى convergence of proper integral يعني
+
+66
+00:04:17,470 --> 00:04:21,690
+الآن بنقول إن ال series هذه summation f of n
+
+67
+00:04:21,690 --> 00:04:26,290
+converges إذا وفقط إذا كان ال proper integral من 1
+
+68
+00:04:26,290 --> 00:04:31,780
+إلى ما لا نهاية الـ f of t dt is convergent In this case
+
+69
+00:04:31,780 --> 00:04:35,940
+لو كان في ال convergence حادث In this case أو in
+
+70
+00:04:35,940 --> 00:04:40,420
+the case of convergence The partial sum Sn وال
+
+71
+00:04:40,420 --> 00:04:43,460
+partial sum اللي هو sequence of partial sum زائد Sn
+
+72
+00:04:43,460 --> 00:04:46,900
+and اللي بيساوي summation F of K, K من عند واحد
+
+73
+00:04:46,900 --> 00:04:51,520
+لعند N and the sum S بيساوي ال summation للـ F of
+
+74
+00:04:51,520 --> 00:04:55,820
+K, K من عند واحد إلى ما لا نهاية satisfy the
+
+75
+00:04:55,820 --> 00:05:02,530
+estimate التاليدايمًا هنلاقي المسافة بين الـ S وال
+
+76
+00:05:02,530 --> 00:05:05,710
+الـ Sn S ناقص Sn هتكون أصغر من أو يساوي ال
+
+77
+00:05:05,710 --> 00:05:09,150
+integration من N إلى ما لا نهاية للـ F of T DT و
+
+78
+00:05:09,150 --> 00:05:13,010
+أكبر من أو يساوي ال integration من N زائد واحد لعند
+
+79
+00:05:13,010 --> 00:05:16,550
+ما لا نهاية يعني الـ S minus Sn S اللي هي مجموع الـ
+
+80
+00:05:16,550 --> 00:05:19,890
+series ناقص Sn اللي هي عبارة عن ال partial sum من
+
+81
+00:05:19,890 --> 00:05:23,780
+واحد لعند N الحاصل ده يثبت دائماً أصغر من أو يساوي الـ
+
+82
+00:05:23,780 --> 00:05:27,300
+integration من N إلى ما لا نهاية للـ F of T  و أكبر من أو
+
+83
+00:05:27,300 --> 00:05:31,340
+يساوي ال N زائد 1 لعند ما لا نهاية هذا كله في حال أن
+
+84
+00:05:31,340 --> 00:05:34,780
+الـ series اللي هي is convergent أو الـ improper
+
+85
+00:05:34,780 --> 00:05:40,240
+integral is convergent خلينا نبرهن اللي موجود
+
+86
+00:05:40,240 --> 00:05:46,560
+الآن عندي الـ function F is positive and
+
+87
+00:05:46,560 --> 00:05:51,380
+decreasing ماشي الحال عندي الـ function is
+
+88
+00:05:51,380 --> 00:05:55,620
+decreasing على كل الفترة من واحد إلى ما لا نهاية
+
+89
+00:05:55,620 --> 00:06:00,280
+يعني الآن عندي هي اللي هي من واحد الـ function من
+
+90
+00:06:00,280 --> 00:06:03,420
+عند واحد إلى ما لا نهاية عاملها شاملها decreasing
+
+91
+00:06:04,130 --> 00:06:07,430
+الآن بقى جبت أجسم اللي هو خليني أخد الفترة هذه
+
+92
+00:06:07,430 --> 00:06:12,210
+ببدأ من عند X knot بواحد X بواحد بصير اثنين اللي
+
+93
+00:06:12,210 --> 00:06:19,470
+هي X واحد بصير مثلًا X واحد وهذا X knot وهذا X
+
+94
+00:06:19,470 --> 00:06:24,410
+ثلاثة اثنين X ثلاثة لعند الفترة النموذجية XK و XK
+
+95
+00:06:24,410 --> 00:06:30,700
+ناقص واحد و XK الآن هذه الفترة بدي أخد التجزئة 
+
+96
+00:06:30,700 --> 00:06:36,760
+بعد إذنكم الـ X12 والـ X23 والـ XK-1 اللي هي عبارة
+
+97
+00:06:36,760 --> 00:06:41,560
+عن K-1 وهذه منين؟ الـ K حر أنا بدي أجزء بالتجزئة
+
+98
+00:06:41,560 --> 00:06:45,540
+اللي أمامي اللي هتخدمني ماشي الحال الآن على الفترة
+
+99
+00:06:45,540 --> 00:06:46,020
+هذه
+
+100
+00:06:48,590 --> 00:06:53,010
+على الفترة هذه هيها عندي اللي هو هذه طولها إيه
+
+101
+00:06:53,010 --> 00:06:56,930
+شاملها طولها بيساوي واحد لأنه من K ناقص واحد لعند
+
+102
+00:06:56,930 --> 00:07:01,790
+مين لعند K اللي هو وأخدت طول كل واحد أجداش عبارة
+
+103
+00:07:01,790 --> 00:07:05,950
+عن واحد فصارت هذه عبارة عن واحد الآن بدي أدرس اللي
+
+104
+00:07:05,950 --> 00:07:11,670
+هو هذه المنطقة وأقارنها اللي هو بالمساحة إلى الـ F 
+
+105
+00:07:11,670 --> 00:07:17,970
+of K و F of K-1 لنشوف إيش اللي بحكي عشان أصل لللي
+
+106
+00:07:17,970 --> 00:07:23,070
+بديه أنت بتحكي الآن لو جينا طلعنا لعند ... عند ...
+
+107
+00:07:23,070 --> 00:07:28,830
+من عند K-1 لعند K لأن K هذه أكيد K عندي اللي هي من
+
+108
+00:07:28,830 --> 00:07:33,050
+اثنين طالع ماشي الحال إن الفطر تبدأ من عند مين من 
+
+109
+00:07:33,050 --> 00:07:36,670
+عند واحد إلى ما لا نهاية إذا عندي K بتساوي اثنين أو
+
+110
+00:07:36,670 --> 00:07:40,390
+ثلاثة أو أربعة أو خمسة إيه اللي بدي إياه اللي هنخليني 
+
+111
+00:07:40,390 --> 00:07:45,670
+أجي المساحة تحت المنحنى هذا المساحة تحت المنحنى هذا
+
+112
+00:07:45,670 --> 00:07:49,290
+هو عبارة عن قيمة ال integration لل function تبعتنا
+
+113
+00:07:49,290 --> 00:07:53,190
+هذه اللي هي decreasing من وين لو عند K ناقص واحد
+
+114
+00:07:53,190 --> 00:07:56,910
+لعند مين لعند K إذا ال integration من K ناقص واحد 
+
+115
+00:07:56,910 --> 00:08:00,630
+لعند K f of t dt لأن ال function positive تمثل هذه
+
+116
+00:08:00,630 --> 00:08:06,260
+المساحة تحت المنحنى طيب، الآن لو جينا للمساحة اللي
+
+117
+00:08:06,260 --> 00:08:11,580
+هي الآن هذا طوله قيمته واحد وهذا الآن قيمته لهنا
+
+118
+00:08:11,580 --> 00:08:16,820
+F of K ناقص واحد المساحة هذه هيها الشكل هذا
+
+119
+00:08:16,820 --> 00:08:21,660
+مساحته اللي هو عبارة عن مساحة المستطيل اللي طوله
+
+120
+00:08:21,660 --> 00:08:26,060
+... اللي عرضه واحد وطوله مين؟ F of K ناقص واحد
+
+121
+00:08:26,060 --> 00:08:29,880
+الآن F of K ناقص واحد في واحد أكيد هذه المساحة 
+
+122
+00:08:29,880 --> 00:08:34,380
+واضحة إنها أكبر من أو يساوي ال integration اللي عندي
+
+123
+00:08:34,380 --> 00:08:39,060
+الآن أو المساحة تحت المنحنى الآن في المقابل لو 
+
+124
+00:08:39,060 --> 00:08:46,420
+جينا تطلعنا لأ اللي هي المساحة اللي بيمثلها F of K
+
+125
+00:08:46,420 --> 00:08:51,910
+F of K هي طوله في مين في اللي هو واحد هذا واحد طوله
+
+126
+00:08:51,910 --> 00:08:56,870
+هذه الآن مساحتها أكيد أصغر من مساحة مين اللي هي
+
+127
+00:08:56,870 --> 00:09:00,890
+المساحة تحت المنحنى يعني بمعنى آخر هيكون هذه
+
+128
+00:09:00,890 --> 00:09:04,770
+المساحة اللي هي F of K في واحد اللي هي F of K يعني 
+
+129
+00:09:04,770 --> 00:09:09,010
+أصغر من integration اللي أمامي اللي عندي يعني 
+
+130
+00:09:09,010 --> 00:09:12,530
+هذا اللي هو تمام هذا اللي أنا مسميها تسعة أو
+
+131
+00:09:12,530 --> 00:09:17,260
+ثمانية أو اللي هي هذه هيكون عندي المساحة الكبيرة
+
+132
+00:09:17,260 --> 00:09:19,960
+هذه أكبر من أو يساوي المساحة تحت الملحانة الـ
+
+133
+00:09:19,960 --> 00:09:26,140
+integration أصغر من أو يساوي أو أكبر من أو يساوي المساحة 
+
+134
+00:09:26,140 --> 00:09:30,680
+الأخيرة اللي هي المستطيل هذا اللي طوله F of K في 
+
+135
+00:09:30,680 --> 00:09:38,690
+مين أو عرضه واحد يعني K في الواحد يعني F of K أصغر من 
+
+136
+00:09:38,690 --> 00:09:39,770
+أصغر وأصغر وأصغر وأصغر وأصغر وأصغر وأصغر و
+
+137
+00:09:39,770 --> 00:09:42,770
+أصغر وأصغر وأصغر وأصغر وأصغر وأصغر وأصغر و
+
+138
+00:09:42,770 --> 00:09:43,150
+أصغر وأصغر وأصغر وأصغر وأصغر وأصغر وأصغر و
+
+139
+00:09:43,150 --> 00:09:44,770
+أصغر وأصغر وأصغر وأصغر وأصغر وأصغر وأصغر و
+
+140
+00:09:44,770 --> 00:09:56,800
+أصغر وأصغر وأصغر وأصغر وأصغر وأصغر وأصغر لأ 
+
+141
+00:09:56,800 --> 00:10:02,120
+اللي هو هذا المقدار كله من عند N من عند 1 لعند N
+
+142
+00:10:02,120 --> 00:10:08,720
+يعني صار عندي الآن الـ summation الـ summation للـ F
+
+143
+00:10:08,720 --> 00:10:14,560
+of K كي من عند 2 لعند N أصغر أو يساوي الـ
+
+144
+00:10:14,560 --> 00:10:22,220
+integration summation طبعاً K-1 لعند K F of T DT K
+
+145
+00:10:22,220 --> 00:10:27,360
+من عند 2 لعند N أصغر أو يساوي الـ summation F of K
+
+146
+00:10:27,360 --> 00:10:35,100
+-1 K من عند 2 لعند N تلاحظ هذا الـ summation اللي
+
+147
+00:10:35,100 --> 00:10:41,060
+هو من عند 2 يعني الـ integration من 1 ل 2 زاد الـ
+
+148
+00:10:41,060 --> 00:10:46,820
+integration من 2 ل 3 زاد من 3 ل 4 لما نقصل من عند
+
+149
+00:10:46,820 --> 00:10:52,140
+اللي هو N ناقص 1 ل عند الـ N يعني كل مجموع هذا
+
+150
+00:10:52,140 --> 00:10:56,800
+هيبقى عبارة عن الـ integration من 1 ل عند الـ N هذا
+
+151
+00:10:56,800 --> 00:11:02,360
+F of T DT أزرع وساوي الـ summation هذا اللي هو
+
+152
+00:11:02,360 --> 00:11:10,170
+عبارة عن F of K من عند 2 F of 2 ناقص F of 1 يعني F of
+
+153
+00:11:10,170 --> 00:11:18,810
+واحد زائد F of 2 زائد F of N ناقص 1 ماشي الحال الآن هذا
+
+154
+00:11:18,810 --> 00:11:22,610
+أكبر أو يساوي هذا الـ summation عبارة عن مين يا
+
+155
+00:11:22,610 --> 00:11:27,670
+جماعة اللي هو عبارة عن F of 2 زي F of 3 لما أصل
+
+156
+00:11:27,670 --> 00:11:32,450
+عند آخر واحد اللي هو F of N في الواقع هذا مين هذا
+
+157
+00:11:32,450 --> 00:11:38,130
+عبارة عن S N نفسه بس خاسس مين منه الـ F of 1 يعني
+
+158
+00:11:38,130 --> 00:11:42,050
+ناقص F of 1 أصغر أو يساوي الـ integration من 1 لـ N
+
+159
+00:11:42,050 --> 00:11:46,970
+F of T DT أصغر أو يساوي هذا عبارة عن الـ summation
+
+160
+00:11:46,970 --> 00:11:51,450
+لمين من عند واحد لعند N ناقص واحد يعني S N ناقص
+
+161
+00:11:51,450 --> 00:11:55,910
+واحد لذا حصلنا على اللي هي الـ equality اللي أمامي
+
+162
+00:11:55,910 --> 00:12:00,910
+اللي هو التالية عند الـ integration من واحد لعند N
+
+163
+00:12:00,910 --> 00:12:06,190
+F of PDT صارت بين الـ S N ناقص واحد وأكبر أو يساوي
+
+164
+00:12:06,190 --> 00:12:13,290
+S N ناقص اللي هي F of واحد طيب نيجي الآن نكمل اللي
+
+165
+00:12:13,940 --> 00:12:21,700
+بدنا إياه أو نصل للي بدنا إياه الآن عندي اللي هو
+
+166
+00:12:21,700 --> 00:12:27,300
+صار اللي هي القيمة هذه هيها بين اللي هو S N ناقص
+
+167
+00:12:27,300 --> 00:12:33,020
+واحد وأكبر أو يساوي S N ناقص مين F of واحد الآن
+
+168
+00:12:33,020 --> 00:12:36,980
+لو فرضنا أن الـ limit للـ S N exist يعني الـ series
+
+169
+00:12:36,980 --> 00:12:40,940
+هذه الـ summation مع نهايتها F of K من واحد لما لها
+
+170
+00:12:40,940 --> 00:12:44,960
+نهاية أو من اثنين لما نهايتها exist هيكون عندي هذا
+
+171
+00:12:44,960 --> 00:12:48,840
+exist وهذا exist لازم الـ limit اللي في النص إيش
+
+172
+00:12:48,840 --> 00:12:52,500
+ماله برضه يطلع إيش ماله exist إذا صار limit
+
+173
+00:12:52,500 --> 00:12:55,680
+للـ improper integral exist يعني لو كانت الـ series
+
+174
+00:12:55,680 --> 00:13:00,280
+converges هتكون الـ improper integral إيش ماله converts
+
+175
+00:13:00,580 --> 00:13:04,540
+الآن بنفس الطريقة هنعمل مين؟ هنعمل اللي هو
+
+176
+00:13:04,540 --> 00:13:08,820
+بالنسبة لمين؟ بالنسبة للي هي conversely بدنا
+
+177
+00:13:08,820 --> 00:13:12,440
+نفترض أن الـ improper integral converge ونصل أنه
+
+178
+00:13:12,440 --> 00:13:19,180
+الـ series converge الآن زي ما قلنا Sn ناقص F of 1
+
+179
+00:13:19,180 --> 00:13:23,720
+طلعت عندي أصغر أو يساوي الـ integration من 1 لـ N F
+
+180
+00:13:23,720 --> 00:13:30,360
+of T DT وهذا أصغر أو يساوي Sn ناقص 1 الآن أنا زي ما
+
+181
+00:13:30,360 --> 00:13:35,360
+حصرت اللي هي فرضت أنا limit الـ Sn exist وحصرت الـ
+
+182
+00:13:35,360 --> 00:13:38,640
+integration بين اللي هو اثنين الـ summation هدول الـ
+
+183
+00:13:38,640 --> 00:13:41,960
+partial sums وقلنا هذا exist الـ limit له وهذا
+
+184
+00:13:41,960 --> 00:13:45,660
+exist له إذا هذا إيه الـ الشمال اللي جوا exist بدي
+
+185
+00:13:45,660 --> 00:13:50,280
+أعمل في الـ integration أو في الـ integration اللي
+
+186
+00:13:50,280 --> 00:13:53,580
+عملته مع اللي هو مين اللي هو الـ partial sums أو
+
+187
+00:13:53,580 --> 00:13:58,310
+الـ improper integral مع الـ series كيف؟ لأن هذا صحيح
+
+188
+00:13:58,310 --> 00:14:04,050
+لكل N ماشي الحال الآن عندي هذا أكيد أكبر أو يساوي
+
+189
+00:14:04,050 --> 00:14:08,310
+الآن لو قلنا أصغر أو يساوي Sn ناقص واحد عندي
+
+190
+00:14:08,310 --> 00:14:11,530
+Sn ناقص F of واحد أكبر أو يساوي هذا أصغر أو يساوي
+
+191
+00:14:11,530 --> 00:14:15,930
+هذا وهذا أصغر أو يساوي مين؟ الثاني اللي عندي هذا
+
+192
+00:14:15,930 --> 00:14:21,830
+الآن عندي بدي أحصر هذا أخليه بين two integrations
+
+193
+00:14:21,830 --> 00:14:26,090
+أو أخلي هذا بين two integrations أي واحد منهم بنفع
+
+194
+00:14:26,680 --> 00:14:30,780
+الآن عندي من هذا نفسه الـ integration من واحد لعند
+
+195
+00:14:30,780 --> 00:14:39,500
+f of t dt صار اللي هو زائد F of واحد أكبر أو يساوي
+
+196
+00:14:39,500 --> 00:14:45,860
+مين الـ Sn ماشي الـ S N من هنا من هنا الـ S N أكبر أو
+
+197
+00:14:45,860 --> 00:14:49,460
+يساوي اللي هو الـ integration من واحد بدل الـ N نقص
+
+198
+00:14:49,460 --> 00:14:54,040
+واحد حطيت مين الـ N ماشي فبيصير عند هذه بدل الـ N
+
+199
+00:14:54,040 --> 00:14:58,740
+برضه بتصير الـ integration من F of T DT من واحد
+
+200
+00:14:58,740 --> 00:15:02,240
+لعند N زائد واحد لأنه هذه أكبر من هذه بزيادة واحد
+
+201
+00:15:02,240 --> 00:15:05,900
+هي هذه أكبر من هذه بواحد من فوق إذا صار عند الـ S
+
+202
+00:15:05,900 --> 00:15:10,300
+N بين هذه الكمية وهذه الكمية لأن لو فرضنا أنه الـ
+
+203
+00:15:10,300 --> 00:15:16,770
+limit للـ integration من 1 لـ N F of T DT as N goes
+
+204
+00:15:16,770 --> 00:15:21,690
+to infinity exist مدام هذا exist الـ limit إذا حصل
+
+205
+00:15:21,690 --> 00:15:25,630
+هذا كله على بعضه هذا limit exist وهذا هيتلع exist
+
+206
+00:15:25,630 --> 00:15:29,370
+إذا اللي هيتلع عنده limit اثر إن إيش exist إذا
+
+207
+00:15:29,370 --> 00:15:32,650
+similarly if limit للـ integration أو الـ improper
+
+208
+00:15:32,650 --> 00:15:37,090
+integral exist إذا هيتلع limit للأثر إن exist هو
+
+209
+00:15:37,090 --> 00:15:42,860
+يعني وضحتها أمامكم therefore اللي أثبتناه إنه الـ
+
+210
+00:15:42,860 --> 00:15:45,860
+summation للـ F of N N من واحد لما لا نهاية اللي هو
+
+211
+00:15:45,860 --> 00:15:49,580
+الـ series exist يعني limit للـ S n exist if and
+
+212
+00:15:49,580 --> 00:15:52,360
+only if الـ improper integral exist يعني limit الـ
+
+213
+00:15:52,360 --> 00:15:56,100
+integration واحد لعند N exist هذا اللي هو اللي
+
+214
+00:15:56,100 --> 00:16:00,820
+أثبتناه لحتى الآن الآن ضال علي أثبت الجزء الثاني
+
+215
+00:16:00,820 --> 00:16:08,360
+من اللي هو النظرية اللي هو في حالة مين الـ
+
+216
+00:16:08,360 --> 00:16:14,140
+Convergence في حالة الـ Convergence لـ Series أو
+
+217
+00:16:14,140 --> 00:16:19,300
+لـ Improper Integral بدنا نحقق الـ Estimate اللي
+
+218
+00:16:19,300 --> 00:16:25,220
+هو... اللي هو عندي S ناقص S N يكون بين اللي هو الـ
+
+219
+00:16:25,220 --> 00:16:29,160
+Two Integration اللي حكينا عنه إشي اللي بقوله نشوف
+
+220
+00:16:29,160 --> 00:16:32,600
+الآن
+
+221
+00:16:32,600 --> 00:16:41,210
+نيجي نركز الآن finally assuming الـ relation a for k
+
+222
+00:16:41,210 --> 00:16:46,810
+بساوي N summing the relation a for k بالن زائد
+
+223
+00:16:46,810 --> 00:16:49,890
+واحد لعند N we obtain إيش هي الـ relation اللي
+
+224
+00:16:49,890 --> 00:16:53,530
+حطيتها قبل شوية اللي عبارة عن الـ integration من
+
+225
+00:16:53,530 --> 00:16:58,430
+واحد لعند N F of T DT أصغر أو يساوي هتبتدي
+
+226
+00:16:58,430 --> 00:17:02,490
+استخدامها كمان مرة للوصول للـ estimation اللي بدي إياها
+
+227
+00:17:03,180 --> 00:17:07,240
+أظهر يساوي Sn ناقص واحد وأكبر أو يساوي مين يا
+
+228
+00:17:07,240 --> 00:17:13,400
+جماعة اللي هو Sn ناقص F of واحد الآن هذه بدنا
+
+229
+00:17:13,400 --> 00:17:17,780
+اللي هو نعمل summation لها من N زائد واحد لعند
+
+230
+00:17:17,780 --> 00:17:24,440
+مين لعند M يعني بدي أجي اللي هو أعمل الـ summation
+
+231
+00:17:24,440 --> 00:17:38,450
+اللي أمامي فبيصير عندي الـ Summation لمن؟ لـ N زائد
+
+232
+00:17:38,450 --> 00:17:43,410
+واحد لعند مين لعند N خلينا نجمحها خد الـ
+
+233
+00:17:43,410 --> 00:17:48,490
+Summation الـ summation عندي هي عندي بيصير الـ
+
+234
+00:17:48,490 --> 00:17:54,990
+summation ل الـ integration اللي
+
+235
+00:17:54,990 --> 00:17:59,390
+أمامي خليني أرجع لكم لها بس عشان تكون الأمور ت...
+
+236
+00:17:59,390 --> 00:18:03,530
+ت... من وين... قبل... لأ آسف مش هذه نيجي لها اللي
+
+237
+00:18:03,530 --> 00:18:07,370
+هي تسعة اللي هالة لأن هذه بعد ما انتجمعت الآن بدي
+
+238
+00:18:07,370 --> 00:18:14,830
+أجمعها من عند اللي هو N زائد واحد لعند اللي هو
+
+239
+00:18:17,110 --> 00:18:23,930
+حيث M أكبر من N خليني أجمحها هذه لأن هذه مجموعة
+
+240
+00:18:23,930 --> 00:18:29,230
+خالصة خليني أجمح هذه لأن خد اجمع لي هذه عندي خد
+
+241
+00:18:29,230 --> 00:18:33,610
+summation حسابات summation K من عند N زائد واحد
+
+242
+00:18:33,610 --> 00:18:39,300
+لعند M حيث اللي هو الـ N مفترضها أكبر من N اللي هي
+
+243
+00:18:39,300 --> 00:18:43,060
+أصغر أو يساوي summation K من N زائد واحد لعند M
+
+244
+00:18:43,060 --> 00:18:48,460
+حسابات summation K من عند M زائد واحد لعند مين
+
+245
+00:18:48,460 --> 00:18:55,170
+لعند M الآن هذا في الواقع يا جماعة احنا قلنا الـ S N
+
+246
+00:18:55,170 --> 00:19:02,070
+هي summation للـ F of K K من عند اللي هو واحد لعند
+
+247
+00:19:02,070 --> 00:19:07,430
+مين لعند N وقلنا الـ S N طبيعي هتكون summation للـ F
+
+248
+00:19:07,430 --> 00:19:14,690
+of K K من عند واحد لعند N الآن اطرح هذه من هذه هيظل
+
+249
+00:19:14,690 --> 00:19:17,870
+الـ summation من N زائد واحد لعند مين عند N يعني
+
+250
+00:19:17,870 --> 00:19:23,030
+هذه في الواقع هي عبارة عن S M ناقص إيش ناقص S N
+
+251
+00:19:23,030 --> 00:19:27,610
+أصغر أو يساوي الـ summation اللي أمامي الـ summation
+
+252
+00:19:27,610 --> 00:19:34,130
+هذا اللي هو من عند N زائد واحد من N زائد واحد لعند
+
+253
+00:19:34,130 --> 00:19:44,700
+N ومن N لعند N زائد اثنين ومن N زائد 2 لعند N زائد
+
+254
+00:19:44,700 --> 00:19:48,900
+3 لما أصل من عند M ناقص واحد لعند M زي ما عملنا
+
+255
+00:19:48,900 --> 00:19:58,590
+قبل شوية هيطلع عبارة عن من N لمين لعند M DT هذا
+
+256
+00:19:58,590 --> 00:20:02,770
+أصغر أو يساوي اللي هو الـ summation اللي هو الأخير
+
+257
+00:20:02,770 --> 00:20:09,050
+بنفس الأسلوب ونشوف إيش اللي هيلزمنا عندي هذا زي ما
+
+258
+00:20:09,050 --> 00:20:11,790
+عملت فوق بالظبط بس هذه بتاخدها في عين الاعتبار إن
+
+259
+00:20:11,790 --> 00:20:16,970
+هي بتبدأ من عند من عند K-1 يعني اللي هي هذه بتبدأ
+
+260
+00:20:16,970 --> 00:20:22,930
+تصير N لعند اللي هو مين اللي هي M-1 يعني بمعنى آخر
+
+261
+00:20:22,930 --> 00:20:29,530
+عبارة عن S M-1 Sn ناقص واحد حسب ما اللي هي حسبنا
+
+262
+00:20:29,530 --> 00:20:34,530
+فوق أو زي ما حسبنا فوق فبنكون حصلنا على هذه الـ
+
+263
+00:20:34,530 --> 00:20:38,310
+Inequality نشوف هذه الـ Inequality كيف بدنا نستخدمها
+
+264
+00:20:38,310 --> 00:20:43,750
+للوصول للي بدنا إياه الآن M أكبر من N أكيد فعندي Sn
+
+265
+00:20:43,750 --> 00:20:48,870
+ناقص Sn اللي هي صارت اللي هي أصغر أو يساوي الـ
+
+266
+00:20:48,870 --> 00:20:52,490
+integration من N لعند M اللي أوجدتها وأصغر أو
+
+267
+00:20:52,490 --> 00:20:55,910
+يساوي الـ Sn ناقص واحد ناقص Sn ناقص واحد زي ما
+
+268
+00:20:55,910 --> 00:21:01,280
+قلنا اللي هذا سميناها إيه يا أستاذ الآن من الـ star
+
+269
+00:21:01,280 --> 00:21:06,560
+خلينا نركز على المنطقة اللي هي الآن بتاخد الـ
+
+270
+00:21:06,560 --> 00:21:11,220
+integration من N زائد واحد عند M زائد واحد F of T
+
+271
+00:21:11,220 --> 00:21:16,420
+DT ماشي الحال هيصير عبارة عن N زائد واحد وهذا M
+
+272
+00:21:16,420 --> 00:21:20,000
+زائد واحد بناء عليها هتصير M زائد واحد ناقص واحد
+
+273
+00:21:20,000 --> 00:21:24,000
+يعني M و N زائد واحد ناقص واحد يعني N فبيصير الـ
+
+274
+00:21:24,000 --> 00:21:27,340
+integration من N زائد واحد عند M زائد واحد F of T
+
+275
+00:21:27,340 --> 00:21:30,360
+DT أصغر وأصغر و Sn ناقص من SN
+
+276
+00:21:33,320 --> 00:21:39,900
+الآن بتنتين مع بعض اللي هي Sm ناقص ل Sn هيها أصغر
+
+277
+00:21:39,900 --> 00:21:43,740
+أو يساوي الـ integration من N لعند M F of T DT هي
+
+278
+00:21:43,740 --> 00:21:49,340
+هذه أصغر أو يساوي هذه كتبت هنا وهذه كتبت هنا Sm
+
+279
+00:21:49,340 --> 00:21:51,660
+ناقص ل Sn أكبر من الـ integration من N زائد واحد
+
+280
+00:21:51,660 --> 00:21:56,850
+لعند مين لعند M زائد واحد لأن احنا متفقين إن الـ 
+
+281
+00:21:56,850 --> 00:22:00,870
+series converge و the proper integral converge إذا
+
+282
+00:22:00,870 --> 00:22:04,030
+الآن خذ لـ M ووديها لما لا نهاية لما إحنا ماخدين ال
+
+283
+00:22:04,030 --> 00:22:07,590
+M شمالها أكبر من الآن بوديها زي ما بده وبتظلها
+
+284
+00:22:07,590 --> 00:22:11,570
+الآن زي ما بدها الآن as M goes to infinity هتصير
+
+285
+00:22:11,570 --> 00:22:15,030
+هذه عبارة عن الـ summation للـ series يعني هتصير S
+
+286
+00:22:15,030 --> 00:22:18,600
+هذه إذاً هذا سيصبح S وهذا سيصبح له proper integral
+
+287
+00:22:18,600 --> 00:22:21,860
+من N زائد واحد إلى ما لا نهاية وهذا سيصبح له
+
+288
+00:22:21,860 --> 00:22:26,260
+proper integral من N إلى ما لا نهاية يعني سيصبح
+
+289
+00:22:26,260 --> 00:22:31,360
+لدي بالضبط الـ S ناقص S N أكبر أو يساوي من N زائد
+
+290
+00:22:31,360 --> 00:22:36,340
+واحد إلى ما لا نهاية ومن N إلى ما لا نهاية وهو هذا
+
+291
+00:22:36,340 --> 00:22:42,040
+اللي مطلوب اللي إحنا طلبناه من أول النظرية وقلنا
+
+292
+00:22:42,040 --> 00:22:46,760
+حيث الـ S هي اللي بتمثل اللي هو limit لـ SM أو هي
+
+293
+00:22:46,760 --> 00:22:51,460
+عبارة عن قيمة الـ series من واحد إلى ما لا نهاية
+
+294
+00:22:51,820 --> 00:22:58,540
+examples بدنا الآن نحاول نستخدم اللي هو النظريات
+
+295
+00:22:58,540 --> 00:23:03,360
+اللي قبل بشوية نوظفها للـ examples اللي عندنا وهذه
+
+296
+00:23:03,360 --> 00:23:07,200
+طبعاً هتلاقيها معظمها إنتوا أخدتوها في الـ calculus
+
+297
+00:23:07,200 --> 00:23:11,700
+نذكرها بشكل سريع بس عشان إنه نشوف الـ applications 
+
+298
+00:23:11,700 --> 00:23:16,440
+لهذه النظريات اللي إحنا مركزين على اللي هو النظـ
+
+299
+00:23:16,440 --> 00:23:20,520
+ر التحليلية لها أو بمعنى آخر على براهين اللي هي
+
+300
+00:23:20,520 --> 00:23:24,020
+النظريات Show that the b series summation 1 ده لأن
+
+301
+00:23:24,020 --> 00:23:29,440
+b diverges for b أصغر أو يساوي 1 الآن بدنا نستخدم
+
+302
+00:23:29,440 --> 00:23:34,920
+الـ comparison test فعنده الآن إن قص بي أصغر أو
+
+303
+00:23:34,920 --> 00:23:38,940
+يساوي أن أكيد لكل أن element in N و الـ بي شمالها
+
+304
+00:23:38,940 --> 00:23:42,120
+أصغر أو يساوي واحد يعني لـ الـ بي اللي أصغر من واحد
+
+305
+00:23:42,120 --> 00:23:47,080
+هيكون أن قص بي أكيد أصغر أو يساوي من أن الآن مقلبه
+
+306
+00:23:47,080 --> 00:23:50,140
+هينقلب واحدة لأن بي أكبر أو يساوي واحدة لأن الآن
+
+307
+00:23:50,140 --> 00:23:54,800
+الـ summation هذا اللي diverse إذا من باب أولى هيكون
+
+308
+00:23:54,800 --> 00:23:58,380
+الكبير by comparison test diverse إذا الـ summation
+
+309
+00:23:58,380 --> 00:24:01,400
+واحد على N بيه diverse for بيه أصغر أو يساوي واحد
+
+310
+00:24:01,400 --> 00:24:04,860
+وهذا الكلام سهل وإنتوا بتعرفوه إذا نيجي للـ
+
+311
+00:24:04,860 --> 00:24:08,540
+summation واحد على N تربيع بدنا نشوف كيف هي إياه
+
+312
+00:24:08,540 --> 00:24:12,740
+converse بدنا الآن نقارنها بـ Series إحنا أخدناها
+
+313
+00:24:12,740 --> 00:24:15,620
+إنها ضعيفة Converse مين الـ Series اللي أخدناها
+
+314
+00:24:15,620 --> 00:24:18,100
+الـ Converse اللي هي الـ Telescoping اللي هي
+
+315
+00:24:18,100 --> 00:24:21,620
+Summation واحدة لـ N في N زائد واحد قلنا عنها دي
+
+316
+00:24:21,620 --> 0:24:24,220
+إيش مالها أثبتناها المرة الماضية إنها Converse
+
+317
+00:24:24,220 --> 00:24:28,640
+طيب، الآن هذه مدام هي هت Converge الـ series اللي عند
+
+318
+00:24:28,640 --> 00:24:34,160
+الـ series هت Converge إذا by example اللي هو 918E هت
+
+319
+00:24:34,160 --> 00:24:37,840
+Converge بدنا اللي هو نستخدم اللي هو الـ
+
+320
+00:24:37,840 --> 00:24:41,180
+Comparison Test الآن ماقدرش نستخدم الـ direct ليش
+
+321
+00:24:41,180 --> 00:24:45,280
+ماقدرش نستخدم الـ direct لإنه الآن الـ summation
+
+322
+00:24:45,280 --> 00:24:50,440
+اللي هو الـ الـ الـ واحد على n في n زائد واحد اللي هي
+
+323
+00:24:50,440 --> 00:24:53,880
+الـ convergence هذه اللي هي أصغر أو يساوي واحد على
+
+324
+00:24:53,880 --> 00:24:57,800
+مين على n تربيع فالآن هذه convergence صح لكن اللي
+
+325
+00:24:57,800 --> 00:25:00,120
+أكبر منها مش شرط إنها تكون convergence وماقدرش
+
+326
+00:25:00,120 --> 00:25:04,080
+نحكم الـ comparison test إذا بدنا نستخدم الـ limit
+
+327
+00:25:04,080 --> 00:25:07,380
+comparison test خذ الـ limit اللي هي 1 على n فان
+
+328
+00:25:07,380 --> 00:25:11,040
+زائد 1 على 1 على n تربيع بيصير limit عبارة عن n
+
+329
+00:25:11,040 --> 00:25:14,680
+على n زائد 1 مع الاختصارات اللي هو طبعاً هذا ال
+
+330
+00:25:14,680 --> 00:25:17,360
+limit اللي هي as n goes to infinity هذي بيصير 1
+
+331
+00:25:17,360 --> 00:25:20,820
+على 1 زائد 1 على n هذي بتروح للسفر وبتظلها 1 و ال
+
+332
+00:25:20,820 --> 00:25:24,140
+1 أكيد مش سفر ما زي ما يطلع عند الـ limit لأ اللي
+
+333
+00:25:24,140 --> 00:25:28,310
+هو ال .. ال .. ال .. ال ..الـ .. ال .. ال .. ال
+
+334
+00:25:28,310 --> 00:25:30,870
+limit لـ ال .. ال .. ال comparison test أو اللي هي
+
+335
+00:25:30,870 --> 00:25:33,990
+الـ two series هذول اللي على بعض الـ XN على الـ YN
+
+336
+00:25:33,990 --> 00:25:37,610
+بيساوى رقم إذا التنتين converged أو التنتين
+
+337
+00:25:37,610 --> 00:25:41,550
+diverged وبناء على الحديث إنه بما إنه هذه اللي هي
+
+338
+00:25:41,550 --> 00:25:45,090
+الـ telescope كانت converged إذا الواحد على N تربيع
+
+339
+00:25:45,090 --> 00:25:50,530
+أو صمشي للواحد على N تربيع is convergent طيب هذا
+
+340
+00:25:50,530 --> 00:25:56,030
+كلام كله إنتوا طبعاً بتاخدوه في الـ .. هو أخدته كثير
+
+341
+00:25:56,030 --> 00:25:58,830
+منه في الـ calculus ولكن إحنا عشان يكتمل الموضوع
+
+342
+00:25:58,830 --> 00:26:02,770
+بدنا ناخد أمثلة على اللي برهنناهم اللي هان show
+
+343
+00:26:02,770 --> 00:26:08,190
+that summation 1 على n بي converts for b يشمل أكبر
+
+344
+00:26:08,190 --> 00:26:12,370
+أو يساوي واحد بي أكبر أو يساوي أسف أكبر من واحد
+
+345
+00:26:12,370 --> 00:26:15,270
+strictly P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+346
+00:26:15,270 --> 00:26:16,850
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+347
+00:26:16,850 --> 00:26:22,690
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+348
+00:26:22,690 --> 00:26:25,810
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+349
+00:26:25,810 --> 00:26:28,150
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+350
+00:26:28,150 --> 00:26:29,090
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+351
+00:26:29,090 --> 00:26:30,170
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+352
+00:26:30,170 --> 00:26:30,770
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+353
+00:26:30,770 --> 00:26:34,550
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+354
+00:26:34,550 --> 00:26:40,020
+أكبر الـ second method بيقولك أنا بدي استخدم ال
+
+355
+00:26:40,020 --> 00:26:44,000
+limit comparison test اللي هو 1 على N أقص بي على 1
+
+356
+00:26:44,000 --> 00:26:48,360
+على N تربيع بيساوى limit 1 على N بي minus 2 و بي
+
+357
+00:26:48,360 --> 00:26:53,000
+أكبر من أو يساوي 2 إذا 1 على N بي minus 2 اللي هو
+
+358
+00:26:53,000 --> 00:26:57,660
+هيساوي limit 0 مدام الـ limit 0 وعندي اللي هي اللي
+
+359
+00:26:57,660 --> 00:27:02,000
+تحت converge إذا من باب أولى اللي فوق تكون
+
+360
+00:27:02,000 --> 00:27:06,130
+converge إذا summation 1 على N بي اللي هو convert
+
+361
+00:27:06,130 --> 00:27:14,370
+by limit comparison test طيب show
+
+362
+00:27:14,370 --> 00:27:19,170
+that the ratio and the root tests fail in the case
+
+363
+00:27:19,170 --> 00:27:22,570
+of B series يعني الآن لو بدنا نجرب نستخدم الـ ratio
+
+364
+00:27:22,570 --> 00:27:26,310
+test و الـ root test مش هتظبط طبعاً الـ limit بنقصته
+
+365
+00:27:26,310 --> 00:27:31,680
+ليش؟ بقولك لو جينا أخدنا limit الـ 1 على N أُس B
+
+366
+00:27:31,680 --> 00:27:36,080
+أُس 1 على N الـ N through test هذا بيساوى الـ limit
+
+367
+00:27:36,080 --> 00:27:41,200
+و N أُس 1 على N أُس minus B ماشي الـ N أُس 1 على N
+
+368
+00:27:41,200 --> 00:27:43,840
+الـ limit اللي لها من example أخدناها في شبطر 3 في
+
+369
+00:27:43,840 --> 00:27:49,080
+الفصل الماضي أو في تحليل 1 هذا وبرضه بتقف تعملوا
+
+370
+00:27:49,080 --> 00:27:52,340
+أصلاً لحالكم الـ limit له بيساوي واحد إذا صار عندي
+
+371
+00:27:52,340 --> 00:27:56,580
+واحد أقصى minus b إذا بيساوي إيش واحد الآن مدام
+
+372
+00:27:56,580 --> 00:28:01,500
+طالع عندي الـ limit اللي هو الـ Xn أقصى واحدة الآن
+
+373
+00:28:01,500 --> 00:28:05,020
+بيساوى واحد إذا بيقول الـ test failed الآن
+
+374
+00:28:05,020 --> 00:28:10,320
+similarly لو جربنا اللي هو الـ ratio test واحدة
+
+375
+00:28:10,320 --> 00:28:13,300
+الآن زيادة واحدة أقصى b على واحدة أن أقصى b بيساوى
+
+376
+00:28:13,300 --> 00:28:18,930
+الـ limit لا اللي هي 1 على 1 زائد 1 على أنقص بي
+
+377
+00:28:18,930 --> 00:28:23,130
+عارفين إيش اللي سوناه اللي هو جسمنا اللي هي اللي
+
+378
+00:28:23,130 --> 00:28:26,770
+هنا على أنقص بي وهنا على أنقص بي صارت 1 هذا على
+
+379
+00:28:26,770 --> 00:28:29,910
+أنقص بي وهذا على أنقص بي بيصير 1 زائد 1 لأن كل أس
+
+380
+00:28:29,910 --> 00:28:34,080
+بي الآن صار عندي limit as n goes to infinity لازم
+
+381
+00:28:34,080 --> 00:28:39,040
+يصير 1 إذا الـ test برضه الـ ratio test فاشل إذا
+
+382
+00:28:39,040 --> 00:28:46,700
+مانفعش انحل الـ b series by الـ ratio test و لا ال
+
+383
+00:28:46,700 --> 00:28:48,200
+anthro test
+
+384
+00:28:55,790 --> 00:29:01,050
+الآن بقول لي إيش رايك تستخدمنا اللي هو الـ
+
+385
+00:29:01,050 --> 00:29:06,360
+Integral Test تشوفه بيظبط في الـ B Series ولا لأ الت
+
+386
+00:29:06,360 --> 00:29:11,680
+F of T بيساوي T Os minus B ده المؤهلة إنها اللي هي
+
+387
+00:29:11,680 --> 00:29:16,560
+تكون اللي هي الاستخدام اللي هي 1 على T أوس بي
+
+388
+00:29:16,560 --> 00:29:21,320
+1 على T أوس بي الآن وهذه الـ series decreasing
+
+389
+00:29:21,320 --> 00:29:24,960
+ويمحلاها إلى آخره and recalled that الـ integration
+
+390
+00:29:24,960 --> 00:29:28,580
+من 1 لعند إن 1 على T DT إيش بيساوي سهل
+
+391
+00:29:28,580 --> 00:29:31,820
+إيجادها كمان عبارة عن لن الان ناقص لن الواحد لن
+
+392
+00:29:31,820 --> 00:29:36,080
+الواحد سفر يعني بتبقى عند لن الان لكن as n goes to
+
+393
+00:29:36,080 --> 00:29:39,700
+infinity واضح إن هذا مباشرة هيروح إلى ما لا نهاية
+
+394
+00:29:39,700 --> 00:29:45,020
+يعني هذا عبارة عن diverse إذا صارت عندي الـ summation
+
+395
+00:29:45,020 --> 00:29:49,040
+للواحد الان diverse by integral test عندي طبعاً الـ
+
+396
+00:29:49,040 --> 00:29:55,360
+b شمالها بي أصغر أو تساوى الواحد الآن في حالة
+
+397
+00:29:55,360 --> 00:30:00,040
+.. لا لا آسف الـ b هنا بتساوي الواحد الآن بدنا نشوف
+
+398
+00:30:00,040 --> 00:30:06,420
+مين إن هي الحالات التانية لو جينا الـ integration
+
+399
+00:30:06,420 --> 00:30:12,560
+إحنا أثبتنا لمين لـ B بتساوي واحد الآن also recall
+
+400
+00:30:12,560 --> 00:30:16,780
+that الـ integration 1 على T قص بي دي T من 1
+
+401
+00:30:16,780 --> 00:30:21,120
+لعند مين 1 لعند أنا بنفضل عندنا الـ بي شمالها هنا
+
+402
+00:30:21,120 --> 00:30:26,040
+لا تساوي 1 كملة الآن بيصير 1 على 1 minus
+
+403
+00:30:26,040 --> 00:30:30,480
+بي انقص 1 على minus بي ناقص 1 بعد ما عوضنا
+
+404
+00:30:30,480 --> 00:30:31,860
+الآن هذه
+
+405
+00:30:34,860 --> 00:30:41,960
+as n goes to infinity وكانت الـ b أكبر من 1 إذا
+
+406
+00:30:41,960 --> 00:30:46,520
+الـ b أكبر من 1 إذا الـ b أكبر من 1 وودينا n
+
+407
+00:30:46,520 --> 00:30:52,400
+إلى ما لا نهاية هذا سيصبح عبارة عن سفر وهذا عبارة
+
+408
+00:30:52,400 --> 00:30:56,240
+عن ناقص 1 يعني الـ limit هذه as n goes to
+
+409
+00:30:56,240 --> 00:31:00,060
+infinity في حالة الـ B أكبر من 1 هتصير هذه عبارة
+
+410
+00:31:00,060 --> 00:31:03,940
+عن ناقص 1 في هذه بيصير 1 على B minus 1
+
+411
+00:31:03,940 --> 00:31:08,540
+هذا في حالة الـ B أكبر من 1 إذا صارت اللي هي الـ
+
+412
+00:31:08,540 --> 00:31:12,640
+integration هذا converge وبناء عليه هتكون الـ B
+
+413
+00:31:12,640 --> 00:31:16,180
+series في حالة الـ B أكبر من 1 by integral test
+
+414
+00:31:16,180 --> 00:31:21,460
+برضه إياه converge لكن لو كانت الـ B أصغر من 1
+
+415
+00:31:22,000 --> 00:31:25,480
+الآن فبيصير عندي هذا اللي هو بيروح إلى ما لا نهاية
+
+416
+00:31:25,480 --> 00:31:29,260
+فبيصير عندي لأن الـ B أصغر من 1 فبيصير عندي الـ
+
+417
+00:31:29,260 --> 00:31:33,500
+integration هذا as N goes to infinity diverges و
+
+418
+00:31:33,500 --> 00:31:37,400
+بناء عليه summation 1 على N B diverges هذا في
+
+419
+00:31:37,400 --> 00:31:42,060
+حالة الـ B شمالها أصغر من 1 و بكون هيك إحنا
+
+420
+00:31:42,060 --> 00:31:46,220
+استخدمنا ال .. ال .. ال B series في إثبات ال .. ال 
+
+421
+00:31:46,220 --> 00:31:49,620
+.. ال integral test في إثبات أنه الـ B series 
+
+422
+00:31:49,620 --> 00:31:56,810
+converges for b أكبر من واحد and diverges for b أيش 
+
+423
+00:31:56,810 --> 00:32:01,950
+ما لها أصغر من أو يساوي واحد وهذه اللي هي أنتو
+
+424
+00:32:01,950 --> 00:32:07,310
+عارفينها الـB Series المشهورة نيجي الآن بدنا نحكي
+
+425
+00:32:07,310 --> 00:32:12,990
+عن اللي هو root test أحيانا اللي هو مدامة اللي هو
+
+426
+00:32:12,990 --> 00:32:18,560
+ال ratio test اللي هو fails في حالة ال limit يطلع
+
+427
+00:32:18,560 --> 00:32:24,380
+لنا واحد أو يساوي واحد فبدنا إيش يخلّينا نقول يحللنا 
+
+428
+00:32:24,380 --> 00:32:28,700
+مشكلة اللي هو ال failure for .. for .. for اللي هو 
+
+429
+00:32:28,700 --> 00:32:33,240
+ظهور ال limit بساوة واحد هنا عندي root test
+
+430
+00:32:33,240 --> 00:32:38,640
+بتعالج الأمر fx بساوة xn is a sequence of non-zero
+
+431
+00:32:38,640 --> 00:32:46,670
+elements لو وجدنا real number a أكبر من واحد and a
+
+432
+00:32:46,670 --> 00:32:50,990
+natural number k such that xn زائد واحد على xn
+
+433
+00:32:50,990 --> 00:32:54,990
+أصغر من أو يساوي واحد ناقص a على n for n أكبر من أو يساوي k then ال
+
+434
+00:32:54,990 --> 00:32:58,890
+summation لل xn is absolutely ايش ماله convergent
+
+435
+00:32:59,220 --> 00:33:02,500
+إذا كان هناك a أصغر من أو يساوي واحد وشكل الـ K طبيعي
+
+436
+00:33:02,500 --> 00:33:06,500
+كذلك الـ absolute value of xn زائد واحد على xn
+
+437
+00:33:06,500 --> 00:33:11,100
+أكبر من أو يساوي واحد ناقص a على n for n أكبر من أو يساوي k فإن 
+
+438
+00:33:11,100 --> 00:33:15,880
+سلسلة xn ليست مطلقا متقاربة يعني باختصار عشان أريحكم
+
+439
+00:33:15,880 --> 00:33:21,920
+إيش بنسوي بنحسبلنا الـ xn زائد واحد على xn إذا
+
+440
+00:33:21,920 --> 00:33:26,480
+وجدنا .. إذا وجدنا نقارن هذه xn زائد واحد على xn
+
+441
+00:33:26,480 --> 00:33:31,280
+بالمقدار واحد ناقص a على n إذا لجينا إن هذا
+
+442
+00:33:31,280 --> 00:33:34,540
+المقدار .. المقدار اسمه واحد ناقص a على n إذا
+
+443
+00:33:34,540 --> 00:33:38,950
+لجينا هذا أصغر من أو يساوي 1 ناقص على a على n وكانت
+
+444
+00:33:38,950 --> 00:33:43,050
+الـ A أكبر من 1 على طول بنحكم على الـ Absolutely 
+
+445
+00:33:43,050 --> 00:33:47,030
+Convergent للـ Series لكن لو لجينا هذا المقدار بعد
+
+446
+00:33:47,030 --> 00:33:51,690
+ما حسبناه أكبر من أو يساوي 1 ناقص A على N حتى لو كانت
+
+447
+00:33:51,690 --> 00:33:56,040
+A أصغر من أو يساوي 1 صغيرة فبنقول إنه في هذه الحالة بنحكم
+
+448
+00:33:56,040 --> 00:33:59,760
+على إيش على إنه ال series is not absolutely
+
+449
+00:33:59,760 --> 00:34:03,500
+convergent يعني العملية عملية حسابات هذه على هذه
+
+450
+00:34:03,500 --> 00:34:08,660
+ونجيبها بدلالة 1 minus a على n أو بنقرنها ب 1
+
+451
+00:34:08,660 --> 00:34:12,840
+minus a على n 1 minus a على n في حالة إن ال a أصغر
+
+452
+00:34:12,840 --> 00:34:16,380
+من أو يساوي واحد هتطلع لنا اللي هي هنا في هذه الحالة
+
+453
+00:34:16,380 --> 00:34:19,140
+it's not absolutely convergent في حالة ال a أكبر
+
+454
+00:34:19,140 --> 00:34:24,710
+من واحد is absolutely convergent وخلّينا نشوف اللي
+
+455
+00:34:24,710 --> 00:34:33,230
+هو البرهان لاللي هي هذه النظرية suppose that عشرة
+
+456
+00:34:33,230 --> 00:34:39,730
+holds عشرة عشرة و اللي هي اللي قبل بشوية حكيناها
+
+457
+00:34:39,730 --> 00:34:42,930
+عشان تكونوا في صورة نقولكم عشرة نذكركم فيها هذه
+
+458
+00:34:42,930 --> 00:34:50,840
+عشرة اللي هي xn زائد واحد xn زائد واحد على xn أصغر
+
+459
+00:34:50,840 --> 00:34:57,220
+من أو يساوي 1 ناقص a على n a أكبر من 1 و n أكبر من أو يساوي k
+
+460
+00:34:57,220 --> 00:35:01,500
+التاني هذا اللي سميناها عشرة اللي سميناها 11 اللي 
+
+461
+00:35:01,500 --> 00:35:07,700
+هو xn زائد 1 على absolute value xn أكبر من أو يساوي
+
+462
+00:35:07,700 --> 00:35:16,820
+اللي هو 1 ناقص a على n و a اللي هي a شمالها أصغر من
+
+463
+00:35:17,510 --> 00:35:23,610
+أو يساوي الواحد ماشي الحال طيب هي هذا عشرة وهذا
+
+464
+00:35:23,610 --> 00:35:28,150
+احد عشرة عشان بعد شوية هنستخدمهم في البرهان خلوكوا
+
+465
+00:35:28,150 --> 00:35:32,800
+معنا ان شاء الله البرهان مش صعب الآن suppose that
+
+466
+00:35:32,800 --> 00:35:39,080
+انه عشرة holds هي for M أكبر من أو يساوي K الآن اضرب
+
+467
+00:35:39,080 --> 00:35:43,280
+لطرفين في وسطين اضرب هذه في هذه بيصير عندي وبدل a
+
+468
+00:35:43,280 --> 00:35:48,980
+ا بدي استخدم اللي هي M عندي بدل M زائد واحد خليني 
+
+469
+00:35:48,980 --> 00:35:51,880
+بيصير عند منح دعش عشان انا اجيب لكم يادي كيف اجت
+
+470
+00:35:51,880 --> 00:35:56,870
+absolute value ل X M زائد واحد أصغر من أو يساوي الـ
+
+471
+00:35:56,870 --> 00:36:02,750
+absolute value للـ XM مضروبة في واحد ناقص A على M،
+
+472
+00:36:02,750 --> 00:36:07,970
+مظبوط؟ طيب، الآن اضربولي الجهتين في مين؟ في M
+
+473
+00:36:07,970 --> 00:36:14,640
+فبصير M هنا، بصير M في هنا هو بيكون حصلنا على M في
+
+474
+00:36:14,640 --> 00:36:19,700
+هذه و M في هذا المقدار دخلولي ال M الآن جوا فبصير
+
+475
+00:36:19,700 --> 00:36:23,580
+absolute value XM زي ما هي أنا بصير M ناقص اللي هي
+
+476
+00:36:23,580 --> 00:36:31,020
+A  الآن هذه بتساوي الآن كتبتها على صورة الآن ضفت
+
+477
+00:36:31,020 --> 00:36:35,720
+اللي هو واحد و طرحت واحد اللي هي هي عندي هنا طرحت
+
+478
+00:36:35,720 --> 00:36:39,800
+واحد و هنا ضفت الواحد فصارت عبارة عن M ناقص واحد
+
+479
+00:36:39,800 --> 00:36:44,830
+XM ناقص A ناقص واحد XM  أكبر من أو يساوي K صار هذا
+
+480
+00:36:44,830 --> 00:36:50,110
+المقدار بعد ما ضفت اللي هو ناقص XM وطرحت ناقص ال
+
+481
+00:36:50,110 --> 00:36:56,590
+XM وضفت اللي هو ناقص اللي هو ضفة ال XM فصار عندي
+
+482
+00:36:56,590 --> 00:37:00,630
+المقدار هو نفسه هذا زي ما قلت لكم لأن من نقطة فلوس
+
+483
+00:37:00,630 --> 00:37:06,680
+ذات عندي ال M ناقص واحد في ال XM ناقص جيبلي هذه هنا
+
+484
+00:37:06,680 --> 00:37:13,940
+وهذه وديها هناك فبصير عندي M-1 في XM ناقص لغاية M
+
+485
+00:37:13,940 --> 00:37:17,820
+في XM زي 1 أكبر من أو يساوي مين اللي جت هنا هذه اللي
+
+486
+00:37:17,820 --> 00:37:24,290
+A-1 في XM اللي هو هذه هتكون أكبر من 0 for M أكبر
+
+487
+00:37:24,290 --> 00:37:28,390
+من أو يساوي K لأن الـA اللي عندنا إيش مفترضينها أكبر
+
+488
+00:37:28,390 --> 00:37:32,250
+من 1 وهذا absolute value إذا صار المقدار هذا أكبر
+
+489
+00:37:32,250 --> 00:37:38,640
+من 0 هذا إيه معناه؟ معناه أن الـ sequence اللي الـ
+
+490
+00:37:38,640 --> 00:37:44,560
+M X M زائد واحد is decreasing sequence لأن اللي
+
+491
+00:37:44,560 --> 00:37:49,040
+قبل ناقص اللي بعد أكبر من أو يساوي سفر يعني صار اللي 
+
+492
+00:37:49,040 --> 00:37:54,940
+هو اللي بعد شماله أصغر من مين من اللي قبل يعني
+
+493
+00:37:54,940 --> 00:37:59,960
+صارت ال sequence M X M زائد واحد is a decreasing
+
+494
+00:37:59,960 --> 00:38:05,790
+sequence for مين M أكبر من أو يساوي اتنين الآن هذه
+
+495
+00:38:05,790 --> 00:38:11,430
+اللي هي ال relation اللي عندي اللي هي 12 بدنا اللي
+
+496
+00:38:11,430 --> 00:38:19,070
+هو نجمعها for K for M بتساوي K لعند مين لعند and
+
+497
+00:38:19,070 --> 00:38:24,290
+and we note the left side تلسكوب اللي هو نشوف كيف
+
+498
+00:38:24,290 --> 00:38:28,750
+ال left side هذا تلسكوب واضح انه تلسكوب we find
+
+499
+00:38:28,750 --> 00:38:37,180
+عندي أخد ال summation من عند N من عند K لعند N
+
+500
+00:38:37,180 --> 00:38:43,840
+عملكم إياها هان من عند K بتساوي أو من عند M بتساوي
+
+501
+00:38:43,840 --> 00:38:51,220
+K لعند مين لعند N أكبر من أو يساوي ال summation من M
+
+502
+00:38:51,220 --> 00:38:58,280
+بتساوي K لعند مين لعند N هذه بتصير اللي هو K ناقص
+
+503
+00:38:58,280 --> 00:39:07,350
+واحد fixed K ناقص اللي هي K في X K زائد واحد اللي
+
+504
+00:39:07,350 --> 00:39:12,190
+بعدها K زائد واحد اللي هي بيصير K في X K زائد واحد
+
+505
+00:39:12,190 --> 00:39:15,250
+راحت مع الأولى ناقص كده فكل واحدة بت cancel
+
+506
+00:39:15,250 --> 00:39:19,570
+الثانية بتظهر أول واحدة و آخر واحدة اللي هي أول
+
+507
+00:39:19,570 --> 00:39:25,470
+واحدة K ناقص واحد في X K ناقص آخر واحدة اللي هي N
+
+508
+00:39:25,470 --> 00:39:30,110
+في X N زائد واحد أكبر من أو يساوي ال summation هذا
+
+509
+00:39:30,110 --> 00:39:34,560
+اللي هو عبارة عن A ناقص واحد عام المشترك لأنه فيها
+
+510
+00:39:34,560 --> 00:39:39,620
+بيت مضروب مضروب في مين؟ في اللي بضر من عند K لعند
+
+511
+00:39:39,620 --> 00:39:44,400
+مين؟ لعند XK XK زائد واحد لعند مين؟ لعند X بكون
+
+512
+00:39:44,400 --> 00:39:51,380
+حصلت على هذه اللي هي ال inequality الآن لاحظوا ما
+
+513
+00:39:51,380 --> 00:39:57,930
+يليه حصلت يا جماعة انه الـ Series هذه أو الـ
+
+514
+00:39:57,930 --> 00:40:02,770
+Sequence هذه عندي هذا المقدار منها مدام الـ
+
+515
+00:40:02,770 --> 00:40:08,810
+Decreasing حصلت و جمعنا و استخدمنا الـ Telescoping
+
+516
+00:40:08,810 --> 00:40:15,640
+حصلنا هذه أكبر من أو يساوي هذه طيب الآن هذا يظهر أن الـ
+
+517
+00:40:15,640 --> 00:40:20,900
+partial sums Sn of سميش الـ Xn اللي هي صار عندهاي
+
+518
+00:40:20,900 --> 00:40:25,920
+اللي هو الـ Sn مظبوط هذا الـ Sn لأنه أصغر من أو يساوي
+
+519
+00:40:25,920 --> 00:40:29,740
+هذا المقدار على A-1 وA-1 عبارة عن إيه؟ عشان ثابت
+
+520
+00:40:30,560 --> 00:40:34,860
+الآن الـ sequence of partial sums Sn اللي هو summation
+
+521
+00:40:34,860 --> 00:40:40,220
+Xn are bounded مدان bounded إذا إيش بده يكون؟ بده
+
+522
+00:40:40,220 --> 00:40:46,580
+يكون convergent ده نشوف إيش اللي بقوله أكتب فوق
+
+523
+00:40:46,580 --> 00:40:53,420
+ولا .. طيب شوفوا عندي إيش
+
+524
+00:40:53,420 --> 00:40:58,990
+اللي حصلنا عليه؟ اللي هو الـ Sn بساوي اللي هو ال
+
+525
+00:40:58,990 --> 00:41:00,810
+summation absolute value لل
+
+526
+00:41:04,710 --> 00:41:10,610
+الـ XK أو قبل حتى قبل الأسئلة حصّلنا على الـ A-1
+
+527
+00:41:10,610 --> 00:41:16,390
+في الـ XK زائد absolute value لـ XN هذا كله على
+
+528
+00:41:16,390 --> 00:41:23,690
+بعضه أصغر من أو يساوي اللي هو K-1 بحكيها K-1 أيشي
+
+529
+00:41:23,690 --> 00:41:29,950
+معين K لأنه من عندها M أكبر من أو يساوي من K K أيشي
+
+530
+00:41:29,950 --> 00:41:36,200
+معين K-1 في ال absolute value لXK ناقص N في الـ
+
+531
+00:41:36,200 --> 00:41:41,040
+absolute value XN زائد واحد ماشي الحال هذه الـ N
+
+532
+00:41:41,040 --> 00:41:51,800
+عالميل على ال A ناقص واحد لأن هذا المقدار أصغر من أو
+
+533
+00:41:51,800 --> 00:41:58,040
+يساوي هذا وهذا أكيد أكيد هذا أصغر من أو يساوي ال K
+
+534
+00:41:58,040 --> 00:42:03,400
+ناقص واحد في absolute value XK على A ناقص واحد
+
+535
+00:42:03,860 --> 00:42:07,840
+لأنه الآن الـ Schilt اللي هو المقدار هذا السالب
+
+536
+00:42:07,840 --> 00:42:12,520
+اللي مطروح إذاً هذا بيكبر فصار هذا المقدار أصغر من أو
+
+537
+00:42:12,520 --> 00:42:17,700
+يساوي هذا هذا ال K عبارة عن fixed رقم fixed number
+
+538
+00:42:17,700 --> 00:42:21,120
+اللي هو لإنه احنا بديه من عند K أكبر أو أكبر يساوي
+
+539
+00:42:21,120 --> 00:42:26,080
+K إذاً K إشي معين بحكي عنه إذاً هذا المقدار من XK
+
+540
+00:42:26,080 --> 00:42:30,720
+لعند ال XN أصغر من أو يساوي هذاماشي الحال إذا صار
+
+541
+00:42:30,720 --> 00:42:42,880
+عندي اللي هو المقدار هذا هو عبارة عن sn-sk-1 مظبوط
+
+542
+00:42:42,880 --> 00:42:47,780
+ولا لأ؟ أكيد للـ absolute values طبعاً يعني بمعنى
+
+543
+00:42:47,780 --> 00:42:52,720
+آخر صار Sn أصغر من أو يساوي Sk-1 برضه عدد عدد عدد
+
+544
+00:42:52,720 --> 00:43:01,500
+معين زائد اللي هو K-1 في XK على A-1 صار هذا Sn
+
+545
+00:43:01,500 --> 00:43:08,570
+أصغر من أو يساوي هذالكل N أكبر من أو يساوي K يعني صارت
+
+546
+00:43:08,570 --> 00:43:11,850
+الـ S N is bounded يعني بمعنى أخر، طبعا هذا أكبر
+
+547
+00:43:11,850 --> 00:43:15,390
+من أو يساوي سفر أكيد الـ N، إذا limit الـ S N as N
+
+548
+00:43:15,390 --> 00:43:19,910
+goes to infinity مهما كبرت الـ N، هذه ما لهاش
+
+549
+00:43:19,910 --> 00:43:23,650
+علاقة فيها الـ N لأنه N أكبر من أو يساويها، إذا أصغر
+
+550
+00:43:23,650 --> 00:43:27,560
+من أو يساوي الـ S K ناقص واحد زائد K ناقص واحد في
+
+551
+00:43:27,560 --> 00:43:31,660
+الـ absolute value of xk على a-1 بمعنى آخر صارت
+
+552
+00:43:31,660 --> 00:43:36,640
+الـ Sn is convergent أو بمعنى آخر الصممش لل
+
+553
+00:43:36,640 --> 00:43:40,040
+absolute value of xn is convergent يعني هتصير
+
+554
+00:43:40,040 --> 00:43:44,660
+السيريز عندي is absolutely convergent
+
+555
+00:43:46,650 --> 00:43:51,190
+طيب نيجي الآن هذا تفسير انه اللي هو this shows the
+
+556
+00:43:51,190 --> 00:43:53,510
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. 
+
+557
+00:43:53,510 --> 00:43:53,850
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. 
+
+558
+00:43:53,850 --> 00:43:54,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+559
+00:43:54,190 --> 00:43:56,030
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. 
+
+560
+00:43:56,030 --> 00:43:57,570
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. 
+
+561
+00:43:57,570 --> 00:43:57,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+562
+00:43:57,730 --> 00:43:57,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+563
+00:43:57,890 --> 00:43:57,990
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+564
+00:43:57,990 --> 00:43:58,010
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+565
+00:43:58,010 --> 00:43:58,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+566
+00:43:58,330 --> 00:44:04,710
+ال .. ال .. ال .. ال .. ال .. ال ..
+
+567
+00:44:04,710 --> 00:44:06,150
+ال .. ال ..
+
+568
+00:44:15,000 --> 00:44:24,940
+نأخذ الجزء الثاني الـ similarly  نشوف كيف suppose
+
+569
+00:44:24,940 --> 00:44:29,660
+that suppose that the relation 11 هيها ال relation
+
+570
+00:44:29,660 --> 00:44:34,700
+11 holds for n أكبر أو يساوي k وطبعا احنا مفترضين ال
+
+571
+00:44:34,700 --> 00:44:39,640
+a أصغر أو يساوي واحد الآن صار عندي ال n ضربنا طرفين
+
+572
+00:44:39,640 --> 00:44:42,800
+في وسطين نفس الشيء فبيصير عندي زي ما عملنا قبل
+
+573
+00:44:42,800 --> 00:44:47,880
+شوية ضربنا هذا بيصير عندي ال n اللي هو xn زائد واحد
+
+574
+00:44:48,690 --> 00:44:53,530
+a أصغر أكبر أو يساوي هذا في هذا وضربنا في n فصارت
+
+575
+00:44:53,530 --> 00:44:57,890
+ال n في xn زائد واحد أكبر أو يساوي لما ضربت ال n
+
+576
+00:44:57,890 --> 00:45:04,070
+هنا بيصير n ناقص a في ال absolute value لل xn الآن
+
+577
+00:45:04,070 --> 00:45:08,910
+ال a أصغر يساوي واحد إذا ناقص ال a أكبر يساوي ناقص 
+
+578
+00:45:08,910 --> 00:45:12,230
+واحد فما دام ناقص ال a أكبر يساوي ناقص واحد إذا
+
+579
+00:45:12,230 --> 00:45:15,710
+صارت عندي n ناقص a في absolute value xn أكبر يساوي
+
+580
+00:45:15,710 --> 00:45:19,070
+n ناقص واحد في absolute value xn لكل n ناقصة وk
+
+581
+00:45:19,070 --> 00:45:24,200
+هذه لأن ال a أصغر يساوي واحد الآن صار عندي الآن واضح
+
+582
+00:45:24,200 --> 00:45:28,580
+أنه ال sequence اللي هو الآن xn زائد واحد أكبر أو
+
+583
+00:45:28,580 --> 00:45:31,960
+يساوي n ناقص واحد xn يعني ال sequence هذه صارت
+
+584
+00:45:31,960 --> 00:45:35,900
+increasing for n أكبر أو يساوي k ما زم increasing
+
+585
+00:45:35,900 --> 00:45:40,680
+إذا there exists c such that الآن في ال absolute
+
+586
+00:45:40,680 --> 00:45:45,300
+value xn زائد واحد أكبر من مين؟ من c for n أكبر أو
+
+587
+00:45:45,300 --> 00:45:49,750
+يساوي k ماشي الحال صارت مدام هذه ال series increasing
+
+588
+00:45:49,750 --> 00:45:55,630
+إذا أكيد هتكون أكبر من أي شيء ومن some c لأنها
+
+589
+00:45:55,630 --> 00:46:00,630
+بتتزايد مدام صارت أكبر من some c وليكن الحد الأول
+
+590
+00:46:00,630 --> 00:46:05,230
+مثلا and some absolute value xn زائد واحد أصغر من
+
+591
+00:46:05,230 --> 00:46:11,300
+c عالمين على ال and قسمنا على مين؟ على الآن الآن هذه
+
+592
+00:46:11,300 --> 00:46:15,460
+ال series diverse تبعتها ال series هذه تبعت اللي
+
+593
+00:46:15,460 --> 00:46:18,760
+هي واحدة الآن diverse إذا من باب أولى بال
+
+594
+00:46:18,760 --> 00:46:23,100
+comparison test هذه تكون diverse أو بمعنى آخر ال
+
+595
+00:46:23,100 --> 00:46:27,580
+series summation xn is not absolutely convergent
+
+596
+00:46:27,930 --> 00:46:33,170
+وهذا هو الـ Reopts Test الآن ناخذ الـ Corollary له
+
+597
+00:46:33,170 --> 00:46:37,150
+الـ Corollary طبعا هتنسحب على إيش يا جماعة؟
+
+598
+00:46:37,150 --> 00:46:41,110
+هتنسحب زي ما هو المنهج اللي بنعمله إحنا بناخد ال
+
+599
+00:46:41,110 --> 00:46:44,910
+test وبناخد ال limit تبعه أو limit test تبعه وهنا
+
+600
+00:46:44,910 --> 00:46:48,870
+ال limit test تبع ال Reopts Test نشوف إيش اللي
+
+601
+00:46:48,870 --> 00:46:51,770
+بيعطينا إياه وعادة اللي هي ال limits بتكون في
+
+602
+00:46:51,770 --> 00:46:56,150
+الغالب أسهل أو أسهل في التعامل من اللي هو ال
+
+603
+00:46:56,150 --> 00:47:01,180
+comparison العادي Latex بيساوي XN بيه sequence of
+
+604
+00:47:01,180 --> 00:47:05,340
+non-zero real numbers يعني إيش مالها sequence of
+
+605
+00:47:05,340 --> 00:47:08,320
+non-zero real numbers ماشي مش .. مش .. مش صفار
+
+606
+00:47:08,320 --> 00:47:11,580
+يعني عشان هيك أصلا فوق احنا لما أخذنا strictly
+
+607
+00:47:11,580 --> 00:47:16,040
+أكبر من C لإنه هنا .. هنا .. هنا يعني مزام
+
+608
+00:47:16,040 --> 00:47:22,130
+sequence of non-zero اللي هو numbers عشان لو حد سأل
+
+609
+00:47:22,130 --> 00:47:27,250
+عن اللي فوق هذه كيف أكبر من C اللي هو strictly
+
+610
+00:47:27,250 --> 00:47:31,190
+هذول non-zero لو كان أول واحد non-zero إذا قيمته
+
+611
+00:47:31,190 --> 00:47:34,550
+strictly أكبر من 0 يعني له قيمة محددة والبعده بيكون
+
+612
+00:47:34,550 --> 00:47:38,750
+أكبر منه إذا أكيد في عندي بديت من رقم C اللي هو
+
+613
+00:47:38,750 --> 00:47:43,010
+اللي هو ال term الأول اللي هو ال XK مثلا وبعده
+
+614
+00:47:43,010 --> 00:47:46,370
+بيصير كل اللي بعده أكبر منه اللي هو أكبر strictly
+
+615
+00:47:46,370 --> 00:47:52,310
+من C وزي ما وصلنا اللي هو diversity إذا الآن let X
+
+616
+00:47:52,310 --> 00:47:55,310
+بيساوي XN بيبقى sequence of non-zero real numbers
+
+617
+00:47:55,310 --> 00:48:01,110
+and let A بيساوي limit N في واحد ناقص XN زائد واحد
+
+618
+00:48:01,110 --> 00:48:04,850
+على XN whenever this limit exists then the series
+
+619
+00:48:04,850 --> 00:48:08,030
+summation XN is absolutely convergent when A أكبر
+
+620
+00:48:08,030 --> 00:48:10,930
+من واحد and this series is not absolutely
+
+621
+00:48:10,930 --> 00:48:13,790
+convergent في A أصغر من واحد وذا كان let A بيساوي
+
+622
+00:48:13,790 --> 00:48:17,450
+واحد فعلا طيب يعني إيش بيقول له؟ بيقول له تعال احسب
+
+623
+00:48:18,370 --> 00:48:23,390
+احسب لي اللي هو limit n في 1 ناقص xn زائد 1 على xn
+
+624
+00:48:23,390 --> 00:48:26,490
+إذا جيت ال limit as n goes to infinity لهذا
+
+625
+00:48:26,490 --> 00:48:30,230
+المقدار وبيكسّلني أصلا إذا جيت ال limit بيساوي
+
+626
+00:48:30,230 --> 00:48:34,890
+رقم a إذا كان اللي كده exist يعني ولو جيت بساوي a
+
+627
+00:48:34,890 --> 00:48:39,990
+بتيجي الآن للحكم إذا a بيساوي 1 بتحكي لك إذا الـ A
+
+628
+00:48:39,990 --> 00:48:43,990
+أكبر من واحد على تقول بتقول converge وإذا كانت الـ
+
+629
+00:48:43,990 --> 00:48:47,570
+A أصغر من واحد بتقول إيه؟  اشماله is not absolutely
+
+630
+00:48:47,570 --> 00:48:50,990
+convergent حتى مش converge absolutely convergent
+
+631
+00:48:50,990 --> 00:48:54,650
+في الأولى لما تكون A أكبر من واحد was not
+
+632
+00:48:54,650 --> 00:48:59,370
+absolutely convergent for A اللي هي أصغر من واحد
+
+633
+00:48:59,370 --> 00:49:05,370
+نيجي الآن ل اللي هو نفترض أنه ال limit هذه exist
+
+634
+00:49:05,370 --> 00:49:11,180
+ونصل ل اللي بدنا إياه الآن هذه الفكرة عملناها قبل هيك
+
+635
+00:49:11,180 --> 00:49:15,940
+في ال proof of Corolla 926 الآن بدنا نفترض suppose
+
+636
+00:49:15,940 --> 00:49:21,040
+that limit 1100-Xn زي 1Xn يساوي إيه؟ أكبر من مين؟ من
+
+637
+00:49:21,040 --> 00:49:25,800
+واحد الآن suppose that
+
+638
+00:49:33,400 --> 00:49:40,040
+limit n في 1 ناقص xn زي 1 على xn بيساوي a أكبر من 1
+
+639
+00:49:40,040 --> 00:49:43,820
+مدام ال limit هذا exist إذا لكل y أكبر من 0 يوجد
+
+640
+00:49:43,820 --> 00:49:47,900
+يوجد اللي هو k such that هذا المقدار ناقص a أصغر
+
+641
+00:49:47,900 --> 00:49:51,280
+من y for every n أكبر يساوي k اللي يعني ال epsilon
+
+642
+00:49:51,280 --> 00:49:54,480
+اللي بدأ اختارها بدأ تخدمني زي ما عملنا قبل هيك في
+
+643
+00:49:54,480 --> 00:49:59,320
+ال proof تبع 109 اللي هو 6 الآن بما أنه a أكبر من
+
+644
+00:49:59,320 --> 00:50:04,180
+واحد يعني الفترة بين a والواحد وال a أكيد في a
+
+645
+00:50:04,180 --> 00:50:09,740
+واحد بينهم الآن عندي ال a واحد ال a واحد ال
+
+646
+00:50:09,740 --> 00:50:14,620
+element واحد وال a لو جيت يعني بمعنى آخر ال a واحد
+
+647
+00:50:14,620 --> 00:50:19,620
+أكبر من ال a وأصغر من ال a الآن خذ ال epsilon let
+
+648
+00:50:19,620 --> 00:50:24,900
+epsilon بيساوي a minus a واحد أكبر من 0 الآن if
+
+649
+00:50:24,900 --> 00:50:30,410
+there exist then There exists K element in N such
+
+650
+00:50:30,410 --> 00:50:35,390
+that for every N أكبر أو يساوي K هيكون عندي اللي هو ال
+
+651
+00:50:35,390 --> 00:50:39,990
+N في الواحد ناقص absolute value XN زائد واحد على
+
+652
+00:50:39,990 --> 00:50:46,090
+ال absolute value لل XN ناقص ال A أصغر من مين؟ من Y
+
+653
+00:50:46,090 --> 00:50:51,050
+اللي هي ال A minus A واحد فوق هذا المقدار هيصير
+
+654
+00:50:51,050 --> 00:50:56,730
+عبارة عن هذا absolute value أصغر من هذا وأكبر من
+
+655
+00:50:56,730 --> 00:51:01,650
+اللي هو A ناقص أو A واحد ناقص A هذا اللي يهمني
+
+656
+00:51:01,650 --> 00:51:06,370
+الآن الآن هتلاحظ إن إن في واحد ناقص absolute value
+
+657
+00:51:06,370 --> 00:51:10,630
+of xn زائد واحد على absolute value of xn اللي هو
+
+658
+00:51:10,630 --> 00:51:17,530
+أصغر جيب هذه hand بيصير عندك اللي هو ناقص إيه
+
+659
+00:51:21,840 --> 00:51:25,820
+أو خلينا لأ من الجهة الثانية أنا مش الجهة دي أكبر
+
+660
+00:51:25,820 --> 00:51:30,260
+من a واحد ناقص a وناقص a بجيبها على الجهة الثانية
+
+661
+00:51:30,260 --> 00:51:35,260
+بيصير زائد a بيصير هذا المقدار أكبر من a زائد a
+
+662
+00:51:35,260 --> 00:51:40,670
+واحد ناقص a يعني بتروح ال a مع ال A نقص واحد وبصير
+
+663
+00:51:40,670 --> 00:51:45,090
+عندي هذا المقدار أكبر من A واحد حيث ال A واحد
+
+664
+00:51:45,090 --> 00:51:50,890
+أكبر من واحد إذا صار عندي A واحد أصغر من هذا
+
+665
+00:51:50,890 --> 00:51:56,100
+المقدار لكل N أكبر أو يساوي K ومنه خلينا بنجيب
+
+666
+00:51:56,100 --> 00:52:01,680
+اللي هو بنجسم على N بيصير اللي هي هذا المقدار 1
+
+667
+00:52:01,680 --> 00:52:06,480
+ناقص هذا المقدار أصغر من A1 على N بنجيب المقدار
+
+668
+00:52:06,480 --> 00:52:09,840
+هذا N وبنجيب هذا N بيصير عندي XN زائد 1 على XN
+
+669
+00:52:09,840 --> 00:52:15,300
+أصغر من 1 ناقص اللي هو A1 على N طبعا بعد ما قسمنا
+
+670
+00:52:15,300 --> 00:52:18,840
+هذا أول شيء وبعدين بنجيب هذا N بعد ما قسمناه
+
+671
+00:52:18,840 --> 00:52:22,120
+وبنجيب هذا N بيطلع عندي هذا المقدار فورأن أكبر
+
+672
+00:52:22,120 --> 00:52:26,400
+شوية صارت اللي هي الصورة هذه صورة مين؟ صورة اللي
+
+673
+00:52:26,400 --> 00:52:31,140
+هي الراقبست الأولى إذا بقى رقابست هيكون عنده اللي
+
+674
+00:52:31,140 --> 00:52:36,990
+هو بما أنه A واحد أكبر من واحد لأنه بين الواحد بين
+
+675
+00:52:36,990 --> 00:52:41,070
+الواحد وال A هيصير عندي اللي هو بيرابستيس
+
+676
+00:52:41,070 --> 00:52:46,890
+الصممشي لل إكسان is absolutely convergent فأصغر من
+
+677
+00:52:46,890 --> 00:52:52,630
+واحد فأصغر من واحد بدو يصير الموضوع الآن مشابه بس
+
+678
+00:52:52,630 --> 00:52:56,090
+بتختلف من هنا خلي أتي نشوف لكم إياه كيف بيختلف
+
+679
+00:52:56,090 --> 00:53:03,220
+الآن for a أصغر من مين؟ من واحد لما تكون a أصغر من
+
+680
+00:53:03,220 --> 00:53:06,040
+واحد بدا تبتلكوا يا له from national exam is not
+
+681
+00:53:06,040 --> 00:53:10,420
+absolutely convergent a أصغر من واحد معناته أنه في
+
+682
+00:53:10,420 --> 00:53:14,680
+بينهم a واحد خلجينا نقول a أصغر من واحد لإنه
+
+683
+00:53:14,680 --> 00:53:16,680
+between any two real numbers there exists a real
+
+684
+00:53:16,680 --> 00:53:21,080
+number اللي هو a واحد بين ال a و بين اللي هو مين؟
+
+685
+00:53:21,080 --> 00:53:26,810
+الواحد اللي عالية epsilon a واحد ناقص a A1-A وهي
+
+686
+00:53:26,810 --> 00:53:30,010
+أكبر من 0 وكله نفسه زي ما هو there exists such
+
+687
+00:53:30,010 --> 00:53:38,030
+that هذا المقدار أصغر من A 1-A هو أكبر من اللي هو
+
+688
+00:53:38,030 --> 00:53:42,530
+سالب اللي هو A-A1 هذه المنطقة بديش إياها باخذ
+
+689
+00:53:42,530 --> 00:53:46,010
+المنطقة هذه بيصير عندي اللي هو زي ما عملنا قبل
+
+690
+00:53:46,010 --> 00:53:50,110
+بالضبط بيصير عندي هذا المقدار وبجيب هذا ال A هام
+
+691
+00:53:50,110 --> 00:53:54,210
+بيصير أصغر لما ناقص A تجهان بيصير زائد A مع ناقص A
+
+692
+00:53:54,210 --> 00:53:58,710
+بتروح بيصير أصغر من مين؟ من A واحد الآن هذا أصغر من
+
+693
+00:53:58,710 --> 00:54:02,130
+A واحد إذا بيصير عندي بكسب الجهتين على N بيصير على
+
+694
+00:54:02,130 --> 00:54:06,090
+N وهذه بنجلها على الجهة هذه وهذه بجيبها هنا
+
+695
+00:54:06,090 --> 00:54:10,030
+بيصير واحد ناقص A واحد على N أصغر من absolute
+
+696
+00:54:10,030 --> 00:54:15,270
+value XN زائد 1 على ال absolute لل XN بكون حصلنا
+
+697
+00:54:15,270 --> 00:54:20,250
+على هذا المقدار أكبر من واحد ناقص A واحد على N وهذا
+
+698
+00:54:20,250 --> 00:54:25,270
+اللي هو لكل N أكبر أو يساوي K إذا حسب B في رقاب ال
+
+699
+00:54:25,270 --> 00:54:30,190
+test بما أن A واحد اللي هي أصغر من واحد إذا هذه
+
+700
+00:54:30,190 --> 00:54:33,450
+اللي هي ال series اللي هي summation لل X absolute
+
+701
+00:54:33,450 --> 00:54:36,810
+value XN is not convergent أو بمعنى آخر summation
+
+702
+00:54:36,810 --> 00:54:40,690
+الـ XN is not absolutely convergent إذا ال exercise
+
+703
+00:54:40,690 --> 00:54:45,390
+هذا هيني وضحت لكم يا جماعة طيب
+
+704
+00:54:47,450 --> 00:54:51,130
+لأن في حالة اللي هي إلا إيه بالساعة واحد قلنا No
+
+705
+00:54:51,130 --> 00:54:54,870
+conclusion where either convergence or divergence
+
+706
+00:54:54,870 --> 00:55:00,490
+is possible طيب خلينا نشوف اللي هو examples على
+
+707
+00:55:00,490 --> 00:55:04,670
+اللي هي الـ Raab's test هنرجع لمين، هنرجع للي هو
+
+708
+00:55:04,670 --> 00:55:08,970
+الـ B series تبعنا ونشوف كيف نوضح اللي هو ال test
+
+709
+00:55:08,970 --> 00:55:12,230
+تبعنا الـ Raab's test أو الـ Corollary اللي عليه
+
+710
+00:55:12,230 --> 00:55:25,120
+كيف اللي هو نستخدمها عندنا في أمثلتنا الآن أخذنا
+
+711
+00:55:25,120 --> 00:55:28,780
+ال limit على طول اللي هو ال X زائد N زائد واحد على
+
+712
+00:55:28,780 --> 00:55:33,520
+ال Xn طبعًا هذه جاهزة و positive أصلًا بيصير عندي
+
+713
+00:55:33,520 --> 00:55:37,980
+اللي هو xn زائد واحد على ال xn واحد ناقصها في n
+
+714
+00:55:37,980 --> 00:55:42,380
+حسبتها و يساوي limit n في واحد ناقص واحد على n
+
+715
+00:55:42,380 --> 00:55:47,140
+غلبتها صارت n<sup>b</sup> على واحد على n زائد واحد الكل أس b و
+
+716
+00:55:47,140 --> 00:55:52,860
+يساوي limit عندي ال n اللي هي أحطت المقامات فصارت N
+
+717
+00:55:52,860 --> 00:55:56,060
+زائد واحد أس b N أس b على N زائد واحد وكل أس b في
+
+718
+00:55:56,060 --> 00:56:03,020
+مين في N ويساوي ال N عبارة عن N زائد واحد أس b ناقص
+
+719
+00:56:03,020 --> 00:56:08,660
+N أس b على واحد على N وهذه جبت مين لحالها واحد
+
+720
+00:56:08,660 --> 00:56:12,300
+على N زائد واحد أس b يعني جبت هذه هنا وهذه فصلت
+
+721
+00:56:12,300 --> 00:56:17,280
+لحالها صارت هذه في هذه لأن هذه limit معروف صار ال N
+
+722
+00:56:17,280 --> 00:56:22,980
+limit اللي هو هذا المقدار الآن واحد على n جيت اللي
+
+723
+00:56:22,980 --> 00:56:29,860
+هو جسمت فوق على n أس b و تحت على n أس b ماشي
+
+724
+00:56:29,860 --> 00:56:33,760
+لما جسمت هذا على n أس b صار هذا عبارة عن واحد
+
+725
+00:56:33,760 --> 00:56:37,760
+زائد واحد على n كل أس b وهذه واحد ناقص واحد
+
+726
+00:56:37,760 --> 00:56:41,140
+وهذه زي ما هي دلت ولما جسمت هذا على n أس b
+
+727
+00:56:41,140 --> 00:56:45,770
+صارت واحد زائد واحد على n أس b الآن و يساوي،
+
+728
+00:56:45,770 --> 00:56:50,550
+الآن limit الأول في limit مين؟ الثاني الآن limit
+
+729
+00:56:50,550 --> 00:56:54,730
+الثاني هذا سهل بيساوي واحد اللي فوق صار عبارة عن
+
+730
+00:56:54,730 --> 00:56:59,210
+الآن اللي هو صفر على صفر، ليش؟ لأن as n goes to
+
+731
+00:56:59,210 --> 00:57:02,110
+infinity، هذه بيصير صفر، هذه بيصير واحد، و واحد
+
+732
+00:57:02,110 --> 00:57:05,030
+بيطلع صفر، و هذه صفر، صفر على صفر، ده نستخدم اللي
+
+733
+00:57:05,030 --> 00:57:07,610
+هو بالتالي الـ L'Hôpital's Rule استخدمت الـ 
+
+734
+00:57:07,610 --> 00:57:11,450
+واشتققت اللي فوق و اللي تحت بالنسبة لل n طبعًا هذا
+
+735
+00:57:11,450 --> 00:57:14,970
+ال limit طلع و خلصنا واحد اشتققنا طالع عبارة عن b
+
+736
+00:57:14,970 --> 00:57:18,870
+في واحد زائد واحد على n كل أس b ناقص واحد فطلع
+
+737
+00:57:18,870 --> 00:57:22,050
+دول جوا ناقص واحد على n تربيع لما فضلت اللي تحت
+
+738
+00:57:22,050 --> 00:57:25,570
+برضه هيطلع ليه ناقص واحد على n تربيع هذا بيروح مع
+
+739
+00:57:25,570 --> 00:57:28,490
+حدّه بيصير عندي as n goes to infinity هذا بيروح
+
+740
+00:57:28,490 --> 00:57:32,310
+للصفر إذا بيصير إيش بيساوي اللي هو عبارة عن b في
+
+741
+00:57:32,310 --> 00:57:36,510
+واحد أس b ناقص واحد يعني عبارة عن إيه؟ عن b الآن
+
+742
+00:57:36,510 --> 00:57:40,390
+ما دام b و b أكبر أو يساوي واحد، إذا من الـ Corollary
+
+743
+00:57:40,390 --> 00:57:47,350
+اللي قبل بشوية الـ B Series إيش مالها، converges
+
+744
+00:57:47,350 --> 00:57:53,140
+for b أكبر من مين من واحد الآن في حالة الواحد قلنا
+
+745
+00:57:53,140 --> 00:57:56,460
+اللي هو لما الـ b بتطلع واحد الـ limit بيكون ال
+
+746
+00:57:56,460 --> 00:58:00,720
+test fail يعني هذه اللي هو بس بنستخدم فيها ال test
+
+747
+00:58:00,720 --> 00:58:04,560
+for convergence بس في حالة اللي هو مين اللي هو ال
+
+748
+00:58:04,560 --> 00:58:08,800
+b أكبر من واحد أثبتنا إنه converge بطريقة اللي
+
+749
+00:58:08,800 --> 00:58:14,260
+يرقب ال test الآن
+
+750
+00:58:14,260 --> 00:58:20,270
+لو كانت b أكبر من واحد لو كانت b أكبر من واحد
+
+751
+00:58:20,270 --> 00:58:26,270
+قلنا اللي هي convergence
+
+752
+00:58:26,270 --> 00:58:31,570
+و for b بيساوي واحد اللي هو no conclusion طيب نيجي
+
+753
+00:58:31,570 --> 00:58:38,400
+الآن لمثال آخر use the Raab's test to the series
+
+754
+00:58:38,400 --> 00:58:42,040
+summation اللي أمامنا اللي هو بنفس الأسلوب بدنا
+
+755
+00:58:42,040 --> 00:58:48,240
+نأخذ اللي هو limit ال xn زائد واحد على xn بيساوي
+
+756
+00:58:48,240 --> 00:58:51,940
+يعني بده يقول لك أنه احنا ما .. ما ظبطش معنى اللي هو
+
+757
+00:58:51,940 --> 00:58:55,920
+مين ال ratio test العادي فبدنا نستخدم اللي هو مين
+
+758
+00:58:55,920 --> 00:58:59,980
+ال Raab's test طيب شوفوا معايا limit xn زائد واحد على
+
+759
+00:58:59,980 --> 00:59:04,480
+xn ال xn زائد واحد اللي هو n زائد واحد على n زائد
+
+760
+00:59:04,480 --> 00:59:08,340
+واحد كله تربيع زائد واحد فإن تربيع زائد واحد على n
+
+761
+00:59:08,340 --> 00:59:11,960
+اللي هي ال xn هذه لما جسمت طبعًا وجلبت في الآخر
+
+762
+00:59:11,960 --> 00:59:19,970
+فبيصير عندي ال n بيساوي جسمت اللي هو هذه على n بيصير
+
+763
+00:59:19,970 --> 00:59:23,150
+عبارة عن هذه جسمتها على هذا n زائد واحد على
+
+764
+00:59:23,150 --> 00:59:26,270
+ال n تطلع عبارة عن واحد زائد واحد على ال n وهذه زي
+
+765
+00:59:26,270 --> 00:59:29,710
+ما هي n تربيع زائد واحد على هذه وهي تساوي limit
+
+766
+00:59:29,710 --> 00:59:35,630
+هذا المقدار هنا برضه جسمت على مين على n تربيع صار
+
+767
+00:59:35,630 --> 00:59:39,230
+واحد زائد واحد على n تربيع وهنا على n تربيع صارت
+
+768
+00:59:39,230 --> 00:59:43,650
+واحد زائد واحد على ال n الكل تربيع زائد واحد على
+
+769
+00:59:43,650 --> 00:59:47,920
+مين n تربيع لأن as n goes to infinity هذه واحد as
+
+770
+00:59:47,920 --> 00:59:51,940
+n goes to infinity هذه واحد وهذه صفر وهذه واحد
+
+771
+00:59:51,940 --> 00:59:54,920
+يعني المحصلة واحد إذا واحد على واحد بيساوي واحد
+
+772
+00:59:54,920 --> 01:00:01,380
+الآن إذا بقصه by corollary 926 does not apply أو
+
+773
+01:00:01,380 --> 01:00:05,640
+corollary 926 اللي هي ال ratio limit limit ratio
+
+774
+01:00:05,640 --> 01:00:12,830
+limit ratio test does not هنا اللي هو applied ليش؟
+
+775
+01:00:12,830 --> 01:00:16,970
+لأن ال limit اللي عندي واحد إذا صار عندي بدنا اللي
+
+776
+01:00:16,970 --> 01:00:22,790
+هو نحاول نوجد طريقة أخرى لو جيت أو وجدت اللي هو
+
+777
+01:00:22,790 --> 01:00:27,370
+برضه بال Raab's test اللي هو limit n في 1 ناقص xn زي
+
+778
+01:00:27,370 --> 01:00:31,190
+1 على xn اللي هو حاول توجد ال limit بنفس الأسلوب
+
+779
+01:00:31,190 --> 01:00:34,330
+اللي فوق بس إلى هذا المقدار احسبهن 1 ناقص هذه
+
+780
+01:00:34,330 --> 01:00:37,130
+وبعدين اضرب من في ال n حاول توجد ال limit هتلاقيه
+
+781
+01:00:37,130 --> 01:00:41,230
+بيساوي 1 إذا صار عندي اللي هو Raab's test برضه أنا
+
+782
+01:00:41,230 --> 01:00:51,310
+أشمله does not apply لكن لو جيت لو جيت اطلعت على
+
+783
+01:00:51,310 --> 01:00:56,760
+الملاحظة التهلية أبدًا نوجد حلل أمر Xn زائد واحد على
+
+784
+01:00:56,760 --> 01:01:00,240
+Xn هتلاقي n زائد واحد على n زائد واحد كل تربيع
+
+785
+01:01:00,240 --> 01:01:03,740
+زائد واحد في n تربيع زائد واحد على n هذا اللي فوق
+
+786
+01:01:03,740 --> 01:01:09,800
+هذا اللي هي Xn زائد واحد وهذا مقلوب من Xn الآن لو
+
+787
+01:01:09,800 --> 01:01:16,060
+جيت حسبت هذه جرب أنت احسب لي أثبت لي أنه it is an
+
+788
+01:01:16,060 --> 01:01:19,220
+exercise to show that ال Xn زيادة واحدة لل Xn أنه
+
+789
+01:01:19,220 --> 01:01:22,400
+هذا المقدار هي اللي طلع عندي هتلاقيه أكبر أو يساوي
+
+790
+01:01:22,400 --> 01:01:28,150
+n ناقص واحد على مين على n الآن ما دام هذا أكبر من هذا
+
+791
+01:01:28,150 --> 01:01:32,550
+وهذا عبارة عن اللي هو عبارة عن واحد ناقص واحد على
+
+792
+01:01:32,550 --> 01:01:36,770
+n therefore by Raab's test اللي هي b the series
+
+793
+01:01:36,770 --> 01:01:41,290
+إيش مالها diverges لأنه كتبت على صورة واحد ناقص
+
+794
+01:01:41,290 --> 01:01:45,710
+واحد على n وهذا ال a تساوي واحد معناه بال Raab's
+
+795
+01:01:45,710 --> 01:01:49,450
+test هيكون ال series هذه اللي هي ال summation لل x
+
+796
+01:01:49,450 --> 01:01:52,570
+and is not convergence is not absolutely
+
+797
+01:01:52,570 --> 01:01:57,310
+convergence أو بمعنى آخر diverges وبكون هيك احنا
+
+798
+01:01:57,310 --> 01:02:02,250
+انهينا اللي هو section اللي هو تسعة اثنين والى
+
+799
+01:02:02,250 --> 01:02:03,310
+لقاء آخر
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/FLAtGDd1wro_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/FLAtGDd1wro_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..75ed0c7ded3c1e1a47e0d8490b7cec7bf9755e0e
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/FLAtGDd1wro_postprocess.srt
@@ -0,0 +1,3196 @@
+1
+00:00:04,960 --> 00:00:09,520
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم 27 مساق
+
+2
+00:00:09,520 --> 00:00:14,620
+تحليل حقيقي 2 طلاب طالبات الجامعة الإسلامية كلية
+
+3
+00:00:14,620 --> 00:00:19,740
+العلوم قسم رياضيات اللي هنكمل اليوم ان شاء الله
+
+4
+00:00:19,740 --> 00:00:23,560
+اللي بدناها المرة الماضية اللي هو tests for
+
+5
+00:00:23,560 --> 00:00:26,400
+absolute convergence tests for absolute
+
+6
+00:00:26,400 --> 00:00:29,770
+convergenceحكينا المرة الماضية على الـ Comparison
+
+7
+00:00:29,770 --> 00:00:33,870
+Test وقلنا إنه الـ Comparison Test بنيجي بنقارن
+
+8
+00:00:33,870 --> 00:00:37,610
+اللي هو Series ال .. ال .. ال .. ال .. ال .. ال ..
+
+9
+00:00:37,610 --> 00:00:37,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+10
+00:00:37,790 --> 00:00:39,290
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+11
+00:00:39,290 --> 00:00:39,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+12
+00:00:39,890 --> 00:00:40,250
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+13
+00:00:40,250 --> 00:00:40,570
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+14
+00:00:40,570 --> 00:00:42,550
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+15
+00:00:42,550 --> 00:00:44,930
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+16
+00:00:44,930 --> 00:00:49,270
+ال ..converges ولو كانت اللي هي الصغيرة diverse من
+
+17
+00:00:49,270 --> 00:00:52,690
+باب أولى هتكون اللي أكبير عايش diverse هذا ال
+
+18
+00:00:52,690 --> 00:00:55,250
+comparison test و بعدين أخدنا ال limit comparison
+
+19
+00:00:55,250 --> 00:00:59,570
+test اللي هو اللي بيقارن بين اللي هو limit XN على
+
+20
+00:00:59,570 --> 00:01:05,070
+YN لو كان عندي لا يساوي سفر معناته يتقل هي ال then
+
+21
+00:01:05,070 --> 00:01:07,930
+اللي هو summation لل XN converts FN دول ال
+
+22
+00:01:07,930 --> 00:01:10,450
+summation converts يعني التنتين يعني converts
+
+23
+00:01:10,450 --> 00:01:14,980
+التنتين diverseلكن الـ N لو كان ال limit في ال ..
+
+24
+00:01:14,980 --> 00:01:19,860
+في ال .. في ال .. في ال limit XN على YN بيساوى 0
+
+25
+00:01:19,860 --> 00:01:24,040
+لو ساوى 0 و كانت اللي هي اللي تحت اللي هي is
+
+26
+00:01:24,040 --> 00:01:26,980
+convergent أكيد اللي هي اللي فوق هتكون is
+
+27
+00:01:26,980 --> 00:01:31,950
+convergentالان اللي هو بعد هيك أخدنا اللي هو الـ
+
+28
+00:01:31,950 --> 00:01:35,350
+Root and Ratio Test الـ Root and Ratio Test قلنا
+
+29
+00:01:35,350 --> 00:01:38,470
+اللي هو اللي بنيجي بنفحص اللي هو Absolute Value لـ
+
+30
+00:01:38,470 --> 00:01:42,030
+X N أصغر و واحدة لـ N لو من عند N أكبر سو K طالع
+
+31
+00:01:42,030 --> 00:01:45,650
+اللي هي عندي X N أصغر و واحدة ل N أصغر سو R الآن
+
+32
+00:01:45,650 --> 00:01:48,910
+ال Series اللي عندي هذه بتكون أشملها Absolutely
+
+33
+00:01:48,910 --> 00:01:53,610
+Convergent لما تكون الـ R أصغر من 1لو كان اللي هو
+
+34
+00:01:53,610 --> 00:01:58,870
+طلع عندى الـ Xn-1 لأن أكبر أو يساوي 1 لكل n أكبر
+
+35
+00:01:58,870 --> 00:02:01,630
+يساوي k بيكون ال series اللي هي summation Xn
+
+36
+00:02:01,630 --> 00:02:06,030
+يشملها is divergent أخدنا كورولري عليها اللي هو
+
+37
+00:02:06,030 --> 00:02:10,150
+بدل ما على ال terms أخدنا ال limit لل Xn-1 لأن
+
+38
+00:02:10,150 --> 00:02:13,270
+اللي هو لو لجناها بتساوي R بيكون ال summation
+
+39
+00:02:13,270 --> 00:02:16,770
+absolutely convergent لما R أصغر من 1 و
+
+40
+00:02:16,770 --> 00:02:24,020
+undivergent لما R أكبر من 1أو لما الـ R بتساوي
+
+41
+00:02:24,020 --> 00:02:28,360
+واحد No conclusion بعدين اجينا أخدنا ال ratio test
+
+42
+00:02:28,360 --> 00:02:32,500
+ال ratio test اللي هو مقارنة في داخل ال series
+
+43
+00:02:32,500 --> 00:02:37,060
+نفسها يعني ال XN زائد واحد على XN اللي هو أصغر سوى
+
+44
+00:02:37,060 --> 00:02:43,470
+R لجناه لكل N أكبر سوى Kولاقينا الار هنا أصغر من
+
+45
+00:02:43,470 --> 00:02:46,290
+واحد فبصير ال submission للإكسان is absolutely
+
+46
+00:02:46,290 --> 00:02:50,030
+convergent لو كانت اللي طلعت عندي هذه أكبر أو
+
+47
+00:02:50,030 --> 00:02:54,670
+يساوى واحد بتكون ال series is divergentهذا حكيناه
+
+48
+00:02:54,670 --> 00:02:57,850
+المرة الماضية وقلنا برضه اللي هو في عندي Corollary
+
+49
+00:02:57,850 --> 00:03:01,130
+لو كان أخدنا limit للإكسان زياد واحد للإكسان لقناه
+
+50
+00:03:01,130 --> 00:03:05,090
+بسوء R الآن حسب اللي هي R ده كانت R أكبر من واحد
+
+51
+00:03:05,090 --> 00:03:08,670
+اللي هو عبارة عن Convergent ولو كانت R أكبر من
+
+52
+00:03:08,670 --> 00:03:11,830
+واحد بتكون Divergent وعند R بسوء واحد ال test فعل
+
+53
+00:03:12,390 --> 00:03:15,930
+الآن أوصلنا لعند مين لعند الـ Integral Test
+
+54
+00:03:15,930 --> 00:03:19,450
+وخلّينا اليوم اللي هو نبحث في اللي هو الـ Integral
+
+55
+00:03:19,450 --> 00:03:23,770
+Test ونشوف كيف نبرهن اللي هو الـ Integral Test
+
+56
+00:03:23,770 --> 00:03:31,720
+ونشوف إيش هوالأن خلّوكوا معنا الانتجرال تست الـ
+
+57
+00:03:31,720 --> 00:03:36,740
+927 let F be a positive decreasing function on T,
+
+58
+00:03:36,800 --> 00:03:40,760
+T أكبر سوء واحد يعني الـ F عبارة عن positive و
+
+59
+00:03:40,760 --> 00:03:44,720
+decreasing function يعني فوق اللي هو الـ X-axis و
+
+60
+00:03:44,720 --> 00:03:48,580
+decreasing عالمين على الفترة من واحد إلى ما لا
+
+61
+00:03:48,580 --> 00:03:56,530
+نهايةالعنوان ثم السيريز الصممشن للأف أن تتعامل إذا
+
+62
+00:03:56,530 --> 00:04:03,170
+أنتقلت من واحد إلى نهاية f of t dt بساوة limit من
+
+63
+00:04:03,170 --> 00:04:07,010
+واحد عند n as n goes to infinity f of t dt exists
+
+64
+00:04:07,590 --> 00:04:12,570
+إذن الآن وكأنه حولنا الحديث من ال convergence اللي
+
+65
+00:04:12,570 --> 00:04:17,470
+هو series إلى convergence of proper integral يعني
+
+66
+00:04:17,470 --> 00:04:21,690
+الآن بنقول إن ال series هذه summation f of n
+
+67
+00:04:21,690 --> 00:04:26,290
+converges إذا وفقط إذا كان ال proper integral من 1
+
+68
+00:04:26,290 --> 00:04:31,780
+إلى ملا نهاية ال f of dt is convergentIn this case
+
+69
+00:04:31,780 --> 00:04:35,940
+لو كان في ال convergence حادث In this case أو in
+
+70
+00:04:35,940 --> 00:04:40,420
+the case of convergence The partial sum S and ال
+
+71
+00:04:40,420 --> 00:04:43,460
+partial sum اللي هو sequence of partial sum زادي S
+
+72
+00:04:43,460 --> 00:04:46,900
+and اللي بيساوي summation F of K, K من عند واحد
+
+73
+00:04:46,900 --> 00:04:51,520
+لعند N and the sum S بيساوي ال summation لل F of
+
+74
+00:04:51,520 --> 00:04:55,820
+K, K من عند واحد إلى ما لا نهاية satisfy the
+
+75
+00:04:55,820 --> 00:05:02,530
+estimate التاليدايمًا هنلاقي المسافة بين الـ S و
+
+76
+00:05:02,530 --> 00:05:05,710
+الـ S N S ناقص S N هتكون أصغر أو يساوي ال
+
+77
+00:05:05,710 --> 00:05:09,150
+integration من N إلى مالة نهاية لل F of T DT و
+
+78
+00:05:09,150 --> 00:05:13,010
+أكبر أو يساوي ال integration من N زايد واحد لعند
+
+79
+00:05:13,010 --> 00:05:16,550
+مالة نهاية يعني ال S minus S N S اللي هي مجموع ال
+
+80
+00:05:16,550 --> 00:05:19,890
+series ناقص S N اللي هي عبارة عن ال partial sum من
+
+81
+00:05:19,890 --> 00:05:23,780
+واحد لعند Nالحاصل ترهن دائما أصغر سواء الـ
+
+82
+00:05:23,780 --> 00:05:27,300
+integration من N إلى M لنهاية للـ F of T و أكبر أو
+
+83
+00:05:27,300 --> 00:05:31,340
+سواء ال N زائد 1 لعيد M لنهاية هذا كله في حال أن
+
+84
+00:05:31,340 --> 00:05:34,780
+الـ series اللي هي is convergent أو الـ improper
+
+85
+00:05:34,780 --> 00:05:40,240
+integral is convergent خلّينا نبرهن اللي موجود
+
+86
+00:05:40,240 --> 00:05:46,560
+الآن عندي الـ function F is positive and
+
+87
+00:05:46,560 --> 00:05:51,380
+decreasingماشي الحال عندي الـ function is
+
+88
+00:05:51,380 --> 00:05:55,620
+decreasing على كل الفترة من واحد إلى ما لا نهاية
+
+89
+00:05:55,620 --> 00:06:00,280
+يعني الآن عندي هي اللي هي من واحد الـ function من
+
+90
+00:06:00,280 --> 00:06:03,420
+عند واحد إلى ما لا نهاية عملها اشمالها decreasing
+
+91
+00:06:04,130 --> 00:06:07,430
+الآن بقى جبت أجسم اللي هو خلّيني أخد الفترة هذه
+
+92
+00:06:07,430 --> 00:06:12,210
+ببدأ من عند X note بواحد X بواحد بصير اتنين اللي
+
+93
+00:06:12,210 --> 00:06:19,470
+هي X واحد بصير مثلا X واحد وهذا X note وهذا X
+
+94
+00:06:19,470 --> 00:06:24,410
+تلاتة اتنين X تلاتة لعند الفترة النموذجية X K و X
+
+95
+00:06:24,410 --> 00:06:30,700
+K minus واحد و X Kالآن هذه الفترة بدي أخد التجزئة
+
+96
+00:06:30,700 --> 00:06:36,760
+بعد إذنكم الـ X12 والـ X23 والـ XK-1 اللي هي عبارة
+
+97
+00:06:36,760 --> 00:06:41,560
+عن K-1 وهذه منين؟ الـ K حر أنا بدي أجزء بالتجزئة
+
+98
+00:06:41,560 --> 00:06:45,540
+اللي أمامي اللي هتخدمني ماشي الحال الآن على الفترة
+
+99
+00:06:45,540 --> 00:06:46,020
+هذه
+
+100
+00:06:48,590 --> 00:06:53,010
+على الفترة هذه هيها عندي اللي هو هذه طولها إيه
+
+101
+00:06:53,010 --> 00:06:56,930
+شمالها طولها بساوي واحد لإنه من K minus واحد لعند
+
+102
+00:06:56,930 --> 00:07:01,790
+مين لعند K اللي هو و أخدت طول كل واحد أجداش عبارة
+
+103
+00:07:01,790 --> 00:07:05,950
+عن واحد فصارت هذه عبارة عن واحد الآن بدي أدرس اللي
+
+104
+00:07:05,950 --> 00:07:11,670
+هو هذه المنطقة و أقارنهااللي هو بالمساحة الى ال F
+
+105
+00:07:11,670 --> 00:07:17,970
+of K و F of K-1 لنشوف إيش اللي بحكي عشان أصل لللي
+
+106
+00:07:17,970 --> 00:07:23,070
+بديه انت بيحكيه الآن لو جينا طلعنا لعند .. عند ..
+
+107
+00:07:23,070 --> 00:07:28,830
+من عند K-1 لعند K لأن K هذه أكيد K عندي اللي هي من
+
+108
+00:07:28,830 --> 00:07:33,050
+اتنينه طالعماشي الحالة ان الفطر تبدأ من عند مين من
+
+109
+00:07:33,050 --> 00:07:36,670
+عند واحد إلى ما لنهاية إذا عندي K بتساوى اتنين او
+
+110
+00:07:36,670 --> 00:07:40,390
+تلاتة او اربع او خمسة ايه اللي بديها اللي هنخليني
+
+111
+00:07:40,390 --> 00:07:45,670
+اجي المساحة تحت المنحنة هذاالمساحة تحت المنحنة هذا
+
+112
+00:07:45,670 --> 00:07:49,290
+هو عبارة عن قيمة ال integration لل function تبعتنا
+
+113
+00:07:49,290 --> 00:07:53,190
+هذه اللي هي decreasing من وين لو عند k نقص واحد
+
+114
+00:07:53,190 --> 00:07:56,910
+لعند مين لعند k إذا ال integration من k minus واحد
+
+115
+00:07:56,910 --> 00:08:00,630
+لعند k f of t dt لأن ال function positive تمثل هذه
+
+116
+00:08:00,630 --> 00:08:06,260
+المساحة تحت المنحنةطيب، الان لو جينا للمساحة اللي
+
+117
+00:08:06,260 --> 00:08:11,580
+هي الان هذا طوله قيمته واحد و هذا الان قيمته لهنا
+
+118
+00:08:11,580 --> 00:08:16,820
+F of K minus واحد المساحة هذه هيها الشكل هذا
+
+119
+00:08:16,820 --> 00:08:21,660
+مساحته اللي هو عبارة عن مساحة المستطيل اللي طوله
+
+120
+00:08:21,660 --> 00:08:26,060
+.. اللي عرضه واحد وطوله مين؟ F of K minus واحد
+
+121
+00:08:26,060 --> 00:08:29,880
+الان F of K minus واحد في واحد أكيد هذه المساحة
+
+122
+00:08:29,880 --> 00:08:34,380
+واضحةإنها أكبر أو يساوي ال integration اللي عندي
+
+123
+00:08:34,380 --> 00:08:39,060
+الان او المساحة تحت المنحنة الان في المقابل لو
+
+124
+00:08:39,060 --> 00:08:46,420
+جينا تطلعنا لأ اللي هي المساحة اللي بيمثلها F of K
+
+125
+00:08:46,420 --> 00:08:51,910
+F of K هي طولهفي مين في اللي هو واحد هذا واحد طوله
+
+126
+00:08:51,910 --> 00:08:56,870
+هذه الآن مساحتها أكيد أصغر من مساحة مين اللي هي
+
+127
+00:08:56,870 --> 00:09:00,890
+المساحة تحت المنحنة يعني بمعنى آخر هيكون هذه
+
+128
+00:09:00,890 --> 00:09:04,770
+المساحة اللي هي F of K في واحد اللي هي F of K يعني
+
+129
+00:09:04,770 --> 00:09:09,010
+أصغر بسهول integration اللي أمامي اللي عندي يعني
+
+130
+00:09:09,010 --> 00:09:12,530
+هذا اللي هو تمام هذا اللي أنا مسميها تسعة أو
+
+131
+00:09:12,530 --> 00:09:17,260
+تمانية أو اللي هي هذه هيكون عندي المساحةالكبيرة
+
+132
+00:09:17,260 --> 00:09:19,960
+هذه أكبر أو يساوي المساحة تحت الملحانة الـ
+
+133
+00:09:19,960 --> 00:09:26,140
+integration أصغر أو يساوي أو أكبر أو يساوي المساحة
+
+134
+00:09:26,140 --> 00:09:30,680
+الأخيرة اللي هي المستطيل هذا اللي طوله F of K في
+
+135
+00:09:30,680 --> 00:09:38,690
+مين أو عرض واحد يعنيK في الواحد يعني F of K أصغر و
+
+136
+00:09:38,690 --> 00:09:39,770
+أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و
+
+137
+00:09:39,770 --> 00:09:42,770
+أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و
+
+138
+00:09:42,770 --> 00:09:43,150
+أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و
+
+139
+00:09:43,150 --> 00:09:44,770
+أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و
+
+140
+00:09:44,770 --> 00:09:56,800
+أصغر و أصغر و أصغر و أصغر و أصغر و أصغر و أصغرلأ
+
+141
+00:09:56,800 --> 00:10:02,120
+اللي هو هذا المقدار كله من عند N من عند 1 لعند N
+
+142
+00:10:02,120 --> 00:10:08,720
+يعني صار عندي الآن ال summation ال summation لل F
+
+143
+00:10:08,720 --> 00:10:14,560
+of K كي من عند 2 لعند Nأصغر أو يساوي ال
+
+144
+00:10:14,560 --> 00:10:22,220
+integration summation طبعاً K-1 لعند K F of T DT K
+
+145
+00:10:22,220 --> 00:10:27,360
+من عند 2 لعند N أصغر أو يساوي ال summation F of K
+
+146
+00:10:27,360 --> 00:10:35,100
+-1 K من عند 2 لعند N تلاحظ هذا ال summation اللي
+
+147
+00:10:35,100 --> 00:10:41,060
+هو من عند 2 يعني ال integration من 1 ل2زاد ال
+
+148
+00:10:41,060 --> 00:10:46,820
+integration من 2 ل 3 زاد من 3 ل 4 لما نقصل من عند
+
+149
+00:10:46,820 --> 00:10:52,140
+اللي هو N ماقص 1 ل عند ال N يعني كل مجموع هذا
+
+150
+00:10:52,140 --> 00:10:56,800
+هيبقى عبارة عن ال integration من 1 ل عند ال N هذا
+
+151
+00:10:56,800 --> 00:11:02,360
+F of T DT أزرع وساوي ال summation هذا اللي هو
+
+152
+00:11:02,360 --> 00:11:10,170
+عبارة عن F ofK من عند 2 أفف 2 ناقص أفف 1 يعني أفف
+
+153
+00:11:10,170 --> 00:11:18,810
+واحد زيد أفف 2 زيد أفف N ناقص 1ماشي الحال الان هذا
+
+154
+00:11:18,810 --> 00:11:22,610
+اكبر او يساوي هذا ال summation عبارة عن مين يا
+
+155
+00:11:22,610 --> 00:11:27,670
+جماعة اللي هو عبارة عن F of 2 زي F of 3 لما اصل
+
+156
+00:11:27,670 --> 00:11:32,450
+عند اخر واحد اللي هو F of N في الواقع هذا مين هذا
+
+157
+00:11:32,450 --> 00:11:38,130
+عبارة عن SN نفسه بس خاسس مين منه ال F of 1 يعني
+
+158
+00:11:38,130 --> 00:11:42,050
+ناقص F of 1 اصغر او ساوي ال integration من 1 and N
+
+159
+00:11:42,050 --> 00:11:46,970
+F of T DTأصغر أو يساوي هذا عبارة عن ال summation
+
+160
+00:11:46,970 --> 00:11:51,450
+لمين من عند واحد لعند N ناقص واحد يعني S N ناقص
+
+161
+00:11:51,450 --> 00:11:55,910
+واحد لذا حصلنا على اللي هي ال equality اللي أمامي
+
+162
+00:11:55,910 --> 00:12:00,910
+اللي هو التالية عند ال integration من واحد لعند N
+
+163
+00:12:00,910 --> 00:12:06,190
+F of PDT صارت بين ال S N ناقص واحد وأكبر أو يساوي
+
+164
+00:12:06,190 --> 00:12:13,290
+S N ناقص اللي هي F of واحد طيب نيجي الآن نكمل اللي
+
+165
+00:12:13,940 --> 00:12:21,700
+بدنا ياه او نوصل للي بدنا ياه الان عندي اللي هو
+
+166
+00:12:21,700 --> 00:12:27,300
+صارت اللي هي القيمة هذه هيها بين اللي هو S N ناقص
+
+167
+00:12:27,300 --> 00:12:33,020
+واحد و اكبر او يساوي S N ناقص مين F of واحد الان
+
+168
+00:12:33,020 --> 00:12:36,980
+لو فرضنا ان ال limit لل S N exist يعني ال series
+
+169
+00:12:36,980 --> 00:12:40,940
+هذه ال summation مع ناخر F of K من واحد لما لها
+
+170
+00:12:40,940 --> 00:12:44,960
+نهاية او من اتنين لما نهاية existهيكون عندى هذا
+
+171
+00:12:44,960 --> 00:12:48,840
+exist و هذا exist لازم ال limit اللى فى النص ايش
+
+172
+00:12:48,840 --> 00:12:52,500
+ماله برضه يطلع ايش ماله exist اذا صار limit
+
+173
+00:12:52,500 --> 00:12:55,680
+للمبروبر انتجرال exist يعنى لو كانت ال series
+
+174
+00:12:55,680 --> 00:13:00,280
+converts هتكون المبروبر انتجرال ايش ماله converts
+
+175
+00:13:00,580 --> 00:13:04,540
+الان بنفس الطريقة هنعمل مين؟ هنعمل اللي هو
+
+176
+00:13:04,540 --> 00:13:08,820
+بالنسبالة مين؟ بالنسبالة اللي هي conversely بدنا
+
+177
+00:13:08,820 --> 00:13:12,440
+نفترض أن الـ improper integral converge ونصل أنه
+
+178
+00:13:12,440 --> 00:13:19,180
+ال series converge الان زي ما قلنا Sn ناقص F of 1
+
+179
+00:13:19,180 --> 00:13:23,720
+طلعت عندي أصغر أو ساوي ال integration من 1 ل N F
+
+180
+00:13:23,720 --> 00:13:30,360
+of T DT وهذا أصغر أو ساوي Sn ناقص 1الان انا زي ما
+
+181
+00:13:30,360 --> 00:13:35,360
+حصرت اللي هي فرضت انا limit الاس ان exist وحصرت ال
+
+182
+00:13:35,360 --> 00:13:38,640
+integration بين اللي هو اتنين ال summation هدول ال
+
+183
+00:13:38,640 --> 00:13:41,960
+partial sums وقلنا هذا exist ال limit له و هذا
+
+184
+00:13:41,960 --> 00:13:45,660
+exist له اذا هذا ايه الشمال اللي جوا exist بدي
+
+185
+00:13:45,660 --> 00:13:50,280
+اعمل في ال integration او في ال integration اللي
+
+186
+00:13:50,280 --> 00:13:53,580
+عملته مع اللي هو مين اللي هو ال partial sums او
+
+187
+00:13:53,580 --> 00:13:58,310
+الimprover integral مع ال series كيف؟لأن هذا صحيح
+
+188
+00:13:58,310 --> 00:14:04,050
+لكل ان باشي الحال الان عندى هذا أكيد أكبر أو يساوي
+
+189
+00:14:04,050 --> 00:14:08,310
+الان لو قولنا أصغر أو يساوي أسئل ناقص واحد عندى
+
+190
+00:14:08,310 --> 00:14:11,530
+أسئل ناقص أفف واحد أكبر أو يساوي هذا أصغر أو يساوي
+
+191
+00:14:11,530 --> 00:14:15,930
+هذا وهذا أصغر أو يساوي مين؟ الثاني اللى عندى هذا
+
+192
+00:14:15,930 --> 00:14:21,830
+الآن عندى بدي أحصر هذا أخليه بين two integrations
+
+193
+00:14:21,830 --> 00:14:26,090
+أو أخلي هذا بين two integrations أي واحد منهم بنفع
+
+194
+00:14:26,680 --> 00:14:30,780
+الأن عندي من هذا نفسه ال integration من واحد لعلن
+
+195
+00:14:30,780 --> 00:14:39,500
+f of t dt صار اللي هو زائد f of واحد أكبر أو يساوي
+
+196
+00:14:39,500 --> 00:14:45,860
+مين ال snماشي ال S N من هنا من هنا ال S N أكبر أو
+
+197
+00:14:45,860 --> 00:14:49,460
+يساوي اللي هو ال integration من واحد بدل ال N نقص
+
+198
+00:14:49,460 --> 00:14:54,040
+واحد حطيت مين ال N ماشي فبصير عند هذه بدل ال N
+
+199
+00:14:54,040 --> 00:14:58,740
+برضه بتصير ال integration من F of T DT من واحد
+
+200
+00:14:58,740 --> 00:15:02,240
+لعند N زائد واحد لأنه هذه أكبر من هذه بيهاشب واحد
+
+201
+00:15:02,240 --> 00:15:05,900
+هي هذه أكبر من هذه بواحد من الفوق إذا صار عند ال S
+
+202
+00:15:05,900 --> 00:15:10,300
+N بين هذه الكمية و هذه الكمية لأن لو فرضنا أنه ال
+
+203
+00:15:10,300 --> 00:15:16,770
+limitللـ integration من 1 ل N F of T DT as N goes
+
+204
+00:15:16,770 --> 00:15:21,690
+to infinity exist مدام هذا exist ال limit إذا حصل
+
+205
+00:15:21,690 --> 00:15:25,630
+هذا كله على بعض هذا limit exist و هذا هيتلع exist
+
+206
+00:15:25,630 --> 00:15:29,370
+إذا اللي هيتلع عنده limit أثر ان إيش exist إذا
+
+207
+00:15:29,370 --> 00:15:32,650
+similarly if limit لل integration أو الimproper
+
+208
+00:15:32,650 --> 00:15:37,090
+integral exist إذا هيتلع limit للأثر ان exist هو
+
+209
+00:15:37,090 --> 00:15:42,860
+يعني وضحتها أمامكمtherefore اللي أثبتناه انه ال
+
+210
+00:15:42,860 --> 00:15:45,860
+summation لل F of N N من واحد لما لا نهاية اللي هو
+
+211
+00:15:45,860 --> 00:15:49,580
+ال series exist يعني limit لل Sun exist if and
+
+212
+00:15:49,580 --> 00:15:52,360
+only if الimproper integral exist يعني limit ال
+
+213
+00:15:52,360 --> 00:15:56,100
+integration واحد لعند N exist هذا اللي هو اللي
+
+214
+00:15:56,100 --> 00:16:00,820
+أثبتناه لحتى الآن الآن ضال علي أثبت الجزء الثاني
+
+215
+00:16:00,820 --> 00:16:08,360
+من اللي هو النظرية اللي هو في حالة مينالـ
+
+216
+00:16:08,360 --> 00:16:14,140
+Convergence في حالة الـ Convergence لـ Series أو
+
+217
+00:16:14,140 --> 00:16:19,300
+لـ Improbable Integral بدنا نحقق الـ Estimate اللي
+
+218
+00:16:19,300 --> 00:16:25,220
+هو .. اللي هو عندي S ناقص S N يكون بين اللي هو الـ
+
+219
+00:16:25,220 --> 00:16:29,160
+Two Integration اللي حكينا عنه اشي اللي بقوله نشوف
+
+220
+00:16:29,160 --> 00:16:32,600
+الان
+
+221
+00:16:32,600 --> 00:16:41,210
+نيجي نركز الان finallyassuming ال relation a for k
+
+222
+00:16:41,210 --> 00:16:46,810
+بساوة n summing the relation a for k بالن زائد
+
+223
+00:16:46,810 --> 00:16:49,890
+واحد لعند n we obtain ايش هي ال relation اللي
+
+224
+00:16:49,890 --> 00:16:53,530
+حطيتها قبل و شوية اللي عبارة عن ال integration من
+
+225
+00:16:53,530 --> 00:16:58,430
+واحد لعند n f of t dt أصغر أو يساوي هتبتدى
+
+226
+00:16:58,430 --> 00:17:02,490
+استخدامها كمان مرة للوصول لل estimation اللي بديها
+
+227
+00:17:03,180 --> 00:17:07,240
+أظهر يساوي أس أن ناقص واحد وأكبر أو يساوي مين يا
+
+228
+00:17:07,240 --> 00:17:13,400
+جماعة اللي هو أس أن ناقص أف of واحد الان هذه بدنا
+
+229
+00:17:13,400 --> 00:17:17,780
+اللي هو نعمل summation لها من أن زائد واحد لعند
+
+230
+00:17:17,780 --> 00:17:24,440
+مين لعند أم يعني بدي أجي اللي هو أعمل ال summation
+
+231
+00:17:24,440 --> 00:17:38,450
+اللي أمامي فبصير عندىالـ Summation لمن ؟ لـ N زائد
+
+232
+00:17:38,450 --> 00:17:43,410
+واحد لعند مين لعند N خلّينا نجمحها خد الـ
+
+233
+00:17:43,410 --> 00:17:48,490
+Summationالـ summation عندي هي عندي بيصير ال
+
+234
+00:17:48,490 --> 00:17:54,990
+summation ل ال integration اللي
+
+235
+00:17:54,990 --> 00:17:59,390
+أمامي خلّيني أرجعلكم لها بس عشان تكون الأمور ت ..
+
+236
+00:17:59,390 --> 00:18:03,530
+ت .. من وين .. قبل .. لأ آسف مش هذه نيجي لها اللي
+
+237
+00:18:03,530 --> 00:18:07,370
+هي تسعة اللي هالة لإن هذه بعد ما انتجمعت الآن بدي
+
+238
+00:18:07,370 --> 00:18:14,830
+أجمعها من عند اللي هو and زائد واحد لعند اللي هو
+
+239
+00:18:17,110 --> 00:18:23,930
+حيث M أكبر من N خلّيني أجمحها هذه لأن هذه مجموعة
+
+240
+00:18:23,930 --> 00:18:29,230
+خالصة خلّيني أجمح هذه لأن خد اجمع لي هذه عندي خد
+
+241
+00:18:29,230 --> 00:18:33,610
+summation حسابات summation K من عند N زائد واحد
+
+242
+00:18:33,610 --> 00:18:39,300
+لعند Mحيث اللي هو الـ N مفترضها أكبر من N اللي هي
+
+243
+00:18:39,300 --> 00:18:43,060
+أصغر أو سوى summation K من N زائد واحد لعند M
+
+244
+00:18:43,060 --> 00:18:48,460
+حسابات summation K من عند M زائد واحد لعند مين
+
+245
+00:18:48,460 --> 00:18:55,170
+لعند Mالان هذا في الواقع يا جماعة احنا قلنا ال S N
+
+246
+00:18:55,170 --> 00:19:02,070
+هي summation لل F of K K من عند اللي هو واحد لعند
+
+247
+00:19:02,070 --> 00:19:07,430
+مين لعند N وقلنا ال S N طبيعي هتكون summation لل F
+
+248
+00:19:07,430 --> 00:19:14,690
+of K K من عند واحد لعند Nالان اطرح هذه من هذه هيظل
+
+249
+00:19:14,690 --> 00:19:17,870
+ال summation من n زائد واحد لعند مين عند ان يعني
+
+250
+00:19:17,870 --> 00:19:23,030
+هذه في الواقع هي عبارة عن S M ناقص إيش ناقص S N
+
+251
+00:19:23,030 --> 00:19:27,610
+أصغر أو يساوي ال summation اللي أمامي ال summation
+
+252
+00:19:27,610 --> 00:19:34,130
+هذا اللي هو من عند n زائد واحد من n زائد واحد لعند
+
+253
+00:19:34,130 --> 00:19:44,700
+n ومن n لعند n زائد اتنينو من N زائد 2 لعند N زائد
+
+254
+00:19:44,700 --> 00:19:48,900
+3 لما أصل من عند M ناقص واحد لعند M زي ما عملنا
+
+255
+00:19:48,900 --> 00:19:58,590
+قبل و شوية هيطلع عبارة عن من N لمين لعند MDT هذا
+
+256
+00:19:58,590 --> 00:20:02,770
+أصغر أو ساوي اللي هو ال summation اللي هو الأخير
+
+257
+00:20:02,770 --> 00:20:09,050
+بنفس الأسلوب ونشوف إيش اللي هيلزمنا عندي هذا زي ما
+
+258
+00:20:09,050 --> 00:20:11,790
+عملت فوق بالظبط بس هذه بتاخدها في عيننا اعتبار ان
+
+259
+00:20:11,790 --> 00:20:16,970
+هي بتبدأ من عند من عند K-1 يعني اللي هي هذه بتبدأ
+
+260
+00:20:16,970 --> 00:20:22,930
+تصير N لعند اللي هو مين اللي هي M-1 يعني بمعنى آخر
+
+261
+00:20:22,930 --> 00:20:29,530
+عبارة عن SM-1أسأل نقص واحد حسب ما اللي هي حسبنا
+
+262
+00:20:29,530 --> 00:20:34,530
+فوق أو زي ما حسبنا فوق فبنكون حصلنا على هذه الـ
+
+263
+00:20:34,530 --> 00:20:38,310
+Inquality نشوف هذه الـ Inquality كيف بدنا نستخدمها
+
+264
+00:20:38,310 --> 00:20:43,750
+للوصول للي بدناياالأن M أكبر من N أكيد فعندي أسأن
+
+265
+00:20:43,750 --> 00:20:48,870
+ناقص أسئن اللي هي صارت اللي هي أصغر أو يساوي ال
+
+266
+00:20:48,870 --> 00:20:52,490
+integration من M لعند M اللي أوجدتها و أصغر أو
+
+267
+00:20:52,490 --> 00:20:55,910
+يساوي الأسئن minus واحد ناقص أسئن ناقص واحد زي ما
+
+268
+00:20:55,910 --> 00:21:01,280
+قلنا اللي هاد سمناها إيه ياش أستارالان من الـ star
+
+269
+00:21:01,280 --> 00:21:06,560
+خلّينا نركز على المنطقة اللي هي الان بتاخد ال
+
+270
+00:21:06,560 --> 00:21:11,220
+integration من N زائد واحد عند M زائد واحد F of T
+
+271
+00:21:11,220 --> 00:21:16,420
+DTماشي الحال هيصير عبارة عن N زائد واحد وهذا M
+
+272
+00:21:16,420 --> 00:21:20,000
+زائد واحد بناء عليها هتصير M زائد واحد ناقص واحد
+
+273
+00:21:20,000 --> 00:21:24,000
+يعني M و N زائد واحد ناقص واحد يعني N فبصير ال
+
+274
+00:21:24,000 --> 00:21:27,340
+integration من N زائد واحد عند M زائد واحد F of T
+
+275
+00:21:27,340 --> 00:21:30,360
+DT أصغر و أسهر و SM ناقص من SN
+
+276
+00:21:33,320 --> 00:21:39,900
+الان بتنتين مع بعض اللي هي SM ناقص لSN هيها أصغر
+
+277
+00:21:39,900 --> 00:21:43,740
+أو شاوي ال integration من N لعند M F of T DT هي
+
+278
+00:21:43,740 --> 00:21:49,340
+هذه أصغر أو شاوي هذه كتبت هان وهذه كتبت هان SM
+
+279
+00:21:49,340 --> 00:21:51,660
+ناقص لSN أكبر من ال integration من N زائد واحد
+
+280
+00:21:51,660 --> 00:21:56,850
+لعند مين لعند M زائد واحدلأن احنا متفجرين ان الـ
+
+281
+00:21:56,850 --> 00:22:00,870
+series converge و البروبر انتيجرة converge اذا
+
+282
+00:22:00,870 --> 00:22:04,030
+الان خد ل M و وديها لما لنهاية لما احنا ماخدين ال
+
+283
+00:22:04,030 --> 00:22:07,590
+M اشمالها اكبر من الان بوديها زي ما بده و بتضلها
+
+284
+00:22:07,590 --> 00:22:11,570
+الآن زي ما بدها الان as M goes to infinity هتصير
+
+285
+00:22:11,570 --> 00:22:15,030
+هذه عبارة عن ال summation لل series يعني هتصير S
+
+286
+00:22:15,030 --> 00:22:18,600
+هذهإذاً هذا سيصبح S وهذا سيصبح لهم proper integral
+
+287
+00:22:18,600 --> 00:22:21,860
+من N زائد واحد إلى ما لا نهاية وهذا سيصبح لهم
+
+288
+00:22:21,860 --> 00:22:26,260
+proper integral من N إلى ما لا نهاية يعني سيصبح
+
+289
+00:22:26,260 --> 00:22:31,360
+لدي بالظبط الـ S ناقص S N أكبر أو يساوي من N زائد
+
+290
+00:22:31,360 --> 00:22:36,340
+واحد إلى ما لا نهاية ومن N إلى ما لا نهايةوهو هذا
+
+291
+00:22:36,340 --> 00:22:42,040
+اللي مطلوب اللي احنا طلبناه من أول النظرية وقلنا
+
+292
+00:22:42,040 --> 00:22:46,760
+حيث الـ S هي اللي بتمثل اللي هو limit لـ SM أو هي
+
+293
+00:22:46,760 --> 00:22:51,460
+عبارة عن قيمة ال series من واحد إلى ملا نهاية
+
+294
+00:22:51,820 --> 00:22:58,540
+examples بدنا الآن نحاول نستخدم اللي هو النظريات
+
+295
+00:22:58,540 --> 00:23:03,360
+اللي قبل بشوية نوظفها لل examples اللي عندنا وهذه
+
+296
+00:23:03,360 --> 00:23:07,200
+طبعا هتلاقيها معظمها انتوا أخدتوها في ال calculus
+
+297
+00:23:07,200 --> 00:23:11,700
+نذكرها بشكل سريع بس عساس انه نشوف ال applications
+
+298
+00:23:11,700 --> 00:23:16,440
+لهذه النظريات اللي احنا مركزين على اللي هو النظر
+
+299
+00:23:16,440 --> 00:23:20,520
+التحليلية لها او بمعنى اخر على براهين اللي هي
+
+300
+00:23:20,520 --> 00:23:24,020
+النظرياتShow that the b series summation 1 ده لأن
+
+301
+00:23:24,020 --> 00:23:29,440
+b diverges for b أصغر أو يساوي 1 الان بدنا نستخدم
+
+302
+00:23:29,440 --> 00:23:34,920
+ال comparison testفعنده الان أن قص بي أصغر أو
+
+303
+00:23:34,920 --> 00:23:38,940
+يساوي أن أكيد لكل أن element in N و ال بي أشمالها
+
+304
+00:23:38,940 --> 00:23:42,120
+أصغر أو يساوي واحد يعني ل ال بي اللي أصغر من واحد
+
+305
+00:23:42,120 --> 00:23:47,080
+هيكون أن قص بي أكيد أصغر أو يساوي من أن الان مقلبه
+
+306
+00:23:47,080 --> 00:23:50,140
+هينقلب واحدة لأن بي أكبر أو يساوي واحدة لأن الان
+
+307
+00:23:50,140 --> 00:23:54,800
+ال summation هذا اللي diverseإذا من باب أولى هيكون
+
+308
+00:23:54,800 --> 00:23:58,380
+الكبير by comparison test diverse إذا ال summation
+
+309
+00:23:58,380 --> 00:24:01,400
+واحد على N بيه diverse for بيه أصغر أو يساوي واحد
+
+310
+00:24:01,400 --> 00:24:04,860
+وهذا الكلام سهل وانتوا بتعرفوه إذا نيجي لل
+
+311
+00:24:04,860 --> 00:24:08,540
+summation واحد على N تربيع بدنا نشوف كيف هي إياش
+
+312
+00:24:08,540 --> 00:24:12,740
+converseبدنا الآن نقارنها بـ Series إحنا أخدناها
+
+313
+00:24:12,740 --> 00:24:15,620
+إنها ضعيفة Converse مين الـ Series اللي أخدناها
+
+314
+00:24:15,620 --> 00:24:18,100
+الـ Converse اللي هي الـ Telescoping اللي هي
+
+315
+00:24:18,100 --> 00:24:21,620
+Summation واحدة لـ N في N زائد واحد قلنا عنها دي
+
+316
+00:24:21,620 --> 00:24:24,220
+إيش مالها أثبتناها المرة الماضية إنها Converse
+
+317
+00:24:24,220 --> 00:24:28,640
+طيب، الآن هذه مدام هي هت Converge السيريز اللي عند
+
+318
+00:24:28,640 --> 00:24:34,160
+السيريز هت Converge إذا by example اللي هو 918E هت
+
+319
+00:24:34,160 --> 00:24:37,840
+Converge بدنا اللي هو نستخدم اللي هو الـ
+
+320
+00:24:37,840 --> 00:24:41,180
+Comparison Testالان ماقدرش نستخدم ال direct ليش
+
+321
+00:24:41,180 --> 00:24:45,280
+ماقدرش نستخدم ال direct لإنه الان ال summation
+
+322
+00:24:45,280 --> 00:24:50,440
+اللي هو ال ال ال واحد على n في n زائد واحد اللي هي
+
+323
+00:24:50,440 --> 00:24:53,880
+ال convergence هذه اللي هي أصغر أو يساوي واحد على
+
+324
+00:24:53,880 --> 00:24:57,800
+مين على n تربيع فالان هذه convergence صح لكن اللي
+
+325
+00:24:57,800 --> 00:25:00,120
+أكبر منها مش شرط انها تكون convergence وماقدرش
+
+326
+00:25:00,120 --> 00:25:04,080
+نحكم ال comparison test إذا بدنا نستخدم ال limit
+
+327
+00:25:04,080 --> 00:25:07,380
+comparison testخد ال limit اللي هي 1 على n فان
+
+328
+00:25:07,380 --> 00:25:11,040
+زائد 1 على 1 على n تربيع بيصير limit عبارة عن n
+
+329
+00:25:11,040 --> 00:25:14,680
+على n زائد 1 مع الاختصارات اللي هو طبعا هذا ال
+
+330
+00:25:14,680 --> 00:25:17,360
+limit اللي هي as n goes to infinity هذي بيصير 1
+
+331
+00:25:17,360 --> 00:25:20,820
+على 1 زائد 1 على n هذي بتروح للسفر و بتظلها 1 و ال
+
+332
+00:25:20,820 --> 00:25:24,140
+1 أكيد مش سفر ما زي ما يطلع عند ال limit لأ اللي
+
+333
+00:25:24,140 --> 00:25:28,310
+هو ال .. ال .. ال .. ال ..الـ .. ال .. ال .. ال
+
+334
+00:25:28,310 --> 00:25:30,870
+limit لـ ال .. ال .. ال comparison test أو اللي هي
+
+335
+00:25:30,870 --> 00:25:33,990
+ال two series هذول اللي على بعض ال XN على ال YN
+
+336
+00:25:33,990 --> 00:25:37,610
+بساوي رقم إذا التنتين converged أو التنتين
+
+337
+00:25:37,610 --> 00:25:41,550
+diverged وبناء على الحديث إنه بما إنه هذه اللي هي
+
+338
+00:25:41,550 --> 00:25:45,090
+ال telescope كانت converged إذا الواحد على N تربيع
+
+339
+00:25:45,090 --> 00:25:50,530
+أو صمشي للواحد على N تربيع is convergent طيب هذا
+
+340
+00:25:50,530 --> 00:25:56,030
+كلام كله انتوا طبعا بتاخدوه في ال ..هو أخدته كثير
+
+341
+00:25:56,030 --> 00:25:58,830
+منه في ال calculus ولكن احنا عشان يكتمل الموضوع
+
+342
+00:25:58,830 --> 00:26:02,770
+بدنا ناخد أمثلة على اللي برهنناهم اللي هان show
+
+343
+00:26:02,770 --> 00:26:08,190
+that summation 1 على n بي converts for b يشمل أكبر
+
+344
+00:26:08,190 --> 00:26:12,370
+أو يساوي واحد بي أكبر أو يساوي أسف أكبر من واحد
+
+345
+00:26:12,370 --> 00:26:15,270
+strictlyP أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+346
+00:26:15,270 --> 00:26:16,850
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+347
+00:26:16,850 --> 00:26:22,690
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+348
+00:26:22,690 --> 00:26:25,810
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+349
+00:26:25,810 --> 00:26:28,150
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+350
+00:26:28,150 --> 00:26:29,090
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+351
+00:26:29,090 --> 00:26:30,170
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+352
+00:26:30,170 --> 00:26:30,770
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+353
+00:26:30,770 --> 00:26:34,550
+أكبر أو P أكبر أو P أكبر أو P أكبر أو P أكبر أو P
+
+354
+00:26:34,550 --> 00:26:40,020
+أكبرالـ second method بيقولك أنا بدي استخدم ال
+
+355
+00:26:40,020 --> 00:26:44,000
+limit comparison test اللي هو 1 على N أقص بي على 1
+
+356
+00:26:44,000 --> 00:26:48,360
+على N تربيع بيساوي limit 1 على N بي minus 2 و بي
+
+357
+00:26:48,360 --> 00:26:53,000
+أكبر من أو يساوي 2 إذا 1 على N بي minus 2 اللي هو
+
+358
+00:26:53,000 --> 00:26:57,660
+هيساوي limit 0 مدام ال limit 0 وعندي اللي هي اللي
+
+359
+00:26:57,660 --> 00:27:02,000
+تحت converge إذا من باب أولى اللي فوق تكون
+
+360
+00:27:02,000 --> 00:27:06,130
+converge إذا summation 1 على N بياللي هو convert
+
+361
+00:27:06,130 --> 00:27:14,370
+by limit comparison test طيب show
+
+362
+00:27:14,370 --> 00:27:19,170
+that the ratio and the root tests fail in the case
+
+363
+00:27:19,170 --> 00:27:22,570
+of B series يعني الآن لو بدنا نجرب نستخدم ال ratio
+
+364
+00:27:22,570 --> 00:27:26,310
+test وال root test مش هتظبط طبعا ال limit بنقصته
+
+365
+00:27:26,310 --> 00:27:31,680
+ليش؟ بقولك لو جينا أخدنا limitالـ 1 على N أُس B
+
+366
+00:27:31,680 --> 00:27:36,080
+أُس 1 على N الـ N through test هذا بيساوي ال limit
+
+367
+00:27:36,080 --> 00:27:41,200
+و N أُس 1 على N أُس minus B ماشي ال N أُس 1 على N
+
+368
+00:27:41,200 --> 00:27:43,840
+ال limit اللي لها من example أخدناها في شبطر 3 في
+
+369
+00:27:43,840 --> 00:27:49,080
+الفصل الماضي أو في تحليل 1 هذا و برضه بتقف تعملوا
+
+370
+00:27:49,080 --> 00:27:52,340
+أصلا لحالكمالـ limit له بيساوي واحد إذا صار عندى
+
+371
+00:27:52,340 --> 00:27:56,580
+واحد أقصى minus b إذا بيساوي إيش واحد الان مدام
+
+372
+00:27:56,580 --> 00:28:01,500
+طالع عندى ال limit اللي هو ال Xn أقصى واحدة الان
+
+373
+00:28:01,500 --> 00:28:05,020
+بيساوي واحد إذا بيقول ال test failed الان
+
+374
+00:28:05,020 --> 00:28:10,320
+similarly لو جربنا اللي هو ال ratio test واحدة
+
+375
+00:28:10,320 --> 00:28:13,300
+الان زيادة واحدة أقصى b على واحدة أن أقصى b بيساوي
+
+376
+00:28:13,300 --> 00:28:18,930
+ال limitلا اللي هي 1 على 1 زائد 1 على أنقص بي
+
+377
+00:28:18,930 --> 00:28:23,130
+عارفين إيش اللي سوناه اللي هو جسمنا اللي هي اللي
+
+378
+00:28:23,130 --> 00:28:26,770
+هنا على أنقص بي وهنا على أنقص بي صارت 1 هذا على
+
+379
+00:28:26,770 --> 00:28:29,910
+أنقص بي وهذا على أنقص بي بيصير 1 زائد 1 لأن كل أس
+
+380
+00:28:29,910 --> 00:28:34,080
+بيالان صار عندى limit as n goes to infinity لازم
+
+381
+00:28:34,080 --> 00:28:39,040
+يصير 1 اذا ال test برضه ال ratio test فاش فال اذا
+
+382
+00:28:39,040 --> 00:28:46,700
+مانفعش انحل ال b series by ال ratio test و لا ال
+
+383
+00:28:46,700 --> 00:28:48,200
+anthro test
+
+384
+00:28:55,790 --> 00:29:01,050
+الان بقول لي ايش رايك تستخدمنا اللي هو الـ
+
+385
+00:29:01,050 --> 00:29:06,360
+Integral Test تشوفه بظبط في الـ B Series ولا لألت
+
+386
+00:29:06,360 --> 00:29:11,680
+F of T بيساوي T Os minus B ده المؤهلة انها اللي هي
+
+387
+00:29:11,680 --> 00:29:16,560
+تكون اللي هي الاستخدام اللي هي واحد على T أوس بي
+
+388
+00:29:16,560 --> 00:29:21,320
+واحد على T أوس بي الان وهذه ال series decreasing
+
+389
+00:29:21,320 --> 00:29:24,960
+ويمحلاها الى اخره and recalled that ال integration
+
+390
+00:29:24,960 --> 00:29:28,580
+من واحد لعند ان واحد على T DT ايش بيساوي سهل
+
+391
+00:29:28,580 --> 00:29:31,820
+ايجادها كمان عبارة عن لن الان ناقص لن الواحد لن
+
+392
+00:29:31,820 --> 00:29:36,080
+الواحد سفر يعني بتبقى عند لن الانلكن as n goes to
+
+393
+00:29:36,080 --> 00:29:39,700
+infinity واضح إن هذا مباشرة هيروح إلى مالة نهاية
+
+394
+00:29:39,700 --> 00:29:45,020
+يعني هذا عبارة عن diverse إذا صارت عندي الصممش
+
+395
+00:29:45,020 --> 00:29:49,040
+للواحد الان diverse by integral test عندي طبعا ال
+
+396
+00:29:49,040 --> 00:29:55,360
+b أشمال هنا بي أصغر أو تساوي الواحد الآن في حالة
+
+397
+00:29:55,360 --> 00:30:00,040
+.. لا لا آسف ال b هنا بتساوي الواحد الآن بدنا نشوف
+
+398
+00:30:00,040 --> 00:30:06,420
+مين إن هي الحالات التانيةلو جينا ال integration
+
+399
+00:30:06,420 --> 00:30:12,560
+احنا اثبتنا لمين لـ B بتساوي واحد الان also recall
+
+400
+00:30:12,560 --> 00:30:16,780
+that ال integration واحد على T قص بي دي T من واحد
+
+401
+00:30:16,780 --> 00:30:21,120
+لعند مين واحد لعند انا بنفضل عندنا ال بي اشمال هنا
+
+402
+00:30:21,120 --> 00:30:26,040
+لاتساوي واحد كملة الآن بيصير واحد على واحد minus
+
+403
+00:30:26,040 --> 00:30:30,480
+بي انقص واحد على minus بي ناقص واحد بعد ما عوضنا
+
+404
+00:30:30,480 --> 00:30:31,860
+الان هذه
+
+405
+00:30:34,860 --> 00:30:41,960
+as n goes to infinity وكانت ال b أكبر من واحد إذا
+
+406
+00:30:41,960 --> 00:30:46,520
+ال b أكبر من واحد إذا ال b أكبر من واحد وودينا n
+
+407
+00:30:46,520 --> 00:30:52,400
+إلى ما لا نهاية هذا سيصبح عبارة عن سفر وهذا عبارة
+
+408
+00:30:52,400 --> 00:30:56,240
+عن ناقص واحديعني ال limit هذه as n goes to
+
+409
+00:30:56,240 --> 00:31:00,060
+infinity في حالة ال B أكبر من واحد هتصير هذه عبارة
+
+410
+00:31:00,060 --> 00:31:03,940
+عن ناقص واحد في هذه بيصير واحد على B minus واحد
+
+411
+00:31:03,940 --> 00:31:08,540
+هذا في حالة ال B أكبر من واحد إذا صارت اللي هي ال
+
+412
+00:31:08,540 --> 00:31:12,640
+integration هذا converge وبناء عليه هتكون ال B
+
+413
+00:31:12,640 --> 00:31:16,180
+series في حالة ال B أكبر من واحد by integral test
+
+414
+00:31:16,180 --> 00:31:21,460
+برضه أيهاش converge لكن لو كانت ال B أصغر من واحد
+
+415
+00:31:22,000 --> 00:31:25,480
+الان فبصير عندي هذا اللي هو بروح إلى مالة نهاية
+
+416
+00:31:25,480 --> 00:31:29,260
+فبصير عندي لأن الـ B أصغر من واحد فبصير عندي ال
+
+417
+00:31:29,260 --> 00:31:33,500
+integration هذا as N goes to infinity diverges و
+
+418
+00:31:33,500 --> 00:31:37,400
+بناء عليه summation واحد على N B diverges هذا في
+
+419
+00:31:37,400 --> 00:31:42,060
+حالة الـ B أشمالها أصغر من واحد و بكون هيك احنا
+
+420
+00:31:42,060 --> 00:31:46,220
+استخدمنا ال .. ال .. ال B series في إثبات ال .. ال
+
+421
+00:31:46,220 --> 00:31:49,620
+.. ال integral test في إثبات أنه ال B series
+
+422
+00:31:49,620 --> 00:31:56,810
+convergesfor b أكبر من واحد and diverges for b أيش
+
+423
+00:31:56,810 --> 00:32:01,950
+ما لها أصغر أو يساوي واحد وهذه اللي هي انتوا
+
+424
+00:32:01,950 --> 00:32:07,310
+عارفينها الـB Series المشهورة نيجي الآن بدنا نحكي
+
+425
+00:32:07,310 --> 00:32:12,990
+عن اللي هو رقاب test أحيانا اللي هو مدامة اللي هو
+
+426
+00:32:12,990 --> 00:32:18,560
+ال ratio testاللي هو fails في حالة ال limit يطلع
+
+427
+00:32:18,560 --> 00:32:24,380
+لنا واحد أو سوى واحد فبدنا إيش يخلّينا نقول يحللنا
+
+428
+00:32:24,380 --> 00:32:28,700
+مشكلة اللي هو ال failure for .. for .. for اللي هو
+
+429
+00:32:28,700 --> 00:32:33,240
+ظهور ال limit بساوة واحد هنا عندي رقابس test
+
+430
+00:32:33,240 --> 00:32:38,640
+بتعالج الأمر fx بساوة xn is a sequence of non-zero
+
+431
+00:32:38,640 --> 00:32:46,670
+elementsلو وجدنا real number a أكبر من واحد and a
+
+432
+00:32:46,670 --> 00:32:50,990
+natural number k such that xn زائد واحد على xn
+
+433
+00:32:50,990 --> 00:32:54,990
+أصغر سوى واحد نقصي n for n أكبر سوى k then ال
+
+434
+00:32:54,990 --> 00:32:58,890
+summation لل xn is absolutely ايش ماله convergent
+
+435
+00:32:59,220 --> 00:33:02,500
+إذا كان هناك a أصغر يساوي واحد وشكل الـ K طبيعي
+
+436
+00:33:02,500 --> 00:33:06,500
+كذلك الـ absolute value of xn زائد واحد على xn
+
+437
+00:33:06,500 --> 00:33:11,100
+أكبر يساوي واحد نقص a على n for n أكبر يساوي k فإن
+
+438
+00:33:11,100 --> 00:33:15,880
+سلسلة xn ليست أكتر مرتبطة يعني باختصار عشان أريحكم
+
+439
+00:33:15,880 --> 00:33:21,920
+إيش بنسوي بنحسبلناالـ xn زائد واحد على xn إذا
+
+440
+00:33:21,920 --> 00:33:26,480
+جدرنا .. إذا جدرنا نقارن هذه xn زائد واحد على xn
+
+441
+00:33:26,480 --> 00:33:31,280
+بالمقدار واحد ناقص a على n إذا لجينا إن هذا
+
+442
+00:33:31,280 --> 00:33:34,540
+المقدار .. المقدار اسمه واحد ناقص a على n إذا
+
+443
+00:33:34,540 --> 00:33:38,950
+لجينا هذاأصغر أو يساوي 1 ناقص على A على N وكانت
+
+444
+00:33:38,950 --> 00:33:43,050
+الـ A أكبر من 1 على طول بنحكم على الـ Absolutely
+
+445
+00:33:43,050 --> 00:33:47,030
+Convergent للـ Series لكن لو لجينا هذا المقدار بعد
+
+446
+00:33:47,030 --> 00:33:51,690
+ما حسبناه أكبر أو يساوي 1 ناقص A على N حتى لو كانت
+
+447
+00:33:51,690 --> 00:33:56,040
+A أصغر يساوي 1 صغيرةفبنقول إنه في هذه الحالة بنحكم
+
+448
+00:33:56,040 --> 00:33:59,760
+على إيش على إنه ال series is not absolutely
+
+449
+00:33:59,760 --> 00:34:03,500
+convergent يعني العملية عملية حسابات هذه على هذه
+
+450
+00:34:03,500 --> 00:34:08,660
+ونجيبها بدلالة 1 minus a على n أو بنقرنها ب 1
+
+451
+00:34:08,660 --> 00:34:12,840
+minus a على n 1 minus a على n في حالة إن ال a أصغر
+
+452
+00:34:12,840 --> 00:34:16,380
+يساوي واحد هتطلع لنا اللي هي هنا في هذه الحالة
+
+453
+00:34:16,380 --> 00:34:19,140
+it's not absolutely convergent في حالة ال a أكبر
+
+454
+00:34:19,140 --> 00:34:24,710
+من واحد isabsolutely convergent وخلّينا نشوف اللي
+
+455
+00:34:24,710 --> 00:34:33,230
+هو البرهان لاللي هي هذه النظرية suppose that عشرة
+
+456
+00:34:33,230 --> 00:34:39,730
+holds عشرة عشرة and اللي هي اللي قبل بشوية حكيناها
+
+457
+00:34:39,730 --> 00:34:42,930
+عشان تكونوا في صورة نقولكم عشرة نذكركم فيها هذه
+
+458
+00:34:42,930 --> 00:34:50,840
+عشرة اللي هي xn زائد واحد xn زائد واحدعلى xn أصغر
+
+459
+00:34:50,840 --> 00:34:57,220
+أو سوى 1 نقص a على n a أكبر من 1 و n أكبر أو سوى k
+
+460
+00:34:57,220 --> 00:35:01,500
+التاني هذا اللي سميناها عشرة اللي سميناها 11 اللي
+
+461
+00:35:01,500 --> 00:35:07,700
+هو xn زائد 1 على absolute value xn أكبر أو سوى
+
+462
+00:35:07,700 --> 00:35:16,820
+اللي هو 1 نقص a على n و a اللي هي a شمالها أصغر من
+
+463
+00:35:17,510 --> 00:35:23,610
+أو يساوي الواحد ماشي الحال طيب هي هذا عشرة وهذا
+
+464
+00:35:23,610 --> 00:35:28,150
+احد عشرة عشان بعد شوية هنستخدمهم في البرهان خلوكوا
+
+465
+00:35:28,150 --> 00:35:32,800
+معنا ان شاء الله البرهان مش صعبالآن suppose that
+
+466
+00:35:32,800 --> 00:35:39,080
+انه عشرة holes هيه for M أكبر أو يساوي K الآن اضرب
+
+467
+00:35:39,080 --> 00:35:43,280
+لطرفين في وسطين اضرب هذه في هذه بيصير عندي وبدل ا
+
+468
+00:35:43,280 --> 00:35:48,980
+ا بدي استخدم اللي هي M عندي بدل M زائد واحد خليني
+
+469
+00:35:48,980 --> 00:35:51,880
+بيصير عند منح دعش عشان انا اجيب لكم يادي كيف اجت
+
+470
+00:35:51,880 --> 00:35:56,870
+absolute value ل X M زائد واحدأصغر أو يساوي الـ
+
+471
+00:35:56,870 --> 00:36:02,750
+absolute value للـ XM مضروبة في واحد ناقص A على M،
+
+472
+00:36:02,750 --> 00:36:07,970
+مظبوط؟ طيب، الآن اضربولي الجهتين في مين؟ في M
+
+473
+00:36:07,970 --> 00:36:14,640
+فبصير M هنا، بصير M في هناهو بيكون حصلنا على M في
+
+474
+00:36:14,640 --> 00:36:19,700
+هذه و M في هذا المقدار دخلولي ال M الآن جوا فبصير
+
+475
+00:36:19,700 --> 00:36:23,580
+absolute value XM زي ما هي أنا بصير M ناقص اللي هي
+
+476
+00:36:23,580 --> 00:36:31,020
+AHA الان هذه بتساوي الان كتبتها على صورة الان ضفت
+
+477
+00:36:31,020 --> 00:36:35,720
+اللي هو واحد و طرحت واحد اللي هي هي عندي هنا طرحت
+
+478
+00:36:35,720 --> 00:36:39,800
+واحد و هنا ضفت الواحد فصارت عبارة عن M ناقص واحد
+
+479
+00:36:39,800 --> 00:36:44,830
+XM ناقص A minus واحد XMم أكبر يساوي K صار هذا
+
+480
+00:36:44,830 --> 00:36:50,110
+المقدار بعد ما ضفت اللي هو ناقص XM وطرحت ناقص ال
+
+481
+00:36:50,110 --> 00:36:56,590
+XM وضفت اللي هو ناقص اللي هو ضفة ال XM فصار عندي
+
+482
+00:36:56,590 --> 00:37:00,630
+المقدار هو نفسه هذا زي ما قلت لكم لأن من نقطة فلوس
+
+483
+00:37:00,630 --> 00:37:06,680
+ذات عندي ال M ناقص واحد في ال XMنقص جيبلي هذه هنا
+
+484
+00:37:06,680 --> 00:37:13,940
+وهذه وديها هناك فبصير عندي M-1 في XM ناقص لغادة M
+
+485
+00:37:13,940 --> 00:37:17,820
+في XM زي 1 أكبر أو يساوي مين اللي جت هنا هذه اللي
+
+486
+00:37:17,820 --> 00:37:24,290
+A-1 في XMاللي هو هذه هتكون أكبر من 0 for M أكبر
+
+487
+00:37:24,290 --> 00:37:28,390
+أوي ساوة K لإن الـA اللي عندنا ايش مفترضينها أكبر
+
+488
+00:37:28,390 --> 00:37:32,250
+من 1 وهذا absolute value إذا صار المقدار هذا أكبر
+
+489
+00:37:32,250 --> 00:37:38,640
+من 0 هذا إيه معناه؟معناه أن الـ sequence اللي الـ
+
+490
+00:37:38,640 --> 00:37:44,560
+M X M زائد واحد is decreasing sequence لأن اللي
+
+491
+00:37:44,560 --> 00:37:49,040
+قبل ناقص اللي بعيد أكبر أو يساوي سفر يعني صار اللي
+
+492
+00:37:49,040 --> 00:37:54,940
+هو اللي بعيد أشماله أصغر من مين من اللي قبل يعني
+
+493
+00:37:54,940 --> 00:37:59,960
+صارت ال sequence M X M زائد واحد is a decreasing
+
+494
+00:37:59,960 --> 00:38:05,790
+sequence for مين M أكبر أو يساوي اتنينالان هذه
+
+495
+00:38:05,790 --> 00:38:11,430
+اللي هي ال relation اللي عندي اللي هي 12 بدنا اللي
+
+496
+00:38:11,430 --> 00:38:19,070
+هو نجمحها for K for M بتساوي K لعند مين لعند and
+
+497
+00:38:19,070 --> 00:38:24,290
+and we note the left side تلسكوب اللي هو نشوف كيف
+
+498
+00:38:24,290 --> 00:38:28,750
+ال left side هذا تلسكوب واضح انه تلسكوب we find
+
+499
+00:38:28,750 --> 00:38:37,180
+عندي أخد ال summation من عندN من عند K لعند N
+
+500
+00:38:37,180 --> 00:38:43,840
+عملكم إياها هان من عند K بتساوي او من عند M بتساوي
+
+501
+00:38:43,840 --> 00:38:51,220
+K لعند مين لعند N أكبر أو يساوي ال summation من M
+
+502
+00:38:51,220 --> 00:38:58,280
+بتساوي K لعند مين لعند N هذه بتصير اللي هو K minus
+
+503
+00:38:58,280 --> 00:39:07,350
+واحد fixed K ناقصاللي هي K في X K زائد واحد اللي
+
+504
+00:39:07,350 --> 00:39:12,190
+بعدها K زائد واحد اللي هي بيصير K في X K زائد واحد
+
+505
+00:39:12,190 --> 00:39:15,250
+راحت مع الأولى ناقص كده فكل واحدة بت cancel
+
+506
+00:39:15,250 --> 00:39:19,570
+الثانية بتظهر أول واحدة و آخر واحدة اللي هي أول
+
+507
+00:39:19,570 --> 00:39:25,470
+واحدة K minus واحد في X K ناقص آخر واحدة اللي هي N
+
+508
+00:39:25,470 --> 00:39:30,110
+في X N زائد واحد أكبر أو يساوي ال summation هذا
+
+509
+00:39:30,110 --> 00:39:34,560
+اللي هو عبارة عن A minus واحدعام المشترك لأنه فيها
+
+510
+00:39:34,560 --> 00:39:39,620
+بيت مضال مضروب في مين؟ في اللي بضر من عند K لعند
+
+511
+00:39:39,620 --> 00:39:44,400
+مين؟ لعند XK XK زائد واحد لعند مين؟ لعند X بكون
+
+512
+00:39:44,400 --> 00:39:51,380
+حصلت على هذه اللي هي ال inequality الان لاحظوا ما
+
+513
+00:39:51,380 --> 00:39:57,930
+يليهحصلت يا جماعة انه الـ Series هذه او الـ
+
+514
+00:39:57,930 --> 00:40:02,770
+Sequence هذه عندي هذا المقدار منها مدام الـ
+
+515
+00:40:02,770 --> 00:40:08,810
+Decreasing حصلت و جمعنا و استخدمنا الـ Telescoping
+
+516
+00:40:08,810 --> 00:40:15,640
+حصلنا هذه أكبر أو سوى هذه طيبالأن هذا يظهر أن الـ
+
+517
+00:40:15,640 --> 00:40:20,900
+partial sums Sn of سميش الـ Xn اللي هي صار عندهاي
+
+518
+00:40:20,900 --> 00:40:25,920
+اللي هو الـ Sn مظبوط هذا الـ Sn لأنه أصغر أو يساوي
+
+519
+00:40:25,920 --> 00:40:29,740
+هذا المقدار على A-1 وA-1 عبارة عن إيه؟ عشان ثابت
+
+520
+00:40:30,560 --> 00:40:34,860
+الآن الـ sequence of 10 sums Sn اللي هو summation
+
+521
+00:40:34,860 --> 00:40:40,220
+Xn are bounded مدان bounded إذا إيش بده يكون؟ بده
+
+522
+00:40:40,220 --> 00:40:46,580
+يكون convergent ده نشوف إيش اللي بقوله أكتب فوق
+
+523
+00:40:46,580 --> 00:40:53,420
+ولا .. طيب شوفوا عندي إيش
+
+524
+00:40:53,420 --> 00:40:58,990
+اللي حصلنا عليه؟ اللي هو الـ Snبساوي اللي هو ال
+
+525
+00:40:58,990 --> 00:41:00,810
+summation absolute value لل
+
+526
+00:41:04,710 --> 00:41:10,610
+الـ XK أو قبل حتى قبل الأسئلة حصّلنا على الـ A-1
+
+527
+00:41:10,610 --> 00:41:16,390
+في الـ XK زائد absolute value لـ XN هذا كله على
+
+528
+00:41:16,390 --> 00:41:23,690
+بعضه أصغر أو يساوي اللي هو K-1 بحكيها K-1 أيشي
+
+529
+00:41:23,690 --> 00:41:29,950
+معين K لأنه من عندها M أكبر أو يساوي من K K أيشي
+
+530
+00:41:29,950 --> 00:41:36,200
+معين K-1 في ال absolute value لXKناقص N في الـ
+
+531
+00:41:36,200 --> 00:41:41,040
+absolute value XN زائد واحد ماشي الحال هذه الـ N
+
+532
+00:41:41,040 --> 00:41:51,800
+عالميل على ال A minus واحد لأن هذا المقدار أصغر أو
+
+533
+00:41:51,800 --> 00:41:58,040
+يساوي هذا وهذا أكيد أكيد هذا أصغر أو يساوي ال K
+
+534
+00:41:58,040 --> 00:42:03,400
+minus واحد في absolute value XK على A minus واحد
+
+535
+00:42:03,860 --> 00:42:07,840
+لأنه الآن الـ Schilt اللي هو المقدار هذا السالب
+
+536
+00:42:07,840 --> 00:42:12,520
+اللي مطروح إذاً هذا بيكبر فصار هذا المقدار أصغر أو
+
+537
+00:42:12,520 --> 00:42:17,700
+يساوي هذا هذا ال K عبارة عن fixed رقم fixed number
+
+538
+00:42:17,700 --> 00:42:21,120
+اللي هو لإنه احنا بديه من عند K أكبر أو أكبر يساوي
+
+539
+00:42:21,120 --> 00:42:26,080
+K إذاً K إشي معين بحكي عنه إذاً هذا المقدار من XK
+
+540
+00:42:26,080 --> 00:42:30,720
+لعند ال XN أصغر أو يساوي هذاماشي الحال إذا صار
+
+541
+00:42:30,720 --> 00:42:42,880
+عندي اللي هو المقدار هذا هو عبارة عن sn-sk-1 مظبوط
+
+542
+00:42:42,880 --> 00:42:47,780
+ولا لأ؟ أكيدللـ absolute values طبعاً يعني بمعنى
+
+543
+00:42:47,780 --> 00:42:52,720
+آخر صار Sn أصغر أو يساوي Sk-1 برضه عدد عدد عدد
+
+544
+00:42:52,720 --> 00:43:01,500
+معين زائد اللي هو K-1 في XK على A-1 صار هذا Sn
+
+545
+00:43:01,500 --> 00:43:08,570
+أصغر أو يساوي هذالكل N أكبر أو يساوي K يعني صارت
+
+546
+00:43:08,570 --> 00:43:11,850
+الـ S N is bounded يعني بمعنى أخر، طبعا هذا أكبر
+
+547
+00:43:11,850 --> 00:43:15,390
+أو يساوي سفر أكيد الـ N، إذا limit الـ S N as N
+
+548
+00:43:15,390 --> 00:43:19,910
+goes to infinity مهما كبرت الـ N، هذه ما لهاش
+
+549
+00:43:19,910 --> 00:43:23,650
+علاقة فيها الـ N لأنه N أكبر أو يساويها، إذا أصغر
+
+550
+00:43:23,650 --> 00:43:27,560
+أو يساوي الـ S K minus واحد زائد K minus واحدفي
+
+551
+00:43:27,560 --> 00:43:31,660
+الـ absolute value of xk على a-1 بمعنى آخر صارت
+
+552
+00:43:31,660 --> 00:43:36,640
+الـ Sn is convergent أو بمعنى آخر الصممش لل
+
+553
+00:43:36,640 --> 00:43:40,040
+absolute value of xn is convergent يعني هتصير
+
+554
+00:43:40,040 --> 00:43:44,660
+السيريز عندي is absolutely convergent
+
+555
+00:43:46,650 --> 00:43:51,190
+طيب نيجي الآن هذا تفسير انه اللي هو this shows the
+
+556
+00:43:51,190 --> 00:43:53,510
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+557
+00:43:53,510 --> 00:43:53,850
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+558
+00:43:53,850 --> 00:43:54,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+559
+00:43:54,190 --> 00:43:56,030
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+560
+00:43:56,030 --> 00:43:57,570
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+561
+00:43:57,570 --> 00:43:57,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+562
+00:43:57,730 --> 00:43:57,890
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+563
+00:43:57,890 --> 00:43:57,990
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+564
+00:43:57,990 --> 00:43:58,010
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+565
+00:43:58,010 --> 00:43:58,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+566
+00:43:58,330 --> 00:44:04,710
+ال .. ال .. ال .. ال .. ال .. ال ..
+
+567
+00:44:04,710 --> 00:44:06,150
+ال .. ال ..
+
+568
+00:44:15,000 --> 00:44:24,940
+نأخد الجزء الثاني الـ similarly تنشوف كيف suppose
+
+569
+00:44:24,940 --> 00:44:29,660
+thatsuppose that the relation 11 هيها ال relation
+
+570
+00:44:29,660 --> 00:44:34,700
+11 holds for n أكبر وساوة k وطبعا احنا مفترضين ال
+
+571
+00:44:34,700 --> 00:44:39,640
+a أصغر أو ساوة واحد الان صار عندي ال n ضربنا طرفين
+
+572
+00:44:39,640 --> 00:44:42,800
+في وساطين نفس الاشي فبصير عندي زي ما عملنا قبل
+
+573
+00:44:42,800 --> 00:44:47,880
+شوية ضربنا هذا بصير عندي ال n اللي هو xn زائد واحد
+
+574
+00:44:48,690 --> 00:44:53,530
+أ أصغر أكبر أو يساوي هذا في هذا وضربنا في n فصارت
+
+575
+00:44:53,530 --> 00:44:57,890
+ال n في xn زائد واحد أكبر أو يساوي لما ضربت ال n
+
+576
+00:44:57,890 --> 00:45:04,070
+هنا بيصير n ناقص a في ال absolute value لل xnالان
+
+577
+00:45:04,070 --> 00:45:08,910
+ال a أصغر يساوي واحد إذا ناقص ال a أكبر يساوي ناقص
+
+578
+00:45:08,910 --> 00:45:12,230
+واحد فما دام ناقص ال a أكبر يساوي ناقص واحد إذا
+
+579
+00:45:12,230 --> 00:45:15,710
+صارت عندي n ناقص a في absolute value xn أكبر يساوي
+
+580
+00:45:15,710 --> 00:45:19,070
+n ناقص واحد في absolute value xn لكل n ناقصة وk
+
+581
+00:45:19,070 --> 00:45:24,200
+هذه لإن ال a أصغر يساوي واحدالأنصار عندي الان واضح
+
+582
+00:45:24,200 --> 00:45:28,580
+انه ال sequence اللي هو الان xn زائد واحد أكبر أو
+
+583
+00:45:28,580 --> 00:45:31,960
+سوى n ناقص واحد xn يعني ال sequence هذه صارت
+
+584
+00:45:31,960 --> 00:45:35,900
+increasing for n أكبر أو سوى k ما زم increasing
+
+585
+00:45:35,900 --> 00:45:40,680
+إذا there exists c such that الان في ال absolute
+
+586
+00:45:40,680 --> 00:45:45,300
+value xn زائد واحد أكبر من مين من c for n أكبر أو
+
+587
+00:45:45,300 --> 00:45:49,750
+سوى kماشي الحال صارت مدام هذه ال series increasing
+
+588
+00:45:49,750 --> 00:45:55,630
+إذا أكيد هتكون أكبر من إياش و من some c لأنها
+
+589
+00:45:55,630 --> 00:46:00,630
+بتتزايد مدام صارت أكبر من some c و ليكن الحد الأول
+
+590
+00:46:00,630 --> 00:46:05,230
+مثلا and sole absolute value xn زائد واحد أصغر من
+
+591
+00:46:05,230 --> 00:46:11,300
+c عالمين على ال andقسمنا على مين على الان الان هذه
+
+592
+00:46:11,300 --> 00:46:15,460
+ال series diverse تبعتها ال series هذه تبعت اللي
+
+593
+00:46:15,460 --> 00:46:18,760
+هي واحدة الان diverse إذا من باب أولى بال
+
+594
+00:46:18,760 --> 00:46:23,100
+comparison test هذه تكون diverse أو بمعنى آخر ال
+
+595
+00:46:23,100 --> 00:46:27,580
+series summation xn is not absolutely convergent
+
+596
+00:46:27,930 --> 00:46:33,170
+وهذا هو الـ Reopts Test الآن ناخد الـ Corollary له
+
+597
+00:46:33,170 --> 00:46:37,150
+الـ Corollary طبعاً هتنسحب على إيش يا جماعة؟
+
+598
+00:46:37,150 --> 00:46:41,110
+هتنسحب زي ما هو المنهج اللي بنعمله إحنا بناخد ال
+
+599
+00:46:41,110 --> 00:46:44,910
+test و بناخد ال limit تبعه أو limit test تبعه وهنا
+
+600
+00:46:44,910 --> 00:46:48,870
+ال limit test تبع ال Reopts Test نشوف إيش اللي
+
+601
+00:46:48,870 --> 00:46:51,770
+بيعطينا ياه و عادة اللي هي ال limits بتكون في
+
+602
+00:46:51,770 --> 00:46:56,150
+الغالب أسهل أو أسهل في التعامل من اللي هو ال
+
+603
+00:46:56,150 --> 00:47:01,180
+comparison العاديLatex بيساوي XN بيه sequence of
+
+604
+00:47:01,180 --> 00:47:05,340
+non-zero real numbers يعني إيش مالها sequence of
+
+605
+00:47:05,340 --> 00:47:08,320
+non-zero real numbers ماشي مش .. مش .. مش صفار
+
+606
+00:47:08,320 --> 00:47:11,580
+يعني عشان هيك أصلا فوق احنا لما ناخدنا strictly
+
+607
+00:47:11,580 --> 00:47:16,040
+أكبر من C لإنه هنا .. هنا .. هنا يعني مزام
+
+608
+00:47:16,040 --> 00:47:22,130
+sequence of non-zeroاللي هو numbers عشان لو حد سأل
+
+609
+00:47:22,130 --> 00:47:27,250
+عن اللي فوق هذه كيف أكبر من C اللي هو strictly
+
+610
+00:47:27,250 --> 00:47:31,190
+هذوله non-zero لو كان أول واحد non-zero إذا قيمته
+
+611
+00:47:31,190 --> 00:47:34,550
+strictly أكبر من 0 يعني له قيمة محددة والبعده بكون
+
+612
+00:47:34,550 --> 00:47:38,750
+أكبر منه إذا أكيد في عندي بديت من رقم C اللي هو
+
+613
+00:47:38,750 --> 00:47:43,010
+اللي هو ال term الأول اللي هو ال XK مثلا وبعده
+
+614
+00:47:43,010 --> 00:47:46,370
+بصير كل اللي بعده أكبر منه اللي هو أكبر strictly
+
+615
+00:47:46,370 --> 00:47:52,310
+من C وزي ما وصلنااللي هو diversity إذا الأن let X
+
+616
+00:47:52,310 --> 00:47:55,310
+بيساوي XN بيبقى sequence of non-zero real numbers
+
+617
+00:47:55,310 --> 00:48:01,110
+and let A بيساوي limit N في واحد ناقص XN زائد واحد
+
+618
+00:48:01,110 --> 00:48:04,850
+على XN whenever this limit exists then the series
+
+619
+00:48:04,850 --> 00:48:08,030
+summation XN is absolutely convergent when A أكبر
+
+620
+00:48:08,030 --> 00:48:10,930
+من واحد and this absolutely is not absolutely
+
+621
+00:48:10,930 --> 00:48:13,790
+convergent في A أصغر من واحد وذا كان let A بيساوي
+
+622
+00:48:13,790 --> 00:48:17,450
+واحد فعلا طيب يعني إيش بيقوليه؟ بيقوليه تعالي حسب
+
+623
+00:48:18,370 --> 00:48:23,390
+احسبلي اللي هو limit n في 1 ناقص xn زائد 1 على xn
+
+624
+00:48:23,390 --> 00:48:26,490
+إذا لجيت ال limit as n goes to infinity لهذا
+
+625
+00:48:26,490 --> 00:48:30,230
+المقدار و بيكسّلني أصلا إذا لجيت ال limit بساوي
+
+626
+00:48:30,230 --> 00:48:34,890
+رقم a إذا كان اللي كده exist يعني و لجيته بساوي a
+
+627
+00:48:34,890 --> 00:48:39,990
+بتيجي الآن للحكم إذا a بساوي 1 بتحكيشلكن إذا الـ A
+
+628
+00:48:39,990 --> 00:48:43,990
+أكبر من واحد على تقول بتقول converge وإذا كانت الـ
+
+629
+00:48:43,990 --> 00:48:47,570
+A أصغر من واحد بتقول ايه اشماله is not absolutely
+
+630
+00:48:47,570 --> 00:48:50,990
+convergent حتى مش converge absolutely convergent
+
+631
+00:48:50,990 --> 00:48:54,650
+في الأولى لما تكون A أكبر من واحد was not
+
+632
+00:48:54,650 --> 00:48:59,370
+absolutely convergent for A اللي هي أصغر من واحد
+
+633
+00:48:59,370 --> 00:49:05,370
+نيجي الآن لاللي هو نفترض أنه ال limit هذه exist
+
+634
+00:49:05,370 --> 00:49:11,180
+ونصل ل اللي بدناهاالان هذه الفكرة عملناها قبل هيك
+
+635
+00:49:11,180 --> 00:49:15,940
+في ال proof of Corolla 926 الان بدنا نفترض suppose
+
+636
+00:49:15,940 --> 00:49:21,040
+that limit 1100-Xn زي 1Xn سوى ايه أكبر من مين من
+
+637
+00:49:21,040 --> 00:49:25,800
+واحد الان suppose that
+
+638
+00:49:33,400 --> 00:49:40,040
+limit n في 1 ناقص xn زي 1 على xn بساوة a أكبر من 1
+
+639
+00:49:40,040 --> 00:49:43,820
+مدام ال limit هذا exist إذا لكل y أكبر من 0 دير
+
+640
+00:49:43,820 --> 00:49:47,900
+exist اللي هو k such that هذا المقدر ناقص a أصغر
+
+641
+00:49:47,900 --> 00:49:51,280
+من y for every n أكبر ساوة k اللي يعني ال epsilon
+
+642
+00:49:51,280 --> 00:49:54,480
+اللي بدأ اختارها بدأ تخدمني زي ما عملنا قبل هيك في
+
+643
+00:49:54,480 --> 00:49:59,320
+ال proof تبع 109 اللي هو 6الان بما انه a أكبر من
+
+644
+00:49:59,320 --> 00:50:04,180
+واحد يعني الفترة بين a والواحد وال a أكيد في a
+
+645
+00:50:04,180 --> 00:50:09,740
+واحد بينهم الان عندي ال a واحد ال a واحد ال
+
+646
+00:50:09,740 --> 00:50:14,620
+element واحد وال a لو جيت يعني بمعنى أخر ال a واحد
+
+647
+00:50:14,620 --> 00:50:19,620
+أكبر من ال a وأصغر من ال a الان خد ال epsilon let
+
+648
+00:50:19,620 --> 00:50:24,900
+epsilon بساوي a minus a واحد أكبر من 0 الان if
+
+649
+00:50:24,900 --> 00:50:30,410
+there exist thenThere exists K element in N such
+
+650
+00:50:30,410 --> 00:50:35,390
+that for every N أكبر وشهو K هيكون عندياللي هو ال
+
+651
+00:50:35,390 --> 00:50:39,990
+N في الواحد ناقص absolute value XN زائد واحد على
+
+652
+00:50:39,990 --> 00:50:46,090
+ال absolute value لل XN ناقص ال A أصغر من مين من Y
+
+653
+00:50:46,090 --> 00:50:51,050
+اللي هي ال A minus A واحد فوق هذا المقدار هيصير
+
+654
+00:50:51,050 --> 00:50:56,730
+عبارة عن هذا absolute value أصغر من هذا وأكبر من
+
+655
+00:50:56,730 --> 00:51:01,650
+اللي هو A ناقص أو A واحد ناقص A هذا اللي بهمني
+
+656
+00:51:01,650 --> 00:51:06,370
+الآنالان هتلاحظ ان ان في واحد ناقص absolute value
+
+657
+00:51:06,370 --> 00:51:10,630
+of xn زائد واحد على absolute value of xn اللي هو
+
+658
+00:51:10,630 --> 00:51:17,530
+اصغر جيب هذه hand بيصير عندك اللي هو ناقص ايه
+
+659
+00:51:21,840 --> 00:51:25,820
+أو خلّينا لأ من الجهة الثانية انا مش الجهة دي اكبر
+
+660
+00:51:25,820 --> 00:51:30,260
+من a واحد ناقص a و ناقص a بجيبها على الجهة الثانية
+
+661
+00:51:30,260 --> 00:51:35,260
+بيصير زائد a بيصير هذا المقدار اكبر من a زائد a
+
+662
+00:51:35,260 --> 00:51:40,670
+واحد ناقص a يعني بتروح ال aمع الـ A نقص واحد وبصير
+
+663
+00:51:40,670 --> 00:51:45,090
+عندي هذا المقدار أكبر من A واحد حيث الـ A واحد
+
+664
+00:51:45,090 --> 00:51:50,890
+أكبر من واحد إذا صار عندي A واحد أصغر من هذا
+
+665
+00:51:50,890 --> 00:51:56,100
+المقدار لكل N أكبر أو يساوي Kومنه خلّينا بنجيب
+
+666
+00:51:56,100 --> 00:52:01,680
+اللي هو بنجسم على N بيصير اللي هي هذا المقدار 1
+
+667
+00:52:01,680 --> 00:52:06,480
+ناقص هذا المقدار أصغر من A1 على N بنجيب المقدار
+
+668
+00:52:06,480 --> 00:52:09,840
+هذا N وبنجيب هذا N بيصير عندي XN زائد 1 على XN
+
+669
+00:52:09,840 --> 00:52:15,300
+أصغر من 1 ناقص اللي هو A1 على N طبعا بعد ما جسمنا
+
+670
+00:52:15,300 --> 00:52:18,840
+هذا أول إشي وبعدين بنجيب هذا N بعد ما جسمناه
+
+671
+00:52:18,840 --> 00:52:22,120
+وبنجيب هذا N بيطلع عندي هذا المقدارفوران أكبر
+
+672
+00:52:22,120 --> 00:52:26,400
+شوكيه صارت اللي هي الصورة هذه صورة مين صورة اللي
+
+673
+00:52:26,400 --> 00:52:31,140
+هي الراقبست الأولى إذا بقى رقابست هيكون عنده اللي
+
+674
+00:52:31,140 --> 00:52:36,990
+هو بما أنه اي واحد أكبر من واحد لأنه بين الواحدبين
+
+675
+00:52:36,990 --> 00:52:41,070
+الواحد وال إيه هيصير عندي اللي هو بيرابستيس
+
+676
+00:52:41,070 --> 00:52:46,890
+الصممشي لل إكسان is absolutely convergent فأصغر من
+
+677
+00:52:46,890 --> 00:52:52,630
+واحد فأصغر من واحد بدو يصير الموضوع الآن مشابه بس
+
+678
+00:52:52,630 --> 00:52:56,090
+بتختلف من هنا خلّي أتي نشوف لكم إياه كيف بيختلف
+
+679
+00:52:56,090 --> 00:53:03,220
+الان for aأصغر من مين من واحد لما تكون a أصغر من
+
+680
+00:53:03,220 --> 00:53:06,040
+واحد بدا تبتلكوا يا له from national exam is not
+
+681
+00:53:06,040 --> 00:53:10,420
+absolutely convergent a أصغر من واحد معناته أنه في
+
+682
+00:53:10,420 --> 00:53:14,680
+بينهم a واحد خلجينا نقول a أصغر من واحد لإنه
+
+683
+00:53:14,680 --> 00:53:16,680
+between any two real numbers there exists a real
+
+684
+00:53:16,680 --> 00:53:21,080
+number اللي هو a واحد بين ال a و بين اللي هو مين
+
+685
+00:53:21,080 --> 00:53:26,810
+الواحد اللي عالية epsilon a واحد ناقص aA1-A وهي
+
+686
+00:53:26,810 --> 00:53:30,010
+أكبر من 0 وكله نفسه زي ما هو there exists such
+
+687
+00:53:30,010 --> 00:53:38,030
+that هذا المقدار أصغر من A 1-A هو أكبر من اللي هو
+
+688
+00:53:38,030 --> 00:53:42,530
+سالبه اللي هو A-A1 هذا المنطقة بديش إياها باخد
+
+689
+00:53:42,530 --> 00:53:46,010
+المنطقة هذه بصير عندي اللي هو زي ما عملنا قبل
+
+690
+00:53:46,010 --> 00:53:50,110
+بالظبط بصير عندي هذا المقدار و بجيب هذا ال A هام
+
+691
+00:53:50,110 --> 00:53:54,210
+بصير أصغرلما ناقص A تجهان بيصير زايد A مع ناقص A
+
+692
+00:53:54,210 --> 00:53:58,710
+بروح بيصير أصغر من مين؟ من A واحد الآن هذا أصغر من
+
+693
+00:53:58,710 --> 00:54:02,130
+A واحد إذا بيصير عندي بكسب الجهتين على N بيصير على
+
+694
+00:54:02,130 --> 00:54:06,090
+N و هذه بنجلها على الجهة هذه و هذه بجيبها هنا
+
+695
+00:54:06,090 --> 00:54:10,030
+بيصير واحد ناقص A واحد على N أصغر من absolute
+
+696
+00:54:10,030 --> 00:54:15,270
+value XN زائد 1 على ال absolute لل XN بكون حصلنا
+
+697
+00:54:15,270 --> 00:54:20,250
+على هذا المقدار أكبر من واحد ناقص A واحد على Nوهذا
+
+698
+00:54:20,250 --> 00:54:25,270
+اللي هو لكل N أكبر أو يساوي K إذا حسب B في رقاب ال
+
+699
+00:54:25,270 --> 00:54:30,190
+test بما أن A واحد اللي هي أصغر من واحد إذا هذه
+
+700
+00:54:30,190 --> 00:54:33,450
+اللي هي ال series اللي هي summation لل X absolute
+
+701
+00:54:33,450 --> 00:54:36,810
+value XN is not convergent أو بمعنى أخر summation
+
+702
+00:54:36,810 --> 00:54:40,690
+لل XN is not absolutely convergent إذا ال exercise
+
+703
+00:54:40,690 --> 00:54:45,390
+هذا هيني وضحتلكم يا هان طيب
+
+704
+00:54:47,450 --> 00:54:51,130
+لأن في حالة اللي هي إلا إيه بالساعة واحد قولنا No
+
+705
+00:54:51,130 --> 00:54:54,870
+conclusion where either convergence or divergence
+
+706
+00:54:54,870 --> 00:55:00,490
+is possible طيب خلينا نشوف اللي هو examples على
+
+707
+00:55:00,490 --> 00:55:04,670
+اللي هي الـ Raab's test هنرجع لمين، هنرجع اللي هو
+
+708
+00:55:04,670 --> 00:55:08,970
+الـ B series تبعنا ونشوف كيف نوضح اللي هو ال test
+
+709
+00:55:08,970 --> 00:55:12,230
+تبعنا الـ Raab's test أو الـ Corollary اللي عليه
+
+710
+00:55:12,230 --> 00:55:25,120
+كيف اللي هو نستخدمها عندنا في أمثلتناالان اخدنا
+
+711
+00:55:25,120 --> 00:55:28,780
+ال limit على طول اللي هو ال X زائد N زائد واحد على
+
+712
+00:55:28,780 --> 00:55:33,520
+ال Xان طبعا هذه جاهزة و positive أصلابصير عندى
+
+713
+00:55:33,520 --> 00:55:37,980
+اللى هو xn زائد واحد على ال xn واحد ناقصها في n
+
+714
+00:55:37,980 --> 00:55:42,380
+حسبتها و يساوي limit n في واحد ناقص واحد ال n
+
+715
+00:55:42,380 --> 00:55:47,140
+غلبتها صارت nb على واحد n زائد واحد الكل اس بيه و
+
+716
+00:55:47,140 --> 00:55:52,860
+يساوي limit عندى ال nاللي هي أحطت المقامات فصارت N
+
+717
+00:55:52,860 --> 00:55:56,060
+زيد واحد أس بي N أس بي على N زيد واحد وكل أس بي في
+
+718
+00:55:56,060 --> 00:56:03,020
+مين في N ويساوي ال N عبارة عن N زيد واحد أس بي نقص
+
+719
+00:56:03,020 --> 00:56:08,660
+N أس بي على واحد على N وهذه جبت مين لحالها واحد
+
+720
+00:56:08,660 --> 00:56:12,300
+على N زيد واحد أس بي يعني جبت هذه هنا وهذه فصلت
+
+721
+00:56:12,300 --> 00:56:17,280
+لحالة صارت هذه في هذه لأن هذه limit معروف صار ال N
+
+722
+00:56:17,280 --> 00:56:22,980
+limit اللي هو هذا المقدارالأن واحد على أن جيت اللي
+
+723
+00:56:22,980 --> 00:56:29,860
+هو جسمت فوق على أن أُس بي و تحت على أن أُس بي ماشي
+
+724
+00:56:29,860 --> 00:56:33,760
+لما جسمت هذا على أن أُس بي صار هذا عبارة عن واحد
+
+725
+00:56:33,760 --> 00:56:37,760
+زائد واحد على أن كل أُس بي وهذه واحد ناقص واحد
+
+726
+00:56:37,760 --> 00:56:41,140
+وهذه زي ما هي دلت و لما جسمت هذا على أن أُس بي
+
+727
+00:56:41,140 --> 00:56:45,770
+صارت واحد زائد واحد على أن أُس بيالان و يساوي،
+
+728
+00:56:45,770 --> 00:56:50,550
+الان limit الأول في limit مين؟ التاني الان limit
+
+729
+00:56:50,550 --> 00:56:54,730
+التاني هذا ساهل بساوي واحد اللي فوق صار عبارة عن
+
+730
+00:56:54,730 --> 00:56:59,210
+الان اللي هو سفر على سفر، ليش؟ لأن as n goes to
+
+731
+00:56:59,210 --> 00:57:02,110
+infinity، هذي بيصير سفر، هذي بيصير واحدة، و أحد
+
+732
+00:57:02,110 --> 00:57:05,030
+بيطلع سفر، و هذي سفر، سفر على سفر، ده نستخدم اللي
+
+733
+00:57:05,030 --> 00:57:07,610
+هو بتالي الزرولاستخدمت الـ L'Hôpital's Rule
+
+734
+00:57:07,610 --> 00:57:11,450
+واشتققت اللي فوق و اللي تحت بالنسبة لل N طبعا هذا
+
+735
+00:57:11,450 --> 00:57:14,970
+ال limit طلع و خلصنا واحد اشتققنا طالع عبارة عن B
+
+736
+00:57:14,970 --> 00:57:18,870
+في واحد زائد واحد على N كل اسم B minus واحد فاطلع
+
+737
+00:57:18,870 --> 00:57:22,050
+دول الجوا ناقص واحد على N تربيع لما فضلت اللي تحت
+
+738
+00:57:22,050 --> 00:57:25,570
+برضه هيطلع ليه ناقص واحد على N تربيع هذا بروح مع
+
+739
+00:57:25,570 --> 00:57:28,490
+حده بيصير عندي as N goes to infinity هذا بتروح
+
+740
+00:57:28,490 --> 00:57:32,310
+للسفر اذا بيصير ايش بيساوي اللي هو عبارة عن B في
+
+741
+00:57:32,310 --> 00:57:36,510
+واحد اسم B minus واحد يعني عبارة عن ايه؟ عن Bالأن
+
+742
+00:57:36,510 --> 00:57:40,390
+مادام B وB أكبر أوسع واحد، إذا من الـ Corollary
+
+743
+00:57:40,390 --> 00:57:47,350
+اللي قبل بشوية الـ B Series إيش مالها، converges
+
+744
+00:57:47,350 --> 00:57:53,140
+for B أكبر من مين من واحدالأن في حالة الواحد قلنا
+
+745
+00:57:53,140 --> 00:57:56,460
+اللي هو لما الـ B بتطلع واحد الـ limit بيكون ال
+
+746
+00:57:56,460 --> 00:58:00,720
+test fail يعني هذه اللي هو بس بنستخدم فيها ال test
+
+747
+00:58:00,720 --> 00:58:04,560
+for convergence بس في حالة اللي هو مين اللي هو الـ
+
+748
+00:58:04,560 --> 00:58:08,800
+B أكبر من واحد أثبتنا إنه converge بطريقة اللي
+
+749
+00:58:08,800 --> 00:58:14,260
+يرقب ال test الآن
+
+750
+00:58:14,260 --> 00:58:20,270
+لو كانت B أكبر من واحدلو كانت بيه أكبر من واحد
+
+751
+00:58:20,270 --> 00:58:26,270
+قلنا اللي هي convergence
+
+752
+00:58:26,270 --> 00:58:31,570
+و for b بيساوي واحد اللي هو no conclusion طيب نيجي
+
+753
+00:58:31,570 --> 00:58:38,400
+الأن لمثال آخر use the Raab's testto the series
+
+754
+00:58:38,400 --> 00:58:42,040
+summation اللي أمامنا اللي هو بنفس الأسلوب بدنا
+
+755
+00:58:42,040 --> 00:58:48,240
+ناخد اللي هو limit ال Xn زائد واحد على Xn بساوي
+
+756
+00:58:48,240 --> 00:58:51,940
+يعني بده يقولك أنه احنا ما .. ماظبطش معنى اللي هو
+
+757
+00:58:51,940 --> 00:58:55,920
+مين ال ratio test العادي فبدنا نستخدم اللي هو مين
+
+758
+00:58:55,920 --> 00:58:59,980
+الrobustestطيب شوفوا معايا limit xn زائد واحد على
+
+759
+00:58:59,980 --> 00:59:04,480
+xn ال xn زائد واحد اللي هو n زائد واحد على n زائد
+
+760
+00:59:04,480 --> 00:59:08,340
+واحد كله تربيع زائد واحد فان تربيع زائد واحد على n
+
+761
+00:59:08,340 --> 00:59:11,960
+اللي هي ال xn هذه لما جسمت طبعا و جلبت في الآخر
+
+762
+00:59:11,960 --> 00:59:19,970
+فبصير عند ال n بساوي جسمت اللي هو هذه على nبصير
+
+763
+00:59:19,970 --> 00:59:23,150
+عبارة عن هذه جسمتها على هذا الان زائد واحد على
+
+764
+00:59:23,150 --> 00:59:26,270
+الان تطلع عبارة عن واحد زائد واحد على الان وهذه زي
+
+765
+00:59:26,270 --> 00:59:29,710
+ما هي ان تربيع زائد واحد على هذه وهي ساوي limit
+
+766
+00:59:29,710 --> 00:59:35,630
+هذا المقدار هنا برضه جسمت على مين على ان تربيع صار
+
+767
+00:59:35,630 --> 00:59:39,230
+واحد زائد واحد على ان تربيع وهنا على ان تربيع صارت
+
+768
+00:59:39,230 --> 00:59:43,650
+واحد زائد واحد على الان الكل تربيع زائد واحد على
+
+769
+00:59:43,650 --> 00:59:47,920
+مين ان تربيعلأن as n goes to infinity هذه واحد as
+
+770
+00:59:47,920 --> 00:59:51,940
+n goes to infinity هذه واحد وهذه سفر وهذه واحد
+
+771
+00:59:51,940 --> 00:59:54,920
+يعني المحصلة واحد اذا واحد على واحد بيسوء واحد
+
+772
+00:59:54,920 --> 01:00:01,380
+الان اذا بقصه by corollary 926 does not apply او
+
+773
+01:00:01,380 --> 01:00:05,640
+corollary 926 اللي هي ال ratio limit limit ratio
+
+774
+01:00:05,640 --> 01:00:12,830
+limit ratio testdoes not هنا اللي هو applied ليش؟
+
+775
+01:00:12,830 --> 01:00:16,970
+لأن ال limit اللي عندى واحد إذا صار عندى بدنا اللي
+
+776
+01:00:16,970 --> 01:00:22,790
+هو نحاول نوجد طريقة أخرى لو جيت أو جدت اللي هو
+
+777
+01:00:22,790 --> 01:00:27,370
+برضه بالرقابs testاللي هو limit n في 1 ناقص xn زي
+
+778
+01:00:27,370 --> 01:00:31,190
+1 على xn اللي هو حاول توجد ال limit بنفس الأسلوب
+
+779
+01:00:31,190 --> 01:00:34,330
+اللي فوق بس إلى هذا المقدار احسبهن 1 نقطص هذه
+
+780
+01:00:34,330 --> 01:00:37,130
+وبعدين اضرب من فى ال n حاول توجد ال limit هتلاقيه
+
+781
+01:00:37,130 --> 01:00:41,230
+بيساوي 1 إذا صار عندي اللي هو الرقابست برضه أنا
+
+782
+01:00:41,230 --> 01:00:51,310
+اشمله does not apply لكن لو جيت لو جيت اتطلعت على
+
+783
+01:00:51,310 --> 01:00:56,760
+الملاحظة التهليةأبد نوجد حلل أمر XN زياد واحد على
+
+784
+01:00:56,760 --> 01:01:00,240
+XN هتلاقي N زياد واحد على N زياد واحد كل تربيع
+
+785
+01:01:00,240 --> 01:01:03,740
+زياد واحد في N تربيع زياد واحد على N هذا اللي فوق
+
+786
+01:01:03,740 --> 01:01:09,800
+هذا اللي هي XN زياد واحد وهذا مقلوب من XNالان لو
+
+787
+01:01:09,800 --> 01:01:16,060
+جيت حسبت هذه جرب انت احسبلي اثبتلي انه it is an
+
+788
+01:01:16,060 --> 01:01:19,220
+exercise to show that ال XN زيادة واحدة لل XN انه
+
+789
+01:01:19,220 --> 01:01:22,400
+هذا المقدار هي اللي طلع عندى هتلاقيه اكبر او سوى
+
+790
+01:01:22,400 --> 01:01:28,150
+اناقص واحد على مين على انالآن مدام هذا أكبر من هذا
+
+791
+01:01:28,150 --> 01:01:32,550
+وهذا عبارة عن اللي هو عبارة عن واحد ناقص واحد على
+
+792
+01:01:32,550 --> 01:01:36,770
+ان therefore by her abstest اللي هي بيه the series
+
+793
+01:01:36,770 --> 01:01:41,290
+هش ما لها diverse لأنه كتبت على صورة واحد ناقص
+
+794
+01:01:41,290 --> 01:01:45,710
+واحد على ان وهذا ال A تساوي واحدمعناته بالرقابس
+
+795
+01:01:45,710 --> 01:01:49,450
+test هيكون ال series هذه اللي هي ال summation لل X
+
+796
+01:01:49,450 --> 01:01:52,570
+and is not convergence is not absolutely
+
+797
+01:01:52,570 --> 01:01:57,310
+convergence او بمعنى اخر diverse وبكون هيك احنا
+
+798
+01:01:57,310 --> 01:02:02,250
+انهينا اللي هو section اللي هو تسعة اتنين والى
+
+799
+01:02:02,250 --> 01:02:03,310
+لقاء اخر
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..57181e2180e58b9b48eb5c633ad81b0fe7e7592d
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8.srt
@@ -0,0 +1,2251 @@
+1
+00:00:05,040 --> 00:00:12,800
+بسم الله الرحمن الرحيم المحاضرة السابعة مساق تحليل
+
+2
+00:00:12,800 --> 00:00:18,640
+النهاري 2 اللي طلبت كلية العلوم بالجامعة الإسلامية
+
+3
+00:00:18,640 --> 00:00:23,800
+قسم الرياضيات اليوم 
+
+4
+00:00:23,800 --> 00:00:29,720
+هيكون عندنا استكمال ل .. اللي هي قواعد أو قاعدة
+
+5
+00:00:29,720 --> 00:00:36,330
+L'Hôpital  اتحدثنا المرة الماضية عن الحالة اللي بتحدث
+
+6
+00:00:36,330 --> 00:00:41,170
+صفر على صفر وكيف انعالجها وتم اللي هو برهان
+
+7
+00:00:41,170 --> 00:00:47,910
+النظريات المعنية في ذلك، الآن بدنا نتحدث على الحالة
+
+8
+00:00:47,910 --> 00:00:57,110
+اللي بتحدث عندنا أيضًا 0 على 0 ولكن the limit ال X
+
+9
+00:00:57,110 --> 00:01:00,830
+بتروح إلى ما لا نهاية أو سالب ما لا نهاية وقلنا عنها
+
+10
+00:01:00,830 --> 00:01:05,790
+صحيحة برضه، وبعد ذلك هنتحدث عن الحالة infinity على
+
+11
+00:01:05,790 --> 00:01:10,510
+infinity، نيجي الآن لنظريتنا اللي وصلنا عندها 
+
+12
+00:01:10,510 --> 00:01:11,990
+suppose that
+
+13
+00:01:16,220 --> 00:01:20,260
+F and G are continuous and differentiable على
+
+14
+00:01:20,260 --> 00:01:24,600
+الفترة من A إلى ما لا نهاية ونفترض أنه limit لل F
+
+15
+00:01:24,600 --> 00:01:27,540
+of X لما X تروح إلى ما لا نهاية هي نفس limit  the G of
+
+16
+00:01:27,540 --> 00:01:31,200
+X لما X تروح إلى ما لا نهاية تساوي إيهاش صفر يعني
+
+17
+00:01:31,200 --> 00:01:36,080
+هذه هتخلقلي حالة اللي هو صفر على صفر ومن ثم نشوف
+
+18
+00:01:36,080 --> 00:01:40,230
+كيف انعالجها، العنوان G of X ذاته ساوة صفر نفترض، وG 
+
+19
+00:01:40,230 --> 00:01:44,830
+prime of X ذاته ساوة صفر لكل X أكبر من مين؟ من اللي
+
+20
+00:01:44,830 --> 00:01:48,290
+هو المقصود هنا بيه اللي هي أيش؟ A، يعني هذه اللي هي 
+
+21
+00:01:48,290 --> 00:01:52,970
+مين اللي هي المقصود أنه A؟ يا ما نخلي هذه A، يا ما
+
+22
+00:01:52,970 --> 00:01:58,330
+هذه A، then limit F of X على G of X لما X تروح لما
+
+23
+00:01:58,330 --> 00:02:01,930
+النهاية هتكون بالظبط أيش بتساوي؟ limit F prime على 
+
+24
+00:02:01,930 --> 00:02:06,050
+G prime of X as X goes to infinity provided that
+
+25
+00:02:06,050 --> 00:02:09,590
+هذا ال limit بتساوي قيمة معينة أو تساوي infinity
+
+26
+00:02:09,590 --> 00:02:15,730
+أو سالب infinity، الآن احنا في الواقع اللي هنسوي
+
+27
+00:02:16,910 --> 00:02:21,910
+وكأنه يعني عملية تحويل اللي نخلّي بدل X تروح إلى
+
+28
+00:02:21,910 --> 00:02:26,950
+ما لا نهاية نخلّي اللي هو متغير وروح لصفر يعني بدنا
+
+29
+00:02:26,950 --> 00:02:31,490
+نعيد تعريف الدالة بحيث أنه يروح هذا المتغير يعني
+
+30
+00:02:31,490 --> 00:02:34,610
+وكأنه نقول 1 على T ويروح لـ .. اه 1 على X 
+
+31
+00:02:34,610 --> 00:02:37,950
+يروح لصفر لما X تروح لما لا نهاية ومن ثم نطبق
+
+32
+00:02:37,950 --> 00:02:41,030
+النظريات اللي أخدناها المرة الماضية، دعونا نشوف إيش
+
+33
+00:02:41,030 --> 00:02:47,050
+اللي بنحكيه الآن عند ..الـ الـ function F و G F و
+
+34
+00:02:47,050 --> 00:02:54,430
+G معرفات من A وما لا نهاية لعند اللي هو R، الآن
+
+35
+00:02:54,430 --> 00:02:57,970
+عندي اللي هو بده أعرف اللي هو عشان أقدر أستخدم 
+
+36
+00:02:57,970 --> 00:03:01,610
+نظرية المرة اللي فاتت المرة الماضية بده أعرف 
+
+37
+00:03:01,610 --> 00:03:08,030
+دالتين F capital و G capital من اللي هو عندي من
+
+38
+00:03:08,030 --> 00:03:15,560
+Zero لعند اللي هو 1 على A لعند اللي هو صفر، واضحة
+
+39
+00:03:15,560 --> 00:03:28,640
+الصورة تقريبا اكيد هنقول define F of G as F of اللي 
+
+40
+00:03:28,640 --> 00:03:36,960
+نسميها اللي هو T بتساوي اللي هو G أو F of 1 على T 
+
+41
+00:03:36,960 --> 00:03:42,460
+لما T اللي هي لا تساوي صفر، وطبعا T أنا معرفها
+
+42
+00:03:42,460 --> 00:03:47,140
+اللي هي في الفترة من Zero لعند 1 على A، وده
+
+43
+00:03:47,140 --> 00:03:51,560
+بيدعرف عند Zero بقول صفر إذا كان T أيش بدها تساوي
+
+44
+00:03:51,560 --> 00:03:59,760
+بتساوي صفر، الآن الـ الـ G of T بتساوي نفس الأسلوب
+
+45
+00:03:59,760 --> 00:04:06,240
+G of 1 على T لما T لا تساوي 0، وصفر إذا كانت T 
+
+46
+00:04:06,240 --> 00:04:13,350
+أشمالها بتساوي 0، الآن واضح العلاقة بين الدالتين اللي
+
+47
+00:04:13,350 --> 00:04:19,510
+هو F و F اللي هو على أساس أني أحول the limit
+
+48
+00:04:19,510 --> 00:04:25,650
+المعطاة عندي limit F of X لما X تروح إلى ما لا نهاية
+
+49
+00:04:25,650 --> 00:04:30,450
+تصير عندي ال limit بالنسبة لهذه اللي هي الـ 1 على X
+
+50
+00:04:30,450 --> 00:04:35,320
+بتاعتنا هتروح لمين؟ في هذه الحالة للصفر، وبنستخدم ومن
+
+51
+00:04:35,320 --> 00:04:40,600
+ثم بنكون حصلنا على المتغير لإن أنا T بروح للصفر as
+
+52
+00:04:40,600 --> 00:04:44,740
+X بتروح لما لا نهاية ومن ثم بنستخدم النظريات اللي 
+
+53
+00:04:44,740 --> 00:04:49,940
+أثبتنا صحتها في حالة T بتروح إلى A من اليمين لإن
+
+54
+00:04:49,940 --> 00:04:53,060
+احنا هنروح لـ Zero من اليمين، هذه اللي هي الخطة اللي
+
+55
+00:04:53,060 --> 00:04:58,480
+هنمشي عليها، بنشوف أول شيء واضح أن الـ F والـ G الـ F 
+
+56
+00:04:59,090 --> 00:05:03,930
+والـ G are differentiable على مين؟ على الفترة من
+
+57
+00:05:03,930 --> 00:05:10,550
+صفر لعند 1 عليه A، 1، 2، ومدام
+
+58
+00:05:10,550 --> 00:05:13,810
+differentiable ده يعني continuous عليها ومش هيك كمان
+
+59
+00:05:13,810 --> 00:05:19,230
+لو جيت أخدت أنت هذه بتحسبها لحالك limit F of T as
+
+60
+00:05:19,230 --> 00:05:27,640
+T بتروح للصفر اللي هي بتساوي limit F of 1 على T as
+
+61
+00:05:27,640 --> 00:05:32,340
+T بتروح للصفر وهتلاقيها إيش هتساوي؟ هتساوي صفر
+
+62
+00:05:32,340 --> 00:05:36,760
+فصارت اللي هي الـ F ال capital is continuous على
+
+63
+00:05:36,760 --> 00:05:43,490
+الفترة من 0 لعند 1 على A، similarly limit G of T لما
+
+64
+00:05:43,490 --> 00:05:47,650
+T تروح للـ Zero، طبعا كل الـ Zero من وين؟ طبيعي من
+
+65
+00:05:47,650 --> 00:05:50,950
+اليمين لأنه احنا عالمنا اللي بنشتغل عليه اللي هي
+
+66
+00:05:50,950 --> 00:05:53,730
+من عند Zero لعند 1 على A، من المنطقة الموجودة بقى
+
+67
+00:05:53,730 --> 00:05:58,750
+إذن هروح للـ Zero من جهة اليمين هيساوي نفس الشيء
+
+68
+00:05:58,750 --> 00:06:03,290
+limit F of 1 على T لما T تروح للـ Zero من 
+
+69
+00:06:03,290 --> 00:06:07,590
+اليمين ويساوي اللي جيها برضه أشمالها بتساوي صفر
+
+70
+00:06:08,590 --> 00:06:12,970
+الآن صارت الآن الـ F والـ G أشمالين are continuous 
+
+71
+00:06:12,970 --> 00:06:17,390
+على الفترة اللي عندنا و differentiable على الفترة 
+
+72
+00:06:17,390 --> 00:06:20,510
+الـ open و .. و .. و .. و .. و .. و .. و .. و .. و 
+
+73
+00:06:20,510 --> 00:06:20,590
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+74
+00:06:20,590 --> 00:06:20,790
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+75
+00:06:20,790 --> 00:06:21,070
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+76
+00:06:21,070 --> 00:06:21,290
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+77
+00:06:21,290 --> 00:06:23,330
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+78
+00:06:23,330 --> 00:06:23,350
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+79
+00:06:23,350 --> 00:06:23,650
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+80
+00:06:23,650 --> 00:06:29,210
+.. و .. و .. و .. و .. و ..
+
+81
+00:06:37,480 --> 00:06:43,680
+بنجي بنحصل على ما يلي، خليني بس اسمحولي أمسح هذه 
+
+82
+00:06:43,680 --> 00:06:49,760
+الdata في الذاكرة عندي، بدي أحسب أنا غاية أن أوجد مين
+
+83
+00:06:49,760 --> 00:06:53,380
+يا جماعة limit اللي هو F of X على G of X لما X 
+
+84
+00:06:53,380 --> 00:07:00,780
+تروح إلى وين؟ إلى ما لا نهاية، لأن limit F of X على G
+
+85
+00:07:00,780 --> 00:07:07,720
+of X لما X تروح إلى ما لا نهاية بتساوي عبارة عن الآن
+
+86
+00:07:07,720 --> 00:07:12,180
+الـ X بتروح إلى ما لا نهاية، F and والـ F  الـ 1 على X 
+
+87
+00:07:12,180 --> 00:07:20,660
+وين بتروح؟ اللي هو الصفر بتساوي limit F of 1 على
+
+88
+00:07:20,660 --> 00:07:26,040
+T خلينا نسميها على G of 1 على T لما T تروح إلى
+
+89
+00:07:26,040 --> 00:07:32,420
+مين؟ إلى الصفر من اليمين، أو إذا كان عندك اضطراب 
+
+90
+00:07:32,420 --> 00:07:38,640
+confusion شيء والتكن X مافي مشكلة، X لما X تروح لـ 0
+
+91
+00:07:38,640 --> 00:07:43,660
+من اليمين اللي هي بتصير عند أسف الـ 1 على X بتروح
+
+92
+00:07:43,660 --> 00:07:47,860
+لـ 0 من اليمين if and only if الـ X بتروح لمين؟ إلى 
+
+93
+00:07:47,860 --> 00:07:51,520
+ما لا نهاية ومن ثم بخطوة ثانية بترجعها للي كتبته 
+
+94
+00:07:51,520 --> 00:07:57,980
+قبل بشوية limit اللي هو عبارة عن F of T على اللي هو
+
+95
+00:07:57,980 --> 00:08:04,420
+G of T لما T تروح لـ 0 من وين؟ من اليمين،  باشي
+
+96
+00:08:04,420 --> 00:08:08,120
+الحال أنا الآن بدي أفضل في الواقع بالنسبة لمن؟
+
+97
+00:08:08,120 --> 00:08:14,040
+بالنسبة له اللي هو الـ X عندي اللي هو وديت واحدة 
+
+98
+00:08:14,040 --> 00:08:19,880
+الـ X من اليمين وصارت عندي اللي هي مكان لأ لأ يا
+
+99
+00:08:19,880 --> 00:08:26,200
+جماعة هاد نظام هي بتضلها آسف أه؟ X X وهنا بتصير
+
+100
+00:08:26,200 --> 00:08:30,900
+أننا مين؟ 1 على T وهنا 1 على T، واضح ليش
+
+101
+00:08:30,900 --> 00:08:36,540
+استبدلنا هنا احنا الـ 1 على X كله بـ T فصارت هذه
+
+102
+00:08:36,540 --> 00:08:41,320
+اللي هي 1 على T وهذه 1 على T، الآن صارت
+
+103
+00:08:41,320 --> 00:08:44,780
+النظرية السابقة مطبقة لأن الـ T بتروح لمين؟ لـ Zero
+
+104
+00:08:44,780 --> 00:08:49,780
+من لمين؟ لأن هدف الواقع مين هي اللي قلنا عنها شيء
+
+105
+00:08:49,780 --> 00:08:57,850
+هذه بتساوي limit F of T على G of T لما T تروح إلى 
+
+106
+00:08:57,850 --> 00:09:01,310
+Zero من وين؟ من اليمين، وهذا متطبق لأن هذا Zero
+
+107
+00:09:01,310 --> 00:09:05,490
+وهذا Zero زي ما عملنا قبل بشوية إذا صار أيش بيساوي
+
+108
+00:09:05,490 --> 00:09:10,990
+تفاضل الأول على تفاضل الثاني في الـ 100 بالنسبة لعن
+
+109
+00:09:10,990 --> 00:09:17,220
+نظرية السابقة إذا بيصير limit التي هي التفاضل هادي
+
+110
+00:09:17,220 --> 00:09:21,060
+من هنا F prime of T أيش بيساوي يا شباب؟ تفاضل
+
+111
+00:09:21,060 --> 00:09:24,960
+هادي، عن T بتروح للـ 0، إذن هي عبارة عن ناقص 1 على
+
+112
+00:09:24,960 --> 00:09:34,000
+T تربيع في F prime of 1 على T تفاضل F of T، F of T 
+
+113
+00:09:34,000 --> 00:09:38,930
+هيها، يعني T لا تساوي صفر تفاضلها F prime بساوي ناقص
+
+114
+00:09:38,930 --> 00:09:42,710
+اللي هو F prime الـ 1 على T فتفاضل اللي جوا اللي 
+
+115
+00:09:42,710 --> 00:09:47,450
+هو عبارة عن أيش؟ ناقص 1 على T تربيع، واضح، على
+
+116
+00:09:47,450 --> 00:09:53,430
+similarly ناقص 1 على T تربيع في G prime of 1 
+
+117
+00:09:53,430 --> 00:10:00,200
+على T لما الـ T تروح لمين؟ إلى الـ 0 من اليمين، النقص 1 
+
+118
+00:10:00,200 --> 00:10:03,160
+دلت الـ T تربيع، النقص 1 دلت T تربيع بروحن مع بعض 
+
+119
+00:10:03,160 --> 00:10:09,780
+نرجع لأصلنا بيصير limit F prime بده استبدل الآن الـ
+
+120
+00:10:09,780 --> 00:10:17,800
+1 على T بالـ X على G prime برضه نفس الشيء على X، والـ
+
+121
+00:10:17,800 --> 00:10:22,540
+T تستبدل بمين؟ اللي هو عبارة عن 1 على X بده تروح للـ
+
+122
+00:10:22,540 --> 00:10:29,270
+0 من اليمين، يعني الـ X بده تروح لمين؟ إلى ما لا نهاية، بيصير 
+
+123
+00:10:29,270 --> 00:10:35,510
+عندي اللي هو limit F of X على G of X بساوي limit F 
+
+124
+00:10:35,510 --> 00:10:40,350
+prime of X على G prime of X وهو المطلوب، نيجي
+
+125
+00:10:40,350 --> 00:10:44,690
+للنظرية بعدها، النظرية اللي بدها شغل، خلينا نشوف
+
+126
+00:10:44,690 --> 00:10:53,110
+النظرية، اطلع لفوق ونركز نشوف أيش هو النظرية بتحكي 
+
+127
+00:10:53,110 --> 00:10:57,270
+ومن ثم نذهب إلى برهان النظرية
+
+128
+00:11:04,010 --> 00:11:11,750
+عشان مساحة اللوحة شوية خلينا نتبع على التلخيص ومن 
+
+129
+00:11:11,750 --> 00:11:19,110
+ثم بنبرهن theorem 636 اللي هي باختصار هي حالة ما لا
+
+130
+00:11:19,110 --> 00:11:22,570
+نهاية على ما لا نهاية، نفترض أن الـ F والـ G are
+
+131
+00:11:22,570 --> 00:11:26,470
+differentiable على الفترة من A و B، يعني إحنا شغلنا
+
+132
+00:11:26,470 --> 00:11:34,230
+الآن على الفترة أي إن كانت هذه الفترة من عند A لعند
+
+133
+00:11:34,230 --> 00:11:41,250
+ما لا نهاية لعند B، لأننا مفترضين أن الـ F والـ G اللي هو
+
+134
+00:11:41,250 --> 00:11:46,250
+قابل للاشتقاق على الفترة A و B، و limit F of X لما 
+
+135
+00:11:46,250 --> 00:11:48,890
+X تروح إلى ما لا نهاية .. إلى Zero من اليمين .. 
+
+136
+00:11:48,890 --> 00:11:53,230
+إلى A من اليمين إيش بيساوي؟ Infinity، و limit G of X 
+
+137
+00:11:53,230 --> 00:11:56,090
+لما X تروح إلى ال A من اليمين برضه إيش مالها؟
+
+138
+00:11:56,090 --> 00:12:01,370
+Infinity، يعني بمعنى آخر صار لما عرضت علينا limit F
+
+139
+00:12:01,370 --> 00:12:06,980
+of X على G of X لما X راحت إلى الـ A من اليمين
+
+140
+00:12:06,980 --> 00:12:10,660
+وجدنا limit اللي فوق ما لا نهاية و limit اللي تحت 
+
+141
+00:12:10,660 --> 00:12:14,260
+ملا نهاية يعني حصلنا على الكمية غير المعينة
+
+142
+00:12:14,260 --> 00:12:18,220
+Infinity على Infinity إذا هذه النظرية ستعالج هذه
+
+143
+00:12:18,220 --> 00:12:23,060
+الحالة طبعا الآن اللي هي بطريقة مشابهة للسابقة
+
+144
+00:12:23,060 --> 00:12:29,080
+والآن احنا طبعا هنقوم ببرهان هذه النظرية نكمل النص
+
+145
+00:12:29,820 --> 00:12:35,900
+الآن فرضنا أيضًا أن اللي هو الـ g of x لا تساوي
+
+146
+00:12:35,900 --> 00:12:40,160
+صفر والـ g prime of x لا تساوي صفر لكل x وإما لها
+
+147
+00:12:40,160 --> 00:12:44,920
+في الفترة a و b يعني مفترض أن الـ g of x لا تساوي
+
+148
+00:12:44,920 --> 00:12:52,860
+صفر على كل الفترة a و b نأتي إلى الجزئية الأولى من
+
+149
+00:12:52,860 --> 00:12:57,380
+النظرية if limit f' على g' يساوي L element in R
+
+150
+00:12:57,380 --> 00:13:02,040
+إذا فlimit f على g برضه أيضًا أيش هتساوي؟ L اللي هي
+
+151
+00:13:02,040 --> 00:13:05,280
+نظريات اللي قبل بشوية بنفس.. بنفس.. خلّيني أقول
+
+152
+00:13:05,280 --> 00:13:10,160
+بنفس المنطق ونفس النصوص بس مبدل 0 على 0 عمالة 
+
+153
+00:13:10,160 --> 00:13:13,560
+نهاية فلان limit f prime على g prime صارت مالها
+
+154
+00:13:13,560 --> 00:13:17,700
+نهاية أو سالب مالا نهاية، برضه النظرية بتظبط، سير
+
+155
+00:13:17,700 --> 00:13:23,310
+limit اللي عندنا هذه هي بالظبط limit الـ F على G as
+
+156
+00:13:23,310 --> 00:13:26,170
+X وتروح لـ M من اليمين يساوي Infinity وسالب 
+
+157
+00:13:26,170 --> 00:13:30,550
+Infinity يعني في النهاية اللي ببحث عنه هذا هو في
+
+158
+00:13:30,550 --> 00:13:34,650
+الحالة هذه أو في الحالة اللي فوق يساوي limit مين
+
+159
+00:13:34,650 --> 00:13:37,750
+الـ F prime على G prime اللي هي الطريقة المحدودة
+
+160
+00:13:37,750 --> 00:13:40,330
+بنفضل اللي فوق و بنفضل اللي تحت و بنوجد limit هين
+
+161
+00:13:40,330 --> 00:13:44,670
+بيكون هين limit اللي هي الأصل اللي احنا بدنا إياها
+
+162
+00:13:45,410 --> 00:13:49,590
+الآن نيجي اللي هو in Berlin اللي هو a و b طبعا
+
+163
+00:13:49,590 --> 00:13:54,410
+بنفس الأسلوب الآن 
+
+164
+00:13:54,410 --> 00:14:02,790
+قبل ما نبدأ احنا لو اجينا و قلنا limit f of x لما
+
+165
+00:14:02,790 --> 00:14:06,610
+x تروح لأي شيء مثلا a من اليمين يساوي L
+
+166
+00:14:11,700 --> 00:14:14,480
+وقلنا اللي هو for every epsilon تعريفها for every
+
+167
+00:14:14,480 --> 00:14:16,660
+epsilon أكبر من صفر there exists a delta أكبر من 
+
+168
+00:14:16,660 --> 00:14:21,300
+صفر such that if x element in A طبعا من اليمين
+
+169
+00:14:21,300 --> 00:14:27,780
+معناته A و A زائد دلتا then اللي هو هيكون عندي f
+
+170
+00:14:27,780 --> 00:14:35,230
+of x ناقص الـ L أصغر من مين؟ من إبسيلون الآن لو كانت عندي
+
+171
+00:14:35,230 --> 00:14:39,330
+الـ epsilon أثبتت أنا هذا الكلام لـ epsilon لـ
+
+172
+00:14:39,330 --> 00:14:45,410
+epsilon لو أثبتت لكل epsilon element in مثلا in
+
+173
+00:14:45,410 --> 00:14:51,970
+صفر و نص أو نص ربع أو نص تلت لو أثبتت أن
+
+174
+00:14:51,970 --> 00:14:54,950
+لكل إبسيلون لجهة دلتا بحيث أن هذا الكلام أصغر من 
+
+175
+00:14:54,950 --> 00:15:01,650
+مين؟ من إبسيلون برضه بيكون يجزئ عن الـ limit ليش؟ لأن
+
+176
+00:15:01,650 --> 00:15:04,950
+المقدار اللي بيكون أصغر من إبسيلون اللي هي أصغر من 
+
+177
+00:15:04,950 --> 00:15:09,830
+النص أكيد بنفع لمين؟ للدلتا بنفع للمقدار اللي الـ
+
+178
+00:15:09,830 --> 00:15:15,450
+إبسيلون أكبر من مين؟ من النص لأنه أصلا اللي هي مشكلة
+
+179
+00:15:15,450 --> 00:15:19,620
+أو خلينا نقول الـ limit في حد ذاتها أنه لما الـ A
+
+180
+00:15:19,620 --> 00:15:24,880
+تروح الـ X تروح إلى الـ A من اليمين، بدنا نجمع أن
+
+181
+00:15:24,880 --> 00:15:27,720
+الـ F of X تقترب من مين؟ من الـ L من اليمين، يعني التعجيز و
+
+182
+00:15:27,720 --> 00:15:31,100
+كأنه بعجزني أنه يقول لي إنك تلاقي الـ Delta في 
+
+183
+00:15:31,100 --> 00:15:34,600
+حالة الـ Epsilon  أكاش اللي بيكون صغيرة فالـ Close 
+
+184
+00:15:34,600 --> 00:15:38,960
+اللي هو تمين to Zero، لإنه أصلا المفهوم اللي
+
+185
+00:15:38,960 --> 00:15:43,160
+بتقيله هذه المسافة تضيق، تضيق، تضيق، بحيث أن F of
+
+186
+00:15:43,160 --> 00:15:46,760
+X تقول إلى الـ مين اللي بتعبر عنها؟ الـ Epsilon،
+
+187
+00:15:46,760 --> 00:15:51,190
+لأن بعطيك Epsilon صغيرة جدًا جدًا بدك تلاقي لي Delta
+
+188
+00:15:51,190 --> 00:15:54,870
+أنا الآن الـ Epsilon بين صفر و نص لقيت لك الـ
+
+189
+00:15:54,870 --> 00:15:59,070
+Delta اللي طلعت هنا معناته اللي نفع للـ Epsilon
+
+190
+00:15:59,070 --> 00:16:03,510
+الصغيرة أكيد بيكون أصغر من مين؟ من الأكبيرة إذا هذا
+
+191
+00:16:03,510 --> 00:16:09,250
+يجزئ بس هذا قبل ما نبدأ لأنه هسأخدم شغلة اللي هو 
+
+192
+00:16:09,250 --> 00:16:14,930
+في هذا الاتجاه نيجي الآن عندي أول شيء المعطى
+
+193
+00:16:14,930 --> 00:16:23,550
+ماتيني LimitF prime of X على G prime of X as X
+
+194
+00:16:23,550 --> 00:16:29,190
+بتروح للـ A من اليمين أيش يساوي؟ يساوي أقل تعريف
+
+195
+00:16:29,190 --> 00:16:32,850
+الـ Limit for every Y أكبر من 0 اللي هتاخد for 
+
+196
+00:16:32,850 --> 00:16:39,190
+every Y element in 0 ونص اللي هي لزوم حسابات، بعد 
+
+197
+00:16:39,190 --> 00:16:44,650
+شوية هنشوفها الآن لكل y تنتمي إلى 0.5 وهذا مشروع
+
+198
+00:16:44,650 --> 00:16:49,270
+حسب ما حكيت قبل بشوية there exist delta أكبر من 0
+
+199
+00:16:49,270 --> 00:16:57,650
+such that اللي هو if x element in a و a زيادة دلتا 
+
+200
+00:16:57,650 --> 00:17:04,230
+لإن رايح لل a من وين؟ من اليمين لجيت اللي هو دلتا
+
+201
+00:17:04,230 --> 00:17:11,420
+بحيث أنه لكل x في الفترة من a لعند a زائد دلتا بصير 
+
+202
+00:17:11,420 --> 00:17:16,780
+عندي لكل x المتنية زائد دلتا بتطلع عندي then f 
+
+203
+00:17:16,780 --> 00:17:23,420
+prime of x على g prime of x ناقص ال L أصغر من مين؟
+
+204
+00:17:23,420 --> 00:17:32,060
+من ال epsilon إذا الآن من هذه ال limit حصلت على أن
+
+205
+00:17:32,060 --> 00:17:36,540
+لأي إبسلون بين الـ 0 و نص بقدر ألاقي Delta بحيث 
+
+206
+00:17:36,540 --> 00:17:40,540
+لكل الإكسات في المنطقة هذه هذه الـ Inequality إيش
+
+207
+00:17:40,540 --> 00:17:44,880
+مالها تتحقق الآن بس خلّيني أكملها دي شوية عشان
+
+208
+00:17:44,880 --> 00:17:52,040
+بستخدمها لشغلات أخرى عند A زائد Delta هذا بس مجرد 
+
+209
+00:17:52,040 --> 00:17:56,340
+تعريف الـ Limit F' على الـ G' لما X تروح للـ A من
+
+210
+00:17:56,340 --> 00:17:59,120
+اليمين الآن
+
+211
+00:18:01,110 --> 00:18:04,910
+بدي أختار.. بدي أسهل على حالي بدل من كل مرة أقول 
+
+212
+00:18:04,910 --> 00:18:08,130
+a زي الـ delta وبعد شوية ألاقي delta prime وأخد
+
+213
+00:18:08,130 --> 00:18:12,010
+الـ minimum بينهم الآخر أجدف عليه عشان اللي بحكيه 
+
+214
+00:18:12,010 --> 00:18:17,910
+بدي أخد اللي هو أقول choose c1 element in a و a زي
+
+215
+00:18:17,910 --> 00:18:24,630
+الـ delta الآن اختار لي c1 من ال a لعند مين؟ لعند الـ
+
+216
+00:18:24,630 --> 00:18:30,340
+a زي ال delta سميّه c1 يعني مجرد اختيار أنا اخترته
+
+217
+00:18:30,340 --> 00:18:38,260
+الآن choose.. choose C1 element in A و A زائد
+
+218
+00:18:38,260 --> 00:18:44,140
+دلتا يعني C1 وين موجود؟ موجود في المنطقة التي
+
+219
+00:18:44,140 --> 00:18:50,140
+تتحقق فيها F' ع G' ناقص أصغر من ميل من إبسل عشان
+
+220
+00:18:50,140 --> 00:18:56,080
+تستخدمها بعد شوية واضح طيب هذه من جهة الآن من الجهة
+
+221
+00:18:56,080 --> 00:19:03,100
+الثانية عند limit f of x لما x تروح إلى مالا نهاية
+
+222
+00:19:03,100 --> 00:19:09,880
+آسف للـ a من اليمين بسوء أيش هو معطيني إياها هي النظرية
+
+223
+00:19:09,880 --> 00:19:13,540
+هي limit f of x لما x تروح إلى ال a من اليمين بسوء 
+
+224
+00:19:13,540 --> 00:19:15,760
+limit g of x لما x تروح إلى ال a من اليمين بسوء
+
+225
+00:19:15,760 --> 00:19:23,170
+أيش ماله؟ مالا نهاية من تعريفها هذا إيش يعني؟ لكل K
+
+226
+00:19:23,170 --> 00:19:29,270
+اللي هو element in R there exists Delta A' أكبر من 
+
+227
+00:19:29,270 --> 00:19:36,590
+0 such that اللي هو F of X أكبر من اللي هو الـ K
+
+228
+00:19:36,590 --> 00:19:42,210
+لكل X و N موجودة في الـ A و A زائد مين؟ Delta 
+
+229
+00:19:42,210 --> 00:19:49,300
+Prime، مظبوط ولا لا؟ ماشي الحال الآن لكل x element
+
+230
+00:19:49,300 --> 00:19:52,200
+in A و A زي الـ delta prime هذه ال F of X أكبر من
+
+231
+00:19:52,200 --> 00:20:02,420
+مين؟ من K الآن لو كانت ال A و ال A.. الآن عندي
+
+232
+00:20:02,420 --> 00:20:07,540
+لكل subset من هذه.. لكل subset.. لو كان عندي A و 
+
+233
+00:20:07,540 --> 00:20:10,940
+C2 مثلا subset من ال A و ال A زي ال delta prime
+
+234
+00:20:12,470 --> 00:20:17,070
+برضه ال F of X أكبر من K هذه بتحققها بتحقق إيش؟ لكل X
+
+235
+00:20:17,070 --> 00:20:24,610
+وين موجودة في الفترة من A لعند مين؟ لعند C2 الآن لو
+
+236
+00:20:24,610 --> 00:20:30,410
+كانت ال Delta اللي لجيتها برا ولا جوا بقدر أختار 
+
+237
+00:20:30,410 --> 00:20:36,990
+جوا اللي هو C2 بحيث أنه لو الـ C2 هذه هي اللي
+
+238
+00:20:36,990 --> 00:20:42,450
+اخترتها جوات من الـ A والـ A زائد دلتا بتظل الـ F 
+
+239
+00:20:42,450 --> 00:20:47,470
+of X A شمالها أكبر من مين؟ من الـ K، واضح؟ إذا من
+
+240
+00:20:47,470 --> 00:20:52,330
+هذه بدي أستفيد شغلتين بدي أطبق التعريف هذا لـ K
+
+241
+00:20:52,330 --> 00:20:56,730
+محددة مين الـ K اللي بدي أطبقها؟ اللي عبارة عن F
+
+242
+00:20:56,730 --> 00:21:02,560
+عند مين؟ عند C1 واضح؟ إذا الآن بما أنه limit f of X 
+
+243
+00:21:02,560 --> 00:21:05,680
+ثم X تروح إلى الـA باليمين يساوي Infinity إذا for 
+
+244
+00:21:05,680 --> 00:21:13,720
+K.. إذا for f of C1 there exists Delta Prime أي 
+
+245
+00:21:13,720 --> 00:21:19,840
+Delta Prime معينة بحيث أن f of X أكبر من 100 من f
+
+246
+00:21:19,840 --> 00:21:27,060
+of C1 لكل X موجودة بين الـA والـA زائد Delta Prime
+
+247
+00:21:27,680 --> 00:21:31,860
+أنا بدي أختار في مين؟ لكل X الموجودة بين الـ A و
+
+248
+00:21:31,860 --> 00:21:37,940
+الـ C2 حيث الـ C2 موجودة في الفترة هذه و بدي إياها من
+
+249
+00:21:37,940 --> 00:21:44,120
+C1 ولجاي إذا عشان هيك بقدر أقول then we can 
+
+250
+00:21:44,120 --> 00:21:50,280
+choose C2 بين A و C1 الـ C2 بقدر أختارها فعلًا
+
+251
+00:21:50,280 --> 00:21:55,640
+بختارها بس طبعًا وين تشتري تشريع اللي اختيارها أنها
+
+252
+00:21:55,640 --> 00:22:01,420
+تكون بين الفترة A و A زائد Delta Prime وبدي إياها
+
+253
+00:22:01,420 --> 00:22:06,900
+تيجي في داخل الـ A و الـ C1 إذا then we can choose
+
+254
+00:22:06,900 --> 00:22:13,200
+C2 element A of C1 بحيث أن ال F of X أكبر من مين؟
+
+255
+00:22:13,200 --> 00:22:22,810
+من F of C1 لكل X وينفي الفترة بين A و C2 طيب
+
+256
+00:22:22,810 --> 00:22:28,050
+هذه معناته أن ال F of X هذه لكل الـ Xات اللي هان الـ
+
+257
+00:22:28,050 --> 00:22:34,290
+F of X أكيد أي شمالها لها تساوي أيش؟ F of C1 هل
+
+258
+00:22:34,290 --> 00:22:38,930
+جد تعرف ليش بدي إياها هذه؟ عشان لزوم تعريف شغل معينة
+
+259
+00:22:38,930 --> 00:22:44,770
+بنفعش تكون ال F of X أيش بتساوي؟ F of C1 الآن 
+
+260
+00:22:44,770 --> 00:22:55,550
+similarly Similarly اللي هو بما أنه limit G of X
+
+261
+00:22:55,550 --> 00:23:00,690
+يساوي مالا نهاية as X بتروح للـ A من اليمين إذا
+
+262
+00:23:00,690 --> 00:23:13,160
+بقدر ألاقي اللي هو C1 برايم بحيث أنه G of X أكبر أو 
+
+263
+00:23:13,160 --> 00:23:17,240
+لا تساوي طبعًا أكبر الـ thrifty يعني لا تساوي G of
+
+264
+00:23:17,240 --> 00:23:27,860
+C1 لكل X موجودة في الـ A و C1 إيش إبراهيم اه G C1
+
+265
+00:23:27,860 --> 00:23:34,680
+إبراهيم اه G C1 إبراهيم الآن
+
+266
+00:23:34,680 --> 00:23:40,760
+الـ..الـ..الـ.. الباخد الـ Minimum عشان طبعًا هذا
+
+267
+00:23:40,760 --> 00:23:46,120
+اللي لجهة N C1' ممكن اللي هي لكل X في الـ A و C1'
+
+268
+00:23:46,620 --> 00:23:52,840
+و لكل X element in A و C2' بط مانش.. مش عارف مين
+
+269
+00:23:52,840 --> 00:23:58,670
+الأكبر من هذول فباخد الـ Minimum من الجهتين و
+
+270
+00:23:58,670 --> 00:24:03,090
+بسميها C1 مثلا أو C2 الـ minimum من التنتين C2
+
+271
+00:24:03,090 --> 00:24:09,550
+فبتصير عندي لأن لكل X في ال A و الـ minimum بينهن
+
+272
+00:24:09,550 --> 00:24:14,630
+هذه بتظبط وهذه بتظبط يعني ال G of X لا تساوي F of
+
+273
+00:24:14,630 --> 00:24:20,670
+C1 والـ F of X لا تساوي مين؟ F of C1 برايم ومنه 
+
+274
+00:24:20,670 --> 00:24:25,870
+بعرف اللي بدي إياه أو بعمل زي ما هو عامل في الكتاب إيش
+
+275
+00:24:25,870 --> 00:24:29,280
+اللي بقوله؟ نشوف اللي بعدها إذا الآن اللي اتفجنا
+
+276
+00:24:29,280 --> 00:24:38,540
+عليه أنه في الفترة من A لعند A زائد Delta هذه
+
+277
+00:24:38,540 --> 00:24:45,480
+متحققة هاي واحد واللي اتفجنا عليه أن F of X لا
+
+278
+00:24:45,480 --> 00:24:50,140
+تساوي F of C1 في الفترة من A لعند C2
+
+279
+00:24:50,140 --> 00:24:55,580
+أشمالها متحققة يعني بمعنى آخر الـ Inequality هذه
+
+280
+00:24:55,580 --> 00:25:03,800
+وهذه التنتين محققات من أين؟ من A لعند C2
+
+281
+00:25:03,800 --> 00:25:05,360
+واضح؟
+
+282
+00:25:11,650 --> 00:25:17,590
+الآن وصلنا لمرحلة أنه نقدر نعرف الدالة اللي بتديها 
+
+283
+00:25:17,590 --> 00:25:23,890
+اللي هي F of X بتساوي 1 ناقص F of C واحد على F 
+
+284
+00:25:23,890 --> 00:25:30,470
+of X و1 ناقص G of C واحد على G of X لكل X وين
+
+285
+00:25:30,470 --> 00:25:37,330
+موجودة بين A وC اثنين و F of C واحد لا تساوي F of X 
+
+286
+00:25:37,330 --> 00:25:43,340
+مظبوط؟ هيّا اعملها أه لإن وين بدي أعرف هذه الدالة F
+
+287
+00:25:43,340 --> 00:25:50,480
+من A لعند مين اللي هي بتتحقق عليها خاصية F of X ده
+
+288
+00:25:50,480 --> 00:25:55,080
+تساوي مين؟ F of C واحد وبتتحقق عليها مين اللي هي
+
+289
+00:25:55,080 --> 00:26:00,480
+الخاصية اللي عندي هذه لإن كله هيلزمني هذا إذا الآن 
+
+290
+00:26:05,340 --> 00:26:09,980
+اتفقنا عليها دي أه عشان بدي امسح أنه عندي f prime
+
+291
+00:26:09,980 --> 00:26:13,800
+على الـ g prime نقصها الأصغر من إبسلون لكل الـ Xات
+
+292
+00:26:13,800 --> 00:26:18,700
+من A لعند A زائد دلتا لكل الـ Xات اللي هنا
+
+293
+00:26:18,700 --> 00:26:22,040
+واتفقنا أن F of X لا تساوي F of C one برضه في
+
+294
+00:26:22,040 --> 00:26:27,350
+الفرق في المنطقة من إيش؟ من A لـ C2 اتفقنا عليه الآن 
+
+295
+00:26:27,350 --> 00:26:33,510
+نيجي نعرف الدالة اللي هتوصلني لهدفي خذ الآن f of x
+
+296
+00:26:33,510 --> 00:26:42,670
+بتساوي اللي هو 1 ناقص f of c واحد على f of x 
+
+297
+00:26:42,670 --> 00:26:52,450
+على 1 ناقص g of c واحد على g of x الآن g of c
+
+298
+00:26:52,450 --> 00:26:55,810
+واحد مستحيل تساوي g of x من أي أسباب اللي حكيناها 
+
+299
+00:26:55,810 --> 00:27:01,710
+وليس سبب آخر أيضا اللي هو ليش أنه عندي الـ g prime
+
+300
+00:27:01,710 --> 00:27:07,570
+الـ g prime of x ده يساوي صفر إذا حسب Rolle's
+
+301
+00:27:07,570 --> 00:27:13,570
+theorem مستحيل الـ g of c واحد اللي هو تساوي g of 
+
+302
+00:27:13,570 --> 00:27:20,530
+x ليش؟ عندي g continuous
+
+303
+00:27:21,550 --> 00:27:29,350
+on a .. طبعا الـ x واللي موجودة جواها منها الآن من x
+
+304
+00:27:29,350 --> 00:27:37,110
+لعند c واحد صح؟ و g is differentiable on x لعند
+
+305
+00:27:37,110 --> 00:27:44,090
+اللي هي c واحد open واضحة؟
+
+306
+00:27:44,090 --> 00:27:48,670
+لأنه أثر هذا continuous و differentiable من a لعند
+
+307
+00:27:48,670 --> 00:27:52,550
+b العلمي إذا في الجزئية هذه إذا أكيد اللي هم تتحقق 
+
+308
+00:27:52,550 --> 00:28:01,270
+هذه الآن لو زي ما بنقول أن g prime لو لو عندي بدي 
+
+309
+00:28:01,270 --> 00:28:09,250
+يكون g of x بسوء g of c واحد معناته حسب role
+
+310
+00:28:09,250 --> 00:28:16,360
+theorem هيعطيني there exist cx element in x و c1
+
+311
+00:28:16,360 --> 00:28:22,800
+such that g prime of cx هي ساوي صفر وهذا مستحيل
+
+312
+00:28:22,800 --> 00:28:27,320
+لإن هو معطيني الـ g prime of x لا تساوي صفر لكل x
+
+313
+00:28:27,320 --> 00:28:34,630
+element من a وb معناته معناه الحديث إنه الـ G of C
+
+314
+00:28:34,630 --> 00:28:41,510
+واحد والـ G of X مستحيل يكون متساويات لكل الـ Xات
+
+315
+00:28:41,510 --> 00:28:47,230
+اللي في الفترة من A لعند مين؟ لعند C اثنين واضحة إذا
+
+316
+00:28:47,230 --> 00:28:50,730
+المقام لا يساوي صفر إذا اللي هو هذه is well
+
+317
+00:28:50,730 --> 00:29:00,950
+defined على مين؟ على الفترة A مظبوط وC2 خليها في
+
+318
+00:29:00,950 --> 00:29:05,070
+الذاكرة طيب اطلع لفوق وحسب لل limit الآن هذا 
+
+319
+00:29:05,070 --> 00:29:12,070
+عرفناها حفظناها بنضطر أن امسح الآن احسب لل limit
+
+320
+00:29:12,070 --> 00:29:20,230
+للي فوق limit F of X لما X تروح الي وين؟ الي a من
+
+321
+00:29:20,230 --> 00:29:23,390
+اليمين بساوي 1
+
+322
+00:29:24,530 --> 00:29:32,650
+ناقص limit F of C1 عدد على F of X لما X تروح للـ A
+
+323
+00:29:32,650 --> 00:29:36,950
+من اليمين اتجرأت لأنه عارف أن ال limit موجودة
+
+324
+00:29:36,950 --> 00:29:42,290
+على التوزيع اتجرأت عليه لأنه عارف limit G of C1
+
+325
+00:29:42,290 --> 00:29:49,530
+على G of X لما X تروح لوين؟ للـ A من اليمين واضحة
+
+326
+00:29:49,530 --> 00:29:56,130
+جدش هذه ال limit صفر لأن الـ F of X وين بتروح؟ إلى مالانهاية 
+
+327
+00:29:56,130 --> 00:30:00,010
+نهاية هي بداية الموضوع مش بداية الموضوع كان عندنا
+
+328
+00:30:00,010 --> 00:30:05,010
+أن ال limit F of X على G of X لما X تروح الى A من 
+
+329
+00:30:05,010 --> 00:30:08,670
+اليمين اللي هو سبب لكل القصة أن هذه ال limit
+
+330
+00:30:08,670 --> 00:30:11,230
+مالانهاية وهذه مالانهاية صارت مالانهاية مالانهاية
+
+331
+00:30:11,230 --> 00:30:15,710
+نهاية وهي اللي خلتني اروح بهذا الاتجاه إذا هذه
+
+332
+00:30:16,610 --> 00:30:19,750
+بتروح إلى مالانهاية إذا هذه بتروح إلى صفر وهذه 
+
+333
+00:30:19,750 --> 00:30:22,330
+المال انهاية بتروح إلى صفر إذا هذا كله على بعض إيش
+
+334
+00:30:22,330 --> 00:30:30,170
+بيساوي؟ بيساوي 1 واضح طيب الآن for every
+
+335
+00:30:30,170 --> 00:30:34,570
+epsilon أكبر من صفر اللي هي اللي فوق خلاص بدنا
+
+336
+00:30:34,570 --> 00:30:39,270
+فيها الآن بيبقى أن ال limit بيساوي 1 إذا there
+
+337
+00:30:39,270 --> 00:30:44,890
+exists Delta أكبر من صفر أي إن كانت الـ Delta أكبر
+
+338
+00:30:44,890 --> 00:30:53,790
+من صفر Such that F of X ناقص 1 أصغر من مين؟ من 
+
+339
+00:30:53,790 --> 00:30:59,190
+الـ Epsilon الـ Epsilon اللي بدنا فيها من الأول هذا لو
+
+340
+00:30:59,190 --> 00:31:04,830
+يعني لكل الـ X اللي في الفترة من a ل a زائد الـ delta
+
+341
+00:31:04,830 --> 00:31:07,910
+هذه الـ delta الجديدة مش صارت تكون الأولى فأنا 
+
+342
+00:31:07,910 --> 00:31:13,330
+عشان أريح حالي بدي اخذ اللي هو أصغر delta بلاقيها 
+
+343
+00:31:13,330 --> 00:31:17,910
+وأقول حطها كمان جواها هادي حر أنا مدام بتنفع لي
+
+344
+00:31:17,910 --> 00:31:21,690
+كبيرة أيضا كده بتنفع لمن؟ للصغيرة فاهمين أنا إيش
+
+345
+00:31:21,690 --> 00:31:28,270
+بقول؟ هذه اللي هي نسميها C3 معايا؟ فبيصير عندي الآن
+
+346
+00:31:28,270 --> 00:31:39,200
+F of X لكل X element in A لعند مين؟ C3 أي
+
+347
+00:31:39,200 --> 00:31:46,120
+سؤال؟ F of X ناقص 1 أصغر من Y أكبر من سالب Y
+
+348
+00:31:46,120 --> 00:31:49,960
+تلزمني هذه المنطقة اللي اللي جاي لأن F of X هذه
+
+349
+00:31:49,960 --> 00:31:56,720
+يعني F of X يعطينا F of X أكبر من 1 ناقص Y 
+
+350
+00:31:59,390 --> 00:32:03,370
+واضحة؟ لأن هذه جلبها .. اللي هذه طبعا 1 ناقص 
+
+351
+00:32:03,370 --> 00:32:07,850
+إبسلون اللي هي بيصير عنده ال .. ال .. ال إبسلون
+
+352
+00:32:07,850 --> 00:32:12,650
+أصغر من مين؟ من نصف الـ 1 ناقص إبسلون أكبر من مين؟
+
+353
+00:32:12,650 --> 00:32:20,670
+اللي هي بيصير أكبر من نصف واضحة؟ اللي هي بيصير 1
+
+354
+00:32:20,670 --> 00:32:28,400
+على f of x اللي هو أصغر من مين؟ هذا لمين؟ لكل
+
+355
+00:32:28,400 --> 00:32:32,760
+الـ Xات اللي من A لعند مين؟ C3 وطبيعي الـ
+
+356
+00:32:32,760 --> 00:32:36,880
+inequalities كلها اللي قبل تتحقق هنا لإنها بتتحقق 
+
+357
+00:32:36,880 --> 00:32:41,360
+من هنا لهنا بعضها وبعضها بتتحقق من هنا لهنا فأكيد
+
+358
+00:32:41,360 --> 00:32:47,040
+كلها هتتحقق للإكسات اللي مين؟ في الـ A وC3 أصلا أنا
+
+359
+00:32:47,040 --> 00:32:52,620
+رايح باتجاه مين؟ رايح باتجاه أثبت لكم أنه limit of
+
+360
+00:32:53,680 --> 00:32:59,060
+of x على g of x لما x تروح لل a من اليمين بساوي
+
+361
+00:32:59,060 --> 00:33:04,880
+limit f prime of x على g prime of x as x تروح لل a
+
+362
+00:33:04,880 --> 00:33:10,080
+من اليمين اللي هو إيش نسميه احنا؟ قال إذا أنا بهمني 
+
+363
+00:33:10,080 --> 00:33:14,920
+مين الـ Xات اللي جنب الـ a لإن أنا رايح للـ a من وين؟
+
+364
+00:33:14,920 --> 00:33:18,800
+من اليمين فأنا بهمني الجوار القريب جدا من الـ a لإن 
+
+365
+00:33:18,800 --> 00:33:21,960
+أنا رايح له أصلا من هنا فالإكسات اللي فيها هي اللي
+
+366
+00:33:21,960 --> 00:33:27,760
+بتلزمني عشان أصل للي بديها خلي هذه في الذاكرة
+
+367
+00:33:27,760 --> 00:33:34,560
+فصار عندي الآن صار 
+
+368
+00:33:34,560 --> 00:33:38,800
+عندي هذا كله حكيناه وخلصنا منه الآن نيجي بدنا نصل
+
+369
+00:33:38,800 --> 00:33:44,620
+للي بدنا ياها بتتذكروا المرة الماضية أنا أصلا جبت 
+
+370
+00:33:44,620 --> 00:33:56,350
+هذه جبت هذه أطلع فيها وقارن لي إياها مع الـ F of X على 
+
+371
+00:33:56,350 --> 00:34:01,310
+الـ G of X اللي أنا بديها لها الـ F of X على الـ G of X
+
+372
+00:34:01,310 --> 00:34:08,170
+لو جيت قارنتها F of X على الـ G of X إيش هتلاقيها؟
+
+373
+00:34:08,170 --> 00:34:14,810
+لو جيت ضربت هذه في F of X وهذه في G of X 
+
+374
+00:34:17,460 --> 00:34:22,500
+بنرجع لـ F of X ناقص F of C واحد و G of X ناقص G of
+
+375
+00:34:22,500 --> 00:34:26,680
+C واحد طب إيش دخلنا فيه هذه F of X ناقص F of C
+
+376
+00:34:26,680 --> 00:34:30,500
+واحد و G of X ناقص G of C واحد هذه اللي بالكوشي
+
+377
+00:34:30,500 --> 00:34:33,920
+mean value theorem اللي هتجيب للـ F prime و G prime
+
+378
+00:34:33,920 --> 00:34:38,340
+اللي أنا أصلا موجودات limited فبحصل على اللي بديها
+
+379
+00:34:40,230 --> 00:34:44,470
+بالضبط الشيء اللي بقوله أنت يعني ليش هو فكر في هذه
+
+380
+00:34:44,470 --> 00:34:50,470
+بالسبب اللي حكيته F of X على D of X بالساوي F of X
+
+381
+00:34:50,470 --> 00:34:59,890
+على D of X في F of X على D of X على F of X مظبوط؟
+
+382
+00:34:59,890 --> 00:35:09,170
+ما عملش شيء الآن اسحب لي هذه خليها وحط لي إياها هذه 1 على
+
+383
+00:35:09,170 --> 00:35:15,210
+f of x ماهي الحالة هذه؟ مين هي في الواقع؟ هي اللي
+
+384
+00:35:15,210 --> 00:35:20,410
+فوق اللي هي عبارة عن اضرب f of x هذه في هذه بيصير
+
+385
+00:35:20,410 --> 00:35:32,250
+1 ويساوي 1 اللي هي ناقص f of c صح؟ f of x 
+
+386
+00:35:32,250 --> 00:35:42,660
+ناقص f of c على g of x نقص g of c هذا مين هي اللي
+
+387
+00:35:42,660 --> 00:35:46,700
+هي f of x على g of x في f of x عوضت هذه وحطيتها و
+
+388
+00:35:46,700 --> 00:35:51,760
+طلع عندي هذا مضروب في كله في مين؟ في واحدة الـ f of
+
+389
+00:35:51,760 --> 00:36:01,080
+x الآن عندي خليني أطبق اللي هو مين؟ الـ Cauchy mean 
+
+390
+00:36:01,080 --> 00:36:06,390
+value theorem على الفترة من a لمين؟ لـ c تلاتة ماشي
+
+391
+00:36:06,390 --> 00:36:11,130
+اللي هو there exist طبعا كله متحقق اللي هو الـ F و
+
+392
+00:36:11,130 --> 00:36:15,230
+الـ G continuous و differentiable على الـ A و الـ C 3
+
+393
+00:36:15,230 --> 00:36:21,430
+إذا there exist اللي هو إيه؟ اللي بدكي اسميها اللي
+
+394
+00:36:21,430 --> 00:36:25,690
+هي مثلا there exist gamma أو زي ما هو مسميها في 
+
+395
+00:36:25,690 --> 00:36:32,230
+الكتاب there exist xi element in A و C تلاتة such
+
+396
+00:36:32,230 --> 00:36:41,500
+that f prime of xi على g prime of xi بساوي بس إن 
+
+397
+00:36:41,500 --> 00:36:44,780
+أنا عشان بتطبقها على مين؟ على الفترة f of x لعند 
+
+398
+00:36:44,780 --> 00:36:48,800
+مين؟ عشان تطلع عندي f of x of مين؟ و f of c واحد
+
+399
+00:36:48,800 --> 00:36:53,120
+معايا لـ Xات اللي وين؟ اللي موجودة من a لعند c
+
+400
+00:36:53,120 --> 00:36:58,060
+تلاتة بعد اذنكم بتطبقها الكوشي mean value theorem 
+
+401
+00:36:58,760 --> 00:37:01,840
+ما هي أصلا continuous و differentiable على الفترة
+
+402
+00:37:01,840 --> 00:37:06,500
+دي كلها من ضمنها مين؟ الفترة A وC تلاتة ومن ضمنها 
+
+403
+00:37:06,500 --> 00:37:11,040
+الفترة A وC واحد اللي أنا بدي أطبق عليها بال end
+
+404
+00:37:11,040 --> 00:37:15,900
+point مين الـ end point C واحد هيها والـ end point
+
+405
+00:37:15,900 --> 00:37:21,890
+الـ X اللي موجودة بين A و B مين؟ C3 واضحة واضحة اللي 
+
+406
+00:37:21,890 --> 00:37:26,350
+بدي .. إذا الآن الآن there exists x i الآن بالضبط
+
+407
+00:37:26,350 --> 00:37:30,630
+بدي أطبق الميكوشي main value term على الفترة اللي هي
+
+408
+00:37:30,630 --> 00:37:37,790
+X و C1 اللي الـ F والـ G differentiable عليها من
+
+409
+00:37:37,790 --> 00:37:40,530
+وين الـ X هذه؟ الـ X اللي فوق هذه اللي بشتغل فيها
+
+410
+00:37:40,530 --> 00:37:45,890
+اللي هي من A لعند مين؟ لعن C3 إذن there exists xi
+
+411
+00:37:45,890 --> 00:37:50,750
+element in x و c واحد such that f prime of xi على
+
+412
+00:37:50,750 --> 00:37:58,770
+g prime of xi في إيش بتساوي؟ f of c واحد أو f of x
+
+413
+00:37:58,770 --> 00:38:05,390
+ناقص f of c واحد فاهمين؟ طبعا على g of x ناقص g of 
+
+414
+00:38:05,390 --> 00:38:10,990
+c واحد بس ضربت في ناقص فوق وناقص صحيح تتعدى زي ما
+
+415
+00:38:10,990 --> 00:38:20,080
+هي لأن هذه هي هذه إذا صارت عندي F of X على G of X
+
+416
+00:38:20,080 --> 00:38:26,000
+بسوء F prime على G prime في 1 على مين؟ على F of
+
+417
+00:38:26,000 --> 00:38:32,060
+X وهو اللي بده يوصلنا للي بدنا هي معليش امسح اللي
+
+418
+00:38:32,060 --> 00:38:35,280
+هان بيصير عندي
+
+419
+00:38:38,180 --> 00:38:45,160
+بيصير عندي الـ F of X على مين؟ F of X على G of X
+
+420
+00:38:45,160 --> 00:38:48,540
+بساوي 
+
+421
+00:38:48,540 --> 00:38:54,120
+اللي هو هدى شلناه وحطينا مكانها مين بساوي F prime
+
+422
+00:38:54,120 --> 00:39:02,140
+of X على G prime of X في مين في واحد على ايه
+
+423
+00:39:02,140 --> 00:39:03,500
+ايش على F
+
+424
+00:39:09,880 --> 00:39:18,360
+واضح أه؟ الآن نمحى هنا هدول الـ Xات اللي هنا هما
+
+425
+00:39:18,360 --> 00:39:23,380
+الـ Xات اللي وين موجودة بين A وC3 ماشي الحال بدي
+
+426
+00:39:23,380 --> 00:39:29,120
+الآن غايتي أني أوجد F of X على G of X ناقص مين؟
+
+427
+00:39:29,120 --> 00:39:34,600
+ناقص L واضحة إذا نلخص كل اللي اخذناه for every
+
+428
+00:39:34,600 --> 00:39:38,800
+epsilon element in zero نص there exists delta أكبر
+
+429
+00:39:38,800 --> 00:39:48,980
+من صفر such that if اللي هو x أكبر من a أصغر من c3
+
+430
+00:39:48,980 --> 00:39:53,260
+أصغر من c2 أصغر من c1 أصغر من a زي ال delta اللي
+
+431
+00:39:53,260 --> 00:40:02,070
+لجناها فاهمين عليها وكون عندي اللي هو قيمة العوض f
+
+432
+00:40:02,070 --> 00:40:08,110
+of x على g of x ناقص ال .. بدي أقبل لك يميها هذا
+
+433
+00:40:08,110 --> 00:40:12,510
+اللي هو أصغر من epsilon في something مش مشكلة و
+
+434
+00:40:12,510 --> 00:40:15,810
+epsilon is arbitrary أيضا بيصير limit زي ما بدنايا
+
+435
+00:40:15,810 --> 00:40:24,170
+واضح هذا الآن بالظبط بيساوي اللي هو العوض اللي هو
+
+436
+00:40:24,170 --> 00:40:28,590
+f of x اللي هي عبارة عن واحد
+
+437
+00:40:32,680 --> 00:40:41,680
+أف برايم of x i على جي برايم of x i في واحد على أف
+
+438
+00:40:41,680 --> 00:40:48,180
+of x ناقص اللي 
+
+439
+00:40:48,180 --> 00:40:54,460
+واضح لحتى الان ناخد هذه عامل مشترك برا يصبح واحد
+
+440
+00:40:54,460 --> 00:41:02,140
+على أف of x في أف برايم of x i على g prime of xi
+
+441
+00:41:02,140 --> 00:41:13,560
+ناقص L في F of X صح؟ أخدت
+
+442
+00:41:13,560 --> 00:41:17,300
+الواحد على F of X عامل مشترك positive أه positive
+
+443
+00:41:17,300 --> 00:41:21,080
+اللي هو F of X هي أكبر من 2 طلعت اللي هو ايش ماله
+
+444
+00:41:21,080 --> 00:41:27,260
+هذا؟ هنا ده بدي أضيف term وأطرح term عشان أحصل على
+
+445
+00:41:27,260 --> 00:41:31,780
+هذه اللي بدياها أصلا اللي هي الجد تفهموه مش مقصودة
+
+446
+00:41:31,780 --> 00:41:38,900
+1 على f of x في f prime of xi على g prime of xi
+
+447
+00:41:38,900 --> 00:41:50,130
+ناقص L زائد اللي هو L ناقص L F of X ايش سويت استخدمت
+
+448
+00:41:50,130 --> 00:41:56,170
+ال triangle inequality بإضافة L وطرح L هذا كله
+
+449
+00:41:56,170 --> 00:42:04,130
+مضروب 100 في 1 على F of X هذا الآن ال F of X أكبر
+
+450
+00:42:04,130 --> 00:42:12,690
+من 2 حصلناها مظبوط بصير أصغر من نص واضحة
+
+451
+00:42:13,760 --> 00:42:18,920
+الآن F' على G' لـ XI الـ XI وين لاجيناها؟ في
+
+452
+00:42:18,920 --> 00:42:24,940
+الفترة بين A وC1 ينطبق عليها اللي هو من رأس الدور
+
+453
+00:42:24,940 --> 00:42:34,580
+اللي هي F' على G' of X ناقص
+
+454
+00:42:34,580 --> 00:42:41,200
+L أصغر من الـ Y من أول ما بدينا يعني إنه هذا أصغر
+
+455
+00:42:41,200 --> 00:42:44,460
+من إبسلون لكل الـ Xات اللي موجودة من A لعند مين؟
+
+456
+00:42:44,460 --> 00:42:48,080
+لعند الـ A زاد دلتها من ضمنهم مين؟ لك فيبراين كلام
+
+457
+00:42:48,080 --> 00:42:55,940
+دقيق هذه في إبسلون زاد الآن هذا ال بطلعه برا عن
+
+458
+00:42:55,940 --> 00:43:01,760
+المشترك ال اللي هي في مين؟ في واحد ناقص F of X
+
+459
+00:43:01,760 --> 00:43:10,240
+واحد ناقص F of X الآن وهذا أصغر من نص في إبسلون
+
+460
+00:43:10,240 --> 00:43:15,440
+زائد absolute value لـ L واحد ناقص F of X هذه ال
+
+461
+00:43:15,440 --> 00:43:20,260
+Xات اللي موجودة بين A وC تلاتة وهذه اللي هي قبل
+
+462
+00:43:20,260 --> 00:43:26,150
+بشوية أصغر من مين من اللي هو إبسلون أصغر من إبسلون
+
+463
+00:43:26,150 --> 00:43:30,030
+واحد ناقص F of X أصغر من مين؟ من إبسلون مش هثبتنا
+
+464
+00:43:30,030 --> 00:43:33,910
+limit F of X بيساوي واحد قبل بشوية اللي هو واحد
+
+465
+00:43:33,910 --> 00:43:37,050
+ناقص F of X اللي هي أصغر من ايش من إبسلون في
+
+466
+00:43:37,050 --> 00:43:42,850
+إبسلون صار عندي الان هذا المقدار اللي هو بيساوي
+
+467
+00:43:42,850 --> 00:43:47,030
+epsilon على اتنين في واحد زائد absolute value
+
+468
+00:43:47,030 --> 00:43:52,810
+لـ L لأن ال epsilon مضروبة فيه إذا as لأن هذا ال
+
+469
+00:43:52,810 --> 00:43:55,430
+epsilon arbitrary وهذا الكلام صحيح for every
+
+470
+00:43:55,430 --> 00:43:59,710
+epsilon epsilon بين zero و نص إذا هذا المقدار بقدر
+
+471
+00:43:59,710 --> 00:44:04,350
+اصغره جد ما بدي بتصغير epsilon لانه مضروب فيه ضرب
+
+472
+00:44:04,350 --> 00:44:08,630
+إذا صار عندي لكل epsilon أكبر من zero و نصلـ G الـ
+
+473
+00:44:08,630 --> 00:44:12,650
+Delta بحيث أنه الـ Xات اللي هنا بيقدّي لي أن هذا
+
+474
+00:44:12,650 --> 00:44:20,810
+المقدار أصغر من أي قيمة بديّها إذا هذا مفهوم limit
+
+475
+00:44:20,810 --> 00:44:31,530
+F of X على G of X as X بتروح لين؟ للـ A من اليمين
+
+476
+00:44:31,530 --> 00:44:38,920
+بساوي الـ L وهو المطلوب الثيورم اللي حكينا عنها
+
+477
+00:44:38,920 --> 00:44:45,060
+برضه صحيحة في حالة اللي هو the same .. under the
+
+478
+00:44:45,060 --> 00:44:50,160
+same conditions for the calculation of limits as x
+
+479
+00:44:50,160 --> 00:44:55,540
+goes to infinity or x as goes mean to سالب infinity
+
+480
+00:44:55,540 --> 00:44:59,140
+بس بورهان يعني بدون modification عن اللي موجود
+
+481
+00:44:59,140 --> 00:45:03,140
+بتصلي اللي بدكيها نيجي ناخد أمثلة الأمثلة هذه طبعا
+
+482
+00:45:03,140 --> 00:45:09,500
+أمثلة سهلة ومثلة calculus نمر عليها اللي هو ونشوف
+
+483
+00:45:09,500 --> 00:45:16,480
+كيف نطبق نظريتنا أو نظرياتنا كيف نوظفها الحساب هذه
+
+484
+00:45:16,480 --> 00:45:23,260
+النهايات عندي شوفوا صلى النبي عليه الصلاة والسلام
+
+485
+00:45:24,800 --> 00:45:30,720
+Find Limit log sin x على log x as x بتروح للـ 0 من
+
+486
+00:45:30,720 --> 00:45:35,480
+وين؟ من اليمين واحنا عارفين .. مشتغلين على الفترة
+
+487
+00:45:35,480 --> 00:45:40,460
+0 or by يعني فترة بجوار مين؟ الصفر من اليمين و
+
+488
+00:45:40,460 --> 00:45:43,540
+بدنا نروح للـ 0 من اليمين هذا طبعا لو جينا عوضنا
+
+489
+00:45:43,540 --> 00:45:48,080
+هتطلع اللي هو sin 0 0 و أنا 0 فبصير ماله نهاية على
+
+490
+00:45:48,080 --> 00:45:53,580
+مين؟ على ماله نهاية ك limits الآن صارت عندي ماله
+
+491
+00:45:53,580 --> 00:45:57,880
+نهاية على ماله نهاية إذا ايش بتنسوه؟ ايش نسوي؟
+
+492
+00:45:57,880 --> 00:46:06,400
+راحين لـ 0 من اليمين بيصير عنده اللي هو بالفاضل
+
+493
+00:46:06,400 --> 00:46:11,400
+هذه وبالفاضل هذه بيصير تفاضلها هذه واضحة وهذه
+
+494
+00:46:11,400 --> 00:46:14,060
+تفاضلها هيك مافيش داعي لنا ندخل في التفاصيل لأن كل
+
+495
+00:46:14,060 --> 00:46:20,320
+بعرفها الآن بنبسط الأمر بيصير X Cos X على Sine X
+
+496
+00:46:20,930 --> 00:46:26,550
+الآن لو جيت اتطلعت لهذه ال limit و لهذه ال limit
+
+497
+00:46:26,550 --> 00:46:29,530
+هذه موجودة وهذه موجودة هذه موجودة لأنه تعويض
+
+498
+00:46:29,530 --> 00:46:33,410
+مباشر واحد هذه موجودة لأنه بيصير صفر على صفر بتعملها
+
+499
+00:46:33,410 --> 00:46:36,570
+global rule بيصير واحد على cosine بتطلع واحد برضه
+
+500
+00:46:36,570 --> 00:46:40,590
+إذا قدرت اوزع لأنه عارف الليمتين الموجودة فبيصير
+
+501
+00:46:40,590 --> 00:46:46,220
+عبارة عن واحد في واحد بيساوي ايه؟ واحد الآن خد على
+
+502
+00:46:46,220 --> 00:46:49,900
+الفترة من Zero لعند مين لعند باي على اتنين limit
+
+503
+00:46:49,900 --> 00:46:53,300
+واحد على X ناقص واحد على sign ال X ثم X تروح ل Zero
+
+504
+00:46:53,300 --> 00:46:57,140
+من وين؟ من اليمين وهذه طبعا شغلات اللي هو درجنا
+
+505
+00:46:57,140 --> 00:47:01,120
+عليها في ال calculus بنوحد المقامات وبصير مكتوبة
+
+506
+00:47:01,120 --> 00:47:05,030
+على صورة sign ال X ناقص X على X في sign ال X ماشي
+
+507
+00:47:05,030 --> 00:47:10,650
+الحل برضه 0 على 0 بنفضلها بيصير cos X ناقص 1 على
+
+508
+00:47:10,650 --> 00:47:15,470
+اللي هو sin X زائد X فcos X لو جينا عوضنا هتطلع
+
+509
+00:47:15,470 --> 00:47:21,250
+برضه 0 على 0 بنشتق كمان مرة بتطلع ناقص sin X على
+
+510
+00:47:21,250 --> 00:47:26,150
+هذا المقدار هذا المقدار هنا بتصفر وهنا بيصير 2
+
+511
+00:47:26,150 --> 00:47:32,680
+وهنا 0 0 على 2 مش بيساوي بيساوي 0 نأتي لهذا المثال
+
+512
+00:47:32,680 --> 00:47:36,440
+معهود ال let I بيساوي من 1 إلى ما لنهاية الـ
+
+513
+00:47:36,440 --> 00:47:39,760
+interval اللي عليها بدنا نشتغل وبدنا ناخد ال
+
+514
+00:47:39,760 --> 00:47:43,600
+limit لما X تروح إلى وين إلى ما لنهاية المقدار 1
+
+515
+00:47:43,600 --> 00:47:48,960
+زائد 1 على X والكل أُس X هذا المقدار الآن بدي
+
+516
+00:47:48,960 --> 00:47:53,460
+استخدم اللي هو احوله ل exponential to the len ما
+
+517
+00:47:53,460 --> 00:47:55,660
+احنا عارفين ال exponential وال len اللي هو n
+
+518
+00:47:55,660 --> 00:47:59,860
+versus لبعض فبصير عندي E to the X لن ال 1 زائد 1
+
+519
+00:47:59,860 --> 00:48:05,120
+على X هذا المقدار بدي اشغل على هذاك خطوة أولى بقول
+
+520
+00:48:05,120 --> 00:48:09,260
+limit ال X لما واحد زائد واحد على X لما X تروح إلى
+
+521
+00:48:09,260 --> 00:48:14,140
+مال نهاية بيصير هذا المقدار limit لما واحد زائد X
+
+522
+00:48:14,140 --> 00:48:18,160
+على واحد على X ليش عملت هيك لأن لما X تروح إلى مال
+
+523
+00:48:18,160 --> 00:48:21,360
+نهاية هذا صفر ولما X تروح إلى مال نهاية هذا صفر و
+
+524
+00:48:21,360 --> 00:48:25,340
+هذا لما واحد فبصير صفر على صفر بقدر استخدم ال loop
+
+525
+00:48:25,340 --> 00:48:30,730
+تالذرول اللي انا برهنتها بقي فاضل اللي فوق وفاصل
+
+526
+00:48:30,730 --> 00:48:33,850
+اللي تحت .. فضلنا اللي فوق هي وفضلنا اللي تحت
+
+527
+00:48:33,850 --> 00:48:37,590
+هي .. بروح هذا المقدار مع هذا المقدار .. بظل
+
+528
+00:48:37,590 --> 00:48:42,800
+limit 1 زي 1 على X ناقص 1 لما X تروح لمدة نهاية ده
+
+529
+00:48:42,800 --> 00:48:47,940
+بروح لصفر بطلع جداش 1 لأن 1 بنرد بنعوض وينها لأن
+
+530
+00:48:47,940 --> 00:48:50,940
+ال exponential is a continuous function لذا نصحي
+
+531
+00:48:50,940 --> 00:48:54,180
+عن عند limit ال 1 زي 1 على X لما X تروح لمدة نهاية
+
+532
+00:48:54,180 --> 00:48:57,920
+to the X وعبارة عن E to the limit لأن ال
+
+533
+00:48:57,920 --> 00:49:01,760
+exponential عبارة عن continuous function فبصير E
+
+534
+00:49:01,760 --> 00:49:08,300
+to the 1 ويساوي E هذا اللي هو بيكون هيك احنا انهينا
+
+535
+00:49:08,300 --> 00:49:16,240
+اللي هي lobitals rules أو قواعد lobital أو صرنا
+
+536
+00:49:16,240 --> 00:49:20,360
+الآن ندخل
+
+537
+00:49:20,360 --> 00:49:28,120
+على اللي هو ال chapter ال section الأخير اللي هو
+
+538
+00:49:28,120 --> 00:49:32,120
+ال section عبارة عن ستة أربعة اللي هو taylor's
+
+539
+00:49:32,120 --> 00:49:38,540
+theorem أو tailors اللي هي .. هنحكي عن tailors
+
+540
+00:49:38,540 --> 00:49:43,640
+polynomial أو tailors أيضا اللي هو approximation
+
+541
+00:49:43,640 --> 00:49:49,820
+كيف اللي هو .. إن مرة جاية إن شاء الله كيف بنقرب
+
+542
+00:49:49,820 --> 00:49:54,840
+بعض الدوال اللي هو المحترمة اللي بتكون
+
+543
+00:49:54,840 --> 00:49:58,220
+differentiable first derivative و second
+
+544
+00:49:58,220 --> 00:50:00,400
+derivative و third derivative لأ عند ال derivative
+
+545
+00:50:00,400 --> 00:50:05,700
+اللي بدنا .. اللي .. اللي هي ما قبل اشتقاق عندها
+
+546
+00:50:05,700 --> 00:50:11,760
+بنقربها ب polynomial وطبعا انتوا عارفين جداش ال
+
+547
+00:50:11,760 --> 00:50:17,380
+polynomial من الدوال السهلة سهلة التعامل سواء في
+
+548
+00:50:17,380 --> 00:50:21,500
+تفاضل أو في تكامل أو حتى لو بدنا نحلها ونجيب
+
+549
+00:50:21,500 --> 00:50:26,340
+جذورها ونجيب كذا في شغل عليها كثير فالناس ترغب في
+
+550
+00:50:26,340 --> 00:50:30,540
+إنها تجيب بعض الدوال اللي بتكون أحيانا معقدة و
+
+551
+00:50:30,540 --> 00:50:35,380
+صعبة التكامل أو خلنا نقول بتغلب شوية في التفاضل أو
+
+552
+00:50:35,380 --> 00:50:40,040
+في وجود الجذور أو كده ونحولها إلى اللي هي
+
+553
+00:50:40,040 --> 00:50:44,020
+polynomial طبعا في مقدار خطأ الخطأ هن .. إن شاء
+
+554
+00:50:44,020 --> 00:50:47,520
+الله ال Taylor's theorem بتقولنا كيف إن هو نوجد
+
+555
+00:50:47,520 --> 00:50:51,320
+هذا الخطأ أو ايش هو الخطأ وايضا Taylor's theorem
+
+556
+00:50:51,320 --> 00:50:55,780
+زي ما انتوا عارفين هنوضح كيف هي عبارة عن تعميم لل
+
+557
+00:50:55,780 --> 00:51:00,340
+main value theorem هي تعميم لل main value theorem
+
+558
+00:51:00,340 --> 00:51:05,140
+في حالة اللي هي n بتساوي صفر بتطلع هي بالظبط ال
+
+559
+00:51:05,140 --> 00:51:09,100
+main value theorem كيف؟
+
+560
+00:51:10,860 --> 00:51:15,100
+الـ Main Value Theorem عبارة الـ Taylor's Theorem
+
+561
+00:51:15,100 --> 00:51:19,900
+عبارة عن تعميم للـ Main Value Theorem خذ الآن
+
+562
+00:51:19,900 --> 00:51:25,020
+بتساوي صفر بتطلع لك الـ Main Value Theorem بيشحمها 
+
+563
+00:51:25,020 --> 00:51:27,740
+و لحمها وإلى لقاء 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8cbd6234b3619056cef81985abe54a63c4d87a8
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/GZcIoIj0HL8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3026, "start": 5.04, "end": 30.26, "text": "بسم الله الرحمن الرحيم المحاضرة السابعة مساق تحليل حقيقي 2 اللي طلبت كلية العلوم بالجامعة الإسلامية قسم الرياضيات اليوم هيكون عندنا استكمال ل .. اللي هي قواعد أو قاعدة Lobital", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 21136, 16758, 27884, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11331, 38436, 38436, 568, 13672, 1829, 23032, 46152, 2655, 28242, 10632, 18863, 1211, 20498, 20666, 7435, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 2423, 16572, 46958, 1829, 9307, 45595, 20498, 39896, 30544, 43242, 8315, 44713, 24793, 6027, 5296, 4386, 13672, 1829, 39896, 12174, 14407, 22488, 34051, 12174, 995, 22488, 3660, 30719, 1686], "avg_logprob": -0.1062297070181215, "compression_ratio": 1.7087912087912087, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 5.04, "end": 5.44, "word": "بسم", "probability": 0.861328125}, {"start": 5.44, "end": 5.64, "word": " الله", "probability": 0.95947265625}, {"start": 5.64, "end": 5.98, "word": " الرحمن", "probability": 0.96044921875}, {"start": 5.98, "end": 6.58, "word": " الرحيم", "probability": 0.99365234375}, {"start": 6.58, "end": 8.78, "word": " المحاضرة", "probability": 0.97265625}, {"start": 8.78, "end": 9.82, "word": " السابعة", "probability": 0.9630533854166666}, {"start": 9.82, "end": 11.4, "word": " مساق", "probability": 0.9026692708333334}, {"start": 11.4, "end": 12.8, "word": " تحليل", "probability": 0.981201171875}, {"start": 12.8, "end": 13.3, "word": " حقيقي", "probability": 0.9744466145833334}, {"start": 13.3, "end": 13.74, "word": " 2", "probability": 0.47314453125}, {"start": 13.74, "end": 14.9, "word": " اللي", "probability": 0.81201171875}, {"start": 14.9, "end": 15.48, "word": " طلبت", "probability": 0.9822591145833334}, {"start": 15.48, "end": 16.0, "word": " كلية", "probability": 0.831298828125}, {"start": 16.0, "end": 16.6, "word": " العلوم", "probability": 0.9519856770833334}, {"start": 16.6, "end": 17.88, "word": " بالجامعة", "probability": 0.94580078125}, {"start": 17.88, "end": 18.64, "word": " الإسلامية", "probability": 0.9681396484375}, {"start": 18.64, "end": 19.72, "word": " قسم", "probability": 0.977294921875}, {"start": 19.72, "end": 20.76, "word": " الرياضيات", "probability": 0.93603515625}, {"start": 20.76, "end": 23.8, "word": " اليوم", "probability": 0.934326171875}, {"start": 23.8, "end": 24.24, "word": " هيكون", "probability": 0.721435546875}, {"start": 24.24, "end": 24.58, "word": " عندنا", "probability": 0.92919921875}, {"start": 24.58, "end": 25.62, "word": " استكمال", "probability": 0.9671223958333334}, {"start": 25.62, "end": 26.28, "word": " ل", "probability": 0.7568359375}, {"start": 26.28, "end": 26.66, "word": " ..", "probability": 0.299072265625}, {"start": 26.66, "end": 26.78, "word": " اللي", "probability": 0.940185546875}, {"start": 26.78, "end": 27.08, "word": " هي", "probability": 0.939453125}, {"start": 27.08, "end": 28.26, "word": " قواعد", "probability": 0.984375}, {"start": 28.26, "end": 28.9, "word": " أو", "probability": 0.81396484375}, {"start": 28.9, "end": 29.72, "word": " قاعدة", "probability": 0.9591064453125}, {"start": 29.72, "end": 30.26, "word": " Lobital", "probability": 0.5982666015625}], "temperature": 1.0}, {"id": 2, "seek": 4477, "start": 31.01, "end": 44.77, "text": "اتحدثنا المرة الماضية عن الحالة اللى بتحدث سفر على سفر وكيف انعلجها وتم اللى هو برهان النظريات المعنية في ذلك", "tokens": [9307, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632, 18871, 21542, 6027, 3660, 13672, 7578, 39894, 24401, 12984, 8608, 5172, 2288, 15844, 8608, 5172, 2288, 4032, 4117, 33911, 16472, 30241, 7435, 11296, 4032, 39237, 13672, 7578, 31439, 4724, 2288, 3224, 7649, 28239, 19913, 16572, 9307, 9673, 3615, 1863, 10632, 8978, 29910, 23275], "avg_logprob": -0.1188826617204918, "compression_ratio": 1.6583333333333334, "no_speech_prob": 3.635883331298828e-06, "words": [{"start": 31.01, "end": 32.43, "word": "اتحدثنا", "probability": 0.841064453125}, {"start": 32.43, "end": 32.79, "word": " المرة", "probability": 0.967041015625}, {"start": 32.79, "end": 33.53, "word": " الماضية", "probability": 0.9939778645833334}, {"start": 33.53, "end": 34.09, "word": " عن", "probability": 0.98583984375}, {"start": 34.09, "end": 35.25, "word": " الحالة", "probability": 0.9908854166666666}, {"start": 35.25, "end": 35.77, "word": " اللى", "probability": 0.7734375}, {"start": 35.77, "end": 36.33, "word": " بتحدث", "probability": 0.9674479166666666}, {"start": 36.33, "end": 36.69, "word": " سفر", "probability": 0.8738606770833334}, {"start": 36.69, "end": 36.93, "word": " على", "probability": 0.8291015625}, {"start": 36.93, "end": 37.41, "word": " سفر", "probability": 0.9982096354166666}, {"start": 37.41, "end": 38.11, "word": " وكيف", "probability": 0.9127604166666666}, {"start": 38.11, "end": 38.89, "word": " انعلجها", "probability": 0.722900390625}, {"start": 38.89, "end": 39.91, "word": " وتم", "probability": 0.611083984375}, {"start": 39.91, "end": 40.19, "word": " اللى", "probability": 0.93505859375}, {"start": 40.19, "end": 40.55, "word": " هو", "probability": 0.83837890625}, {"start": 40.55, "end": 41.17, "word": " برهان", "probability": 0.951416015625}, {"start": 41.17, "end": 42.37, "word": " النظريات", "probability": 0.9373779296875}, {"start": 42.37, "end": 44.07, "word": " المعنية", "probability": 0.9775390625}, {"start": 44.07, "end": 44.31, "word": " في", "probability": 0.71533203125}, {"start": 44.31, "end": 44.77, "word": " ذلك", "probability": 0.996826171875}], "temperature": 1.0}, {"id": 3, "seek": 7198, "start": 45.29, "end": 71.99, "text": "الآن بدنا نتحدث على الحالة اللي بتحدث عندنا أيضًا 0 على 0 ولكن ال limit ال X بتروح إلى مالة نهاية أو سالب مالة نهاية وقلنا عنها صحيحة برضه وبعد ذلك هنتحدث عن الحالة infinity على infinity نيجي الآن لنظريتنا اللي وصلنا عندها suppose that", "tokens": [6027, 148, 48506, 47525, 8315, 8717, 2655, 24401, 12984, 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"end": 46.93, "word": " على", "probability": 0.53955078125}, {"start": 46.93, "end": 47.91, "word": " الحالة", "probability": 0.98828125}, {"start": 47.91, "end": 48.55, "word": " اللي", "probability": 0.88623046875}, {"start": 48.55, "end": 49.93, "word": " بتحدث", "probability": 0.97607421875}, {"start": 49.93, "end": 51.31, "word": " عندنا", "probability": 0.86767578125}, {"start": 51.31, "end": 53.63, "word": " أيضًا", "probability": 0.7894287109375}, {"start": 53.63, "end": 53.99, "word": " 0", "probability": 0.54296875}, {"start": 53.99, "end": 54.25, "word": " على", "probability": 0.83642578125}, {"start": 54.25, "end": 54.55, "word": " 0", "probability": 0.98291015625}, {"start": 54.55, "end": 55.37, "word": " ولكن", "probability": 0.78125}, {"start": 55.37, "end": 55.73, "word": " ال", "probability": 0.650390625}, {"start": 55.73, "end": 56.71, "word": " limit", "probability": 0.72900390625}, {"start": 56.71, "end": 56.91, "word": " ال", "probability": 0.71044921875}, {"start": 56.91, "end": 57.11, "word": " X", "probability": 0.6455078125}, {"start": 57.11, "end": 57.49, "word": " بتروح", "probability": 0.9676106770833334}, {"start": 57.49, "end": 57.65, "word": " إلى", "probability": 0.8828125}, {"start": 57.65, "end": 57.95, "word": " مالة", "probability": 0.674560546875}, {"start": 57.95, "end": 58.47, "word": " نهاية", "probability": 0.9298502604166666}, {"start": 58.47, "end": 59.43, "word": " أو", "probability": 0.91064453125}, {"start": 59.43, "end": 59.79, "word": " سالب", "probability": 0.7861328125}, {"start": 59.79, "end": 60.03, "word": " مالة", "probability": 0.9423828125}, {"start": 60.03, "end": 60.25, "word": " نهاية", "probability": 0.9378255208333334}, {"start": 60.25, "end": 60.59, "word": " وقلنا", "probability": 0.73150634765625}, {"start": 60.59, "end": 60.83, "word": " عنها", "probability": 0.994384765625}, {"start": 60.83, "end": 61.35, "word": " صحيحة", "probability": 0.97578125}, {"start": 61.35, "end": 61.77, "word": " برضه", "probability": 0.9866536458333334}, {"start": 61.77, "end": 62.65, "word": " وبعد", "probability": 0.7315673828125}, {"start": 62.65, "end": 63.01, "word": " ذلك", "probability": 0.9931640625}, {"start": 63.01, "end": 63.69, "word": " هنتحدث", "probability": 0.9808349609375}, {"start": 63.69, "end": 63.87, "word": " عن", "probability": 0.99462890625}, {"start": 63.87, "end": 64.31, "word": " الحالة", "probability": 0.99169921875}, {"start": 64.31, "end": 64.85, "word": " infinity", "probability": 0.4892578125}, {"start": 64.85, "end": 65.79, "word": " على", "probability": 0.88916015625}, {"start": 65.79, "end": 66.77, "word": " infinity", "probability": 0.677734375}, {"start": 66.77, "end": 67.49, "word": " نيجي", "probability": 0.850341796875}, {"start": 67.49, "end": 67.73, "word": " الآن", "probability": 0.63720703125}, {"start": 67.73, "end": 68.55, "word": " لنظريتنا", "probability": 0.9010416666666666}, {"start": 68.55, "end": 69.21, "word": " اللي", "probability": 0.930419921875}, {"start": 69.21, "end": 69.99, "word": " وصلنا", "probability": 0.8883463541666666}, {"start": 69.99, "end": 70.51, "word": " عندها", "probability": 0.99267578125}, {"start": 70.51, "end": 71.41, "word": " suppose", "probability": 0.84130859375}, {"start": 71.41, "end": 71.99, "word": " that", "probability": 0.94921875}], "temperature": 1.0}, {"id": 4, "seek": 9712, "start": 76.22, "end": 97.12, "text": "F and D are continuous and differentiable على الفترة من A إلى ما لا نهاية ونفترض أنه limit لل F of X لما X تروح إلى ما لا نهاية هي نفس limit D of X لما X تروح إلى ما لا نهاية تساوي إيهاش صفر يعني هذه هتخلقلي حالة اللي هو صفر على صفر ومن ثم نشوف كيف انعليجها", "tokens": [37, 293, 413, 366, 10957, 293, 819, 9364, 15844, 27188, 2655, 25720, 9154, 316, 30731, 19446, 20193, 8717, 11296, 10632, 4032, 1863, 5172, 2655, 43042, 14739, 3224, 4948, 24976, 479, 295, 1783, 5296, 15042, 1783, 6055, 32887, 5016, 30731, 19446, 20193, 8717, 11296, 10632, 39896, 8717, 36178, 4948, 413, 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0.9443359375}, {"start": 78.62, "end": 79.52, "word": " differentiable", "probability": 0.931884765625}, {"start": 79.52, "end": 80.26, "word": " على", "probability": 0.5185546875}, {"start": 80.26, "end": 80.66, "word": " الفترة", "probability": 0.9778645833333334}, {"start": 80.66, "end": 80.84, "word": " من", "probability": 0.97607421875}, {"start": 80.84, "end": 81.1, "word": " A", "probability": 0.787109375}, {"start": 81.1, "end": 81.4, "word": " إلى", "probability": 0.86083984375}, {"start": 81.4, "end": 81.6, "word": " ما", "probability": 0.450927734375}, {"start": 81.6, "end": 81.7, "word": " لا", "probability": 0.498046875}, {"start": 81.7, "end": 82.2, "word": " نهاية", "probability": 0.9060872395833334}, {"start": 82.2, "end": 83.78, "word": " ونفترض", "probability": 0.903125}, {"start": 83.78, "end": 84.02, "word": " أنه", "probability": 0.3961181640625}, {"start": 84.02, "end": 84.22, "word": " limit", "probability": 0.94384765625}, {"start": 84.22, "end": 84.44, "word": 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اللي قبل بشوية بنفس .. بنفس .. خلّيني أقول بنفس المنطق ونفس النصوص بس مبدل 0 على 0 عمالة نهاية", "tokens": [1863, 10721, 31371, 30731, 25724, 11622, 19986, 10632, 16247, 12610, 7578, 9154, 28239, 19913, 2288, 10632, 498, 4948, 283, 6, 15844, 290, 6, 4724, 3794, 995, 45865, 441, 4478, 294, 497, 11933, 15730, 6156, 4197, 270, 283, 15844, 290, 4724, 43042, 3224, 36632, 11242, 995, 5551, 1829, 8592, 8032, 2655, 3794, 995, 45865, 441, 13672, 1829, 39896, 8717, 19913, 16572, 9307, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 44945, 36178, 4386, 44945, 36178, 4386, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 44945, 36178, 9673, 1863, 9566, 4587, 4032, 1863, 36178, 28239, 9381, 2407, 9381, 4724, 3794, 3714, 44510, 1211, 1958, 15844, 1958, 6225, 2304, 6027, 3660, 8717, 11296, 10632], "avg_logprob": -0.3476914494961232, "compression_ratio": 1.7116279069767442, "no_speech_prob": 4.827976226806641e-06, "words": [{"start": 769.4599999999999, "end": 770.18, "word": "نأتي", "probability": 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"text": "فلان limit f prime على g prime صارت مالة نهاية أو سالب مالة نهاية، برضه النظرية بتظبط، سير limit اللي عندنا هذا", "tokens": [5172, 1211, 7649, 4948, 283, 5835, 15844, 290, 5835, 20328, 9640, 2655, 3714, 6027, 3660, 8717, 11296, 10632, 34051, 8608, 6027, 3555, 3714, 6027, 3660, 8717, 11296, 10632, 12399, 4724, 43042, 3224, 28239, 19913, 2288, 10632, 39894, 19913, 3555, 9566, 12399, 8608, 13546, 4948, 13672, 1829, 43242, 8315, 23758], "avg_logprob": -0.3240624988079071, "compression_ratio": 1.3875968992248062, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 791.16, "end": 791.74, "word": "فلان", "probability": 0.3826904296875}, {"start": 791.74, "end": 791.98, "word": " limit", "probability": 0.59912109375}, {"start": 791.98, "end": 792.22, "word": " f", "probability": 0.47314453125}, {"start": 792.22, "end": 792.52, "word": " prime", "probability": 0.3623046875}, {"start": 792.52, "end": 792.64, "word": " على", "probability": 0.35400390625}, {"start": 792.64, 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{"id": 55, "seek": 133732, "start": 1308.06, "end": 1337.32, "text": "الـ C2 بقدر اختارها فعلا بختارها بس طبعا وين تشتري تشريع اللي اختيارها انها تكون بين الفترة A و A زائد Delta Prime و بدياها تيجي في داخل الـ A و الـ C1 اذا then we can choose C2 element A of C1 بحيث ان ال F of X أكبر من مين من F of C1 لكل X وين", "tokens": [6027, 39184, 383, 17, 4724, 28543, 2288, 1975, 46456, 9640, 11296, 6156, 3615, 15040, 4724, 46456, 9640, 11296, 4724, 3794, 23032, 3555, 3615, 995, 4032, 9957, 6055, 8592, 2655, 16572, 6055, 8592, 16572, 3615, 13672, 1829, 1975, 9778, 31371, 9640, 11296, 16472, 11296, 6055, 30544, 49374, 27188, 2655, 25720, 316, 4032, 316, 30767, 16373, 3215, 18183, 9655, 4032, 4724, 16254, 995, 11296, 6055, 1829, 7435, 1829, 8978, 11778, 47283, 1211, 2423, 39184, 316, 4032, 2423, 39184, 383, 16, 1975, 15730, 550, 321, 393, 2826, 383, 17, 4478, 316, 295, 383, 16, 4724, 5016, 1829, 12984, 16472, 2423, 479, 295, 1783, 5551, 4117, 26890, 9154, 3714, 9957, 9154, 479, 295, 383, 16, 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diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/H5lXnSx9bxw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/H5lXnSx9bxw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4eaffd5a07a9f59a0dd53d6d9310f2c2a186a12c
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/H5lXnSx9bxw.srt
@@ -0,0 +1,4096 @@
+1
+00:00:04,890 --> 00:00:10,370
+بسم الله الرحمن الرحيم المحاضرة رقم 12 في مساق
+
+2
+00:00:10,370 --> 00:00:14,870
+تحليل حقيقي 2 لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:14,870 --> 00:00:20,710
+كلية العلوم قسم رياضيات وهي المحاضرة الثانية بعد 
+
+4
+00:00:20,710 --> 00:00:25,150
+الطوارئ لمواجهة فيروس كورونا
+
+5
+00:00:27,610 --> 00:00:31,150
+السيكشن اليوم إن شاء الله اللي هنبدأ فيه اللي هو
+
+6
+00:00:31,150 --> 00:00:35,050
+سيكشن سبعة اثنين اللي هو عبارة عن الـ Properties of
+
+7
+00:00:35,050 --> 00:00:38,290
+the Riemann Integral أو اللي هو خواص الـ
+
+8
+00:00:38,290 --> 00:00:43,310
+ريمان انتيجرول هنبنيها على عدد من الأسئلة اليوم أنه
+
+9
+00:00:43,310 --> 00:00:47,190
+لو كانت عندي في عندي اللي هو two functions f و g
+
+10
+00:00:47,190 --> 00:00:51,650
+اللي هو عبارة عن integrable functions على some
+
+11
+00:00:51,650 --> 00:00:56,070
+bounded closed interval I هل مجموعهما هيكون
+
+12
+00:00:56,070 --> 00:01:01,440
+integrable ولا لأ؟ هل حاصل ضرب ثابت في الـ
+
+13
+00:01:01,440 --> 00:01:03,620
+F اللي هي الـ integrable function هيطلع الـ 
+
+14
+00:01:03,620 --> 00:01:09,340
+KF is integrable؟ هل حاصل ضرب دالتين F و G is
+
+15
+00:01:09,340 --> 00:01:13,700
+integrable؟ هل لو أجينا كان في عندي two functions
+
+16
+00:01:13,700 --> 00:01:17,720
+F و G integrable؟ وكان اللي هو معرفة على أساس الـ
+
+17
+00:01:17,720 --> 00:01:20,900
+composition بينهما يكون معرف؟ وكان التنتين 
+
+18
+00:01:20,900 --> 00:01:24,560
+integrable؟ هل الـ F composite G integrable
+
+19
+00:01:24,560 --> 00:01:29,020
+ولا لأ؟ أيضًا لو مش integrable طب إيش نحط condition
+
+20
+00:01:29,020 --> 00:01:32,640
+على واحدة منه عشان يصير integrable؟ هتجاوب عليه
+
+21
+00:01:32,640 --> 00:01:37,280
+نظرية اللي هو هنحكي عنها أنه لو كانت إحداهما اللي
+
+22
+00:01:37,280 --> 00:01:41,600
+هي continuous فهيكون عندي اللي هو أو إذا كانت الـ F
+
+23
+00:01:41,600 --> 00:01:45,200
+is continuous يكون F composite G is integrable
+
+24
+00:01:45,200 --> 00:01:49,800
+وهنشوف هذا الكلام إن شاء الله خلال الـ
+
+25
+00:01:49,800 --> 00:01:54,180
+section وهنوظف الـ نظرية الـ composition هذه في
+
+26
+00:01:54,180 --> 00:01:58,210
+إثبات اللي هو بعض الدوال كيف هتكون الـ 
+
+27
+00:01:58,210 --> 00:02:02,410
+integrable نبدأ الآن في الـ النظرية الأولى
+
+28
+00:02:02,410 --> 00:02:06,650
+اللي هتجاوب لنا على اللي سألناه السؤال الأول أنه لو 
+
+29
+00:02:06,650 --> 00:02:11,090
+كانت عندي الـ theorem 711 لو كانت I عبارة عن 
+
+30
+00:02:11,090 --> 00:02:14,960
+closed bounded interval A وB  الـ F والـ G عبارة
+
+31
+00:02:14,960 --> 00:02:18,760
+عن two functions من I لعند R وفرضنا إن الـ two functions
+
+32
+00:02:18,760 --> 00:02:21,600
+إيه شمال هنا؟ Are integrable يعني 
+
+33
+00:02:21,600 --> 00:02:25,740
+نفترض let F and G be two integrable functions on I
+
+34
+00:02:25,740 --> 00:02:29,960
+الآن if K element in R عبارة عن .. عبارة عن ثابت
+
+35
+00:02:29,960 --> 00:02:35,380
+then the functions اللي هو الإجابة الآن K في F و K
+
+36
+00:02:35,380 --> 00:02:39,220
+في G يعني حاصل ضرب الثابت في الـ F هيطلع عند عبارة
+
+37
+00:02:39,220 --> 00:02:43,300
+عن integrable function وهيطلع f زائد g integrable
+
+38
+00:02:43,300 --> 00:02:47,700
+function يعني هيكون اللي هو اللي هي بدر دول f زائد 
+
+39
+00:02:47,700 --> 00:02:50,860
+g is integrable وطبعًا لو أثبتنا هذا integrable
+
+40
+00:02:50,860 --> 00:02:54,000
+وهذا integrable على طول ال f ناقص g is integrable
+
+41
+00:02:54,000 --> 00:02:59,640
+ليش؟ لأن f is integrable و g is integrable هيعطيني 
+
+42
+00:02:59,640 --> 00:03:05,720
+اللي هو f زائد f و K في g برضه integrable حسب اللي
+
+43
+00:03:05,720 --> 00:03:12,610
+هو مين اللي حاكيناها هذا في حالة إثباتهم دام اتكافى
+
+44
+00:03:12,610 --> 00:03:16,070
+g is integrable لكل K طبعًا element are من ضمنها
+
+45
+00:03:16,070 --> 00:03:19,790
+ناقص واحد يعني هيصير عندي اف وناقص g integrable
+
+46
+00:03:19,790 --> 00:03:24,890
+يعني هيصير عندي حسب الـ F زائد g بصير F زائد
+
+47
+00:03:24,890 --> 00:03:29,210
+ناقص g is integrable يعني F ناقص g برضه هيطلع إيه
+
+48
+00:03:29,210 --> 00:03:33,790
+شماله is integrable هذه ملاحظات سريعة أيضًا هيطلع
+
+49
+00:03:33,790 --> 00:03:39,890
+عندي حسب الـ نظرية هذه أنه in general F زائد K 
+
+50
+00:03:39,890 --> 00:03:43,330
+في g هيكون integrable و لو كان في عندي constant
+
+51
+00:03:43,330 --> 00:03:47,130
+ثاني K prime هيطلع الـ linear combination بينهم K
+
+52
+00:03:47,130 --> 00:03:52,630
+prime f زائد g برضه is integrable هذا كله في حال
+
+53
+00:03:52,630 --> 00:03:56,810
+أثبتنا إن الـ KF والـ F زائد g is integrable عندما
+
+54
+00:03:56,810 --> 00:04:00,330
+تكون F و d is integrable خلينا نبدأ الآن اللي هو 
+
+55
+00:04:00,330 --> 00:04:05,330
+نثبت الـ KF is integrable قبل ما نثبت خليني أذكركم
+
+56
+00:04:05,330 --> 00:04:10,700
+ببعض اللي هي الـ قوانين أو الـ 
+
+57
+00:04:10,700 --> 00:04:14,180
+definitions اللي احنا حكيناها سابقًا عشان هستخدمها 
+
+58
+00:04:14,180 --> 00:04:20,420
+اليوم اللي هو lower sum للـ partition P و G الـ
+
+59
+00:04:20,420 --> 00:04:22,880
+partition P هو عبارة عن الـ partition للـ interval I
+
+60
+00:04:22,880 --> 00:04:26,700
+اللي معرف عليها G هو عبارة عن summation MK في XK 
+
+61
+00:04:26,700 --> 00:04:30,440
+ناقص XK ناقص 1 والـ MK زي ما أنتم عارفين هي عبارة
+
+62
+00:04:30,440 --> 00:04:34,050
+عن الـ infimum لقيمة الدالة على اللي هي الـ
+
+63
+00:04:34,050 --> 00:04:39,430
+Subinterval اللي بنحكي عنها XK-1 و XK والـ L of G 
+
+64
+00:04:39,430 --> 00:04:43,890
+اللي هو الـ Lower Integral اللي هو عبارة عن الـ 
+
+65
+00:04:43,890 --> 00:04:49,330
+Supremum لكل الـ P و G لكل P element in the set of 
+
+66
+00:04:49,330 --> 00:04:54,720
+all partition P of I  وأيضًا الـ UPG هي عبارة عن 
+
+67
+00:04:54,720 --> 00:04:57,380
+summation نفس اللي فوق بس بدل اللي هي الـ infimum
+
+68
+00:04:57,380 --> 00:05:01,340
+بنحط M كابيتال K اللي هي عبارة عن اللي هي الـ
+
+69
+00:05:01,340 --> 00:05:04,180
+supremum لقيمة الدوال زي ما أنتم عارفين أو
+
+70
+00:05:04,180 --> 00:05:07,320
+زي ما شرحناها سابقًا و الـ U of G في هذه الحالة
+
+71
+00:05:07,320 --> 00:05:11,740
+اللي هو عبارة عن الـ upper integral هو عبارة عن الـ
+
+72
+00:05:11,740 --> 00:05:17,180
+infimum للّي هي كل الـ upper sums للـ partitions 
+
+73
+00:05:17,180 --> 00:05:20,160
+بيه element in P of I هذا خليه على أساس أنه بدأ
+
+74
+00:05:20,160 --> 00:05:26,510
+نستخدمه بعد شوية في هذا البرهان للنظرية الآن بدأ
+
+75
+00:05:26,510 --> 00:05:30,510
+أبرهن الـ KF is integrable بالواحد وبعد هيك بدأ
+
+76
+00:05:30,510 --> 00:05:33,530
+أثبت لكم إن الـ integration لـ KFF بيساوي كيف الـ 
+
+77
+00:05:33,530 --> 00:05:38,750
+integration لمين لـ LF الآن بدأ أخذ ثلاث حالات بدأ 
+
+78
+00:05:38,750 --> 00:05:42,290
+أخذ طبعًا هذا كل K أملتنا ألهار بدأ أخذ حالة K بتساوي
+
+79
+00:05:42,290 --> 00:05:47,050
+صفر وحالة K أصغر من صفر وحالة K أكبر من إياش من
+
+80
+00:05:47,050 --> 00:05:51,740
+صفر كل حالة فيها بروحانها الحالة الأولى K بساوي
+
+81
+00:05:51,740 --> 00:05:56,240
+صفر حالة سهلة وحالة trivial لماذا؟ لأن إذا كانت KF
+
+82
+00:05:56,240 --> 00:06:01,340
+بساوي صفر هيصير الـ KF عبارة عن الـ zero function
+
+83
+00:06:01,340 --> 00:06:04,720
+والـ zero function is continuous يعني constant ما
+
+84
+00:06:04,720 --> 00:06:08,220
+دام continuous حسب النظرية المرة الماضية هتكون 
+
+85
+00:06:08,220 --> 00:06:11,900
+اللي هو إيه شمالها is integrable إذا في حالة الـ K 
+
+86
+00:06:11,900 --> 00:06:15,700
+بيساوي صفر trivial KF is integrable ومش هيك كمان 
+
+87
+00:06:15,700 --> 00:06:19,540
+و K في الـ integration لل F هذا عبارة عن integrable
+
+88
+00:06:19,540 --> 00:06:23,760
+يعني قيمة عددية وهذا Zero بيصير بيساوي Zero والـ 
+
+89
+00:06:23,760 --> 00:06:26,860
+integration للـ Zero function على الفترة A B اللي 
+
+90
+00:06:26,860 --> 00:06:29,900
+هو عبارة عن الـ K في الـ F في هذه الحالة هيساوي صفر
+
+91
+00:06:29,900 --> 00:06:33,880
+إذا صار عندي من اللي هو الجهتين هذه لـ K في الـ
+
+92
+00:06:33,880 --> 00:06:38,220
+integration لل F بيساوي الـ integration للـ KF من A
+
+93
+00:06:38,220 --> 00:06:42,780
+لـ B من A لـ B بيساوي 0 in the case of ك بتساوي إياش
+
+94
+00:06:42,780 --> 00:06:47,380
+0 إذا زي ما قلنا فعلاً لحالة ك بتساوي صفر حالة سهلة 
+
+95
+00:06:47,380 --> 00:06:52,120
+و trivial case نيجي الآن بدنا نحكي عن مين يا جماعة
+
+96
+00:06:52,120 --> 00:06:58,000
+عن الحالة الثانية اللي هو إذا كانت ك أصغر من 0 في 
+
+97
+00:06:58,000 --> 00:07:02,620
+حالة الـ K أصغر من 0 إذا شغلنا الآن على الـ K أصغر 
+
+98
+00:07:02,620 --> 00:07:07,760
+من 0 طيب لحظة
+
+99
+00:07:07,760 --> 00:07:13,480
+ما هي ليه؟ خلينا نركز على الحالة اللي هو K أصغر
+
+100
+00:07:13,480 --> 00:07:21,380
+من 0 عندي K أصغر من 0 عندي
+
+101
+00:07:21,380 --> 00:07:32,980
+بدي أوجد الـ L بي و K F الـ LBQF الـ B أشماله Any
+
+102
+00:07:32,980 --> 00:07:36,820
+Partition أخذت الـ B أشماله Any Partition بسوء X
+
+103
+00:07:36,820 --> 00:07:41,400
+نوت X1 لعند XN Any Partition of مين؟ Of the
+
+104
+00:07:41,400 --> 00:07:46,000
+interval I اللي بنحكي عنها إذا الـ BKF حسب التعريف
+
+105
+00:07:46,000 --> 00:07:51,000
+اللي كاتبه فوق إيش بيساوي الـ summation للـ M 
+
+106
+00:07:51,000 --> 00:07:54,700
+لمين؟ للـ M للـ function الجديدة اللي هي اسمها 
+
+107
+00:07:54,700 --> 00:08:00,520
+إيش؟ KF اللي هي عبارة عن مين؟ عن الـ infimum هذه
+
+108
+00:08:00,520 --> 00:08:04,280
+الـ K اللي هي إيش؟ الـ MK small اللي هي الـ
+
+109
+00:08:04,280 --> 00:08:11,850
+infimum لأ اللي هي الدالة تبعتنا KF of X لكل X وين
+
+110
+00:08:11,850 --> 00:08:16,350
+موجودة في الـ sub interval هذه بس بلاش عشان ما يصيرش 
+
+111
+00:08:16,350 --> 00:08:19,090
+conflict بين الـ K اللي هنا والـ K اللي هنا خليني 
+
+112
+00:08:19,090 --> 00:08:23,990
+أسميها بعد إذنكم اسمها اللي هي Ii اللي هي الـ sub
+
+113
+00:08:23,990 --> 00:08:28,410
+interval اللي هو Xi ناقص واحد لعند مين لعند Xi 
+
+114
+00:08:28,410 --> 00:08:33,350
+هذه i من عند واحد لعند N مضروبة في مين؟ في طول
+
+115
+00:08:33,350 --> 00:08:38,810
+الفترة هذه اللي هي Xi ناقص Xi ناقص واحد هذه
+
+116
+00:08:38,810 --> 00:08:45,710
+اللي هي الـ LBK و F ياساوينك إيش يا جماعة احنا 
+
+117
+00:08:45,710 --> 00:08:50,850
+بنشتغل ك أصغر من صفر بنشتغل على الحالة ك أشماله 
+
+118
+00:08:50,850 --> 00:08:55,470
+أصغر من صفر إذا حيساوي الـ summation الـ K لما تطلع
+
+119
+00:08:55,470 --> 00:08:59,650
+برا الـ infimum وهي سالبة على طول بتجلب الـ infimum 
+
+120
+00:08:59,650 --> 00:09:04,650
+إلى إيش؟ إلى supremum إذا بيصير ك في الـ supremum للـ 
+
+121
+00:09:04,650 --> 00:09:11,490
+F of X such that X element in Ii من عند 1 لعند N
+
+122
+00:09:11,490 --> 00:09:18,530
+ومضروب هذا في Xi ناقص Xi ناقص 1 ويساوي الآن
+
+123
+00:09:18,530 --> 00:09:22,030
+خلينا نطلع الـ K هذه برا الـ summation بالمرة لأن 
+
+124
+00:09:22,030 --> 00:09:25,530
+الـ K عبارة عن إيش يا شباب عبارة عن K عبارة عن ثابت
+
+125
+00:09:25,530 --> 00:09:28,510
+وبيطلع برا الـ summation عادي وكأنه عامل مشترك
+
+126
+00:09:28,510 --> 00:09:33,690
+بيصير K في الـ summation الآن لمين؟ للـ supremum للـ F
+
+127
+00:09:33,690 --> 00:09:39,590
+of X والـ x element in Ii في مضروب في مين؟ في الـ
+
+128
+00:09:39,590 --> 00:09:43,070
+Xi ناقص Xi ناقص واحد اللي هو طول الـ interval 
+
+129
+00:09:43,070 --> 00:09:47,190
+و هذا الكلام I من عند واحد لعند N إلى إن هذا يا
+
+130
+00:09:47,190 --> 00:09:55,220
+شباب كله عبارة عن إيش؟ عبارة عن بالظبط تعريف الـ UP
+
+131
+00:09:55,220 --> 00:09:58,580
+ومين؟ والـ function اللي عندي هنا إيش هي اللي
+
+132
+00:09:58,580 --> 00:10:06,360
+بشتغل عليها هنا F إذا حيساوي K في الـ U لـ P ومين؟
+
+133
+00:10:06,360 --> 00:10:13,360
+و F إذا اللي وصلت له يا جماعة إن عندي الـ
+
+134
+00:10:14,150 --> 00:10:21,110
+L of K و P و F بيساوي K في الـ UP و F Similarly
+
+135
+00:10:21,110 --> 00:10:29,990
+وبنفس الطريقة بقدر أحصل على الـ U بنفس الطريقة الـ U
+
+136
+00:10:29,990 --> 00:10:44,090
+لأ الـ P و KF اللي هو هتساوي K في الـ LP و F هتساوي
+
+137
+00:10:44,090 --> 00:10:53,090
+بنفس الطريقة K في الـ L, P و F خلي 
+
+138
+00:10:53,090 --> 00:10:58,450
+هذا في الذاكرة إن اللي حصلنا عليه اللي قلته هاي 
+
+139
+00:10:58,450 --> 00:11:03,030
+هذا الكلام خليني أسجلها اللي حصلت عليها لإني بدي 
+
+140
+00:11:03,030 --> 00:11:07,510
+أستخدمها بعد شوية اللي هو بيساوي K 
+
+141
+00:11:08,960 --> 00:11:15,580
+في الـ U,B والـ F وزي ما قلنا similarly الـ U الـ U,B
+
+142
+00:11:15,580 --> 00:11:24,670
+والـ K والـ F بساوي K في الـ L,B والـ F ماشي الحال طبعا هذه لو
+
+143
+00:11:24,670 --> 00:11:29,250
+لو حد حابب يعرف التفاصيل التفاصيل سهلة خليني بس على
+
+144
+00:11:29,250 --> 00:11:35,050
+السريع أحكيها شفويا الـ U P Q F إيش هيصير هنا بيصير
+
+145
+00:11:35,050 --> 00:11:39,190
+الـ summation لأن الـ supremum بدل الـ M K capital
+
+146
+00:11:39,190 --> 00:11:44,090
+هذه بيصير اللي هي supremum لمين بدل الـ G K F فلما
+
+147
+00:11:44,090 --> 00:11:48,730
+... لما أطلع الـ K برة عامل مشترك بيصير الـ supremum
+
+148
+00:11:48,730 --> 00:11:54,160
+infimum بيصير اللي هو الـ K برة وهنا الـ infimum مع
+
+149
+00:11:54,160 --> 00:11:59,480
+هذه اللي هي بالضبط تعريف مين الـ L of B أو F ماشي
+
+150
+00:11:59,480 --> 00:12:05,060
+الحال؟ طيب، الآن بكون إحنا أثبتنا الجهتين أنا وين
+
+151
+00:12:05,060 --> 00:12:09,930
+رايح؟ أنا بدي أثبت إن الـ K في الـ F is integrable
+
+152
+00:12:09,930 --> 00:12:13,410
+in the case K أصغر من 100 من 0 طيب احسبولي يا
+
+153
+00:12:13,410 --> 00:12:19,030
+جماعة احسبولي الـ L of K F إيش بتساوي حسب تعريفنا
+
+154
+00:12:19,030 --> 00:12:27,730
+اللي فوق عبارة عن الـ supremum لمين للـ L of B و K F
+
+155
+00:12:27,730 --> 00:12:34,210
+حيث B element in the set of partitions B of I ماشي
+
+156
+00:12:34,210 --> 00:12:37,090
+الحال يا جماعة ويساوي الآن
+
+157
+00:12:39,190 --> 00:12:45,190
+الـ LBKF أنا حضرتله أصلا بيساوي K في الـ U ويساوي
+
+158
+00:12:45,190 --> 00:12:50,790
+بطلع الـ K برة هذه بيصير الـ supremum لـ K الـ U, B
+
+159
+00:12:50,790 --> 00:12:59,930
+والـ F such that B element in B of I ويساوي بطلع الـ K
+
+160
+00:12:59,930 --> 00:13:05,370
+برة بيصير K لأن K سالب يا شباب بيصير K في مين؟ في
+
+161
+00:13:05,370 --> 00:13:12,730
+الـ infimum للـ U بي والـ F واضح أه؟ such that B
+
+162
+00:13:12,730 --> 00:13:22,080
+element in B of I الآن الـ infimum للـ U للـ B والـ F
+
+163
+00:13:22,080 --> 00:13:25,960
+على الشغل عمين الآن عن الـ function F ديروا بالكم
+
+164
+00:13:25,960 --> 00:13:31,800
+إذاً هيساوي ك... في مين هذه تعريف؟ تعريف بالضبط
+
+165
+00:13:31,800 --> 00:13:39,240
+الـ infimum لهذه اللي هو عبارة عن الـ U of F الـ U
+
+166
+00:13:39,240 --> 00:13:46,800
+of F هاي واحد اثنين من جهة أخرى نعتمد على هذه اللي
+
+167
+00:13:46,800 --> 00:13:57,360
+هو الـ U of ب ... آسف الـ U of K F بدورها الـ U of K
+
+168
+00:13:57,360 --> 00:14:05,400
+والـ F إيش حييساوي؟ حييساوي الـ infimum له اللي هي الـ L
+
+169
+00:14:05,400 --> 00:14:14,160
+الـ U of B و K F such that B element in B of I
+
+170
+00:14:14,730 --> 00:14:19,750
+هتلاقوها بتشبه اللي فوق ويساوي هذه أثبتناها إيش
+
+171
+00:14:19,750 --> 00:14:26,610
+بتساوي K في الـ L ويساوي الـ infimum لأ بدل الـ U إيش
+
+172
+00:14:26,610 --> 00:14:34,510
+بده يصير عنده ك الـ B والـ F الآن such that B element
+
+173
+00:14:34,510 --> 00:14:40,810
+in B of I ويساوي الآن الـ K بضطلحها برة الـ M في
+
+174
+00:14:40,810 --> 00:14:44,430
+مامي الجماعة الـ K سالبة إذا إيش هتصير عبارة عن
+
+175
+00:14:44,430 --> 00:14:49,470
+إيش؟ عن K في الـ supremum إذا ويساوي K في الـ
+
+176
+00:14:49,470 --> 00:14:56,430
+supremum للـ L بي والـ F such that B element in B of I
+
+177
+00:14:56,940 --> 00:15:03,060
+الآن هذه الـ supremum هذه هي بالضبط تعريف من الـ L
+
+178
+00:15:03,060 --> 00:15:13,180
+of F إذا بيصير ويساوي K في L of F K في L of F إذا
+
+179
+00:15:13,180 --> 00:15:19,980
+صارت الآن بتصور الصورة جربت أوضح هاي عندي L of K
+
+180
+00:15:19,980 --> 00:15:28,570
+of F أثبتناها بتساوي K of U of F والـ U K of F
+
+181
+00:15:28,570 --> 00:15:34,990
+بتساوي K L of F خليني ألخصها يا شباب فوق ونقارن
+
+182
+00:15:34,990 --> 00:15:40,950
+بينها ونصل لنتيجة اللي بدنا إياها طيب صار عندي
+
+183
+00:15:40,950 --> 00:15:51,130
+يا جماعة اللي هي L of K F بتساوي K U of F وفي نفس
+
+184
+00:15:51,130 --> 00:16:01,230
+الجهة U of K F بتساوي اللي هو K L of F طيب ما إحنا
+
+185
+00:16:01,230 --> 00:16:07,430
+بنقول إيش إحنا مفترضين ما إحنا مفترضين إن F is
+
+186
+00:16:07,430 --> 00:16:12,130
+integrable ما دام F is integrable إذا إيش هيكون
+
+187
+00:16:12,130 --> 00:16:19,770
+عندي L of F هي نفس الـ U of F إذا الآن من هذه ومن
+
+188
+00:16:19,770 --> 00:16:26,710
+اللي فوق بيصير عندي Lof K F التي بتساوي K في U of
+
+189
+00:16:26,710 --> 00:16:31,910
+F التي بتساوي K 
+
+190
+00:16:31,910 --> 00:16:38,470
+في U
+
+191
+00:16:38,470 --> 00:16:46,360
+of F إذن بين الجهتين طلع عندي L of K of F بيساوي U
+
+192
+00:16:46,360 --> 00:16:58,180
+K F وهذا يعني إذن K F is integrable إذن صار عندي
+
+193
+00:16:58,180 --> 00:17:05,040
+الـ K F is integrable طيب الآن اللي بعده سهل نشوف
+
+194
+00:17:05,040 --> 00:17:11,870
+إيش اللي بعده ضل إيش أثبت إنه ال integration الـ
+
+195
+00:17:11,870 --> 00:17:16,350
+integration للـ KF بيساوي KF ال integration لل F
+
+196
+00:17:16,350 --> 00:17:19,550
+اللي في الأول اللي هو اللي حكيناه في الأول يا شباب
+
+197
+00:17:19,550 --> 00:17:28,970
+تشوفوه حاضر أيوة
+
+198
+00:17:28,970 --> 00:17:33,930
+يا جماعة بدنا نثبت إنه ال جيت أثبتنا إن KF is
+
+199
+00:17:33,930 --> 00:17:38,060
+integrable دلوقتي أثبت هذه بتساوي هذه سهل الأمر طيب
+
+200
+00:17:38,060 --> 00:17:42,920
+إحنا الآن ما دام اللي هو KF is integrable إذا ال
+
+201
+00:17:42,920 --> 00:17:47,140
+integration من A لـ B للـ KF اللي هي صارت integrable
+
+202
+00:17:47,140 --> 00:17:52,080
+بيساوى اللي هو الـ L of K of F والـ U of K of F
+
+203
+00:17:52,080 --> 00:17:56,680
+بيساوى U of K F مثلا ويساوي الـ U K of F إيش هتساوي
+
+204
+00:17:56,680 --> 00:18:01,900
+من هنا اللي هتبتنعها ده K في الـ L of F أو الـ U of
+
+205
+00:18:01,900 --> 00:18:05,600
+F مش مشكلة كتير ويساوي ما هي الـ F is integrable
+
+206
+00:18:05,600 --> 00:18:09,660
+إذا الـ L of F هو عبارة عن إيش؟ عن ال integration من
+
+207
+00:18:09,660 --> 00:18:15,330
+A لـ B للـ F والـ K برة لأن الـ F هو من ال
+
+208
+00:18:15,330 --> 00:18:19,150
+integration من A لـ B لـ F لأن الـ F is integrable
+
+209
+00:18:19,150 --> 00:18:22,610
+إذا صار عند الآن ال integration من A لـ B ك F سواء
+
+210
+00:18:22,610 --> 00:18:27,070
+كيف ال integration من A لـ B لـ F الآن ظلت الحالة
+
+211
+00:18:27,070 --> 00:18:32,990
+الأخيرة يا شباب اللي هي حالة إن K اللي هو أكبر من
+
+212
+00:18:32,990 --> 00:18:38,170
+صفر K أكبر من صفر Similarly تماما زي الحالة اللي
+
+213
+00:18:38,170 --> 00:18:42,690
+هي مين هي اللي قبل بشوية K أصغر من صفر بس لما نطلع
+
+214
+00:18:42,690 --> 00:18:46,250
+الـ K برة الـ supremum بتظل الـ supremum supremum و
+
+215
+00:18:46,250 --> 00:18:49,690
+لما نطلع الـ K برة الـ infimum بتظل الـ infimum 
+
+216
+00:18:49,690 --> 00:18:54,950
+infimum ما دام كله بظل زي بعضه بناء عليه اللي توه
+
+217
+00:18:54,950 --> 00:19:04,090
+قبل بشوية إحنا أثبتنا بيصير عندي الـ L الـ L الـ L of
+
+218
+00:19:04,090 --> 00:19:11,270
+F أو الـ L of B و KF حيصير عبارة عن K في الـ L، B
+
+219
+00:19:11,270 --> 00:19:15,170
+والـ F لأن كل الدنيا هتظلها ماشية طبيعية لأن الـ K
+
+220
+00:19:15,170 --> 00:19:17,910
+أكبر من 0 لما تطلع من ال Infant Mom بتظلها زي ما
+
+221
+00:19:17,910 --> 00:19:21,090
+هي Infant Mom ولما تطلع من الـ Supremum بتظلها زي
+
+222
+00:19:21,090 --> 00:19:27,980
+ما هي Supremum والـ U of K,B و K,F هتطلع بتساوي K في
+
+223
+00:19:27,980 --> 00:19:35,060
+الـ U,B والـ F وبناء عليه حيصير عندي الـ U of K,F
+
+224
+00:19:35,060 --> 00:19:43,680
+هيساوي K في U of F و Lof K F هي ساوي K في الـ L of
+
+225
+00:19:43,680 --> 00:19:49,860
+F ومن الجهتين بنحصل بما إنه زي اللي فوق بالضبط إنه
+
+226
+00:19:49,860 --> 00:19:53,740
+الـ F is integrable بيصير U of F بيساوي L of F وعلى
+
+227
+00:19:53,740 --> 00:19:57,080
+طول بتطلع هذه بتساوي هذه وبنكمل زي ما كملنا هنا
+
+228
+00:19:57,080 --> 00:20:01,420
+بالضبط إذا اللي تركينه إحنا exercise K أكبر من 0 هي
+
+229
+00:20:01,420 --> 00:20:05,420
+الحالة الأسهل وهي شرحت اللي هو الـ hint على كيف
+
+230
+00:20:05,420 --> 00:20:10,000
+تكون اللي هو نثبت ال integration للـ K F بيساوي كيف
+
+231
+00:20:10,000 --> 00:20:14,620
+ال integration لل F وبذلك بكون إن هنا هذا الجزء من
+
+232
+00:20:14,620 --> 00:20:22,760
+النظرية لكل K element in R طيب نيجي الآن يا شباب
+
+233
+00:20:25,560 --> 00:20:29,360
+نثبت اللي هو الجزء الثاني من النظرية اللي هو الـ
+
+234
+00:20:29,360 --> 00:20:34,300
+integration إنه لو كانت F و G are integrable هيطلع
+
+235
+00:20:34,300 --> 00:20:40,660
+عندي برضه F زائد G is integrable خلينا نشوف يا
+
+236
+00:20:40,660 --> 00:20:49,460
+جماعة مع بعض نفترض إنه F و G F و G من I لعند R are
+
+237
+00:20:49,460 --> 00:20:54,820
+integrable functions بدنا نثبت إنه اللي هو الـ F
+
+238
+00:20:54,820 --> 00:20:58,960
+زائد G is integrable وكأني بدي أثبت إن الـ L of F
+
+239
+00:20:58,960 --> 00:21:05,860
+زائد G بيساوي الـ U لمين للـ F زائد G ماشي يا جماعة
+
+240
+00:21:05,860 --> 00:21:13,300
+طيب بدي أثبت الآن زي ما قلنا إنه F زائد G is
+
+241
+00:21:13,300 --> 00:21:14,540
+integrable
+
+242
+00:21:17,640 --> 00:21:22,580
+بس في شغلتين هيك يعني ب... ب... بذكركم فيه إن اللي
+
+243
+00:21:22,580 --> 00:21:27,840
+هو من... من الـ real واحد هنستخدمهم بعد شوية عندي
+
+244
+00:21:27,840 --> 00:21:34,320
+الآن لو
+
+245
+00:21:34,320 --> 00:21:38,160
+كان عندي two functions وبده أشوف اللي هو ال
+
+246
+00:21:38,160 --> 00:21:44,080
+supremum للـ F of X زائد G of X such that X element
+
+247
+00:21:44,080 --> 00:21:47,200
+in some interval اللي بدكم إياها اسمها I I زي ما
+
+248
+00:21:47,200 --> 00:21:53,740
+هم سميها هيكون أصغر أو يساوي الـ supremum للـ F of X
+
+249
+00:21:53,740 --> 00:21:59,870
+such that X element in I I زائد الـ supremum لـ g of
+
+250
+00:21:59,870 --> 00:22:04,690
+x such that x element in I I هذه معلومة سابقة من
+
+251
+00:22:04,690 --> 00:22:10,090
+اللي هو تحليل واحد نذكركم فيها الـ infimum برضه
+
+252
+00:22:10,090 --> 00:22:14,310
+شيء مشابه بس بعكس اللي موجود زائد g of x طبعا كله
+
+253
+00:22:14,310 --> 00:22:17,570
+... كله... هذا إيه الإثبات وكله أسباب أخذناها في
+
+254
+00:22:17,570 --> 00:22:23,010
+تحليل واحد x element in I I أكبر أو يساوي اللي هو
+
+255
+00:22:23,010 --> 00:22:29,660
+الـ infimum ل اللي هو f of x such that x element in
+
+256
+00:22:29,660 --> 00:22:35,700
+I I زائد الـ infimum ل g of x such that x element
+
+257
+00:22:35,700 --> 00:22:40,880
+in I I هدول الآن بدي اللي هي استخدمهم عشان اللي
+
+258
+00:22:40,880 --> 00:22:48,140
+هو أصل اللي بدي إياه الآن لو أجينا حسبنا اللي هو
+
+259
+00:22:48,140 --> 00:22:59,910
+الـ U لـ L of B of F زائد G عشان نصل لـ L F زي الـ G
+
+260
+00:22:59,910 --> 00:23:03,590
+بسوء الـ U F زي الـ G اعتمادا على إن الـ F والـ G
+
+261
+00:23:03,590 --> 00:23:07,030
+انتجربل يعني اعتماده على إن القلة الـ F هي الـ U
+
+262
+00:23:07,030 --> 00:23:11,050
+الـ F والقلة الـ G هي الـ U G شوفوا معايا تبقوا
+
+263
+00:23:11,050 --> 00:23:14,470
+معايا هذا حسب التعريف أشهر سبب هو يسوي الـ
+
+264
+00:23:14,470 --> 00:23:18,850
+summation الآن ال... ال... ال... ال... ال... M
+
+265
+00:23:18,850 --> 00:23:27,350
+small K بس لمين هذه لمين للـ F زائد G هذه لمين يا
+
+266
+00:23:27,350 --> 00:23:32,770
+جماعة للـ F زائد G مضروبة في XI minus XI minus 1 أو
+
+267
+00:23:32,770 --> 00:23:36,470
+XK زي ما هو نسميها زي ما بدكم نسميها سميناها فوق I
+
+268
+00:23:36,470 --> 00:23:44,020
+خلينا نسميها I I minus 1 I من عند 1 لعند N الـ M I
+
+269
+00:23:44,020 --> 00:23:46,980
+هذه إيه يا شباب؟ الـ F زائد G هي عبارة على جهة
+
+270
+00:23:46,980 --> 00:23:54,040
+عشان منها هننطلق الـ M I F زائد G يعني الـ M I هذه
+
+271
+00:23:54,040 --> 00:23:56,740
+لمين؟ للـ function الجديدة اللي اسمها F زائد G
+
+272
+00:23:56,740 --> 00:24:05,270
+بيساوى الـ infimum للـ F زائد G of X such that X
+
+273
+00:24:05,270 --> 00:24:10,310
+element in I, I وهذه من اللي كتبته الآن هنا اللي
+
+274
+00:24:10,310 --> 00:24:14,510
+قدمته لكم يا جماعة الانفمام اللي هنا أكبر يساوي
+
+275
+00:24:14,510 --> 00:24:18,990
+الانفمام لهذه زائد الانفمام لهذه الـ infimum لهذه
+
+276
+00:24:18,990 --> 00:24:24,350
+اللي هو اللي إحنا بنسميها M K Small للـ function F
+
+277
+00:24:24,350 --> 00:24:29,530
+وهذه اللي بنسميها مين الـ M K Small للـ function
+
+278
+00:24:29,530 --> 00:24:34,230
+مين؟ للـ function G معلش الرموز لكن واضح إنه
+
+279
+00:24:34,230 --> 00:24:38,030
+اللي هو إحنا بنحكي عن إيش عشان نميز بين الـ M K
+
+280
+00:24:38,030 --> 00:24:43,830
+أو الـ M I سنة مسمينها I الـ M I هنا والـ M I للـ 
+
+281
+00:24:43,830 --> 00:24:49,310
+فـ للـ J و للـ F زائد J للـ F زائد J هيها وهي من
+
+282
+00:24:49,310 --> 00:24:53,850
+اللي فوق هذه أكبر أو يساوي الـ infimum على الأولى
+
+283
+00:24:53,850 --> 00:24:57,830
+للـ F زائد الـ infimum على الـ M على الـ J يعني
+
+284
+00:24:57,830 --> 00:25:02,590
+هذا بمعنى آخر لأن هذا قيمة موجبة بقى صار أكبر أو
+
+285
+00:25:02,590 --> 00:25:10,260
+يساوي الـ summation اللي هو لمين؟ للـ MI F زائد M I
+
+286
+00:25:10,260 --> 00:25:15,760
+J هذا أكبر أو يساوي من ال equality اللي فوق في X I
+
+287
+00:25:15,760 --> 00:25:21,660
+ناقص X I ناقص واحد I من عند واحد لعند N نوزع ال N
+
+288
+00:25:21,660 --> 00:25:30,680
+هذا بالظبط بيساوي summation للـ M I F في xi-xi-1 i من
+
+289
+00:25:30,680 --> 00:25:34,980
+عند 1 لعند n زائد ال summation نفسه على مين الآن؟
+
+290
+00:25:34,980 --> 00:25:44,080
+mij في xi-xi-1 i من 1 لعند n واضح يا شباب؟ اه
+
+291
+00:25:44,080 --> 00:25:48,980
+المفروض أن الكلام واضح، صرنا عيدنا الفكرة عدة مرات
+
+292
+00:25:48,980 --> 00:25:52,940
+وكلنا... كله بندور حول اللي هو فعلاً التعريف للـ
+
+293
+00:25:52,940 --> 00:25:55,580
+upper thumb وال lower thumb وال upper integral
+
+294
+00:25:55,580 --> 00:25:58,960
+وال lower integral بس الواحد يستذكر التعريف هيلاقي
+
+295
+00:25:58,960 --> 00:26:04,020
+الأمور سهلة بإذن الله هذه بتساوي... هذه مين هي؟
+
+296
+00:26:04,020 --> 00:26:10,060
+بالظبط يا شباب؟ هي عبارة عن الللـ Partition B اللي 
+
+297
+00:26:10,060 --> 00:26:13,820
+بدأنا فيه الـ Arbitrary بالنسبة لمين الآن؟ للـ 
+
+298
+00:26:13,820 --> 00:26:20,340
+Function F زائد هذا بين هذا الـ L of B وبالنسبة 
+
+299
+00:26:20,340 --> 00:26:28,510
+لمين؟ لـ G صار عند الـ LB و F زائد G أصغر أو يساوي
+
+300
+00:26:28,510 --> 00:26:33,630
+آسف، أكبر يساوي ال B و F زائد مين؟ ال B of G خلينا
+
+301
+00:26:33,630 --> 00:26:37,090
+نخزن هذه المعلومة يا شباب، وخلّيني أكتبها بعد
+
+302
+00:26:37,090 --> 00:26:42,930
+إذنكم، هان أخزن المعلومة لأن بعد بشوية هاجي
+
+303
+00:26:42,930 --> 00:26:49,890
+أستعملها أنا وصلت لل L B F زائد G هيكون أكبر أو 
+
+304
+00:26:49,890 --> 00:26:59,790
+يساوي ال LP و F زائد ال L D و G هذه المعلومة
+
+305
+00:26:59,790 --> 00:27:06,750
+حصلناها، هأحصلك على إيش؟ مشابه جداً لل U هتصير ال U P
+
+306
+00:27:06,750 --> 00:27:11,430
+و F زائد G أصغر أو يساوي تبعاً للخاصية هذه اللي 
+
+307
+00:27:11,430 --> 00:27:15,550
+اعتمدنا عليها في البرهان، هنعتمد عليها الآن برهان في
+
+308
+00:27:15,550 --> 00:27:21,070
+ال U إيش اللي بقوله؟ بقول ما يليه، عارفين؟ بدي اشتغل 
+
+309
+00:27:21,070 --> 00:27:25,750
+على هذه أو أرجوكم جدّاً الأمور سهلة، شيل هذه و احكي
+
+310
+00:27:25,750 --> 00:27:30,170
+عن مين؟ عن ال U لأن مدام حكيت عن ال U إذا بدي يصير
+
+311
+00:27:30,170 --> 00:27:33,630
+بدل ما هي M small مين بحكي؟ بدل ال infinite بدي
+
+312
+00:27:33,630 --> 00:27:37,390
+يصير مين؟ M I اللي هي ال supremum اللي هي الـ
+
+313
+00:27:37,390 --> 00:27:40,930
+supremum إذا M I هذه لل F زائد G هي عبارة عن الـ
+
+314
+00:27:40,930 --> 00:27:45,110
+supremum لل F of X زائد G of X X element in I لأن
+
+315
+00:27:45,110 --> 00:27:50,000
+ال supremum للمجموع اللي هو هذه للـ F زائد G بدل ما
+
+316
+00:27:50,000 --> 00:27:54,220
+هيكون أكبر، إيش هيساوي يا شباب؟ أصغر أو يساوي الـ
+
+317
+00:27:54,220 --> 00:28:00,140
+supremum هذا اللي هو عبارة عن M I F وهذا مين هو يا 
+
+318
+00:28:00,140 --> 00:28:06,900
+شباب؟ ال M I G إذا صار الموضوع واضح هيصير أصغر أو 
+
+319
+00:28:06,900 --> 00:28:15,770
+يساوي اللي هو MI F و M I J ونفسه بظله زي ما هو، و
+
+320
+00:28:15,770 --> 00:28:22,590
+هنا مساواة حقيقية M I بغير M I وزعت زي ما وزعت قبل
+
+321
+00:28:22,590 --> 00:28:27,090
+هذا عبارة عن مين صار يا شباب؟ مدام ال M I capital
+
+322
+00:28:27,090 --> 00:28:33,490
+إذا صار U B F وهذا صار مين؟ عبارة عن U B J إذا
+
+323
+00:28:33,490 --> 00:28:42,790
+اللي حصلنا الآن ال U B F زائد G أصغر أو يساوي UBF
+
+324
+00:28:42,790 --> 00:28:48,110
+زائد UBJ وهي كما نكون حصلنا أو بدنا نخزن المعلومة
+
+325
+00:28:48,110 --> 00:29:00,980
+الثانية UBF زائد G أصغر أو يساوي UBF زائد UBG هذا
+
+326
+00:29:00,980 --> 00:29:05,760
+الآن بيكون احنا حصلنا اللي هي الـ ال two
+
+327
+00:29:05,760 --> 00:29:09,120
+inequalities هدولة اللي هم هم هم هم هم هم هم هم هم
+
+328
+00:29:09,120 --> 00:29:10,140
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+329
+00:29:10,140 --> 00:29:10,980
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+330
+00:29:10,980 --> 00:29:11,100
+هم هم هم هم هم هم هم هم هم
+
+331
+00:29:19,180 --> 00:29:23,620
+عبارة عن على كل Partition بيه، لكل Partition بيه في
+
+332
+00:29:23,620 --> 00:29:28,960
+الدنيا الآن أنا عشان أصل لل Integrability ياما
+
+333
+00:29:28,960 --> 00:29:35,700
+بأثبت ال U of اف زائد جي بيساوي الال بيقل اف زائد
+
+334
+00:29:35,700 --> 00:29:41,640
+جي وهذه يمكن شوية سنة بتغلب أو أن أستخدم اللي هو
+
+335
+00:29:41,640 --> 00:29:49,020
+Integrability criteria ان اوصل انه لكل أبسلون أكبر من
+
+336
+00:29:49,020 --> 00:29:53,510
+صفر there exist a partition بإبسلون بحيث أن U
+
+337
+00:29:53,510 --> 00:29:57,670
+بإبسلون و F زائد G ناقص ال L بإبسلون و F زائد G يكون
+
+338
+00:29:57,670 --> 00:30:01,610
+أصغر من إبسلون، إذا حصلت هيك بكون على طول أثبتت أن
+
+339
+00:30:01,610 --> 00:30:07,010
+ال F زائد G is integrable واضح؟ طيب، وحروح بهذا
+
+340
+00:30:07,010 --> 00:30:14,350
+الاتجاه، طيب، شوفوا معايا الآن إحنا فرضين أن F is
+
+341
+00:30:14,350 --> 00:30:19,150
+integrable إذن، مدام F is integrable إذن، by
+
+342
+00:30:19,760 --> 00:30:25,000
+Integrability criterion there exist لكل إبسلون
+
+343
+00:30:25,000 --> 00:30:31,120
+طبعاً أخدت الآن إبسلون أكبر من صفر given أنا إبسلون
+
+344
+00:30:31,120 --> 00:30:34,680
+ماشي، مدام F is integrable فانحارس بالـ
+
+345
+00:30:34,680 --> 00:30:39,860
+Integrability criterion there exist B F و إبسلون
+
+346
+00:30:39,860 --> 00:30:47,500
+partition B F و إبسلون such that U B F و إبسلون
+
+347
+00:30:48,590 --> 00:30:54,970
+والـ Function F ناقص... ناقص ال... معايا شباب؟
+
+348
+00:30:54,970 --> 00:31:00,890
+تذكرتوا هالنظرية؟ F و Epsilon و F أصغر من مين؟
+
+349
+00:31:00,890 --> 00:31:03,550
+أصغر من Epsilon على 2 للحسابات الـ Epsilon على 2
+
+350
+00:31:03,550 --> 00:31:08,270
+ماشي... الآن خليني بس عشان أسهل عملية الحسابات
+
+351
+00:31:08,270 --> 00:31:12,070
+إليه، بتنقل هذه هنا بعد إذنكم، وأقول هذا الكلام
+
+352
+00:31:12,070 --> 00:31:17,130
+أصغر من اللي هو هذا زائد هذا، واضح إيش اللي بعمله؟
+
+353
+00:31:17,130 --> 00:31:20,590
+اللي صار عندي الآن بما أنه F is integrable إذا 
+
+354
+00:31:20,590 --> 00:31:24,230
+بلاقي partition F إبسلون بحيث أنه هذا أصغر من هذا 
+
+355
+00:31:24,230 --> 00:31:33,030
+زائد هذا، واضح؟ Similarly for G G is integrable
+
+356
+00:31:33,030 --> 00:31:41,770
+Similarly for G G is integrable بيعطيني
+
+357
+00:31:42,670 --> 00:31:47,530
+for every ε أكبر من 0 there exists بي ابسلون خاص 
+
+358
+00:31:47,530 --> 00:31:51,610
+بال G خليني أسميه بعد ذلك بي جي ابسلون such that
+
+359
+00:31:51,610 --> 00:31:54,290
+طبعاً partition of نفس ال interval اللي بنشتغل عليها 
+
+360
+00:31:54,290 --> 00:31:56,350
+لإن ال F وال G دير بالكم معرفة على نفس الـ
+
+361
+00:31:56,350 --> 00:32:05,530
+interval such that اللي هو ال U بي G و ابسلون و G
+
+362
+00:32:05,530 --> 00:32:12,270
+الآن ال function اللي بحكي عنها أصغر من L بجي 
+
+363
+00:32:12,270 --> 00:32:17,250
+وإبسلون أو الـ function ash جي زائد برضه مين؟
+
+364
+00:32:17,250 --> 00:32:21,690
+إبسلون على اتنين، واضح يا جماعة؟ إذا من الـ 
+
+365
+00:32:21,690 --> 00:32:25,430
+integrability للـ F لجي تلها partition ومن الـ
+
+366
+00:32:25,430 --> 00:32:29,190
+integrability للـ G لجي تلها partition الآن زي ما 
+
+367
+00:32:29,190 --> 00:32:33,030
+عملنا المرة الفاتة بدي أخد partition عشان أستخدم
+
+368
+00:32:33,030 --> 00:32:38,370
+هذه وأستخدم هذه فبقول let بإبسلون وهذا بقول اللي 
+
+369
+00:32:38,370 --> 00:32:42,570
+بتدعي ان اللي حلقيه اللي يثبت الـ Integrability أو 
+
+370
+00:32:42,570 --> 00:32:45,970
+اللي هي criterion Integrability خدوا مين هو؟ أكيد
+
+371
+00:32:45,970 --> 00:32:53,150
+كلكم حتقوله خد F و E اتحاد B G و E عشان يصير 
+
+372
+00:32:53,150 --> 00:32:57,710
+بإبسلون refinement لهذه للأولى و refinement للثانية 
+
+373
+00:32:57,710 --> 00:33:03,150
+وتظبط معانا أن ال refinement تحسين بيصير ال lower
+
+374
+00:33:03,150 --> 00:33:09,830
+للتحسين يكبر عشان يروح للاش... لنساحة تحت المنحنى
+
+375
+00:33:09,830 --> 00:33:15,430
+بالظبط في حالة الموجبة بقى، والتحسين اللي يصير ال U
+
+376
+00:33:15,430 --> 00:33:20,390
+يصغر فبلتجن مع بعض فبعملنا بعملنا الـ الـ
+
+377
+00:33:20,390 --> 00:33:23,990
+integrability ماشي الحال سيانا عادينا كثير هذا
+
+378
+00:33:23,990 --> 00:33:27,920
+الكلام، طيب صلى على النبي عليه الصلاة والسلام، صلى
+
+379
+00:33:27,920 --> 00:33:32,720
+عليه الصلاة والسلام، الآن عندي صار هذا عندي موجود 
+
+380
+00:33:32,720 --> 00:33:38,280
+وهذا عندي إيش موجود؟ أنا غرض مين؟ غرض هيه لهذه، اه 
+
+381
+00:33:38,280 --> 00:33:44,520
+عندي U الآن، بدأ، أبدأ أجهز أن أصل U بإبسلون وافذائت
+
+382
+00:33:44,520 --> 00:33:50,860
+G اللي هو ناقص الـ P Y و F زائد G أصغر من إبسلون
+
+383
+00:33:50,860 --> 00:33:54,440
+بيكون خلصت بيصير عندي ال F زائد G is integrable
+
+384
+00:33:54,440 --> 00:34:02,640
+إذا خلينا نقول U بي إبسلون و F زائد G ماشي شباب؟ 
+
+385
+00:34:02,640 --> 00:34:10,050
+طيب هذه الآن أكيد أصغر أو يساوي من اللي أثبت هذا
+
+386
+00:34:10,050 --> 00:34:12,650
+أثبتنا لمين يا جماعة؟ في الأول اللي حضرناه وقلنا
+
+387
+00:34:12,650 --> 00:34:16,690
+اتعبنا عليه هذا قلنا صحيح لكل Partition في الدنيا
+
+388
+00:34:16,690 --> 00:34:21,570
+من ضمنه مين؟ الـ BY اللي جاته إذن هذا بيصير أصغر أو
+
+389
+00:34:21,570 --> 00:34:30,620
+يساوي U BY و F زائد U BY و G ماشي يا أبو حسن؟ منيح
+
+390
+00:34:30,620 --> 00:34:34,600
+هيك بيكون أصغر أو يساوي هذه، زي أن أصغر أو يساوي
+
+391
+00:34:34,600 --> 00:34:41,060
+اللي هي الثانية، طيب الآن ال... ال U P Y الآن ال P
+
+392
+00:34:41,060 --> 00:34:47,060
+Y refinement لمين؟ لل P F Y و refinement لمين برضه
+
+393
+00:34:47,060 --> 00:34:52,740
+يا جماعة؟ ل P G Y مدام refinement إذن اللي هو
+
+394
+00:34:54,270 --> 00:34:59,450
+التحسين... التحسين للـ U بصغر، إذا هيصير عندي هذا 
+
+395
+00:34:59,450 --> 00:35:05,270
+التحسين أكيد أصغر أو يساوي من الـ U بـ F وإبسلون 
+
+396
+00:35:05,270 --> 00:35:11,310
+اللي هو هذا تحسين لهذا و F زائد برضه التحسين هذا
+
+397
+00:35:11,310 --> 00:35:17,250
+هيكون أصغر من اللي اتحسنله اللي هو الـ U بـ G
+
+398
+00:35:17,250 --> 00:35:26,010
+وإبسلون أو G ماشي الحال، طيب نفس الأشياء عندنا احنا
+
+399
+00:35:26,010 --> 00:35:36,130
+بنعرف أن هذا المقدار U بإبسلون و F F و إبسلون
+
+400
+00:35:36,130 --> 00:35:39,830
+طلعوا على هنا هيو، أصغر يساوي هذه زائد إبسلون على
+
+401
+00:35:39,830 --> 00:35:43,730
+اتنين وهذه هيها أصلاً بالعمد أن احنا عملنا الأسرع
+
+402
+00:35:43,730 --> 00:35:52,370
+عشان نعوض بيصير من هذه ومن هذه بيصير أصغر من ال of
+
+403
+00:35:52,370 --> 00:35:59,850
+B F و Epsilon مع ال F زائد Epsilon على 2 زائد بدل
+
+404
+00:35:59,850 --> 00:36:08,170
+هذه اللي هي هيها منها نقل L B G و Epsilon و G زائد
+
+405
+00:36:08,170 --> 00:36:12,510
+Epsilon على 2 إن شاء الله ما خرب، 12 لأ، ما خرب 12 الآن
+
+406
+00:36:12,510 --> 00:36:19,590
+صار عندي هذي y على اتنين و y على اتنين واتنين
+
+407
+00:36:19,590 --> 00:36:20,810
+واتنين واتنين واتنين واتنين واتنين واتنين و
+
+408
+00:36:20,810 --> 00:36:21,390
+اتنين واتنين واتنين واتنين واتنين واتنين و
+
+409
+00:36:21,390 --> 00:36:24,390
+اتنين واتنين واتنين واتنين واتنين واتنين و
+
+410
+00:36:24,390 --> 00:36:24,410
+اتنين واتنين واتنين واتنين واتنين واتنين و
+
+411
+00:36:24,410 --> 00:36:25,230
+اتنين واتنين واتنين واتنين واتنين واتنين و
+
+412
+00:36:25,230 --> 00:36:33,730
+اتنين واتنين واتنين واتنين واتنين واتنين 
+
+413
+00:36:33,730 --> 00:36:44,290
+واتنين واتنين واتنين وامن أو يساوي الـ
+
+414
+00:36:44,290 --> 00:36:55,010
+refinement للـ L of B ε و F زائد اللي هو L أو B ε
+
+415
+00:36:55,010 --> 00:36:59,910
+OG سبحان الله، كل الأمور متناسقة عشان في الآخر برضه
+
+416
+00:36:59,910 --> 00:37:06,150
+هذه الخاصية نستخدم اللي فوق وهذا تناسق في الخلق
+
+417
+00:37:06,150 --> 00:37:10,690
+ما بين ما ينتجه العقل وما تنتجه الطبيعة اللي هو
+
+418
+00:37:10,690 --> 00:37:16,190
+هذا الآن المقدار ال بيبسلون، ال بيبسلون هي هذا
+
+419
+00:37:16,190 --> 00:37:21,890
+المقدار تطلع عليه من هنا، أصغر أو يساوي ال بي أف 
+
+420
+00:37:21,890 --> 00:37:26,990
+زائد إيش؟ جي، فبيصير هذا أصغر أو يساوي، عوضت من هنا يا 
+
+421
+00:37:26,990 --> 00:37:35,150
+شباب الـ  B و F زائد G يعني إبسلون طبعاً لأن هذا
+
+422
+00:37:35,150 --> 00:37:38,550
+الكلام صحيح لكل partition زي ما قلنا من ضمن إن الـ
+
+423
+00:37:38,550 --> 00:37:45,880
+B إبسلون زائد إيش إبسلون؟ صار عندي الآن اللي بديها
+
+424
+00:37:45,880 --> 00:37:50,540
+الـ U بيبسلون F زائد G أصغر أو يساوي L بيبسلون F
+
+425
+00:37:50,540 --> 00:37:54,260
+زائد G زائد Y يعني عشان اللي وصلت له أخدت Y
+
+426
+00:37:54,260 --> 00:37:59,320
+arbitrary لجهة partition بيبسلون بحيث أن الـ U
+
+427
+00:37:59,320 --> 00:38:06,210
+بيبسلون F زائد G ناقص القلبي Y F زائد G أصغر من Y
+
+428
+00:38:06,210 --> 00:38:10,950
+وهذا يعني أنه احنا حققنا الـ Integrable criterion
+
+429
+00:38:10,950 --> 00:38:18,070
+بمعنى أنه صارت الـ F زائد G is integrable إذن الآن
+
+430
+00:38:18,070 --> 00:38:26,510
+أثبتنا أن الـ F زائد G is integrable نيجي الآن
+
+431
+00:38:26,510 --> 00:38:31,450
+نحاول نخلي بس هدول اللي هستخدمهن بعد شوية هنخليه 
+
+432
+00:38:31,450 --> 00:38:35,610
+الموجودات وده يعني مسحناها نضطرنا مسحناها نرجع
+
+433
+00:38:35,610 --> 00:38:39,770
+للتلخيص ركزوا معايا إيش اللي بقوله إيش اللي بحكيه
+
+434
+00:38:39,770 --> 00:38:41,150
+عندي
+
+435
+00:38:47,360 --> 00:38:49,720
+الآن بدي أثبت أن ال integration لل F زي ال G يا
+
+436
+00:38:49,720 --> 00:38:52,460
+شباب سواء ال integration لل F زي ال integration لل
+
+437
+00:38:52,460 --> 00:38:54,280
+G يعني الخطوة الأولى احنا أثبتنا أن F زي ال G 
+
+438
+00:38:54,280 --> 00:38:56,820
+integrable الآن بدي أثبت أن ال integration لل F زي
+
+439
+00:38:56,820 --> 00:39:00,280
+ال G سواء ال integration لل F زي ال integration لل
+
+440
+00:39:00,280 --> 00:39:06,320
+G شوفوا عليها نيجي الآن ال integration من A ل B لل
+
+441
+00:39:06,320 --> 00:39:11,600
+F زي ال G ماهي الحالة ال integration لل F زي ال G
+
+442
+00:39:12,860 --> 00:39:16,920
+بتساوي الـ U of F زائد G صح ولا لأ؟ آه لأن الـ
+
+443
+00:39:16,920 --> 00:39:20,760
+Sort of زائد G is integrable إذا بتساوي الـ U of F
+
+444
+00:39:20,760 --> 00:39:25,060
+زائد G الـ U of F زائد G هي عبارة عن إيش يا جماعة؟
+
+445
+00:39:25,060 --> 00:39:30,620
+هي عبارة عن الـ infimum لكل الـ U of زائد G مع
+
+446
+00:39:30,620 --> 00:39:35,570
+الpartition B إذن أي واحدة من اللي بموجود عليهم الـ
+
+447
+00:39:35,570 --> 00:39:40,490
+infimum هتكون هذا أصغر منها، هيصير عندي هذه أصغر
+
+448
+00:39:40,490 --> 00:39:47,990
+أو يساوي الـ U بيبسلون الـ F زائد D، آه أكيد،
+
+449
+00:39:47,990 --> 00:39:52,790
+عارفين ليش؟ لأن هذه الـ infimum لكل الـ U زلة زي
+
+450
+00:39:52,790 --> 00:39:57,850
+هيك حيث الـ PY عبارة عن الـ partition وين موجودة في
+
+451
+00:39:57,850 --> 00:40:02,410
+P of I هذه الـ U عبارة عن الـ infimum إلهم إذا
+
+452
+00:40:02,410 --> 00:40:05,890
+الواحد منهم أكبر أو يساوي اللي هو هذا الـ infimum
+
+453
+00:40:05,890 --> 00:40:10,790
+اللي هو الرابع .. ال grades اللي هو الرابع طيب هذا
+
+454
+00:40:10,790 --> 00:40:17,650
+U PY F زائد G U PY F زائد G لجناه أصغر أو يساوي
+
+455
+00:40:18,450 --> 00:40:23,430
+اللي هو ال بي أبسلون و F و بي أبسلون جي زائد
+
+456
+00:40:23,430 --> 00:40:26,010
+إبسلون شايفين هو من هنا يا شباب هاي اللي بدأ
+
+457
+00:40:26,010 --> 00:40:30,390
+استخدمه الآن هاي اللي بدأ تلزمني هنا هاي هذه هاي
+
+458
+00:40:30,390 --> 00:40:37,570
+هذه أثبتناها أصغر أو يساوي هذه خليني الآن أستخدمها
+
+459
+00:40:37,570 --> 00:40:41,570
+فوق فده ننجلها فوق هذه أصغر أو يساوي اللي بالأزرق
+
+460
+00:40:41,570 --> 00:40:46,510
+هذه أصغر أو يساوي الجيت بتعرفي أشي بتسوي ال بي
+
+461
+00:40:46,510 --> 00:40:47,650
+أبسلون و F
+
+462
+00:40:55,470 --> 00:41:02,070
+معايا شباب طيب ما هو ال F is integrable إذا ال
+
+463
+00:41:02,070 --> 00:41:10,870
+integration لل F بيساوي L و F أكيد بيساوي U و F لأن هذه
+
+464
+00:41:10,870 --> 00:41:15,650
+الـ L of F هي عبارة عن الـ Supremum لهذه كلها إذن
+
+465
+00:41:15,650 --> 00:41:23,090
+أكيد هذا أصغر أو يساوي الـ L of F زائد و L of G
+
+466
+00:41:23,090 --> 00:41:26,350
+برضه أكبر أو يساوي هذه لأن هذه عبارة عن الـ
+
+467
+00:41:26,350 --> 00:41:29,610
+Supremum لكل الأشكال اللي زي هذه و L of F هي عبارة
+
+468
+00:41:29,610 --> 00:41:34,230
+عن الـ Supremum لكل الـ B's و F لكل اللي هو ال
+
+469
+00:41:34,230 --> 00:41:36,190
+partitions اللي في set of all partitions
+
+470
+00:41:36,190 --> 00:41:42,590
+partitions B of I زائد مين؟ زائد أبسلون ولأن F is
+
+471
+00:41:42,590 --> 00:41:45,490
+integrable إذا هذا بيساوي بالظبط ال integration من
+
+472
+00:41:45,490 --> 00:41:49,330
+A ل B لل F زائد ال integration لأن G is integrable
+
+473
+00:41:49,330 --> 00:41:55,810
+ماعطينايها أصلاً G من A ل B زائد H زائد أبسلون صار
+
+474
+00:41:55,810 --> 00:42:00,250
+عندي الآن ال integration اللي حصلته يا شباب اللي
+
+475
+00:42:00,250 --> 00:42:06,510
+حصلته مالي اللي حصلته أنه صار عندي ال integration
+
+476
+00:42:06,510 --> 00:42:14,970
+لل F زائد G من a ل b أشماله أصغر أو يساوي ال
+
+477
+00:42:14,970 --> 00:42:18,250
+integration لل F من a ل عند b زائد ال integration
+
+478
+00:42:18,250 --> 00:42:23,710
+لل g من a ل b زائد ابسلون هذا لكل ابسلون في الدنيا
+
+479
+00:42:23,710 --> 00:42:28,920
+لكل ابسلون في الدنيا هذا صحيح إذا المدام صحيح لكل
+
+480
+00:42:28,920 --> 00:42:33,380
+إبسلون إذا أكيد هيطلع لل integration لل F زائد G
+
+481
+00:42:33,380 --> 00:42:37,200
+من A ل B أصغر أو يساوي ال integration لل F زائد ال
+
+482
+00:42:37,200 --> 00:42:41,580
+integration لل G من A ل B من A ل B لأن اللي فوق
+
+483
+00:42:41,580 --> 00:42:46,880
+صحيح لمين؟ لأي إبسلون في الدنيا اللي بتستشكل عليه
+
+484
+00:42:46,880 --> 00:42:51,060
+الاب أنه يفهمها عن طريق أنه since إبسلون was
+
+485
+00:42:51,060 --> 00:42:55,540
+arbitrary then هذا أصغر أو يساوي هذا يأخذ الحالة
+
+486
+00:42:55,540 --> 00:42:59,540
+الخاصة للإبسلونات لأن لكل إبسلون هذا صحيح من ضمنها
+
+487
+00:42:59,540 --> 00:43:04,280
+الإبسلونات اللي بيساوي 1 على N لكل N بيظل هذا ال
+
+488
+00:43:04,280 --> 00:43:07,940
+integration لل F زائد G أصغر إذا كان ال
+
+489
+00:43:07,940 --> 00:43:11,380
+integration لل F زائد ال integration لل G زائد 1
+
+490
+00:43:11,380 --> 00:43:14,720
+على N لكل N في الدنيا لأن هذا صحيح على كل إبسلون
+
+491
+00:43:14,720 --> 00:43:19,600
+من ضمنها ال 1 على N مات ال N every N يعني الآن مدام
+
+492
+00:43:19,600 --> 00:43:23,640
+هذه صحيحة بناء على هذه صحيحة خد ال limit للجهتين
+
+493
+00:43:23,640 --> 00:43:28,240
+as n goes to infinity ال limit للجهتين as n goes
+
+494
+00:43:28,240 --> 00:43:31,280
+to infinity هذا independent of n وهذا independent
+
+495
+00:43:31,280 --> 00:43:34,920
+of n وهذا as n goes to infinity بتروح للصفر بيصير
+
+496
+00:43:34,920 --> 00:43:39,220
+عنده اللي هو ال integration لل F زائد G هيكون أصغر
+
+497
+00:43:39,220 --> 00:43:42,420
+السهولة integration لل F زائد integration لمن؟ لل
+
+498
+00:43:42,420 --> 00:43:46,740
+G هذا فهم آخر اللي بشوية بتغلب من قصة since Y هو
+
+499
+00:43:46,740 --> 00:43:52,090
+الواضع الاربتردن كذا كده طيب إذا صار عندي الآن
+
+500
+00:43:52,090 --> 00:43:57,250
+إثباتة ال integration ل F زي ال G ظهر سواء ال
+
+501
+00:43:57,250 --> 00:44:03,230
+integration ل F زي ال integration ل G اللي هان بده
+
+502
+00:44:03,230 --> 00:44:05,970
+يأثبت المساواة بده يثبت العكس بده ياخد الـ
+
+503
+00:44:05,970 --> 00:44:09,390
+integration للـ F زي الـ integration للـ G و أصل
+
+504
+00:44:09,390 --> 00:44:14,350
+للي بديه شوف كيف اتفجنا الآن إيش أثبتنا يا شباب
+
+505
+00:44:14,350 --> 00:44:19,210
+خليني أسجلها هان أخزنها ال integration للـ F زي
+
+506
+00:44:19,210 --> 00:44:24,490
+الـ G من A ل B أصغر أو يساوي ال integration للـ F من A
+
+507
+00:44:24,490 --> 00:44:29,570
+ل B زي ال integration للـ G من A ل B وهذا أثبتناه
+
+508
+00:44:29,570 --> 00:44:32,970
+بالدفت بت اللي هو conversely برضه اعتمادا على
+
+509
+00:44:32,970 --> 00:44:44,310
+الحديث الأولاني خليني 
+
+510
+00:44:44,310 --> 00:44:48,850
+اكتب بالأسود هنا عشان أتميز بين الجهتين عند الآن
+
+511
+00:44:48,850 --> 00:44:53,330
+ال integration لل F من A ل B زائد ال integration لل
+
+512
+00:44:53,330 --> 00:45:02,420
+G من A ل B ماشي الحال هذا اللي هو أصغر أو يساوي
+
+513
+00:45:02,420 --> 00:45:07,360
+اللي هو نفس المنطق الأولاني هذا اللي هو عبارة عن
+
+514
+00:45:07,360 --> 00:45:13,760
+اللي بالظبط بيساوي ال U of F زائد ال U of G و ال U
+
+515
+00:45:13,760 --> 00:45:17,380
+of F هذه عبارة عن ال infimum على كل ال U's اللي هي
+
+516
+00:45:17,380 --> 00:45:20,000
+ال lower ال upper sums اللي هي أصغر أو يساوي ال U
+
+517
+00:45:20,000 --> 00:45:27,620
+لل بي إبسلون و F زائد ال U لل بي إبسلون و جي مظبوط
+
+518
+00:45:27,620 --> 00:45:31,540
+ولا لأ؟ أكيد مظبوط لأن هذا عبارة عن الام في مملكة
+
+519
+00:45:31,540 --> 00:45:35,060
+كل هذول وهذه عبارة عن ال supreme مملكة لكل هذول
+
+520
+00:45:35,060 --> 00:45:46,120
+ماشي الآن عندي هذا نفسه ال U بي إبسلن و أف و ال U
+
+521
+00:45:46,120 --> 00:45:51,880
+بي أل إبسلن و أف أثبتناها نتطلع عليها نستخدم حاجة
+
+522
+00:45:51,880 --> 00:45:56,220
+هنا يو بي إبسل و أف و يو بي إبسل و أف أصغر يساوي
+
+523
+00:45:56,220 --> 00:46:05,420
+مين؟ هايها ال بي إبسلون و أف زائد جي صحيح؟ واضح
+
+524
+00:46:05,420 --> 00:46:11,180
+عشان بابا يعني بدت أستخدم الآن هاي هذي يو بي
+
+525
+00:46:11,180 --> 00:46:16,550
+إبسلون شايفينها؟ هي اللي بحكي بشويش عشان تتركزوا
+
+526
+00:46:16,550 --> 00:46:19,890
+معايا اللي بالأزرق هذا اللي بالأصفر آسف معها دي
+
+527
+00:46:19,890 --> 00:46:23,970
+هذا كله أثبتناه إذا مين ده؟ استخدمه إذا هذا أصفر
+
+528
+00:46:23,970 --> 00:46:31,650
+أو يساوي اللي هي L بي أبسلون و F زائد G زائد 100
+
+529
+00:46:31,650 --> 00:46:38,270
+زائد أبسلون معايا يا شباب أكيد اللي هو وضحت إيش
+
+530
+00:46:38,270 --> 00:46:44,690
+بدي أسوي هذا نفسه اللي هو أصغر أو يساوي L of F زي
+
+531
+00:46:44,690 --> 00:46:48,430
+الـ G زي الـ Epsilon لأن L of F مين زي الـ G
+
+532
+00:46:48,430 --> 00:46:51,070
+يقولونها كتير إيش هي دي؟ عبارة عن الـ Supremum لكل
+
+533
+00:46:51,070 --> 00:46:56,860
+دولة آه على كل ال partitions إذا أكيد ال L of F هو
+
+534
+00:46:56,860 --> 00:47:00,580
+أكبر أو يساوي هذا المقدر ال L of F زائد G عبارة عن
+
+535
+00:47:00,580 --> 00:47:05,680
+ال sobremom لكل اللي هي lower sums اللي إنصار عندي
+
+536
+00:47:05,680 --> 00:47:09,940
+و هذا لأن F زائد G أثبتناها inintegrable بيساوي ال
+
+537
+00:47:09,940 --> 00:47:15,860
+integration من A ل B لل F زائد G لكل أشماله زائد Y
+
+538
+00:47:16,670 --> 00:47:20,990
+إذا حصلنا الـ F زائد الـ integration للـ A للـ F
+
+539
+00:47:20,990 --> 00:47:23,470
+من A إلى B زائد الـ integration للـ G من A إلى B
+
+540
+00:47:23,470 --> 00:47:26,930
+أصغر أو يساوي ال integration من A إلى B للـ F زائد
+
+541
+00:47:26,930 --> 00:47:32,510
+G زائد مين؟ زائد إبسنون مظبوط يا شباب الآن نفس
+
+542
+00:47:32,510 --> 00:47:38,580
+القصة الأولى بما أن إبسلون كان مخصصًا وبنفس المنطق
+
+543
+00:47:38,580 --> 00:47:43,320
+اللي حكيته قبل بشوية إذا ال integration لل F من A
+
+544
+00:47:43,320 --> 00:47:47,800
+لعند B زائد ال integration لل G من A لعند B هيكون
+
+545
+00:47:47,800 --> 00:47:53,720
+أصغر أو يساوي ال integration لل F زائد G هذه الآن
+
+546
+00:47:53,720 --> 00:47:58,520
+اللي بالأصفر مع هذه اللي بالأحمر يعطينا أن ال
+
+547
+00:47:58,520 --> 00:48:06,520
+integration للـ F زائد G من A لعند B يساوي بالظبط
+
+548
+00:48:06,520 --> 00:48:10,340
+integration من A لB للF زائد integration من A لB
+
+549
+00:48:10,340 --> 00:48:13,360
+للG وهو المطلوب
+
+550
+00:48:15,210 --> 00:48:20,010
+و بكون احنا هي كأثبتنا الجزء الثاني من النظرية
+
+551
+00:48:20,010 --> 00:48:23,770
+اللي هي الأولى اللي هو ال integration لل F زي ال G
+
+552
+00:48:23,770 --> 00:48:28,990
+بسبب ال integration لل F زائد ال integration لمين؟
+
+553
+00:48:28,990 --> 00:48:34,370
+لل G فيكم تصلوا علينا بيه؟ عليه الصلاة والسلام وصلى
+
+554
+00:48:34,370 --> 00:48:38,310
+الله عليه وسلم يا حمد طيب يا شباب شوفوا النظرية
+
+555
+00:48:38,310 --> 00:48:44,610
+اللي عندي كما يلي نظريتنا بقول لو كانت F من الـ
+
+556
+00:48:44,610 --> 00:48:48,270
+closed bounded interval A وB لعند الـ R بـ
+
+557
+00:48:48,270 --> 00:48:52,310
+Integrable function On I اللي هي دالة قابلة
+
+558
+00:48:52,310 --> 00:48:57,210
+للتكامل بالنسبة للرمان وكانت الدالة F of X أكبر أو
+
+559
+00:48:57,210 --> 00:49:01,530
+يساوي صفر يعني المنحنى وين؟ فوق اللي هو محور
+
+560
+00:49:01,530 --> 00:49:06,090
+السينات إذا حيكون ال integration للـ F نفسه برضه 
+
+561
+00:49:06,090 --> 00:49:12,370
+أشماله أكبر أو يساوي صفر يعني الآن بقولي F of X
+
+562
+00:49:13,950 --> 00:49:17,850
+أكبر أو يساوي صفر on I اللي بيعطيني ال integration
+
+563
+00:49:17,850 --> 00:49:23,490
+على ال I من A ل B لل F أكبر أو يساوي أيش برضه صفر
+
+564
+00:49:23,490 --> 00:49:29,250
+و proof سهل الأمر و ما أعطيك F integrable كمان
+
+565
+00:49:29,250 --> 00:49:34,990
+ما أعطيك F أشماله is integrable معايا مدام ال F is
+
+566
+00:49:34,990 --> 00:49:40,690
+integrable إذا أكيد ال integrationللـ F من عند A ل
+
+567
+00:49:40,690 --> 00:49:45,750
+B بساوي L of F مثلا أو بساوي U of F زي ما بدك
+
+568
+00:49:45,750 --> 00:49:53,410
+بساوي L of F الـ L of F أكيد أكبر أو يساوي لإنه الـ L of
+
+569
+00:49:53,410 --> 00:49:57,270
+F عبارة عن إيش يا شباب عبارة عن طبعا الـ L of F هنا
+
+570
+00:49:57,270 --> 00:50:02,670
+بتظبط معنا الـ L of F عبارة عن إيش عبارة عن الـ
+
+571
+00:50:02,670 --> 00:50:09,210
+Supremumلمين؟ لكل ال partitions إذا أكيد هي أكبر
+
+572
+00:50:09,210 --> 00:50:18,650
+أو يساوي الـ L of P أو P أو F إيش الـ L of P أو F؟
+
+573
+00:50:18,650 --> 00:50:23,790
+some partition أنا بديها Partition مين؟ للفترة A و B
+
+574
+00:50:23,790 --> 00:50:28,590
+اللي هي الفترة مين؟ I اللي هي A و B هذا فترة نهار
+
+575
+00:50:28,590 --> 00:50:33,090
+الآن أنا بقول الـ L of F اللي هو الـ supremum على كل
+
+576
+00:50:33,090 --> 00:50:37,650
+ال partitions دولة للـ L على كل ال partitions دولة
+
+577
+00:50:37,650 --> 00:50:41,350
+أكيد هيكون أكبر أو يساوي طيب هذا إيش معنى هذا
+
+578
+00:50:41,350 --> 00:50:44,590
+اخترته هل جيت بتشوفوا إيش معنى اخترته؟ إيش ال
+
+579
+00:50:44,590 --> 00:50:48,290
+partition هذا B A و B؟ هذا ال partition هو B A و B
+
+580
+00:50:48,290 --> 00:50:52,310
+هو بس ال partition اللي في نقطتين أول نقطة و آخر
+
+581
+00:50:52,310 --> 00:50:55,670
+نقطة يعني ما .. ما جزأت الـ interval إلا لحالها هي
+
+582
+00:50:55,670 --> 00:50:58,510
+.. هي التجزئة هي الـ interval a و b بصحيح اللي هو
+
+583
+00:50:58,510 --> 00:51:02,930
+طبعا I partition للـ a و الـ b طيب إيش تعريفه هذا ..
+
+584
+00:51:02,930 --> 00:51:07,550
+هذا .. هذا .. إيش تعريفه هذا بساوي اللي هو الـ
+
+585
+00:51:07,550 --> 00:51:11,910
+summation مش هنحتاج الـ summation لأنه بس إيش مالها
+
+586
+00:51:11,910 --> 00:51:15,750
+ما فيش تغير صفر الـ interval واحدة إذا بساوي اللي هو
+
+587
+00:51:15,750 --> 00:51:25,230
+الـ M summation للـ M Kأه في إيش في xk-xk-1 لكن أصلا
+
+588
+00:51:25,230 --> 00:51:28,690
+أنا باخد بس اللي هو ما فيش غير sub interval واحدة
+
+589
+00:51:28,690 --> 00:51:33,530
+اللي هي الـ a و الـ b يعني هذه بمعنى آخر b minus
+
+590
+00:51:33,530 --> 00:51:37,910
+a minus a و ال mk هنا واحدة بس مين هي ال
+
+591
+00:51:37,910 --> 00:51:43,790
+maximum اللي هي خلينا نسميها m a و b هذه MAP ماذا
+
+592
+00:51:43,790 --> 00:51:49,290
+بتساوي حسب التعريف الـ infimum للـ F of X حيث الـ X
+
+593
+00:51:49,290 --> 00:51:54,220
+موجودة في الـ sub interval هذه اللي هي I نفسه الآن
+
+594
+00:51:54,220 --> 00:51:57,680
+هيك باخد الـ .. الـ .. الـ .. ال partition صار عندي
+
+595
+00:51:57,680 --> 00:52:01,900
+الآن هذا أكبر يساوي m of P في مين؟ ف أنا هذه
+
+596
+00:52:01,900 --> 00:52:05,460
+infimum من الـ F of X و أحنا فرضين إن الـ F of X أكبر
+
+597
+00:52:05,460 --> 00:52:09,040
+يساوي صفر يعني الـ infimum غصب بين عنا هيطلع F أكبر
+
+598
+00:52:09,040 --> 00:52:13,060
+يساوي صفر إذا هذه أكبر أو يساوي صفر و هذه أكبر أو
+
+599
+00:52:13,060 --> 00:52:16,760
+يساوي صفر إذا مع بعض التنتين إيش شماله؟ أكبر أو
+
+600
+00:52:16,760 --> 00:52:20,460
+يساوي صفر إذا ال integration من A ل B لل F أكبر أو
+
+601
+00:52:20,460 --> 00:52:21,720
+يساوي صفر
+
+602
+00:52:24,180 --> 00:52:31,620
+هذه هي النظرية 722 نجي الآن للـ remark اللي بعدها و
+
+603
+00:52:31,620 --> 00:52:36,860
+الـ remark اللي بعدها يعني على اللي هي النظرية
+
+604
+00:52:36,860 --> 00:52:42,800
+الفهم النظرية هذه على طول بنستوعبها إن شاء الله و
+
+605
+00:52:42,800 --> 00:52:43,360
+بنفهمها
+
+606
+00:52:48,870 --> 00:52:52,690
+ما هي النظرية اللي تريد أن تقولها؟ إذا كانت f من I
+
+607
+00:52:52,690 --> 00:52:56,850
+a و b لعند R is integrable لكل x element in I
+
+608
+00:52:56,850 --> 00:53:00,590
+لجينا أن f of x بين مين؟ بين قيمتين بين M و بين
+
+609
+00:53:00,590 --> 00:53:04,330
+مين؟ بين M capital دائما الـ f of x يعني كأنه
+
+610
+00:53:04,330 --> 00:53:10,190
+دلتنا دلتنا هي ها هي عنا ال function أي إن كانت
+
+611
+00:53:10,190 --> 00:53:16,380
+و هي الفترة a و b عندنا من هنا a و b و B و هاي اللي
+
+612
+00:53:16,380 --> 00:53:20,720
+هو M small و هاي M capital يعني الدالة بين ..
+
+613
+00:53:20,720 --> 00:53:25,340
+دايما و اجعة بين هدول النغطين اللي هو بين M small و
+
+614
+00:53:25,340 --> 00:53:30,260
+بين M capital إذا ال integration تبعها من A ل B لل
+
+615
+00:53:30,260 --> 00:53:35,260
+F أكبر يساوي M في B minus A و أصغر من M في B minus
+
+616
+00:53:35,260 --> 00:53:42,380
+A capital واضح؟ طيب شوف
+
+617
+00:53:42,380 --> 00:53:50,950
+الآن أول حاجة مدام F is integrable إذا بدك تلاحظ أن
+
+618
+00:53:50,950 --> 00:53:56,830
+الـ L of F بساوي الـ U of F بساوي قيمة ال
+
+619
+00:53:56,830 --> 00:54:02,430
+integration من A ل B لل F of X DX، مظبوط؟ هذا من
+
+620
+00:54:02,430 --> 00:54:07,770
+تعريف أن الـ F أشماله F is integrable تعالي الـ L
+
+621
+00:54:07,770 --> 00:54:12,180
+of F زي ما عملنا قبل بشوية L of F اللي هي أشماله
+
+622
+00:54:12,180 --> 00:54:16,560
+أكبر أو يساوي لإن الـ supremum على كل مين على ال
+
+623
+00:54:16,560 --> 00:54:21,160
+partitions اللي لها إذا أكبر أو يساوي اللي هو ال
+
+624
+00:54:21,160 --> 00:54:28,960
+الـ L of P أو P و F اللي قبل شوية عملته ماشي اللي
+
+625
+00:54:28,960 --> 00:54:34,780
+هو L أو P و F بساوي اللي هو الـ infimum للـ F of X
+
+626
+00:54:34,780 --> 00:54:41,000
+such that X element in the interval A و B هذا الـ
+
+627
+00:54:41,000 --> 00:54:44,220
+sub interval في الشغل هي واحدة اللي هو مضروب في
+
+628
+00:54:44,220 --> 00:54:46,380
+مين؟ في طول الـ interval اللي هي مين طول ال
+
+629
+00:54:46,380 --> 00:54:49,700
+interval في هذه الحالة؟ أو الـ sub interval B minus
+
+630
+00:54:49,700 --> 00:54:52,940
+A هي سماشي لكن أنا أصلا ما عنديش غير sub interval
+
+631
+00:54:52,940 --> 00:54:57,780
+واحدة هيك مجزقة أنا الفترة إلى جزء واحد بس الآن ال
+
+632
+00:54:57,780 --> 00:55:01,240
+infimum هذا عمالي بقول أنا الـ F of X أكبر يساوي
+
+633
+00:55:01,240 --> 00:55:07,050
+مين؟ M إذاً، حيكون عند الـ infimum له أكيد هيكون
+
+634
+00:55:07,050 --> 00:55:12,830
+أكبر أو يساوي الـ M هذه في مين؟ في الـ B minus A
+
+635
+00:55:12,830 --> 00:55:18,090
+كمان مرة الـ F of X أكبر أو يساوي M إذاً، الـ
+
+636
+00:55:18,090 --> 00:55:22,390
+infimum تبعه أكيد هيظل أكبر أو يساوي مين؟ أكبر أو
+
+637
+00:55:22,390 --> 00:55:30,080
+يساوي M هذه من جهة الآن، صار عندي الآن اللي عملته
+
+638
+00:55:30,080 --> 00:55:36,600
+L of F هذا أتبعته أكبر أو يساوي M في B minus A
+
+639
+00:55:36,600 --> 00:55:40,520
+Similarly الآن بدي أشتغل على مين يا شباب بدي أشتغل
+
+640
+00:55:40,520 --> 00:55:44,460
+على الـ U عشان أسيب أجيب اللي هي أصغر أو يساوي شوف
+
+641
+00:55:44,460 --> 00:55:50,730
+كيف بدي أعملها الـ U of F إيش بيساوي؟ طبعا الـ U في
+
+642
+00:55:50,730 --> 00:55:54,250
+F إيش ماله؟ هو الـ infimum على كل ال other sums
+
+643
+00:55:54,250 --> 00:56:01,890
+إذن هيكون أصغر أو يساوي الـ U على الـ B .. الـ B A و
+
+644
+00:56:01,890 --> 00:56:06,970
+B نفس ال partition بتاخده و مين و الـ F الـ U of F هو
+
+645
+00:56:06,970 --> 00:56:12,890
+عبارة عن الـ infimum على كل ال other sums هذا الأن
+
+646
+00:56:12,890 --> 00:56:16,610
+إيش بيساوي؟ بيساوي اللي هو بس الـ sub interval
+
+647
+00:56:16,610 --> 00:56:19,290
+واحدة مين هي؟ أنا باخدها اللي بردش إن أنا بس
+
+648
+00:56:19,290 --> 00:56:22,570
+نقطتين إذا الـ sub interval واحدة اللي هي B minus
+
+649
+00:56:22,570 --> 00:56:29,250
+A بيصير عند الـ supremum لم K Capital لأ الـ F of X
+
+650
+00:56:29,250 --> 00:56:35,080
+such that X element in A و B هو مضروب في مين في طول
+
+651
+00:56:35,080 --> 00:56:38,780
+الفترة اللي هي الـ sub interval عند بي minus ايه
+
+652
+00:56:38,780 --> 00:56:44,150
+الآن و يساوي هذا الـ supremum معلقها يا شباب أكيد
+
+653
+00:56:44,150 --> 00:56:49,290
+مدامة الـ F of X أصغر أو يساوي M إذاً هيكون الـ
+
+654
+00:56:49,290 --> 00:56:53,070
+Supremum لأن هذا الـ Supremum إيش شماله؟ الـ Least
+
+655
+00:56:53,070 --> 00:56:58,550
+Upper Bound مدامة الـ M عبارة عن Upper Bound للـ F
+
+656
+00:56:58,550 --> 00:57:01,810
+of X لأنها أكبر يساوي F of X إذاً هيكون عند الـ
+
+657
+00:57:01,810 --> 00:57:05,090
+Least Upper Bound اللي هو الـ Supremum أصغر أو
+
+658
+00:57:05,090 --> 00:57:10,310
+يساوي الـ Upper Bound M في الـ B minus A إذاً صار
+
+659
+00:57:10,310 --> 00:57:15,540
+Luv F أصغر أو يساوي B M في B minus A هذا صار عندي
+
+660
+00:57:15,540 --> 00:57:19,400
+اللي هو أصغر أو يساوي الـ M في B minus A اللي هو
+
+661
+00:57:19,400 --> 00:57:23,860
+بيساوي هذا طبعا معطى بيصير أصغر أو يساوي M في B
+
+662
+00:57:23,860 --> 00:57:29,340
+minus A فبيصير فعلا ال integration تبعها بين M في B
+
+663
+00:57:29,340 --> 00:57:35,120
+minus A و بين M في B minus A capital M اللي
+
+664
+00:57:35,120 --> 00:57:39,320
+ما أوضحت لهوش هذه بنفس الطريقة اللي هنا عند الـ M صارت
+
+665
+00:57:39,320 --> 00:57:42,780
+lower bound لهذه و الـ infimum هذه عبارة عن
+
+666
+00:57:42,780 --> 00:57:45,480
+greatest lower bound مدام greatest lower bound ده
+
+667
+00:57:45,480 --> 00:57:48,180
+الأكبر أو يساوي واحد من الـ lower bound اللي هو مين
+
+668
+00:57:48,180 --> 00:57:52,720
+اللي هو الـ M ماشي الحالة و الباقي زي ما هو هيك
+
+669
+00:57:52,720 --> 00:57:56,040
+بيكون أثبتنا اللي هي الـ remark اللي عندي
+
+670
+00:58:06,640 --> 00:58:12,280
+إن ييجي إلى الـ Corollary للنظرية اللي قبل بشوية
+
+671
+00:58:12,280 --> 00:58:19,460
+برضه
+
+672
+00:58:19,460 --> 00:58:33,220
+الإثبات إن شاء الله سهل شوفوا
+
+673
+00:58:33,220 --> 00:58:38,690
+يا شباب عندي الآن الـ Corollary بتقول ما يلي F F و
+
+674
+00:58:38,690 --> 00:58:43,730
+G من I لعند R ر انتيجرابل on I فعندي F و G
+
+675
+00:58:43,730 --> 00:58:47,870
+انتيجرابل و F of X أصغر يساوي G of X لكل X element
+
+676
+00:58:47,870 --> 00:58:51,050
+on I ده ال integration من A لB للF أصغر ال
+
+677
+00:58:51,050 --> 00:58:56,890
+integration من A لB لمن لل G ماشي الحال فبيصير عندي
+
+678
+00:58:56,890 --> 00:59:03,230
+الآن ال integration أنه لو كانت الـ F of X أصغر
+
+679
+00:59:03,230 --> 00:59:08,820
+يساوي G of X on I بيعطيني ال integration للـ F على
+
+680
+00:59:08,820 --> 00:59:11,380
+الـ I اللي هو من A و لا B نظرها لتعرف ال
+
+681
+00:59:11,380 --> 00:59:21,080
+integration من A لB لمن لـ G طيب عندي F و G
+
+682
+00:59:21,080 --> 00:59:25,860
+integrable صح ولا لأ إذا أكيد زي ما حكيت في أول
+
+683
+00:59:25,860 --> 00:59:30,900
+المحاضرة حسب اللي هو إنه F integrable و G
+
+684
+00:59:30,900 --> 00:59:35,230
+integrable إذا مجموعهم انتجرابل أو حاصل طرح الـ
+
+685
+00:59:35,230 --> 00:59:38,910
+Integrable بناء على إنه K في F انتجرابل أو K في G
+
+686
+00:59:38,910 --> 00:59:41,910
+انتجرابل أو بناء على إنه بيصير ناقص G is
+
+687
+00:59:41,910 --> 00:59:46,970
+integrable بيطلع عندي الـ F ناقص G أشماله is
+
+688
+00:59:46,970 --> 00:59:55,830
+integrable مش الحال طيب و مش هيك كمان و قلنا ال
+
+689
+00:59:55,830 --> 01:00:02,270
+integration للـ F ناقص G أو الـ G - F تلزمني أنا الـ
+
+690
+01:00:02,270 --> 01:00:08,830
+G - F فهن الـ G - F is integrable مدام G - F is
+
+691
+01:00:08,830 --> 01:00:14,150
+integrable إذا الـ G - F حسب اللي .. النظرية قبل
+
+692
+01:00:14,150 --> 01:00:20,770
+بشوية الـ G minus F من هنا بصير G ناقص F of X أكبر
+
+693
+01:00:20,770 --> 01:00:24,670
+أو يساوي صفر من I إذا حيكون الـ G minus F على من A
+
+694
+01:00:24,670 --> 01:00:27,390
+ل B أكبر أو يساوي صفر حسب النظرية اللي هاد
+
+695
+01:00:27,390 --> 01:00:32,170
+الـ Corollary إلها طيب و من جهة أخرى بالنظرية اللي
+
+696
+01:00:32,170 --> 01:00:35,870
+حكيناها في الأول اللي هو مجموع دالتين أو حاصل طرحين
+
+697
+01:00:35,870 --> 01:00:42,110
+بساوي ال integration إن الـ G من A لB زائد ال
+
+698
+01:00:42,110 --> 01:00:51,410
+integration من A إلى B للـ
+
+699
+01:00:51,410 --> 01:00:58,230
+G ناقص ال integration من A إلى B للـ F اعتمدت هنا
+
+700
+01:00:58,230 --> 01:01:02,430
+في التوزيع و في إخراج النقص على الـ K F Integrable
+
+701
+01:01:02,430 --> 01:01:04,710
+و الـ K في ال integration بيساوي ال integration
+
+702
+01:01:04,710 --> 01:01:09,190
+للـ K و اللي هو اعتمادا على ال integration للـ F زي
+
+703
+01:01:09,190 --> 01:01:11,190
+الـ G بيساوي ال integration للـ F زي ال integration
+
+704
+01:01:11,190 --> 01:01:15,250
+للـ G من هنا صار عندي أنقل هذا بس على الجهة الثانية
+
+705
+01:01:15,250 --> 01:01:18,930
+بيصير ال integration للـ G من A لـ B لما انقل هذا
+
+706
+01:01:18,930 --> 01:01:23,130
+على الجهة الثانية أكبر أو يساوي ال integration للـ
+
+707
+01:01:23,130 --> 01:01:30,850
+F من A لـ B وهو المطلوب. طيب يا شباب نيجي للنظرية
+
+708
+01:01:30,850 --> 01:01:36,970
+اللي بعدها. خلونا نركز شوية لأنه البرهان يعني طويل 
+
+709
+01:01:36,970 --> 01:01:45,850
+شوية لكن إن شاء الله بتستوعبوه. نشوف إيش النظرية 
+
+710
+01:01:45,850 --> 01:01:54,690
+بتقول النظرية
+
+711
+01:01:54,690 --> 01:02:02,260
+تقول ما يلي: let I عبارة عن فترة من A لعند B، هاي 
+
+712
+01:02:02,260 --> 01:02:09,460
+الفترة اللي عندي. هاي الفترة من A لعند B، وعندي ماخد
+
+713
+01:02:09,460 --> 01:02:15,220
+أنا C نقطة في داخل الفترة A و B. طبعا النظرية
+
+714
+01:02:15,220 --> 01:02:17,900
+هتلاقوها مش غريبة عليكم. مرة تلاقوكم الكلكولات ولكن
+
+715
+01:02:17,900 --> 01:02:22,330
+البرهان اللي بده شغل. let I بيساوي من A لعند B and
+
+716
+01:02:22,330 --> 01:02:25,830
+let C be an element in A و B and let F من كل I 
+
+717
+01:02:25,830 --> 01:02:29,210
+لعند R be a bounded function. يعني ال function اللي
+
+718
+01:02:29,210 --> 01:02:32,830
+بنشتغل عليها bounded جاهزة يعني. and then النتيجة 
+
+719
+01:02:32,830 --> 01:02:36,970
+بقولي F is integrable on I. هتكون الـ F integrable 
+
+720
+01:02:36,970 --> 01:02:42,990
+على كل الفترة اللي هي I من A و B إذا و فقط إذا F
+
+721
+01:02:42,990 --> 01:02:51,480
+is integrable على مين؟ على on both I واحد من A لـ C و
+
+722
+01:02:51,480 --> 01:03:00,520
+I2 من C لعند B. ومش هيك بقولك وكمان هيكون عند الـ
+
+723
+01:03:00,520 --> 01:03:03,080
+integration من A لـ B لـ F سوى ال integration من A لـ
+
+724
+01:03:03,080 --> 01:03:05,820
+C لـ F زائد ال integration من C لـ عند B لـ F اللي هي
+
+725
+01:03:05,820 --> 01:03:09,460
+الشيء المعود عندنا. إذا الأن بقولي الإعلان اللي
+
+726
+01:03:09,460 --> 01:03:12,560
+بقوله مالي إذا كانت F is a bounded function on the
+
+727
+01:03:12,560 --> 01:03:18,080
+interval كلها I اللي سمينها من A لـ عند B، I. أه إذا 
+
+728
+01:03:18,080 --> 01:03:22,800
+كانت F is bounded function عليها إذا F is 
+
+729
+01:03:22,800 --> 01:03:32,220
+integrable on I if and only if F is integrable on
+
+730
+01:03:32,220 --> 01:03:42,140
+I1 and F is integrable on I2. وفي هذه الحالة سيكون
+
+731
+01:03:42,140 --> 01:03:46,500
+عنده ال integration من A لعند B سوى ال integration 
+
+732
+01:03:46,500 --> 01:03:52,470
+من A لـ C زائد ال integration من C لعند B. بدنا نفترض 
+
+733
+01:03:52,470 --> 01:03:58,550
+في الأول أن F is integrable على I1 و I2 ونصل أنه
+
+734
+01:03:58,550 --> 01:04:01,450
+اللي هو إيه شماله؟ اللي هو ال function is
+
+735
+01:04:01,450 --> 01:04:07,430
+integrable عالميا على كل الفترة اللي هي I. إذا الأن
+
+736
+01:04:07,430 --> 01:04:15,030
+أول حاجة بدنا نفترضها انتبهوا عندي إيش بنسوي، صبوز
+
+737
+01:04:17,840 --> 01:04:32,080
+that F is integrable on I1 and I2. ستجدون أننا
+
+738
+01:04:32,080 --> 01:04:37,580
+نعتمد كثير على الـ Integrable criterion. ستجدون كم 
+
+739
+01:04:37,580 --> 01:04:42,820
+هي مهمة في إثبات هذه النظريات. مادام F is 
+
+740
+01:04:42,820 --> 01:04:48,300
+integrable على I1 خلّينا ناخد Y أكبر من صفر 
+
+741
+01:04:48,300 --> 01:04:52,260
+arbitrary. for every Y أكبر من صفر بما أن F is 
+
+742
+01:04:52,260 --> 01:05:00,440
+integrable on I1 then there exists B1Y. هذا 
+
+743
+01:05:00,440 --> 01:05:06,260
+partition عالميا على I1 such that لأن F is 
+
+744
+01:05:06,260 --> 01:05:14,210
+integrable على I1 such that الـ UB1 و Epsilon و
+
+745
+01:05:14,210 --> 01:05:20,490
+الـ function F ناقص الـ LB1 و Epsilon و الـ
+
+746
+01:05:20,490 --> 01:05:25,250
+function F أصغر من مين؟ من Epsilon على 2 للحسابات
+
+747
+01:05:25,250 --> 01:05:30,770
+ماشي الحال. هذا
+
+748
+01:05:30,770 --> 01:05:36,590
+استخداما للـ integrability للـ function F عالمين
+
+749
+01:05:36,590 --> 01:05:44,720
+على الـ I1. Similarly, There exist B2
+
+750
+01:05:44,720 --> 01:05:48,920
+و Epsilon بما أن F Integra بالعالم I2 إذاً there 
+
+751
+01:05:48,920 --> 01:05:58,140
+exist B2 و Epsilon such that U B2 و Epsilon هذا
+
+752
+01:05:58,140 --> 01:06:02,160
+partition لمين؟ للفترة التانية I2 اللي هي من C
+
+753
+01:06:02,160 --> 01:06:10,740
+لعند B و F ناقص الـ LB2 و Epsilon و F أصغر من مين
+
+754
+01:06:10,740 --> 01:06:15,180
+يا جماعة أصغر برضه من Epsilon على اتنين. ماشي الحال
+
+755
+01:06:15,180 --> 01:06:21,100
+الآن أنا غرضي أن أثبت أن F is Integra بالعالمين
+
+756
+01:06:21,100 --> 01:06:30,050
+على كل الفترة I من A لعند مين؟ لعند B. الان let ما
+
+757
+01:06:30,050 --> 01:06:34,130
+دام بده .. بده اللي هو أثبت الـ Integrability للـ 
+
+758
+01:06:34,130 --> 01:06:38,270
+F يا شباب على كل الـ I. إذا بدي partition على كل
+
+759
+01:06:38,270 --> 01:06:43,070
+الـ I، ال partition المؤهل ليكون الـ I الـ B1 و Y
+
+760
+01:06:43,070 --> 01:06:48,530
+جزء هذه و الـ B2 و Y جزء هذه. إذا حاكيد عند let B
+
+761
+01:06:48,530 --> 01:06:55,170
+اللي هو بيساوي أو بي اللي هو .. امسميه بي إبسلون 
+
+762
+01:06:55,170 --> 01:07:04,240
+بيساوي B1 و Epsilon اتحاد B2 و Epsilon. واضحة؟
+
+763
+01:07:04,240 --> 01:07:10,000
+وهذا هيكون إشمال و partition. partition لمين؟ لكل
+
+764
+01:07:10,000 --> 01:07:17,140
+الـ I معايا يا شباب، اه؟ إذا صار عندي الآن اخترت أنا
+
+765
+01:07:17,140 --> 01:07:22,900
+الـ بي إبسلون عبارة عن B1 إبسلون اتحاد B2 
+
+766
+01:07:22,900 --> 01:07:26,760
+إبسلون وبدأ أصل للـ UB إبسلون نال أقل الـ LB
+
+767
+01:07:26,760 --> 01:07:32,300
+إبسلون أصغر من إبسلون. واضح اه؟ عشان أثبت أنه الـ
+
+768
+01:07:32,300 --> 01:07:36,180
+function F is integrable على كل الـ I. هذا إيش ماله؟
+
+769
+01:07:36,180 --> 01:07:44,020
+صار let BY بسوا كده which هذا المهم is a partition
+
+770
+01:07:44,020 --> 01:07:50,640
+of I كلها لأن الأولان جزء هذا العندلهان والتاني
+
+771
+01:07:50,640 --> 01:07:54,960
+جزء هذا العندلهان إذا إتحادا هيجزء كل المنطقة
+
+772
+01:07:54,960 --> 01:08:06,000
+المطلوبة. طيب شوف الآن احسبلي الآن U,B,Y,F-L,B,Y,F
+
+773
+01:08:06,000 --> 01:08:10,360
+ويساوي الـ
+
+774
+01:08:10,360 --> 01:08:15,700
+U,B,Y,F عبارة عن إيش يا جماعة؟ الـ U,B,Y,F خلينا 
+
+775
+01:08:15,700 --> 01:08:20,320
+نقول U,B,Y,F اللي هو عبارة عن some U بتحت عشان
+
+776
+01:08:20,320 --> 01:08:27,020
+تشوفوا إيش اللي بعمله. U,B,Y,F عبارة
+
+777
+01:08:27,020 --> 01:08:38,620
+عن summation لأ الـ MK الـ N و Xk minus Xk minus
+
+778
+01:08:38,620 --> 01:08:43,580
+واحد. K مثلا من واحد لعند مين؟ لعند N. هذه اللي
+
+779
+01:08:43,580 --> 01:08:52,700
+بتجزئلي من عند A لعند مين؟ لعند B. و أكيد هتمر في C
+
+780
+01:08:52,700 --> 01:08:58,570
+ليش؟ أكيد C هتكون نقطة من النقاط، ليش هتكون نقطة من
+
+781
+01:08:58,570 --> 01:09:03,230
+النقاط؟ لأنه أنا أخدت بي إبسلون هي اتحاد هذه مع
+
+782
+01:09:03,230 --> 01:09:08,210
+هذه. و آخر نقطة في هذه هي الـ C و أول نقطة في هذه
+
+783
+01:09:08,210 --> 01:09:11,210
+هي الـ C. كيف هذه partition لهذه و هذه partition
+
+784
+01:09:11,210 --> 01:09:14,470
+لهذه؟ مش لما نعمل partition لكل الفترة بيكون أول 
+
+785
+01:09:14,470 --> 01:09:18,390
+نقطة و أخر نقطة من ضمن ال partition؟ أكيد. و إذن الـ
+
+786
+01:09:18,390 --> 01:09:22,230
+partition للفترة الصغيرة هتكون اللي هي من عند A
+
+787
+01:09:22,230 --> 01:09:26,430
+لعند C إذا الـ C هنا و الـ C هنا. إذا مضمون الـ C
+
+788
+01:09:26,430 --> 01:09:32,570
+واحدة من هدول. ماشي الحال. إذا هذا الآن باجي الـ Mk 
+
+789
+01:09:32,570 --> 01:09:37,600
+هي عبارة عن نفترض أنه من عند X Note لعند XN وهنا
+
+790
+01:09:37,600 --> 01:09:42,040
+الـ XL اللي هي الـ C واحدة من عناصر اللي هي ال ..
+
+791
+01:09:42,040 --> 01:09:46,020
+ال .. ال .. ال partition. إذن الآن بقدر أجزء هذا
+
+792
+01:09:46,020 --> 01:09:55,690
+لجزئين. Mk في Xk minus Xk minus 1 من كام؟ من عند 1 لعند
+
+793
+01:09:55,690 --> 01:10:00,710
+اللي هي النقطة الـ K اللي خلّيني أسميها M حيث الـ
+
+794
+01:10:00,710 --> 01:10:08,330
+XM هي الـ C زائد الـ summation للـ MK الـ Xk minus
+
+795
+01:10:08,330 --> 01:10:13,110
+Xk minus 1 كام؟ من
+
+796
+01:10:13,110 --> 01:10:19,210
+عند واحد، آسف، كام؟ من عند مين؟ اللي بعدها اللي هي الـ M
+
+797
+01:10:19,210 --> 01:10:26,820
+اللي عند الـ M عند الـ N. هذه اللي هي مين؟ XM بيساوي
+
+798
+01:10:26,820 --> 01:10:32,720
+الـ C. إذا في الحالتين هنا عند هذا زائد هذا الـ
+
+799
+01:10:32,720 --> 01:10:36,520
+summation هو الـ summation هذا على ال intervals
+
+800
+01:10:36,520 --> 01:10:41,000
+بضلي أجزء أجزء لمن أصل عند هذه بكون اللي هو
+
+801
+01:10:41,000 --> 01:10:45,980
+التجزئة الأولى وبعدين التجزئة الثانية بكمل من هنا
+
+802
+01:10:45,980 --> 01:10:51,810
+و بضلي طالعة و بوجد الـ MK للنهانة و الـ MK للنهانة
+
+803
+01:10:51,810 --> 01:11:00,010
+المجموع النهانة هو عبارة عن هيعمله اللي هو الـ UB
+
+804
+01:11:00,010 --> 01:11:04,910
+إبسلون طبعا MK capital، آسف، هذه و هذا MK capital
+
+805
+01:11:04,910 --> 01:11:09,190
+لأنه بحكي عن الـ other اللي مهم الفكرة الـ UB
+
+806
+01:11:09,190 --> 01:11:16,730
+إبسلون واحد F اللي هي الـ partition الأول اللي بنيت
+
+807
+01:11:16,730 --> 01:11:21,140
+عليه مين؟ اللي هو partition بي إبسلون سميته واحد و
+
+808
+01:11:21,140 --> 01:11:28,180
+إبسلون زائد اللي هو mean المتبقي اللي هو U بي تنين
+
+809
+01:11:28,180 --> 01:11:33,400
+و إبسلون و F. هذا كله mean الـ UB إبسلون و F
+
+810
+01:11:33,400 --> 01:11:37,140
+similarly mean الآن 
+
+811
+01:11:40,410 --> 01:11:45,370
+Similarly mean الـ L of B, Epsilon و F برضه هذا 
+
+812
+01:11:45,370 --> 01:11:49,970
+بجزء المنطقة ككل وهو مبني على أساس تجزئة اللي هو
+
+813
+01:11:49,970 --> 01:11:54,450
+B1 و Epsilon اتحاد B2 و Epsilon. إذا بالظبط هذا
+
+814
+01:11:54,450 --> 01:12:04,030
+برضه بيساوي ناقص اللي هو الـ LB1 و Epsilon و F
+
+815
+01:12:04,030 --> 01:12:16,290
+زائد L الجزء الثاني B2 Epsilon و F و يساوي الان
+
+816
+01:12:16,290 --> 01:12:26,530
+هذا ناقص هذا U B1 Epsilon و F ناقص الـ LB1 Epsilon و
+
+817
+01:12:26,530 --> 01:12:34,990
+F. أخدت هذا يا جماعة مع هذا خلصنا منه زائد اللي هو
+
+818
+01:12:34,990 --> 01:12:43,780
+اللي متبقي اللي هو هذا ناقص هذا اللي هو U B2 و 
+
+819
+01:12:43,780 --> 01:12:51,520
+Epsilon و F ناقص L B2 و Epsilon و F. هذا الآن
+
+820
+01:12:51,520 --> 01:12:59,880
+هيه من فوق اللي حضرناله أصغر من Epsilon على اتنين و
+
+821
+01:12:59,880 --> 01:13:04,320
+هذا حضرناله برضه أصغر من Epsilon على اتنين. إذا صار
+
+822
+01:13:04,320 --> 01:13:10,240
+هذا الطرح بينهم أصغر من مين؟ من Epsilon. صرنا مثل تين 
+
+823
+01:13:10,240 --> 01:13:13,980
+لكل Epsilon أكبر من صفر there exist B2, there exist
+
+824
+01:13:13,980 --> 01:13:18,180
+بإبسلون such that U بإبسلون و F ناقصها L إبسلون و F
+
+825
+01:13:18,180 --> 01:13:23,180
+أصغر من مين؟ من إبسلون. إذا صارت عندي F is 
+
+826
+01:13:23,180 --> 01:13:30,890
+integrable on I اللي لجينا ال partition لها هذا
+
+827
+01:13:30,890 --> 01:13:34,470
+الجزء الأول من النظرية. الآن بدنا نثبت اللي هو
+
+828
+01:13:34,470 --> 01:13:40,710
+conversely. بدنا نفترض أنه F is integrable على كل
+
+829
+01:13:40,710 --> 01:13:46,810
+الفترة ومن ثم نثبت أنه integrable على كل
+
+830
+01:13:46,810 --> 01:13:54,570
+subinterval من التنتين اللي موجودة. إذا الآن الجزء
+
+831
+01:13:54,570 --> 01:13:57,550
+الثاني بنقول suppose
+
+832
+01:14:00,050 --> 01:14:14,710
+that F is integrable on I لها بتساوي A و B و بدنا
+
+833
+01:14:14,710 --> 01:14:20,470
+نثبت أنها integrable عالميا على الفترة الأولى A و 
+
+834
+01:14:20,470 --> 01:14:26,560
+C و الفترة الثانية C. طيب خلّينا نكمل اللي هو نقول
+
+835
+01:14:26,560 --> 01:14:27,600
+conversely.
+
+836
+01:14:34,910 --> 01:14:37,530
+مادام اللي هي F is integrable إذا بالـ Cauchy 
+
+837
+01:14:37,530 --> 01:14:41,810
+criterion لكل ي أكبر من صفر there exists B اللي هو
+
+838
+01:14:41,810 --> 01:14:44,950
+partition اللي هو مسميه B ممكن نسميه احنا بي
+
+839
+01:14:44,950 --> 01:14:48,170
+إبسلون element in B of I. هذا طبعا ال partition 
+
+840
+01:14:48,170 --> 01:14:52,570
+بيعتمد على مين؟ على إبسلون such that U, B و F ناقص
+L, B و F أصغر من مين؟ من إبسلون.
+
+841
+01:14:52,570 --> 01:14:56,370
+الـ U of F أصغر من مين من إبسلون هذا لأن F is
+
+842
+01:14:56,370 --> 01:15:00,630
+integrable اللي هي by Cauchy .. by .. by 
+
+843
+01:15:00,630 --> 01:15:06,140
+integrability criterion حصلنا على هذه الآن لمين
+
+844
+01:15:06,140 --> 01:15:11,400
+رايح بدي أثبت الـ Integrability لعالفترة A وC و
+
+845
+01:15:11,400 --> 01:15:15,040
+Integrability لفترة B وC فانا بدي في الـ partition
+
+846
+01:15:15,040 --> 01:15:22,140
+اللي أصل له بدي أصل للـ U لل partition B مثلا معينة
+
+847
+01:15:22,140 --> 01:15:30,020
+B' و F- L B' و F بدي أصل أصغر من مين أصل أصغر من
+
+848
+01:15:30,020 --> 01:15:34,080
+إبسلون وهذه تكون الـ B' partition لمين للفترة
+
+849
+01:15:34,080 --> 01:15:38,000
+الأولى فعشان تكون للفترة الأولى لازم تكون الـ C
+
+850
+01:15:38,000 --> 01:15:42,620
+موجودة فيها فبناء عليه أنا مش عارف الـ B' الـ B اللي
+
+851
+01:15:42,620 --> 01:15:46,560
+لجيت فيه الـ C ولا لأ إذا بتاخدوا بعين الاعتبار
+
+852
+01:15:46,560 --> 01:15:51,760
+عشان أصل لمين للـ B' اللي تكون فيها الـ C عشان هيك
+
+853
+01:15:51,760 --> 01:15:58,130
+أنا إيش جيت قلنا لما لجينا الـ B هذه وفقا للـ F is
+
+854
+01:15:58,130 --> 01:16:02,690
+integrable وبتحقق هذه جيت خليني وقلت خليني ناخد
+
+855
+01:16:02,690 --> 01:16:07,730
+B' إيش بتساوي يا شباب بتساوي B اتحاد الـ C يعني
+
+856
+01:16:07,730 --> 01:16:13,390
+ضفت للـ partition اللي لجيت من الـ C وهو هذا الـ
+
+857
+01:16:13,390 --> 01:16:19,070
+B' برضه هيحقق للي بدي اه اللي هو A شماله صار B'
+
+858
+01:16:19,510 --> 01:16:24,420
+refinement للـ B ما دام الـ Refinement للـ B إذا
+
+859
+01:16:24,420 --> 01:16:29,960
+UB' و F أكيد الـ Refinement هذا هيصغر عن الأصل
+
+860
+01:16:29,960 --> 01:16:36,960
+اللي هو الـ UBF بينما الـ B' of F هيكبر عن مين؟ عن
+
+861
+01:16:36,960 --> 01:16:41,980
+الأصل فلمّا أضربه في سالب هيصغر إذا حيصير عند U B'
+
+862
+01:16:42,300 --> 01:16:48,080
+F ناقص الـ B' F أصغر يساوي U B و F ناقص الـ B و F
+
+863
+01:16:48,080 --> 01:16:52,900
+وهذا أصلا أصغر من مين؟ من Epsilon إذا طلع عند ال
+
+864
+01:16:52,900 --> 01:16:58,390
+B' اللي أنا احتجته اللي في الأصل هو الـ B الأصلية
+
+865
+01:16:58,390 --> 01:17:03,550
+اللي لجيت اتحاد الـ C طلع برضه الـ U B' F ناقص
+
+866
+01:17:03,550 --> 01:17:08,590
+الـ B' F أصغر من إبسلون اللي أنا بعد شوية هحتاجه
+
+867
+01:17:08,590 --> 01:17:13,850
+في عملية إثبات أنه اللي هو الـ F is integrable على
+
+868
+01:17:13,850 --> 01:17:17,710
+الجزء الأول اللي هو I1 و F is integrable على الجزء
+
+869
+01:17:17,710 --> 01:17:22,410
+الثاني اللي هو I2 طب كيف بده يحصل هنا؟ شوف كيف بده
+
+870
+01:17:22,410 --> 01:17:28,890
+يحصل الـ Partition الأولاني B1 براين مثلا B1 براين
+
+871
+01:17:28,890 --> 01:17:33,070
+اللي بيخللي هذا أصغر من إبسلون وهذا partition
+
+872
+01:17:33,070 --> 01:17:38,670
+للجزء الأول مما يؤدي لو وجدته هذا أن الـ F is
+
+873
+01:17:38,670 --> 01:17:42,150
+integrable على الفترة الأولى و similarly حلاجة على
+
+874
+01:17:42,150 --> 01:17:47,180
+الفترة الثانية وبكون خلصت النظرية هيك نشوف كيف الآن
+
+875
+01:17:47,180 --> 01:17:52,660
+وجدنا الـ B' أو اللي هو B اتحاد الـ C يحقق هذه
+
+876
+01:17:52,660 --> 01:17:57,800
+اللي هي المعادلة أو هذه المتباينة أصغر من مين من
+
+877
+01:17:57,800 --> 01:18:02,160
+Epsilon شوف الآن كيف دي بارتشني للجزء الأول من A
+
+878
+01:18:02,160 --> 01:18:07,760
+لعين C بكل بساطة قطع للـ B' هذا مع مين؟ مع A و C
+
+879
+01:18:07,760 --> 01:18:12,580
+أكيد هذا في C أكيد وفي A إذا النقطة الأولى موجودة
+
+880
+01:18:12,580 --> 01:18:16,680
+والنقطة C موجودة إذا هو فعلا partition لمين؟ هيكون
+
+881
+01:18:16,680 --> 01:18:21,200
+B' partition للـ A والـ C وبنفس الطريقة and let B
+
+882
+01:18:21,200 --> 01:18:27,880
+T2' بيساوي B' تقاطع الـC والـB إذا الـC موجودة هنا
+
+883
+01:18:27,880 --> 01:18:32,280
+والـB موجودة هنا إذا صار هذا بحتوي الـ partition
+
+884
+01:18:32,280 --> 01:18:36,080
+على الـC وعلى الـB إذا فعلا هو partition لمين
+
+885
+01:18:36,080 --> 01:18:42,640
+للفترة الثانية is a partition of C وB so that إذا
+
+886
+01:18:42,640 --> 01:18:49,380
+الآن بحضر إن لجيت اللي هو B1' وB2' واحد partition
+
+887
+01:18:49,380 --> 01:18:54,540
+للـA والـC والتاني للـC والـB وبدّعي إن هما ال
+
+888
+01:18:54,540 --> 01:18:59,540
+partitions اللي هوصلني على هذه و similarly زيها
+
+889
+01:18:59,540 --> 01:19:03,020
+للتانية اللي بتعطيني ال integrability للـF على
+
+890
+01:19:03,020 --> 01:19:08,780
+الأولى و integrability للـF على الثانية نشوف إيش
+
+891
+01:19:08,780 --> 01:19:14,720
+اللي بيقوله يلا صلوا علينا يا شباب صلاة والسلام عندي
+
+892
+01:19:15,170 --> 01:19:20,550
+أحسبني الآن بس خليني بس عشان تكون واضحة قدامك اللي
+
+893
+01:19:20,550 --> 01:19:26,010
+هي واحد اللي بدي أستخدمها بعد شوية طيب شوفوا يا
+
+894
+01:19:26,010 --> 01:19:38,970
+جماعة أحسبني الآن U بي برايم و F اللي هو بتساوي U
+
+895
+01:19:38,970 --> 01:19:44,740
+بي برايم واحد و F زي U بي اتنين برايم و F اللي قبل
+
+896
+01:19:44,740 --> 01:19:48,660
+بشوية عملناها هو الـ partition هذا بي برايم هو
+
+897
+01:19:48,660 --> 01:19:55,790
+عبارة عن اتحاد هذا اتحاد هذا ماشي الحال ماشي الآن و
+
+898
+01:19:55,790 --> 01:19:59,610
+نفس الشيء عملتها قبل هيك الـ b prime of f سواء الـ b
+
+899
+01:19:59,610 --> 01:20:03,470
+prime واحد أو الـ b2 prime حيث بي اتنين برايم بي
+
+900
+01:20:03,470 --> 01:20:08,050
+واحد برايم بيساوي اتحاد هنا شماله هو بي برايم إذا
+
+901
+01:20:08,050 --> 01:20:12,370
+زي ما عملنا قبل بشوية هذه اللي هي ال equality
+
+902
+01:20:12,370 --> 01:20:17,190
+الثانية الآن من واحد ومن اتنين بدي أصل للي بدي اه
+
+903
+01:20:17,190 --> 01:20:25,950
+إيش اللي بدي اه احسب لي الآن UB1' F زي UB2' F ناقص ال
+
+904
+01:20:25,950 --> 01:20:34,350
+B1' F زي ال B2' of F اللي هو من وين هذا جبت اللي
+
+905
+01:20:34,350 --> 01:20:41,050
+هو عند هي من واحد هي هذه اتقوط عنها بالقيمة هذه من
+
+906
+01:20:41,050 --> 01:20:47,720
+وين هذه من الآن من هنا شيلت اللي هو .. هاي من هذول
+
+907
+01:20:47,720 --> 01:20:50,780
+يا جماعة من اللي حاطط عليهم أحمر أنا ثلاثة ..
+
+908
+01:20:50,780 --> 01:20:56,140
+التنتين هذول عند شيلت هذول .. هذه وحطيت هذه
+
+909
+01:20:56,140 --> 01:21:04,180
+مكانها طلعت هذه .. هيها .. رايحة؟ وشيلت هذه وحطيت هذه 
+
+910
+01:21:04,180 --> 01:21:05,500
+مكانها
+
+911
+01:21:08,330 --> 01:21:13,550
+صارت هذه مكانها إذا هذه ناقص هذه اللي هي هذه ناقص
+
+912
+01:21:13,550 --> 01:21:17,290
+هذه اللي كانت أصغر من إبسلون هتصير أصغر من إبسلون
+
+913
+01:21:17,290 --> 01:21:24,150
+إذا صار عندي هذا اللي هو الـ U أوضح لكي أنا U بواحد
+
+914
+01:21:24,150 --> 01:21:36,350
+برايم و F زائد U بيتنين برايم و F ناقص الـ of بواحد
+
+915
+01:21:36,350 --> 01:21:46,170
+برايم و F زائد الـ B2 prime و F هذا كله أصغر من
+
+916
+01:21:46,170 --> 01:21:50,810
+إبسلون لأن هذا أصلا كله .. ليش هذا صح؟ لأن هذا
+
+917
+01:21:50,810 --> 01:22:00,330
+أصلا هو عبارة عن U B prime و F وهذا الـ B prime و
+
+918
+01:22:00,330 --> 01:22:06,440
+F اللي هو في الأصل هذا من عندي من هنا أصغر من إيش
+
+919
+01:22:06,440 --> 01:22:09,860
+من إبسلون إذاً هذا صار أصغر من إبسلون خلّي هذا
+
+920
+01:22:09,860 --> 01:22:13,160
+الكلام في الذاكرة أصغر من إبسلون لأنه هيفيدني بعد
+
+921
+01:22:13,160 --> 01:22:19,900
+بشوية شوف الآن فوزع خلّيني بس أمسح اللي على اللوح
+
+922
+01:22:19,900 --> 01:22:29,960
+ووزع الآن عندي هذا بيصير إيش هو هذا بيصير U ب U
+
+923
+01:22:31,310 --> 01:22:36,370
+ب1 برايم و F ناقص
+
+924
+01:22:36,370 --> 01:22:47,190
+الـ ب واحد برايم و F كل هذا مع بعضه زائد U ب اتنين
+
+925
+01:22:47,190 --> 01:22:55,930
+برايم و F ناقص الـ ب اتنين برايم و F هذا كله أصغر
+
+926
+01:22:55,930 --> 01:23:01,160
+من مين يا جماعة من إبسلون هذول الكميتين هذه زائد
+
+927
+01:23:01,160 --> 01:23:06,080
+هذه أصغر من إبسلون وهذه موجبة وهذه موجبة إذا
+
+928
+01:23:06,080 --> 01:23:12,140
+الكمية هذه أكيد لحالها أصغر من إبسلون والكمية هذه
+
+929
+01:23:12,140 --> 01:23:17,900
+لحالها إيش أصغر من إبسلون هذه أصغر من إبسلون تعني
+
+930
+01:23:17,900 --> 01:23:22,520
+أن لكل إبسلون لجينا partition بي واحد برايم بحيث
+
+931
+01:23:22,520 --> 01:23:26,620
+أن هذا ناقص هذا أصغر من إبسلون يعني F is
+
+932
+01:23:26,620 --> 01:23:38,540
+integrable on I واحد اللي هي من A لـ C لجينا
+
+933
+01:23:38,540 --> 01:23:45,180
+partition B2' بحيث أنه هذا ناقص B2' لمين لـ I2 هيكون
+
+934
+01:23:45,180 --> 01:23:49,500
+هذا ناقص هذا أصغر من إبسلون وهذا يعني أن F is
+
+935
+01:23:49,500 --> 01:24:00,780
+integrable on I2 كده نكون هي كإحنا وصلنا للي
+
+936
+01:24:00,780 --> 01:24:08,840
+بدي من ناحية إثبات أن F is integrable on I if and
+
+937
+01:24:08,840 --> 01:24:15,760
+only if F is integrable on I واحد and on I اتنين
+
+938
+01:24:15,760 --> 01:24:23,380
+دل على الجزء الأخير اللي أثبته أن عندي اللي هو الـ
+
+939
+01:24:23,380 --> 01:24:28,900
+integration من A إلى B أصغر أو يساوي بالبساوي ال
+
+940
+01:24:28,900 --> 01:24:32,780
+integration من A إلى C زائد ال integration من C
+
+941
+01:24:32,780 --> 01:24:39,840
+لعند B ركزوا معايا عشان نختصر الوقت شبيه باللي
+
+942
+01:24:39,840 --> 01:24:42,780
+شرحته قبل بشوية في النظرية اللي قبلها ال
+
+943
+01:24:42,780 --> 01:24:45,860
+integration من A لـ B للـ F مدام إن F is Integra
+
+944
+01:24:45,860 --> 01:24:50,400
+بالفرض إحنا إذا هذا بيساوي عبارة عن الـ U of F و
+
+945
+01:24:50,400 --> 01:24:53,600
+الـ U of F أكيد اللي هي M في مملة كل هذول إذا أظهر
+
+946
+01:24:53,600 --> 01:24:58,320
+يساوي U B prime و F B prime partition من A لعند مين
+
+947
+01:24:58,320 --> 01:25:03,280
+لعند B وهذا قبل بشوية إيش قلنا عنه بيساوي UB1 of F
+
+948
+01:25:03,280 --> 01:25:10,760
+زائد UB2 of F هذا أكيد أصغر يساوي الأل تبعه وهذا
+
+949
+01:25:10,760 --> 01:25:16,420
+أكيد أصغر يساوي الأل اللي إله زائد 2 إبسلون من وين
+
+950
+01:25:16,420 --> 01:25:22,960
+جبته هذا قلنا بما أن F is integrable إذا U ناقص
+
+951
+01:25:22,960 --> 01:25:29,840
+هذا أصغر من إبسلون و U ناقص هذا أصغر من إبسلون إذا
+
+952
+01:25:29,840 --> 01:25:34,220
+صار عندي U زائد هذا أصغر من هذا زائد هذا زائد مين
+
+953
+01:25:34,220 --> 01:25:38,620
+2 إبسلون من وين جبت هذا يا جماعة من اللي هي
+
+954
+01:25:38,620 --> 01:25:45,660
+الـ integrability criterion for مين for F on the
+
+955
+01:25:45,660 --> 01:25:50,520
+interval I واحد حيكون الـ U بواحد برايم و F ناقص الـ
+
+956
+01:25:50,520 --> 01:25:54,400
+بواحد برايم و F أصغر من إبسلون أو بمعنى آخر الـ U
+
+957
+01:25:54,400 --> 01:25:55,580
+بواحد
+
+958
+01:25:57,750 --> 01:26:03,830
+أصغر من L بي واحد إبراهيم و F زائد إبسلون هذا جبته
+
+959
+01:26:03,830 --> 01:26:09,610
+من سببه أن الـ F is integrable on I واحد كلها
+
+960
+01:26:09,610 --> 01:26:15,580
+Similarly since F is integrable on I واحد كلها I2
+
+961
+01:26:15,580 --> 01:26:19,360
+كلها إذا بيلاقي بي اتنين برايم بحيث إن U بي اتنين
+
+962
+01:26:19,360 --> 01:26:23,940
+برايم و F أصغر من L بي اتنين برايم و F زائد إبسلون
+
+963
+01:26:23,940 --> 01:26:30,900
+مع بعض صار هذا زائد هذا زائد إيش 2 إبسلون بنفس
+
+964
+01:26:30,900 --> 01:26:34,380
+الطريقة اللي حكيتها قبل بشوية F is Integrable وهذا
+
+965
+01:26:34,380 --> 01:26:36,960
+أقله في F فالأقل في F هو ال supremum لها دول إذا
+
+966
+01:26:36,960 --> 01:26:40,500
+هذا أكبر وشوية هذا وهذا أكبر وشوية هذا إذا صار
+
+967
+01:26:40,500 --> 01:26:45,060
+عندي هذا المقدار أكبر أصغر وشوية هذا زائد هذا زائد
+
+968
+01:26:45,060 --> 01:26:49,270
+إيه شماله 2 إبسلون وزي ما حكينا قبل بشوية since
+
+969
+01:26:49,270 --> 01:26:53,290
+إبسلون was arbitrary وبنفس التوضيح الأولاني بطلع
+
+970
+01:26:53,290 --> 01:26:55,470
+عند ال integration من LB لـ LF آخر شهر ال
+
+971
+01:26:55,470 --> 01:26:59,110
+integration للأول زائد ال integration للتاني بدون
+
+972
+01:26:59,110 --> 01:27:03,250
+الإبسلون وقلنا ليش هذا الكلام صحيح الآن الاتجاه
+
+973
+01:27:03,250 --> 01:27:06,230
+الثاني similarly برضه هتلاقي اللي هو البرهان
+
+974
+01:27:06,230 --> 01:27:12,370
+متشابه الآن بنفس المنطق وبنفس الطريقة و similarly
+
+975
+01:27:19,820 --> 01:27:22,620
+طبعا عارفين إيه رايح أنا؟ أنا راح أثبت إن هذا
+
+976
+01:27:22,620 --> 01:27:25,540
+المقدار أصغر أو يساوي هذا المقدار عند ال
+
+977
+01:27:25,540 --> 01:27:28,700
+integration هذا زائد ال integration هذا F is
+
+978
+01:27:28,700 --> 01:27:33,240
+integrable إذا هي بساوي الـ U الـ U of F الـ U of F
+
+979
+01:27:33,240 --> 01:27:36,860
+هي ال infimum إذا أكيد أصغر أو يساوي الـ U واحدة
+
+980
+01:27:36,860 --> 01:27:40,580
+منهم وهذه برضه الـ U of F على الفترة هذه برضه أصغر
+
+981
+01:27:40,580 --> 01:27:43,280
+أو  ساويّة واحدة منها إذا أصغر أو ساويّة الـ U هذه
+
+982
+01:27:43,280 --> 01:27:47,820
+زائد الـ U هذه في مقابله قبل قليل أثبتنا أنه .. قلنا
+
+983
+01:27:47,820 --> 01:27:51,440
+أنه مدام تفز integrable إذا بالـ .. integrability
+
+984
+01:27:51,440 --> 01:27:55,980
+criterion الفرق بين هذه وهذه أصغر من إبسلون إذا
+
+985
+01:27:55,980 --> 01:28:00,260
+صار هذه أصغر من هذه زائد إبسلون وهذه نفس الشيء
+
+986
+01:28:00,260 --> 01:28:03,740
+للأفز integrable على الفترة التانية نفس اللي قلته
+
+987
+01:28:03,740 --> 01:28:07,760
+أصغر من هذه زائد إبسلون إذا صار المقدار هذا كله
+
+988
+01:28:07,760 --> 01:28:10,560
+على بعضه أصغر من هذه زائد هذه زائد اثنين إبسلون
+
+989
+01:28:10,560 --> 01:28:17,430
+لكن هذولا الثنتين اللي هنابساوين اللي هو LB'F في
+
+990
+01:28:17,430 --> 01:28:22,530
+هنا إيش مالها مساواة بساوين هذا المقدار لأن الـ LB
+
+991
+01:28:22,530 --> 01:28:26,450
+'F إيش مالها عبارة عن هذه اتحاد هذه عملناها قبل 
+
+992
+01:28:26,450 --> 01:28:31,150
+شويّة و هذا المقدار عندي اللي هو أصغر أو ساوي هذا
+
+993
+01:28:31,150 --> 01:28:36,290
+لأن هذا عبارة عن LF و LF على هذه الفترة اللي هو 
+
+994
+01:28:36,290 --> 01:28:39,210
+عبارة عن الـ supreme أو أكبر أو ساوي هذه إذا صار
+
+995
+01:28:39,210 --> 01:28:43,120
+فيه عندي هذا المقدار أصغر أو يساوي الـ integration
+
+996
+01:28:43,120 --> 01:28:47,360
+زائد اثنين إبسلون إذا حصلنا على هذا المقدار أكبر أو
+
+997
+01:28:47,360 --> 01:28:50,800
+يساوي هذا for every إبسلون بنفس المنطق since
+
+998
+01:28:50,800 --> 01:28:54,160
+إبسلون was arbitrary إذا الـ integration هذا زائد
+
+999
+01:28:54,160 --> 01:28:58,460
+الـ integration هذا أصغر أو يساوي من هذه ومن اللي
+
+1000
+01:28:58,460 --> 01:29:03,660
+جابلها هذه بيطلع عندي المساواة وهو المطلوب وهيك
+
+1001
+01:29:03,660 --> 01:29:09,860
+بنكون احنا برهنا هذه النظرية أيضا بشكل كامل في
+
+1002
+01:29:09,860 --> 01:29:17,330
+ملاحظة أخيرة على النظرية النظرية بتقول إنه عندي لو
+
+1003
+01:29:17,330 --> 01:29:21,990
+كانت c1 أصغر من c2 أصغر من cn حيث و c1 و c2 و cn 
+
+1004
+01:29:21,990 --> 01:29:26,050
+في الفترة a و b اللي هو هيكون اللي هو بنقدر اللي
+
+1005
+01:29:26,050 --> 01:29:32,470
+هي نطبق النظرية هذه عدة مرات فعندي هي a و هي b و
+
+1006
+01:29:32,470 --> 01:29:38,320
+هي c1 هذه C2 وهذه C3 لعند Cn مثلا بيصير أو خلّيني
+
+1007
+01:29:38,320 --> 01:29:41,720
+أقول C1 من هنا وهنا Cn من هنا بيصير الـ integration
+
+1008
+01:29:41,720 --> 01:29:46,500
+من A لـ B بيساوي الـ integration من A لـ C1 زيادة الـ
+
+1009
+01:29:46,500 --> 01:29:49,520
+integration من C1 لـ C2 زيادة المقصر اللي عند أخر
+
+1010
+01:29:49,520 --> 01:29:55,980
+واحدة الـ integration من Cn لعند B للـ function وهذه
+
+1011
+01:29:55,980 --> 01:30:04,230
+اللي هو الملاحظة معهودة الآن في عندي اللي هي
+
+1012
+01:30:04,230 --> 01:30:08,930
+النظرية اللي .. ال .. ال .. ال .. المشهورة اللي هي 
+
+1013
+01:30:08,930 --> 01:30:16,510
+composition theorem إن لو كان عندي F is a function
+
+1014
+01:30:16,510 --> 01:30:24,630
+من I لعند R وفي function من اللي هو domain الـ I من
+
+1015
+01:30:24,630 --> 01:30:28,690
+range الـ I .. الـ F كاسف لعند الـ .. لعند الـ R
+
+1016
+01:30:32,310 --> 01:30:36,870
+و كانت had integrable و كانت had integrable هل الـ
+
+1017
+01:30:36,870 --> 01:30:40,430
+composition بينهم integrable طبعا هذا الكلام need
+
+1018
+01:30:40,430 --> 01:30:44,570
+not to be true in general هنشوف مثال بعد شويّة لكن 
+
+1019
+01:30:44,570 --> 01:30:48,790
+لو كانت الـ Phi continuous يعني قوّينا الشرط الآن 
+
+1020
+01:30:48,790 --> 01:30:54,290
+شويّة هيصير عندي الـ Phi composite ف F is integrable
+
+1021
+01:30:54,290 --> 01:30:58,410
+يعني بمعنى آخر لو كانت F is integrable الـ Phi is
+
+1022
+01:30:58,410 --> 01:31:01,510
+continuous حيكون الـ Phi composition أفضل لما يكون
+
+1023
+01:31:01,510 --> 01:31:05,730
+الـ composition معرف عبارة عن integrable function
+
+1024
+01:31:05,730 --> 01:31:13,350
+و احنا إن شاء الله المرة القادمة بنكمل وإلى لقاء 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0ba49f1ffa886bad41cc2b88ef525e94baba3aaa
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/POarYOfvYB0_postprocess.srt
@@ -0,0 +1,1572 @@
+1
+00:00:04,890 --> 00:00:08,570
+بسم الله الرحمن الرحيم الان نتحدث عن الجزء الثاني
+
+2
+00:00:08,570 --> 00:00:14,690
+من المحاضرة الخامسة لطلبة قسم رياضيات في كلية
+
+3
+00:00:14,690 --> 00:00:18,850
+العلوم بالجامعة الإسلامية بغزا الجزء الثاني طبعا
+
+4
+00:00:18,850 --> 00:00:22,050
+زي ما وعدناكم في البداية قلنا اللي هو هنكمل فيه
+
+5
+00:00:22,050 --> 00:00:25,970
+اللي هو 6 اتنين اللي هي تطبيقات على ال mean value
+
+6
+00:00:25,970 --> 00:00:28,490
+theorem او applications on mean value theorem
+
+7
+00:00:28,490 --> 00:00:32,390
+هيكون في عندنا two applicationsاللي هو الـ
+
+8
+00:00:32,390 --> 00:00:34,790
+Application الأول على الـ Mean Value Theorem هو
+
+9
+00:00:34,790 --> 00:00:38,290
+عبارة عن اللي هو Bernoulli's Inquality، هنبرهن
+
+10
+00:00:38,290 --> 00:00:42,150
+Bernoulli's Inquality، و بعدين هنتحدث عن اللي هو
+
+11
+00:00:42,150 --> 00:00:47,370
+Daraboux's Theorem، تشوف كيف اللي هو بيصير الأمور،
+
+12
+00:00:47,370 --> 00:00:51,960
+نبدأ الآن في الجزء الأول، اللي هوعبارة عن
+
+13
+00:00:51,960 --> 00:00:55,840
+Bernoulli Inquality Bernoulli's Inquality اللي هي
+
+14
+00:00:55,840 --> 00:00:58,700
+بتقولنا لو كانت عندي Alpha عبارة عن real number
+
+15
+00:00:58,700 --> 00:01:02,500
+أكبر من واحد هيكون عندي الواحد زايد X to the Alpha
+
+16
+00:01:02,500 --> 00:01:06,900
+أكبر يساوي واحد زايد Alpha X لكل X أكبر من مين من
+
+17
+00:01:06,900 --> 00:01:10,780
+ناقص واحد with equality if and only if عند X مين
+
+18
+00:01:10,780 --> 00:01:15,140
+عند X بالساوية سفر عندنا ال equality عند X أيش
+
+19
+00:01:15,140 --> 00:01:20,390
+بتساوي بتساوي سفر شوفزي ما عملنا المرة الماضية
+
+20
+00:01:20,390 --> 00:01:26,070
+اللي هو E to the X اللي هي لما أخدناها وثبتنا إنها
+
+21
+00:01:26,070 --> 00:01:29,550
+أكبر أو يساوي اللي هي الواحد زائد Alpha X
+
+22
+00:01:29,550 --> 00:01:33,990
+والمساوية F and W الساوية اللي هو واحد الان see
+
+23
+00:01:33,990 --> 00:01:42,510
+Bernoulli's inequality Bernoulli's inequality اللي
+
+24
+00:01:42,510 --> 00:01:50,040
+هي كما يعني عندى خد Alpha أكبر من واحدف ألف أكبر
+
+25
+00:01:50,040 --> 00:01:55,740
+من واحد then لو واحد زائد X to the ألف أكبر يساوي
+
+26
+00:01:55,740 --> 00:02:01,460
+واحد زائد Alpha X لكل X أكبر من ناقص واحد والشغل
+
+27
+00:02:01,460 --> 00:02:05,980
+التاني ان ال equality ال equality بتحدث if and
+
+28
+00:02:05,980 --> 00:02:13,300
+only if X بتساوي سفر طبعا الان لو X بتساوي سفر
+
+29
+00:02:13,300 --> 00:02:19,180
+automatic automatic بيصير عندى واحد بساوي واحدA لو
+
+30
+00:02:19,180 --> 00:02:22,920
+X بتساوي صفر Conversely هيطلع من خلال البروحان
+
+31
+00:02:22,920 --> 00:02:27,520
+باقي البروحان تنشوف كيف plan approved صلوا على
+
+32
+00:02:27,520 --> 00:02:32,280
+النبي عليه الصلاة والسلام نسجلها الأولى if X
+
+33
+00:02:32,280 --> 00:02:38,780
+بتساوي صفر it is clearthat واحد زياد اكس تقريبا
+
+34
+00:02:38,780 --> 00:02:43,760
+ألفة اللي هي بتساوي واحد بتساوي واحد زياد ألف اكس
+
+35
+00:02:43,760 --> 00:02:50,320
+هذه ده case اكس ايش بتساوي بتساوي سفر طيب الان بدأ
+
+36
+00:02:50,320 --> 00:02:55,230
+اثبت ال inequality هذههأثبتلك في الواقع اللي هو
+
+37
+00:02:55,230 --> 00:02:58,470
+strict inequality أكبر strictly من واحد زاد Alpha
+
+38
+00:02:58,470 --> 00:03:03,190
+X لكل X أكبر من ناقص واحد ولا تساوي سفر في هذه
+
+39
+00:03:03,190 --> 00:03:06,930
+الحالة بيكون A شمالنا أثبتنا لاتجاه الثاني طيب،
+
+40
+00:03:06,930 --> 00:03:14,900
+بتنشوف كيف، الآن خد X for X أكبر من سفرالان احنا
+
+41
+00:03:14,900 --> 00:03:17,460
+بنحكي عن تطبيقات للـ Mean Value Theorem اذا انا
+
+42
+00:03:17,460 --> 00:03:20,260
+متوقع ان انا اطبقها الـ Mean Value Theorem طبعا
+
+43
+00:03:20,260 --> 00:03:24,480
+لاحظ ان الـ 1 زاد X to the Alpha هذه اللي هي
+
+44
+00:03:24,480 --> 00:03:27,640
+الدالة اللي بدي استخدمها اللي بتطبق عليها الـ Mean
+
+45
+00:03:27,640 --> 00:03:31,060
+Value Theorem وهذه اصلا is differentiable
+
+46
+00:03:31,060 --> 00:03:36,360
+everywhere it is defined قابلة الاشتقاق لكل X أكبر
+
+47
+00:03:36,360 --> 00:03:41,560
+مناقص واحد و لكل Alpha أكبر من 100 من 1ماشي الحالة
+
+48
+00:03:41,560 --> 00:03:50,160
+إذا الأن for x أكبر من سفر we apply the mean value
+
+49
+00:03:50,160 --> 00:03:57,400
+theorem on .. مين هو؟ on f of x بسوا 1 زاد x to
+
+50
+00:03:57,400 --> 00:04:03,340
+the alpha ع ال interval .. on the interval مين هي
+
+51
+00:04:03,340 --> 00:04:07,920
+بنتوقع؟ اللي هي سفرو X زي ما عملنا المرة الماضية
+
+52
+00:04:07,920 --> 00:04:12,380
+لأننا مهتم بمين بالمنطقة 0 و X على أساس أن نحصل
+
+53
+00:04:12,380 --> 00:04:18,260
+على هذه ال inequality زي ما هنشوف كيف واضح أه؟ إيش
+
+54
+00:04:18,260 --> 00:04:20,400
+ال mean value of a theorem بتقول إذا كانت F
+
+55
+00:04:20,400 --> 00:04:23,820
+continuous على هذه و differentiable على ال open و
+
+56
+00:04:23,820 --> 00:04:30,940
+هذا كله متحقق إذا then there exists C element in 0
+
+57
+00:04:30,940 --> 00:04:41,560
+X such that اللي هوF prime of C بساوي اللي هو F of
+
+58
+00:04:41,560 --> 00:04:47,840
+X ناقص F of Zero على X minus Zero اللي مضربة وين
+
+59
+00:04:47,840 --> 00:04:53,820
+وكأنه في X على X minus Zero يعني وكأنه هدهش مضربة
+
+60
+00:04:53,820 --> 00:05:00,260
+في X واضح أه؟الان ال F prime للدالة هذه اللي
+
+61
+00:05:00,260 --> 00:05:03,680
+أخدتها ال F prime إلها أكيد كلكم بعرفى كام إلها
+
+62
+00:05:03,680 --> 00:05:08,800
+على جهة ال F prime بتحسبها عند مين عند C فبصير X
+
+63
+00:05:08,800 --> 00:05:15,780
+في ال F prime إلها Alpha في واحد زايد X أس Alpha
+
+64
+00:05:15,780 --> 00:05:20,440
+ناقص واحد لكن بتحسبها عند مين عند C إذا هذه بتكون
+
+65
+00:05:20,440 --> 00:05:27,340
+C بساوياللي هو f of x قداش اللي هي واحد زائد x to
+
+66
+00:05:27,340 --> 00:05:30,700
+the alpha وهي اللي بديها انا f of zero ايش بتساوي
+
+67
+00:05:30,700 --> 00:05:36,400
+f of zero بتساوي واحد ناقص واحد اللي صار عندي اذا
+
+68
+00:05:36,400 --> 00:05:44,260
+اللي هو واحد زائد x to the alpha بتساوي واحد زائد
+
+69
+00:05:44,260 --> 00:05:51,850
+x في alpha في واحد زائد c أس alpha ناقص واحدمعايا
+
+70
+00:05:51,850 --> 00:06:00,130
+يا شباب هذي سميها واحد واضح
+
+71
+00:06:00,130 --> 00:06:06,770
+اه؟ الان عندى ال alpha أكبر من مين؟ من واحد لأن
+
+72
+00:06:06,770 --> 00:06:12,590
+but alpha ناقص واحد أكبر من مين؟ من سفر لأن ال
+
+73
+00:06:12,590 --> 00:06:19,130
+alpha أكبر من واحدوعندي هذه الـ C أشمالها بين الـ
+
+74
+00:06:19,130 --> 00:06:26,650
+0 والـ X يعني أكبر من 0 and C أكبر من 0 إذا صار
+
+75
+00:06:26,650 --> 00:06:37,420
+عند المقدار هذا 1 زائد C نفسه أكبر من 1ولمّا ترفعه
+
+76
+00:06:37,420 --> 00:06:43,080
+لأس موجب، هيظل أكبر من مين؟ و strictly أكبر من
+
+77
+00:06:43,080 --> 00:06:47,660
+واحد، والمساواة بس عند مين، عند الـC بالساوية سفر،
+
+78
+00:06:47,660 --> 00:06:53,730
+واضح أه؟ طيبالأن صار هذا المقدار أكبر من واحد إذا
+
+79
+00:06:53,730 --> 00:07:00,250
+عندي X موجبة و Alpha موجبة مظبوط ولا لأ لأن X هي
+
+80
+00:07:00,250 --> 00:07:05,790
+أكبر من 0 و Alpha أكبر من 1 إذا أضرب الجهتين في
+
+81
+00:07:05,790 --> 00:07:13,510
+Alpha في X بيصير عندي Alpha في X and so Alpha في X
+
+82
+00:07:13,510 --> 00:07:22,710
+بالضرر أكبر من مين Alpha Xفى الـ 1 زي الـ c plus
+
+83
+00:07:22,710 --> 00:07:27,110
+alpha minus 1 بيبقى أكبر من 100 من alpha في x
+
+84
+00:07:27,110 --> 00:07:30,670
+واضحش اللي سويته ضربت alpha x في الجهتين و ال
+
+85
+00:07:30,670 --> 00:07:33,890
+alpha x موجبة ضلت ال inequality زي ما هي طبعا لا
+
+86
+00:07:33,890 --> 00:07:39,370
+تساوي الصفة بالألف ولا ال X إذا من 1 و من 2 we
+
+87
+00:07:39,370 --> 00:07:44,530
+have done from 1
+
+88
+00:07:44,530 --> 00:07:51,270
+and 2من واحد عند اتنين بيطلع عندى اللى هو واحد
+
+89
+00:07:51,270 --> 00:07:57,130
+زياد اكس طول الف اللى هو بساوى المقدار هذا اللى
+
+90
+00:07:57,130 --> 00:08:02,070
+هذا الجزء منه اثبتنا انه اكبر من مين من الف في اكس
+
+91
+00:08:02,070 --> 00:08:13,800
+لذا صار هذا اكبر من واحد زياد الف اكس اي سؤالإذا
+
+92
+00:08:13,800 --> 00:08:18,120
+في حالة ال X أكبر من 0 وجدنا ال 1 زاد X أو أكبر من
+
+93
+00:08:18,120 --> 00:08:25,580
+1 زاد الف X لأن هنعمل نفس الاشي بس في الحالة مين؟
+
+94
+00:08:25,580 --> 00:08:32,400
+في حالة ال X أصغر من 0 وطبعا أكبر من مين؟ من سالب
+
+95
+00:08:32,400 --> 00:08:37,860
+1 إذا بدي أخد ال X أكبر من 0 و أكبر من نقص 1 وأصغر
+
+96
+00:08:37,860 --> 00:08:42,250
+من مين؟ من 0لاحظ لما تكون X أكبر من ناقص واحد أصغر
+
+97
+00:08:42,250 --> 00:08:46,110
+من صفر برضه نطبق الـ mean value theorem على هذه
+
+98
+00:08:46,110 --> 00:08:53,450
+نفس الدالة الان on the interval mean الان X و صفر
+
+99
+00:08:53,450 --> 00:08:57,850
+لأن X هي مالها الصغيرة على ال interval X و صفر لأن
+
+100
+00:08:57,850 --> 00:09:03,110
+X سالبة طيب إذا برضه there exists C element ال
+
+101
+00:09:03,110 --> 00:09:11,000
+mean in X و Zero is نفس البرهان such that Xف F
+
+102
+00:09:11,000 --> 00:09:15,000
+prime of C بيسوي F of X ناقص F of Zero نفس الحاجة
+
+103
+00:09:15,000 --> 00:09:19,140
+بيصير ال X في Alpha في هذا المقدار و هذا المقدار
+
+104
+00:09:19,140 --> 00:09:23,160
+ماتغيرش ولا شيء بيصير واحد زاد X و ده Alpha بيسوي
+
+105
+00:09:23,160 --> 00:09:26,360
+واحد زاد X في Alpha في واحد زاد C أُس Alpha ناقص
+
+106
+00:09:26,360 --> 00:09:31,560
+واحد الآن بيجي الأسباب هنا ال Alpha ناقص واحد
+
+107
+00:09:31,560 --> 00:09:36,840
+أشمله أكبر من سفر زي ما هو لكن ال C الآن اللي
+
+108
+00:09:36,840 --> 00:09:41,110
+لاجيناها وين موجودةفي المنطقة السالبة ده الـ C إيش
+
+109
+00:09:41,110 --> 00:09:47,830
+هتصير معاينتوش يا بابا هتصير الـ C أصغر من مين من
+
+110
+00:09:47,830 --> 00:09:53,990
+صفر سالبة مدام الـ C سالبة إذا واحد زائد C هتصير
+
+111
+00:09:53,990 --> 00:10:01,310
+أصغر من مين من واحد واحد زائد C أصغر من واحد واضح
+
+112
+00:10:01,310 --> 00:10:09,690
+طيب مدام واحد زائد C أصغر من واحد هيكون عندىand so
+
+113
+00:10:09,690 --> 00:10:19,130
+أضرب الجهتين الآن في اللي هي Alpha Alpha Alpha
+
+114
+00:10:19,130 --> 00:10:22,410
+بتظل زي ما هي لما نضرب في Alpha لأن Alpha إيه
+
+115
+00:10:22,410 --> 00:10:26,370
+معناها موجة ده لو ضربت في Alpha هنا و Alpha هنا
+
+116
+00:10:26,370 --> 00:10:31,600
+بتظل زي ما هيلأن بدنا نضرب في مين؟ في X و X
+
+117
+00:10:31,600 --> 00:10:37,740
+أشمالها سالبة فهتنجلي بالإشارة كمان مرة بيصير and
+
+118
+00:10:37,740 --> 00:10:44,220
+so X في Alpha في واحد زائد C أس Alpha ناقص واحد
+
+119
+00:10:44,220 --> 00:10:51,150
+هتصير أكبر من Alpha في X لأن X سالبةإذا صار عندى
+
+120
+00:10:51,150 --> 00:10:56,590
+هذا المقدار أكبر من هذا لأن من واحد ومن اتنين زى
+
+121
+00:10:56,590 --> 00:11:00,650
+ما عملنا قبل بشوية بتصير المقدار هذا اللى هو أكبر
+
+122
+00:11:00,650 --> 00:11:04,750
+من واحد زايد Alpha X strictly لاحظوا أنه في
+
+123
+00:11:04,750 --> 00:11:11,630
+الجهتين سواء X أكبر من سفر أو أصغر من سفر لجينا أن
+
+124
+00:11:11,630 --> 00:11:16,350
+ال inequality هذه متحقق أو strictly متحقق
+
+125
+00:11:19,030 --> 00:11:25,190
+الان المساوى وين صارت؟ عند السفر فالان عشان ناخد
+
+126
+00:11:25,190 --> 00:11:29,090
+بعين الاعتبار الحالة اللي هي x أكبر من ناقص واحد و
+
+127
+00:11:29,090 --> 00:11:33,430
+أصغر من سفر و حالة x أكبر من سفر و حالة x بتساوي
+
+128
+00:11:33,430 --> 00:11:38,870
+سفر بيصير هذا المقدار أكبر أو يساوي لكل x لكل x
+
+129
+00:11:38,870 --> 00:11:43,760
+ماله أكبر من ناقص واحدلأن الاتجاه الثاني من هذا
+
+130
+00:11:43,760 --> 00:11:48,880
+أثبتناه في الواقع إيش هو إنه لو كان فيه equality X
+
+131
+00:11:48,880 --> 00:11:54,280
+بتساوي 0 أو بمعنى آخر X لا تساوي 0 بيعطي إيه
+
+132
+00:11:54,280 --> 00:12:01,720
+أشماله non equality is not equal وهذا حدث كيف حدث
+
+133
+00:12:01,720 --> 00:12:06,240
+أثبتنا إنه لما X أكبر من نقص واحد وأصغر من 0 أو X
+
+134
+00:12:06,240 --> 00:12:10,720
+أكبر من 0 لجينا إنه هذي strictly أكبر يعني بتساوي
+
+135
+00:12:10,720 --> 00:12:15,260
+hashإذا صار عند الـ equality تحدث if and only if X
+
+136
+00:12:15,260 --> 00:12:22,580
+F بساوة سفر أي سؤال؟
+
+137
+00:12:22,580 --> 00:12:30,240
+طيب نيجي الآن نيجي الآن لل intermediate value of
+
+138
+00:12:30,240 --> 00:12:35,960
+property of derivative خلّيني ألقى في عينتها إذا
+
+139
+00:12:35,960 --> 00:12:42,760
+بتتذكروا في ال intermediate value of propertyاللي
+
+140
+00:12:42,760 --> 00:12:46,660
+هو for a continuous function إذا بتذكروا فيه اللي
+
+141
+00:12:46,660 --> 00:12:53,540
+هو real واحد اللي كانت تقول إذا كانت تقول إنه لو
+
+142
+00:12:53,540 --> 00:13:01,880
+كانت F function continuous على a closed open على
+
+143
+00:13:01,880 --> 00:13:07,020
+closed interval من A لعند B continuous على الفترة
+
+144
+00:13:07,020 --> 00:13:16,060
+هذهو إجيت أخدت أي نقطة K بين ال F of A و بين ال F
+
+145
+00:13:16,060 --> 00:13:22,900
+of B إجيت أخدت أي نقطة .. خد مثلا نقطة K بين F of
+
+146
+00:13:22,900 --> 00:13:31,240
+A .. هي F of A و هي F of B .. هي F of A و هي F of
+
+147
+00:13:31,240 --> 00:13:36,540
+B لو إجيت أخدت أي K بينهم هتلاقي .. هو خلي ناخد K
+
+148
+00:13:36,540 --> 00:13:43,830
+هنا مثلاهتلاقي على الأقل نقطة في الفترة A وBبتكون
+
+149
+00:13:43,830 --> 00:13:49,890
+اللي هو صورتها عبارة عن مين؟ عن الـ K يعني بمعنى
+
+150
+00:13:49,890 --> 00:13:55,970
+أخر there exists C element in A و B such that F of
+
+151
+00:13:55,970 --> 00:14:01,050
+C هي مين الـ K و لا أصلا مش هتلاقيها continuous لو
+
+152
+00:14:01,050 --> 00:14:05,530
+مافشلها فئلة و جينا مدينا خطنا هلجيت و مالجيناش
+
+153
+00:14:05,530 --> 00:14:09,290
+ولا واحدة من هذه النقاط اللي هو تقطع الخط معناته
+
+154
+00:14:09,290 --> 00:14:14,410
+أنه صار فيه jump مش هيكون في continuityالان هنا مش
+
+155
+00:14:14,410 --> 00:14:19,890
+في نقطة هي نقطة هي نقطتين هي تلاتة كلهم صورتين هي
+
+156
+00:14:19,890 --> 00:14:27,610
+C1 هي C2 هي C3 كلهم F of C1 K F of C2 K F of C3 K
+
+157
+00:14:27,610 --> 00:14:33,150
+المهم على الأقل في C element in A وB اللي هي بحيث
+
+158
+00:14:33,150 --> 00:14:36,210
+F of C بالساوة K هذا لو كان اتقفز continuous على
+
+159
+00:14:36,210 --> 00:14:40,650
+closed اللي هي bounded interval اللي عندك الآن
+
+160
+00:14:43,230 --> 00:14:47,090
+الحديث بيقول لي في اشي مشابه في حالة ان ال F' is
+
+161
+00:14:47,090 --> 00:14:53,950
+differentiable الان بيقولك لو كانت K بين ال F' لل
+
+162
+00:14:53,950 --> 00:14:58,970
+A و ال F' لل Bبرضه هنلاقيها بتتحقق اللي هو there
+
+163
+00:14:58,970 --> 00:15:03,810
+exists C بحيث ان F prime of C بتساوي اللي هو الكلب
+
+164
+00:15:03,810 --> 00:15:10,530
+نحكي عنها بالرغم انه مش مفترضين احنا في النظرية
+
+165
+00:15:10,530 --> 00:15:14,190
+اللي هو ال continuity ال continuity لل F prime
+
+166
+00:15:16,020 --> 00:15:19,360
+فضبجنا على الـ F' لكن مش .. لأنهم افترضينا على طول
+
+167
+00:15:19,360 --> 00:15:22,300
+تتطبق الـ Intermediate Value Theorem بس على الدالة
+
+168
+00:15:22,300 --> 00:15:26,980
+الـ F' لكن لأ ما هو مخزون في دالة .. خلال الـ F'
+
+169
+00:15:27,380 --> 00:15:33,140
+من معلومات أهلها أنه في حالة F is differentiable
+
+170
+00:15:33,140 --> 00:15:37,940
+على ال interval Iوالـ F ب .. و لجينا .. وفي عندي
+
+171
+00:15:37,940 --> 00:15:43,120
+أخدت أي K بين الـ F' of A و الـ F' of B هتلاقي C
+
+172
+00:15:43,120 --> 00:15:48,380
+في الـ A و الـ B بحيث انه اللي هي F' of C هي هذه
+
+173
+00:15:48,380 --> 00:15:51,920
+الـ K هنشوفها هذه اللي بنسميها Daraboxes theorem
+
+174
+00:15:51,920 --> 00:15:55,980
+قبل ما نروح للـ Daraboxes theorem خلينا نيجي لللمة
+
+175
+00:15:55,980 --> 00:16:00,680
+اللي جابلة اللي هنستخدمها في إثبات الـ Daraboxes
+
+176
+00:16:00,680 --> 00:16:07,340
+theorem الآنالنظرية هذه أو اللمّة هذه اللي هو
+
+177
+00:16:07,340 --> 00:16:10,880
+خلّينا نستذكرها من خلال الرسم ممكن يكون أسهل لكم
+
+178
+00:16:10,880 --> 00:16:16,680
+من خلال الرسم بتقولّي إنه لو كانت عندنا function F
+
+179
+00:16:16,680 --> 00:16:22,300
+is differentiable على اللي هو interval معينة
+
+180
+00:16:22,300 --> 00:16:29,120
+ولجينا عند C معينة هي F primeعند C موجبة F prime
+
+181
+00:16:29,120 --> 00:16:33,940
+عند C موجبة يعني F prime at some C أكبر من 0 يعني
+
+182
+00:16:33,940 --> 00:16:37,160
+مين المماس إيه اللي شماله اللي هو زاوية حادة عامل
+
+183
+00:16:37,160 --> 00:16:43,660
+زاوية حادة ماشي الان بقولي هتلاقي الان بده يبحث عن
+
+184
+00:16:43,660 --> 00:16:49,260
+نقاط تكون أكبر من مين من F of C الان هتلاقي اللي
+
+185
+00:16:49,260 --> 00:16:56,370
+هو هذا C اللي بتحكي عنها وهنااللي هو في جوار حوالي
+
+186
+00:16:56,370 --> 00:16:59,410
+هذين there exist إذا كان f of rank of c أكبر من
+
+187
+00:16:59,410 --> 00:17:03,630
+سفر there exists delta أكبر من سفر such that f of
+
+188
+00:17:03,630 --> 00:17:11,960
+xهنلاقيها أكبر من F of C لكل X وين متوقع أنا هان
+
+189
+00:17:11,960 --> 00:17:17,300
+لإنها الميل هيه إذا في الوين عشان C ل C زائد Delta
+
+190
+00:17:17,300 --> 00:17:19,620
+مش في الفترة اللي جابلة، في الفترة اللي جابلة
+
+191
+00:17:19,620 --> 00:17:23,960
+هتلاقي اللي هي النقطات أشملها أجل لأنا الآن ببحث
+
+192
+00:17:23,960 --> 00:17:29,420
+.. ببحث لم تبعت هيك بدهااللي هو there exist دلتا
+
+193
+00:17:29,420 --> 00:17:32,120
+أكبر من صفر ساشداد F of X أكبر من F of C لكل X
+
+194
+00:17:32,120 --> 00:17:40,200
+والي موجود من الـ C للـ C زائد دلتا معايا؟ الآن
+
+195
+00:17:40,200 --> 00:17:47,320
+بقولك لو لجينا F prime للـ C عند نقطة ما F prime
+
+196
+00:17:47,320 --> 00:17:54,130
+للـ C هي الـ C التانية لو لجينا F prime للـ Cأصغر
+
+197
+00:17:54,130 --> 00:17:57,210
+من صفر عشان .. عشان ما تحفظهاش حفظ عشان لو انسيتها
+
+198
+00:17:57,210 --> 00:18:00,890
+تستنتجها لحالك لو كان F' للـC أصغر من صفر يعني ميل
+
+199
+00:18:00,890 --> 00:18:06,710
+المماس سلب يعني زاوية منفرجة الآن هتلاقي Delta
+
+200
+00:18:06,710 --> 00:18:13,360
+أكبر من صفر يعني تمثل جواربحيث أن F of X برضه أكبر
+
+201
+00:18:13,360 --> 00:18:19,000
+من F of C لكل X وين موجودة هي وارحة منها لكل X
+
+202
+00:18:19,000 --> 00:18:24,340
+موجودة وين جابلها من C نقص دلتة لعند مين؟ لعند C
+
+203
+00:18:24,340 --> 00:18:29,800
+من C نقص دلتة لعند C هذه بس اللممة للاستذكار، إيش
+
+204
+00:18:29,800 --> 00:18:32,780
+بتقول اللممة؟ تعالى نشوف بالظبط اللي بتقوله اللي
+
+205
+00:18:32,780 --> 00:18:36,220
+حكيته أنا بقول اللممة let I subset من R be an
+
+206
+00:18:36,220 --> 00:18:40,260
+intervaland let F من I ل R و let C element in I
+
+207
+00:18:40,260 --> 00:18:44,700
+and assume that F has a derivative at C نفترض ان
+
+208
+00:18:44,700 --> 00:18:50,120
+ال F الهياشق مشتقة عند النقطة C مقولي إذا F prime
+
+209
+00:18:50,120 --> 00:18:54,200
+أكبر من 0 عند ال C هاي اللي قلته هان إذا نيوجد
+
+210
+00:18:54,200 --> 00:18:58,500
+دلتة أكبر من 0 بحيث أن F of X أكبر من F of C لكل
+
+211
+00:18:58,500 --> 00:19:02,560
+ال X وين موجودة بين ال C و C زائد دلتة اللي هي
+
+212
+00:19:02,560 --> 00:19:03,280
+الجبل هنا
+
+213
+00:19:06,510 --> 00:19:10,590
+الثانية، إذا كانت F' أصغر من 0، حلاقي Delta بحيث
+
+214
+00:19:10,590 --> 00:19:15,430
+أن F of C أصغر واحدة في الجوار، يعني F of C أو في
+
+215
+00:19:15,430 --> 00:19:19,010
+الجزء من الجوار، هذا الجزء اللي لجاي، F of C أصغر
+
+216
+00:19:19,010 --> 00:19:24,370
+من F of X، وين هاي الـ F of X هنا؟ أكبر من F of C،
+
+217
+00:19:24,370 --> 00:19:29,870
+واضح؟ لكل X وين موجودة في الـ C minus Delta والـ C
+
+218
+00:19:31,220 --> 00:19:36,360
+أي سؤال البرهن هو A خلّينا نبرهن بيه نحنا بيه
+
+219
+00:19:36,360 --> 00:19:40,980
+خلّينا نبرهن مع بعض بيه
+
+220
+00:19:40,980 --> 00:19:46,840
+الان
+
+221
+00:19:46,840 --> 00:19:53,820
+بدنا نقول نفترض ان F برايم بيه
+
+222
+00:19:53,820 --> 00:20:02,190
+approved الان ماعطينا F برايم of Cأصغر من سفر،
+
+223
+00:20:02,190 --> 00:20:11,750
+مظبوط؟ لأن بتقول since f prime of c أصغر من سفر
+
+224
+00:20:11,750 --> 00:20:21,070
+then limit f of x ناقص f of c على x minus c لما x
+
+225
+00:20:21,070 --> 00:20:27,540
+تروح لل c إشماله أصغر من سفرماشي، مدام أصغر من سفر
+
+226
+00:20:27,540 --> 00:20:31,080
+عند .. قلنا قبل هيك في نظرية إذا كان اللي هو
+
+227
+00:20:31,080 --> 00:20:35,600
+المقدار هذا أصغر من سفر إذا بقدر ألاقي جوار
+
+228
+00:20:35,600 --> 00:20:41,240
+حواليها بتكون القيم كلها إشمالها أصغر من سفر إذا
+
+229
+00:20:41,240 --> 00:20:48,560
+then there exist V Delta of C اللي هو جوار جوار من
+
+230
+00:20:48,560 --> 00:20:55,260
+عند C minus Delta لعند C زائد Deltaماشي؟ اللي هو
+
+231
+00:20:55,260 --> 00:20:58,980
+احنا أخدناها من هذا المنطقة من C نقص دلتا ل C زائد
+
+232
+00:20:58,980 --> 00:21:06,700
+دلتا such that اللي هو F of X نقص F of C على X
+
+233
+00:21:06,700 --> 00:21:16,220
+minus C أصغر من سفر لكل X وين في V دلتا of C أنا
+
+234
+00:21:16,220 --> 00:21:22,300
+غرضي أني أخلي اللي هو أوجد mean أن F of X أكبر من
+
+235
+00:21:22,300 --> 00:21:25,900
+100من F of C بدا وجد المنطقة اللي بتكون فيها F of
+
+236
+00:21:25,900 --> 00:21:31,880
+X أكبر من مين من F of C لاحظ انه هذا بديها وكأن F
+
+237
+00:21:31,880 --> 00:21:36,480
+of X ناقص F of C بديها أكبر من 0 صح عشان أحصل F of
+
+238
+00:21:36,480 --> 00:21:40,420
+X أكبر من مين من F of C لذن عشان أحصل على هذا
+
+239
+00:21:40,420 --> 00:21:45,000
+المقدار أكبر من 0 وانا بعرف ان هذا كله أصغر من 0
+
+240
+00:21:45,000 --> 00:21:48,880
+بدي المنطقة هذه تكون أصغر من 0 وين هتكون أصغر من
+
+241
+00:21:48,880 --> 00:21:57,510
+0؟ في المنطقة هذه، ماشي الحال؟الان but for every x
+
+242
+00:21:57,510 --> 00:22:05,650
+element in c نقص delta و c ال x minus c أصغر من
+
+243
+00:22:05,650 --> 00:22:15,800
+سفر واضحة؟ إذن الآن من هذه و من هذه henceأف of X
+
+244
+00:22:15,800 --> 00:22:23,300
+ناقص أف of C اللي هي بتساوي X minus C في أف of X
+
+245
+00:22:23,300 --> 00:22:30,300
+ناقص أف of C على X minus C هذا سالب وهذا سالب لذا
+
+246
+00:22:30,300 --> 00:22:35,260
+حصل ضرب بين أشماله هكون أكبر من سفر سالب في سالب
+
+247
+00:22:35,260 --> 00:22:42,720
+موجه مظبوط لهذا الكلام لكل X وين موجودة في الـC
+
+248
+00:22:43,730 --> 00:22:52,150
+-Delta OC وهذا معنى أن F of X أكبر من F of C لنقطة
+
+249
+00:22:52,150 --> 00:22:59,950
+المذكورة لنقات المذكورة واضح؟ أي سؤال؟ نيجي الآن
+
+250
+00:22:59,950 --> 00:23:04,930
+اللي هو انبرهن الـDrabowski's theorem اللي حكينا
+
+251
+00:23:04,930 --> 00:23:08,350
+عنها وقدمنا لها قبل بشوية إيش الـDrabowski's
+
+252
+00:23:08,350 --> 00:23:15,010
+theorem بتقول أنه عندي ال Fهو مستخدم للتحدي في بعض
+
+253
+00:23:15,010 --> 00:23:19,250
+الانترالين
+
+254
+00:23:19,250 --> 00:23:19,950
+A وB
+
+255
+00:23:23,800 --> 00:23:29,540
+اللي هي أي K بين F' و F'
+
+256
+00:23:32,040 --> 00:23:36,580
+of A و F' of B إذا نحن نلاقي الـ C بقيت أن F' of C
+
+257
+00:23:36,580 --> 00:23:42,020
+هي الـ K كمان مرة Drabowski's theorem بتقول if F
+
+258
+00:23:42,020 --> 00:23:47,520
+is differentiable on A و B و if K is any number
+
+259
+00:23:47,520 --> 00:23:53,610
+between F' of A و F' of Bthen there exists at
+
+260
+00:23:53,610 --> 00:23:56,350
+least one point C في الـA والـB بحيث أن الـAlpha
+
+261
+00:23:56,350 --> 00:24:02,650
+Prime of C أيش بتساوي؟ بتساوي K ماشي يا شباب طيب
+
+262
+00:24:02,650 --> 00:24:06,890
+اللي زي ما علقنا قبل بشوية بالرغم إنه إحنا ماحدش
+
+263
+00:24:06,890 --> 00:24:11,810
+جاب سيرة إن الـAlpha Prime هتكون continuousلأ،
+
+264
+00:24:11,810 --> 00:24:16,310
+قلنا ما في الـ F' من مخزون، derivative من مخزون في
+
+265
+00:24:16,310 --> 00:24:21,530
+داخلنا المعلومات أهلها إنها تقدر تصل أنه لأي K بين
+
+266
+00:24:21,530 --> 00:24:27,190
+الـ F A و الـ F' A و الـ F' B بالـ Legacy، بحيث أن
+
+267
+00:24:27,190 --> 00:24:31,170
+F' اللي عند الـ C هي الـ K. إيه المرحلة دلوقتي؟
+
+268
+00:24:31,170 --> 00:24:41,150
+شوف، نفترض أنه Proofنفترض أن G of A أصغر من K أصغر
+
+269
+00:24:41,150 --> 00:24:52,230
+من مين من G أو F prime of A أصغر من F prime of B
+
+270
+00:24:52,230 --> 00:24:56,450
+ماشي الحال واضح
+
+271
+00:24:56,450 --> 00:25:02,430
+هذا فرضناهالآن بدنا نلاقي C بحيث انه F' للـ C هو
+
+272
+00:25:02,430 --> 00:25:06,530
+الـ K الان define هالجيه تعرف ليش اعرفت defining
+
+273
+00:25:06,530 --> 00:25:15,590
+function G of X بساوي K في ال X ناقص F of X عندي
+
+274
+00:25:15,590 --> 00:25:18,790
+اللي هي هذه الدالة هي الدالة اللي هتوصلني للي
+
+275
+00:25:18,790 --> 00:25:23,800
+بديهاالان واضح ان الـ g of x بيساوي kx ناقص f of x
+
+276
+00:25:23,800 --> 00:25:29,660
+انها differentiable اللي هو هذه وين ما كان و هذي
+
+277
+00:25:29,660 --> 00:25:32,080
+differentiable على ال I إذا صار ان التنتين
+
+278
+00:25:32,080 --> 00:25:35,960
+differentiable على مين؟ على ال A و ال B و طبيعي
+
+279
+00:25:35,960 --> 00:25:40,440
+continuous على ال A و ال B إذا بما أن هذا الدالة
+
+280
+00:25:40,440 --> 00:25:44,440
+is continuous على closed bounded interval then it
+
+281
+00:25:44,440 --> 00:25:47,580
+attains its maximum and its minimum on this
+
+282
+00:25:47,580 --> 00:25:51,870
+intervalبتنه نشتغل عليه ال maximum و لو حد بده
+
+283
+00:25:51,870 --> 00:25:58,670
+يشتغل عليه المنه مابنفع برضه الان then g of x
+
+284
+00:25:58,670 --> 00:26:09,810
+attains its maximum on mean on a و bلأن إيش اللي
+
+285
+00:26:09,810 --> 00:26:15,370
+بيدثبتلك هي بيدثبتلك إن الـ G هيكون ال maximum
+
+286
+00:26:15,370 --> 00:26:21,150
+إلها لا عند ال A ولا عند ال B إذا هتكون وين؟ في
+
+287
+00:26:21,150 --> 00:26:25,870
+نقطة داخلية مدام في نقطة داخلية وإحنا عارفين إن
+
+288
+00:26:25,870 --> 00:26:29,490
+الـ G differentiable على كل المنطقة هذه إذا صارت
+
+289
+00:26:29,490 --> 00:26:33,050
+غصب عني إنه لازم مدام عندها maximum و interior
+
+290
+00:26:33,050 --> 00:26:38,390
+point إذا الـ G prime إيش هتساوي؟ هتساوي 0واضح؟
+
+291
+00:26:38,390 --> 00:26:42,590
+مدام جي برايم ما هتساوي سفر هتصير ال F prime of X
+
+292
+00:26:42,590 --> 00:26:46,550
+ال F of some C بتساوي ال K و بيكون خلصنا البرهان
+
+293
+00:26:46,550 --> 00:26:49,950
+تشوفيش اللي بقوله طيب صلوا على النبي عليه الصلاة
+
+294
+00:26:49,950 --> 00:27:05,390
+والسلام الآن عندي ال G prime of X هتساوي K ناقص F
+
+295
+00:27:05,390 --> 00:27:11,520
+prime of مين؟of X صح ولا لأ؟ طيب الآن لو جينا
+
+296
+00:27:11,520 --> 00:27:21,540
+حسبنا الـ G' عند ال A إيش هتلاقيها؟ K ناقص F' عند
+
+297
+00:27:21,540 --> 00:27:28,740
+مين؟ عند ال A صح ولا لأ؟ K ناقص F' عند ال A هتكون
+
+298
+00:27:28,740 --> 00:27:35,260
+أكبر من مين؟ من 0 واضح مدام ال G' على ال A أكبر من
+
+299
+00:27:35,260 --> 00:27:35,520
+0
+
+300
+00:27:39,110 --> 00:27:49,430
+K-F' أكبر من سفر بما أن J' بسوء K-F' أكبر من سفر
+
+301
+00:27:49,430 --> 00:27:53,450
+يعني هذا أكبر من سفر حسب اللي قبل قليل حكينا عنها
+
+302
+00:27:53,450 --> 00:28:06,330
+ثم هناك دلت أكبر من سفر such that G' of X أكبر من
+
+303
+00:28:06,330 --> 00:28:13,400
+G of Aاللي كنا بسمينا C فاهمين عليها الـ G of X
+
+304
+00:28:13,400 --> 00:28:22,800
+أكبر من G of A for every X element inمتذكرين اللي
+
+305
+00:28:22,800 --> 00:28:27,480
+قبل بشوية لما كانت جي برايم لما كانت الجي برايم
+
+306
+00:28:27,480 --> 00:28:32,860
+أكبر من سفر كانت اللي هي وين لجاي X element لغاية
+
+307
+00:28:32,860 --> 00:28:40,920
+أسف X element in C اللي هي A هنا وA زائد دلتا اللي
+
+308
+00:28:40,920 --> 00:28:45,240
+ما اللي قبل بشوية إذا صارت عند جي of X أكبر من 100
+
+309
+00:28:46,010 --> 00:28:50,890
+من الـ G of A واضح لمين؟ لكل الإكسات اللي هي في نص
+
+310
+00:28:50,890 --> 00:28:57,290
+الجوار هذا صارت عندي اللي هي الـ G of A مش maximum
+
+311
+00:28:57,290 --> 00:29:08,650
+لأن في قيم أكبر منها واضح؟ إذا أكيد then G does
+
+312
+00:29:08,650 --> 00:29:18,150
+not have a maximum at Aإذا الفش مش maximum عند
+
+313
+00:29:18,150 --> 00:29:23,990
+مين؟ عند الـ A أي
+
+314
+00:29:23,990 --> 00:29:27,750
+سؤال؟
+
+315
+00:29:27,750 --> 00:29:36,990
+Similarly .. Similarly G' عند ال B معايا يا شباب
+
+316
+00:29:36,990 --> 00:29:44,340
+G' عند ال B بساوي K نقص F' عند ال Bو K ناقص F
+
+317
+00:29:44,340 --> 00:29:49,840
+prime عند الـ B أصغر من مين؟ أصغر من 0 إذا بنفس
+
+318
+00:29:49,840 --> 00:29:54,600
+اللمّة بس على الجهة الثانية then there exists
+
+319
+00:29:54,600 --> 00:30:01,000
+Delta أكبر من 0 such that G of X أكبر من G of B
+
+320
+00:30:01,000 --> 00:30:11,520
+لكل X وان الآن من عند B ناقص Delta لعند الـ B صح؟
+
+321
+00:30:12,880 --> 00:30:19,600
+وهنا end points هذول فمش هتكون برضه مين ال b مش
+
+322
+00:30:19,600 --> 00:30:24,940
+هتكون عندها maximum لأنه منها ولا جوا ال b end
+
+323
+00:30:24,940 --> 00:30:28,920
+point منها ولا جوا ال g of x أكبر من ال g of b إذن
+
+324
+00:30:28,920 --> 00:30:38,160
+مش maximum إذن hence g does not have a maximum at
+
+325
+00:30:38,160 --> 00:30:45,380
+b from هناو from هنا from here and here we have g
+
+326
+00:30:45,380 --> 00:30:48,700
+has
+
+327
+00:30:48,700 --> 00:31:00,180
+the maximum inside a و b، مظبوط؟ يعني بمعنى آخر،
+
+328
+00:31:00,180 --> 00:31:06,100
+مدام احنا أكيد attained its maximum there exists c
+
+329
+00:31:06,100 --> 00:31:13,970
+element in a و b such thatجي هز ا maximum مدام جي
+
+330
+00:31:13,970 --> 00:31:18,770
+هز ا maximum و interior point اذا جي برايم عند ال
+
+331
+00:31:18,770 --> 00:31:23,390
+C ايش بتساوي؟ بتساوي سفر مدام جي برايم عند ال C
+
+332
+00:31:23,390 --> 00:31:28,090
+بتساوي سفر اذا صار عندي hence
+
+333
+00:31:30,200 --> 00:31:33,960
+وهنا اكتب جي برايم عند الـ C ايش بيساوي؟ بيساوي
+
+334
+00:31:33,960 --> 00:31:39,120
+سفر ايش جي برايم بيساوي؟ K ناقص F برايم اذا that
+
+335
+00:31:39,120 --> 00:31:43,020
+is K
+
+336
+00:31:43,020 --> 00:31:50,510
+ان هي بدل جي برايمنقص F' عند C بيساوي سفر أو بمعنى
+
+337
+00:31:50,510 --> 00:31:57,090
+آخر F' عند C أش بيساوي بيساوي K فعلا لقينا C في ال
+
+338
+00:31:57,090 --> 00:32:02,770
+A و ال B بحيث أن F' عند C أش بتساوي بيساوي K كما
+
+339
+00:32:02,770 --> 00:32:13,170
+هو مطلوب هيها أي سؤال الآن
+
+340
+00:32:14,940 --> 00:32:21,600
+عندي المثال الأخير بقول لي use Daraboux's theorem
+
+341
+00:32:21,600 --> 00:32:25,120
+هو في الواقع مثال على Daraboux's theorem بقول لي
+
+342
+00:32:25,120 --> 00:32:32,060
+the function g من
+
+343
+00:32:32,060 --> 00:32:36,080
+ناطس واحد وواحد لعند ال R defined by معرفه g of x
+
+344
+00:32:36,080 --> 00:32:39,320
+أيش بالساوية واحد إذا كانت x أكبر من صفر وأصغر
+
+345
+00:32:39,320 --> 00:32:43,680
+بسوا واحد0 إذا كانت X بيساوي واحد و ناقص واحد إذا
+
+346
+00:32:43,680 --> 00:32:46,180
+كانت X أكبر من ناقص واكبر بيساوي ناقص واحد و
+
+347
+00:32:46,180 --> 00:32:52,360
+بيساوي سفر بقول لي أثبت أن هذه الدالة is not the
+
+348
+00:32:52,360 --> 00:32:57,160
+derivative is not a derivative of any function
+
+349
+00:32:57,160 --> 00:33:01,580
+يعني مافيش function في الدنيا بتكون مشتقتها هي هذه
+
+350
+00:33:01,580 --> 00:33:06,420
+الـG هذه الـG is not a derivative of any function
+
+351
+00:33:07,400 --> 00:33:10,800
+بدا اقول suppose not ونصلى contradiction ماشي
+
+352
+00:33:10,800 --> 00:33:15,440
+الحال اذا الان ال
+
+353
+00:33:15,440 --> 00:33:27,280
+.. النظرية .. ال .. البثال بقول mainly المثال
+
+354
+00:33:27,280 --> 00:33:35,540
+بقول example example show that
+
+355
+00:33:38,010 --> 00:33:47,490
+G من نقص واحد لعند الواحد لعند ال R Defined by G
+
+356
+00:33:47,490 --> 00:33:53,610
+of X بساوي واحد إذا كانت X أكبر من سفر وأصغر يسوء
+
+357
+00:33:53,610 --> 00:33:59,290
+واحد سفر X بتساوي سفر نقص واحد X أكبر يسوء نقص
+
+358
+00:33:59,290 --> 00:34:08,330
+واحد وأصغر من سفر is not a derivativeof any
+
+359
+00:34:08,330 --> 00:34:20,610
+function on ناقص واحد واحد solution او proof اللي
+
+360
+00:34:20,610 --> 00:34:25,930
+قاعدك تقول suppose that
+
+361
+00:34:25,930 --> 00:34:36,550
+there exist f من ناقص واحد واحد لعند ال R suchthat
+
+362
+00:34:36,550 --> 00:34:46,630
+f prime of x بساوي g of x لكل x element ناقص واحد
+
+363
+00:34:46,630 --> 00:34:51,870
+و واحد ماشي الحال ايش هذه الدالة هي في الواقع
+
+364
+00:34:51,870 --> 00:34:59,310
+الدالة هي ال g of x هذه عندي سفر و انا عند الواحد
+
+365
+00:34:59,310 --> 00:35:04,550
+عند الواحد و انا سلب واحد
+
+366
+00:35:07,910 --> 00:35:16,170
+لعند اللي هو سنة واحد هيدّه ده اه لأن افترض انه F
+
+367
+00:35:16,170 --> 00:35:19,130
+بين نقص واحد واحد such that F prime of X بيساوي G
+
+368
+00:35:19,130 --> 00:35:22,650
+of X واضح انه F is different مدهن اذا قلت F prime
+
+369
+00:35:22,650 --> 00:35:25,390
+of X بيساوي G of X لكل X اللي منتقل نقص واحد واحد
+
+370
+00:35:25,390 --> 00:35:30,070
+صارت ال F ايش ما لأ is differentiable مظبوط ولا لأ
+
+371
+00:35:30,070 --> 00:35:39,050
+is differentiable واتنين لأن butالنص ينتبه إلى
+
+372
+00:35:39,050 --> 00:35:43,850
+الفترة ناقص واحد وواحد اللي هي إيش بتساوي اللي هي
+
+373
+00:35:43,850 --> 00:35:50,590
+عبارة عن الفترة هذه عبارة عن اللي هي F prime of
+
+374
+00:35:50,590 --> 00:36:03,650
+ناقص واحد و F prime of واحد باضح
+
+375
+00:36:03,650 --> 00:36:13,290
+أه؟هذه F' هي مين؟ G صح ولا لا؟ فمين؟ وهذه ايه؟ F'
+
+376
+00:36:13,550 --> 00:36:21,810
+G لأن G of واحد واحد، G of ناقص واحد ونص في الفترة
+
+377
+00:36:21,810 --> 00:36:22,170
+هذه
+
+378
+00:36:25,820 --> 00:36:30,060
+أصلا كل قيم الـ F' أو الـ D هي واحد صفر وناقص واحد
+
+379
+00:36:30,060 --> 00:36:34,360
+هذا هيسببلك الخلال مش نص بس تقدر تختار ربع تلت خمس
+
+380
+00:36:34,360 --> 00:36:38,680
+أي حاجة غير الـ Zero و الواحد والسلب واحد ايش ال
+
+381
+00:36:38,680 --> 00:36:49,400
+.. ايش الشد في الأمر but نص element كده and D
+
+382
+00:36:49,400 --> 00:37:00,740
+F is differentiable on ناقص واحد واحدصح؟ then by
+
+383
+00:37:00,740 --> 00:37:09,800
+Darabaux's theorem there exist c element ناقص واحد
+
+384
+00:37:09,800 --> 00:37:19,200
+وواحد such that اللي هو g of c او f prime of c
+
+385
+00:37:19,200 --> 00:37:28,990
+بيساوي ايش نص صح؟Ie بمعنى آخر F prime of C اللي هو
+
+386
+00:37:28,990 --> 00:37:39,590
+G of C بساوة نص Which is impossible Therefore
+
+387
+00:37:39,590 --> 00:37:46,480
+our first assumption is not truethat is there is
+
+388
+00:37:46,480 --> 00:37:50,740
+no F من ناقص واحد لعند واحد .. من واحد ناقص واحد
+
+389
+00:37:50,740 --> 00:37:54,960
+لواحد لعند ال R بحيث أن F' بيساوي G أو بمعنى أخر G
+
+390
+00:37:54,960 --> 00:38:03,680
+is not a derivative of any function وهكذا
+
+391
+00:38:03,680 --> 00:38:07,780
+نكون خلصنا ستة اتنين والمرة اللي جاي ان شاء الله
+
+392
+00:38:07,780 --> 00:38:13,980
+بنكمل في ستة تلاتة ويوم الأحد القادم بنناقش ستة
+
+393
+00:38:13,980 --> 00:38:16,010
+اتنينأسئلة 6
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/PVuSVTtYhJQ_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/PVuSVTtYhJQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..81b4124d8d0f8d22c6e0aae9700c2449a1442977
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/PVuSVTtYhJQ_raw.json
@@ -0,0 +1 @@
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{"start": 38.48, "end": 38.72, "word": " الـ", "probability": 0.96435546875}, {"start": 38.72, "end": 39.38, "word": " Pointwise", "probability": 0.93798828125}, {"start": 39.38, "end": 39.56, "word": " و", "probability": 0.51611328125}, {"start": 39.56, "end": 39.86, "word": " الـ", "probability": 0.874267578125}, {"start": 39.86, "end": 40.34, "word": " Uniform", "probability": 0.97900390625}, {"start": 40.34, "end": 41.34, "word": " Convergence", "probability": 0.9597981770833334}, {"start": 41.34, "end": 42.2, "word": " على", "probability": 0.830078125}, {"start": 42.2, "end": 42.84, "word": " اللي", "probability": 0.971923828125}, {"start": 42.84, "end": 43.24, "word": " هو", "probability": 0.99169921875}, {"start": 43.24, "end": 43.8, "word": " بعض", "probability": 0.98388671875}, {"start": 43.8, "end": 44.04, "word": " الـ", "probability": 0.9521484375}, {"start": 44.04, "end": 44.52, "word": " Sequence", "probability": 0.942626953125}, {"start": 44.52, "end": 44.7, "word": " 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62.32, "word": " pointwise", "probability": 0.7822265625}, {"start": 62.32, "end": 62.8, "word": " convergence", "probability": 0.97509765625}, {"start": 62.8, "end": 63.04, "word": " ان", "probability": 0.83935546875}, {"start": 63.04, "end": 63.32, "word": " يكون", "probability": 0.833984375}, {"start": 63.32, "end": 64.02, "word": " continuous", "probability": 0.9599609375}, {"start": 64.02, "end": 64.68, "word": " ولا", "probability": 0.73291015625}, {"start": 64.68, "end": 65.32, "word": " بلزمها", "probability": 0.91962890625}, {"start": 65.32, "end": 65.68, "word": " دعم", "probability": 0.98828125}, {"start": 65.68, "end": 66.22, "word": " شوية", "probability": 0.8699544270833334}, {"start": 66.22, "end": 66.88, "word": " نخلي", "probability": 0.7198079427083334}, {"start": 66.88, "end": 67.56, "word": " اللي", "probability": 0.982666015625}, {"start": 67.56, "end": 67.92, "word": " هو", "probability": 0.98779296875}, {"start": 67.92, "end": 68.48, "word": " بدل", 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limit اللي لما يكون اللي هو ال Fn بتروح لل F point twice أو ال Fn بتروح لل F uniform convergence؟", "tokens": [6027, 39184, 2445, 13672, 1829, 39894, 9566, 1211, 3615, 6055, 9566, 1211, 3615, 10957, 49429, 5296, 10721, 22807, 8032, 1863, 8592, 38688, 2423, 28820, 10943, 23758, 25124, 17082, 1211, 6024, 104, 7649, 1829, 8032, 1863, 8592, 38688, 14739, 3224, 45164, 25961, 2655, 2423, 2445, 307, 16200, 424, 638, 8032, 1211, 2423, 8310, 295, 6828, 307, 16200, 424, 638, 22807, 8032, 1211, 2423, 4948, 13672, 1829, 5296, 15042, 7251, 30544, 13672, 1829, 31439, 2423, 479, 77, 39894, 32887, 5016, 24976, 479, 935, 6091, 34051, 2423, 479, 77, 39894, 32887, 5016, 24976, 479, 9452, 32181, 22807], "avg_logprob": -0.2269736829556917, "compression_ratio": 1.75, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 72.8, "end": 73.22, "word": "الـ", "probability": 0.6474609375}, {"start": 73.22, "end": 73.7, "word": " function", "probability": 0.3037109375}, {"start": 73.7, "end": 73.9, "word": 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integration يعني ال limit بتدخل جوا ال integration ولا لأ؟ هل دخولها يعني بال point wise بحافظ على المساواة ولا لأ بال زمن اللي هو ال uniform convergence؟ هنشوفه والشغل التالثة هل انه لو كان في عندي sequence of differentiable functions هتطلع ان هو لو كان عندي F unconverged زي ال F", "tokens": [3224, 1211, 23758, 36764, 24401, 9154, 16095, 4724, 1829, 28543, 11703, 1829, 16472, 3224, 2423, 10980, 24976, 4948, 4724, 1829, 3794, 995, 45865, 2423, 4948, 24976, 10980, 37495, 22653, 2423, 4948, 39894, 3215, 9778, 1211, 10874, 14407, 2423, 10980, 49429, 5296, 10721, 22807, 8032, 1211, 11778, 9778, 12610, 11296, 37495, 22653, 20666, 935, 10829, 4724, 5016, 31845, 19913, 15844, 9673, 3794, 995, 14407, 3660, 49429, 5296, 10721, 20666, 30767, 27842, 13672, 1829, 31439, 2423, 9452, 32181, 22807, 8032, 1863, 8592, 38688, 3224, 16070, 8592, 17082, 1211, 16712, 6027, 12984, 3660, 8032, 1211, 16472, 3224, 45164, 25961, 8978, 18871, 16254, 8310, 295, 819, 9364, 6828, 8032, 2655, 9566, 1211, 3615, 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ال limit موجودة طبعا هذا pointwise convergence اللي هو ال pointwise convergence هنا طلعلي اللي هو ال sequence of functions GN limitها مش continuous ماقدرش يطلع اللي هو continuous function هذا ال pointwise convergence بالرغم إنه GN of X is اللي هو continuously differentiable الآن ناخد مثال آخر إذا", "tokens": [40228, 22653, 20666, 2288, 17082, 2304, 36145, 2423, 4948, 3714, 29245, 23328, 3660, 23032, 3555, 3615, 995, 23758, 935, 3711, 32181, 13672, 1829, 31439, 2423, 935, 3711, 32181, 34105, 23032, 1211, 3615, 20292, 13672, 1829, 31439, 2423, 8310, 295, 6828, 46411, 4948, 11296, 37893, 10957, 19446, 28543, 2288, 8592, 7251, 9566, 1211, 3615, 13672, 1829, 31439, 10957, 2445, 23758, 2423, 935, 3711, 32181, 20666, 2288, 17082, 2304, 36145, 3224, 46411, 295, 1783, 307, 13672, 1829, 31439, 15684, 819, 9364, 6024, 48506, 8717, 47283, 3215, 50113, 6027, 19753, 34740, 11933, 15730], "avg_logprob": -0.15556318583069267, "compression_ratio": 1.854625550660793, "no_speech_prob": 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هي", "probability": 0.896484375}, {"start": 741.46, "end": 741.6, "word": " ال", "probability": 0.93115234375}, {"start": 741.6, "end": 742.04, "word": " uniform", "probability": 0.91064453125}, {"start": 742.04, "end": 743.68, "word": " convergence", "probability": 0.9775390625}, {"start": 743.68, "end": 743.88, "word": " و", "probability": 0.791015625}, {"start": 743.88, "end": 744.32, "word": " هنشوف", "probability": 0.9246826171875}, {"start": 744.32, "end": 744.56, "word": " هذا", "probability": 0.98046875}, {"start": 744.56, "end": 745.06, "word": " الكلام", "probability": 0.9609375}], "temperature": 1.0}, {"id": 35, "seek": 76669, "start": 745.25, "end": 766.69, "text": "من خلال النظريات القادمة أول نظرية عندنا هذه النظرية اللي هي هتتعلق بالـ sequence of continuous functions كيف أنه لو كانت اللي هي sequence of continuous functions converts uniformly to some function F then F must be continuous", "tokens": [27842, 16490, 1211, 6027, 28239, 19913, 16572, 9307, 25062, 18513, 46007, 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0.6990966796875}, {"start": 757.25, "end": 757.49, "word": " لو", "probability": 0.98046875}, {"start": 757.49, "end": 757.99, "word": " كانت", "probability": 0.9921875}, {"start": 757.99, "end": 758.15, "word": " اللي", "probability": 0.896728515625}, {"start": 758.15, "end": 758.45, "word": " هي", "probability": 0.95947265625}, {"start": 758.45, "end": 759.31, "word": " sequence", "probability": 0.93701171875}, {"start": 759.31, "end": 759.51, "word": " of", "probability": 0.97412109375}, {"start": 759.51, "end": 760.09, "word": " continuous", "probability": 0.8828125}, {"start": 760.09, "end": 760.79, "word": " functions", "probability": 0.90185546875}, {"start": 760.79, "end": 761.39, "word": " converts", "probability": 0.59912109375}, {"start": 761.39, "end": 762.13, "word": " uniformly", "probability": 0.9609375}, {"start": 762.13, "end": 762.39, "word": " to", "probability": 0.9638671875}, {"start": 762.39, "end": 762.61, "word": " some", "probability": 0.91015625}, {"start": 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على الفترة A subset من R and suppose that اللي هي الـ Fn converges uniformly on A to a function F من A لعند R، بقول إذا ولا يهمك مضمون إن الـ F نفسها تكون إيش ما لها is a continuous function، إذاً", "tokens": [266, 257, 992, 316, 25993, 9154, 497, 12399, 11933, 15730, 14111, 479, 77, 6225, 3555, 9640, 3660, 18871, 44650, 2655, 16758, 27884, 9154, 32748, 2407, 6027, 1829, 9673, 2655, 36520, 3660, 15844, 27188, 2655, 25720, 316, 25993, 9154, 497, 293, 7297, 300, 13672, 1829, 39896, 2423, 39184, 479, 77, 9652, 2880, 48806, 322, 316, 281, 257, 2445, 479, 9154, 316, 5296, 3615, 41260, 497, 12399, 4724, 39648, 11933, 15730, 49429, 7251, 16095, 4117, 3714, 11242, 2304, 11536, 36145, 2423, 39184, 479, 8717, 36178, 11296, 6055, 30544, 11933, 1829, 8592, 19446, 5296, 11296, 307, 257, 10957, 2445, 12399, 11933, 15730, 14111], "avg_logprob": -0.20467202262123033, "compression_ratio": 1.5780590717299579, "no_speech_prob": 2.9206275939941406e-06, "words": [{"start": 779.42, "end": 779.76, "word": 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المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المستمرة المست", "tokens": [45340, 4587, 995, 20498, 3660, 5296, 19528, 3615, 10943, 1211, 9307, 9673, 14851, 29973, 3660, 39896, 3714, 14851, 29973, 3660, 4724, 995, 14851, 9778, 3215, 10943, 9673, 3615, 10943, 37977, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 14851, 29973, 3660, 9673, 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"probability": 0.94482421875}, {"start": 1331.44, "end": 1331.74, "word": " point", "probability": 0.9453125}, {"start": 1331.74, "end": 1332.12, "word": " twice", "probability": 0.7275390625}, {"start": 1332.12, "end": 1332.86, "word": " convergence", "probability": 0.98583984375}, {"start": 1332.86, "end": 1333.62, "word": " يكون", "probability": 0.989501953125}, {"start": 1333.62, "end": 1334.28, "word": " limitه", "probability": 0.612548828125}, {"start": 1334.28, "end": 1334.92, "word": " continuous", "probability": 0.94921875}, {"start": 1334.92, "end": 1335.48, "word": " function", "probability": 0.9697265625}, {"start": 1335.48, "end": 1335.7, "word": " لما", "probability": 0.935791015625}, {"start": 1335.7, "end": 1335.92, "word": " تكون", "probability": 0.99169921875}, {"start": 1335.92, "end": 1336.3, "word": " sequence", "probability": 0.94580078125}, {"start": 1336.3, "end": 1336.42, "word": " of", "probability": 0.88525390625}, {"start": 1336.42, "end": 1336.78, "word": " continuous", "probability": 0.91015625}, {"start": 1336.78, "end": 1337.2, "word": " functions", "probability": 0.6396484375}], "temperature": 1.0}, {"id": 60, "seek": 136289, "start": 1337.43, "end": 1362.89, "text": "طبيعي لكن احنا بنقول الضمان انه يطلع continuous انها تكون uniform convergence وجبنا مثال على انه اللي هو اللي هي sequence of continuous functions converge pointwise to some function that is not continuous زي ما شوفنا في المثال الأول نيجي الآن نحكي عن موضوع او الجزء المتعلق بمين", "tokens": [9566, 21292, 3615, 1829, 44381, 1975, 5016, 8315, 44945, 39648, 6024, 114, 2304, 7649, 16472, 3224, 7251, 9566, 1211, 3615, 10957, 16472, 11296, 6055, 30544, 9452, 32181, 4032, 7435, 3555, 8315, 50113, 6027, 15844, 16472, 3224, 13672, 1829, 31439, 13672, 1829, 39896, 8310, 295, 10957, 6828, 41881, 935, 3711, 281, 512, 2445, 300, 307, 406, 10957, 30767, 1829, 19446, 13412, 38688, 8315, 8978, 9673, 12984, 6027, 16247, 12610, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 5016, 4117, 1829, 18871, 3714, 2407, 11242, 45367, 1975, 2407, 25724, 11622, 38207, 9673, 2655, 30241, 4587, 4724, 2304, 9957], "avg_logprob": -0.14843750589837632, "compression_ratio": 1.675, "no_speech_prob": 1.537799835205078e-05, "words": [{"start": 1337.43, "end": 1338.01, "word": "طبيعي", "probability": 0.9290771484375}, {"start": 1338.01, "end": 1338.85, "word": " لكن", "probability": 0.6630859375}, {"start": 1338.85, "end": 1339.27, "word": " احنا", "probability": 0.884765625}, {"start": 1339.27, "end": 1339.75, "word": " بنقول", "probability": 0.951416015625}, {"start": 1339.75, "end": 1340.81, "word": " الضمان", "probability": 0.823486328125}, {"start": 1340.81, "end": 1341.09, "word": " انه", "probability": 0.841552734375}, {"start": 1341.09, "end": 1341.39, "word": " يطلع", "probability": 0.9832763671875}, {"start": 1341.39, "end": 1342.19, "word": " continuous", "probability": 0.85009765625}, {"start": 1342.19, "end": 1342.89, "word": " انها", "probability": 0.873046875}, {"start": 1342.89, "end": 1343.35, "word": " تكون", "probability": 0.98828125}, {"start": 1343.35, "end": 1343.99, "word": " uniform", "probability": 0.82177734375}, {"start": 1343.99, "end": 1345.01, "word": " convergence", "probability": 0.97900390625}, {"start": 1345.01, "end": 1345.95, "word": " وجبنا", "probability": 0.78179931640625}, {"start": 1345.95, "end": 1346.55, "word": " مثال", "probability": 0.985107421875}, {"start": 1346.55, "end": 1346.83, "word": " على", "probability": 0.76953125}, {"start": 1346.83, "end": 1347.45, "word": " انه", "probability": 0.913818359375}, {"start": 1347.45, "end": 1347.91, "word": " اللي", "probability": 0.929443359375}, {"start": 1347.91, "end": 1348.25, "word": " هو", "probability": 0.66357421875}, {"start": 1348.25, "end": 1348.85, "word": " اللي", "probability": 0.78955078125}, {"start": 1348.85, "end": 1349.19, "word": " هي", "probability": 0.9326171875}, {"start": 1349.19, "end": 1350.53, "word": " sequence", "probability": 0.8447265625}, {"start": 1350.53, "end": 1350.83, "word": " of", "probability": 0.953125}, {"start": 1350.83, "end": 1351.35, "word": " continuous", "probability": 0.8564453125}, {"start": 1351.35, "end": 1351.89, "word": " functions", "probability": 0.8427734375}, {"start": 1351.89, "end": 1352.67, "word": " converge", "probability": 0.51953125}, {"start": 1352.67, "end": 1353.73, "word": " pointwise", "probability": 0.615966796875}, {"start": 1353.73, "end": 1353.87, "word": " to", "probability": 0.93798828125}, {"start": 1353.87, "end": 1354.13, "word": " some", "probability": 0.912109375}, {"start": 1354.13, "end": 1354.63, "word": " function", "probability": 0.89404296875}, {"start": 1354.63, "end": 1354.95, "word": " that", "probability": 0.89111328125}, {"start": 1354.95, "end": 1355.17, "word": " is", "probability": 0.95556640625}, {"start": 1355.17, "end": 1355.43, "word": " not", "probability": 0.955078125}, {"start": 1355.43, "end": 1356.01, "word": " continuous", "probability": 0.900390625}, {"start": 1356.01, "end": 1356.27, "word": " زي", "probability": 0.901123046875}, {"start": 1356.27, "end": 1356.33, "word": " ما", "probability": 0.96337890625}, {"start": 1356.33, "end": 1356.61, "word": " شوفنا", "probability": 0.83203125}, {"start": 1356.61, "end": 1356.73, "word": " في", "probability": 0.9013671875}, {"start": 1356.73, "end": 1357.11, "word": " المثال", "probability": 0.9793294270833334}, {"start": 1357.11, "end": 1357.45, "word": " الأول", "probability": 0.8701171875}, {"start": 1357.45, "end": 1358.47, "word": " نيجي", "probability": 0.65216064453125}, {"start": 1358.47, "end": 1358.83, "word": " الآن", "probability": 0.730712890625}, {"start": 1358.83, "end": 1359.57, "word": " نحكي", "probability": 0.9835205078125}, {"start": 1359.57, "end": 1359.71, "word": " عن", "probability": 0.98876953125}, {"start": 1359.71, "end": 1360.29, "word": " موضوع", "probability": 0.9678955078125}, {"start": 1360.29, "end": 1361.27, "word": " او", "probability": 0.7373046875}, {"start": 1361.27, "end": 1361.61, "word": " الجزء", "probability": 0.98876953125}, {"start": 1361.61, "end": 1362.33, "word": " المتعلق", "probability": 0.9718017578125}, {"start": 1362.33, "end": 1362.89, "word": " بمين", "probability": 0.9596354166666666}], "temperature": 1.0}, {"id": 61, "seek": 138775, "start": 1363.87, "end": 1387.75, "text": "الجزء المتعلق بالـ Integrable Functions الآن نشوف أيش العلاج لإنه نضمن الـ Limit للـ Integration بساوي الـ Integration للـ Limit أو اللي هو لما ندخل الـ Limit للـ Integration متى بنقدر ندخله ويظل المحافظة على المساوية Let FN be a sequence of functions that are integrable on A وB", "tokens": [6027, 7435, 11622, 38207, 9673, 2655, 30241, 4587, 20666, 39184, 5681, 1146, 424, 638, 11166, 3916, 6024, 48506, 8717, 8592, 38688, 36632, 8592, 18863, 1211, 26108, 5296, 28814, 1863, 3224, 8717, 11242, 27842, 2423, 39184, 16406, 270, 24976, 39184, 47713, 4724, 3794, 995, 45865, 2423, 39184, 47713, 24976, 39184, 16406, 270, 34051, 13672, 1829, 31439, 5296, 15042, 8717, 3215, 9778, 1211, 2423, 39184, 16406, 270, 24976, 39184, 47713, 44650, 7578, 44945, 28543, 2288, 8717, 3215, 9778, 43761, 4032, 1829, 19913, 1211, 9673, 5016, 31845, 19913, 3660, 15844, 9673, 3794, 995, 2407, 10632, 961, 479, 45, 312, 257, 8310, 295, 6828, 300, 366, 16200, 424, 638, 322, 316, 4032, 33], "avg_logprob": -0.22656249309127982, "compression_ratio": 1.70995670995671, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1363.87, "end": 1364.49, "word": "الجزء", "probability": 0.8455810546875}, {"start": 1364.49, "end": 1365.41, "word": " المتعلق", "probability": 0.9761962890625}, {"start": 1365.41, "end": 1366.53, "word": " بالـ", "probability": 0.494384765625}, {"start": 1366.53, "end": 1367.77, "word": " Integrable", "probability": 0.77398681640625}, {"start": 1367.77, "end": 1368.45, "word": " Functions", "probability": 0.6796875}, {"start": 1368.45, "end": 1369.43, "word": " الآن", "probability": 0.5611572265625}, {"start": 1369.43, "end": 1370.83, "word": " نشوف", "probability": 0.7628580729166666}, {"start": 1370.83, "end": 1371.59, "word": " أيش", "probability": 0.6646728515625}, {"start": 1371.59, "end": 1372.25, "word": " العلاج", "probability": 0.9485677083333334}, {"start": 1372.25, "end": 1373.27, "word": " لإنه", "probability": 0.70556640625}, {"start": 1373.27, "end": 1373.97, "word": " نضمن", "probability": 0.9793294270833334}, {"start": 1373.97, "end": 1374.15, "word": " الـ", "probability": 0.616943359375}, {"start": 1374.15, "end": 1374.37, "word": " Limit", "probability": 0.701171875}, {"start": 1374.37, "end": 1374.55, "word": " للـ", "probability": 0.841796875}, {"start": 1374.55, "end": 1375.01, "word": " Integration", "probability": 0.7724609375}, {"start": 1375.01, "end": 1375.35, "word": " بساوي", "probability": 0.5849609375}, {"start": 1375.35, "end": 1375.53, "word": " الـ", "probability": 0.848876953125}, {"start": 1375.53, "end": 1375.95, "word": " Integration", "probability": 0.6982421875}, {"start": 1375.95, "end": 1376.27, "word": " للـ", "probability": 0.786865234375}, {"start": 1376.27, "end": 1376.51, "word": " Limit", "probability": 0.959228515625}, {"start": 1376.51, "end": 1376.73, "word": " أو", "probability": 0.8818359375}, {"start": 1376.73, "end": 1376.89, "word": " اللي", "probability": 0.8818359375}, {"start": 1376.89, "end": 1377.09, "word": " هو", "probability": 0.990234375}, {"start": 1377.09, "end": 1377.65, "word": " لما", "probability": 0.91015625}, {"start": 1377.65, "end": 1378.05, "word": " ندخل", "probability": 0.973388671875}, {"start": 1378.05, "end": 1378.21, "word": " الـ", "probability": 0.887939453125}, {"start": 1378.21, "end": 1378.53, "word": " Limit", "probability": 0.973388671875}, {"start": 1378.53, "end": 1378.97, "word": " للـ", "probability": 0.91064453125}, {"start": 1378.97, "end": 1379.41, "word": " Integration", "probability": 0.869140625}, {"start": 1379.41, "end": 1379.85, "word": " متى", "probability": 0.737060546875}, {"start": 1379.85, "end": 1380.21, "word": " بنقدر", "probability": 0.8751627604166666}, {"start": 1380.21, "end": 1380.63, "word": " ندخله", "probability": 0.990478515625}, {"start": 1380.63, "end": 1380.97, "word": " ويظل", "probability": 0.733154296875}, {"start": 1380.97, "end": 1381.61, "word": " المحافظة", "probability": 0.9453125}, {"start": 1381.61, "end": 1381.75, "word": " على", "probability": 0.947265625}, {"start": 1381.75, "end": 1382.61, "word": " المساوية", "probability": 0.866015625}, {"start": 1382.61, "end": 1383.85, "word": " Let", "probability": 0.282470703125}, {"start": 1383.85, "end": 1384.25, "word": " FN", "probability": 0.69189453125}, {"start": 1384.25, "end": 1384.43, "word": " be", "probability": 0.7421875}, {"start": 1384.43, "end": 1384.59, "word": " a", "probability": 0.970703125}, {"start": 1384.59, "end": 1385.03, "word": " sequence", "probability": 0.9140625}, {"start": 1385.03, "end": 1385.27, "word": " of", "probability": 0.9814453125}, {"start": 1385.27, "end": 1385.77, "word": " functions", "probability": 0.8515625}, {"start": 1385.77, "end": 1386.09, "word": " that", "probability": 0.8974609375}, {"start": 1386.09, "end": 1386.37, "word": " are", "probability": 0.9521484375}, {"start": 1386.37, "end": 1387.07, "word": " integrable", "probability": 0.86865234375}, {"start": 1387.07, "end": 1387.29, "word": " on", "probability": 0.8935546875}, {"start": 1387.29, "end": 1387.47, "word": " A", "probability": 0.90869140625}, {"start": 1387.47, "end": 1387.75, "word": " وB", "probability": 0.7998046875}], "temperature": 1.0}, {"id": 62, "seek": 141255, "start": 1388.61, "end": 1412.55, "text": "and suppose that FN converges uniformly من A و B to F then إذا لما تكون ال convergence uniform then ال F is integrable من A و B هاي واحد اتنين ال integration لل F of X DX من A لعين B بسوء ال limit لل integration يعني بمعنى أخر ال limit لل integration بسوء ال integration لل limit", "tokens": [474, 7297, 300, 479, 45, 9652, 2880, 48806, 9154, 316, 4032, 363, 281, 479, 550, 11933, 15730, 5296, 15042, 6055, 30544, 2423, 32181, 9452, 550, 2423, 479, 307, 16200, 424, 638, 9154, 316, 4032, 363, 8032, 47302, 36764, 24401, 1975, 2655, 1863, 9957, 2423, 10980, 24976, 479, 295, 1783, 48817, 9154, 316, 5296, 3615, 9957, 363, 4724, 3794, 2407, 38207, 2423, 4948, 24976, 10980, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 2423, 4948, 24976, 10980, 4724, 3794, 2407, 38207, 2423, 10980, 24976, 4948], "avg_logprob": -0.2796148300863976, "compression_ratio": 1.756218905472637, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1388.61, "end": 1388.89, "word": "and", "probability": 0.06512451171875}, {"start": 1388.89, "end": 1389.45, "word": " suppose", "probability": 0.87109375}, {"start": 1389.45, "end": 1390.25, "word": " that", "probability": 0.93359375}, {"start": 1390.25, "end": 1390.99, "word": " FN", "probability": 0.388916015625}, {"start": 1390.99, "end": 1391.87, "word": " converges", "probability": 0.681396484375}, {"start": 1391.87, "end": 1392.41, "word": " uniformly", "probability": 0.9697265625}, {"start": 1392.41, "end": 1392.63, "word": " من", "probability": 0.424560546875}, {"start": 1392.63, "end": 1392.81, "word": " A", "probability": 0.873046875}, {"start": 1392.81, "end": 1392.95, "word": " و", "probability": 0.82470703125}, {"start": 1392.95, "end": 1393.11, "word": " B", "probability": 0.5869140625}, {"start": 1393.11, "end": 1393.33, "word": " to", "probability": 0.6884765625}, {"start": 1393.33, "end": 1393.67, "word": " F", "probability": 0.9912109375}, {"start": 1393.67, "end": 1394.49, "word": " then", "probability": 0.476318359375}, {"start": 1394.49, "end": 1395.39, "word": " إذا", "probability": 0.6038818359375}, {"start": 1395.39, "end": 1395.87, "word": " لما", "probability": 0.890380859375}, {"start": 1395.87, "end": 1396.49, "word": " تكون", "probability": 0.965087890625}, {"start": 1396.49, "end": 1397.09, "word": " ال", "probability": 0.912109375}, {"start": 1397.09, "end": 1398.01, "word": " convergence", "probability": 0.708984375}, {"start": 1398.01, "end": 1398.55, "word": " uniform", "probability": 0.908203125}, {"start": 1398.55, "end": 1399.15, "word": " then", "probability": 0.541015625}, {"start": 1399.15, "end": 1400.07, "word": " ال", "probability": 0.58203125}, {"start": 1400.07, "end": 1400.35, "word": " F", "probability": 0.6982421875}, {"start": 1400.35, "end": 1400.57, "word": " is", "probability": 0.83935546875}, {"start": 1400.57, "end": 1401.23, "word": " integrable", "probability": 0.8733723958333334}, {"start": 1401.23, "end": 1401.39, "word": " من", "probability": 0.61767578125}, {"start": 1401.39, "end": 1401.53, "word": " A", "probability": 0.97265625}, {"start": 1401.53, "end": 1401.65, "word": " و", "probability": 0.98291015625}, {"start": 1401.65, "end": 1401.81, "word": " B", "probability": 0.88232421875}, {"start": 1401.81, "end": 1402.03, "word": " هاي", "probability": 0.5167236328125}, {"start": 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"probability": 0.836767578125}, {"start": 2397.66, "end": 2397.84, "word": " إيش", "probability": 0.7859700520833334}, {"start": 2397.84, "end": 2398.16, "word": " بتقول", "probability": 0.991455078125}, {"start": 2398.16, "end": 2398.54, "word": " bounded", "probability": 0.450439453125}, {"start": 2398.54, "end": 2399.16, "word": " convergence", "probability": 0.95654296875}, {"start": 2399.16, "end": 2400.04, "word": " theorem؟", "probability": 0.891357421875}], "temperature": 1.0}, {"id": 107, "seek": 242344, "start": 2400.77, "end": 2423.45, "text": "النظرية بتقول let FN be a sequence of functions that are integrable in A وB مفترضين إنها integrable and suppose that بدي يبعد عن ال uniform convergence بتقول لو شيلنا ال uniform convergence ممكن نبدله بإيش إيه؟ ويظل محافظنا على ال limit لل integration بساوي ال integration لل limit؟ آه، بنفع، نشوف كيف", "tokens": [6027, 1863, 19913, 2288, 10632, 39894, 39648, 718, 479, 45, 312, 257, 8310, 295, 6828, 300, 366, 16200, 424, 638, 294, 316, 4032, 33, 3714, 5172, 2655, 43042, 9957, 36145, 11296, 16200, 424, 638, 293, 7297, 300, 4724, 16254, 7251, 3555, 22488, 18871, 2423, 9452, 32181, 39894, 39648, 45164, 13412, 26895, 8315, 2423, 9452, 32181, 3714, 43020, 8717, 44510, 1211, 3224, 4724, 28814, 1829, 8592, 11933, 1829, 3224, 22807, 4032, 1829, 19913, 1211, 3714, 5016, 31845, 19913, 8315, 15844, 2423, 4948, 24976, 10980, 4724, 3794, 995, 45865, 2423, 10980, 24976, 4948, 22807, 19753, 3224, 12399, 44945, 5172, 3615, 12399, 8717, 8592, 38688, 9122, 33911], "avg_logprob": -0.25029761450631277, "compression_ratio": 1.5708812260536398, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 2400.77, "end": 2401.25, "word": "النظرية", "probability": 0.9140625}, {"start": 2401.25, "end": 2401.55, "word": " بتقول", "probability": 0.931396484375}, {"start": 2401.55, "end": 2401.73, "word": " let", "probability": 0.306396484375}, {"start": 2401.73, "end": 2402.05, "word": " FN", "probability": 0.592041015625}, {"start": 2402.05, "end": 2402.19, "word": " be", "probability": 0.708984375}, {"start": 2402.19, "end": 2402.31, "word": " a", "probability": 0.96044921875}, {"start": 2402.31, "end": 2402.65, "word": " sequence", "probability": 0.9658203125}, {"start": 2402.65, "end": 2402.85, "word": " of", "probability": 0.97216796875}, {"start": 2402.85, "end": 2403.45, "word": " functions", "probability": 0.8681640625}, {"start": 2403.45, "end": 2404.41, "word": " that", "probability": 0.80419921875}, {"start": 2404.41, "end": 2405.61, "word": " are", "probability": 0.94580078125}, {"start": 2405.61, "end": 2406.41, "word": " integrable", "probability": 0.8802083333333334}, {"start": 2406.41, "end": 2406.63, "word": " in", "probability": 0.537109375}, {"start": 2406.63, "end": 2406.83, "word": " A", "probability": 0.89013671875}, {"start": 2406.83, "end": 2407.15, "word": " وB", "probability": 0.705322265625}, {"start": 2407.15, "end": 2408.71, "word": " مفترضين", "probability": 0.928515625}, {"start": 2408.71, "end": 2408.93, "word": " إنها", "probability": 0.7242431640625}, {"start": 2408.93, "end": 2409.71, "word": " integrable", "probability": 0.7195638020833334}, {"start": 2409.71, "end": 2410.51, "word": " and", "probability": 0.7158203125}, {"start": 2410.51, "end": 2411.07, "word": " suppose", "probability": 0.90869140625}, {"start": 2411.07, "end": 2411.49, "word": " that", "probability": 0.8623046875}, {"start": 2411.49, "end": 2412.07, "word": " بدي", "probability": 0.720703125}, {"start": 2412.07, "end": 2412.53, "word": " يبعد", "probability": 0.8194986979166666}, {"start": 2412.53, "end": 2412.77, "word": " عن", "probability": 0.99462890625}, {"start": 2412.77, "end": 2412.91, "word": " ال", "probability": 0.9755859375}, {"start": 2412.91, "end": 2413.19, "word": " uniform", "probability": 0.76220703125}, {"start": 2413.19, "end": 2413.87, "word": " convergence", "probability": 0.94677734375}, {"start": 2413.87, "end": 2414.33, "word": " بتقول", "probability": 0.59197998046875}, {"start": 2414.33, "end": 2414.49, "word": " لو", "probability": 0.95947265625}, {"start": 2414.49, "end": 2414.77, "word": " شيلنا", "probability": 0.9609375}, {"start": 2414.77, "end": 2414.85, "word": " ال", "probability": 0.99169921875}, {"start": 2414.85, "end": 2415.09, "word": " uniform", "probability": 0.86669921875}, {"start": 2415.09, "end": 2415.83, "word": " convergence", "probability": 0.97119140625}, {"start": 2415.83, "end": 2416.71, "word": " ممكن", "probability": 0.975830078125}, {"start": 2416.71, "end": 2417.37, "word": " نبدله", "probability": 0.7626953125}, {"start": 2417.37, "end": 2417.73, "word": " بإيش", "probability": 0.74200439453125}, {"start": 2417.73, "end": 2418.03, "word": " إيه؟", "probability": 0.72760009765625}, {"start": 2418.03, "end": 2418.55, "word": " ويظل", "probability": 0.761474609375}, {"start": 2418.55, "end": 2419.17, "word": " محافظنا", "probability": 0.8232421875}, {"start": 2419.17, "end": 2419.41, "word": " على", "probability": 0.93896484375}, {"start": 2419.41, "end": 2419.55, "word": " ال", "probability": 0.46240234375}, {"start": 2419.55, "end": 2419.75, "word": " limit", "probability": 0.85791015625}, {"start": 2419.75, "end": 2419.89, "word": " لل", "probability": 0.943359375}, {"start": 2419.89, "end": 2420.41, "word": " integration", "probability": 0.880859375}, {"start": 2420.41, "end": 2420.75, "word": " بساوي", "probability": 0.732421875}, {"start": 2420.75, "end": 2420.85, "word": " ال", "probability": 0.91064453125}, {"start": 2420.85, "end": 2421.19, "word": " integration", "probability": 0.97265625}, {"start": 2421.19, "end": 2421.39, "word": " لل", "probability": 0.505859375}, {"start": 2421.39, "end": 2421.81, "word": " limit؟", "probability": 0.8720703125}, {"start": 2421.81, "end": 2422.05, "word": " آه،", "probability": 0.5992024739583334}, {"start": 2422.05, "end": 2422.83, "word": " بنفع،", "probability": 0.8802490234375}, {"start": 2422.83, "end": 2423.17, "word": " نشوف", "probability": 0.8395182291666666}, {"start": 2423.17, "end": 2423.45, "word": " كيف", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 108, "seek": 244873, "start": 2424.06, "end": 2448.74, "text": "لت أفأن بـ sequence of functions that are integrable in A وB بس بده يدفع ثمن برضه integrable in A وB and suppose that أفأن converts in A وB to an integrable function F يعني أفأن بتروح للـ F على الفترة هذه اللي هو point twice ماجالش uniformly بس الآن بده يفترض شغلة بده يقيد الأفأن", "tokens": [1211, 2655, 5551, 5172, 33456, 4724, 39184, 8310, 295, 6828, 300, 366, 16200, 424, 638, 294, 316, 4032, 33, 4724, 3794, 47525, 3224, 7251, 3215, 5172, 3615, 38637, 27842, 4724, 43042, 3224, 3572, 712, 294, 316, 4032, 33, 293, 7297, 300, 5551, 5172, 33456, 38874, 294, 316, 4032, 33, 281, 364, 16200, 424, 638, 2445, 479, 37495, 22653, 5551, 5172, 33456, 39894, 32887, 5016, 24976, 39184, 479, 15844, 27188, 2655, 25720, 29538, 13672, 1829, 31439, 935, 6091, 19446, 7435, 6027, 8592, 48806, 4724, 3794, 6024, 48506, 47525, 3224, 7251, 5172, 2655, 43042, 13412, 17082, 37977, 47525, 3224, 7251, 4587, 25708, 16247, 5172, 33456], "avg_logprob": -0.24939903559593055, "compression_ratio": 1.6118143459915613, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 2424.06, "end": 2424.42, "word": "لت", "probability": 0.6431884765625}, {"start": 2424.42, "end": 2424.74, "word": " أفأن", "probability": 0.4742024739583333}, {"start": 2424.74, "end": 2424.92, "word": " بـ", "probability": 0.5030517578125}, {"start": 2424.92, "end": 2425.2, "word": " sequence", "probability": 0.29345703125}, {"start": 2425.2, "end": 2425.52, "word": " of", "probability": 0.943359375}, {"start": 2425.52, "end": 2425.92, "word": " functions", "probability": 0.78466796875}, {"start": 2425.92, "end": 2426.18, "word": " that", "probability": 0.61962890625}, {"start": 2426.18, "end": 2426.4, "word": " are", "probability": 0.92919921875}, {"start": 2426.4, "end": 2426.94, "word": " integrable", "probability": 0.8636067708333334}, {"start": 2426.94, "end": 2427.1, "word": " in", "probability": 0.234130859375}, {"start": 2427.1, "end": 2427.2, "word": " A", "probability": 0.64404296875}, {"start": 2427.2, "end": 2427.34, "word": " وB", "probability": 0.6953125}, {"start": 2427.34, "end": 2427.52, "word": " بس", "probability": 0.88134765625}, {"start": 2427.52, "end": 2427.66, "word": " بده", "probability": 0.602294921875}, {"start": 2427.66, "end": 2427.84, "word": " يدفع", "probability": 0.8486328125}, {"start": 2427.84, "end": 2428.1, "word": " ثمن", "probability": 0.819580078125}, {"start": 2428.1, "end": 2428.52, "word": " برضه", "probability": 0.9900716145833334}, {"start": 2428.52, "end": 2429.68, "word": " integrable", "probability": 0.6014404296875}, {"start": 2429.68, "end": 2429.84, "word": " in", "probability": 0.78759765625}, {"start": 2429.84, "end": 2429.98, "word": " A", "probability": 0.970703125}, {"start": 2429.98, "end": 2430.18, "word": " وB", "probability": 0.93408203125}, {"start": 2430.18, "end": 2430.38, "word": " and", "probability": 0.81396484375}, {"start": 2430.38, "end": 2430.98, "word": " suppose", "probability": 0.923828125}, {"start": 2430.98, "end": 2431.74, "word": " that", "probability": 0.9443359375}, {"start": 2431.74, "end": 2432.54, "word": " أفأن", "probability": 0.8072916666666666}, {"start": 2432.54, "end": 2433.2, "word": " converts", "probability": 0.6474609375}, {"start": 2433.2, "end": 2433.48, "word": " in", "probability": 0.68994140625}, {"start": 2433.48, "end": 2433.7, "word": " A", "probability": 0.9775390625}, {"start": 2433.7, "end": 2433.98, "word": " وB", "probability": 0.961669921875}, {"start": 2433.98, "end": 2434.18, "word": " to", "probability": 0.88232421875}, {"start": 2434.18, "end": 2434.4, "word": " an", "probability": 0.84619140625}, {"start": 2434.4, "end": 2434.96, "word": " integrable", "probability": 0.8629557291666666}, {"start": 2434.96, "end": 2435.38, "word": " function", "probability": 0.9501953125}, {"start": 2435.38, "end": 2435.7, "word": " F", "probability": 0.8154296875}, {"start": 2435.7, "end": 2436.02, "word": " يعني", "probability": 0.898193359375}, {"start": 2436.02, "end": 2436.4, "word": " أفأن", "probability": 0.9293619791666666}, {"start": 2436.4, "end": 2436.76, "word": " بتروح", "probability": 0.94580078125}, {"start": 2436.76, "end": 2436.98, "word": " للـ", "probability": 0.6226806640625}, {"start": 2436.98, "end": 2437.2, "word": " F", "probability": 0.8193359375}, {"start": 2437.2, "end": 2437.78, "word": " على", "probability": 0.91552734375}, {"start": 2437.78, "end": 2438.94, "word": " الفترة", "probability": 0.91943359375}, {"start": 2438.94, "end": 2439.4, "word": " هذه", "probability": 0.84130859375}, {"start": 2439.4, "end": 2440.18, "word": " اللي", "probability": 0.958740234375}, {"start": 2440.18, "end": 2440.76, "word": " هو", "probability": 0.9931640625}, {"start": 2440.76, "end": 2441.78, "word": " point", "probability": 0.92626953125}, {"start": 2441.78, "end": 2442.5, "word": " twice", "probability": 0.728515625}, {"start": 2442.5, "end": 2443.34, "word": " ماجالش", "probability": 0.60845947265625}, {"start": 2443.34, "end": 2443.84, "word": " uniformly", "probability": 0.81103515625}, {"start": 2443.84, "end": 2444.7, "word": " بس", "probability": 0.982177734375}, {"start": 2444.7, "end": 2445.12, "word": " الآن", "probability": 0.7412109375}, {"start": 2445.12, "end": 2445.54, "word": " بده", "probability": 0.926513671875}, {"start": 2445.54, "end": 2446.06, "word": " يفترض", "probability": 0.9771728515625}, {"start": 2446.06, "end": 2446.52, "word": " شغلة", "probability": 0.8899739583333334}, {"start": 2446.52, "end": 2446.92, "word": " بده", "probability": 0.809814453125}, {"start": 2446.92, "end": 2447.56, "word": " يقيد", "probability": 0.9635416666666666}, {"start": 2447.56, "end": 2448.74, "word": " الأفأن", "probability": 0.8346354166666666}], "temperature": 1.0}, {"id": 109, "seek": 247873, "start": 2449.45, "end": 2478.73, "text": "بشغلة معينة شغلة كبيرة برضه التقييد مش جليل طبعا لكن بيضل اشي يعني منفذ تاني suppose also that there exist B أكبر من سفر بحيث انه FN of X أصغر شهر بيه لكل X element in A و B و لكل N element in B هذا في الواقع اللي هو uniform boundedness ليش؟ لأن هو مفترض ان ال sequence FN of X", "tokens": [3555, 8592, 17082, 37977, 20449, 9957, 3660, 13412, 17082, 37977, 9122, 3555, 48923, 4724, 43042, 3224, 16712, 38436, 25708, 37893, 10874, 20292, 1211, 23032, 3555, 3615, 995, 44381, 4724, 1829, 11242, 1211, 1975, 8592, 1829, 37495, 22653, 9154, 5172, 8848, 6055, 7649, 1829, 7297, 611, 300, 456, 2514, 363, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 4724, 5016, 1829, 12984, 16472, 3224, 479, 45, 295, 1783, 5551, 9381, 17082, 2288, 13412, 3224, 2288, 4724, 1829, 3224, 5296, 28820, 1783, 4478, 294, 316, 4032, 363, 4032, 5296, 28820, 426, 4478, 294, 363, 23758, 8978, 2423, 14407, 4587, 3615, 13672, 1829, 31439, 9452, 37498, 1287, 32239, 8592, 22807, 5296, 33456, 31439, 3714, 5172, 2655, 43042, 16472, 2423, 8310, 479, 45, 295, 1783], "avg_logprob": -0.22740186245973446, "compression_ratio": 1.5223880597014925, "no_speech_prob": 6.794929504394531e-06, "words": [{"start": 2449.45, "end": 2450.15, "word": "بشغلة", "probability": 0.82568359375}, {"start": 2450.15, "end": 2450.77, "word": " معينة", "probability": 0.9695638020833334}, {"start": 2450.77, "end": 2451.11, "word": " شغلة", "probability": 0.7301432291666666}, {"start": 2451.11, "end": 2451.47, "word": " كبيرة", "probability": 0.9822591145833334}, {"start": 2451.47, "end": 2451.73, "word": " برضه", "probability": 0.84814453125}, {"start": 2451.73, "end": 2452.23, "word": " التقييد", "probability": 0.6034342447916666}, {"start": 2452.23, "end": 2452.39, "word": " مش", "probability": 0.884765625}, {"start": 2452.39, "end": 2452.85, "word": " جليل", "probability": 0.79052734375}, {"start": 2452.85, "end": 2453.45, "word": " طبعا", "probability": 0.9713134765625}, {"start": 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{"start": 2459.83, "end": 2460.33, "word": " أكبر", "probability": 0.90576171875}, {"start": 2460.33, "end": 2460.53, "word": " من", "probability": 0.97900390625}, {"start": 2460.53, "end": 2460.89, "word": " سفر", "probability": 0.596923828125}, {"start": 2460.89, "end": 2463.03, "word": " بحيث", "probability": 0.76251220703125}, {"start": 2463.03, "end": 2463.63, "word": " انه", "probability": 0.693115234375}, {"start": 2463.63, "end": 2464.09, "word": " FN", "probability": 0.4444580078125}, {"start": 2464.09, "end": 2464.25, "word": " of", "probability": 0.82373046875}, {"start": 2464.25, "end": 2464.45, "word": " X", "probability": 0.9580078125}, {"start": 2464.45, "end": 2464.81, "word": " أصغر", "probability": 0.9471435546875}, {"start": 2464.81, "end": 2465.03, "word": " شهر", "probability": 0.50341796875}, {"start": 2465.03, "end": 2465.23, "word": " بيه", "probability": 0.8321940104166666}, {"start": 2465.23, "end": 2465.61, "word": " لكل", "probability": 0.97412109375}, 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بدنا", "probability": 0.770751953125}, {"start": 2880.33, "end": 2880.63, "word": " ناخده", "probability": 0.982421875}, {"start": 2880.63, "end": 2880.99, "word": " منه", "probability": 0.9853515625}, {"start": 2880.99, "end": 2881.77, "word": " اللي", "probability": 0.927490234375}, {"start": 2881.77, "end": 2882.15, "word": " هي", "probability": 0.82958984375}, {"start": 2882.15, "end": 2883.43, "word": " بتجاوبنا", "probability": 0.77802734375}, {"start": 2883.43, "end": 2883.67, "word": " على", "probability": 0.888671875}, {"start": 2883.67, "end": 2884.23, "word": " هذا", "probability": 0.9296875}, {"start": 2884.23, "end": 2885.11, "word": " الأمر", "probability": 0.876220703125}, {"start": 2885.11, "end": 2885.59, "word": " و", "probability": 0.9619140625}, {"start": 2885.59, "end": 2886.21, "word": " نشوف", "probability": 0.908203125}, {"start": 2886.21, "end": 2886.57, "word": " أيش", "probability": 0.755615234375}, {"start": 2886.57, "end": 2887.07, "word": " النظرية", 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interval اللي عندي لعند ارف واحدة اتنين ارف تلاتة الاخرين وبدنا نفترض", "tokens": [18767, 292, 15035, 1269, 37893, 1269, 37893, 6156, 9640, 28671, 20449, 40294, 257, 5395, 37893, 5395, 37893, 6156, 9640, 28671, 2423, 7649, 293, 718, 283, 77, 312, 257, 8310, 295, 6828, 322, 361, 37495, 22653, 6225, 3555, 4587, 7578, 18871, 16254, 18871, 16254, 283, 77, 8310, 295, 6828, 283, 77, 8310, 295, 6828, 15844, 3714, 9957, 22807, 15844, 2423, 39184, 361, 13672, 1829, 39896, 2423, 15035, 13672, 1829, 18871, 16254, 5296, 3615, 41260, 1975, 28480, 36764, 24401, 3660, 1975, 2655, 1863, 9957, 1975, 28480, 6055, 1211, 9307, 3660, 2423, 47283, 2288, 9957, 4032, 44510, 8315, 8717, 5172, 2655, 43042], "avg_logprob": -0.28968748927116394, "compression_ratio": 1.8525345622119815, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2896.9, "end": 2897.4, "word": "bounded", "probability": 0.71142578125}, {"start": 2897.4, "end": 2897.9, "word": " interval", "probability": 0.9619140625}, {"start": 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functions مفترض إن F N sequence of differentiable functions ومش هيك، وبيقولك إن هذه الـ F N' converts uniformly on J to some function F يعني بيقولك F N' exists", "tokens": [40228, 22653, 3714, 5172, 2655, 43042, 36145, 2423, 39184, 479, 426, 6, 8198, 37495, 22653, 479, 426, 8310, 295, 819, 9364, 6828, 3714, 5172, 2655, 43042, 36145, 479, 426, 8310, 295, 819, 9364, 6828, 4032, 2304, 8592, 39896, 4117, 12399, 4032, 21292, 39648, 4117, 36145, 29538, 2423, 39184, 479, 426, 6, 38874, 48806, 322, 508, 281, 512, 2445, 479, 37495, 22653, 4724, 1829, 39648, 4117, 479, 426, 6, 8198], "avg_logprob": -0.24330356482948576, "compression_ratio": 1.668639053254438, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2967.25, "end": 2967.71, "word": "يعني", "probability": 0.79248046875}, {"start": 2967.71, "end": 2968.37, "word": " مفترض", "probability": 0.9793701171875}, {"start": 2968.37, "end": 2968.57, "word": " إن", "probability": 0.32861328125}, {"start": 2968.57, "end": 2968.81, 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some G بكل الأنظم مع وجود هذه الشروط اللي حكينا عليها then the sequence FN converges uniformly to a function F بعد هذا بعد هذا بنلاقي أن FN غصب إن عنا لازم تكون converges uniformly to some function mean F ومش هيك", "tokens": [1353, 512, 460, 4724, 28820, 16247, 1863, 19913, 2304, 20449, 49610, 23328, 29538, 25124, 32887, 9566, 13672, 1829, 11331, 4117, 1829, 8315, 25894, 11296, 550, 264, 8310, 479, 45, 9652, 2880, 48806, 281, 257, 2445, 479, 39182, 23758, 39182, 23758, 44945, 15040, 38436, 14739, 479, 45, 32771, 9381, 3555, 36145, 6225, 8315, 5296, 31377, 2304, 6055, 30544, 9652, 2880, 48806, 281, 512, 2445, 914, 479, 4032, 2304, 8592, 39896, 4117], "avg_logprob": -0.265184846562399, "compression_ratio": 1.4676616915422886, "no_speech_prob": 1.245737075805664e-05, "words": [{"start": 3012.93, "end": 3013.03, "word": "to", "probability": 0.40283203125}, {"start": 3013.03, "end": 3013.29, "word": " some", "probability": 0.87255859375}, {"start": 3013.29, "end": 3013.63, "word": " G", 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Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges uniformly Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually Converges usually", "tokens": [9838, 331, 2880, 48806, 2656, 331, 2880, 48806, 2656, 331, 2880, 48806, 2656, 331, 2880, 48806, 2656, 331, 2880, 48806, 2656, 331, 2880, 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{"id": 175, "seek": 395842, "start": 3928.94, "end": 3958.42, "text": "مدام continuous و أثبتت FM بتروح converts uniformly لها إذا ال limit هذه هتطلع برضه إيش ماله is continuous و هذه خلوها في الذاكرة مكون احنا أوصلنا أو أثبتنا الجزء الأول من النظرية أن FM converts uniformly to F و ال limit لها سمناها F و هيطلع لنا عبارة عن continuous function شوفوا يا جماعة الآن", "tokens": [2304, 3215, 10943, 10957, 4032, 5551, 12984, 3555, 2655, 2655, 29614, 39894, 32887, 5016, 38874, 48806, 5296, 11296, 11933, 15730, 2423, 4948, 29538, 8032, 2655, 9566, 1211, 3615, 4724, 43042, 3224, 11933, 1829, 8592, 3714, 6027, 3224, 307, 10957, 4032, 29538, 16490, 1211, 2407, 11296, 8978, 32545, 995, 4117, 25720, 3714, 30544, 1975, 5016, 8315, 34051, 36520, 8315, 34051, 5551, 12984, 3555, 2655, 8315, 25724, 11622, 38207, 16247, 12610, 9154, 28239, 19913, 2288, 10632, 14739, 29614, 38874, 48806, 281, 479, 4032, 2423, 4948, 5296, 11296, 8608, 2304, 8315, 11296, 479, 4032, 39896, 9566, 1211, 3615, 5296, 8315, 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{"start": 3953.48, "end": 3953.82, "word": " و", "probability": 0.9501953125}, {"start": 3953.82, "end": 3954.32, "word": " هيطلع", "probability": 0.8455810546875}, {"start": 3954.32, "end": 3954.54, "word": " لنا", "probability": 0.789794921875}, {"start": 3954.54, "end": 3954.94, "word": " عبارة", "probability": 0.996826171875}, {"start": 3954.94, "end": 3955.14, "word": " عن", "probability": 0.98388671875}, {"start": 3955.14, "end": 3955.66, "word": " continuous", "probability": 0.9306640625}, {"start": 3955.66, "end": 3956.64, "word": " function", "probability": 0.9755859375}, {"start": 3956.64, "end": 3957.6, "word": " شوفوا", "probability": 0.97412109375}, {"start": 3957.6, "end": 3957.72, "word": " يا", "probability": 0.99267578125}, {"start": 3957.72, "end": 3958.06, "word": " جماعة", "probability": 0.9892578125}, {"start": 3958.06, "end": 3958.42, "word": " الآن", "probability": 0.830322265625}], "temperature": 1.0}, {"id": 176, "seek": 396376, "start": 3962.6, "end": 3963.76, "text": "صار عندي الآن", "tokens": [9381, 9640, 18871, 16254, 6024, 48506], "avg_logprob": -0.4040178486279079, "compression_ratio": 0.6857142857142857, "no_speech_prob": 0.0, "words": [{"start": 3962.6, "end": 3963.02, "word": "صار", "probability": 0.828125}, {"start": 3963.02, "end": 3963.3, "word": " عندي", "probability": 0.6588134765625}, {"start": 3963.3, "end": 3963.76, "word": " الآن", "probability": 0.695556640625}], "temperature": 1.0}, {"id": 177, "seek": 399469, "start": 3965.85, "end": 3994.69, "text": "أثبتنا أن Fn تتعامل بشكل مرتبط سمينا limit Fn بسوء F which is continuous because Fn زي ما قلنا is continuous لأنه في الأصل هي differentiable و Fn بتروح لل F إذن صارت ال F اللي هي نفسها continuous الآن بدي أستخدم ال continuity عند ال F بدي أصل اللي بديه طيب خد C الآن ب any fixed point in J الآن بدي أروح إلى إثبات أنه", "tokens": [10721, 12984, 3555, 2655, 8315, 14739, 479, 77, 6055, 2655, 3615, 10943, 1211, 4724, 8592, 28820, 3714, 43500, 3555, 9566, 8608, 2304, 1829, 8315, 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"probability": 0.3431396484375}, {"start": 3967.03, "end": 3967.49, "word": " تتعامل", "probability": 0.54400634765625}, {"start": 3967.49, "end": 3967.65, "word": " بشكل", "probability": 0.6817220052083334}, {"start": 3967.65, "end": 3967.83, "word": " مرتبط", "probability": 0.552886962890625}, {"start": 3967.83, "end": 3969.33, "word": " سمينا", "probability": 0.63409423828125}, {"start": 3969.33, "end": 3969.57, "word": " limit", "probability": 0.22705078125}, {"start": 3969.57, "end": 3969.99, "word": " Fn", "probability": 0.769775390625}, {"start": 3969.99, "end": 3970.31, "word": " بسوء", "probability": 0.4324798583984375}, {"start": 3970.31, "end": 3970.53, "word": " F", "probability": 0.892578125}, {"start": 3970.53, "end": 3970.81, "word": " which", "probability": 0.18408203125}, {"start": 3970.81, "end": 3971.05, "word": " is", "probability": 0.9521484375}, {"start": 3971.05, "end": 3971.61, "word": " continuous", "probability": 0.8955078125}, {"start": 3971.61, "end": 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"end": 3975.81, "word": " و", "probability": 0.58935546875}, {"start": 3975.81, "end": 3976.25, "word": " Fn", "probability": 0.7396240234375}, {"start": 3976.25, "end": 3976.63, "word": " بتروح", "probability": 0.7682291666666666}, {"start": 3976.63, "end": 3976.79, "word": " لل", "probability": 0.7294921875}, {"start": 3976.79, "end": 3977.03, "word": " F", "probability": 0.494140625}, {"start": 3977.03, "end": 3977.35, "word": " إذن", "probability": 0.4783121744791667}, {"start": 3977.35, "end": 3977.71, "word": " صارت", "probability": 0.9510091145833334}, {"start": 3977.71, "end": 3977.87, "word": " ال", "probability": 0.6884765625}, {"start": 3977.87, "end": 3978.13, "word": " F", "probability": 0.84375}, {"start": 3978.13, "end": 3978.61, "word": " اللي", "probability": 0.6890869140625}, {"start": 3978.61, "end": 3978.79, "word": " هي", "probability": 0.873046875}, {"start": 3978.79, "end": 3979.27, "word": " نفسها", "probability": 0.9894205729166666}, {"start": 3979.27, "end": 3979.95, "word": " continuous", "probability": 0.94287109375}, {"start": 3979.95, "end": 3980.99, "word": " الآن", "probability": 0.6815185546875}, {"start": 3980.99, "end": 3982.11, "word": " بدي", "probability": 0.4677734375}, {"start": 3982.11, "end": 3982.63, "word": " أستخدم", "probability": 0.8524169921875}, {"start": 3982.63, "end": 3982.81, "word": " ال", "probability": 0.91845703125}, {"start": 3982.81, "end": 3983.33, "word": " continuity", "probability": 0.90771484375}, {"start": 3983.33, "end": 3983.69, "word": " عند", "probability": 0.95849609375}, {"start": 3983.69, "end": 3983.83, "word": " ال", "probability": 0.7451171875}, {"start": 3983.83, "end": 3984.05, "word": " F", "probability": 0.955078125}, {"start": 3984.05, "end": 3984.35, "word": " بدي", "probability": 0.867431640625}, {"start": 3984.35, "end": 3984.65, "word": " أصل", "probability": 0.9541015625}, {"start": 3984.65, "end": 3984.83, "word": " اللي", "probability": 0.85595703125}, {"start": 3984.83, "end": 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بدي", "probability": 0.818603515625}, {"start": 3992.09, "end": 3992.43, "word": " أروح", "probability": 0.9283854166666666}, {"start": 3992.43, "end": 3992.65, "word": " إلى", "probability": 0.83447265625}, {"start": 3992.65, "end": 3993.51, "word": " إثبات", "probability": 0.892578125}, {"start": 3993.51, "end": 3994.69, "word": " أنه", "probability": 0.79296875}], "temperature": 1.0}, {"id": 178, "seek": 401445, "start": 3995.31, "end": 4014.45, "text": "الـ Limit للـ F of X ناقص F of C على X minus C as X بتروح للـ C هذه الـ C وينها؟ الـ C أخذناها arbitrary في X in J إذا أثبتت لهذا الـ C اللي هو بساوي اللي هي G of C", "tokens": [6027, 39184, 16406, 270, 24976, 39184, 479, 295, 1783, 8717, 995, 4587, 9381, 479, 295, 383, 15844, 1783, 3175, 383, 382, 1783, 39894, 32887, 5016, 24976, 39184, 383, 29538, 2423, 39184, 383, 4032, 9957, 11296, 22807, 2423, 39184, 383, 5551, 9778, 8848, 8315, 11296, 23211, 8978, 1783, 294, 508, 11933, 15730, 5551, 12984, 3555, 2655, 2655, 46740, 15730, 2423, 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" C", "probability": 0.97021484375}, {"start": 4000.93, "end": 4001.67, "word": " على", "probability": 0.75341796875}, {"start": 4001.67, "end": 4002.03, "word": " X", "probability": 0.94677734375}, {"start": 4002.03, "end": 4002.41, "word": " minus", "probability": 0.67041015625}, {"start": 4002.41, "end": 4002.95, "word": " C", "probability": 0.98876953125}, {"start": 4002.95, "end": 4003.53, "word": " as", "probability": 0.37451171875}, {"start": 4003.53, "end": 4003.81, "word": " X", "probability": 0.9892578125}, {"start": 4003.81, "end": 4004.17, "word": " بتروح", "probability": 0.9111328125}, {"start": 4004.17, "end": 4004.41, "word": " للـ", "probability": 0.8310546875}, {"start": 4004.41, "end": 4004.55, "word": " C", "probability": 0.71826171875}, {"start": 4004.55, "end": 4004.97, "word": " هذه", "probability": 0.77685546875}, {"start": 4004.97, "end": 4005.63, "word": " الـ", "probability": 0.760009765625}, {"start": 4005.63, "end": 4005.81, "word": " C", "probability": 0.8662109375}, {"start": 4005.81, "end": 4006.31, "word": " وينها؟", "probability": 0.7972412109375}, {"start": 4006.31, "end": 4006.37, "word": " الـ", "probability": 0.8037109375}, {"start": 4006.37, "end": 4006.43, "word": " C", "probability": 0.951171875}, {"start": 4006.43, "end": 4006.97, "word": " أخذناها", "probability": 0.8021484375}, {"start": 4006.97, "end": 4007.39, "word": " arbitrary", "probability": 0.49658203125}, {"start": 4007.39, "end": 4007.73, "word": " في", "probability": 0.53759765625}, {"start": 4007.73, "end": 4007.95, "word": " X", "probability": 0.95361328125}, {"start": 4007.95, "end": 4008.23, "word": " in", "probability": 0.328857421875}, {"start": 4008.23, "end": 4008.51, "word": " J", "probability": 0.86865234375}, {"start": 4008.51, "end": 4009.09, "word": " إذا", "probability": 0.95263671875}, {"start": 4009.09, "end": 4009.67, "word": " أثبتت", "probability": 0.98671875}, {"start": 4009.67, "end": 4010.13, "word": " لهذا", "probability": 0.752685546875}, {"start": 4010.13, "end": 4010.33, "word": " الـ", "probability": 0.974853515625}, {"start": 4010.33, "end": 4010.63, "word": " C", "probability": 0.95263671875}, {"start": 4010.63, "end": 4011.29, "word": " اللي", "probability": 0.848388671875}, {"start": 4011.29, "end": 4011.47, "word": " هو", "probability": 0.98876953125}, {"start": 4011.47, "end": 4012.11, "word": " بساوي", "probability": 0.8931884765625}, {"start": 4012.11, "end": 4012.61, "word": " اللي", "probability": 0.807861328125}, {"start": 4012.61, "end": 4012.95, "word": " هي", "probability": 0.8642578125}, {"start": 4012.95, "end": 4013.69, "word": " G", "probability": 0.806640625}, {"start": 4013.69, "end": 4013.99, "word": " of", "probability": 0.962890625}, {"start": 4013.99, "end": 4014.45, "word": " C", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 179, "seek": 403191, "start": 4014.91, "end": 4031.91, "text": "معناته إذا أثبتت هذا معناته أثبتت أن F' of C exist وهي ساوي G of C ومعناته أثبتت أن F بتساوي G على كل J لأن C ماخدها arbitrary but fixed يعني إيش بده أثبت في هذا؟", "tokens": [2304, 3615, 8315, 47395, 11933, 15730, 5551, 12984, 3555, 2655, 2655, 23758, 20449, 8315, 47395, 5551, 12984, 3555, 2655, 2655, 14739, 479, 6, 295, 383, 2514, 37037, 1829, 8608, 995, 45865, 460, 295, 383, 4032, 2304, 3615, 8315, 47395, 5551, 12984, 3555, 2655, 2655, 14739, 479, 39894, 3794, 995, 45865, 460, 15844, 28242, 508, 5296, 33456, 383, 3714, 47283, 3215, 11296, 23211, 457, 6806, 37495, 22653, 11933, 1829, 8592, 47525, 3224, 5551, 12984, 3555, 2655, 8978, 23758, 22807], "avg_logprob": -0.24980222650721104, "compression_ratio": 1.58125, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 4014.91, "end": 4015.67, "word": "معناته", "probability": 0.815673828125}, {"start": 4015.67, "end": 4015.87, "word": " إذا", "probability": 0.77734375}, {"start": 4015.87, "end": 4016.25, "word": " أثبتت", "probability": 0.84365234375}, {"start": 4016.25, "end": 4016.43, "word": " هذا", "probability": 0.58837890625}, {"start": 4016.43, "end": 4016.87, "word": " معناته", "probability": 0.8689778645833334}, {"start": 4016.87, "end": 4017.35, "word": " أثبتت", "probability": 0.97431640625}, {"start": 4017.35, "end": 4017.47, "word": " أن", "probability": 0.47314453125}, {"start": 4017.47, "end": 4017.75, "word": " F'", "probability": 0.2344970703125}, {"start": 4018.11, "end": 4018.75, "word": " of", "probability": 0.1622314453125}, {"start": 4018.75, "end": 4019.11, "word": " C", "probability": 0.77099609375}, {"start": 4019.11, "end": 4019.69, "word": " exist", "probability": 0.50341796875}, {"start": 4019.69, "end": 4020.03, "word": " وهي", "probability": 0.747802734375}, {"start": 4020.03, "end": 4020.29, "word": " ساوي", "probability": 0.6220703125}, {"start": 4020.29, "end": 4020.47, "word": " G", "probability": 0.72705078125}, {"start": 4020.47, "end": 4020.65, "word": " of", "probability": 0.755859375}, {"start": 4020.65, "end": 4020.97, "word": " C", "probability": 0.990234375}, {"start": 4020.97, "end": 4022.15, "word": " ومعناته", "probability": 0.94814453125}, {"start": 4022.15, "end": 4022.97, "word": " أثبتت", "probability": 0.99404296875}, {"start": 4022.97, "end": 4023.59, "word": " أن", "probability": 0.79931640625}, {"start": 4023.59, "end": 4024.41, "word": " F", "probability": 0.76806640625}, {"start": 4024.41, "end": 4025.05, "word": " بتساوي", "probability": 0.70721435546875}, {"start": 4025.05, "end": 4025.33, "word": " G", "probability": 0.8603515625}, {"start": 4025.33, "end": 4025.61, "word": " على", "probability": 0.80908203125}, {"start": 4025.61, "end": 4025.99, "word": " كل", "probability": 0.8779296875}, {"start": 4025.99, "end": 4026.45, "word": " J", "probability": 0.423095703125}, {"start": 4026.45, "end": 4027.11, "word": " لأن", "probability": 0.823974609375}, {"start": 4027.11, "end": 4027.53, "word": " C", "probability": 0.5732421875}, {"start": 4027.53, "end": 4028.31, "word": " ماخدها", "probability": 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412951, "start": 4111.81, "end": 4129.51, "text": "ماشي الحال طبقت الـ Mean Value Theorem على الدالة ال .. اللي هي Fm ناقص Fn لكل M O N الان خدوا الحسبة الان خد X لا تساوى C لإنه .. 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epsilon", "probability": 0.9296875}, {"start": 4373.11, "end": 4373.85, "word": " اذا", "probability": 0.665771484375}, {"start": 4373.85, "end": 4374.47, "word": " الان", "probability": 0.794921875}, {"start": 4374.47, "end": 4375.45, "word": " صار", "probability": 0.98583984375}, {"start": 4375.45, "end": 4375.97, "word": " عندى", "probability": 0.945068359375}, {"start": 4375.97, "end": 4376.55, "word": " التنتين", "probability": 0.98779296875}, {"start": 4376.55, "end": 4377.93, "word": " متحققات", "probability": 0.97958984375}, {"start": 4377.93, "end": 4378.79, "word": " لكل", "probability": 0.97705078125}, {"start": 4378.79, "end": 4379.13, "word": " N", "probability": 0.6708984375}, {"start": 4379.13, "end": 4379.59, "word": " أكبر", "probability": 0.9580078125}, {"start": 4379.59, "end": 4379.83, "word": " او", "probability": 0.794677734375}, {"start": 4379.83, "end": 4380.33, "word": " يساوي", "probability": 0.8294677734375}, {"start": 4380.33, "end": 4380.63, "word": " K", "probability": 0.94189453125}, {"start": 4380.63, "end": 4381.37, "word": " ومشروع", "probability": 0.944921875}, {"start": 4381.37, "end": 4382.11, "word": " استخدامه", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 195, "seek": 438775, "start": 4382.67, "end": 4387.75, "text": "الآن من جهة ثانية بدي استخدم الـ FK' of C إنها exist", "tokens": [6027, 148, 48506, 9154, 10874, 3224, 3660, 38637, 7649, 10632, 4724, 16254, 44713, 9778, 40448, 2423, 39184, 479, 42, 6, 295, 383, 36145, 11296, 2514], "avg_logprob": -0.3473557818394441, "compression_ratio": 0.9425287356321839, "no_speech_prob": 0.0, "words": [{"start": 4382.67, "end": 4383.11, "word": "الآن", "probability": 0.5707600911458334}, {"start": 4383.11, "end": 4383.67, "word": " من", "probability": 0.83251953125}, {"start": 4383.67, "end": 4384.01, "word": " جهة", "probability": 0.96630859375}, {"start": 4384.01, "end": 4384.53, "word": " ثانية", "probability": 0.9762369791666666}, {"start": 4384.53, "end": 4385.35, "word": " بدي", "probability": 0.482666015625}, {"start": 4385.35, "end": 4385.89, "word": " استخدم", "probability": 0.88134765625}, {"start": 4385.89, "end": 4386.09, "word": " الـ", "probability": 0.79443359375}, {"start": 4386.09, "end": 4386.43, "word": " FK'", "probability": 0.511962890625}, {"start": 4386.71, "end": 4386.97, "word": " of", "probability": 0.114013671875}, {"start": 4386.97, "end": 4387.13, "word": " C", "probability": 0.8798828125}, {"start": 4387.13, "end": 4387.33, "word": " إنها", "probability": 0.843017578125}, {"start": 4387.33, "end": 4387.75, "word": " exist", "probability": 0.6982421875}], "temperature": 1.0}, {"id": 196, "seek": 441282, "start": 4391.04, "end": 4412.82, "text": "إذا صارت عندي هذه زي ما قلنا وهذه هاتين تان بحجله استخدمهم لكل ان أكبر أو ساو كي بدي استخدم هذه كمان و أربط هذه مع هذه و أخلص اللي بديها since fk prime of c exist مين ال K هذه ال K هذه اللي خدتها ال superman بين هذه و هذه عشان ينفع استخدم هذه و هذه و هذه بعد شوية", "tokens": 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0.9130859375}, {"start": 4399.72, "end": 4399.96, "word": " هذه", "probability": 0.85791015625}, {"start": 4399.96, "end": 4400.06, "word": " و", "probability": 0.89453125}, {"start": 4400.06, "end": 4400.66, "word": " أخلص", "probability": 0.969970703125}, {"start": 4400.66, "end": 4400.96, "word": " اللي", "probability": 0.920166015625}, {"start": 4400.96, "end": 4401.48, "word": " بديها", "probability": 0.81640625}, {"start": 4401.48, "end": 4402.14, "word": " since", "probability": 0.58984375}, {"start": 4402.14, "end": 4402.62, "word": " fk", "probability": 0.4166259765625}, {"start": 4402.62, "end": 4402.9, "word": " prime", "probability": 0.64208984375}, {"start": 4402.9, "end": 4403.14, "word": " of", "probability": 0.958984375}, {"start": 4403.14, "end": 4403.4, "word": " c", "probability": 0.74658203125}, {"start": 4403.4, "end": 4403.82, "word": " exist", "probability": 0.52294921875}, {"start": 4403.82, "end": 4404.18, "word": " مين", "probability": 0.712890625}, {"start": 4404.18, "end": 4404.36, "word": " ال", "probability": 0.92529296875}, {"start": 4404.36, "end": 4404.52, "word": " K", "probability": 0.344482421875}, {"start": 4404.52, "end": 4404.96, "word": " هذه", "probability": 0.75146484375}, {"start": 4404.96, "end": 4405.72, "word": " ال", "probability": 0.376953125}, {"start": 4405.72, "end": 4405.94, "word": " K", "probability": 0.81591796875}, {"start": 4405.94, "end": 4406.2, "word": " هذه", "probability": 0.87646484375}, {"start": 4406.2, "end": 4406.36, "word": " اللي", "probability": 0.987060546875}, {"start": 4406.36, "end": 4406.74, "word": " خدتها", "probability": 0.8846435546875}, {"start": 4406.74, "end": 4406.86, "word": " ال", "probability": 0.6005859375}, {"start": 4406.86, "end": 4407.32, "word": " superman", "probability": 0.73583984375}, {"start": 4407.32, "end": 4407.54, "word": " بين", "probability": 0.93310546875}, {"start": 4407.54, "end": 4407.9, "word": " هذه", "probability": 0.85205078125}, {"start": 4407.9, "end": 4408.04, "word": " و", "probability": 0.7529296875}, {"start": 4408.04, "end": 4408.28, "word": " هذه", "probability": 0.7900390625}, {"start": 4408.28, "end": 4408.7, "word": " عشان", "probability": 0.9363606770833334}, {"start": 4408.7, "end": 4409.48, "word": " ينفع", "probability": 0.86517333984375}, {"start": 4409.48, "end": 4410.06, "word": " استخدم", "probability": 0.90478515625}, {"start": 4410.06, "end": 4410.74, "word": " هذه", "probability": 0.92822265625}, {"start": 4410.74, "end": 4411.18, "word": " و", "probability": 0.8701171875}, {"start": 4411.18, "end": 4411.66, "word": " هذه", "probability": 0.8984375}, {"start": 4411.66, "end": 4411.94, "word": " و", "probability": 0.9638671875}, {"start": 4411.94, "end": 4412.18, "word": " هذه", "probability": 0.8232421875}, {"start": 4412.18, "end": 4412.38, "word": " بعد", "probability": 0.923828125}, {"start": 4412.38, "end": 4412.82, "word": " شوية", "probability": 0.8919270833333334}], "temperature": 1.0}, {"id": 197, "seek": 444289, "start": 4414.44, "end": 4442.9, "text": "then مدام fk prime of c exist then if x minus c أكبر من صفر أصغر من دلتا دلتا k طبعا الدلتا هتعتمد على اللي هو ال epsilon نسميها دلتا k لإنها اعتمدت على مين؟ على الكل يعنى then there exists دلتا k بحيث x minus c أصغر من دلتا يعطيني fk of x ناقص fk of c على x minus c اللي هي ناقص fk prime of c أصغر من إبسلون فاهمين هذا؟ مدام fk", "tokens": [19096, 3714, 3215, 10943, 283, 74, 5835, 295, 269, 2514, 550, 498, 2031, 3175, 269, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 11778, 1211, 2655, 995, 11778, 1211, 2655, 995, 350, 23032, 3555, 3615, 995, 32748, 1211, 2655, 995, 8032, 2655, 34268, 2304, 3215, 15844, 13672, 1829, 31439, 2423, 17889, 8717, 38251, 1829, 11296, 11778, 1211, 2655, 995, 350, 5296, 28814, 1863, 11296, 1975, 34268, 2304, 3215, 2655, 15844, 3714, 9957, 22807, 15844, 2423, 28820, 37495, 1863, 7578, 550, 456, 8198, 11778, 1211, 2655, 995, 350, 4724, 5016, 1829, 12984, 2031, 3175, 269, 5551, 9381, 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"word": " دلتا", "probability": 0.8502197265625}, {"start": 4421.7, "end": 4421.8, "word": " k", "probability": 0.445556640625}, {"start": 4421.8, "end": 4422.08, "word": " طبعا", "probability": 0.96728515625}, {"start": 4422.08, "end": 4422.46, "word": " الدلتا", "probability": 0.75445556640625}, {"start": 4422.46, "end": 4423.3, "word": " هتعتمد", "probability": 0.801025390625}, {"start": 4423.3, "end": 4423.64, "word": " على", "probability": 0.8525390625}, {"start": 4423.64, "end": 4424.24, "word": " اللي", "probability": 0.630859375}, {"start": 4424.24, "end": 4424.36, "word": " هو", "probability": 0.92138671875}, {"start": 4424.36, "end": 4424.48, "word": " ال", "probability": 0.83544921875}, {"start": 4424.48, "end": 4424.86, "word": " epsilon", "probability": 0.241455078125}, {"start": 4424.86, "end": 4426.02, "word": " نسميها", "probability": 0.82830810546875}, {"start": 4426.02, "end": 4426.36, "word": " دلتا", "probability": 0.93359375}, {"start": 4426.36, "end": 4426.48, "word": " k", "probability": 0.7763671875}, {"start": 4426.48, "end": 4426.7, "word": " لإنها", "probability": 0.83489990234375}, {"start": 4426.7, "end": 4427.14, "word": " اعتمدت", "probability": 0.950390625}, {"start": 4427.14, "end": 4427.3, "word": " على", "probability": 0.7998046875}, {"start": 4427.3, "end": 4427.66, "word": " مين؟", "probability": 0.5740559895833334}, {"start": 4427.66, "end": 4427.8, "word": " على", "probability": 0.7607421875}, {"start": 4427.8, "end": 4428.16, "word": " الكل", "probability": 0.871826171875}, {"start": 4428.16, "end": 4428.42, "word": " يعنى", "probability": 0.5578206380208334}, {"start": 4428.42, "end": 4429.12, "word": " then", "probability": 0.71630859375}, {"start": 4429.12, "end": 4429.36, "word": " there", "probability": 0.9130859375}, {"start": 4429.36, "end": 4429.66, "word": " exists", "probability": 0.59423828125}, {"start": 4429.66, "end": 4430.04, "word": " دلتا", "probability": 0.83660888671875}, {"start": 4430.04, "end": 4430.26, "word": " k", "probability": 0.958984375}, {"start": 4430.26, "end": 4430.66, "word": " بحيث", "probability": 0.9488525390625}, {"start": 4430.66, "end": 4430.88, "word": " x", "probability": 0.927734375}, {"start": 4430.88, "end": 4431.14, "word": " minus", "probability": 0.98486328125}, {"start": 4431.14, "end": 4431.36, "word": " c", "probability": 0.97021484375}, {"start": 4431.36, "end": 4431.7, "word": " أصغر", "probability": 0.9942626953125}, {"start": 4431.7, "end": 4431.84, "word": " من", "probability": 0.99658203125}, {"start": 4431.84, "end": 4432.46, "word": " دلتا", "probability": 0.9371337890625}, {"start": 4432.46, "end": 4433.38, "word": " يعطيني", "probability": 0.842041015625}, {"start": 4433.38, "end": 4433.92, "word": " fk", "probability": 0.9189453125}, {"start": 4433.92, "end": 4434.14, "word": " of", "probability": 0.86376953125}, {"start": 4434.14, "end": 4434.48, "word": " x", "probability": 0.9716796875}, {"start": 4434.48, "end": 4434.86, "word": " ناقص", "probability": 0.9490966796875}, {"start": 4434.86, "end": 4435.14, "word": " fk", "probability": 0.955810546875}, {"start": 4435.14, "end": 4435.26, "word": " of", "probability": 0.97900390625}, {"start": 4435.26, "end": 4435.38, "word": " c", "probability": 0.88232421875}, {"start": 4435.38, "end": 4435.52, "word": " على", "probability": 0.5927734375}, {"start": 4435.52, "end": 4435.68, "word": " x", "probability": 0.96044921875}, {"start": 4435.68, "end": 4435.86, "word": " minus", "probability": 0.9931640625}, {"start": 4435.86, "end": 4436.14, "word": " c", "probability": 0.953125}, {"start": 4436.14, "end": 4436.7, "word": " اللي", "probability": 0.9404296875}, {"start": 4436.7, "end": 4436.84, "word": " هي", "probability": 0.787109375}, {"start": 4436.84, "end": 4437.16, "word": " ناقص", "probability": 0.996337890625}, {"start": 4437.16, "end": 4437.54, "word": " fk", "probability": 0.943359375}, {"start": 4437.54, "end": 4438.04, "word": " prime", "probability": 0.88330078125}, {"start": 4438.04, "end": 4438.28, "word": " of", "probability": 0.9853515625}, {"start": 4438.28, "end": 4438.48, "word": " c", "probability": 0.9765625}, {"start": 4438.48, "end": 4438.92, "word": " أصغر", "probability": 0.9908447265625}, {"start": 4438.92, "end": 4439.12, "word": " من", "probability": 0.994140625}, {"start": 4439.12, "end": 4439.94, "word": " إبسلون", "probability": 0.768994140625}, {"start": 4439.94, "end": 4440.3, "word": " فاهمين", "probability": 0.927001953125}, {"start": 4440.3, "end": 4441.44, "word": " هذا؟", "probability": 0.4420166015625}, {"start": 4441.44, "end": 4442.38, "word": " مدام", "probability": 0.9488932291666666}, {"start": 4442.38, "end": 4442.9, "word": " fk", "probability": 0.94921875}], "temperature": 1.0}, {"id": 198, "seek": 446485, "start": 4443.62, "end": 4464.86, "text": "prime of c بيساو limit exist إذا حساو limit f of x ناقص f of c بprime على x minus c طبعا كك كله as x بتروح لل c صار exist يعني forever epsilon أكبر من 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"end": 4686.43, "word": " الـ", "probability": 0.777587890625}, {"start": 4686.43, "end": 4686.57, "word": " G", "probability": 0.67626953125}, {"start": 4686.57, "end": 4686.85, "word": " of", "probability": 0.8837890625}, {"start": 4686.85, "end": 4687.15, "word": " C", "probability": 0.9853515625}, {"start": 4687.15, "end": 4687.75, "word": " وزي", "probability": 0.8824869791666666}, {"start": 4687.75, "end": 4687.85, "word": " ما", "probability": 0.9755859375}, {"start": 4687.85, "end": 4688.17, "word": " قلنا", "probability": 0.92041015625}, {"start": 4688.17, "end": 4688.31, "word": " في", "probability": 0.93701171875}, {"start": 4688.31, "end": 4688.73, "word": " الأول", "probability": 0.958740234375}, {"start": 4688.73, "end": 4689.15, "word": " since", "probability": 0.53662109375}, {"start": 4689.15, "end": 4689.43, "word": " C", "probability": 0.93896484375}, {"start": 4689.43, "end": 4689.73, "word": " was", "probability": 0.93408203125}, {"start": 4689.73, "end": 4690.29, "word": " arbitrary", "probability": 0.76708984375}, {"start": 4690.29, "end": 4690.67, "word": " in", "probability": 0.94775390625}, {"start": 4690.67, "end": 4690.91, "word": " G", "probability": 0.5}, {"start": 4690.91, "end": 4691.53, "word": " then", "probability": 0.7197265625}, {"start": 4691.53, "end": 4692.03, "word": " صارت", "probability": 0.9798177083333334}, {"start": 4692.03, "end": 4692.17, "word": " اللي", "probability": 0.794189453125}, {"start": 4692.17, "end": 4692.33, "word": " هي", "probability": 0.708984375}, {"start": 4692.33, "end": 4692.53, "word": " F", "probability": 0.9267578125}, {"start": 4692.53, "end": 4693.03, "word": " بتساوي", "probability": 0.751434326171875}, {"start": 4693.03, "end": 4693.23, "word": " G", "probability": 0.8935546875}, {"start": 4693.23, "end": 4693.51, "word": " على", "probability": 0.90966796875}, {"start": 4693.51, "end": 4693.91, "word": " كل", "probability": 0.99267578125}, {"start": 4693.91, "end": 4694.61, "word": " مين", "probability": 0.879638671875}, {"start": 4694.61, "end": 4695.43, "word": " على", "probability": 0.8798828125}, {"start": 4695.43, "end": 4696.05, "word": " كل", "probability": 0.99560546875}, {"start": 4696.05, "end": 4696.47, "word": " الـ", "probability": 0.5908203125}, {"start": 4696.47, "end": 4696.75, "word": " G", "probability": 0.533203125}, {"start": 4696.75, "end": 4697.73, "word": " وهيك", "probability": 0.65228271484375}, {"start": 4697.73, "end": 4698.19, "word": " بنكون", "probability": 0.739013671875}, {"start": 4698.19, "end": 4698.99, "word": " خلصنا", "probability": 0.9896240234375}, {"start": 4698.99, "end": 4699.71, "word": " النظرية", "probability": 0.9617919921875}, {"start": 4699.71, "end": 4701.63, "word": " وانهينا", "probability": 0.8677734375}, {"start": 4701.63, "end": 4701.77, "word": " ال", "probability": 0.875}, {"start": 4701.77, "end": 4702.13, "word": " section", "probability": 0.80078125}, {"start": 4702.13, "end": 4702.53, "word": " اللي", "probability": 0.97314453125}, {"start": 4702.53, "end": 4702.65, "word": " هو", "probability": 0.978515625}, {"start": 4702.65, "end": 4702.99, "word": " تمانية", "probability": 0.75732421875}, {"start": 4702.99, "end": 4703.33, "word": " اتنين", "probability": 0.9395751953125}, {"start": 4703.33, "end": 4703.71, "word": " وهيك", "probability": 0.8607177734375}, {"start": 4703.71, "end": 4703.95, "word": " بنكون", "probability": 0.913330078125}, {"start": 4703.95, "end": 4704.57, "word": " خلصنا", "probability": 0.99462890625}, {"start": 4704.57, "end": 4705.31, "word": " الحديث", "probability": 0.9866536458333334}, {"start": 4705.31, "end": 4705.43, "word": " اللي", "probability": 0.980224609375}, {"start": 4705.43, "end": 4706.05, "word": " بنتحدثه", "probability": 0.89892578125}, {"start": 4706.05, "end": 4706.13, "word": " في", "probability": 0.958984375}, {"start": 4706.13, "end": 4706.37, "word": " chapter", "probability": 0.473876953125}, {"start": 4706.37, "end": 4706.95, "word": " تمانية", "probability": 0.8582356770833334}, {"start": 4706.95, "end": 4708.21, "word": " وعندنا", "probability": 0.849609375}, {"start": 4708.21, "end": 4708.53, "word": " طبعا", "probability": 0.90869140625}, {"start": 4708.53, "end": 4709.07, "word": " الأسئلة", "probability": 0.971923828125}, {"start": 4709.07, "end": 4709.63, "word": " المطلوبة", "probability": 0.97705078125}, {"start": 4709.63, "end": 4709.91, "word": " هيها", "probability": 0.929931640625}, {"start": 4709.91, "end": 4710.01, "word": " في", "probability": 0.9248046875}, {"start": 4710.01, "end": 4710.37, "word": " نهاية", "probability": 0.88525390625}, {"start": 4710.37, "end": 4710.57, "word": " كل", "probability": 0.91845703125}, {"start": 4710.57, "end": 4710.89, "word": " section", "probability": 0.490478515625}, {"start": 4710.89, "end": 4711.21, "word": " تمانية", "probability": 0.93798828125}, {"start": 4711.21, "end": 4711.39, "word": " واحد", "probability": 0.970703125}, {"start": 4711.39, "end": 4711.77, "word": " وتمانية", "probability": 0.76318359375}, {"start": 4711.77, "end": 4712.17, "word": " اتنين", "probability": 0.9771728515625}, {"start": 4712.17, "end": 4712.93, "word": " وإلى", "probability": 0.9153645833333334}, {"start": 4712.93, "end": 4713.43, "word": " لقاء", "probability": 0.95947265625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4714.2080625, "duration_after_vad": 4625.11750000001}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..98d6cc2950d7c0945cbc61f035afee713a541536
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/TzsvHsJiIFE_postprocess.srt
@@ -0,0 +1,2864 @@
+1
+00:00:11,170 --> 00:00:17,190
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم خمستاشر
+
+2
+00:00:17,190 --> 00:00:25,090
+لمساق تحليل حقيقي اتنين لطلبات وطالبات الجامعة
+
+3
+00:00:25,090 --> 00:00:31,380
+الإسلاميةكلية العلوم قسم الرياضيات المحاضرة اليوم
+
+4
+00:00:31,380 --> 00:00:35,940
+إن شاء الله اللي هي ستكون على جزئين الجزء الأول
+
+5
+00:00:35,940 --> 00:00:40,940
+هنكمل اللي بدناه المرة الماضية اللي هو اللي نكمل
+
+6
+00:00:40,940 --> 00:00:45,100
+اللي هي تطبيقات على الـ Fundamental Theorem of
+
+7
+00:00:45,100 --> 00:00:50,540
+Calculus الجزء الأول هذا التطبيق طبعاً هو هيكون عن
+
+8
+00:00:50,540 --> 00:00:53,880
+evaluation of integrals برضه بدنا فيه المرة
+
+9
+00:00:53,880 --> 00:00:58,220
+الماضية و هنكمله اليوم إن شاء اللهالجزء الثاني من
+
+10
+00:00:58,220 --> 00:01:04,180
+المحاضرة هنتحدث عن اللي هو التكامل أن ندخل
+
+11
+00:01:04,180 --> 00:01:08,620
+لتعاملية التكامل بطريقة غير ال upper sum والlower
+
+12
+00:01:08,620 --> 00:01:15,060
+sum عن طريق حاجة اسمها الرمان sumهذا الآن هو الجزء
+
+13
+00:01:15,060 --> 00:01:19,080
+الثاني الآن بدنا نبدأ في الجزء الأول بس على السريع
+
+14
+00:01:19,080 --> 00:01:22,540
+نطلع على اللي حكيناه المرة الماضية بدنا حكينا عن
+
+15
+00:01:22,540 --> 00:01:26,120
+الـ Fundamental Theorem of Calculus وحكينا عن اللي
+
+16
+00:01:26,120 --> 00:01:30,800
+هو الـ Two Forms إيها أو التفاضل والتكامل زي ما
+
+17
+00:01:30,800 --> 00:01:35,240
+حكينا وتكامل التفاضل Roughly الكلام و بعدين أتينا
+
+18
+00:01:35,240 --> 00:01:38,980
+لبعض الملاحظات وبعض التعريفات وحكينا عن ال
+
+19
+00:01:38,980 --> 00:01:42,780
+evaluation of integralsبدأنا في evaluation of
+
+20
+00:01:42,780 --> 00:01:46,600
+integrals اللي هو اللي بيمثل الجزء الأول من هذه
+
+21
+00:01:46,600 --> 00:01:51,320
+المحاضرة اليوم حكينا عن اللي هو ال integration by
+
+22
+00:01:51,320 --> 00:01:55,480
+parts ال integration by parts حكينا عنه المرة
+
+23
+00:01:55,480 --> 00:02:02,130
+الماضية وشرحناها وقفنا عند اللي هوالـ ال .. ال ..
+
+24
+00:02:02,130 --> 00:02:06,230
+ال .. ال .. ال first substitution form اللي هنبدأ
+
+25
+00:02:06,230 --> 00:02:10,650
+فيها اليوم إن شاء الله الآن ال first substitution
+
+26
+00:02:10,650 --> 00:02:15,310
+form أو اللي هو التكامل بالتعويض عن طريق اللي هي
+
+27
+00:02:15,310 --> 00:02:18,870
+التعويض وهذه طبعا طريقة كنا نستخدمها زي ما
+
+28
+00:02:18,870 --> 00:02:22,670
+استخدمنا اللي هي طريقة ال integration by parts في
+
+29
+00:02:22,670 --> 00:02:27,910
+calculus B أيضا استخدمنا اللي هو التكامل بالتعويض
+
+30
+00:02:27,910 --> 00:02:36,840
+للإيجادأو لعملية إيجاد اللي هي التكامل الآن بدنا
+
+31
+00:02:36,840 --> 00:02:41,720
+نعطي النظرية اللي بتشرع لنا أو نثبت النظرية اللي
+
+32
+00:02:41,720 --> 00:02:46,840
+بتسمح لنا بالتكامل بالتعويض نيجي نطلع لنظريتنا
+
+33
+00:02:46,840 --> 00:02:51,120
+اللي هي ال first substitution theorem نيجي ناخد
+
+34
+00:02:51,120 --> 00:02:55,300
+اللي هو ال J فترة عبارة عن ال close interval Alpha
+
+35
+00:02:55,300 --> 00:03:01,120
+و Betaإن ناخد فاي function من J لعند R have a
+
+36
+00:03:01,120 --> 00:03:04,620
+continuous derivative on J يعني أخدنا الآن يا
+
+37
+00:03:04,620 --> 00:03:09,660
+جماعة فاي عبارة عن function من اللي هي الفترة
+
+38
+00:03:09,660 --> 00:03:17,090
+Alpha و Betaلعين بـ R وفرضنا إن هذه الدالة اللي هي
+
+39
+00:03:17,090 --> 00:03:22,050
+Phi ال derivative إلها موجودة ونفسها إشمالها
+
+40
+00:03:22,050 --> 00:03:26,690
+continuous إذا فرضنا إن اللي هو الـ Phi have a
+
+41
+00:03:26,690 --> 00:03:31,230
+continuous derivative on the interval J اللي
+
+42
+00:03:31,230 --> 00:03:35,080
+سمناها ليه Alpha و Betaلأن لو كان في عندي function
+
+43
+00:03:35,080 --> 00:03:39,300
+F is continuous on any interval I containing Phi
+
+44
+00:03:39,300 --> 00:03:46,160
+of J لأن فرضنا أن F دالة على I تحتوي Phi of J عساس
+
+45
+00:03:46,160 --> 00:03:51,180
+إن بعد شوية هعرّق .. هيلزمني اللي هو composition
+
+46
+00:03:51,180 --> 00:03:55,160
+of two functions عشان هيك أنا باخد ال F عبارة عن
+
+47
+00:03:55,160 --> 00:04:00,840
+function من I لعند مين؟ لعند ال R إيش ال I هذه؟
+
+48
+00:04:00,840 --> 00:04:08,290
+هذه I intervalبتحتوي اللي هي مين الـ Phi of Jاللي
+
+49
+00:04:08,290 --> 00:04:13,790
+عندى، يعني هيصير عندى بناء عليها هيصير عندى F of
+
+50
+00:04:13,790 --> 00:04:20,270
+Phi of I T فيه اللي هي الـ J عبارة عن قيمة معرفة
+
+51
+00:04:20,270 --> 00:04:24,790
+عشان تكون ال composition معرفة، إذا الآن باختصار
+
+52
+00:04:24,790 --> 00:04:28,010
+Phi اللي هي ال derivative اللي موجودة و ال
+
+53
+00:04:28,010 --> 00:04:31,670
+derivative continuous و ال function F small هذي is
+
+54
+00:04:31,670 --> 00:04:35,510
+continuous و هنا ال interval I، thenالان نجي
+
+55
+00:04:35,510 --> 00:04:40,050
+للنتيجة اللى احنا بنمارسها عمليا دائما اللى هو
+
+56
+00:04:40,050 --> 00:04:46,790
+بكون عندى ال integration من Alpha ل Beta لF of Phi
+
+57
+00:04:46,790 --> 00:04:53,960
+of T Phi prime of TDT احنا بندعي بتساوي كنا نيجي
+
+58
+00:04:53,960 --> 00:04:58,100
+ايش نسوي ناخد هذه اللي هي نعوض عن Phi of T ب X
+
+59
+00:04:58,100 --> 00:05:03,360
+بناء عليها بيصير عبارة عن هذا ال integration F of
+
+60
+00:05:03,360 --> 00:05:09,920
+X و Phi prime of T بنعوض عن Phi of T ب X فبيصير
+
+61
+00:05:09,920 --> 00:05:14,200
+عند Phi prime of T DT هو عبارة عن مين DX كنا هيك
+
+62
+00:05:14,200 --> 00:05:17,890
+نسوي في ال calculusالآن نيجي نقول DX بسوء Phi
+
+63
+00:05:17,890 --> 00:05:22,670
+prime T DT أو DX على DT بسوء Phi prime of T ونشيل
+
+64
+00:05:22,670 --> 00:05:26,630
+Phi prime of T DT ونحط مكان هي شمالها DX حدود ال
+
+65
+00:05:26,630 --> 00:05:30,110
+integration كانت من Alpha ل Beta يعني لما كانت T
+
+66
+00:05:30,110 --> 00:05:33,350
+بAlpha بصير X اللي هي Phi of T اللي هي Phi of
+
+67
+00:05:33,350 --> 00:05:39,190
+Alpha بتروح لمين؟ لأ اللي هي Phi of مين؟ Phi of
+
+68
+00:05:39,190 --> 00:05:45,180
+Betaليش؟ لأنه لما كانت T بساوي Beta أكيد الـ X
+
+69
+00:05:45,180 --> 00:05:48,760
+اللي هي Phi of T بتساوي الـ X بتساوي Phi of T، الـ
+
+70
+00:05:48,760 --> 00:05:53,640
+X بتساوي Phi of Beta إذن نظريتنا هذه اللي أمامنا
+
+71
+00:05:53,640 --> 00:05:59,160
+هي نظرية إحنا يعني استعملناها أو بنستعملها عادة في
+
+72
+00:05:59,160 --> 00:06:02,600
+اللي هو إيجاد الـ integration وإحدى الطرق لإيجاد
+
+73
+00:06:02,600 --> 00:06:07,860
+الـ integration فعندي
+
+74
+00:06:07,860 --> 00:06:14,140
+الآنهذه الآن نظريتنا، بدنا نبرهن هذه النظرية ونشوف
+
+75
+00:06:14,140 --> 00:06:18,840
+كيف نبرهنها، برهانها بسيط، الآن هي اللي بدنا
+
+76
+00:06:18,840 --> 00:06:23,280
+نبرهنه، خلّينا نشوف كيف البرهانة وكيف نبرهن
+
+77
+00:06:23,280 --> 00:06:26,380
+الكتاب،
+
+78
+00:06:26,380 --> 00:06:32,520
+عنده يجينا عرفنا، بدنا نعرف function F، لأن عرش
+
+79
+00:06:32,520 --> 00:06:35,990
+function Fتنسوش هذا الـ Function ايش مالها يا
+
+80
+00:06:35,990 --> 00:06:40,070
+جماعة؟ Continuous وهذا بتعني كتير بالنسبة للـ
+
+81
+00:06:40,070 --> 00:06:43,210
+Fundamental Theorem أعرف الـ Function F من الـ
+
+82
+00:06:43,210 --> 00:06:50,310
+Interval I لعند مين R F Capital أعرف الـ F Capital
+
+83
+00:06:50,310 --> 00:06:59,070
+F of U بساوة الـ Integration من اللي هو عند الـ I
+
+84
+00:06:59,070 --> 00:07:04,870
+بتحتوي مين الـ Phi of J يعني هي الـ Interval Iهي
+
+85
+00:07:04,870 --> 00:07:08,870
+الـ interval I وفي داخلها Phi of J Phi of J طبعاً
+
+86
+00:07:08,870 --> 00:07:12,330
+في عند Phi of Alpha لعند Phi of Beta لو كانت اللي
+
+87
+00:07:12,330 --> 00:07:15,590
+هي Alpha أكبر من Beta الاخرى Phi of J اللي هم
+
+88
+00:07:15,590 --> 00:07:19,990
+مفترضينها احنا وين في داخل الفترة اللي أمامي الآن
+
+89
+00:07:19,990 --> 00:07:24,050
+بتاخد ال integration تعرفه من عند Phi of Alpha
+
+90
+00:07:24,050 --> 00:07:29,980
+لعند main U الـ U المتغيرةاللي هتكون وين موجودة في
+
+91
+00:07:29,980 --> 00:07:35,240
+داخل الـ I اللي بتحتوي الـ Phi of G إذا عرفت
+
+92
+00:07:35,240 --> 00:07:37,440
+function f of u بيستوي ال integration من Phi of
+
+93
+00:07:37,440 --> 00:07:42,780
+Alpha ثابت Phi of Alpha يا جماعة لعند U لمين؟ للf
+
+94
+00:07:42,780 --> 00:07:49,410
+of x dxلاحظ هذه الدالة اللي عندي اللي عرفتها من
+
+95
+00:07:49,410 --> 00:07:53,830
+الـ Fundamental theorem بما أن F is continuous إذا
+
+96
+00:07:53,830 --> 00:07:58,810
+هذا كله الآن اللي هو صار function في U عبارة عن
+
+97
+00:07:58,810 --> 00:08:03,990
+differentiable ومش هيك كمان و F prime of U هتساوي
+
+98
+00:08:03,990 --> 00:08:11,090
+مين؟ اللي هي الدالة F of Uإذا من الـ Fundamental
+
+99
+00:08:11,090 --> 00:08:15,350
+theorem بما أن F is continuous إذا F prime of U
+
+100
+00:08:15,350 --> 00:08:20,210
+بتساوي F of U اللي هي by Fundamental theorem of
+
+101
+00:08:20,210 --> 00:08:23,370
+calculus إذا by Fundamental theorem of calculus فF
+
+102
+00:08:23,370 --> 00:08:27,710
+of X .. F of U طبعا هذه صيحوها بسوء ال integration
+
+103
+00:08:27,710 --> 00:08:32,200
+من C .. C اللي هو احنا بسميه همين هياللي هي Phi of
+
+104
+00:08:32,200 --> 00:08:35,820
+Alpha مابديش أخبركم في التسميات على طول من Phi of
+
+105
+00:08:35,820 --> 00:08:40,140
+Alpha لعند مين لعنديه إذا اللي سويته أنا بس لحتى
+
+106
+00:08:40,140 --> 00:08:46,340
+الآن إن عرفت دالة اللي هي ال func ال F capital هذه
+
+107
+00:08:46,340 --> 00:08:53,760
+ال F capital عرفتها من I من I لعند R by F of U
+
+108
+00:08:53,760 --> 00:08:58,060
+بسوء ال integration من C ل U F of X DX for U
+
+109
+00:08:58,060 --> 00:09:03,310
+element من in ال interval Iالان قاعد بحضر للي
+
+110
+00:09:03,310 --> 00:09:08,630
+بديها and now consider the function H من J لعند R
+
+111
+00:09:08,630 --> 00:09:12,690
+بعد ما عرفت ال function F هذه اللي أمامي بدي
+
+112
+00:09:12,690 --> 00:09:18,330
+أعرفلكم دالة تانية الدالة اللي بدي أعرفها يا جماعة
+
+113
+00:09:18,330 --> 00:09:26,530
+هي عبارة عن HH هذه بدي أعرفها من J لعند R شوف كيف
+
+114
+00:09:26,530 --> 00:09:30,510
+بدي أعرفها بطريقة اللي هي تخدمني بعد شوية للوصول
+
+115
+00:09:30,510 --> 00:09:36,730
+للنتيجة اللي بديها اللي هي H of T بدي أعرفها H of
+
+116
+00:09:36,730 --> 00:09:46,170
+T بساوية F capital هذه اللي عرفتها of Phi of T Phi
+
+117
+00:09:46,170 --> 00:09:52,220
+of Tالان جهة دي اليمين هي الفترة Alpha و Beta Phi
+
+118
+00:09:52,220 --> 00:09:57,740
+of Tاللي هي إذا T من في J Phi of T معرّفة على الـJ
+
+119
+00:09:57,740 --> 00:10:03,440
+الـJ Phi of T إشمالها معرّفة على الـJ الـF إلها
+
+120
+00:10:03,440 --> 00:10:07,640
+معرّفة لإن الـF domainها I اللي هو اللي بيحتوى Phi
+
+121
+00:10:07,640 --> 00:10:11,360
+of J يعني فعلا Phi of T موجودة في Phi of J اللي هي
+
+122
+00:10:11,360 --> 00:10:14,600
+موجودة في مين في I إذا المعرّفة اللي دالها H of T
+
+123
+00:10:14,600 --> 00:10:23,370
+بيساوي Phi of I of T طيبالأن الـ F اتفاجنا للـ F
+
+124
+00:10:23,370 --> 00:10:27,030
+هذه إنها differentiable الـ F كابيتال والـ Phi
+
+125
+00:10:27,030 --> 00:10:29,470
+differentiable ليش differentiable؟ لأن Phi prime
+
+126
+00:10:29,470 --> 00:10:32,390
+موجودة و continuous إذا بقدر .. هي أفاضل هذه
+
+127
+00:10:32,390 --> 00:10:38,340
+الدالة إذا بقدر أقول إنه عند الـ H primeof T
+
+128
+00:10:38,340 --> 00:10:44,340
+بيساوي F' Phi of T بتشيرن رول طبعا يا جماعة في Phi
+
+129
+00:10:44,340 --> 00:10:51,460
+prime of T فإذا تفاضل ال H' هو F' في Phi prime of
+
+130
+00:10:51,460 --> 00:10:59,000
+T زي ما احنا ذكرين في برهان النظرية هان الآن عندي
+
+131
+00:10:59,000 --> 00:11:03,540
+ايضا احنا قلنا ال F prime of U ايش بتساوي F of U
+
+132
+00:11:03,540 --> 00:11:08,920
+وقلنا ليش السببالان لو اجينا كل هذا تحضير للي
+
+133
+00:11:08,920 --> 00:11:13,980
+بديها بعد شوية المعلومات هذه الان عندي احسبلي H of
+
+134
+00:11:13,980 --> 00:11:22,380
+Alpha H of Alpha من هذه H of Alpha اكيد كلكم شاف
+
+135
+00:11:22,380 --> 00:11:29,960
+ان H of Alpha بتساوي عوض بتساوي Fof Phi of Alpha
+
+136
+00:11:29,960 --> 00:11:33,560
+صحيه يا جماعة ويساوي F of Phi of Alpha طب إيش
+
+137
+00:11:33,560 --> 00:11:37,980
+تعريف F of U؟ هي عبارة عن ال integration من Phi of
+
+138
+00:11:37,980 --> 00:11:43,520
+Alpha لعند U U أنا الآن إيش هي؟ اسمها Uاللي هو 5
+
+139
+00:11:43,520 --> 00:11:46,420
+Alpha إذا من 5 Alpha ل 5 Alpha يعني ال integration
+
+140
+00:11:46,420 --> 00:11:51,100
+إيش هيساوي هذا بساوي سفر إذا أتشوف Alpha فعلا إيش
+
+141
+00:11:51,100 --> 00:11:55,200
+بتساوي .. بتساوي إيش .. بتساوي سفر إذا تلت حاجات
+
+142
+00:11:55,200 --> 00:11:59,860
+الآن عرفت ال F من I ل عند R بالطريقة اللي أمامي
+
+143
+00:12:00,190 --> 00:12:05,030
+وجدت أن F' بيساوي F of U الشغل الثاني عرفت H of T
+
+144
+00:12:05,030 --> 00:12:08,530
+بيساوي F of Phi of T اللي هو F is differentiable,
+
+145
+00:12:08,590 --> 00:12:11,950
+Phi is differentiable إذا نفسي H is differentiable
+
+146
+00:12:11,950 --> 00:12:14,850
+و ال derivative إليها إيه الشمال هذه بيساوي اللي
+
+147
+00:12:14,850 --> 00:12:19,670
+أمامي و الشغل الثاني اللي حصلنا عليها أن H of
+
+148
+00:12:19,670 --> 00:12:25,010
+Alpha إيش هيساوي يا شباب؟ هو يساوي 0 نيجي الآن
+
+149
+00:12:25,010 --> 00:12:31,250
+بدنا نوصل لمين إحنا؟أحنا هدفنا يا جماعة اللي هو
+
+150
+00:12:31,250 --> 00:12:38,310
+هدفنا سامحونا على اللوح الصغير اللوح هدفنا هو ال
+
+151
+00:12:38,310 --> 00:12:47,210
+integration من Alpha لعند Beta F of Phi of T Phi
+
+152
+00:12:47,210 --> 00:12:54,670
+prime of T dt بساوة ال integration لل F of XDX من
+
+153
+00:12:54,670 --> 00:12:59,290
+Phi of Alpha لعين Phi of Beta هذا اللي بدنا نثبته
+
+154
+00:12:59,290 --> 00:13:09,190
+شوف كيف بدنا نصل لهذا اللي هو المطلوب نيجي
+
+155
+00:13:09,190 --> 00:13:16,090
+لهو ال integration اللي قبلنا هذا اللي هو الطرف
+
+156
+00:13:16,090 --> 00:13:20,580
+اللي احنا بدنا نثبته بساوى هذا الطرفهذا الطرف اللي
+
+157
+00:13:20,580 --> 00:13:23,340
+أنا ساويه هذا، نبدأ بهذا الطرف اللي هنا ونبنع
+
+158
+00:13:23,340 --> 00:13:26,920
+المعلومات ونحصل على اللي بدناه بكل سهولة الآن ال
+
+159
+00:13:26,920 --> 00:13:29,920
+integration من Alpha لعين ال Beta F of five T five
+
+160
+00:13:29,920 --> 00:13:35,620
+prime of T DT بتساوي الان ال F هذه في الواقع مين
+
+161
+00:13:35,620 --> 00:13:41,850
+هي؟ هذه هي عبارة عن F primeإذا صار عندي الآن هذا
+
+162
+00:13:41,850 --> 00:13:45,790
+المقدار هو عبارة عن f prime of five a t five prime
+
+163
+00:13:45,790 --> 00:13:51,350
+a شماله of t يعني وكأنني مين بفاضل أنا بفاضل كل
+
+164
+00:13:51,350 --> 00:13:58,890
+هذا المقدار طلع مين هو h prime of t وكل أموره حلوة
+
+165
+00:13:58,890 --> 00:14:05,170
+ومحترمة ال fاللي هي continuous والـ Phi prime
+
+166
+00:14:05,170 --> 00:14:09,090
+continuous معطينيها إذاً هذه صارت الـ H' كلها يشمع
+
+167
+00:14:09,090 --> 00:14:11,970
+لها continuous إذا ال integration من Alpha ل Beta
+
+168
+00:14:11,970 --> 00:14:17,390
+لH' of T اللي هو ال integration بـ cancel ال
+
+169
+00:14:17,390 --> 00:14:19,990
+differentiation اللي هي الجزء الأول من ال
+
+170
+00:14:19,990 --> 00:14:22,790
+fundamental theorem of calculus يا جماعة فبيصير
+
+171
+00:14:22,790 --> 00:14:29,910
+إيش بيساوي الجواب H of Beta ناقص H of mean of
+
+172
+00:14:29,910 --> 00:14:33,960
+Alphaإذن صار عندى الان h of alpha قبل شوية شهية
+
+173
+00:14:33,960 --> 00:14:36,720
+نفكرة و كده لسه كتبه إنها إيش بتساوي سفر إذا صار
+
+174
+00:14:36,720 --> 00:14:41,860
+المقدار هذا كله اللي أنا بديه إيش صار بيساوي h of
+
+175
+00:14:41,860 --> 00:14:47,720
+b إذا اللي أثبتته تقريبا عندي خلصت أثبتت إن ال
+
+176
+00:14:47,720 --> 00:14:54,080
+integration ال layأمامي هذا كله بيساوي مين؟ H of B
+
+177
+00:14:54,080 --> 00:15:01,480
+خلّينا نحسب H of B H of T احنا F of Phi of T إذا H
+
+178
+00:15:01,480 --> 00:15:08,220
+of B بيساوي F of Phi of Beta H of Beta بيساوي F of
+
+179
+00:15:08,220 --> 00:15:14,040
+Phi of Beta الآن ما يساوي؟الـ integration .. ال
+
+180
+00:15:14,040 --> 00:15:17,260
+integration سبوكوا من ال D لأن أنا ماستخدمش الرموز
+
+181
+00:15:17,260 --> 00:15:23,040
+هذه إيش هذا بيساوي؟ بيصير عند F .. F اللي هو of
+
+182
+00:15:23,040 --> 00:15:28,260
+Phi of B حسب التعريف F of U هاي و أماني بيساوي ال
+
+183
+00:15:28,260 --> 00:15:37,600
+integration من Phi of Alpha لعن Phi of Beta F of X
+
+184
+00:15:37,600 --> 00:15:45,960
+DXوهو هذا المطلوب صار عند ال integration ل .. اللي
+
+185
+00:15:45,960 --> 00:15:49,600
+هي f of x dx من five of alpha لعند five of beta
+
+186
+00:15:49,600 --> 00:15:54,460
+اللي هو h of b بساوي اللي هو ال integration اللي
+
+187
+00:15:54,460 --> 00:16:02,040
+أمامي وهو المطلوب طيب نيجي الآن للنظرية الثانية
+
+188
+00:16:02,040 --> 00:16:08,740
+النظرية الثانية اللي هي second substitution
+
+189
+00:16:08,740 --> 00:16:20,020
+theoremاللي هي .. أيضًا بنستخدمها وحنشوف إيش اللي
+
+190
+00:16:20,020 --> 00:16:26,260
+هي هذا النظرية وكيف انبرهن النظرية والبرهان برضه
+
+191
+00:16:26,260 --> 00:16:33,080
+مش صعب أو البرهان اللي هو سهل هنشوف ال second
+
+192
+00:16:33,080 --> 00:16:36,960
+substitution theorem بتقول ما يلي عند في function
+
+193
+00:16:38,340 --> 00:16:42,180
+فاي من جي لعين بار جي هي نفس الفترة اللي .. الفترة
+
+194
+00:16:42,180 --> 00:16:45,700
+اللي احنا حكينا عنها اللي هي عبارة عن Alpha و Beta
+
+195
+00:16:45,700 --> 00:16:49,980
+بدنا نفترض ان الفاي هذه have a continuous
+
+196
+00:16:49,980 --> 00:16:57,700
+derivativeبرضه نفس اللي هي المعتل أولاني ونفترض I
+
+197
+00:16:57,700 --> 00:17:02,700
+عبارة عن interval بتحتوي Phi of J نفس المعتل في
+
+198
+00:17:02,700 --> 00:17:07,220
+النظرية السابقة الآن المعتل جديد بدنا نفترض أنه
+
+199
+00:17:07,220 --> 00:17:12,160
+فيه function ψ من I لعند Rبـ a function اللي هو
+
+200
+00:17:12,160 --> 00:17:16,740
+inverse لـ mean اللي هي الـ Phi يعني عندي Phi
+
+201
+00:17:16,740 --> 00:17:24,140
+بشروط النظرية اللي فاتت من J لعند مين لعند R وعندي
+
+202
+00:17:24,140 --> 00:17:29,800
+ب Psi من عند I لعند R ومفترضين أنه بPsi هي ال
+
+203
+00:17:29,800 --> 00:17:33,940
+inverse ل mean للـ Phi يعني Phi composite بPsi
+
+204
+00:17:35,340 --> 00:17:39,940
+بساومين الـ identity function أو Psi composite الـ
+
+205
+00:17:39,940 --> 00:17:45,960
+Phi عبارة عن ال identity function وكل اللي هو عندى
+
+206
+00:17:45,960 --> 00:17:53,460
+مفترضين ان Phi of J subset من مين من الـ I عشان
+
+207
+00:17:53,460 --> 00:18:00,680
+يكون اللي هو ال composition معرف احنا
+
+208
+00:18:08,270 --> 00:18:15,850
+صارت بـ Psi هي ال inverse لـ Phi و F برضه نفس
+
+209
+00:18:15,850 --> 00:18:20,230
+المعطيات الفاترة continuous on I إذا ما يعني، إذا
+
+210
+00:18:20,230 --> 00:18:25,190
+يعني اللي بحكيه و كأنه نفس شروط النظرية السابقة بس
+
+211
+00:18:25,190 --> 00:18:30,190
+اللي أنضفنا إن الـ Phi اللي عندنا في هذه الحالة
+
+212
+00:18:30,190 --> 00:18:35,220
+فيه إلها inverseفي الها inverse فبتعطيني مجال
+
+213
+00:18:35,220 --> 00:18:39,900
+للتحرك أكثر من الأولى الألهة دي بتفترضش أنه في
+
+214
+00:18:39,900 --> 00:18:42,900
+الها inverse وبنبدأ بنعوض زي ما عوضنا قبل ايش
+
+215
+00:18:42,900 --> 00:18:48,580
+النتيجة طيب النتيجة هي ما يلي اللي هو إذا ال
+
+216
+00:18:48,580 --> 00:18:56,560
+integration أبو حسين ازيحه بس نجاعي شوية
+
+217
+00:19:03,530 --> 00:19:21,050
+النص اللي لدك على الحيط أصلا السلام
+
+218
+00:19:21,050 --> 00:19:22,150
+عليكم السلام عليكم
+
+219
+00:19:41,080 --> 00:19:43,960
+خلاص ساعة سبعة يا عزيزي خلاص خلاص
+
+220
+00:19:46,210 --> 00:19:50,670
+إذا الآن ال .. ال .. ال .. ال .. second
+
+221
+00:19:50,670 --> 00:19:54,290
+substitution theorem نفس شروط اللي هو ال fair
+
+222
+00:19:54,290 --> 00:19:58,590
+substitution theorem بس الآن اللي هيضفنا عليها أنه
+
+223
+00:19:58,590 --> 00:20:02,150
+بـ Psi عندي فرضنا أنه في عندي Psi function من I
+
+224
+00:20:02,150 --> 00:20:07,270
+لعند R هي عبارة عن ال inverse لمين لفاي بناء ..
+
+225
+00:20:07,270 --> 00:20:12,990
+بناء عليه هيصير ال integration من Alpha لعند BetaF
+
+226
+00:20:12,990 --> 00:20:19,230
+of Phi of T DT لأن مش ظاهرة عندنا هنا مين الـ
+
+227
+00:20:19,230 --> 00:20:23,650
+derivative لمين لإي اللي هي الـ Phi بالرغم من هيك
+
+228
+00:20:23,650 --> 00:20:27,470
+هيطلع عندى بساوة ال integration F of X ب Phi prime
+
+229
+00:20:27,470 --> 00:20:31,810
+of X DX اللي هو عندى من Phi of Alpha لعند مين؟
+
+230
+00:20:31,810 --> 00:20:33,770
+لعند Phi of Beta
+
+231
+00:20:36,860 --> 00:20:42,520
+الان نشوف اللي هو كيف انبرهن نظريتنا خلينا نكتب
+
+232
+00:20:42,520 --> 00:20:46,800
+هذه على جهة عشان نعرف احنا لوين رايحين ال
+
+233
+00:20:46,800 --> 00:20:55,880
+integration من Alpha لعين Beta F of Phi of T dt
+
+234
+00:20:55,880 --> 00:21:08,520
+بساوة ال integration لPsi of Alpha F ofأو F of X
+
+235
+00:21:08,520 --> 00:21:21,440
+Phi prime of .. Psi prime of X DX Phi prime of X
+
+236
+00:21:21,440 --> 00:21:27,600
+DX من Phi of Alpha عن
+
+237
+00:21:27,600 --> 00:21:36,060
+Phi of Beta دعونا نشوف كيف .. نيجي نشوف البرهانجرب
+
+238
+00:21:36,060 --> 00:21:42,560
+انت لحالك عوض اللي هو عشان تشوف منطقية النظرية زي
+
+239
+00:21:42,560 --> 00:21:49,880
+ما كنا نعوض في ال calculus عوض عن X ب Phi of T ها
+
+240
+00:21:49,880 --> 00:21:55,540
+هيطلع عندك اللي هو في النهاية DT هو عبارة عن كل
+
+241
+00:21:55,540 --> 00:21:59,890
+هذهلو عوضت طبعاً باستخدام اللي هو العلاقة بين ال
+
+242
+00:21:59,890 --> 00:22:03,170
+.. ال .. ال inverse اللي هي الـ Psi إنها inverse
+
+243
+00:22:03,170 --> 00:22:07,210
+على Phi هتحصل على اللي هو .. اللي هو كل هذا
+
+244
+00:22:07,210 --> 00:22:12,750
+المقدار هو هيطلع مين هو دي T و هتسير بدل Alpha Phi
+
+245
+00:22:12,750 --> 00:22:15,550
+of Alpha و Beta Phi of Beta زي ما أنتوا عارفين
+
+246
+00:22:15,550 --> 00:22:19,490
+لأنه لما كانت T بتساوية Alpha طلعت اللي هي Phi of
+
+247
+00:22:19,490 --> 00:22:21,970
+T لعوضة مكانها اللي هي Phi of Alpha و التانية
+
+248
+00:22:21,970 --> 00:22:29,420
+هتطلع Phi of Beta طب نيجي الآن لبرهان النظريةالان
+
+249
+00:22:29,420 --> 00:22:34,860
+عندى اول حاجة five prime of T بعطينا اياها اشمالها
+
+250
+00:22:34,860 --> 00:22:39,660
+لا تساوى سفر طبعا هذا لزوم لزوم ان تكون ال inverse
+
+251
+00:22:39,660 --> 00:22:44,900
+موجودة five prime of T لا تساوى سفر يعنى الان five
+
+252
+00:22:44,900 --> 00:22:49,180
+prime of T يا اكبر من سفر يا اصغر من سفرعندي
+
+253
+00:22:49,180 --> 00:22:52,680
+المنطق اللي هيكون عندي اللي هي strictly increasing
+
+254
+00:22:52,680 --> 00:22:55,860
+أو strictly decreasing على المنطقة اللي هي فيها
+
+255
+00:22:55,860 --> 00:23:00,060
+إذا في عندى بمعنى آخر strictly monotone مدام
+
+256
+00:23:00,060 --> 00:23:04,940
+strictly monotone إذا ال inverse إلها موجود و في
+
+257
+00:23:04,940 --> 00:23:08,900
+بتساوي في inverse زي ما هو معطينا إياها طبعا إحنا
+
+258
+00:23:08,900 --> 00:23:14,410
+معطينا ال فيالـ Phi مش differentiable بس Phi مش
+
+259
+00:23:14,410 --> 00:23:17,990
+differentiable اللي هو ال derivative موجودة و
+
+260
+00:23:17,990 --> 00:23:22,310
+الاشمالها continuous طيب لان بما انه اللي هي Phi
+
+261
+00:23:22,310 --> 00:23:27,850
+prime exist إذا بنظرية أخدناها اللي هي 6 1 9 هتكون
+
+262
+00:23:27,850 --> 00:23:32,170
+ال Phi prime existوبتساوي واحد على في برايم في
+
+263
+00:23:32,170 --> 00:23:36,350
+مين؟ في بساي كمان مرة يا جماعة أذكركم في النظرية
+
+264
+00:23:36,350 --> 00:23:41,410
+الآن عندى مدامة بساي بساوي في انفرس والفي نفسها
+
+265
+00:23:41,410 --> 00:23:45,450
+عبارة عن differentiable هتكون ال inverse اللي هي
+
+266
+00:23:45,450 --> 00:23:48,910
+بساي is differentiable وال derivative اللي هي بساي
+
+267
+00:23:48,910 --> 00:23:53,490
+برايم هي عبارة عن واحد على في برايم ماله composite
+
+268
+00:23:53,490 --> 00:23:58,400
+بساياللي هي .. أو مش هيك هتطلع .. هتطلع continuous
+
+269
+00:23:58,400 --> 00:24:01,500
+ليش continuous؟ لأنه أصلا مافيش أسفار في المقام
+
+270
+00:24:01,500 --> 00:24:05,100
+أكيد وعند Phi prime نفسها Phi prime نفسها
+
+271
+00:24:05,100 --> 00:24:08,520
+continuous ماتينياها و ب Psi is continuous لأنها
+
+272
+00:24:08,520 --> 00:24:11,800
+أصلا differentiable فهتطلع عند اللي ب Psi prime
+
+273
+00:24:11,800 --> 00:24:17,180
+برضه مالها is continuous إذن اللي استنتجناه الآن
+
+274
+00:24:17,180 --> 00:24:22,590
+أن ال inverse function is continuous وقيمتهاالـ
+
+275
+00:24:22,590 --> 00:24:26,310
+Derivative إليها هي عبارة عن واحد على Psi Prime في
+
+276
+00:24:26,310 --> 00:24:31,890
+Phi Prime في مين؟ في Psi نشوف الآن بدنا نعرف اللي
+
+277
+00:24:31,890 --> 00:24:36,850
+هو بأسلوب مشابه قبل بشوية أنه نعرف دوال بحيث أنه
+
+278
+00:24:36,850 --> 00:24:41,810
+لما نيجي اللي هو ناخده تبقى derivative لشيء سهل
+
+279
+00:24:41,810 --> 00:24:45,210
+إيجاده ولمّا ناخده له ال integration يطلع اللي هو
+
+280
+00:24:45,210 --> 00:24:48,350
+نفس الدالة عند نقطة الأولى نقصه النقطة الثانية
+
+281
+00:24:48,350 --> 00:24:50,950
+اللي هو باستعماله في أنظم التلفيرموفكالكلاس أيش
+
+282
+00:24:50,950 --> 00:24:55,480
+اللي بقوله؟ خلّيني نشوفهاللي هنعرّف ليها جمعة جيه
+
+283
+00:24:55,480 --> 00:24:59,360
+من جيه لعند R اللي هي عبارة علّف ليها أنها تكون
+
+284
+00:24:59,360 --> 00:25:02,960
+إيه شمالها Anti-derivative لل continuous function
+
+285
+00:25:02,960 --> 00:25:06,500
+of composite phiF composite Phi continuous؟ أه
+
+286
+00:25:06,500 --> 00:25:09,440
+continuous لأن الـ Phi is continuous قلنا ال
+
+287
+00:25:09,440 --> 00:25:12,160
+derivative إليها continuous كمان مش كايكوا بس و ال
+
+288
+00:25:12,160 --> 00:25:16,340
+F معطينا إليها continuous فلمّا أقول إن عرف G
+
+289
+00:25:16,340 --> 00:25:19,180
+هتكون antiderivative لمين هذه طب هدي إليها
+
+290
+00:25:19,180 --> 00:25:21,320
+antiderivative؟ أه مدام continuous و المرة اللي
+
+291
+00:25:21,320 --> 00:25:23,260
+فاتت قولنا ده كانت الدالة continuous على طول فيه
+
+292
+00:25:23,260 --> 00:25:26,640
+إليها antiderivative إيش يعني؟ يعني ال G prime
+
+293
+00:25:26,640 --> 00:25:33,270
+هتكون مين؟ ال F composite Phi طيبالآن دي إذا مدام
+
+294
+00:25:33,270 --> 00:25:37,130
+اللي هي الـ G Antiderivative للـ F Composite Phi
+
+295
+00:25:37,130 --> 00:25:40,530
+إذا الـ G' Exists إذا الـ G Differentiable و لو
+
+296
+00:25:40,530 --> 00:25:42,690
+بصي Differentiable إذا الـ Composition اللي هو إيش
+
+297
+00:25:42,690 --> 00:25:47,870
+برضه هيطلع Differentiableأيش يعني طيب .. طب و إيش
+
+298
+00:25:47,870 --> 00:25:50,950
+يعني الـ differentiable؟ ها .. هالـ gate هيوصّلني
+
+299
+00:25:50,950 --> 00:25:54,290
+لإن Decomposite Phi Prime of X ده وجود الـ
+
+300
+00:25:54,290 --> 00:25:56,970
+derivative بنعرف أنه وجود الـ derivative هي عبارة
+
+301
+00:25:56,970 --> 00:26:01,610
+عن D Prime of Psi of X Psi Prime of X اللي هي
+
+302
+00:26:01,610 --> 00:26:07,600
+Chain Rule استخدام الـ Chain Rule ويساوي لأنقلنا
+
+303
+00:26:07,600 --> 00:26:11,480
+جي برايم هي مين الـ F composite في إذا بشيل الجي
+
+304
+00:26:11,480 --> 00:26:15,320
+برايم و بحط مكانها F composite إيش يا جماعة في في
+
+305
+00:26:15,320 --> 00:26:19,840
+بساي of X اللي هو هيها F composite .. هي دي بدلها
+
+306
+00:26:19,840 --> 00:26:24,720
+F composite في of بساي of X في بساي برايم من of X
+
+307
+00:26:24,720 --> 00:26:32,120
+و يساوي F of اللي هو في composite بساي of X في
+
+308
+00:26:32,120 --> 00:26:37,570
+بساي برايم من of Xكتبتها بس على صورة هو اللي هي
+
+309
+00:26:37,570 --> 00:26:41,510
+فكّت ال composition إيه الآن؟ ليش عملت هيك؟ عشان
+
+310
+00:26:41,510 --> 00:26:44,530
+أسهل عليكم و أقولكم أحنا بيقولوا Psi أشملن ال
+
+311
+00:26:44,530 --> 00:26:47,310
+inverse لل Phi مزام ال inverse مع بعض ده هو ال
+
+312
+00:26:47,310 --> 00:26:49,850
+identity ده هو ال identity of X ده هو ال X يعني
+
+313
+00:26:49,850 --> 00:26:54,850
+كلها هتصير F of X Psi prime إذا صار عندي هذا
+
+314
+00:26:54,850 --> 00:27:02,220
+شايفينه؟هو عبارة عن F small of X في Psi prime of X
+
+315
+00:27:02,220 --> 00:27:07,800
+طيب سهلة الموضوع الآن إذا نخد ال integration من
+
+316
+00:27:07,800 --> 00:27:11,100
+Phi of Alpha ل Phi of Beta ل F of X بPsi prime of
+
+317
+00:27:11,100 --> 00:27:15,540
+X DX إيش هذه؟ أه هذه اللي بدنا إياها هيها Psi
+
+318
+00:27:15,540 --> 00:27:20,130
+prime of X DX إذا نوصلناإذا الـ integration هذا
+
+319
+00:27:20,130 --> 00:27:23,290
+بيساوي ال integration لهذا ال integration لهذا
+
+320
+00:27:23,290 --> 00:27:30,570
+عندي هذه اللي هان جي كوميزيت في بسايد الكل برايم
+
+321
+00:27:30,570 --> 00:27:37,870
+of x dx الان الان هنا ال domain هذه اللي هيكون من
+
+322
+00:27:37,870 --> 00:27:42,600
+عندي اللي هي ال Iيعني لما ال .. ال .. ال .. ال ..
+
+323
+00:27:42,600 --> 00:27:43,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+324
+00:27:43,320 --> 00:27:43,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+325
+00:27:43,440 --> 00:27:44,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+326
+00:27:44,420 --> 00:27:45,660
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+327
+00:27:45,660 --> 00:27:50,280
+..
+
+328
+00:27:50,280 --> 00:27:54,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+329
+00:27:54,440 --> 00:27:55,100
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+330
+00:27:55,100 --> 00:27:57,300
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+331
+00:27:57,300 --> 00:28:06,760
+.. ال .. ال .. ال ..الآن صارت الـ derivative إلها
+
+332
+00:28:06,760 --> 00:28:09,620
+الـ integration هيلغى الـ derivative اللي هي by
+
+333
+00:28:09,620 --> 00:28:12,300
+fundamental theorem of calculus وكل الشروط زي ما
+
+334
+00:28:12,300 --> 00:28:17,420
+قلنا وانتحققها هيصير هذه اللي جوا عند هذه وهذه
+
+335
+00:28:17,420 --> 00:28:24,060
+اللي جوا عند هذه حاصل طرحين اللي هي G Phi
+
+336
+00:28:24,060 --> 00:28:29,140
+Composite Psiالكل of a G composed of Psi الكل of
+
+337
+00:28:29,140 --> 00:28:33,540
+Phi of X اللي هي ال X في هذه الحالة إيش اسمها اللي
+
+338
+00:28:33,540 --> 00:28:39,600
+هي Alpha معلش و هذه التانية ال Beta آسف اللي قولها
+
+339
+00:28:39,600 --> 00:28:44,660
+Beta حد الأول و هذه الحد اللي تحت Alpha ماشي
+
+340
+00:28:44,660 --> 00:28:49,430
+الحالة هذه يعني كلها على بعضزي ما عملنا قبل هيك
+
+341
+00:28:49,430 --> 00:28:53,370
+الـPsi و الـPhi اللي هو عبارة عن inverse لبعض، إذا
+
+342
+00:28:53,370 --> 00:28:58,530
+الـIdentity يعني هتصير الـG of Beta وهذا هتصير
+
+343
+00:28:58,530 --> 00:29:04,270
+الـG of Alpha، إذا صار عند المقدار اللي أمامي هذا
+
+344
+00:29:04,270 --> 00:29:11,130
+اللي هو اللي أنا ببحث عنه، هذا المقدار، شايفينه؟
+
+345
+00:29:11,130 --> 00:29:15,790
+هذا المقدارطلع عبارة عن عشان استخدمه بعد شوية
+
+346
+00:29:15,790 --> 00:29:22,650
+خلينا يمكن أوضح يكون هيصير عبارة عن g of beta ناقص
+
+347
+00:29:22,650 --> 00:29:26,910
+g of alpha بتثبت لكم الثاني برضه هيكون g of beta
+
+348
+00:29:26,910 --> 00:29:31,850
+ناقص g of alpha وبكون خلصنا اللي هو برهان النظرية
+
+349
+00:29:31,850 --> 00:29:36,990
+خلصنا هذا الجزء نيجي لا اللي هو الجزء الثاني اللي
+
+350
+00:29:36,990 --> 00:29:38,410
+أسهل كمان
+
+351
+00:29:41,370 --> 00:29:44,990
+شوف يا جماعة صلى الله عليه وسلم بالسلامة احنا قلنا
+
+352
+00:29:44,990 --> 00:29:47,790
+الـ G هي الـ antiderivative لهذه يعني الـ G' بساوة
+
+353
+00:29:47,790 --> 00:29:51,850
+هذا المقدار اذا الان بنقدر نستخدم اللي هو ال
+
+354
+00:29:51,850 --> 00:29:53,930
+fundamental theorem of calculus او اللي هو ال
+
+355
+00:29:53,930 --> 00:29:58,090
+corollary لها بكون عند ال integration هيه للمقدار
+
+356
+00:29:58,090 --> 00:30:02,790
+هذا هيطلع ليه اللي هو مباشرة بساوية يعني ممكن
+
+357
+00:30:02,790 --> 00:30:07,230
+بعضكم لاحظ الاشي اللي بتسويه من قبل ما اشرحالان ال
+
+358
+00:30:07,230 --> 00:30:09,670
+integration f of I of T من Alpha ل Beta ايش
+
+359
+00:30:09,670 --> 00:30:14,370
+بيساوي؟ هذا كله بدك تشيل مكانه منين؟ تحطه G' ال
+
+360
+00:30:14,370 --> 00:30:19,390
+integration ل G' of T dt من Alpha ل عند Beta نفس
+
+361
+00:30:19,390 --> 00:30:22,690
+الحدود لأنه ماغيرناش اللي هو ال variability اللي
+
+362
+00:30:22,690 --> 00:30:26,170
+بدنا نكامل بالنسبة له، مايساويعلى طول هذه اللي هي
+
+363
+00:30:26,170 --> 00:30:30,330
+تفاضل ب cancel اللي هي أو التكامل ب cancel التفاضل
+
+364
+00:30:30,330 --> 00:30:32,730
+اللي هي ال corollary اللي حكينا عنها اللي هي
+
+365
+00:30:32,730 --> 00:30:36,090
+corollary of fundamental theorem of calculus بساوة
+
+366
+00:30:36,090 --> 00:30:41,480
+Gof beta ناقص g of alpha الآن هذه صارت g of beta
+
+367
+00:30:41,480 --> 00:30:44,620
+ناقص g of alpha وهذه صارت g of beta ناقص g of
+
+368
+00:30:44,620 --> 00:30:48,320
+alpha إذا صار عندي هذا المقدار بساوي هذا المقدار
+
+369
+00:30:48,320 --> 00:30:51,400
+أو ال integration بساوي ال integration وبكون هيك
+
+370
+00:30:51,400 --> 00:30:55,160
+أثبتنا اللي هي النظرية الثانية أو اللي هو second
+
+371
+00:30:55,160 --> 00:31:00,200
+substitution theorem الآن تطبيقات هذه النظريات ما
+
+372
+00:31:00,200 --> 00:31:04,500
+هو هدولة تطبيقاتهم اللي هو إشبعنا فيها من Calculus
+
+373
+00:31:04,500 --> 00:31:04,780
+B
+
+374
+00:31:08,400 --> 00:31:14,420
+فبصير بس انه انت لحالك في البيت لو قعدت وعملتلك
+
+375
+00:31:14,420 --> 00:31:18,380
+سؤال سؤالين على ال substitution في الحالتين بتكون
+
+376
+00:31:18,380 --> 00:31:23,680
+اللي هو خليني نقول عمقت المفهوم عندك بشكل أكبر
+
+377
+00:31:23,680 --> 00:31:30,370
+نيجي الآننحكي عن اللي هو احنا طبعا حكينا عن الـ
+
+378
+00:31:30,370 --> 00:31:32,690
+mean value theorem أو نظرية القيمة المتوسطة في
+
+379
+00:31:32,690 --> 00:31:36,730
+حالة ال differentiation الآن هنحكي عن القيمة
+
+380
+00:31:36,730 --> 00:31:44,470
+المتوسطة في حالة ال integration اللي
+
+381
+00:31:44,470 --> 00:31:48,190
+هو نوجينا
+
+382
+00:31:49,730 --> 00:31:53,670
+أخدنا مثلا خلّيني أخد المنطقة الموجب عشان أسهل في
+
+383
+00:31:53,670 --> 00:31:57,850
+الحديث هي عندي اللي هو function f على الفترة من a
+
+384
+00:31:57,850 --> 00:32:02,790
+ل عند b الآن بتقوللي اللي هو بتقوللي هذا طبعا نظري
+
+385
+00:32:02,790 --> 00:32:06,010
+أكثر من هيك أبعد من هيك بس خلّيني أقول خلّيني أخد
+
+386
+00:32:06,010 --> 00:32:11,370
+الحالة السهلة أو خلّيني أخد الحالة اللي بتوضح
+
+387
+00:32:11,370 --> 00:32:17,210
+معانا القيمة المتوسطة الآن قيمة ال integration من
+
+388
+00:32:17,210 --> 00:32:23,660
+a ل عند bهو عبارة عن المنطقة هذه ككل مسحتها لو
+
+389
+00:32:23,660 --> 00:32:31,070
+جسمناها على الـ B minus Aوكأننا بناخد متوسط قيمة
+
+390
+00:32:31,070 --> 00:32:34,850
+الدالة لإنه لو اتخيلنا إنه هي قيمة الدالة و
+
+391
+00:32:34,850 --> 00:32:38,810
+بنضربها يعني تخيل إنها دي مساحة خط جنب خط جنب خط
+
+392
+00:32:38,810 --> 00:32:42,070
+جنب خط جنب خط لما اتخلص أدولها إلى أن حصل ضرب
+
+393
+00:32:42,070 --> 00:32:45,530
+الفترة هذه كلها P minus A في قيمة ال .. الها دي
+
+394
+00:32:45,530 --> 00:32:48,530
+اللي هي اللي عنده لو فرضنا إنهم يعني ال .. ال ..
+
+395
+00:32:48,530 --> 00:32:52,550
+ال .. هذه القيمة المتوسطة لهم يعني متوسطهم فبصير
+
+396
+00:32:52,550 --> 00:32:57,080
+عند كله على بعض المساحة بساوياللي هو حصل ضرب P
+
+397
+00:32:57,080 --> 00:33:02,700
+minus A في متوسط قيمة التكامل اللي هو عند نقطة
+
+398
+00:33:02,700 --> 00:33:07,370
+معاه وهذا اللي بتقوله هي بتقول إذا كانت Fاللي هي
+
+399
+00:33:07,370 --> 00:33:11,370
+في شروط معينة بكون عند F of X DX على B minus A
+
+400
+00:33:11,370 --> 00:33:18,210
+بساوي F of C for some C وين موجودة بين الـ A و الـ
+
+401
+00:33:18,210 --> 00:33:23,230
+B وهذه اللي هي القيمة المتوسطة للمساحة أو قيمة ال
+
+402
+00:33:23,230 --> 00:33:27,930
+integration على طول اللي هي الفترة إذن هذه اللي هي
+
+403
+00:33:27,930 --> 00:33:34,290
+خلّيني أقول حالة خاصة من نظرية القيمة المتوسطة
+
+404
+00:33:34,290 --> 00:33:38,300
+اللي بصورة عامةاللي هي .. اللي هي .. اللي نسميها
+
+405
+00:33:38,300 --> 00:33:41,960
+الـ Mean Value Theorem for Integrals نشوف الكلام،
+
+406
+00:33:41,960 --> 00:33:45,800
+يمكن الآن الكلام يكون أوضح في المن .. بشكل أوضح
+
+407
+00:33:45,800 --> 00:33:48,920
+لما نبرهن النظرية وناخد نصها وناخد الـ Corollary
+
+408
+00:33:48,920 --> 00:33:54,070
+اللي عليها اللي هي الحالة اللي ذكرتهالأن ما بحكيه
+
+409
+00:33:54,070 --> 00:33:57,170
+عبارة عن الـ Mean Value Theorem for اللي هي أياش
+
+410
+00:33:57,170 --> 00:34:01,910
+integrals نظرية القيمة المتوسطة على التكامل طبعا
+
+411
+00:34:01,910 --> 00:34:05,470
+أنتم متذكرين القيمة المتوسطة العادية أنه لو كانت F
+
+412
+00:34:05,470 --> 00:34:08,410
+is continuous على closed interval differentiable
+
+413
+00:34:08,410 --> 00:34:11,710
+على ال open إذاً there exists C element in A وB
+
+414
+00:34:11,710 --> 00:34:17,310
+such that اللي هي F prime of C سوى F of B ناقص F
+
+415
+00:34:17,310 --> 00:34:22,940
+of A على B minus Aهنا الأن بقولك اللي في الجزئية
+
+416
+00:34:22,940 --> 00:34:28,020
+هذه أن F is continuous على الـA والـB إذن there
+
+417
+00:34:28,020 --> 00:34:32,220
+exists C في الـA والـB such that ال integration من
+
+418
+00:34:32,220 --> 00:34:38,160
+A لعند B F of X DX بساوي F of C على B minus A
+
+419
+00:34:38,160 --> 00:34:44,180
+بساوي مين؟ بساوي اللي هي الـF of C roughly ..
+
+420
+00:34:44,180 --> 00:34:47,940
+roughly .. roughly .. roughly اتخيل أنه الآن هذه
+
+421
+00:34:47,940 --> 00:34:51,880
+عبارة عن الـderivativeF هذا ثابت طبعا ال
+
+422
+00:34:51,880 --> 00:34:54,920
+derivative F prime of C وهذه اللي خدنا derivative
+
+423
+00:34:54,920 --> 00:34:58,580
+لان integration كان اللي هو اللي هي متغيرات فبصير
+
+424
+00:34:58,580 --> 00:35:00,580
+عند F of B بروح ال integration مع ال
+
+425
+00:35:00,580 --> 00:35:04,040
+differentiation بصير F of B ناقص F of A اللي فوق
+
+426
+00:35:04,040 --> 00:35:07,300
+هذا الكلام رفلي بس على أساس ان هو ان انت اللي هو
+
+427
+00:35:07,300 --> 00:35:11,260
+تستذكر العلاقة اللي هو بين هذه وبين اللي هي
+
+428
+00:35:11,260 --> 00:35:16,550
+الأصليةأما القيمة المتوسطة المفهوم بالمتوسط اللي
+
+429
+00:35:16,550 --> 00:35:20,510
+هو مساحة اللي هو قيمة ال integration على طول فترته
+
+430
+00:35:20,510 --> 00:35:24,370
+اللي هو بتطلع قيمة متوسطة هذه القيمة اللي هو عبارة
+
+431
+00:35:24,370 --> 00:35:29,050
+عن متوسط قيمة وكأنه كل اللي هي قيمة ال integration
+
+432
+00:35:29,050 --> 00:35:33,630
+عنده اللي هو تحت اللي هي النقطة اللي عنده في F of
+
+433
+00:35:33,630 --> 00:35:37,150
+C بتساوي قيمة هذا ال integration على B minus A أو
+
+434
+00:35:37,150 --> 00:35:41,590
+متوسط المساحة على طول الفترة اللي هي بتساوي قيمة
+
+435
+00:35:41,590 --> 00:35:47,800
+الدالةF of C وفعلا الـ C موجودة هي المهم ان الـ C
+
+436
+00:35:47,800 --> 00:35:51,000
+هي دي فعلا حنلاجيها موجودة وبتمثل قيمة ال
+
+437
+00:35:51,000 --> 00:35:54,620
+integration على طول الفترة وهذا معناته اللي هو
+
+438
+00:35:54,620 --> 00:35:58,340
+المتوسط قيمة ال integration على طول الفترة حنلاجيه
+
+439
+00:35:58,340 --> 00:36:02,620
+فعلا بمثله مقبسي بين ال A و ال B وهذا بسميها
+
+440
+00:36:02,620 --> 00:36:08,510
+القيمة المتوسطةmean value theorem for integrals
+
+441
+00:36:08,510 --> 00:36:12,930
+let F be continuous on I and let B be integrable
+
+442
+00:36:12,930 --> 00:36:16,920
+function on Iالـ B هذه أنا مااخدها تقبل بشوية في
+
+443
+00:36:16,920 --> 00:36:22,680
+مثالي على أنها بتساوي واحد طيب let F be continuous
+
+444
+00:36:22,680 --> 00:36:25,560
+on I of A و B and let B be an integrable function
+
+445
+00:36:25,560 --> 00:36:29,740
+on I and نفترض أنه B of X أكبر يساوي سفر for every
+
+446
+00:36:29,740 --> 00:36:32,900
+X element in I then there exists C element in I
+
+447
+00:36:32,900 --> 00:36:37,880
+such that الآن هاي الـ C اللي هي بدها تمثل اللي هي
+
+448
+00:36:37,880 --> 00:36:40,980
+النقطة اللي بنلاقيها في الـ I بحيث أنه ال
+
+449
+00:36:40,980 --> 00:36:46,230
+integration من A لB F of X DX DXعلى اللي هي ال
+
+450
+00:36:46,230 --> 00:36:48,170
+integration من a إلى b بيقوم باقوم باقوم باقوم
+
+451
+00:36:48,170 --> 00:36:49,190
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+452
+00:36:49,190 --> 00:36:50,170
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+453
+00:36:50,170 --> 00:36:55,050
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+454
+00:36:55,050 --> 00:36:55,210
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+455
+00:36:55,210 --> 00:36:56,930
+باقوم باقوم باقوم باقوم باقوم باقوم باقوم باقوم
+
+456
+00:36:56,930 --> 00:37:02,790
+باقوم باقوم
+
+457
+00:37:02,790 --> 00:37:04,290
+ب
+
+458
+00:37:11,900 --> 00:37:19,760
+الـ integration من a ل b f of x b of x dx على ال
+
+459
+00:37:19,760 --> 00:37:23,820
+integration نفترض أنه ليس فارق بيه بيه بيه بيه بيه
+
+460
+00:37:23,820 --> 00:37:25,260
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+461
+00:37:25,260 --> 00:37:26,640
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+462
+00:37:26,640 --> 00:37:29,220
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+463
+00:37:29,220 --> 00:37:38,400
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+464
+00:37:38,400 --> 00:37:43,710
+بو بيصير هذه واحد اللي هي بيصير هذه P minus A اللي
+
+465
+00:37:43,710 --> 00:37:48,390
+قلت قبل شوية اللي هو قيمة المساحة أو قيمة ال
+
+466
+00:37:48,390 --> 00:37:52,670
+integration على طول الفترة بساوي فعلا مقطة فعلية
+
+467
+00:37:52,670 --> 00:38:00,790
+في الفترة I نيجي نبره ان هذه هي بصورة عامة عند F
+
+468
+00:38:00,790 --> 00:38:08,600
+continuous إذا F is integrable and so F اللي هوA
+
+469
+00:38:08,600 --> 00:38:12,760
+of X في B of X is Integrable لأن B Integrable و F
+
+470
+00:38:12,760 --> 00:38:15,300
+Integrable صار الـ composition اللي هنا Integrable
+
+471
+00:38:15,300 --> 00:38:19,280
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+472
+00:38:19,280 --> 00:38:19,580
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+473
+00:38:19,580 --> 00:38:20,220
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+474
+00:38:20,220 --> 00:38:20,300
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+475
+00:38:20,300 --> 00:38:20,360
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+476
+00:38:20,360 --> 00:38:20,380
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+477
+00:38:20,380 --> 00:38:21,740
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+478
+00:38:21,740 --> 00:38:23,080
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+479
+00:38:23,080 --> 00:38:25,040
+اللي هنا Integrable اللي هنا Integrable اللي هنا
+
+480
+00:38:25,040 --> 00:38:27,280
+Integrable اللي هنا Integrable اللي هنا Integrable
+
+481
+00:38:27,280 --> 00:38:34,460
+اللي هنا Integrable اللي هنا Integ
+
+482
+00:38:42,230 --> 00:38:46,930
+عندي F continuous إذا انتيجرابل و B-integrable إذا
+
+483
+00:38:46,930 --> 00:38:52,610
+FB-integrableسمّيلي الـ M small هي الـ infimum للـ
+
+484
+00:38:52,610 --> 00:38:55,830
+F of I موجودة أه طبعا و هي F is integrable is
+
+485
+00:38:55,830 --> 00:39:00,610
+unbounded M capital بسوى ال supremum لمين لل F of
+
+486
+00:39:00,610 --> 00:39:05,210
+I إذن الآن الدروب صارت عندي ال F of X بين ال M
+
+487
+00:39:05,210 --> 00:39:09,030
+small و بين ال M capital الدروب لكل انفمين في B of
+
+488
+00:39:09,030 --> 00:39:14,190
+X وبنقدر أه بنقدر لإن بي بيضالها زي ما هي أه لإن
+
+489
+00:39:14,190 --> 00:39:20,450
+بي موجبةإذا صار عندى الآن هذه ال inequality صحيحة
+
+490
+00:39:20,450 --> 00:39:23,830
+و كلها integrable إذا ال integration على الأولى
+
+491
+00:39:23,830 --> 00:39:26,350
+أصغر أو سوى ال integration على الثانية أصغر أو سوى
+
+492
+00:39:26,350 --> 00:39:29,850
+ال integration على الثالثة و ال M بتطلع برا لإنه
+
+493
+00:39:29,850 --> 00:39:38,110
+ال M يشملها ثابتة الآن لو ال integration لل .. لل
+
+494
+00:39:38,110 --> 00:39:44,710
+.. لل .. لل B بساوى 0 إذا ال integration هيكوناللي
+
+495
+00:39:44,710 --> 00:39:49,730
+هو اللي فوق ال .. ال .. ال .. ال .. النظرية بتصلح
+
+496
+00:39:49,730 --> 00:39:55,930
+لأي قيمة اللي هو للـ C لأنه هيكون إيش بيساوي ..
+
+497
+00:39:55,930 --> 00:40:00,310
+أنا أطلعلكم فوق لأن لو فرضنا ال integration للـ B
+
+498
+00:40:00,310 --> 00:40:05,930
+بيساوي سفر integration للـ B بيساوي سفربصير اللي
+
+499
+00:40:05,930 --> 00:40:10,990
+هو هذه برضه ال integration هذا هيساوي أيش؟ هيساوي
+
+500
+00:40:10,990 --> 00:40:14,810
+سفر عارفين ليش؟ لأنه مادام ال integration هذا سفر
+
+501
+00:40:14,810 --> 00:40:16,710
+و ال integration هذا سفر إذا ال integration اللي
+
+502
+00:40:16,710 --> 00:40:22,170
+في النص أيش هيساوي؟ سفر إذا صارت هذا المقدار سفر
+
+503
+00:40:22,170 --> 00:40:28,430
+وهذا سفر إيش ما تختار C هتتحقق اللي هي مين طرفي
+
+504
+00:40:28,430 --> 00:40:33,790
+المعادلةإذن الآن حالة الصفر is a trivial case يعني
+
+505
+00:40:33,790 --> 00:40:36,890
+حالة أن تكون هذه صفر is a trivial case لأن
+
+506
+00:40:36,890 --> 00:40:39,890
+automatic زي ما قلنا مدامة هذه صفر وهذه صفر دمنا
+
+507
+00:40:39,890 --> 00:40:43,310
+في النص صفر إذن اللي هو أي اختيار للـC هيكون طرف
+
+508
+00:40:43,310 --> 00:40:47,410
+أي معادلة صحيحة يعني اللي هو ال equality تبعتنا
+
+509
+00:40:47,410 --> 00:40:51,470
+صحيحة الآن بدنا نيجي لمين يا جماعة؟ إيش غرضنا؟
+
+510
+00:40:51,470 --> 00:40:56,460
+غرضنا نلاقي C بحيث أن هذا بساوي هذاخلصنا حالة اللي
+
+511
+00:40:56,460 --> 00:40:59,240
+هي ال integration بساوة سفر نفترض ان ال
+
+512
+00:40:59,240 --> 00:41:02,480
+integration مش سفر ليش انه بدي أكسب عنه إذا صار
+
+513
+00:41:02,480 --> 00:41:05,860
+عندي ال integration أكسب الجهتين عن ال integration
+
+514
+00:41:05,860 --> 00:41:09,360
+لل B ال integration لل B اللي فرضنا انه مش سفر إذا
+
+515
+00:41:09,360 --> 00:41:11,580
+صار ال integration هذا على ال integration هذا بين
+
+516
+00:41:11,580 --> 00:41:16,840
+ال M small و ال M أشمالها capital ماشي الحالة الآن
+
+517
+00:41:16,840 --> 00:41:25,420
+احنا بنقول ان هذا صار رقمبين الـ M small والـ M
+
+518
+00:41:25,420 --> 00:41:35,540
+capital وبنقول أن F continuous on الفترة A وB then
+
+519
+00:41:35,540 --> 00:41:46,560
+أي رقم .. أي رقم الآن للدالة اللي هو .. هوضح لكم
+
+520
+00:41:46,560 --> 00:41:48,900
+هي .. اذكركم الـ intermediate value theorem اللي
+
+521
+00:41:48,900 --> 00:41:53,720
+نسيها هي عندى مثلا هي أعلى قيمةأقل قيمة وهي أعلى
+
+522
+00:41:53,720 --> 00:42:02,140
+قيمة هذه الآن الـ function f of x اللي هي بين اللي
+
+523
+00:42:02,140 --> 00:42:12,640
+هو ام capital ام small او بين مين ام capital الان
+
+524
+00:42:12,640 --> 00:42:20,220
+لو اجينا اخدنا اي قيمةأي قيمة عدد أي عدد A بين الـ
+
+525
+00:42:20,220 --> 00:42:23,980
+M small والـ M capital متامة الـ F continuously عن
+
+526
+00:42:23,980 --> 00:42:28,200
+أي قيمة هنا أخدناها قيمة هنلاقي اللي هو there
+
+527
+00:42:28,200 --> 00:42:32,040
+exists C element في الفترة A وB المعرف عليها
+
+528
+00:42:32,040 --> 00:42:38,040
+الدائرة هتسميها C مثلا أو D هنلاقي الـ C في الفترة
+
+529
+00:42:38,040 --> 00:42:45,030
+بين A وB بحيث أن F of C هي مين القيمة F of Dاللي
+
+530
+00:42:45,030 --> 00:42:47,050
+هي الـ Intermediate Value Theorem اللي انتوا
+
+531
+00:42:47,050 --> 00:42:50,790
+عارفينها اللي هي Four Continuous Function اذا بما
+
+532
+00:42:50,790 --> 00:42:55,790
+انه الـ function F is continuous و هذه القيمة بين
+
+533
+00:42:55,790 --> 00:43:00,490
+أعلى قيمة .. بين أعلى قيمة و أقل قيمة للدالة إذا
+
+534
+00:43:00,490 --> 00:43:05,950
+أكيد هقدر ألاقي C element in I بحيث ان F of C
+
+535
+00:43:05,950 --> 00:43:10,830
+بساوي هذا الرقم اللي هو هذه القيمة اللي هو ال
+
+536
+00:43:10,830 --> 00:43:16,520
+integrationبساوى اللي هو F of C في القيمة هذه وهو
+
+537
+00:43:16,520 --> 00:43:22,000
+المطلوب يعني النظرية برهانة بسيطة يا جماعة بس مدام
+
+538
+00:43:22,000 --> 00:43:27,740
+حصرنا قيمة للقيمة هذه اللي هي بين اللي هي ال M و
+
+539
+00:43:27,740 --> 00:43:30,840
+ال M إذا بال intermediate value theorem في C
+
+540
+00:43:30,840 --> 00:43:37,500
+وخلصنا طيب اللي بعده ال quaternary حكيتها هذه إن
+
+541
+00:43:37,500 --> 00:43:38,360
+لو كانت F
+
+542
+00:43:43,100 --> 00:43:47,820
+الـ Corollary حكيتها لو كانت F continuous على اللي
+
+543
+00:43:47,820 --> 00:43:50,940
+هي الـ closed interval A و B هلاجي الـC في الـI
+
+544
+00:43:50,940 --> 00:43:53,720
+بحيث ان ال integration من A لB للF سواء F of C في
+
+545
+00:43:53,720 --> 00:44:00,900
+B minus A قلنا هذه اللي هي حالة خاصة من النظرية بس
+
+546
+00:44:00,900 --> 00:44:08,160
+حطلي الـF الـP of X بساوية 1 حالة خاصة من النظرية
+
+547
+00:44:08,160 --> 00:44:10,480
+النظريتنا
+
+548
+00:44:11,580 --> 00:44:17,340
+إن الـ integration للـ F في B بساوي F of C في الـ
+
+549
+00:44:17,340 --> 00:44:21,320
+integration للـ B من Alpha لعند Beta و لا من A
+
+550
+00:44:21,320 --> 00:44:29,620
+لعند B من A لعند B for some C element in I، مظبوط؟
+
+551
+00:44:29,620 --> 00:44:33,180
+الآن بقول لي اللي هو ال integration للـ F بساوية F
+
+552
+00:44:33,180 --> 00:44:36,720
+of C في B minus A for some C حط الـ B بساوية،
+
+553
+00:44:36,720 --> 00:44:41,420
+هتجسي ال integration للـ Fبس بي بي بي بي بي بي بي
+
+554
+00:44:41,420 --> 00:44:48,320
+بي بي بي بي بي بي بي
+
+555
+00:44:51,410 --> 00:44:58,470
+اللي هو dx y ساوي اللي هو f of c هدف b minus a وهو
+
+556
+00:44:58,470 --> 00:45:02,690
+المطلوب هيلحقناه كمان مرة إذا الـ Corollary اللي
+
+557
+00:45:02,690 --> 00:45:09,030
+هي اللي أمامنا تم برهانها مرة أخرى نيجي الآن للي
+
+558
+00:45:09,030 --> 00:45:13,310
+هي Taylor's theorem أخدناها Taylor's theorem كان
+
+559
+00:45:13,310 --> 00:45:20,900
+ال remainder اللي هو اللي هو إشي مفاضلأو الـ
+
+560
+00:45:20,900 --> 00:45:26,560
+Taylor's theorem إذا صح التعبير for integration و
+
+561
+00:45:26,560 --> 00:45:29,500
+Taylor's theorem for differentiations الآن الجزء
+
+562
+00:45:29,500 --> 00:45:33,060
+اللي هو الـ for integration نشوف أشي اللي بقوله
+
+563
+00:45:35,050 --> 00:45:38,890
+suppose that the function f and its derivatives f
+
+564
+00:45:38,890 --> 00:45:43,030
+prime of w prime عند fn and fn زائد واحد are كلهم
+
+565
+00:45:43,030 --> 00:45:46,330
+إيه شمالهم continuous يعني نفترض أن الانث
+
+566
+00:45:46,330 --> 00:45:49,710
+derivative الانث زائد واحد derivative is
+
+567
+00:45:49,710 --> 00:45:53,890
+continuous exist وcontinuous نفترض أن الدالة f
+
+568
+00:45:53,890 --> 00:45:59,610
+عبارة عن دالة قابلة للاشتقاق n زائد واحد من المرات
+
+569
+00:45:59,610 --> 00:46:05,310
+وتكون الان زائد واحد كمان نفسها continuousماشي على
+
+570
+00:46:05,310 --> 00:46:10,290
+الفترة a و b then بقوللي اللي هو f of b بيساوي f
+
+571
+00:46:10,290 --> 00:46:14,170
+of a زي f prime of v على 1 factorial في b minus a
+
+572
+00:46:14,170 --> 00:46:18,990
+زي f double prime of a على 2 factorial في b minus
+
+573
+00:46:18,990 --> 00:46:22,410
+a تربيع زائد لما أصل عند f n of a على n factorial
+
+574
+00:46:22,410 --> 00:46:26,530
+في b minus a الكولوسن هذا كله إيش معلهعارفينه قبل
+
+575
+00:46:26,530 --> 00:46:30,050
+ليك وعملنا زائد مين ال remainder are n ال
+
+576
+00:46:30,050 --> 00:46:34,730
+remainder are n كتبوا على صورة integration بس ال
+
+577
+00:46:34,730 --> 00:46:37,550
+remainder are n كتب على صورة واحدة ال N factorial
+
+578
+00:46:37,550 --> 00:46:41,150
+في ال integration من a ل b بي ماينس تي وصة ن ففن
+
+579
+00:46:41,150 --> 00:46:50,010
+زي واحد of T دي تي إذن الآن بقولك أف of بي أف of
+
+580
+00:46:50,010 --> 00:47:02,410
+بي بساوي ال summation أف .. أف Nهو FK of A على
+
+581
+00:47:02,410 --> 00:47:10,470
+K factorial في B minus A أس K K من عند و .. من صفر
+
+582
+00:47:10,470 --> 00:47:19,390
+K من عند صفر لعند مين لعند N زائد ال remainder مين
+
+583
+00:47:19,390 --> 00:47:27,090
+RNالـ remainder are N مين هو بساوي اللي هو 1 على N
+
+584
+00:47:27,090 --> 00:47:35,390
+factorial في ال integration من A لعند B بي minus T
+
+585
+00:47:35,390 --> 00:47:45,690
+أس N في F N زائد 1 of T دي T نثبت لكم إن ال F of B
+
+586
+00:47:45,690 --> 00:47:52,520
+can be written as thisحيث الـ Rn هو هذا الآن
+
+587
+00:47:52,520 --> 00:47:59,500
+الفكرة في الحل أو الفكرة في البرهان أنه أنا بدي
+
+588
+00:47:59,500 --> 00:48:05,260
+أجي أوجد قيمة الـ remainder Rn اللي هو هذا المقدار
+
+589
+00:48:05,260 --> 00:48:10,700
+و بدي أثبتلكم أن هذا المقدار اللي هو منه بقدر أكتب
+
+590
+00:48:10,700 --> 00:48:14,040
+اللي هو يعني الـ Rn أثبتلكي هي عبارة عن F of B
+
+591
+00:48:14,040 --> 00:48:19,720
+ناقص هذا الـ summationيعني بدي أثبتلكم أن الـ RN
+
+592
+00:48:19,720 --> 00:48:23,560
+بتساوي F of B نقص ال machine هذا يعني بدي أبدأ
+
+593
+00:48:23,560 --> 00:48:30,700
+بهذا الآن يعني بدي أبدأ بالـ RN بساوي هذا المقدار
+
+594
+00:48:30,700 --> 00:48:34,740
+شايفينه هذا المقدار من A لعند B وحدة لـN factorial
+
+595
+00:48:34,740 --> 00:48:42,380
+بدي أكامله أكامله by partsأه بده كامل وشوفوا كيف
+
+596
+00:48:42,380 --> 00:48:47,280
+بتطلع الأمور ان شاء الله سلسة ومنيحة by parts خدوا
+
+597
+00:48:47,280 --> 00:48:53,160
+ال U عبارة هسموها عبارة عن U وهذه سموها ايش يا
+
+598
+00:48:53,160 --> 00:48:59,970
+جماعة DV ماشي الحال بيصير القرأن هو عبارة عناللي
+
+599
+00:48:59,970 --> 00:49:07,490
+هو UDV يعني بيساوي UV ناقص V DU تحت مين تحت ال
+
+600
+00:49:07,490 --> 00:49:11,310
+integration هذا كلام تعرفوه انتوا الآن برضه من وين
+
+601
+00:49:11,310 --> 00:49:16,150
+لوين من A لعند B على السريع عساسي اللي هو تاخدوا
+
+602
+00:49:16,150 --> 00:49:20,100
+الفكرةاللي هي الحسابات انت بتعرف تعملوها الكل
+
+603
+00:49:20,100 --> 00:49:24,620
+بيعرف يعملها هي أخدنا ال U زي ما أخدناها هنا
+
+604
+00:49:24,620 --> 00:49:30,200
+كتبتها على اللوح وهي ال DV هيها لأفن زي واحد of T
+
+605
+00:49:30,200 --> 00:49:36,300
+DT الان ال DU أكيد اللي هو تفاضل هذا N في B minus
+
+606
+00:49:36,300 --> 00:49:41,100
+Tأس N ناقص واحد في تفاضل اللي هو اللي جوا ناقص
+
+607
+00:49:41,100 --> 00:49:45,900
+واحد بيصير عندي ناقص N في B minus T أس N ناقص واحد
+
+608
+00:49:45,900 --> 00:49:51,040
+DT هذه مين هي الـ DU اللي بدي أحطها هانالان ال V
+
+609
+00:49:51,040 --> 00:49:57,380
+ال D V هيها ال V هتطلع ال integration هذه بيخف
+
+610
+00:49:57,380 --> 00:50:01,340
+واحد من ال derivatives بيصير عندي F N of T طبعا
+
+611
+00:50:01,340 --> 00:50:05,620
+فاهمين اش بقول ال V بيساوي F N of T الان بيجي
+
+612
+00:50:05,620 --> 00:50:09,260
+بنعوض بيصير عندي عبارة عن ال integration اللي هو
+
+613
+00:50:09,260 --> 00:50:15,160
+بيساوي ال R N بيساوي U في V U اللي هو عبارة عن B
+
+614
+00:50:15,160 --> 00:50:24,580
+minus T أس Nفي U هذه U في V V اللي هو عبارة عن FN
+
+615
+00:50:24,580 --> 00:50:37,200
+of T، مظبوط؟ هذا اللي هو U طبعا الـ RN احنا مضروب
+
+616
+00:50:37,200 --> 00:50:41,730
+كله في meanفى 1 على n factorial لأن هى اللى فضلنا
+
+617
+00:50:41,730 --> 00:50:47,110
+هى الجزء اللى حسبناه هذا 1 على n factorial موجودة
+
+618
+00:50:47,110 --> 00:50:50,490
+فيها 1 على n factorial بيصير هنا برضه على n
+
+619
+00:50:50,490 --> 00:51:00,050
+factorial بدت أمورنا تظهر ناقص 1 على n factorial
+
+620
+00:51:00,050 --> 00:51:06,310
+فى ال integration من a لعند b mean v , v هي ف
+
+621
+00:51:08,970 --> 00:51:18,530
+of T مظبوط دي T في D U D U ايش D U D U اللي هو
+
+622
+00:51:18,530 --> 00:51:30,650
+ناقص N ناقص N في B minus T أس
+
+623
+00:51:30,650 --> 00:51:32,330
+N ناقص واحد
+
+624
+00:51:35,190 --> 00:51:43,550
+واضحة الصورة نجي نخلي صورة منيحة B-T أُس N على N
+
+625
+00:51:43,550 --> 00:51:51,210
+factorial F N of T خلصنا منه هذا ناقص وهذا ناقص
+
+626
+00:51:51,210 --> 00:51:56,250
+يصبح زاد يصبح هذا أشمل هواحد على N واحد factorial
+
+627
+00:51:56,250 --> 00:52:04,450
+في ال integration من A لعند BB-T أُس N ناقص واحد
+
+628
+00:52:04,450 --> 00:52:12,530
+FN of T DT مظبوط؟ مظبوط هذا أوجدنا مين الـ RN
+
+629
+00:52:12,530 --> 00:52:18,350
+بساوي هذا زائد هذا طيب اللي عملناه مين هو هذا أصلا
+
+630
+00:52:18,350 --> 00:52:23,570
+الـ RN اللي أوجدناه هيه اللي هو B-1 T أس N FN زائد
+
+631
+00:52:23,570 --> 00:52:29,370
+واحد of T DT طلع عبارة عن اللي هو اللي جوا هذا بأس
+
+632
+00:52:29,370 --> 00:52:38,770
+Nوهذا زي ما هو أسن ناقص بيصير هو هذا زائد واحد صار
+
+633
+00:52:38,770 --> 00:52:42,670
+زائد طبعا ما عرفتوا كيفي صارت زائد واحد على أن
+
+634
+00:52:42,670 --> 00:52:46,130
+ناقص واحد factorial واحد على أن ناقص واحد
+
+635
+00:52:46,130 --> 00:52:49,850
+factorial في هذا المقدار لاحظوا أن هذا المقدار
+
+636
+00:52:49,850 --> 00:52:56,610
+شبيه بال remainderيعني بالظبط اللي عملناه على الـ
+
+637
+00:52:56,610 --> 00:53:01,750
+remainder بنعملهان بنعمله على هذا اللي هنعملهان
+
+638
+00:53:01,750 --> 00:53:05,810
+هيطلع مقدار زي هذا و مقدار زي هذا بس هينجس كمان
+
+639
+00:53:05,810 --> 00:53:09,770
+واحد اللي أن هيصير هذا أن نقص اتنين كان أن .. كان
+
+640
+00:53:09,770 --> 00:53:13,210
+أن صار هيصير أن نقص اتنين و الخطوة اللي بعدها
+
+641
+00:53:13,210 --> 00:53:15,850
+بنعمل كمان مرة بنوجد بيصير أن نقص ثلاثة و أن نقص
+
+642
+00:53:15,850 --> 00:53:20,070
+أربعة في الآخر الـ and finite إذا هنصل للنهاية إذا
+
+643
+00:53:20,070 --> 00:53:29,950
+هذا هيصير بساويB-T أُس N على N factorial FN of T
+
+644
+00:53:29,950 --> 00:53:35,250
+زائد هذا بتعمله بالظبط زي ما عملت مين زي ما عملت
+
+645
+00:53:35,250 --> 00:53:42,150
+ال RN يعني و كأنه اسم هذا RN-1بصير بنفس الأسلوب B
+
+646
+00:53:42,150 --> 00:53:49,410
+minus T أس N ناقص واحد على N ناقص واحد factorial F
+
+647
+00:53:49,410 --> 00:54:00,270
+N ناقص واحد of T زائد بعتقد
+
+648
+00:54:00,270 --> 00:54:08,770
+بس في ناقص هنا في ال U في V U في V
+
+649
+00:54:17,570 --> 00:54:22,590
+أه ماحسبناش عند A و B أه بس هذا نسينا نحسب هذا عند
+
+650
+00:54:22,590 --> 00:54:27,990
+B، من عند A لعند B، معلش سامحونا، من عند A لعند B
+
+651
+00:54:27,990 --> 00:54:33,230
+هذا الكلام صحيح، بس بدي أحسبه من A لعند B، عند B
+
+652
+00:54:33,230 --> 00:54:38,250
+صفر، صح؟ عند B صفر، مش احنا حسبنا قيمة الـ
+
+653
+00:54:38,250 --> 00:54:40,830
+remainder، قيمة ال integration، هذا ال integration
+
+654
+00:54:40,830 --> 00:54:47,820
+اللي هو من وين لوين، من A لعند Bالآن هذا من a لعند
+
+655
+00:54:47,820 --> 00:54:56,920
+b بيصير عند بي ناقص b بصير سفر الان ناقص من b ناقص
+
+656
+00:54:56,920 --> 00:55:01,680
+a فبصير هذه اشمالها b ناقص a وهنا ناقص وهنا a
+
+657
+00:55:01,680 --> 00:55:06,760
+شمالها f of a لان عوضنا عن مين عن ايه فبصير عند بي
+
+658
+00:55:06,760 --> 00:55:11,220
+ناقص a أس n بالسالب على n factor of n of a زائد
+
+659
+00:55:11,220 --> 00:55:15,190
+هذا المقدرلأن هذا المقدار زي هذا المقدار هذا
+
+660
+00:55:15,190 --> 00:55:19,010
+المقدار بنفس الأسلوب زي ما قلنا بيصير عبارة عن زي
+
+661
+00:55:19,010 --> 00:55:24,650
+هذاماشي بس برضه هيطلع لي إيش برضه هيطلع لي نقص لما
+
+662
+00:55:24,650 --> 00:55:27,730
+نعوض بيصير b minus a أسئلة ناقص واحدة الان ناقص
+
+663
+00:55:27,730 --> 00:55:33,830
+واحدة factorial f n ناقص واحد of 2 of a زائد اللي
+
+664
+00:55:33,830 --> 00:55:38,630
+بيطلع هنا n ناقص 2 factorial في ال integration من
+
+665
+00:55:38,630 --> 00:55:47,770
+a لb b minus t أسئلة ناقص 2 الان وهذه f n ناقص
+
+666
+00:55:47,770 --> 00:55:55,740
+واحدةof T D T نفس
+
+667
+00:55:55,740 --> 00:55:59,960
+اللي عملته على هذا بدي أعمله على هذا هضلي مستمر
+
+668
+00:55:59,960 --> 00:56:10,880
+لما يصلي عندي اللي هو .. وين بدي أكتب؟
+
+669
+00:56:10,880 --> 00:56:12,360
+خليني أكتب فوق
+
+670
+00:56:16,010 --> 00:56:22,150
+الان اتفجنا يا جماعة ان الـ RN هيوا هذا اللي هو RN
+
+671
+00:56:22,150 --> 00:56:28,690
+بساوي هذا المقدار ناقص هذا المقدار ناقص ناقص زائد
+
+672
+00:56:28,690 --> 00:56:34,370
+هذا إذا صار عند الـ RN بساوي
+
+673
+00:56:34,370 --> 00:56:49,900
+ناقص B minus A أس N على N factorialf n of a ناقص b
+
+674
+00:56:49,900 --> 00:56:54,740
+minus a plus n ناقص واحد على n ناقص واحد factorial
+
+675
+00:56:54,740 --> 00:57:04,840
+f n ناقص واحد of a زائد المقدار هذا الآن بتعملوا
+
+676
+00:57:04,840 --> 00:57:09,500
+هذا اللي عملته مع جابلو هيظلوا بنفس الأسلوب ماشي
+
+677
+00:57:10,430 --> 00:57:17,990
+لما أصل لعند اللي هو آخر term اللي هو هيكون عندي
+
+678
+00:57:17,990 --> 00:57:28,270
+هيطلع عندي اللي هو B minus A في F يعني N اللي هي
+
+679
+00:57:28,270 --> 00:57:41,300
+بيصير باتنين B minus A في F prime of A علىاللي هو
+
+680
+00:57:41,300 --> 00:57:46,360
+1 factorial زي ما هي زائد اللي بعدها ال
+
+681
+00:57:46,360 --> 00:57:51,200
+integration تبعها اللي هي هذه عند N بجداشها أنا ب2
+
+682
+00:57:51,200 --> 00:57:56,060
+N ب2 اللي هي بيصير 1 إلى 0 factorial يعني بيصير
+
+683
+00:57:56,060 --> 00:58:00,060
+اللي هو 1 بمعنى آخر فال integration من A لعند B
+
+684
+00:58:00,060 --> 00:58:06,660
+وهذا بيصير B minus T أُس 0 يعني 1 في F prime of DT
+
+685
+00:58:08,080 --> 00:58:12,180
+لما اكرر العملية اظل اكررها لما اصل لهذه الخطوة
+
+686
+00:58:12,180 --> 00:58:17,620
+وحنتي لأن الان is finite ويساوي اللي هو المقدار
+
+687
+00:58:17,620 --> 00:58:20,220
+هذا كله اللي هو عبارة عن ال summation طبعا كله
+
+688
+00:58:20,220 --> 00:58:23,060
+بالسالب هذا مع هذا الأخير بالموجة بيصير نقص ال
+
+689
+00:58:23,060 --> 00:58:32,660
+summation ل B minus A أس K على K factorial ف FK of
+
+690
+00:58:32,660 --> 00:58:43,520
+A K الان من عنداللي هو واحد عند واحد هيها لعند مين
+
+691
+00:58:43,520 --> 00:58:51,280
+لعند الأن هذا مجموع من هنا من هنا لهنا هذا كله في
+
+692
+00:58:51,280 --> 00:58:56,640
+قيب واحد بتطلع هذهكيب 2 بتطلع اللي هان كيب 3 لما
+
+693
+00:58:56,640 --> 00:58:59,580
+قصها لكيب n بتطلع اللي عنده هان زائد ال
+
+694
+00:58:59,580 --> 00:59:02,580
+integration هذا ال integration هذا اللي هي f
+
+695
+00:59:02,580 --> 00:59:05,660
+continuous اللي عند ال integration للـ f طبعا ال f
+
+696
+00:59:05,660 --> 00:59:08,820
+نفسها كانت continuous فال integration هذا بفرن ضمن
+
+697
+00:59:08,820 --> 00:59:11,140
+ال interferon of calculus على طول بطلع عبارة عن f
+
+698
+00:59:11,140 --> 00:59:20,780
+of b ناقص من f of a ماشي الحال فبصير الآن اللي هو
+
+699
+00:59:20,780 --> 00:59:28,010
+أوصلنا للي بدناهكيف؟ شوف كيف وصلنا للبيتمية الآن
+
+700
+00:59:28,010 --> 00:59:37,210
+طلعت عندي خلّي اللي هو الـ remainder احنا ال F of
+
+701
+00:59:37,210 --> 00:59:42,430
+P خليها في الجهة هذه و انقل كله هنا فبصير F of P
+
+702
+00:59:42,430 --> 00:59:48,760
+بساوي هذه بتنضف لهذه ما هي ناقص التانيةبيصير ..
+
+703
+00:59:48,760 --> 00:59:51,380
+لما تيجي الجهتين علي الجهتين بيصير موجة بس
+
+704
+00:59:51,380 --> 00:59:57,440
+summation لـ B minus A أُس K FK ال derivative هذه
+
+705
+00:59:57,440 --> 01:00:04,160
+of A على K factorial K الـ N من واحد لعند N وهذه
+
+706
+01:00:04,160 --> 01:00:09,340
+حالة السفر K من سفر لعند Nزائد مين الـ remainder
+
+707
+01:00:09,340 --> 01:00:13,900
+are n ليش حالة السفر هذه لأن في حالة K بسفر بيصير
+
+708
+01:00:13,900 --> 01:00:17,500
+هذا واحد وهذا واحد وهذا مافيش derivative يعني
+
+709
+01:00:17,500 --> 01:00:22,320
+بيصير F of A فبيصير عندي اللي هو F of B بساوي ال
+
+710
+01:00:22,320 --> 01:00:25,160
+summation زائد ال remainder are n ال remainder
+
+711
+01:00:25,160 --> 01:00:30,500
+اللي هو اللي احنا بدأنا فيه وهو المطلوب فعلا انا
+
+712
+01:00:30,500 --> 01:00:36,940
+قدرت اكتب اللي هي ال F of B على الصورة اللي أماميو
+
+713
+01:00:36,940 --> 01:00:42,600
+هيك بنكون احنا برهننا Taylor's theorem و هي اخر
+
+714
+01:00:42,600 --> 01:00:48,860
+جزء في هذا ال section و الان ان شاء الله بكون
+
+715
+01:00:48,860 --> 01:00:54,800
+خلصنا الجزء الاول من المحاضرة و نبدأ ان شاء الله
+
+716
+01:00:54,800 --> 01:00:58,740
+بعد شوية في الجزء الثاني برك الله فيكم
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7425398db6c6f63dd50c452e38149d4e2c6e661
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/VMrrs0aJBPM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3452, "start": 5.28, "end": 34.52, "text": "بسم الله الرحمن الرحيم المحاضرة الرابعة مساق تحليل حقيقة 2 لطلبة الجامعة الإسلامية كلية العلوم قسم الرياضيات نستكمل الحديث عن نظرية القيمة المتوسطة أو the mean value theorem وما يتعلق بذلك تحدثنا المرة الماضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 34892, 16758, 27884, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11331, 38436, 28671, 568, 5296, 9566, 46152, 3660, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 18863, 1211, 20498, 12174, 38251, 2423, 16572, 46958, 1829, 9307, 8717, 14851, 24793, 1211, 21542, 16254, 12984, 18871, 8717, 19913, 2288, 10632, 25062, 32640, 3660, 9673, 2655, 41779, 9566, 3660, 34051, 264, 914, 2158, 20904, 4032, 15042, 7251, 2655, 30241, 4587, 4724, 8848, 23275, 6055, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632], "avg_logprob": -0.08701795022538368, "compression_ratio": 1.7632850241545894, "no_speech_prob": 2.682209014892578e-06, "words": [{"start": 5.28, "end": 5.64, "word": "بسم", "probability": 0.887939453125}, {"start": 5.64, "end": 5.86, "word": " الله", "probability": 0.953125}, {"start": 5.86, "end": 6.26, "word": " الرحمن", "probability": 0.9762369791666666}, {"start": 6.26, "end": 6.82, "word": " الرحيم", "probability": 0.9949544270833334}, {"start": 6.82, "end": 8.6, "word": " المحاضرة", "probability": 0.970703125}, {"start": 8.6, "end": 9.52, "word": " الرابعة", "probability": 0.9716796875}, {"start": 9.52, "end": 10.82, "word": " مساق", "probability": 0.92041015625}, {"start": 10.82, "end": 12.08, "word": " تحليل", "probability": 0.9718017578125}, {"start": 12.08, "end": 12.64, "word": " حقيقة", "probability": 0.7757975260416666}, {"start": 12.64, "end": 13.06, "word": " 2", "probability": 0.70947265625}, {"start": 13.06, "end": 15.2, "word": " لطلبة", "probability": 0.950439453125}, {"start": 15.2, "end": 15.64, "word": " الجامعة", "probability": 0.9860026041666666}, {"start": 15.64, "end": 16.48, "word": " الإسلامية", "probability": 0.9822998046875}, {"start": 16.48, "end": 17.62, "word": " كلية", "probability": 0.6817626953125}, {"start": 17.62, "end": 18.22, "word": " العلوم", "probability": 0.9640299479166666}, {"start": 18.22, "end": 18.78, "word": " قسم", "probability": 0.970458984375}, {"start": 18.78, "end": 19.62, "word": " الرياضيات", "probability": 0.94267578125}, {"start": 19.62, "end": 22.5, "word": " نستكمل", "probability": 0.96875}, {"start": 22.5, "end": 23.32, "word": " الحديث", "probability": 0.9934895833333334}, {"start": 23.32, "end": 23.82, "word": " عن", "probability": 0.99560546875}, {"start": 23.82, "end": 25.02, "word": " نظرية", "probability": 0.8294677734375}, {"start": 25.02, "end": 25.46, "word": " القيمة", "probability": 0.9558919270833334}, {"start": 25.46, "end": 26.48, "word": " المتوسطة", "probability": 0.99287109375}, {"start": 26.48, "end": 27.06, "word": " أو", "probability": 0.8203125}, 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minimum معرفناها المرة الماضية و أتحدثنا أيضًا عن اللي هو ال interior extreme theorem ال interior extreme theorem اللي هي جوابتنا على السؤال اللي بنحكي فيه", "tokens": [2304, 3615, 1863, 7578, 4972, 1279, 265, 1696, 8608, 2407, 16606, 4972, 6674, 34051, 4972, 7285, 34051, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 2423, 8236, 2423, 2654, 6674, 4032, 2423, 2654, 7285, 20449, 28480, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 4032, 5551, 2655, 24401, 12984, 8315, 36632, 11242, 14111, 995, 18871, 13672, 1829, 31439, 2423, 10636, 8084, 20904, 2423, 10636, 8084, 20904, 13672, 1829, 39896, 10874, 14407, 3555, 2655, 8315, 15844, 21136, 33604, 6027, 13672, 1829, 44945, 5016, 4117, 1829, 8978, 3224], "avg_logprob": -0.20790441386839922, "compression_ratio": 1.8349514563106797, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 35.99000000000001, "end": 36.95, "word": "معنى", "probability": 0.85107421875}, {"start": 36.95, "end": 37.35, "word": " relative", "probability": 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44.47, "word": " ال", "probability": 0.299072265625}, {"start": 44.47, "end": 45.05, "word": " local", "probability": 0.57373046875}, {"start": 45.05, "end": 45.75, "word": " maximum", "probability": 0.96875}, {"start": 45.75, "end": 46.47, "word": " و", "probability": 0.54248046875}, {"start": 46.47, "end": 46.79, "word": " ال", "probability": 0.93212890625}, {"start": 46.79, "end": 47.15, "word": " local", "probability": 0.85546875}, {"start": 47.15, "end": 47.45, "word": " minimum", "probability": 0.97705078125}, {"start": 47.45, "end": 48.21, "word": " معرفناها", "probability": 0.8594970703125}, {"start": 48.21, "end": 48.53, "word": " المرة", "probability": 0.96484375}, {"start": 48.53, "end": 49.09, "word": " الماضية", "probability": 0.9928385416666666}, {"start": 49.09, "end": 51.17, "word": " و", "probability": 0.28369140625}, {"start": 51.17, "end": 52.09, "word": " أتحدثنا", "probability": 0.865234375}, {"start": 52.09, "end": 52.69, "word": " أيضًا", "probability": 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هي", "probability": 0.93115234375}, {"start": 60.29, "end": 61.49, "word": " جوابتنا", "probability": 0.926953125}, {"start": 61.49, "end": 61.75, "word": " على", "probability": 0.91455078125}, {"start": 61.75, "end": 62.33, "word": " السؤال", "probability": 0.9962565104166666}, {"start": 62.33, "end": 62.49, "word": " اللي", "probability": 0.969970703125}, {"start": 62.49, "end": 63.03, "word": " بنحكي", "probability": 0.9583740234375}, {"start": 63.03, "end": 63.43, "word": " فيه", "probability": 0.966552734375}], "temperature": 1.0}, {"id": 3, "seek": 8523, "start": 63.77, "end": 85.23, "text": "أين يمكن إيجاد القيم العظمى أو القيم الصغرى النظرية اللي بتحكي كانت ان لو كانت C عبارة عن interior point اللي هي ال interval I اللي عندها اللي هي ال function F ال derivative موجودة", "tokens": [10721, 9957, 7251, 43020, 11933, 1829, 7435, 18513, 25062, 32640, 18863, 19913, 2304, 7578, 34051, 25062, 32640, 31767, 17082, 2288, 7578, 28239, 19913, 2288, 10632, 13672, 1829, 39894, 5016, 4117, 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{"start": 69.17, "end": 70.75, "word": " النظرية", "probability": 0.81280517578125}, {"start": 70.75, "end": 71.09, "word": " اللي", "probability": 0.662353515625}, {"start": 71.09, "end": 72.01, "word": " بتحكي", "probability": 0.911376953125}, {"start": 72.01, "end": 72.37, "word": " كانت", "probability": 0.8203125}, {"start": 72.37, "end": 72.55, "word": " ان", "probability": 0.380126953125}, {"start": 72.55, "end": 72.81, "word": " لو", "probability": 0.91162109375}, {"start": 72.81, "end": 73.29, "word": " كانت", "probability": 0.958251953125}, {"start": 73.29, "end": 73.61, "word": " C", "probability": 0.52685546875}, {"start": 73.61, "end": 74.53, "word": " عبارة", "probability": 0.9833984375}, {"start": 74.53, "end": 74.73, "word": " عن", "probability": 0.9912109375}, {"start": 74.73, "end": 75.35, "word": " interior", "probability": 0.6748046875}, {"start": 75.35, "end": 76.29, "word": " point", "probability": 0.98388671875}, {"start": 76.29, "end": 77.55, "word": " اللي", 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ال", "probability": 0.99072265625}, {"start": 352.88, "end": 353.46, "word": " interval", "probability": 0.360595703125}, {"start": 353.46, "end": 354.68, "word": " قلنا", "probability": 0.7998046875}, {"start": 354.68, "end": 354.96, "word": " أن", "probability": 0.50244140625}, {"start": 354.96, "end": 355.4, "word": " F", "probability": 0.640625}, {"start": 355.4, "end": 355.78, "word": " is", "probability": 0.958984375}, {"start": 355.78, "end": 356.72, "word": " increasing", "probability": 0.9736328125}, {"start": 356.72, "end": 358.2, "word": " إذا", "probability": 0.935791015625}, {"start": 358.2, "end": 358.74, "word": " كانت", "probability": 0.98486328125}, {"start": 358.74, "end": 358.9, "word": " اللى", "probability": 0.91162109375}, {"start": 358.9, "end": 359.26, "word": " هى", "probability": 0.914794921875}], "temperature": 1.0}, {"id": 16, "seek": 37603, "start": 360.25, "end": 376.03, "text": "أخدنا أي نقطتين في الـ I X1 و X2 بحقق ان X1 أصغر من X2 إذا قدلنا هذا أن أف X1 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0.97607421875}, {"start": 443.1, "end": 444.08, "word": " نتفحص", "probability": 0.86953125}, {"start": 444.08, "end": 445.22, "word": " إيش", "probability": 0.7433268229166666}, {"start": 445.22, "end": 445.56, "word": " هي", "probability": 0.8720703125}, {"start": 445.56, "end": 445.92, "word": " نظرية", "probability": 0.9598388671875}, {"start": 445.92, "end": 446.66, "word": " بتقول", "probability": 0.9814453125}, {"start": 446.66, "end": 447.26, "word": " و", "probability": 0.96484375}, {"start": 447.26, "end": 447.5, "word": " من", "probability": 0.8359375}, {"start": 447.5, "end": 447.96, "word": " ثم", "probability": 0.985107421875}, {"start": 447.96, "end": 448.8, "word": " نشوف", "probability": 0.9763997395833334}, {"start": 448.8, "end": 449.7, "word": " لماذا", "probability": 0.9690755208333334}], "temperature": 1.0}, {"id": 20, "seek": 47822, "start": 450.1, "end": 478.22, "text": "اللي هو هي صحيحة عندي نظرية بتقوللي theorem 6.2.7 اللي بتحكي النظرية بتقوللي لو كان عندي F let F من I لعنب R be differentiable on", "tokens": [6027, 20292, 31439, 39896, 20328, 5016, 1829, 5016, 3660, 18871, 16254, 8717, 19913, 2288, 10632, 39894, 39648, 20292, 20904, 1386, 13, 17, 13, 22, 13672, 1829, 39894, 5016, 4117, 1829, 28239, 19913, 2288, 10632, 39894, 39648, 20292, 45164, 25961, 18871, 16254, 479, 718, 479, 9154, 286, 5296, 3615, 1863, 3555, 497, 312, 819, 9364, 322], "avg_logprob": -0.199358251744083, "compression_ratio": 1.4, "no_speech_prob": 4.303455352783203e-05, "words": [{"start": 450.1, "end": 450.48, "word": "اللي", "probability": 0.799072265625}, {"start": 450.48, "end": 450.9, "word": " هو", "probability": 0.69189453125}, {"start": 450.9, "end": 451.64, "word": " هي", "probability": 0.70361328125}, {"start": 451.64, "end": 453.1, "word": " صحيحة", "probability": 0.98828125}, {"start": 453.1, "end": 458.96, "word": " عندي", "probability": 0.70556640625}, {"start": 458.96, "end": 459.76, "word": " نظرية", "probability": 0.918212890625}, {"start": 459.76, 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538.95, "end": 565.13, "text": "و هنبرهن اللي هو A أو B في الكتاب نبرهن A خلّينا نبرهن مين نبرهن B و هتكون A similarly for B الان بي .. بدنا نفترض suppose that F is decreasing on I", "tokens": [2407, 8032, 1863, 26890, 3224, 1863, 13672, 1829, 31439, 316, 34051, 363, 8978, 33251, 2655, 16758, 8717, 26890, 3224, 1863, 316, 16490, 1211, 11703, 9957, 995, 8717, 26890, 3224, 1863, 3714, 9957, 8717, 26890, 3224, 1863, 363, 4032, 8032, 2655, 30544, 316, 14138, 337, 363, 2423, 7649, 4724, 1829, 4386, 47525, 8315, 8717, 5172, 2655, 43042, 7297, 300, 479, 307, 23223, 322, 286], "avg_logprob": -0.21594238048419356, "compression_ratio": 1.3584905660377358, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 538.95, "end": 539.31, "word": "و", "probability": 0.86181640625}, {"start": 539.31, "end": 540.19, "word": " هنبرهن", "probability": 0.84189453125}, {"start": 540.19, "end": 540.77, "word": " اللي", "probability": 0.8837890625}, {"start": 540.77, "end": 541.27, "word": " هو", "probability": 0.97216796875}, {"start": 541.27, "end": 542.15, "word": " A", "probability": 0.45849609375}, {"start": 542.15, "end": 542.51, "word": " أو", "probability": 0.7841796875}, {"start": 542.51, "end": 542.81, "word": " B", "probability": 0.97119140625}, {"start": 542.81, "end": 543.57, "word": " في", "probability": 0.70654296875}, {"start": 543.57, "end": 543.93, "word": " الكتاب", "probability": 0.9796549479166666}, {"start": 543.93, "end": 544.43, "word": " نبرهن", "probability": 0.87451171875}, {"start": 544.43, "end": 544.53, "word": " A", "probability": 0.93701171875}, {"start": 544.53, "end": 544.97, "word": " خلّينا", "probability": 0.663671875}, {"start": 544.97, "end": 545.41, "word": " نبرهن", "probability": 0.992431640625}, {"start": 545.41, "end": 545.81, "word": " مين", "probability": 0.627685546875}, {"start": 545.81, "end": 546.93, "word": " نبرهن", "probability": 0.8702392578125}, {"start": 546.93, "end": 547.21, "word": " B", "probability": 0.865234375}, 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0.806884765625}, {"start": 821.31, "end": 822.01, "word": " بناء", "probability": 0.95166015625}, {"start": 822.01, "end": 822.27, "word": " على", "probability": 0.62890625}, {"start": 822.27, "end": 822.55, "word": " هذا", "probability": 0.95556640625}, {"start": 822.55, "end": 823.19, "word": " الحديث", "probability": 0.9866536458333334}, {"start": 823.19, "end": 823.83, "word": " صار", "probability": 0.879150390625}, {"start": 823.83, "end": 824.17, "word": " F", "probability": 0.96875}, {"start": 824.17, "end": 824.89, "word": " prime", "probability": 0.86865234375}, {"start": 824.89, "end": 825.57, "word": " of", "probability": 0.97705078125}, {"start": 825.57, "end": 826.07, "word": " X", "probability": 0.9912109375}, {"start": 826.07, "end": 827.09, "word": " أصغر", "probability": 0.9920654296875}, {"start": 827.09, "end": 827.27, "word": " أو", "probability": 0.97216796875}, {"start": 827.27, "end": 827.63, "word": " يساوي", "probability": 0.9754638671875}, {"start": 827.63, "end": 828.03, "word": " سفر", "probability": 0.90625}, {"start": 828.03, "end": 828.57, "word": " لكل", "probability": 0.980224609375}, {"start": 828.57, "end": 829.05, "word": " X", "probability": 0.97021484375}, {"start": 829.05, "end": 830.05, "word": " element", "probability": 0.9189453125}, {"start": 830.05, "end": 830.37, "word": " in", "probability": 0.9306640625}, {"start": 830.37, "end": 830.57, "word": " I", "probability": 0.99658203125}, {"start": 830.57, "end": 830.87, "word": " لأنه", "probability": 0.6510416666666666}, {"start": 830.87, "end": 831.23, "word": " كانت", "probability": 0.95654296875}, {"start": 831.23, "end": 831.47, "word": " C", "probability": 0.9462890625}, {"start": 831.47, "end": 832.29, "word": " is", "probability": 0.880859375}, {"start": 832.29, "end": 833.09, "word": " arbitrary", "probability": 0.67626953125}], "temperature": 1.0}, {"id": 35, "seek": 86010, "start": 833.32, "end": 860.1, "text": "هذا اللي هو الجزء الأول من النظرية من اللي هو B أنه بدنا الأن نيجي ل conversely بدنا نفترض هذا أصحى و أصحى و صفر و نوصل لمين لل F is decreasing نيجي الأن conversely و نشوف كيف نبرهن conversely الأن conversely", "tokens": [3224, 15730, 13672, 1829, 31439, 25724, 11622, 38207, 16247, 12610, 9154, 28239, 19913, 2288, 10632, 9154, 13672, 1829, 31439, 363, 14739, 3224, 47525, 8315, 16247, 1863, 8717, 1829, 7435, 1829, 5296, 2615, 736, 47525, 8315, 8717, 5172, 2655, 43042, 23758, 5551, 9381, 5016, 7578, 4032, 5551, 9381, 5016, 7578, 4032, 20328, 5172, 2288, 4032, 8717, 2407, 36520, 5296, 2304, 9957, 24976, 479, 307, 23223, 8717, 1829, 7435, 1829, 16247, 1863, 2615, 736, 4032, 8717, 8592, 38688, 9122, 33911, 8717, 26890, 3224, 1863, 2615, 736, 16247, 1863, 2615, 736], "avg_logprob": -0.24947332532218333, "compression_ratio": 1.7351351351351352, "no_speech_prob": 1.4901161193847656e-05, "words": [{"start": 833.32, "end": 834.5, "word": "هذا", "probability": 0.79345703125}, {"start": 834.5, "end": 834.6, "word": " اللي", "probability": 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"end": 840.68, "word": " نيجي", "probability": 0.8853759765625}, {"start": 840.68, "end": 840.8, "word": " ل", "probability": 0.8251953125}, {"start": 840.8, "end": 841.44, "word": " conversely", "probability": 0.8515625}, {"start": 841.44, "end": 841.66, "word": " بدنا", "probability": 0.6124267578125}, {"start": 841.66, "end": 842.06, "word": " نفترض", "probability": 0.992919921875}, {"start": 842.06, "end": 842.3, "word": " هذا", "probability": 0.82275390625}, {"start": 842.3, "end": 842.56, "word": " أصحى", "probability": 0.654541015625}, {"start": 842.56, "end": 842.82, "word": " و", "probability": 0.57080078125}, {"start": 842.82, "end": 842.86, "word": " أصحى", "probability": 0.8585205078125}, {"start": 842.86, "end": 842.94, "word": " و", "probability": 0.88818359375}, {"start": 842.94, "end": 843.18, "word": " صفر", "probability": 0.640380859375}, {"start": 843.18, "end": 843.8, "word": " و", "probability": 0.94580078125}, {"start": 843.8, "end": 844.14, "word": " نوصل", "probability": 0.9599609375}, {"start": 844.14, "end": 844.72, "word": " لمين", "probability": 0.6819661458333334}, {"start": 844.72, "end": 845.26, "word": " لل", "probability": 0.368408203125}, {"start": 845.26, "end": 845.7, "word": " F", "probability": 0.473876953125}, {"start": 845.7, "end": 846.58, "word": " is", "probability": 0.875}, {"start": 846.58, "end": 847.44, "word": " decreasing", "probability": 0.95947265625}, {"start": 847.44, "end": 848.74, "word": " نيجي", "probability": 0.9647216796875}, {"start": 848.74, "end": 849.04, "word": " الأن", "probability": 0.810546875}, {"start": 849.04, "end": 850.0, "word": " conversely", "probability": 0.91455078125}, {"start": 850.0, "end": 851.06, "word": " و", "probability": 0.98095703125}, {"start": 851.06, "end": 851.48, "word": " نشوف", "probability": 0.9352213541666666}, {"start": 851.48, "end": 851.8, "word": " كيف", "probability": 0.97216796875}, {"start": 851.8, "end": 852.56, "word": " نبرهن", "probability": 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0.545806884765625}, {"start": 862.57, "end": 863.17, "word": " برضه", "probability": 0.9427083333333334}, {"start": 863.17, "end": 863.45, "word": " انا", "probability": 0.728515625}, {"start": 863.45, "end": 865.03, "word": " conversely", "probability": 0.6107177734375}, {"start": 865.03, "end": 867.71, "word": " suppose", "probability": 0.7734375}, {"start": 867.71, "end": 870.81, "word": " that", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 37, "seek": 89435, "start": 872.17, "end": 894.35, "text": "F prime of X أصغر أو سوى سفر لكل X موجودة في الآية ماشي الحال شوفوا صلى الله عليه الصلاة والسلام أنا بدأ أثبت أن F is decreasing يعني بدأ أفترض أن X أصغر أو أخد أي قيمتين X واحد و X اتنين element اتنين", "tokens": [37, 5835, 295, 1783, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 8608, 5172, 2288, 5296, 28820, 1783, 3714, 29245, 23328, 3660, 8978, 6024, 95, 10632, 3714, 33599, 1829, 21542, 6027, 13412, 38688, 14407, 20328, 23942, 21984, 47356, 31767, 15040, 3660, 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{"start": 882.07, "end": 882.53, "word": " الصلاة", "probability": 0.8375651041666666}, {"start": 882.53, "end": 883.03, "word": " والسلام", "probability": 0.9482421875}, {"start": 883.03, "end": 883.79, "word": " أنا", "probability": 0.74853515625}, {"start": 883.79, "end": 884.07, "word": " بدأ", "probability": 0.598876953125}, {"start": 884.07, "end": 884.31, "word": " أثبت", "probability": 0.868896484375}, {"start": 884.31, "end": 884.43, "word": " أن", "probability": 0.7314453125}, {"start": 884.43, "end": 884.69, "word": " F", "probability": 0.7978515625}, {"start": 884.69, "end": 884.89, "word": " is", "probability": 0.56884765625}, {"start": 884.89, "end": 885.43, "word": " decreasing", "probability": 0.9609375}, {"start": 885.43, "end": 886.47, "word": " يعني", "probability": 0.95703125}, {"start": 886.47, "end": 886.81, "word": " بدأ", "probability": 0.6683349609375}, {"start": 886.81, "end": 887.17, "word": " أفترض", "probability": 0.909912109375}, {"start": 887.17, "end": 887.35, "word": " أن", "probability": 0.779296875}, {"start": 887.35, "end": 887.81, "word": " X", "probability": 0.9814453125}, {"start": 887.81, "end": 888.83, "word": " أصغر", "probability": 0.951171875}, {"start": 888.83, "end": 888.99, "word": " أو", "probability": 0.80615234375}, {"start": 888.99, "end": 889.91, "word": " أخد", "probability": 0.7688802083333334}, {"start": 889.91, "end": 890.19, "word": " أي", "probability": 0.73388671875}, {"start": 890.19, "end": 891.13, "word": " قيمتين", "probability": 0.944580078125}, {"start": 891.13, "end": 891.37, "word": " X", "probability": 0.71044921875}, {"start": 891.37, "end": 891.85, "word": " واحد", "probability": 0.810791015625}, {"start": 891.85, "end": 892.35, "word": " و", "probability": 0.85791015625}, {"start": 892.35, "end": 892.57, "word": " X", "probability": 0.79248046875}, {"start": 892.57, "end": 893.13, "word": " اتنين", "probability": 0.8194580078125}, {"start": 893.13, "end": 893.65, "word": " element", "probability": 0.5068359375}, {"start": 893.65, "end": 894.35, "word": " اتنين", "probability": 0.77813720703125}], "temperature": 1.0}, {"id": 38, "seek": 91553, "start": 895.01, "end": 915.53, "text": "أخدت أي two elements element x1 وx2 element in I تحقق such that x1 أصغر من مين من x2 أصغر أو يساوي x .. x1 أصغر أو يساوي x2 بس في حالة ال x1 بيساوي x2 ما هي automatic F of x1 بيساوي F of x2 يعني متحققة", "tokens": [10721, 9778, 3215, 2655, 36632, 732, 4959, 4478, 2031, 16, 4032, 87, 17, 4478, 294, 286, 6055, 5016, 4587, 4587, 1270, 300, 2031, 16, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 2031, 17, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2031, 4386, 2031, 16, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2031, 17, 4724, 3794, 8978, 11331, 6027, 3660, 2423, 2031, 16, 4724, 1829, 3794, 995, 45865, 2031, 17, 19446, 39896, 12509, 479, 295, 2031, 16, 4724, 1829, 3794, 995, 45865, 479, 295, 2031, 17, 37495, 22653, 44650, 5016, 4587, 28671], "avg_logprob": 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"probability": 0.99267578125}, {"start": 911.45, "end": 911.59, "word": " ما", "probability": 0.595703125}, {"start": 911.59, "end": 911.73, "word": " هي", "probability": 0.6845703125}, {"start": 911.73, "end": 912.59, "word": " automatic", "probability": 0.82470703125}, {"start": 912.59, "end": 912.85, "word": " F", "probability": 0.453369140625}, {"start": 912.85, "end": 913.03, "word": " of", "probability": 0.642578125}, {"start": 913.03, "end": 913.41, "word": " x1", "probability": 0.96240234375}, {"start": 913.41, "end": 913.75, "word": " بيساوي", "probability": 0.87041015625}, {"start": 913.75, "end": 913.93, "word": " F", "probability": 0.9765625}, {"start": 913.93, "end": 914.07, "word": " of", "probability": 0.96875}, {"start": 914.07, "end": 914.49, "word": " x2", "probability": 0.993896484375}, {"start": 914.49, "end": 914.71, "word": " يعني", "probability": 0.930419921875}, {"start": 914.71, "end": 915.53, "word": " متحققة", "probability": 0.9498291015625}], "temperature": 1.0}, {"id": 39, "seek": 94162, "start": 915.9, "end": 941.62, "text": "إذن الان x1 أصغر من x2 عملتها strictly عشان بتعمل منها interval وحالتي ال x1 بيساوي x2 is a trivial case تتحقق مدامة x1 أصغر تساوي x2 إذن عشان a function f of x1 بيساوي f of x2 إذا التحقق اللي هي مين ال decreasing واضحة الان x1 أصغر من x2 الآن we apply", "tokens": [28814, 8848, 1863, 2423, 7649, 2031, 16, 5551, 9381, 17082, 2288, 9154, 2031, 17, 6225, 42213, 2655, 11296, 20792, 6225, 8592, 7649, 39894, 25957, 1211, 9154, 11296, 15035, 4032, 5016, 6027, 31371, 2423, 2031, 16, 4724, 1829, 3794, 995, 45865, 2031, 17, 307, 257, 26703, 1389, 6055, 2655, 5016, 4587, 4587, 3714, 3215, 10943, 3660, 2031, 16, 5551, 9381, 17082, 2288, 6055, 3794, 995, 45865, 2031, 17, 11933, 8848, 1863, 6225, 8592, 7649, 257, 2445, 283, 295, 2031, 16, 4724, 1829, 3794, 995, 45865, 283, 295, 2031, 17, 11933, 15730, 16712, 5016, 4587, 4587, 13672, 1829, 39896, 3714, 9957, 2423, 23223, 4032, 46958, 5016, 3660, 2423, 7649, 2031, 16, 5551, 9381, 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937.2, "end": 938.44, "word": " x1", "probability": 0.899658203125}, {"start": 938.44, "end": 938.68, "word": " أصغر", "probability": 0.9891357421875}, {"start": 938.68, "end": 938.78, "word": " من", "probability": 0.99462890625}, {"start": 938.78, "end": 939.34, "word": " x2", "probability": 0.99658203125}, {"start": 939.34, "end": 940.34, "word": " الآن", "probability": 0.6263427734375}, {"start": 940.34, "end": 941.1, "word": " we", "probability": 0.88427734375}, {"start": 941.1, "end": 941.62, "word": " apply", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 40, "seek": 96420, "start": 945.1, "end": 964.2, "text": "الـ Mean Value Theorem لأن احنا هذه نبارع كورولرز أو نظريات على الـ Mean Value Theorem فالمتوقع أن نستخدم الـ Mean Value Theorem في أثباتها فهنا سنستخدم الـ Mean Value Theorem نطبق الـ Mean Value Theorem على الانترفل الموجود بين X1 و X2", "tokens": [6027, 39184, 12302, 39352, 440, 37956, 5296, 33456, 1975, 5016, 8315, 29538, 8717, 3555, 9640, 3615, 9122, 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X2 يعني موجودة في الـ I اللي هي لإن هذي جزئية من مين من I there exist C such that F prime of C بساوي F of X1 أو F of X2 ناقص", "tokens": [28814, 15730, 13412, 32887, 9566, 2423, 39184, 12302, 39352, 440, 37956, 3714, 6027, 11296, 44650, 5016, 4587, 28671, 11933, 15730, 456, 2514, 550, 456, 2514, 383, 6055, 29399, 2304, 1829, 30731, 27188, 2655, 25720, 1783, 16, 4032, 1783, 17, 37495, 22653, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 286, 13672, 1829, 39896, 5296, 28814, 1863, 8032, 8848, 1829, 10874, 11622, 19986, 10632, 9154, 3714, 9957, 9154, 286, 456, 2514, 383, 1270, 300, 479, 5835, 295, 383, 4724, 3794, 995, 45865, 479, 295, 1783, 16, 34051, 479, 295, 1783, 17, 8717, 995, 4587, 9381], "avg_logprob": -0.25847739773861905, "compression_ratio": 1.444954128440367, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 977.94, "end": 978.28, "word": "إذا", "probability": 0.6904296875}, {"start": 978.28, "end": 978.98, "word": " شروط", "probability": 0.7991536458333334}, 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تكعيب بالشكل هذا هذا الان strictly ايه شمالها decreasing هذه F is strictly decreasing", "tokens": [3555, 3794, 995, 2407, 8608, 6027, 3555, 1783, 6055, 4117, 3615, 1829, 3555, 23758, 32748, 6027, 3660, 23758, 32748, 6027, 3660, 44945, 25957, 1211, 1895, 260, 655, 50113, 1211, 479, 295, 1783, 8608, 995, 2407, 8608, 6027, 3555, 1783, 6055, 4117, 3615, 1829, 3555, 20666, 8592, 28820, 23758, 23758, 2423, 7649, 20792, 1975, 1829, 3224, 13412, 2304, 6027, 11296, 23223, 29538, 479, 307, 20792, 23223], "avg_logprob": -0.3001893943909443, "compression_ratio": 1.6689655172413793, "no_speech_prob": 6.377696990966797e-06, "words": [{"start": 1415.22, "end": 1415.74, "word": "بساو", "probability": 0.733154296875}, {"start": 1415.74, "end": 1416.28, "word": " سالب", "probability": 0.70751953125}, {"start": 1416.28, "end": 1416.52, "word": " X", "probability": 0.6630859375}, {"start": 1416.52, "end": 1417.12, "word": " تكعيب", "probability": 0.92978515625}, {"start": 1417.12, "end": 1417.96, "word": 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95, "seek": 234478, "start": 2329.44, "end": 2344.78, "text": "نجرها بس من عندنا هنا هي اللي قلته بس نجرها من النظرية let f be continuous on the interval a و b إذا إيش مخصر دين إن ال function is continuous على فترة a و b و ناخد c عبارة عن interior point لمين", "tokens": [1863, 7435, 2288, 11296, 4724, 3794, 9154, 43242, 8315, 34105, 39896, 13672, 1829, 12174, 1211, 47395, 4724, 3794, 8717, 7435, 2288, 11296, 9154, 28239, 19913, 2288, 10632, 718, 283, 312, 10957, 322, 264, 15035, 257, 4032, 272, 11933, 15730, 11933, 1829, 8592, 3714, 9778, 9381, 2288, 11778, 9957, 36145, 2423, 2445, 307, 10957, 15844, 6156, 2655, 25720, 257, 4032, 272, 4032, 8717, 47283, 3215, 269, 6225, 3555, 9640, 3660, 18871, 10636, 935, 32767, 9957], "avg_logprob": -0.3145833277702332, "compression_ratio": 1.5053763440860215, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2329.44, "end": 2330.0, "word": "نجرها", "probability": 0.609130859375}, {"start": 2330.0, "end": 2330.22, "word": " بس", 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3431.46, "word": " 0", "probability": 0.84716796875}, {"start": 3431.46, "end": 3431.92, "word": ",x", "probability": 0.86962890625}, {"start": 3431.92, "end": 3432.72, "word": " such", "probability": 0.93310546875}, {"start": 3432.72, "end": 3433.26, "word": " that", "probability": 0.95849609375}, {"start": 3433.26, "end": 3434.0, "word": " f", "probability": 0.55029296875}, {"start": 3434.0, "end": 3434.5, "word": " prime", "probability": 0.6083984375}, {"start": 3434.5, "end": 3434.88, "word": " of", "probability": 0.95654296875}, {"start": 3434.88, "end": 3435.46, "word": " c", "probability": 0.9326171875}, {"start": 3435.46, "end": 3436.6, "word": " بيساوي", "probability": 0.674609375}, {"start": 3436.6, "end": 3436.94, "word": " f", "probability": 0.84765625}, {"start": 3436.94, "end": 3437.18, "word": " of", "probability": 0.7939453125}, {"start": 3437.18, "end": 3437.7, "word": " x", "probability": 0.9892578125}, {"start": 3437.7, "end": 3438.7, "word": " ناقص", "probability": 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3460.35, "word": " Sin", "probability": 0.76953125}, {"start": 3460.35, "end": 3460.91, "word": " X", "probability": 0.9931640625}, {"start": 3460.91, "end": 3462.23, "word": " بيساوي", "probability": 0.80458984375}, {"start": 3462.23, "end": 3462.75, "word": " X", "probability": 0.98193359375}, {"start": 3462.75, "end": 3463.49, "word": " في", "probability": 0.70263671875}, {"start": 3463.49, "end": 3463.95, "word": " Cos", "probability": 0.96142578125}, {"start": 3463.95, "end": 3464.53, "word": " C", "probability": 0.96435546875}, {"start": 3464.53, "end": 3465.87, "word": " لكن", "probability": 0.9365234375}, {"start": 3465.87, "end": 3466.33, "word": " الآن", "probability": 0.6158447265625}, {"start": 3466.33, "end": 3466.57, "word": " أنا", "probability": 0.62451171875}, {"start": 3466.57, "end": 3466.87, "word": " عندي", "probability": 0.79833984375}, {"start": 3466.87, "end": 3467.33, "word": " Cos", "probability": 0.9453125}, {"start": 3467.33, "end": 3467.99, "word": " C", 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20328, 9957, 2423, 1783, 49374, 8717, 4587, 9381, 1783, 4032, 1783, 5296, 28820, 1783, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 20328, 5172, 2288, 4032, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984], "avg_logprob": -0.2496448809450323, "compression_ratio": 1.6931818181818181, "no_speech_prob": 0.066162109375, "words": [{"start": 3495.37, "end": 3495.85, "word": "أظهر", "probability": 0.598236083984375}, {"start": 3495.85, "end": 3496.15, "word": " يساوي", "probability": 0.76678466796875}, {"start": 3496.15, "end": 3496.55, "word": " X", "probability": 0.6357421875}, {"start": 3496.55, "end": 3497.49, "word": " وأكبر", "probability": 0.8391927083333334}, {"start": 3497.49, "end": 3497.67, "word": " أو", "probability": 0.85595703125}, {"start": 3497.67, "end": 3498.11, "word": " يساوي", "probability": 0.9569091796875}, {"start": 3498.11, "end": 3498.65, "word": " سالب", "probability": 0.73828125}, {"start": 3498.65, "end": 3499.11, "word": " X", "probability": 0.99072265625}, {"start": 3499.11, "end": 3499.95, "word": " هذا", "probability": 0.87548828125}, {"start": 3499.95, "end": 3500.37, "word": " الأن", "probability": 0.68408203125}, {"start": 3500.37, "end": 3500.79, "word": " لكل", "probability": 0.97509765625}, {"start": 3500.79, "end": 3501.09, "word": " X", "probability": 0.97998046875}, {"start": 3501.09, "end": 3501.53, "word": " لاتش", "probability": 0.3600260416666667}, {"start": 3501.53, "end": 3501.87, "word": " أكبر", "probability": 0.9659830729166666}, {"start": 3501.87, "end": 3502.05, "word": " من", "probability": 0.994140625}, {"start": 3502.05, "end": 3502.45, "word": " صفر", "probability": 0.7049967447916666}, {"start": 3502.45, "end": 3503.05, "word": " but", "probability": 0.292236328125}, {"start": 3503.05, "end": 3503.43, "word": " for", "probability": 0.93212890625}, {"start": 3503.43, "end": 3503.67, "word": " X", "probability": 0.966796875}, {"start": 3503.67, "end": 3504.15, "word": " بتساوي", "probability": 0.9443359375}, {"start": 3504.15, "end": 3504.51, "word": " zero", "probability": 0.3857421875}, {"start": 3504.51, "end": 3504.77, "word": " this", "probability": 0.67529296875}, {"start": 3504.77, "end": 3504.93, "word": " is", "probability": 0.958984375}, {"start": 3504.93, "end": 3505.55, "word": " trivial", "probability": 0.607421875}, {"start": 3505.55, "end": 3506.15, "word": " إذا", "probability": 0.7314453125}, {"start": 3506.15, "end": 3506.49, "word": " صار", "probability": 0.88427734375}, {"start": 3506.49, "end": 3506.81, "word": " صين", "probability": 0.6376953125}, {"start": 3506.81, "end": 3506.95, "word": " ال", "probability": 0.54296875}, {"start": 3506.95, "end": 3507.23, "word": " X", "probability": 0.95458984375}, {"start": 3507.23, "end": 3507.53, "word": " بين", "probability": 0.95458984375}, {"start": 3507.53, "end": 3507.87, "word": " نقص", "probability": 0.8719075520833334}, {"start": 3507.87, "end": 3508.13, "word": " X", "probability": 0.98681640625}, {"start": 3508.13, "end": 3508.31, "word": " و", "probability": 0.9501953125}, {"start": 3508.31, "end": 3508.71, "word": " X", "probability": 0.71435546875}, {"start": 3508.71, "end": 3509.67, "word": " لكل", "probability": 0.9677734375}, {"start": 3509.67, "end": 3510.17, "word": " X", "probability": 0.99072265625}, {"start": 3510.17, "end": 3510.89, "word": " أكبر", "probability": 0.974609375}, {"start": 3510.89, "end": 3511.09, "word": " أو", "probability": 0.96826171875}, {"start": 3511.09, "end": 3511.73, "word": " يساوي", "probability": 0.985595703125}, {"start": 3511.73, "end": 3512.87, "word": " صفر", "probability": 0.9715169270833334}, {"start": 3512.87, "end": 3513.25, "word": " و", "probability": 0.5703125}, {"start": 3513.25, "end": 3513.63, "word": " المرة", "probability": 0.7587890625}, {"start": 3513.63, "end": 3514.23, "word": " القادمة", "probability": 0.98974609375}, {"start": 3514.23, "end": 3514.47, "word": " ان", "probability": 0.5361328125}, {"start": 3514.47, "end": 3514.73, "word": " شاء", "probability": 0.9873046875}, {"start": 3514.73, "end": 3514.97, "word": " الله", "probability": 0.95166015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3515.315375, "duration_after_vad": 3384.018124999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Xd6TZqtP5_4_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Xd6TZqtP5_4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24c69ea1078d4077a7c63afd6e6f838ec81f5561
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/Xd6TZqtP5_4_raw.srt
@@ -0,0 +1,1864 @@
+1
+00:00:04,930 --> 00:00:09,090
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:09,090 --> 00:00:12,830
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:12,830 --> 00:00:19,690
+أجمعين هذه المحاضرة رقم عشرين في مساق تحليل حقيقه
+
+4
+00:00:19,690 --> 00:00:24,630
+اتنين لطلاب وطالبات الجامعة الإسلامية كلية العلوم
+
+5
+00:00:24,630 --> 00:00:32,660
+قسم رياضياتهنستكمل اليوم الحديث في chapter 8 اللي
+
+6
+00:00:32,660 --> 00:00:38,380
+هو sequences of functions بالظبط هنستكمل الحديث في
+
+7
+00:00:38,380 --> 00:00:42,800
+ال section الأول اللي وجفنا عند نقطة فيه اللي هو
+
+8
+00:00:42,800 --> 00:00:46,680
+ال section كان تحت عنوان born twice and uniform
+
+9
+00:00:46,680 --> 00:00:51,660
+convergenceوفرّجنا بين اللي هو الـ pointwise و ال
+
+10
+00:00:51,660 --> 00:00:54,540
+uniform convergence قلنا أي uniform convergence
+
+11
+00:00:54,540 --> 00:00:58,140
+هيكون pointwise ولكن ال convergence لا يجب أن تكون
+
+12
+00:00:58,140 --> 00:01:01,920
+حقيقية في الجامعة و أخدنا بعض النظريات أول اشي
+
+13
+00:01:01,920 --> 00:01:04,980
+أعرفنا شو معناته اللي هو ال pointwise convergence
+
+14
+00:01:04,980 --> 00:01:11,180
+و بعدين أخدنا مثال على اللي هي ال function g of a
+
+15
+00:01:11,180 --> 00:01:14,440
+g n of x او sequence of functions g n of x بيستوي
+
+16
+00:01:14,440 --> 00:01:18,950
+x أس انو أثبتنا إن هذه pointwise convergence على
+
+17
+00:01:18,950 --> 00:01:23,190
+الفترة المفتوحة بالنقص 1 1 لدلة g of x بالساوية 0
+
+18
+00:01:23,190 --> 00:01:29,210
+1 زي ما هي أمامنا بعد هيك جينا حكينا عن اللي هو
+
+19
+00:01:29,210 --> 00:01:34,410
+مثال آخر أخدنا limit 1 على n sin n x زائد n قلنا
+
+20
+00:01:34,410 --> 00:01:37,970
+هذه ال sequence of functions برضه converts to the
+
+21
+00:01:37,970 --> 00:01:44,540
+zero function أو كانت اللي هو هذه مثال آخرعلى الـ
+
+22
+00:01:44,540 --> 00:01:50,020
+Point Convergence على كل R الآن إيجينا بعد هيك
+
+23
+00:01:50,020 --> 00:01:55,080
+اللي أخدنا لمّا و كيف اللي هو ان ترجم شو معناته Fn
+
+24
+00:01:55,080 --> 00:02:00,400
+Converges Point Twice قولنا الـ K اللي بيلاقيها
+
+25
+00:02:00,400 --> 00:02:04,720
+بتعتمد على Y و X في ال Point Twice لإنه نقطة نقطة
+
+26
+00:02:04,720 --> 00:02:09,550
+ال convergenceو بعدين اجينا عرفنا شو معناه uniform
+
+27
+00:02:09,550 --> 00:02:12,750
+convergence و قولنا في حالة ال uniform convergence
+
+28
+00:02:12,750 --> 00:02:16,630
+هيكون عندي اللي هو ال K اللي بنلاقيها بس بتعتمد
+
+29
+00:02:16,630 --> 00:02:20,730
+على ال epsilon و الباقي زي ما هو يعني بتنفع ال K
+
+30
+00:02:20,730 --> 00:02:24,730
+هذه لكل ال Xات اللي في ال A note عشان هيك بنسمي
+
+31
+00:02:24,730 --> 00:02:28,110
+uniform convergenceوقلنا إذا كانت الـ sequence
+
+32
+00:02:28,110 --> 00:02:31,530
+uniformly convergence أكيد هتكون convergence و
+
+33
+00:02:31,530 --> 00:02:36,230
+بعدين أخدنا ال criterion أو اللمّة اللي بننفي فيها
+
+34
+00:02:36,230 --> 00:02:40,170
+أو بنقول شو معناه Fn does not converge uniformly
+
+35
+00:02:40,170 --> 00:02:46,400
+to اللي هو function Fقلنا ان الـ fn لا يتعامل مع
+
+36
+00:02:46,400 --> 00:02:51,400
+عمليات الـ fn لا يتعامل مع عمليات الـ f إذا كان
+
+37
+00:02:51,400 --> 00:02:58,280
+لجينا إبسلون و سبسيكوينس fnk of fn سبسيكوينس من
+
+38
+00:02:58,280 --> 00:03:04,040
+سيكوينس الـ functions هذه وعندي سيكوينس xkفي الـ A
+
+39
+00:03:04,040 --> 00:03:08,600
+Note بحيث تحقق F N K of X K ناقص F of X K أكبر شهر
+
+40
+00:03:08,600 --> 00:03:14,000
+Y Note هذا على بعضه يعني أن الـ F N does not
+
+41
+00:03:14,000 --> 00:03:17,320
+converge uniformly to الـ function اللي أمامنا
+
+42
+00:03:17,320 --> 00:03:22,320
+اللي هي F هذا حكينا عنه المرة الماضية و أثبتناها و
+
+43
+00:03:22,320 --> 00:03:27,240
+بعدين أخدنا مثال قلنا خد اللي هو G N of X بيساوي X
+
+44
+00:03:27,240 --> 00:03:31,670
+plus Nsequence of functions على الـ R أحنا أثبتنا
+
+45
+00:03:31,670 --> 00:03:35,810
+إنه هذه اللي هي الـ sequence قبل بشوية اللي شفناها
+
+46
+00:03:35,810 --> 00:03:43,610
+إنها converge to G of X هذه 1 0 X بساوة 1 و X
+
+47
+00:03:43,610 --> 00:03:48,450
+element نقص 1 1 converge point-wise لهذه الـ
+
+48
+00:03:48,450 --> 00:03:52,350
+functionالان و أثبتناها برضه و أثبتناها المرة
+
+49
+00:03:52,350 --> 00:03:56,370
+الماضية ان GM لا تتعامل بشكل عام لهذه الـ function
+
+50
+00:03:56,370 --> 00:04:00,070
+على الفترة وهذا تأكيد على كلامنا ان الـ point wise
+
+51
+00:04:00,070 --> 00:04:06,110
+convergence لا يتعامل بشكل عام و هي مثال على ذلك
+
+52
+00:04:06,740 --> 00:04:12,940
+الآن أعرفنا شو معنات اللي هو برضه لو كانت عندي
+
+53
+00:04:12,940 --> 00:04:16,280
+function Phi اللي هي bounded function شو معنات
+
+54
+00:04:16,280 --> 00:04:19,900
+normها قولنا ال norm لـ function A على اللي هي ال
+
+55
+00:04:19,900 --> 00:04:24,060
+6A هو عبارة عن ال supremum لقيمة ال function 5X X
+
+56
+00:04:24,060 --> 00:04:27,660
+element A هذا في حالة اللي هي mean ال bounded
+
+57
+00:04:27,660 --> 00:04:33,100
+function اللي هي اللي هي سمنها Phi بعد هيك جينا
+
+58
+00:04:34,730 --> 00:04:38,450
+وحكينا عن اللمّة اللي أمامنا هذه أنه لو كان اللي
+
+59
+00:04:38,450 --> 00:04:41,450
+هي a sequence of unbounded functions on A subset
+
+60
+00:04:41,450 --> 00:04:44,890
+من R اللي هي the sequence of meal يعني هذا test
+
+61
+00:04:44,890 --> 00:04:47,170
+للـ uniform convergence أو عدم الـ uniform
+
+62
+00:04:47,170 --> 00:04:51,670
+convergence لعائلة من الدوال أو sequence of
+
+63
+00:04:51,670 --> 00:04:55,580
+functions اللي هي of unbounded functionfunctions
+
+64
+00:04:55,580 --> 00:04:59,680
+إذن هذه بتنفع لمين للـbounded functions بتعملي
+
+65
+00:04:59,680 --> 00:05:04,280
+test عليها إنها uniform ولا مش uniform ببساطة بس
+
+66
+00:05:04,280 --> 00:05:08,680
+بنجيب norm ال FN نقص F وبنشوفه إذا كان norm مع ال
+
+67
+00:05:08,680 --> 00:05:12,700
+A بروح للسفر معناته على طول بنقول FN converges
+
+68
+00:05:12,700 --> 00:05:16,260
+uniformly to مين؟ To F إذا كان ال norm هذا does
+
+69
+00:05:16,260 --> 00:05:20,160
+not converge to zero معناته كل سنة و انت تسأل مين؟
+
+70
+00:05:20,160 --> 00:05:24,360
+اللي هو ال FN does not converge uniformly to مين؟
+
+71
+00:05:24,360 --> 00:05:29,060
+To Fهذه الآن اللي وصلنا عندها اللي هي اللي ما
+
+72
+00:05:29,060 --> 00:05:36,380
+واخدنا مثال برضه عليها اللي هو GN of XN قلنا هذا
+
+73
+00:05:36,380 --> 00:05:40,260
+اللي هو المثال
+
+74
+00:05:40,260 --> 00:05:45,890
+اللي أمامناكيف نحله على اللي هي ال .. ال .. ال ..
+
+75
+00:05:45,890 --> 00:05:49,550
+النظرية اللي قبل بشوية قولنا خد GN of X بالساوية X
+
+76
+00:05:49,550 --> 00:05:55,810
+أُس N على الفترة مين؟ سفر واحد لجينا انه .. انه GN
+
+77
+00:05:55,810 --> 00:06:00,510
+converts uniformly لمين؟ لـG of X على الفترة اللي
+
+78
+00:06:00,510 --> 00:06:05,410
+أمامنا اللي هي هذه اللي هي فترة Zero وواحد طبعا با
+
+79
+00:06:05,410 --> 00:06:09,180
+.. واضح انه الدالة هذهbounded على هذه الفترة عشان
+
+80
+00:06:09,180 --> 00:06:13,220
+هي تنفي عن السخدم اللي هي النظرية اللي فوق هذه
+
+81
+00:06:13,220 --> 00:06:17,980
+المرة الماضية برضه حكيناها أو جينا أو جفنا عند
+
+82
+00:06:17,980 --> 00:06:23,260
+اللي هي المثال التاني طبعا اللي هي المثال الفجاني
+
+83
+00:06:23,260 --> 00:06:28,300
+لو على السريع ذكرناكم فيها الان ال function مين هي
+
+84
+00:06:28,300 --> 00:06:34,460
+عندى ال function عبارة عن g n of x او sequence of
+
+85
+00:06:34,460 --> 00:06:39,410
+functions بسوء x أس nالان لو جي ده أخدت ال norm
+
+86
+00:06:39,410 --> 00:06:44,870
+لجي ان ناقص الجي هي ال جي ان وهي الجي خد ال norm
+
+87
+00:06:44,870 --> 00:06:50,730
+إلها خد ال norm إلها معايا
+
+88
+00:06:50,730 --> 00:06:54,650
+يا جماعة هي ال norm إلها لجي ان ناقص جي بساوي اللي
+
+89
+00:06:54,650 --> 00:06:59,170
+هو عبارة عن ال supremum X أس ان ناقص سفر يعني X أس
+
+90
+00:06:59,170 --> 00:07:05,750
+ان لمن؟ لل X المتزير واحد او الجزء الثاني X أس ان
+
+91
+00:07:05,750 --> 00:07:10,970
+ناقص واحداللي هي في حالة ال X بالساوية واحد لكن في
+
+92
+00:07:10,970 --> 00:07:13,490
+حالة ال X بالساوية واحد بيصير G and X and بيتساوية
+
+93
+00:07:13,490 --> 00:07:17,370
+واحد واحد نقص واحد بيصير سفر بيصير عندي ال norm
+
+94
+00:07:17,370 --> 00:07:20,490
+هذا عبارة عن ال supremum X and X في الفترة Zero
+
+95
+00:07:20,490 --> 00:07:24,340
+واحد و Zero لما ال X بالساوية واحدالـ Supremum
+
+96
+00:07:24,340 --> 00:07:29,600
+للقيمة هذه عندي أكيد إيش هيساوي عند اللي هي X
+
+97
+00:07:29,600 --> 00:07:34,380
+بتساوي واحد و Y ساوي اللي هو عبارة أو قبل اللي هي
+
+98
+00:07:34,380 --> 00:07:40,620
+ال Supremum ل ال 6 هذه طبعا هنا X element in 01 و
+
+99
+00:07:40,620 --> 00:07:44,780
+1 اللي هي not included فبكون عندي ال Supremum
+
+100
+00:07:44,780 --> 00:07:50,060
+للقيم X أسن في الفترة من 01 إيش هيساوي؟ هيساوي
+
+101
+00:07:50,060 --> 00:07:57,150
+واحد يعني ال Supremumلأ x أسن such that x element
+
+102
+00:07:57,150 --> 00:08:05,210
+in zero و واحد حتى لو كانت closed هذه و اللي هو
+
+103
+00:08:05,210 --> 00:08:08,730
+اتحاد
+
+104
+00:08:08,730 --> 00:08:13,690
+ال zero ال supreme لها طبعا لل x أسن ايش حيساو في
+
+105
+00:08:13,690 --> 00:08:17,330
+النهاية حيساو واحد و ممكن اثبات هذا اللي هو عن
+
+106
+00:08:17,330 --> 00:08:21,900
+طريق ال least upper boundكيف نثبته زي ما كنا نثبت
+
+107
+00:08:21,900 --> 00:08:26,540
+فيه اللي هو تحليل واحد مش ماكانوا نثبته لان فبصير
+
+108
+00:08:26,540 --> 00:08:30,280
+عندي ال norm لجي عن نقص جي اش بساوي واحدما دام الـ
+
+109
+00:08:30,280 --> 00:08:33,980
+norm لجي أن بيساوي واحد إذا ال norm لجي أن نقص جي
+
+110
+00:08:33,980 --> 00:08:40,920
+does not converge as if الجي أن لا يتعامل مع الجي
+
+111
+00:08:40,920 --> 00:08:47,040
+أن نقص جي أن نقص جي أن نقص جي أن نقص جي أن نقص جي
+
+112
+00:08:47,040 --> 00:08:54,180
+أن نقص جي أن نقص جي أن نقص جي أن نقص جي أن نقص جي
+
+113
+00:08:54,180 --> 00:08:54,660
+أن نقص جي أن نقص جي أن نقص جي أن نقص جي أن نقص جي
+
+114
+00:08:54,660 --> 00:08:54,660
+أن نقص جي أن نقص جي أن نقص جي أن نقص جي أن نقص جي
+
+115
+00:08:54,660 --> 00:08:54,660
+أن نقص جي أن نقص جي أن نقص جي أن نقص جي أن نقص جي
+
+116
+00:08:54,660 --> 00:08:55,450
+أن نقص جي أن نقص جي أن نقص جي أن نقص جي أن نقنقص
+
+117
+00:08:55,450 --> 00:09:00,190
+الـ G برضه هيروح على مين؟ على القيمة واحد يعني مش
+
+118
+00:09:00,190 --> 00:09:05,890
+هيروح للسفر يعني إذاً GN does not converge
+
+119
+00:09:05,890 --> 00:09:10,850
+uniformly to مين؟ to G وهذا مثال عليه اللي هو does
+
+120
+00:09:10,850 --> 00:09:16,030
+not converge uniformly على الـ G مثال على اللي هو
+
+121
+00:09:16,030 --> 00:09:20,250
+توظيف هذه النظرية الجابلة بشوية لإثبات عدم ال
+
+122
+00:09:20,250 --> 00:09:23,930
+uniformlyconvergent أو لو بدنا نثبت انه formally
+
+123
+00:09:23,930 --> 00:09:29,910
+convergent ممكن نستخدم هذه بس نثبت ان ال norm بروح
+
+124
+00:09:29,910 --> 00:09:33,710
+لصفر بس بحيث انه تكون اللي هي ال GN عبارة عن
+
+125
+00:09:33,710 --> 00:09:38,350
+sequence زي ما قلنا of bounded functions طيب ميجي
+
+126
+00:09:38,350 --> 00:09:42,030
+مثال آخر ماعليش سريع لأنه حكينا المرة الماضية ميجي
+
+127
+00:09:42,030 --> 00:09:48,070
+لا اللي هو مثلنا هذانجي لمثالنا fn of x بيساوي x
+
+128
+00:09:48,070 --> 00:09:53,050
+على n مش x أسان x على n for every x element in R
+
+129
+00:09:53,050 --> 00:09:58,950
+اللي هم بيقوللي show that limit fn of x as x بتروح
+
+130
+00:09:58,950 --> 00:10:02,850
+إلى infinity بيساوي f of xلأ كل x element in R
+
+131
+00:10:02,850 --> 00:10:08,430
+where f of x ايش بتساوي سفر and fn x بتروح ل f of
+
+132
+00:10:08,430 --> 00:10:11,610
+x من R هذا معناته اللي هو pointwise convergence
+
+133
+00:10:11,610 --> 00:10:16,330
+يعني بده limit ال fn of x ناخد اي x element in R
+
+134
+00:10:16,330 --> 00:10:19,490
+ناخد x element in R نثبت ان limit fn x ايش هتساوي
+
+135
+00:10:19,490 --> 00:10:24,830
+هتساوي سفرالان هذا اللي هو عبارة عن اللي هو الـ
+
+136
+00:10:24,830 --> 00:10:30,110
+pointwise convergence بعد شوية هنثبت انه عندنا هذا
+
+137
+00:10:30,110 --> 00:10:34,530
+مش هيكون فيه عندى اللي هو uniform convergence على
+
+138
+00:10:34,530 --> 00:10:40,790
+مكان ما في الأرض نرجع لمثالنا اللي هو عندى مثال
+
+139
+00:10:40,790 --> 00:10:48,880
+اللي هو Fn X بسوية X على Nلـ X element in R عندي F
+
+140
+00:10:48,880 --> 00:10:52,820
+of X بيساوي 0 لكل X element in R بدنا نثبت أن F N
+
+141
+00:10:52,820 --> 00:10:56,500
+of X بتروح pointwise ل F of X لكل X element in R
+
+142
+00:10:56,500 --> 00:11:01,180
+وبدنا نثبت أن F N does not converge لـ F uniformly
+
+143
+00:11:01,180 --> 00:11:04,500
+لـ F on R يعني هذا هو عبارة عن pointwise
+
+144
+00:11:04,500 --> 00:11:10,170
+convergence لكن مش uniform convergenceبس هنا جيبنا
+
+145
+00:11:10,170 --> 00:11:14,310
+المثال عشان نقولك انه مش هنقدر نستخدم اللي هي
+
+146
+00:11:14,310 --> 00:11:17,630
+اللمّة اللي قبل بشوية لإنه عندي sequence of
+
+147
+00:11:17,630 --> 00:11:23,910
+functions Fn على R اللي هي is not bounded يعني لو
+
+148
+00:11:23,910 --> 00:11:29,150
+جينا أخدنا F1 of X بتساوي X على 1لكل x element in
+
+149
+00:11:29,150 --> 00:11:33,310
+R، وكأن f1 of x عبارة عن x، طبعا الـ x is not
+
+150
+00:11:33,310 --> 00:11:36,790
+bounded function، f2x التي هي x على 2 برضه is not
+
+151
+00:11:36,790 --> 00:11:40,250
+bounded، لأنها تبقى مالا نهاية رايحة من الجهتين،
+
+152
+00:11:40,250 --> 00:11:42,510
+واحد مالا نهاية و واحد سالب مالا نهاية،
+
+153
+00:11:48,910 --> 00:11:54,190
+عشان هيك ما بنقدرش نستخدم اللي هو عشان نثبت ال FN
+
+154
+00:11:54,190 --> 00:11:58,150
+does not converge uniformly بنقدرش نستخدم normal
+
+155
+00:11:58,150 --> 00:12:03,310
+FN ناقص F اللي هو يروح للسفر لإن هذه ال FN is not
+
+156
+00:12:03,530 --> 00:12:07,550
+bounded functions are not bounded functions يعني
+
+157
+00:12:07,550 --> 00:12:11,190
+اللي هو اللمّة لا تنطبق عليها عشان هيك هنضطر نروح
+
+158
+00:12:11,190 --> 00:12:15,450
+بالاستخدام التعريف أو نفي التعريف لل uniformly
+
+159
+00:12:15,450 --> 00:12:18,690
+convergence زي ما عملنا في مثال المرة الماضية
+
+160
+00:12:18,690 --> 00:12:25,290
+وخلّينا نشوف الحل نيجي الآن الجزء الأول الجزء
+
+161
+00:12:25,290 --> 00:12:32,700
+الأول سهل على طول اللي هو عندي لكل XElement in R
+
+162
+00:12:32,700 --> 00:12:40,460
+أكيد عندي limit of N of X لما N تروح إلى ماله
+
+163
+00:12:40,460 --> 00:12:47,240
+نهاية بساوي limit of N of X هي عبارة عن X على N as
+
+164
+00:12:47,240 --> 00:12:50,860
+N goes to infinity ويساوي كلكم بعرفيش هتساوي،
+
+165
+00:12:50,860 --> 00:12:56,030
+بتساوي سفريعني بمعنى آخر اللي هي الـ fn of x
+
+166
+00:12:56,030 --> 00:13:00,990
+converge لمين للـ f اللي هي of x اللي بتساوي سفر
+
+167
+00:13:00,990 --> 00:13:04,610
+وهذا ال convergence عبارة عن pointwise convergence
+
+168
+00:13:04,610 --> 00:13:10,070
+شوف الآن كيف بدنا نثبت خلصنا من انه احنا نثبت fn x
+
+169
+00:13:10,070 --> 00:13:14,590
+بتروح pointwise لمين لاللي هي ال function zero
+
+170
+00:13:14,590 --> 00:13:18,350
+بدنا نركز الآن نثبت ان fn does not converge
+
+171
+00:13:18,350 --> 00:13:24,080
+uniformly لل function f on Rاللي هو زي ما قلنا الـ
+
+172
+00:13:24,080 --> 00:13:27,940
+sequence of functions عندي هنا are not bounded
+
+173
+00:13:27,940 --> 00:13:32,620
+functions so we can't use our لمّة اللي قبل بشوية
+
+174
+00:13:32,620 --> 00:13:36,060
+اللي هي normal of a نقص of a converges to zero إذا
+
+175
+00:13:36,060 --> 00:13:41,100
+هنتضرر نروح للتعريف أو للمّة قبلها إذا بتتذكروا
+
+176
+00:13:41,100 --> 00:13:44,820
+اللمّة قلنا of a that does not convergeUniform للـ
+
+177
+00:13:44,820 --> 00:13:48,620
+F إيش بدنا نلاقي؟ بدنا نلاقي Epsilon Note أكبر من
+
+178
+00:13:48,620 --> 00:13:57,080
+0 و Sub-Sequence FNK و Sequence XK in R بحيث أنه
+
+179
+00:13:57,080 --> 00:14:03,060
+اللي هو هيها بدنا نلاقي Epsilon Note و نلاقي Sub
+
+180
+00:14:03,060 --> 00:14:06,440
+-Sequence FNK و نلاقي Sequence XK in R بحيث أنه
+
+181
+00:14:06,440 --> 00:14:14,340
+الـ Norm أو الـ Absolute Value للـ FNK of XK-F of
+
+182
+00:14:14,340 --> 00:14:21,180
+XK يكون أكبر من مين من Y note اللي عندنا اللي
+
+183
+00:14:21,180 --> 00:14:25,240
+بنقول لجميعها إذا عملنا زيك بيكون معناته أن F does
+
+184
+00:14:25,240 --> 00:14:28,900
+not converge uniformly to مين، to F خلّينا نيجي
+
+185
+00:14:28,900 --> 00:14:34,100
+إلى اللي هو ونشوف كيف نسويزي ما عملنا المرة
+
+186
+00:14:34,100 --> 00:14:39,940
+الماضية الفكرة انه الان ال fnk of xk نخليها عبارة
+
+187
+00:14:39,940 --> 00:14:44,640
+عن ثابت لو خلناها ثابت وهذه طبعا سفر بيصير الثابت
+
+188
+00:14:44,640 --> 00:14:49,600
+أكبر بيطلع ثابت خمسة ستة سبعة واحد اتنين بنختار
+
+189
+00:14:49,600 --> 00:14:52,600
+ابسلونوت اللي هي اصغر منه بيطلع حد اكبر من
+
+190
+00:14:52,600 --> 00:14:58,660
+الابسلونوت بيكون خلصناه ده نشوف كيف عندي fn of x
+
+191
+00:14:58,660 --> 00:15:04,320
+ايش بالساوي x على nلو جينا اخترنا اللي هو الـ NK
+
+192
+00:15:04,320 --> 00:15:08,060
+الـ NK الـ subsequence يعني اللي هي الـ NK
+
+193
+00:15:08,060 --> 00:15:13,540
+اخترناها الـ K بيصير اللي هي FNK اللي هي of X
+
+194
+00:15:13,540 --> 00:15:18,620
+بيساوي FK of X بيصير هذا K X على K طب ال X ايش
+
+195
+00:15:18,620 --> 00:15:25,240
+نختارها عشان نخلي هذا ثابت اختارهاK , 2K , 3K زي
+
+196
+00:15:25,240 --> 00:15:30,480
+ما بدك كله حيكون وين موجود في R وكله حيثبت لمين
+
+197
+00:15:30,480 --> 00:15:33,820
+اللي هي ال function اللي عندى و تصير أموري تمام
+
+198
+00:15:33,820 --> 00:15:39,840
+تمام ايش عامل هنا بقول ليه let F and K او let NK
+
+199
+00:15:39,840 --> 00:15:47,440
+هي let NK بساوي K يعني بمعنى اخر اخد ال F and K هو
+
+200
+00:15:47,440 --> 00:15:53,360
+او بتعبير اخر F خد ال F and K هي ال FK اختار الـ
+
+201
+00:15:53,360 --> 00:15:57,320
+FNK المميزة بـ Sequence اللي هي FK و Epsilon
+
+202
+00:15:57,320 --> 00:16:00,800
+خلّينا بعدين نختارها و XK زي ما قلنا ايش راح
+
+203
+00:16:00,800 --> 00:16:06,820
+نختارها بتساوي K أكيد وين موجودة في R then FNK of
+
+204
+00:16:06,820 --> 00:16:14,380
+XK ايش هتساوي اللي هي FK of XK ويساوي اللي هي
+
+205
+00:16:14,380 --> 00:16:20,080
+عبارة عن XKعلى k حسب اللي هي الدقلة اللي عندى او
+
+206
+00:16:20,080 --> 00:16:22,720
+ال sequence of functions طب ما هي ال xk ايش انا
+
+207
+00:16:22,720 --> 00:16:27,420
+بختارها بتساوي k فبصير k على k هو يساوي واحد اذا
+
+208
+00:16:27,420 --> 00:16:34,210
+طلعت عندى fnk of xk بيساوي واحدهيحسب للـ fnk of xk
+
+209
+00:16:34,210 --> 00:16:37,410
+للـ subsequence اللي عملناها ناقص f of xk إيش
+
+210
+00:16:37,410 --> 00:16:41,770
+هتساوي هذه عبارة عن واحد وهذه دالة دايما ثابتة f
+
+211
+00:16:41,770 --> 00:16:45,610
+عند أي قيمة بتساوي سفر فبصير اللي هو عبارة عن إيش
+
+212
+00:16:45,610 --> 00:16:49,030
+القيمة واحد إيش أختار epsilon note اللي بدك إياها
+
+213
+00:16:49,030 --> 00:16:54,680
+أي إيش أصغر منيه من الواحد وليكن إيش نصفبصير عندى
+
+214
+00:16:54,680 --> 00:17:00,140
+FN K هيها FK و Epsilon بساوة نص و XK بساوة K هي
+
+215
+00:17:00,140 --> 00:17:05,460
+sub sequence من ال FN و هي الي هو Epsilon نص و هي
+
+216
+00:17:05,460 --> 00:17:09,620
+sequence XK in R بحيث أن هذا ال absolute value
+
+217
+00:17:09,620 --> 00:17:13,660
+أكبر من مين؟ اللي هو طلع واحد اللي هو أكيد أكبر من
+
+218
+00:17:13,660 --> 00:17:17,900
+إيش؟ من نص اللي هي Epsilon نص وهذا يعني أن FN does
+
+219
+00:17:17,900 --> 00:17:24,390
+not converge uniformly للF on Rهكذا أثبتنا أن الـ
+
+220
+00:17:24,390 --> 00:17:27,310
+Fn لا يتعامل بشكل عام بشكل عام بشكل عام بشكل عام
+
+221
+00:17:27,310 --> 00:17:29,790
+بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل
+
+222
+00:17:29,790 --> 00:17:31,210
+عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام
+
+223
+00:17:31,210 --> 00:17:31,710
+بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل
+
+224
+00:17:31,710 --> 00:17:32,470
+عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام
+
+225
+00:17:32,470 --> 00:17:32,470
+بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل
+
+226
+00:17:32,470 --> 00:17:34,290
+عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام
+
+227
+00:17:34,290 --> 00:17:36,760
+بشكل عام بشكل عام بشكل عام بشكل عامأو الثالث في
+
+228
+00:17:36,760 --> 00:17:42,160
+المثال، بدنا نثبت أن الـ F Unconverges للـ F
+
+229
+00:17:42,160 --> 00:17:48,640
+Uniformly على الفترة مين؟ على الفترة 01، يعني لما
+
+230
+00:17:48,640 --> 00:17:53,080
+نغيرنا الفترة، هيصير اللي هو الـ Pointwise ماقدرش
+
+231
+00:17:53,080 --> 00:17:57,040
+اللي هو الـ Uniform convergence على الـ R، ماقدرش
+
+232
+00:17:57,200 --> 00:18:01,420
+اللي هو يكون uniform convergence لكن لو زغرنا
+
+233
+00:18:01,420 --> 00:18:06,420
+الفترة أو غيرنا الفترة ممكن نحصل على اللي هو ال
+
+234
+00:18:06,420 --> 00:18:11,480
+uniform convergence وهذا طبيعي، هنشوف كيف، الان
+
+235
+00:18:11,480 --> 00:18:16,640
+عشان اللي هو نظريتنا سهلة الاستخدام اللي قبل بشوية
+
+236
+00:18:16,640 --> 00:18:22,580
+اللي هو normal Fن ناقص F بدي أحسبه و أشوفه على
+
+237
+00:18:22,580 --> 00:18:27,240
+الفترة 0 و 1 اللي هو conversion to 0 ولا لأ؟ آه
+
+238
+00:18:27,240 --> 00:18:30,520
+الآن قبلها بدي أشوف ال sequence of functions عندي
+
+239
+00:18:30,520 --> 00:18:36,520
+هذه هل bounded على الفترة 0 و 1؟ Fn X بتساوي X على
+
+240
+00:18:36,520 --> 00:18:44,140
+N يعني صار عندي FN of X بيساوي X على N لوين X في
+
+241
+00:18:44,140 --> 00:18:47,860
+الفترة 0 و 1 خلاص الـ X في الفترة 0 و 1 جد ما تكون
+
+242
+00:18:47,860 --> 00:18:51,600
+ليها الـ X نفسها محصورة بين 0 و 1 يعني بتضل الـ X
+
+243
+00:18:51,600 --> 00:18:57,040
+على N عبارة عن قيمة محدودة قيمة محدودة أكيد اللي
+
+244
+00:18:57,040 --> 00:19:00,680
+هو الـ absolute value اللي هي هذه أصغر أو يساوي
+
+245
+00:19:00,680 --> 00:19:05,100
+اللي هو 1 على N إذا صار عند .. لكل .. طبعا هذا
+
+246
+00:19:05,100 --> 00:19:10,510
+محدودة بالنسبة لـ Xأه بيصير F1 أصغر بيساوي 1 F2
+
+247
+00:19:10,510 --> 00:19:15,350
+أصغر بيساوي نص F3 أصغر بيساوي تلت و هكذا إذن هي
+
+248
+00:19:15,350 --> 00:19:21,790
+عبارة عن F1 F2 F3 sequence of bounded functions on
+
+249
+00:19:21,790 --> 00:19:26,570
+the interval 0 و 1 إذن الآن الأمر مشروع ليه أني
+
+250
+00:19:26,570 --> 00:19:31,970
+أستخدم اللمّة اللي حكينا عنها قبل بشوية و نشوف كيف
+
+251
+00:19:31,970 --> 00:19:36,110
+نثبت ال uniform convergence نحسب مع بعض أكيد لكلكم
+
+252
+00:19:36,440 --> 00:19:43,380
+اللي هو Fn ناقص الـ F over A بساوي الـ Supremum لـ
+
+253
+00:19:43,380 --> 00:19:50,380
+Fn of X ناقص F of X Such that X و M هو وجودة في
+
+254
+00:19:50,380 --> 00:19:57,120
+الفترة 0 و 1 و يساوي الـ Supremum لـ Fn of X اللي
+
+255
+00:19:57,120 --> 00:20:03,270
+هي أشكل عنها عبارة عن X على Nx على n ناقصها دي سفر
+
+256
+00:20:03,270 --> 00:20:07,110
+بتضل x على n such that x where موجودة في ال zero
+
+257
+00:20:07,110 --> 00:20:10,330
+أو إيش أو واحد ال suprem أهم إلها زي ما تقولنا
+
+258
+00:20:10,330 --> 00:20:14,790
+أشملها أصغرشها واحد على n هتطلع عبارة عن أ واحد
+
+259
+00:20:14,790 --> 00:20:21,670
+على nهذه اللي هي مين ال norm للأف أن ناقص أف طيب
+
+260
+00:20:21,670 --> 00:20:26,530
+واضح الأمر مدام ال norm للأف أن ناقص أف بسوى حتى
+
+261
+00:20:26,530 --> 00:20:35,220
+الأن إذا norm للأف أن ناقص أفA goes to zero لأن FN
+
+262
+00:20:35,220 --> 00:20:38,880
+goes to infinity قيمة هذا الواحدة الان هتروح إلى
+
+263
+00:20:38,880 --> 00:20:42,960
+سفر يعني norm هذا بروح للزيرو وهذا يعني أن FN
+
+264
+00:20:42,960 --> 00:20:49,240
+converts uniformly ل F on الفترة زيرو وواحد وبكون
+
+265
+00:20:49,240 --> 00:20:54,180
+هيك أثبتنا اللي هو باستخدام النظرية أن هذا المثال
+
+266
+00:20:54,180 --> 00:20:58,680
+فعلااللي هو F Unconverged uniformly للـ F On The
+
+267
+00:20:58,680 --> 00:21:03,380
+Interval 01 But It Does Not Converge Uniformly On
+
+268
+00:21:03,380 --> 00:21:10,120
+R ككل لكن Pointwise على الـ R To The كل طيب نيجي
+
+269
+00:21:10,120 --> 00:21:16,300
+الآن اللي هوالتعبير آخر على الـ uniform
+
+270
+00:21:16,300 --> 00:21:19,880
+convergence عبرنا عن الـ uniform convergence
+
+271
+00:21:19,880 --> 00:21:26,180
+بواسطة اللي هي التعريف عبرنا عنه للعائلة of
+
+272
+00:21:26,180 --> 00:21:30,890
+bounded functions بواسطة الـ norm للأفئناللي هو
+
+273
+00:21:30,890 --> 00:21:37,190
+ناقص الـ F بروح للـ 0 الآن بدنا نعرف عنه .. نعبر
+
+274
+00:21:37,190 --> 00:21:40,070
+عنه عن طريق .. برضه للـ sequence of bounded
+
+275
+00:21:40,070 --> 00:21:43,230
+functions عن طريق حاجة اسمها الـ Cauchy criterion
+
+276
+00:21:43,230 --> 00:21:47,270
+for uniform convergence وكأنه بدنا ندخل المفهوم
+
+277
+00:21:47,270 --> 00:21:53,590
+الـ Cauchy اللي هي sequence في هذا اللي هو النظرية
+
+278
+00:21:53,590 --> 00:21:57,470
+نشوفكوشي كريتيريا لتحويل المستوى المستوى المستوى
+
+279
+00:21:57,470 --> 00:21:58,350
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+280
+00:21:58,350 --> 00:22:03,130
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+281
+00:22:03,130 --> 00:22:06,950
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+282
+00:22:06,950 --> 00:22:06,950
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+283
+00:22:06,950 --> 00:22:10,330
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+284
+00:22:10,330 --> 00:22:10,350
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+285
+00:22:10,350 --> 00:22:10,410
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+286
+00:22:10,410 --> 00:22:10,430
+المستوى المستوى المستوى المستوى المستوى المستوى
+
+287
+00:22:10,430 --> 00:22:15,740
+المستوى المستF يعني بتكون F unconverted لـ bounded
+
+288
+00:22:15,740 --> 00:22:20,220
+function F F and only F لكل Y أكبر من 0 there
+
+289
+00:22:20,220 --> 00:22:23,680
+exists H of Y للـ N such that for every M و N أكبر
+
+290
+00:22:23,680 --> 00:22:28,180
+يساوي H of Y حيكون الـ FM مقصلة F أصغر أو يساوي Y
+
+291
+00:22:28,180 --> 00:22:32,940
+وهذا هيذكرنا اللي هو بالكوشي sequences إذا نسيناها
+
+292
+00:22:33,270 --> 00:22:37,270
+يعني وكأنه خلّيني نقوله roughly بيقول لـ F N تحت
+
+293
+00:22:37,270 --> 00:22:42,950
+الظروف اللي موجودة بتروح للـ F uniformly يكافئ أنه
+
+294
+00:22:42,950 --> 00:22:47,510
+لكل إبسلون أكبر من 0 هذا الـ N الجزء هنا هو اللي
+
+295
+00:22:47,510 --> 00:22:51,070
+يكوش criterion في الواقع for every إبسلون أكبر من
+
+296
+00:22:51,070 --> 00:22:56,950
+0 there exists H of إبسلون element in N such that
+
+297
+00:22:56,950 --> 00:23:03,680
+for every N و M element in Nأو اللي هي أكبر أو
+
+298
+00:23:03,680 --> 00:23:08,140
+يساوي اتشوف إبسلون حيكون عندك الـ epsilon norm لل
+
+299
+00:23:08,140 --> 00:23:17,100
+FM ناقص FM أصغر من 100 أو يساوي اللي هو إبسلونهذه
+
+300
+00:23:17,100 --> 00:23:20,180
+اللي هي عبارة عن الـ Cauchy criterion يعني أحيانًا
+
+301
+00:23:20,180 --> 00:23:24,160
+نحن نعرف .. نكونش عارفين الـ Fn لمين رايحة لكن
+
+302
+00:23:24,160 --> 00:23:27,380
+متأكدين أنها converges uniformly to some function
+
+303
+00:23:27,380 --> 00:23:32,600
+F طب الآن في هذه الحالة اللي بصعفنا في الاستخدام
+
+304
+00:23:32,600 --> 00:23:38,480
+اللي هو أنه ناخد اللي هو بدلالات ال terms اللي هي
+
+305
+00:23:38,480 --> 00:23:42,440
+ال Fn و ال Fm و نبعد عن ال F لأنه احنا مش عارفينها
+
+306
+00:23:42,440 --> 00:23:45,260
+عشان هيك بنقول Fn converges uniformly to some
+
+307
+00:23:45,260 --> 00:23:50,340
+function Fيعني هيك تصرفها إذا و فقط إذا اللي هو
+
+308
+00:23:50,340 --> 00:23:53,920
+لكل إبسلون أكبر من سفر الـ Epsilon element in N
+
+309
+00:23:53,920 --> 00:23:56,300
+such that forever N و M أكبر من سفر الـ Epsilon
+
+310
+00:23:56,300 --> 00:23:59,680
+بيعطينا norm هذه أصغر من minimum إبسلون و كأنه
+
+311
+00:23:59,680 --> 00:24:03,650
+بنقول اللي هو ال function FNis a Cauchy sequence
+
+312
+00:24:03,650 --> 00:24:08,250
+roughly in the space of functions اللي هي ال norm
+
+313
+00:24:08,250 --> 00:24:11,470
+بساوي ال supremum اللي هو هذا الموضوع طبعا مش
+
+314
+00:24:11,470 --> 00:24:15,170
+موضوعنا موضوع ناخده بالتفصيل في اللي هو ال
+
+315
+00:24:15,170 --> 00:24:19,870
+functional analysis طيب شوفوا علينا نيجي اللي هو
+
+316
+00:24:19,870 --> 00:24:26,710
+انبرهن النظرية بدنا نفترض ان ال FNالان بدنا نفترض
+
+317
+00:24:26,710 --> 00:24:31,970
+انه norm أو الـ F un converge uniformly to some
+
+318
+00:24:31,970 --> 00:24:37,790
+function F و نصل لهذا اللي هو الجزء سهل ان شاء
+
+319
+00:24:37,790 --> 00:24:44,450
+الله شوفوا ركزولنا الان suppose that F un converge
+
+320
+00:24:44,450 --> 00:24:49,390
+uniformly ل F on A إذا الان من التعريف تبع ال
+
+321
+00:24:49,390 --> 00:24:54,480
+uniform convergence لكل Y أكبر من 0There exists K
+
+322
+00:24:54,480 --> 00:24:58,420
+of Y على 2 element in N such that for every N أكبر
+
+323
+00:24:58,420 --> 00:25:03,180
+أو يساوي K of Y ولكل X element in A برضه بظبط اللي
+
+324
+00:25:03,180 --> 00:25:08,180
+هو FN of X ناقص F of X أصغر من Y على 2 هذا
+
+325
+00:25:08,180 --> 00:25:11,000
+باستخدام التعريف الـ N باستخدام النظرية اللي قبل
+
+326
+00:25:11,000 --> 00:25:14,720
+بشوية لإنه بنفع لإن النظرية احنا قلنا FN converges
+
+327
+00:25:14,720 --> 00:25:19,540
+uniformly إيش معناته هذا؟معناته more من الـ F and
+
+328
+00:25:19,540 --> 00:25:25,720
+ناقص الـ F goes to 0 over mean over a هذه صار
+
+329
+00:25:25,720 --> 00:25:30,160
+تعريف عادي للـ limit إيش معناته هذا لكل إبسلون
+
+330
+00:25:30,160 --> 00:25:35,980
+أكبر من سفر there exists اللي هو مسميها هو إيش
+
+331
+00:25:35,980 --> 00:25:42,440
+مسميها K of إبسلون على 2 element in M such that
+
+332
+00:25:43,150 --> 00:25:50,370
+اللي هو norm الـ Fn ناقص الـ F هيكون أصغر من إبسل
+
+333
+00:25:50,370 --> 00:25:54,630
+على اتنين for every N أكبر أو يساوي مين K of إبسل
+
+334
+00:25:54,630 --> 00:25:57,770
+على اتنين اللي عندك هذا اللي هو تعريف الدهانية
+
+335
+00:25:57,770 --> 00:26:01,590
+العادية اللي هو sequence O السيكوانس العادية هذه
+
+336
+00:26:01,590 --> 00:26:04,440
+الـ sequence converts to zero لأنها أعداداللي هي
+
+337
+00:26:04,440 --> 00:26:06,560
+converse to zero إذا لكل ي أكبر من صفر there
+
+338
+00:26:06,560 --> 00:26:10,740
+exists K بحيث أنه F أن ناقص F أصغر من ي على اتنين
+
+339
+00:26:10,740 --> 00:26:19,460
+لكل N أكبر أو سوء K of ي على اتنين طيب الآن عندي
+
+340
+00:26:19,460 --> 00:26:25,520
+ال .. ال .. ال F هذه بمقدر نترجمها اللي هو على طول
+
+341
+00:26:25,520 --> 00:26:31,660
+مباشرة إذا اللي هي عندي ال Fما دام هذا أصغر يساوي
+
+342
+00:26:31,660 --> 00:26:35,880
+Y على 2 يعني ال suprem أصغر يساوي Y على 2 وهذا
+
+343
+00:26:35,880 --> 00:26:40,360
+نفسه أكبر أوي يساوي ايش عارفين انتوا Fn of X ناقص
+
+344
+00:26:40,360 --> 00:26:44,280
+F of X، مظبوط؟ لأن هذا ال suprem ملهن، إذا صار
+
+345
+00:26:44,280 --> 00:26:53,530
+عندي إذا Fnنقص f of x صار نفسه أصغر من مين من y
+
+346
+00:26:53,530 --> 00:27:00,550
+على 2 خليها في الذاكرة الآن عندي احسبلي بناء عليه
+
+347
+00:27:00,550 --> 00:27:09,430
+احسبلين of X ناقص FM of X هذا لمين؟ هذا حسب ليه
+
+348
+00:27:09,430 --> 00:27:16,230
+لمين؟ لكل أنه طبعا هذا الكلام صحيح لكل X وين؟ لكل
+
+349
+00:27:16,230 --> 00:27:22,340
+X في الـA تبعتنااحسبلي لكل N و M أكبر من مين من
+
+350
+00:27:22,340 --> 00:27:26,620
+الـ K اللي لجيها هنا K of Epsilon على 2 F N of X
+
+351
+00:27:26,620 --> 00:27:30,580
+ناقص F M of X أكيد أصغر أو يساوي بالـ Triangling
+
+352
+00:27:30,580 --> 00:27:38,940
+Quality F N of X ناقص F of X زائد F M of X ناقص F
+
+353
+00:27:38,940 --> 00:27:43,560
+of X واضح عشان سويت ضفت الـ F of X وطرحتها و بعدين
+
+354
+00:27:43,560 --> 00:27:48,460
+أخدت Triangling Quality الآن هذاصحيح أصغر من Y على
+
+355
+00:27:48,460 --> 00:27:55,590
+2 لكل Nلكل N أكبر من K طب ما أنا مختار ال N و ال M
+
+356
+00:27:55,590 --> 00:27:59,830
+أكبر من K إذن بنطبق عليها هذا سواء لهذه أو هذه إذن
+
+357
+00:27:59,830 --> 00:28:04,630
+هذه صارت أصغر من Y على 2 وهذه أصغر من Y على 2 يعني
+
+358
+00:28:04,630 --> 00:28:10,530
+صار ال FN of X ناقص FMA of X أشماله أصغر من Y أصغر
+
+359
+00:28:10,530 --> 00:28:15,110
+من مين؟ من Y يعني الآن اللي وصلت إليه ما يالي يا
+
+360
+00:28:15,110 --> 00:28:19,590
+جماعة بدأت بال FN بتروح لل F اللي هو uniformly
+
+361
+00:28:20,520 --> 00:28:25,460
+ووصلت إلى مالي وصلت إنه لكل epsilon أكبر من 0 لجيت
+
+362
+00:28:25,460 --> 00:28:30,480
+K of epsilon على 2 element in N such that for
+
+363
+00:28:30,480 --> 00:28:35,680
+every N و M أكبر أو يساوي K of epsilon على 2 لجيت
+
+364
+00:28:35,680 --> 00:28:46,360
+إن ال FN of Xنقص fm of x أصغر من مين من إبسلون هذا
+
+365
+00:28:46,360 --> 00:28:52,420
+لكل x وين موجودة في الـA ماشي الحال إذا مدام هذا
+
+366
+00:28:52,420 --> 00:28:57,140
+أصغر من إبسلون لكل x element in A صارت الإبسلون
+
+367
+00:28:57,140 --> 00:29:01,030
+عبارة عن upper bound لهذهإذاً الـ Epsilon هتكون
+
+368
+00:29:01,030 --> 00:29:05,050
+أكبر أو تساوي ال least upper bound إذاً يعني بمعنى
+
+369
+00:29:05,050 --> 00:29:09,850
+آخر إذا ال least upper bound اللي هو FN ناقص FM
+
+370
+00:29:09,850 --> 00:29:15,190
+نفسه أصغر من مين أصغر أو يساوي Epsilon وهذا يعني
+
+371
+00:29:15,190 --> 00:29:19,920
+إنه احنافعلاً لجينا أنه في حالة الـ F N conversion
+
+372
+00:29:19,920 --> 00:29:23,960
+form للـ F لجينا لكل Y أكبر من 0 there exists K
+
+373
+00:29:23,960 --> 00:29:29,260
+بحيث لكل N أ أو M أكبر سوء K يطلع عندي Normal FN
+
+374
+00:29:29,260 --> 00:29:34,080
+نقص FM أصغر من مين من إبسلون وهو المطلوب وطبعاً في
+
+375
+00:29:34,080 --> 00:29:37,360
+الآخر جالك ت choose اللي هي K of Epsilon هي اسمها
+
+376
+00:29:37,360 --> 00:29:40,880
+H of Epsilon كان ممكن الأول نسميها H of Epsilon
+
+377
+00:29:40,880 --> 00:29:45,880
+كان مجرد تسميةالان نيجي نمين اللي هو the converse
+
+378
+00:29:45,880 --> 00:29:49,460
+of the theorem conversely بدنا نفترض ان ال
+
+379
+00:29:49,460 --> 00:29:52,820
+condition متحقق و نثبت اللي هو ال uniform
+
+380
+00:29:52,820 --> 00:30:08,320
+convergence الان
+
+381
+00:30:08,320 --> 00:30:13,390
+بدنا نفترضإن سبب ذات لكل Y أكبر من 0 there exists
+
+382
+00:30:13,390 --> 00:30:18,730
+H of Y بحيث إنه لما M و N تكون أكبر من H of Y
+
+383
+00:30:18,730 --> 00:30:24,710
+هيعطيني ال F ماطس أفن أصغر سوى Y هذا على بعض بدي
+
+384
+00:30:24,710 --> 00:30:32,290
+أثب من خلاله إنه لازم ال F أن تروح لل F uniformly
+
+385
+00:30:32,290 --> 00:30:36,230
+شوف كيف بده يعمل وهو الفكرة سهلة إن شاء الله
+
+386
+00:30:36,230 --> 00:30:42,630
+وبسيطة والبرهان كمان سلسانشوف ايش بقول البرهان
+
+387
+00:30:42,630 --> 00:30:47,370
+تبعنا بقول ما يليه الان
+
+388
+00:30:48,590 --> 00:30:53,150
+ما دام هذا الشرط هيوه، هذا الشرط متحقق، إذا لكل X
+
+389
+00:30:53,150 --> 00:30:59,790
+element إيه؟ عندي أكيد الـFM of X ناقص FN X أصغر
+
+390
+00:30:59,790 --> 00:31:03,910
+أو ساوي FM ناقص FN، لأن هذا هو الـSupremum لهدولة
+
+391
+00:31:03,910 --> 00:31:07,990
+كلهم، إذا صار عندي هذا أكبر أو ساوي هذا، إذا صار
+
+392
+00:31:07,990 --> 00:31:13,870
+هذا أصغر من مين؟ من إبسلونإيش معناته هذا؟ صارت
+
+393
+00:31:13,870 --> 00:31:18,270
+الآن الـ F .. بنحكي عن لكل X element in A X
+
+394
+00:31:18,270 --> 00:31:22,990
+arbitrarily back-fixed صارت عندي الـ F M of X بناء
+
+395
+00:31:22,990 --> 00:31:26,130
+على هذا الحديث مذاب الـ Absolute Value اللي قالها
+
+396
+00:31:26,130 --> 00:31:30,690
+الـ F M ناقص F N أصغر من Y يعني بمعنى آخر لكل Y
+
+397
+00:31:30,690 --> 00:31:34,710
+أكبر من 0 لجينا H of Y بحيث لما تكون M و N أكبر من
+
+398
+00:31:34,710 --> 00:31:39,330
+H of Y طلعلي الـ F M of X ناقص F N of X أصغر من
+
+399
+00:31:39,330 --> 00:31:44,990
+100 من Yصارت الـ F M of X أو F N of X زي ما بدك
+
+400
+00:31:44,990 --> 00:31:49,850
+تسميها صارت عبارة عن كوشي سيكوانس مدام كوشي
+
+401
+00:31:49,850 --> 00:31:55,470
+سيكوانس إذا حسب كوشي سيكوانس of numbers إذا أكيد
+
+402
+00:31:55,470 --> 00:32:01,250
+الـ F N of X converts يعني السيكوانس هذه إيش مالها
+
+403
+00:32:01,250 --> 00:32:09,130
+converts خلّينا نسمي limitالـ Fn of X بيساوي F of
+
+404
+00:32:09,130 --> 00:32:13,110
+X as N goes to infinity ليش F of X؟ لأنه القيمة
+
+405
+00:32:13,110 --> 00:32:16,550
+اللي بتطلع بتعتمد على الـ X لأنه Fn of X واحد لها
+
+406
+00:32:16,550 --> 00:32:20,770
+قيمة، Fn of X اتنين لها قيمة ك sequence، اتكلمت ك
+
+407
+00:32:20,770 --> 00:32:25,510
+sequence الآن صارت عندي هذه ال limit exist و
+
+408
+00:32:25,510 --> 00:32:32,710
+بتساوي رقم الآن منها بدي أقولك define Fمن عند الـ
+
+409
+00:32:32,710 --> 00:32:38,010
+a اللي هي اللي لكل x element in a هذا صحيح اللي fn
+
+410
+00:32:38,010 --> 00:32:42,710
+of x converge ويلها قيمة define f من a لعند ال R
+
+411
+00:32:42,710 --> 00:32:49,740
+by limitالـ F N of X as N goes to infinity
+
+412
+00:32:49,740 --> 00:32:56,760
+بيساومين F of X طيب الـ N بدأاش احنا رايحين يا
+
+413
+00:32:56,760 --> 00:33:02,440
+جماعة رايحين نثبت انه F N converts uniformly للـ F
+
+414
+00:33:02,440 --> 00:33:08,880
+on A او بمعنى اخر رايحين نثبت ان F N ناقص F over A
+
+415
+00:33:08,880 --> 00:33:15,800
+converts لـ 0 بتنشوف مع بعض الـ Nبالتالي كما قلنا
+
+416
+00:33:15,800 --> 00:33:20,200
+هذا أصغر من Y ومنه اللي هو إذا تنتجنا FN is a
+
+417
+00:33:20,200 --> 00:33:24,360
+Cauchy sequence in R ثم By theorem 3.5.4 اللي هو
+
+418
+00:33:24,360 --> 00:33:27,780
+اللي بتقول إن الـ Cauchy sequence .. a sequence is
+
+419
+00:33:27,780 --> 00:33:31,590
+Cauchy فندولي if it convergesis convergent
+
+420
+00:33:31,590 --> 00:33:34,930
+sequence define f من a لعنى r by f of x سواء اللي
+
+421
+00:33:34,930 --> 00:33:38,590
+ميت f of n of x زي ما قلنا لأن if we let n in a
+
+422
+00:33:38,590 --> 00:33:42,430
+star goes to infinity الآن بدنا نودي n إلى وين هنا
+
+423
+00:33:42,430 --> 00:33:47,170
+إلى ما لا نهاية مع الاحتفاظ بال m زي ما هي عندي
+
+424
+00:33:47,170 --> 00:33:50,170
+بقدر اعمل هيك اه بقدر اعمل هيك لأنه بقدر اخد ال n
+
+425
+00:33:50,630 --> 00:33:56,570
+أكبر من M والتنتين اللي هى أكبر أو يساوي H of
+
+426
+00:33:56,570 --> 00:33:59,610
+Epsilon فالان لما ال N تروح الى ماله نهاية هى حرة
+
+427
+00:33:59,610 --> 00:34:03,370
+بتروح الى ماله نهاية M بتظلها جاعدة زى ما هى الان
+
+428
+00:34:03,370 --> 00:34:11,750
+زى ما قلنا نيجى لمين نودي
+
+429
+00:34:11,750 --> 00:34:15,290
+N الى ماله نهاية وين في ال star هى ال star هى ال
+
+430
+00:34:15,290 --> 00:34:15,630
+star
+
+431
+00:34:20,280 --> 00:34:24,360
+ودي ال M إلى ما لنهاية لما تودي ال M إلى ما لنهاية
+
+432
+00:34:24,360 --> 00:34:28,700
+هذه بتروح limit ال M ال FN of X هتروح ل .. اللي هي
+
+433
+00:34:28,700 --> 00:34:34,060
+ال F of X بصير عندي الآن طب امبسلون ثابت مالهاش
+
+434
+00:34:34,060 --> 00:34:38,620
+علاقة إذا صار عندي الآن هذه إيش بتعطيني .. بتعطيني
+
+435
+00:34:38,620 --> 00:34:43,420
+F M of X limit ال FN of X لأنه بتدخل على ال .. ال
+
+436
+00:34:43,420 --> 00:34:45,520
+absolute value لأن ال limit ال .. ال absolute
+
+437
+00:34:45,520 --> 00:34:48,300
+value is a continuous function إذا بتدخل عليه إذا
+
+438
+00:34:48,300 --> 00:34:52,760
+Fm of x ناقص limit fn of x as n goes to infinity
+
+439
+00:34:52,760 --> 00:34:55,780
+أصغر أو يسوى مين إبسلون سيبك من هذه ماعلاش علاقة
+
+440
+00:34:55,780 --> 00:34:59,460
+فيها نحكي عن هذه و هذه الآن ال limit هذا إيش سمناه
+
+441
+00:34:59,460 --> 00:35:04,220
+إحنا سمناه هنا عبارة عن f of x إذا صار عندي الآن
+
+442
+00:35:04,220 --> 00:35:09,300
+اللي هو f m of x ناقص f of x أصغر أو يسوى إيش
+
+443
+00:35:09,300 --> 00:35:14,110
+إبسلونإذا صار عندي الآن اللي حصلت عليه لكل ي أكبر
+
+444
+00:35:14,110 --> 00:35:19,010
+من سفر there exists h of ي بحيث أن fm of x ناقص f
+
+445
+00:35:19,010 --> 00:35:24,310
+of x أصغر سواء ي لكل m أكبر أو سواء مين؟ h of ي
+
+446
+00:35:24,310 --> 00:35:30,800
+لأن هذا إيش معناته؟ هذا صحيح لكل xإذا صار عندى زى
+
+447
+00:35:30,800 --> 00:35:34,280
+ما قلنا قبل شوية الـ Epsilon Upper Bound لهذه مدام
+
+448
+00:35:34,280 --> 00:35:37,700
+Epsilon Upper Bound إذا اللى حيصير ال Epsilon أكبر
+
+449
+00:35:37,700 --> 00:35:40,900
+أو يساوي ال least upper bound مين هو ال least
+
+450
+00:35:40,900 --> 00:35:45,480
+upper bound ال norm لل FM نقص FM يعني بمعنى آخر من
+
+451
+00:35:45,480 --> 00:35:49,880
+هنا حصلت على norm لل FM نقص FM اللى هو اللى هو
+
+452
+00:35:49,880 --> 00:35:54,740
+أصغر أو يساوي Epsilon هذا لكل مين لكل M أكبر أو
+
+453
+00:35:54,740 --> 00:35:59,870
+يساوي اللى هو H of Epsilon وهذا مع بعضالذي حصلنا
+
+454
+00:35:59,870 --> 00:36:03,150
+عليه لكل y أكبر من 0 there exists h of epsilon
+
+455
+00:36:03,150 --> 00:36:07,290
+such that for every m أكبر أو سوى h of epsilon فم
+
+456
+00:36:07,290 --> 00:36:13,470
+ناقص f أصغر أو سوى y هذا معناه limit ال Fالنورم
+
+457
+00:36:13,470 --> 00:36:18,690
+الـ FM ناقص الـ F over A as M goes to infinity
+
+458
+00:36:18,690 --> 00:36:25,450
+بساوة Zero و هذا حسب اللي هو النظرية الـ FM أو الـ
+
+459
+00:36:25,450 --> 00:36:31,230
+FM converts uniformly to mean to F وبهيك بنكون
+
+460
+00:36:31,230 --> 00:36:37,850
+حصلنا على اللي هو برهان النظرية و أثبتنا إنه لما
+
+461
+00:36:37,850 --> 00:36:44,080
+نكون اللي هيالـ condition الكوشي كريتيريا المتحقق
+
+462
+00:36:44,080 --> 00:36:51,920
+هذا بكون عندي اللي هي الـ FM أو الـ FN converts
+
+463
+00:36:51,920 --> 00:36:57,800
+uniformly to ال function اللي عندنا اللي هي F
+
+464
+00:36:57,800 --> 00:37:02,740
+وبهيك بنكون احنا انتهينا من ال section الأول
+
+465
+00:37:02,740 --> 00:37:08,000
+تمانية واحد وإن شاء الله بنكمل المحاضرة القادمة
+
+466
+00:37:08,000 --> 00:37:09,320
+وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b0fb3b3c44a7d0b20cf08431ece0ea66c0c10f2e
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/YaYohwowYOA.srt
@@ -0,0 +1,2759 @@
+1
+00:00:04,820 --> 00:00:10,480
+بسم الله الرحمن الرحيم المحاضرة الثانية في مساق
+
+2
+00:00:10,480 --> 00:00:18,480
+تحليل رياضي 2 أو تحليل حقيقي 2  تحدثنا 
+
+3
+00:00:18,480 --> 00:00:24,100
+المرة الماضية عن الـ differentiation بدأنا بشروط
+
+4
+00:00:24,100 --> 00:00:28,200
+ستة بدأنا في الـ section الأول 6.1 اللي هو الـ
+
+5
+00:00:28,200 --> 00:00:32,600
+derivative أو اللي هو الاشتقاق أو المشتق الأولى
+
+6
+00:00:32,600 --> 00:00:37,840
+وعرفنا شو معناه اللي هو الاشتقاق عرفنا شو معناه أن
+
+7
+00:00:37,840 --> 00:00:44,910
+الدالة تكون differentiable عند نقطة اللي هي في 
+
+8
+00:00:44,910 --> 00:00:49,970
+interval I حيث أخذنا F عبارة عن الـ function من I 
+
+9
+00:00:49,970 --> 00:00:55,230
+لـ R وقلنا C element in I بتكون الدالة عندها قابلة
+
+10
+00:00:55,230 --> 00:01:01,490
+للاشتقاق يعني F prime of C exist if the following
+
+11
+00:01:01,490 --> 00:01:08,230
+limit exist اللي هو limit f of x ناقص f of c على x
+
+12
+00:01:08,230 --> 00:01:14,230
+ناقص c as x goes to c exist إذا كانت هذه الـ
+
+13
+00:01:14,230 --> 00:01:20,210
+limit exist بنقول عن الـ f برايم exist و بتكون هي
+
+14
+00:01:20,210 --> 00:01:26,650
+قيمة هذه الـ limit الآن وبعد ذلك مرّينا على اللي 
+
+15
+00:01:26,650 --> 00:01:34,600
+هو بعض الخواص وقلنا الخاصية الأولى عندنا اللي هي
+
+16
+00:01:34,600 --> 00:01:41,540
+أن لو كانت الدالة اللي هي differentiable at C
+
+17
+00:01:41,540 --> 00:01:45,520
+بتكون continuous برضه وين؟ عند C يعني أي
+
+18
+00:01:45,520 --> 00:01:50,080
+differentiable function must be continuous قلنا إن
+
+19
+00:01:50,080 --> 00:01:53,960
+الـ converse need not to be true in general  وأخذنا
+
+20
+00:01:53,960 --> 00:01:58,020
+مثال قلنا f of x بتساوي الـ absolute value للـ x
+
+21
+00:01:58,020 --> 00:02:01,780
+اللي هي عبارة عن continuous function لكن مش
+
+22
+00:02:01,780 --> 00:02:05,460
+differentiable عند الـ zero continuous everywhere
+
+23
+00:02:05,460 --> 00:02:09,340
+but it is not differentiable at zero وبرهنّا الكلام
+
+24
+00:02:09,340 --> 00:02:13,140
+هذا وأخذنا مثال آخر على f of x بتساوي الـ summation
+
+25
+00:02:13,140 --> 00:02:17,760
+لـ x ناقص c<sub>i</sub> من عند واحد لعند n وقلنا إن هذا
+
+26
+00:02:17,760 --> 00:02:22,600
+الدالة برضه is continuous everywhere but it is not
+
+27
+00:02:22,600 --> 00:02:29,440
+differentiable at c<sub>1</sub>, c<sub>2</sub>, c<sub>3</sub> لعند c<sub>n</sub> بعد ذلك سألنا
+
+28
+00:02:29,440 --> 00:02:34,100
+وقلنا هل ممكن أن تجيء دالة تكون continuous وين
+
+29
+00:02:34,100 --> 00:02:39,790
+ما كانت مش differentiable ولا في مكان؟ قلنا اه و
+
+30
+00:02:39,790 --> 00:02:42,470
+قلنا أخذ الدالة f of x بساعة الـ summation 1 على
+
+31
+00:02:42,470 --> 00:02:47,350
+2<sup>n</sup> x 3<sup>n</sup> x هذه الدالة is 
+
+32
+00:02:47,350 --> 00:02:51,850
+continuous everywhere but it is not differentiable
+
+33
+00:02:51,850 --> 00:02:56,310
+anywhere وبعد هيك أتينا 
+
+34
+00:03:04,880 --> 00:03:11,100
+حكينا عن بعض اللي هو قوانين الاشتقاق قلنا لو كانت
+
+35
+00:03:11,100 --> 00:03:16,520
+الدالة F والدالة G التنتين من نفس الـ domain
+
+36
+00:03:16,520 --> 00:03:22,000
+والتنتين قابلتان للاشتقاق عند نقطة اسمها C سميناها
+
+37
+00:03:22,000 --> 00:03:26,560
+قلنا اللي هو مجموع الدالتين هيكون مشتقتهم موجودة
+
+38
+00:03:26,560 --> 00:03:31,660
+عند هذه النقطة وحاصل ضربهما وحاصل قسمتهما أيضا
+
+39
+00:03:31,660 --> 00:03:35,860
+provided that G of C اللي في المقام لا تساوي صفر
+
+40
+00:03:35,860 --> 00:03:41,950
+وأيضا الـ a في الـ F a constant برضه a في F قابلة
+
+41
+00:03:41,950 --> 00:03:46,290
+للاشتقاق وأثبتنا
+
+42
+00:03:46,290 --> 00:03:53,330
+هذا الكلام وبرهنّاه ووصلنا لعند اللي هو التعميم
+
+43
+00:03:53,330 --> 00:04:00,030
+قلنا لو كانت F<sub>1</sub> وF<sub>2</sub> وF<sub>3</sub> لعند F<sub>n</sub> كلهم دوال قابلة
+
+44
+00:04:00,030 --> 00:04:04,710
+للاشتقاق حيكون حاصل جمعها قابل للاشتقاق وحاصل ضربهما
+
+45
+00:04:04,710 --> 00:04:09,510
+أيضا قابل للاشتقاق وفق القوانين اللي ذكرناها سابقا
+
+46
+00:04:10,150 --> 00:04:14,370
+وجئنا عند اللي هو النقطة اللي هي the chain rule أو 
+
+47
+00:04:14,370 --> 00:04:20,650
+قاعدة السلسلة قاعدة السلسلة طبعا ليست غريبة عنكم
+
+48
+00:04:20,650 --> 00:04:29,240
+مرت علينا في تفاضل 1 ومرت علينا في الـ complex أو 
+
+49
+00:04:29,240 --> 00:04:32,780
+مرت علينا اللي هو استخدمناها في الـ differential
+
+50
+00:04:32,780 --> 00:04:38,220
+equations وفي مساقات أخرى الآن نظرة نظرة تحليلية 
+
+51
+00:04:38,220 --> 00:04:44,060
+فهنشوف اللي هو كيف أثبتنا أو كيف بدنا نثبت اللي هو
+
+52
+00:04:44,060 --> 00:04:48,840
+قاعدة السلسلة أي سؤال بتقدر تسأله يعني اللي بدكم
+
+53
+00:04:48,840 --> 00:04:53,960
+إياه وتتفاعلوا بالطريقة اللي بتلاقوها مناسبة let i
+
+54
+00:04:53,960 --> 00:04:56,200
+و j be intervals and let g
+
+55
+00:04:59,060 --> 00:05:06,800
+عبارة عن دالة دي
+
+56
+00:05:06,800 --> 00:05:14,660
+عبارة عن دالة من I لعند مين؟ لعند R والـ F عبارة عن 
+
+57
+00:05:14,660 --> 00:05:21,700
+دالة من عند J لعند R حيث I و J اللي هو أشمل عبارة 
+
+58
+00:05:21,700 --> 00:05:26,440
+عن intervals الآن أنا اللي هي الـ chain rule هي في
+
+59
+00:05:26,440 --> 00:05:33,380
+الواقع عملية فحص إمكانية إنها تكون الـ composition
+
+60
+00:05:33,380 --> 00:05:37,780
+of two functions is differentiable ولا لأ؟ وإيش
+
+61
+00:05:37,780 --> 00:05:41,200
+الشروط اللي بتخلي اللي هو g composite of f is 
+
+62
+00:05:41,200 --> 00:05:45,620
+differentiable؟ إذا أنا بدي أحكي عن g composite of
+
+63
+00:05:45,620 --> 00:05:49,590
+اللي هو الـ derivative إيه لها؟ ما دام بدي أحكي عن g 
+
+64
+00:05:49,590 --> 00:05:56,690
+composite of f إذا أنا الآن domain الـ g الـ domain
+
+65
+00:05:56,690 --> 00:06:03,850
+الـ f هيكون من عند g لعند مين؟ لعند r معناته أن f of 
+
+66
+00:06:03,850 --> 00:06:09,310
+g عشان تكون g معرفة لازم تكون من ضمن مين؟ اللي هو
+
+67
+00:06:09,310 --> 00:06:16,680
+domain الـ I إذا أنا بدي أفترض أن f of J جزئية من I 
+
+68
+00:06:16,680 --> 00:06:22,020
+على أساس أن هتكون الـ G composite F is defined
+
+69
+00:06:22,020 --> 00:06:29,960
+وهتكون defined من وين؟ من عند J لعند R عشان هيك
+
+70
+00:06:29,960 --> 00:06:34,400
+احنا لما بدنا نيجي للي هو .. اللي نفترض .. هنفترض
+
+71
+00:06:34,400 --> 00:06:40,220
+G من I لعند R وF من عند G لعند R دوال ونقول F of I
+
+72
+00:06:40,220 --> 00:06:43,640
+subset أو F of G subset من I عشان تصير اللي هو
+
+73
+00:06:43,640 --> 00:06:46,980
+اللي بنحكي عنه قاعدة السلسلة اللي هي بمعنى آخر
+
+74
+00:06:46,980 --> 00:06:50,040
+التفاضل الـ composition of two functions is well
+
+75
+00:06:50,040 --> 00:06:54,420
+defined أو is defined اللي هم let C element in مين؟
+
+76
+00:06:54,420 --> 00:07:00,120
+in G؟ بدنا ناخذ الـ C element in G اللي هم بقولي C 
+
+77
+00:07:00,120 --> 00:07:06,430
+element in G عشان أقدر أحكي عن g composite of f 
+
+78
+00:07:06,430 --> 00:07:12,530
+prime of c تكون exist بده شرطين الشرط الأول بده الـ
+
+79
+00:07:12,530 --> 00:07:17,190
+f تكون differentiable عند مين؟ عند الـ c
+
+80
+00:07:17,190 --> 00:07:22,150
+والشرط الثاني أن الـ g تكون differentiable عند الـ f
+
+81
+00:07:22,150 --> 00:07:30,530
+of c واضح؟ إذن الآن إذا كان الـ F مميز لـ C والـ G
+
+82
+00:07:30,530 --> 00:07:36,710
+مميز لـ F of C فإن مفهوم الـ G مميز لـ F يجب أن
+
+83
+00:07:36,710 --> 00:07:42,410
+يكون مميز لـ C وبكون عنده الـ G مميز لـ F' of C
+
+84
+00:07:42,410 --> 00:07:48,710
+إيش حيساوي؟ حيساوي G' of F of C في F' لمن؟ للـ F
+
+85
+00:07:48,710 --> 00:07:54,350
+of C اللي كنا نقول عنه في التفاضل أنه تفاضل اللي هو
+
+86
+00:07:54,350 --> 00:08:01,320
+القوس ثم تفاضل ما فيه داخل القوس واضح؟ أو تفاضل
+
+87
+00:08:01,320 --> 00:08:05,280
+الدالة في تفاضل ما بداخل الدالة هو طبعا في الواقع
+
+88
+00:08:05,280 --> 00:08:07,940
+اللي هو عبارة عن تفاضل لـ composition of two
+
+89
+00:08:07,940 --> 00:08:12,200
+functions أو اللي هو الـ chain rule وكنا إذا
+
+90
+00:08:12,200 --> 00:08:16,680
+بتتذكروا كانت صورة أخرى للـ chain rule غير الصورة
+
+91
+00:08:16,680 --> 00:08:23,100
+هذه اللي هي g prime of f of c في f prime of c كنا
+
+92
+00:08:23,100 --> 00:08:29,900
+ناخذ صورة أخرى نقول dy by dx اللي هو عبارة عن ..
+
+93
+00:08:29,900 --> 00:08:38,960
+عبارة عن dy مثلا by du في du by d إيش؟ dx اللي هو
+
+94
+00:08:38,960 --> 00:08:44,620
+الـ y وكأنها بتتمثل اللي هي الـ g تفاضل الـ g والـ u
+
+95
+00:08:44,620 --> 00:08:48,600
+بتكون اللي هي مين؟ اللي هي الـ F اللي هي F برايم
+
+96
+00:08:48,600 --> 00:08:52,180
+فكانت اللي هي هذه الصورة أو هذه الصورة احنا الآن 
+
+97
+00:08:52,180 --> 00:08:59,630
+خلينا نحكي عن هذه الصورة ونبرهن اللي هيكيف اللي
+
+98
+00:08:59,630 --> 00:09:07,290
+هو نثبت أن هذا الكلام صحيح الآن بس خلينا نحط ..
+
+99
+00:09:07,290 --> 00:09:13,730
+نشوف .. نشوف عندنا الآن نشوف إيش اللي بدنا نثبته
+
+100
+00:09:13,730 --> 00:09:16,770
+احنا في الواقع اللي بدنا نثبته .. بدنا نجوّه ..
+
+101
+00:09:16,770 --> 00:09:22,290
+بدنا نثبت أن G composite F a prime of C exist عشان 
+
+102
+00:09:22,290 --> 00:09:29,500
+نثبت أنها exist بإيش بتلزمني؟ بدي أخذ limit G of
+
+103
+00:09:29,500 --> 00:09:39,520
+F, G circle F اللي هي GF of X ناقص G of F of C على
+
+104
+00:09:39,520 --> 00:09:46,960
+X ناقص C لما X تروح للـ C نثبت أن هذا إيش ماله
+
+105
+00:09:46,960 --> 00:09:51,920
+exist واضح؟ عشان اللي بدنا نسويه؟ بدنا نثبت أنه 
+
+106
+00:09:51,920 --> 00:09:55,800
+exist عشان نثبت أنه هذا exist بلزمني عاملين
+
+107
+00:09:55,800 --> 00:10:01,020
+مساعدات الآن هنشوف كيف نعمل هذول العاملين طبعا
+
+108
+00:10:01,020 --> 00:10:05,200
+طبيعي طبيعي أنا معطى أن هو الـ F' موجودة والـ G'
+
+109
+00:10:05,480 --> 00:10:10,600
+موجودة إذا أكيد أنا هعمل حسابي أن أستخدمهم على
+
+110
+00:10:10,600 --> 00:10:14,280
+أساس أن أصل للهدف اللي بدي إياه الآن خلينا نيجي 
+
+111
+00:10:14,280 --> 00:10:14,900
+للبرهان
+
+112
+00:10:20,860 --> 00:10:26,680
+الحين الـ proof بدنا
+
+113
+00:10:26,680 --> 00:10:36,080
+نثبت أنه اللي هو الـ G بنثبت إنه لو كانت G وF
+
+114
+00:10:36,080 --> 00:10:39,980
+differentiable الأول عند F of C والثاني عند C
+
+115
+00:10:39,980 --> 00:10:45,840
+بيعطينا هذا إنه G composed of F prime of C exist
+
+116
+00:10:45,840 --> 00:10:50,420
+ويساوي G prime of F of C في F prime of C هذا ما
+
+117
+00:10:50,420 --> 00:10:58,000
+بنثبته شوف كيف يعني
+
+118
+00:10:58,000 --> 00:11:06,450
+بقى بدنا نبرهن النظرية خليني أعرّف الآن Define G
+
+119
+00:11:06,450 --> 00:11:14,850
+Capital من I لعند الـ R By شوف كيف بدي .. اللي هي
+
+120
+00:11:14,850 --> 00:11:21,050
+يعني أعرّف الـ G بطريقة توصّلني لحساب D composed of 
+
+121
+00:11:21,050 --> 00:11:24,890
+F prime of إيش؟ of C جبل بشوية قلنا D composed of 
+
+122
+00:11:24,890 --> 00:11:30,590
+F prime of C المتوقع لها إنها تكون عبارة عن إذا كانت
+
+123
+00:11:30,590 --> 00:11:34,850
+تكون موجودة هي عبارة عن الـ limit لـ G F of X نقص G
+
+124
+00:11:34,850 --> 00:11:41,270
+F of C على X ناقص C أو G of Y نقص G F of C ماشي
+
+125
+00:11:41,270 --> 00:11:47,250
+الحال الآن بدي أعرّف G على هذا الأساس G of Y بتساوي
+
+126
+00:11:47,250 --> 00:12:01,160
+اللي هو G of F of Y عند ناقص g f of c على y ناقص 
+
+127
+00:12:01,160 --> 00:12:06,480
+f of c الآن قسمت على y ناقص f of c أكيد اللي هو
+
+128
+00:12:06,480 --> 00:12:15,600
+الـ y أنا بديش إياها تساوي f of c الآن g of y إيش
+
+129
+00:12:15,600 --> 00:12:23,980
+بدي إياها؟ بدي إياها الـ limit المتوقع الـ limit 
+
+130
+00:12:23,980 --> 00:12:30,300
+لهذه لما y تروح للـ F of C اللي هو وكأنه عبارة عن 
+
+131
+00:12:30,300 --> 00:12:37,540
+D prime of مين؟ of F of C فالآن بتديها D prime of F
+
+132
+00:12:37,540 --> 00:12:44,180
+of C ليش هالـ gate بتشوف ليش اللي بنحكيها الآن عرفت
+
+133
+00:12:44,180 --> 00:12:49,140
+اللي هي الـ function طبعا هذا الكلام مستقى من 
+
+134
+00:12:49,140 --> 00:12:54,120
+اللي هو f prime of c إيش متوقع limitه تساوي؟ هذا
+
+135
+00:12:54,120 --> 00:12:58,200
+مستقى .. مستقى منه بعد شوية هتلاقيني هذه كتبت على
+
+136
+00:12:58,200 --> 00:13:02,980
+صورة هذه في شغل تانية برضه موجودة اللي هي f prime 
+
+137
+00:13:02,980 --> 00:13:07,260
+of c اه 
+
+138
+00:13:07,260 --> 00:13:16,350
+آسف g of y الآن نشوف هذه الدالة لو جيت للدالة اللي
+
+139
+00:13:16,350 --> 00:13:26,010
+عندي هذه خذ limit g of y لما y تروح للـ F of C إيش
+
+140
+00:13:26,010 --> 00:13:32,500
+هتلاقيها بتساوي؟ بتساوي limit G of Y بعوض جاهز Y 
+
+141
+00:13:32,500 --> 00:13:38,080
+تروح للـ F of C يعني Y  أشمالها لا تساوي F of C ناقص
+
+142
+00:13:38,080 --> 00:13:45,340
+G of F of C على مين؟ على Y minus F of C لما Y تروح 
+
+143
+00:13:45,340 --> 00:13:51,560
+لمين؟ للـ F of C وهذه بالظبط هي تعريف مين؟ تعريف الـ
+
+144
+00:13:51,560 --> 00:13:56,480
+derivative للـ G عند النقطة مين؟ النقطة اسمها F of
+
+145
+00:13:56,480 --> 00:14:01,280
+C واضح؟ لأن الـ C من الـ A .. من الـ J الـ F of C
+
+146
+00:14:01,280 --> 00:14:08,260
+وين هتكون؟ من مين؟ من الـ I واضح؟ فالآن هذه عبارة
+
+147
+00:14:08,260 --> 00:14:16,920
+عن G prime للـ F of C ليش هذا؟ because ..G is
+
+148
+00:14:16,920 --> 00:14:25,200
+differentiable at mean at F of C هذا معطى طيب الآن
+
+149
+00:14:25,200 --> 00:14:30,160
+الـ limit لـ G of Y طلعت لما يتروح لـ F of C أش طلعت
+
+150
+00:14:30,160 --> 00:14:34,520
+G prime لـ F of C أصلا هذا السبب اللي أنا عارف أنه
+
+151
+00:14:34,520 --> 00:14:37,440
+هتطلع حاجة السبب اللي خلاني أعرف الـ G of Y أش
+
+152
+00:14:37,440 --> 00:14:44,510
+متساوي G prime F of C عشان تطلعلي منه هذا بساوي G
+
+153
+00:14:44,510 --> 00:14:52,510
+عند مين؟ عند Y بتساوي F of C يعني هذا سبب لإنه الـ
+
+154
+00:14:52,510 --> 00:14:57,610
+G هذه تصير إيش ماله؟ is continuous عند مين؟ عند ال F
+
+155
+00:14:57,610 --> 00:15:07,490
+of C إذا hence G is continuous at F of C طب ليش 
+
+156
+00:15:07,490 --> 00:15:15,570
+هذا بعد شوية هنشوف وين هنستخدمها الآن limit g of y
+
+157
+00:15:15,570 --> 00:15:22,890
+طالع عندي بيساوي g of f of c اللي هي هذه g of f of
+
+158
+00:15:22,890 --> 00:15:29,550
+c بيساوي g prime f of c نيجي الآن أنا إيش اللي بدي 
+
+159
+00:15:29,550 --> 00:15:35,910
+أ.. بدي الآن اثبت لك أن g composite f prime of c
+
+160
+00:15:35,910 --> 00:15:48,970
+بيساوي limit gof F of X ناقص G of F of C على X
+
+161
+00:15:48,970 --> 00:15:55,410
+minus C لما X تروح للـ C بدي أثبت أنه exist بظبط؟
+
+162
+00:15:55,410 --> 00:16:02,610
+واضح هاه؟ طيب بناءً عليه خليني أكتب هذه بدلالة إشي
+
+163
+00:16:02,610 --> 00:16:11,060
+بوصلني للي بديها شوف كيف الآن نحسب هذه هذه لمين؟ for
+
+164
+00:16:11,060 --> 00:16:22,260
+x element n اللي هي j أو x لا تساوي مين؟ لا تساوي c
+
+165
+00:16:22,260 --> 00:16:30,120
+معايا اه الآن احسبولي هذه هذه عبارة عن تساوي g of
+
+166
+00:16:30,120 --> 00:16:37,650
+f of x اللي هونقص g f of c بدي اكتبها بطريقة g f
+
+167
+00:16:37,650 --> 00:16:49,250
+of x نقص g of f of c على f of x نقص f of c في f of
+
+168
+00:16:49,250 --> 00:16:58,630
+x نقص f of c على x minus c دخلت هذا المقدار في الـ
+
+169
+00:16:58,630 --> 00:17:04,410
+bust و هنا في المقام اللي هو على أساس ان احصل على
+
+170
+00:17:04,410 --> 00:17:10,530
+هذه مضروبة في هذه اللي أنا عندي معلومات عن هذه و
+
+171
+00:17:10,530 --> 00:17:20,290
+عن هذه واضح؟ أي سؤال؟ و يساوي؟ الآن هذا كله على
+
+172
+00:17:20,290 --> 00:17:33,910
+بعضه مين هو عبارة عن جي capital of F of X اه F
+
+173
+00:17:33,910 --> 00:17:40,510
+of X اللي هي G of Y بدل ال Y إيش اسمها؟ F of X واضح
+
+174
+00:17:40,510 --> 00:17:46,790
+مضروبة في مين؟ هذا المقدار طلع هذا مضروب في F of X
+
+175
+00:17:48,050 --> 00:17:54,710
+نقص f of c على x minus c خد الآن الـ limit للجهتين
+
+176
+00:17:54,710 --> 00:18:01,550
+الـ limit للجهتين بيصير الـ limit لهذا المقدار الـ
+
+177
+00:18:01,550 --> 00:18:09,430
+limit لهذا المقدار معايا يا شباب لما x تروح للـ c
+
+178
+00:18:09,430 --> 00:18:18,040
+بيساوي خلينا أمسح هان بهمش بعد إذنكم اثبتنا احنا
+
+179
+00:18:18,040 --> 00:18:22,940
+الـ G كابيتال continuous خليني انجل هذا الكلام فوق
+
+180
+00:18:22,940 --> 00:18:32,700
+إذا صارت عندي limit الـ G of F of X ناقص G of F of
+
+181
+00:18:32,700 --> 00:18:42,160
+C على X minus C لما X تروح للـ C بساوي limit اللي
+
+182
+00:18:42,160 --> 00:18:54,190
+هو G of F of X لما X تروح للـ C أه فيه limit اللي
+
+183
+00:18:54,190 --> 00:19:00,710
+هو F of X ناقص F of C على X minus C لما X تروح
+
+184
+00:19:00,710 --> 00:19:07,820
+لمين؟ للـ C طبعا طبيعي لما X تروح للـ C الـ F of X
+
+185
+00:19:07,820 --> 00:19:13,660
+نفسها هتروح لمين؟ للـ F of C، مظبوط؟ لما X تروح للـ
+
+186
+00:19:13,660 --> 00:19:18,960
+C، الـ F of X هتروح لمين؟ للـ F of C، لأن أصلا F is
+
+187
+00:19:18,960 --> 00:19:23,240
+differential، بالإذن continuous، معايا؟ طيب، إذن
+
+188
+00:19:23,240 --> 00:19:29,380
+الآن عندي بدي أستخدم الـ continuity لمين؟ للـ G،
+
+189
+00:19:29,380 --> 00:19:35,050
+limit G of F of C لما .. لو سمينا هذه كلها على بعض
+
+190
+00:19:35,050 --> 00:19:39,770
+Y قلنا لما X تروح للـ C الـ Y اللي هي F of X بتروح
+
+191
+00:19:39,770 --> 00:19:45,430
+لمين؟ للـ F of C بتصير هذه وكأنها اسمها G of Y و
+
+192
+00:19:45,430 --> 00:19:52,190
+بدل هذه بنحط Y بتروح لمين؟ للـ F of C والـ G
+
+193
+00:19:52,190 --> 00:19:56,450
+capital is continuous عند الـ F of C إذا على طول
+
+194
+00:19:56,450 --> 00:20:05,010
+limitها بتساوي G of F of C مظبوط؟ مضروبة في مين؟ في
+
+195
+00:20:05,010 --> 00:20:08,010
+limit F of X نقص F of C على X minus C لما X تروح
+
+196
+00:20:08,010 --> 00:20:14,190
+لمين؟ لـ C ليها دي تعريف مين؟ المشتقة الأولى للـ F
+
+197
+00:20:14,190 --> 00:20:19,310
+عند الـ C نرجع الآن G of F of C إيش بتساوي حسب
+
+198
+00:20:19,310 --> 00:20:22,610
+التعريف الأولاني؟ بساوي G prime
+
+199
+00:20:26,140 --> 00:20:36,180
+للـ F of C بدل هذه في F prime of C وهو المطلوب أي
+
+200
+00:20:36,180 --> 00:20:41,000
+سؤال؟
+
+201
+00:20:41,000 --> 00:20:46,740
+لذلك الآن أثبتنا أنه لو كانت F is differentiable
+
+202
+00:20:46,740 --> 00:20:53,080
+أو G is differentiable ويكون الـ composite الهن is
+
+203
+00:20:53,080 --> 00:20:57,900
+differentiable طبعا ما أخذ بعين الاعتبار أنه يكون
+
+204
+00:20:57,900 --> 00:21:00,600
+جي كمبوسيت F is defined
+
+205
+00:21:16,030 --> 00:21:25,010
+في عندنا اللي هو المثال الأول مثال
+
+206
+00:21:25,010 --> 00:21:30,750
+يعني بسيط كلنا بنعرف انفاضه بس بنشوف كيف احنا
+
+207
+00:21:30,750 --> 00:21:35,530
+بنستخدم الـ .. الـ .. الـ .. الـ chain rule الصورة
+
+208
+00:21:35,530 --> 00:21:39,470
+اللي احنا كتبناها في اللي هو ايجاد الـ derivative
+
+209
+00:21:39,470 --> 00:21:46,520
+جاي اللي عند في example جاي اللي خد Example جاي لنت
+
+210
+00:21:46,520 --> 00:21:56,300
+F من عند I لعند R بيه a differentiable function من
+
+211
+00:21:56,300 --> 00:22:00,080
+هنا نفترض أن الـ F أشبه لها يا جماعة عبارة عندها
+
+212
+00:22:00,080 --> 00:22:05,860
+لقابلة للاشتقاق عند نقطة وين؟ على الـ I أو عند الـ I
+
+213
+00:22:05,860 --> 00:22:13,230
+كلها مش مشكلة ماشي الحال بقول لك اثبت لي بس قبل ما
+
+214
+00:22:13,230 --> 00:22:20,750
+بتخلينا نقل تقول احنا بتوجد لنا الـ Fn لأن في عندي
+
+215
+00:22:20,750 --> 00:22:24,890
+دالة اسمها Fn يعني F مرفوعة للقوة أنا بدي اوجد لها
+
+216
+00:22:24,890 --> 00:22:30,140
+الـ derivative طبعا الـ Fn كله prime of X من
+
+217
+00:22:30,140 --> 00:22:36,040
+معلوماتنا في الـ Calculus كنا نقول أن تفاضل القوس
+
+218
+00:22:36,040 --> 00:22:41,560
+كله نهو N في F N ناقص واحد في تفاضل ما بداخل القوس
+
+219
+00:22:41,560 --> 00:22:47,990
+اللي هو عبارة عن F prime of X هذا تفضل الآن بدنا
+
+220
+00:22:47,990 --> 00:22:54,650
+نبرهن هذا الكلام باستخدام نظرية الـ chain rule
+
+221
+00:22:54,650 --> 00:22:58,050
+يعني هذا شغل المكان زي ما بقوله الآن بدنا نشوف كيف
+
+222
+00:22:58,050 --> 00:23:01,670
+بتشتغل المكينة أو إيش اللي شغل المكينة طيب الـ
+
+223
+00:23:01,670 --> 00:23:13,110
+proof الـ proof لندن كده بدي اعرف function let g
+
+224
+00:23:13,110 --> 00:23:23,530
+from some interval J لعند R defined by G يعني أصلا
+
+225
+00:23:23,530 --> 00:23:30,330
+ممكن أعرفها من R حتى G of Y بيساوي Y أساش N element
+
+226
+00:23:30,330 --> 00:23:35,070
+in N يعني حتى لو أعرفتها من R مابعرفها الدالة
+
+227
+00:23:35,070 --> 00:23:46,200
+معايا الآن بناء على هيك صار عندي الآن اللي هو الـ G
+
+228
+00:23:46,200 --> 00:23:56,700
+composite F of X إيش هي هتطلع؟ G of F of X يعني
+
+229
+00:23:56,700 --> 00:24:05,340
+هتطلع Fn of X صح ولا لأ؟ إذن هاي دالتنا اللي بدنا
+
+230
+00:24:05,340 --> 00:24:12,000
+نفضلها كتبتها على صورة مين؟ G composite F والـ F of
+
+231
+00:24:12,000 --> 00:24:17,520
+X الـ F of X اللي هي الـ F of X من وين جاي بترمي
+
+232
+00:24:17,520 --> 00:24:22,680
+في الـ R يعني بترمي في مين؟ في domain الـ G واضح
+
+233
+00:24:22,680 --> 00:24:27,840
+أه إذا كل أموري تمام وهذه الدالة الدالة الأسية is
+
+234
+00:24:27,840 --> 00:24:30,980
+differentiable وهو جاي اللي أن الـ F is
+
+235
+00:24:30,980 --> 00:24:33,780
+differentiable إذا جي كومبوزيت F حسب الـ channel
+
+236
+00:24:33,780 --> 00:24:38,140
+أشمالها is differentiable و الـ derivative لها جي
+
+237
+00:24:38,140 --> 00:24:42,900
+كومبوزيت F prime of X حسب الـ channel اللي حكيناها
+
+238
+00:24:42,900 --> 00:24:49,560
+اللي برهنناها بساوي G prime of F of X في f prime of
+
+239
+00:24:49,560 --> 00:24:53,580
+x وي ساون and g of y بيساوي y أس 2 الـ derivative
+
+240
+00:24:53,580 --> 00:24:59,420
+الهنين هي and y أس n ناقص واحد يعني and y أس n
+
+241
+00:24:59,420 --> 00:25:04,220
+ناقص واحد في f prime of x لكن احنا بنفاضل عند مين؟
+
+242
+00:25:04,220 --> 00:25:08,860
+عند f of x فبنشي الـ y بنحكم مكانها قيمتها اللي هي
+
+243
+00:25:08,860 --> 00:25:14,240
+f of x فبتطلع and f of x n ناقص واحد في f prime of
+
+244
+00:25:14,240 --> 00:25:19,610
+x هذه اللي هي اللي احنا بنشتغلها وبدون ما .. طبعا
+
+245
+00:25:19,610 --> 00:25:24,930
+احنا هذا تشريع لاستخدام اللي هو Kedemstrain rule
+
+246
+00:25:24,930 --> 00:25:28,150
+it's اللي احنا بنعرفها زي ما نيجي لما كنا نقول لكم
+
+247
+00:25:28,150 --> 00:25:34,810
+مثلا اوجد الـ derivative y لعندك y بالساوى sin x
+
+248
+00:25:34,810 --> 00:25:39,460
+تكعيب مثلا كنتش تسوي على طول ماتيش إيش تقول والله
+
+249
+00:25:39,460 --> 00:25:44,040
+بيضاف رضاف of X بيساوي X تتعيب و G of Y تساوي Sin
+
+250
+00:25:44,040 --> 00:25:47,600
+Y و تقول إذا صارت هذه عبارة عن composite of two
+
+251
+00:25:47,600 --> 00:25:53,240
+functions خلاص بنتجاوز المرحلة هذه وعرفنا وين أصل
+
+252
+00:25:53,240 --> 00:25:58,160
+الأمر اللي بيقول لنا why prime بتساوي تفاضل اللي
+
+253
+00:25:58,160 --> 00:26:03,760
+برا اللي هو cosine x كعيب في تفاضل اللي جوا تلاتة
+
+254
+00:26:03,760 --> 00:26:08,100
+x تربيع هذا في الواقع هو عبارة عن استخدام mean للـ
+
+255
+00:26:08,100 --> 00:26:19,080
+chain rule واضح أي سؤال؟ طيب هذا عندنا في عندنا
+
+256
+00:26:19,080 --> 00:26:31,850
+مثال آخر المثال .. نعم المثال اللي هو .. يمكن مرشك
+
+257
+00:26:31,850 --> 00:26:36,330
+للمثال حتى معاكم في تحليل واحد لكن كان هدفه اللي
+
+258
+00:26:36,330 --> 00:26:42,910
+هو في حينه الـ continuity إذا اعطيك F of X بتساوي
+
+259
+00:26:42,910 --> 00:26:52,400
+هاي B مثال B F of X بتساوي اللي هو X تربيع Sin 1
+
+260
+00:26:52,400 --> 00:26:59,800
+على X لما X لا تساوي سفر أو سفر لما X إيش بتساوي
+
+261
+00:26:59,800 --> 00:27:07,140
+سفر الآن بيقول لي بيعطيني طبعا هو بيسأل سؤال جاب له
+
+262
+00:27:07,140 --> 00:27:10,640
+تعليق سؤال في الكتاب بيقول لي لو كانت الـ F is
+
+263
+00:27:10,640 --> 00:27:14,040
+differentiable ركز معه لو كانت الـ F is
+
+264
+00:27:14,040 --> 00:27:17,800
+differentiable الشرط أن الـ derivative تماما تطلع
+
+265
+00:27:17,800 --> 00:27:23,590
+continuous هذا ليس شرطا، هذا بس وينفي الـ R لما
+
+266
+00:27:23,590 --> 00:27:26,430
+نحكي عن الهو نحكي عن الـ real valued functions
+
+267
+00:27:26,430 --> 00:27:33,210
+from R to R كمان لكن في الـ complex الأمر بيختلف الـ
+
+268
+00:27:33,210 --> 00:27:36,610
+complex أو الـ derivative مرة لجيتها معناته اللي
+
+269
+00:27:36,610 --> 00:27:39,210
+بعيدها واللي بعيدها واللي بعيدها هتظلها أشمالها
+
+270
+00:27:39,210 --> 00:27:43,830
+موجودة يعني if F prime exists then F double prime
+
+271
+00:27:43,830 --> 00:27:48,630
+and F triple F كذا إذا هتطلع مجرد ما تكون الدالة
+
+272
+00:27:48,630 --> 00:27:53,230
+analytic أو differentiable هتظلها على طول
+
+273
+00:27:53,230 --> 00:27:56,750
+differentiable و continuous و و و الآخرين هذا وين
+
+274
+00:27:56,750 --> 00:28:01,890
+في الـ complex أما في الـ real الوضع ليس كذلك وهي
+
+275
+00:28:01,890 --> 00:28:07,970
+مثال على F is differentiable everywhere طبعا is
+
+276
+00:28:07,970 --> 00:28:11,310
+differentiable عنده نقطة zero بالذات لكن its
+
+277
+00:28:11,310 --> 00:28:15,450
+derivative is not continuous at this point واضح
+
+278
+00:28:15,450 --> 00:28:20,330
+اليوم اه طيب الآن show
+
+279
+00:28:23,010 --> 00:28:30,750
+that F prime of X exists everywhere
+
+280
+00:28:30,750 --> 00:28:41,270
+but F prime is not continuous at zero و proof
+
+281
+00:28:41,270 --> 00:28:45,470
+البرهان.. طبعا البرهان كامل موجود هنا بس خلينا
+
+282
+00:28:45,470 --> 00:28:50,670
+نبرهن لك.. نوضح إيش الـ.. إيش البرهان شوفوا صلى
+
+283
+00:28:50,670 --> 00:28:56,670
+الله عليه الصلاة والسلام الآن f prime exist طبيعي
+
+284
+00:28:56,670 --> 00:29:03,310
+for x لا يساوي 0  مقبول سهل مجرد تفاضل عادي f prime
+
+285
+00:29:03,310 --> 00:29:07,290
+of x لأن هذه الدالة قابلة للاشتقاق عند كل نقطة ما
+
+286
+00:29:07,290 --> 00:29:11,430
+عدا عند الـ x  بالمساواة 0 هذه بحكي عن هذه لحالها f
+
+287
+00:29:11,430 --> 00:29:19,020
+prime of x بالمساواة 2x sin 1 على x لأن x تربيع في
+
+288
+00:29:19,020 --> 00:29:24,360
+sin تفاضل الـ sin cos  و تفاضل اللي جوا سالب x
+
+289
+00:29:24,360 --> 00:29:30,440
+تربيع x minus 2 بتروح حد مع حد فبيصير سالب cos 1
+
+290
+00:29:30,440 --> 00:29:36,480
+على x الآن هذا for x لا تساوي صفر طب for x مساويا
+
+291
+00:29:36,480 --> 00:29:39,660
+صفر for x مساويا صفر الوضع اللي لأن بختلف اللي هو
+
+292
+00:29:39,660 --> 00:29:43,880
+فيه عندي اللي هو الدالة أصلا مش معرفة عند الـ zero
+
+293
+00:29:43,880 --> 00:29:47,620
+لكن معرفة الدالة ككل عند الـ zero عند من بتساوي
+
+294
+00:29:47,620 --> 00:29:52,060
+صفر فمضطر أنا أستخدم التعريف لإثبات أو فحص إذا 
+
+295
+00:29:52,060 --> 00:29:56,680
+كانت الدالة لها مشتقة عند الصفر ولا لأ فبأجي بقول
+
+296
+00:29:56,680 --> 00:30:03,810
+الآن بتبدأ فحص limit اللي هو F of X ناقص F of Zero
+
+297
+00:30:03,810 --> 00:30:08,910
+على X minus Zero as X بتروح للزيرو بدي أشوف هل هذه
+
+298
+00:30:08,910 --> 00:30:13,250
+الـ limit موجودة ولا مش موجودة ماشي الحال Y مساويا
+
+299
+00:30:13,250 --> 00:30:16,930
+هذا
+
+300
+00:30:16,930 --> 00:30:20,370
+عشان خاطر أوجد من أشوف الـ F prime عند الـ Zero
+
+301
+00:30:20,370 --> 00:30:25,630
+موجودة أو لا بمساواة limit F of X من هي عبارة عن X
+
+302
+00:30:25,630 --> 00:30:29,030
+تربيع.. لأن X بتروح للزيرو، لأن X مش صفر، اللي هي 
+
+303
+00:30:29,030 --> 00:30:34,450
+عبارة عن X تربيع sin واحد على X ناقص F of Zero اللي
+
+304
+00:30:34,450 --> 00:30:39,310
+هي عبارة عن صفر على X minus صفر لما X تروح لمن
+
+305
+00:30:39,310 --> 00:30:46,870
+للصفر ومساويا limit x term x sin 1 على x لما x تروح
+
+306
+00:30:46,870 --> 00:30:50,670
+لمن للصفر هذه اللي هي by sandwich theorem حلقيها
+
+307
+00:30:50,670 --> 00:30:56,650
+إيش بتساوي صفر كيف by sandwich theorem عندك x sin
+
+308
+00:30:56,650 --> 00:31:00,470
+1 على x absolute value أصغر أو مساويا الـ absolute
+
+309
+00:31:00,470 --> 00:31:05,050
+value للـ x وهذه الطبيعي أكبر أو مساويا من صفر as x
+
+310
+00:31:05,050 --> 00:31:07,870
+goes to zero هذه بتروح للزيرو وهذه بتروح للزيرو
+
+311
+00:31:07,870 --> 00:31:10,570
+إذا اللي في النص هذه لازم الـ limit هيروح لمن
+
+312
+00:31:10,570 --> 00:31:15,840
+للصفر ومن ثم للـ continuity للـ بسبب الـ continuity
+
+313
+00:31:15,840 --> 00:31:18,040
+للـ للـ absolute value بتطلع الـ limit اللي جوا
+
+314
+00:31:18,040 --> 00:31:20,740
+برضه أشمالها بتساوي 0 لأن الـ limit الـ absolute
+
+315
+00:31:20,740 --> 00:31:23,380
+value بيساوي absolute value للـ limit إذا صار عندي
+
+316
+00:31:23,380 --> 00:31:32,120
+limit اللي جوا بيساوي 0 معايا؟ طيب
+
+317
+00:31:32,120 --> 00:31:35,940
+بما أنه الـ limit هذه موجودة بتساوي 0 إذا بنقول
+
+318
+00:31:35,940 --> 00:31:42,580
+بعيدها since كده بيساوي كده then F prime of 0
+
+319
+00:31:42,580 --> 00:31:50,520
+بتساوي صفر إذا اللي أثبتنا إحنا إنه F prime exist
+
+320
+00:31:50,520 --> 00:31:55,460
+وين ما كان وإيش الـ F prime اللي أثبتناها كمان
+
+321
+00:31:55,460 --> 00:32:01,160
+أثبتنا إنه الآن F prime of X أثبتناها إنها بتساوي
+
+322
+00:32:02,250 --> 00:32:08,870
+2x sin 1 على x ناقص cos 1 على x لما x إيش معناه لأ
+
+323
+00:32:08,870 --> 00:32:13,070
+تساوي صفر واتبعتناها بتساوي صفر لما x بتساوي صفر
+
+324
+00:32:13,070 --> 00:32:16,990
+إذا صارت الـ F is functional everywhere الآن بدنا
+
+325
+00:32:16,990 --> 00:32:23,350
+نثبت إنه is not this F prime is not continuous at
+
+326
+00:32:23,350 --> 00:32:27,150
+zero شوف
+
+327
+00:32:27,150 --> 00:32:29,410
+الآن عندي
+
+328
+00:32:31,690 --> 00:32:41,570
+بدي أشوف limit اللي هي 2x sin 1 على x ناقص cos 1 
+
+329
+00:32:41,570 --> 00:32:49,080
+على x لما x تروح للزيرو exist ولا لأ الآن limit الـ
+
+330
+00:32:49,080 --> 00:32:53,540
+أولى 2x sin 1 على x مضمون إنه exist قبل مش
+
+331
+00:32:53,540 --> 00:32:57,560
+ويعملناها نفسها باي اللي هو sandwich theorem هتطلع
+
+332
+00:32:57,560 --> 00:33:03,720
+صفر إذا الآن أول حاجة أكتب لها since الآن limit
+
+333
+00:33:03,720 --> 00:33:09,420
+sin 1 على x بيساوي صفر exist الآن
+
+334
+00:33:09,420 --> 00:33:19,480
+but but limit cos 1 على x لما x تروح لصفر does not
+
+335
+00:33:19,480 --> 00:33:24,360
+exist وهلجت بنشوف ليش does not exist but this
+
+336
+00:33:24,360 --> 00:33:26,140
+limit أشمالها does not exist
+
+337
+00:33:28,950 --> 00:33:33,830
+ما دام هذا exist وهذا does not exist حاصل جمع أو
+
+338
+00:33:33,830 --> 00:33:38,290
+طرح أكيد إيش ماله does not exist لأنه لو exist
+
+339
+00:33:38,290 --> 00:33:42,810
+معناه تصير هذا اللي يطلع وهذا exist بيصير مجموع
+
+340
+00:33:42,810 --> 00:33:45,170
+أو طرح مساويا هذا أيضا صار هذا exist وهذا
+
+341
+00:33:45,170 --> 00:33:51,550
+contradiction فاهمين آه الآن hence limit اتنين x
+
+342
+00:33:51,550 --> 00:33:56,410
+sin واحد على x ناقص cosine واحد على x لما x تروح
+
+343
+00:33:56,410 --> 00:34:05,340
+للصفر اللي هو does not exist دل عليا بس أوضح اللي
+
+344
+00:34:05,340 --> 00:34:12,220
+هو ليش هذا does not exist بده أوضح ليش هذا does
+
+345
+00:34:12,220 --> 00:34:18,740
+not exist أخذتو أنتو أخذتو اللي هو إيش نظرية إن
+
+346
+00:34:18,740 --> 00:34:28,240
+لو كانت limit F of X لما X بتروح لـ A بيساوي L إذا أي
+
+347
+00:34:28,240 --> 00:34:34,560
+sequence XN بتروح للـ A لازم يعطيك اللي هو F of XN
+
+348
+00:34:34,560 --> 00:34:39,780
+برضه يروح لمن للـ L، بصبوط؟ هذه كـ continuity اللي
+
+349
+00:34:39,780 --> 00:34:43,530
+بتحكي عنها اللي كده كانت limit F of X لما X تروح
+
+350
+00:34:43,530 --> 00:34:48,930
+للـ A بيساوي L و إذا تأخذت أي sequence XN بتروح للـ
+
+351
+00:34:48,930 --> 00:34:54,670
+A هيطلع limit F of XN مش بيروح بيساوي لـ L ماشي هذه
+
+352
+00:34:54,670 --> 00:35:00,780
+اللي هي النظرية بناء على هذه النظرية كنا نقول إنه
+
+353
+00:35:00,780 --> 00:35:07,180
+لو وجيت two sequences على الأقل يكون بروح للـ A
+
+354
+00:35:07,180 --> 00:35:13,500
+لكن بروح لـ Limits مختلفات أو واحدة من Limits does
+
+355
+00:35:13,500 --> 00:35:18,600
+not exist بكفالك إن الـ Limit هذه أشمالها does not
+
+356
+00:35:18,600 --> 00:35:25,170
+exist واضح؟ الآن إذا بدي اعتمد على هذه في إثبات إنه
+
+357
+00:35:25,170 --> 00:35:29,690
+limit cosine واحد على X does not exist أكيد كلكم
+
+358
+00:35:29,690 --> 00:35:40,730
+جال take the sequences أو the two sequences X and
+
+359
+00:35:40,730 --> 00:35:50,290
+بمساواة واحد على اتنين n by n and Y n بمساواة واحد
+
+360
+00:35:50,290 --> 00:35:57,030
+على اتنين n زائد واحد في n مظبوط أكيد قلته هيك
+
+361
+00:35:57,030 --> 00:36:05,290
+where x n goes to zero and y n goes to zero
+
+362
+00:36:05,290 --> 00:36:13,130
+but cosine واحد على إيه؟ cosine واحد على x n
+
+363
+00:36:13,130 --> 00:36:23,100
+اللي هو بيساوي أو goes to واحد and cosine 1 على y
+
+364
+00:36:23,100 --> 00:36:30,500
+n goes to ناقص واحد أوضحها
+
+365
+00:36:30,500 --> 00:36:35,600
+أووضحها أذكركم الآن
+
+366
+00:36:35,600 --> 00:36:39,980
+هذا بيصير cosine من اتنين n by اتنين n by إيش
+
+367
+00:36:39,980 --> 00:36:45,470
+مالها واحد اتنين n زائد واحد لكل في باقي إيش
+
+368
+00:36:45,470 --> 00:36:49,030
+بتصير؟ اللي هو سالب واحد فبيصير هاد الـ cosine
+
+369
+00:36:49,030 --> 00:36:53,450
+converts لواحد وهاد الـ cosine converts لمن؟ لسالب
+
+370
+00:36:53,450 --> 00:36:58,490
+واحد إذا حسب اللي حكيناها قبل شوية hence hence
+
+371
+00:36:58,490 --> 00:37:05,910
+hence limit cosine واحد على x لما x تروح لـ zero
+
+372
+00:37:05,910 --> 00:37:17,800
+does not exist هذا توضيح.. توضيح لماذا اللي هو cos
+
+373
+00:37:17,800 --> 00:37:24,000
+1 على x does not exist لاحظ التالي على جهة لكن لو
+
+374
+00:37:24,000 --> 00:37:28,440
+كانت.. بالمناسبة لو كانت هذه does not exist
+
+375
+00:37:28,440 --> 00:37:33,640
+limitها وهذه does not exist بقدرش أؤكد على إن الـ
+
+376
+00:37:33,640 --> 00:37:40,460
+limit للطرح أو الجمع does not exist صح؟ في مثال؟
+
+377
+00:37:45,330 --> 00:37:50,850
+آه وخروجتها واحدة لأن واحدة لأن بينهم سالم بيصير 
+
+378
+00:37:50,850 --> 00:37:53,450
+limit لها دي موجودة أو limit لها دي موجودة.. آسف
+
+379
+00:37:53,450 --> 00:37:55,890
+limit لها دي مش موجودة أو limit لها دي مش موجودة
+
+380
+00:37:55,890 --> 00:38:01,490
+لكن اللي هو حصل إيش طرح موجود أو لو بدك جمع بتحط
+
+381
+00:38:01,490 --> 00:38:04,890
+اللي هو للتانية تأخذ واحدة لأن ونقص واحدة لأن و
+
+382
+00:38:04,890 --> 00:38:10,490
+هكذا أي سؤال؟
+
+383
+00:38:10,490 --> 00:38:11,330
+طيب
+
+384
+00:38:15,770 --> 00:38:21,510
+اللي يجي الآن إلى
+
+385
+00:38:21,510 --> 00:38:37,290
+النقطة اللي بعيدها أين
+
+386
+00:38:37,290 --> 00:38:38,330
+رحلت أنا؟
+
+387
+00:38:48,090 --> 00:38:53,250
+طيب انتبهوا خلينا لهذه النظرية نحكي عن نصها أو
+
+388
+00:38:53,250 --> 00:39:00,150
+الشيء بالتفصيل وبعدين نيجي نلخص لكم كل المعلومة
+
+389
+00:39:00,150 --> 00:39:05,130
+اللي.. اللي في الأول هنحس إنها بتغلب في اللي هو
+
+390
+00:39:05,130 --> 00:39:13,470
+صفر ومن ثم نحاول نبرهنها آه
+
+391
+00:39:13,470 --> 00:39:18,970
+.. آه.. آه.. لأ.. آه.. let I subsequent R be an
+
+392
+00:39:18,970 --> 00:39:19,610
+interval
+
+393
+00:39:28,670 --> 00:39:34,370
+لأنه احنا بتتذكروا في real واحد خلاص اللي هي الـ..
+
+394
+00:39:34,370 --> 00:39:37,010
+الـ..الـ..الـ..الشيء اللي بده شغل اللي هو
+
+395
+00:39:37,010 --> 00:39:39,890
+النقطة اللي بتكون في الـ interval اللي بتكون
+
+396
+00:39:39,890 --> 00:39:42,250
+cluster point اللي مش cluster point automatic
+
+397
+00:39:42,250 --> 00:39:45,970
+هتكون الـ limit exist فمش داعي أصلا لدراسة الموضوع
+
+398
+00:39:45,970 --> 00:39:52,440
+لأنه بيصير كثير من الأمور trivial عشان هي احنا 
+
+399
+00:39:52,440 --> 00:39:55,740
+بنشتغل على الـ Intervals let I subset من R بيكون
+
+400
+00:39:55,740 --> 00:39:59,680
+Interval and let F من I لعند R بيكون strictly
+
+401
+00:39:59,680 --> 00:40:09,720
+Monotone F من عند هذه theorem أنا مكتبش الـ theorem
+
+402
+00:40:09,720 --> 00:40:19,060
+تمام لأنه موجود هنا theorem 618 عند F من I لعند R
+
+403
+00:40:19,060 --> 00:40:25,440
+غير عنها strictly monotone
+
+404
+00:40:25,440 --> 00:40:36,900
+ماشي الحال و continuous and continuous الآن لاحظ
+
+405
+00:40:36,900 --> 00:40:41,100
+على الـ function هذى دام حكالة عنها strictly
+
+406
+00:40:41,100 --> 00:40:44,540
+monotone يعني strictly increasing أو strictly
+
+407
+00:40:44,540 --> 00:40:49,240
+decreasing معناته صارت automatic اتدالة أشمالها
+
+408
+00:40:49,240 --> 00:40:53,800
+one to one ليش؟ لأنه لو كانت strictly increasing
+
+409
+00:40:53,800 --> 00:40:59,060
+معناته x1 أصغر من x2 اللي بتعطيني f of x1 أصغر
+
+410
+00:40:59,060 --> 00:41:03,840
+strictly من f of x2 هذا في حالة نين strictly
+
+411
+00:41:03,840 --> 00:41:09,540
+increasing آه مش ممكنية للمساواة هاالآن في حالة
+
+412
+00:41:09,540 --> 00:41:14,520
+strictly decreasing X1 أكبر من X2 بيعطيني F of X1
+
+413
+00:41:14,520 --> 00:41:21,220
+أصغر من F of X2 هذا strictly decreasing الآن سواء
+
+414
+00:41:21,220 --> 00:41:25,060
+هنا الحالة هذه أو الحالة هذه هيكون عندي الـ
+
+415
+00:41:25,060 --> 00:41:29,200
+function one to one غصب عنها، ليش؟ لأن لو كانت X1
+
+416
+00:41:29,200 --> 00:41:35,640
+لا تساوي X2 يا أصغر يا أكبر، ما زال مقت أصغرهتكون
+
+417
+00:41:35,640 --> 00:41:40,680
+strictly أصغر يعني بمعنى آخر f of x1 لا تساوي f of
+
+418
+00:41:40,680 --> 00:41:45,460
+x2 ولو كانت هذه أكبر هتكون f of x1 أكبر برضه هتكون
+
+419
+00:41:45,460 --> 00:41:49,060
+أشمالها لا تساوي و similarly في حالة الـ decreasing
+
+420
+00:41:49,850 --> 00:41:56,250
+إذن واضح إن X1 ≤ X2 بيعطينا F X1 ≤ F X2 أو بمعنى 
+
+421
+00:41:56,250 --> 00:42:03,730
+آخر F X1 هذه هي الـcontraposition لـ F X1 ≤ F X2
+
+422
+00:42:03,730 --> 00:42:10,010
+بيعطينا X1 ≤ X2 وهذا يعني الـ F أشمالها is one to 
+
+423
+00:42:10,010 --> 00:42:15,810
+one يعني الآن أنا بوضحليش أعطاني F strictly
+
+424
+00:42:15,810 --> 00:42:20,790
+monotone؟ عشان شكله أصلا احنا قاعد .. هذه النظرية
+
+425
+00:42:20,790 --> 00:42:25,030
+الحاكية عن الـ inverse بدنا نشوف العلاقة بين الـ
+
+426
+00:42:25,030 --> 00:42:27,950
+derivative للـ inverse و الـ derivative للدالة
+
+427
+00:42:27,950 --> 00:42:32,520
+الأصلية إذا بدأ أهل الدالة الأصلية أن يكون لها 
+
+428
+00:42:32,520 --> 00:42:36,640
+inverse عشان يكون لها inverse لازم أفترض أن الدالة
+
+429
+00:42:36,640 --> 00:42:40,740
+أشمالها one to one فالآن فرضنا إنها strictly
+
+430
+00:42:40,740 --> 00:42:43,980
+monotone يعني strictly increasing أو strictly
+
+431
+00:42:43,980 --> 00:42:50,920
+decreasing الآن مدامة one to one إذا في إمكانية
+
+432
+00:42:50,920 --> 00:42:58,230
+نحكيعن inverse إلها F inverse إلها اللي هو بده
+
+433
+00:42:58,230 --> 00:43:03,290
+يسميه هو الآن بده يسميه G هو بده يسميه G هياخد الـ
+
+434
+00:43:03,290 --> 00:43:10,950
+G من وين من الـ range للـ F يعني من الـ F of I لعند
+
+435
+00:43:10,950 --> 00:43:17,150
+مين لعند الـ R ماشي الـ F of I هذي مسميها مين هو
+
+436
+00:43:17,150 --> 00:43:25,150
+مسميها هو J يعني ماياخد الـ G من G لعند R الـ G هي
+
+437
+00:43:25,150 --> 00:43:30,750
+عبارة عن مين؟ عن الـ F inverse معايا؟ قولي يا محمد
+
+438
+00:43:30,750 --> 00:43:42,570
+لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ
+
+439
+00:43:42,570 --> 00:43:42,670
+R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R
+
+440
+00:43:42,670 --> 00:43:43,910
+.. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R ..
+
+441
+00:43:43,910 --> 00:43:44,630
+لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ
+
+442
+00:43:44,630 --> 00:43:47,530
+R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R
+
+443
+00:43:47,530 --> 00:43:47,590
+.. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R ..
+
+444
+00:43:47,590 --> 00:43:47,610
+لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ R .. لـ
+
+445
+00:43:47,610 --> 00:43:53,500
+R .. لـ R .. لـ R .. لـبس لما نكتب I R ايش برضه
+
+446
+00:43:53,500 --> 00:43:57,420
+صحيح بس على أساس انه .. خلاني أقول المعلومات بت ..
+
+447
+00:43:57,420 --> 00:44:01,780
+بت .. بتأهلني أن أكون أدق لعند مين لعند I خلان
+
+448
+00:44:01,780 --> 00:44:06,600
+صحيح طيب الآن عشان ما نبعدش عن اللي بدنايا F من I
+
+449
+00:44:06,600 --> 00:44:12,080
+لـ R strictly monotone و G من F of I ل عند I أصلا
+
+450
+00:44:12,080 --> 00:44:15,140
+إذا كانت الـ F من I ل عند R strictly monotone و
+
+451
+00:44:15,140 --> 00:44:19,960
+continuous هتكون الـ G اللي هي الـ F inverse من F of
+
+452
+00:44:19,960 --> 00:44:24,400
+I لـ I برضه strictly monotone و إيش و continuous
+
+453
+00:44:24,400 --> 00:44:27,940
+strictly monotone و continuous إذن الآن الـ F عند
+
+454
+00:44:27,940 --> 00:44:30,660
+me strictly monotone و continuous و الـ F inverse
+
+455
+00:44:30,660 --> 00:44:41,160
+برضه strictly monotone و إيش و continuous معايا ؟
+
+456
+00:44:41,160 --> 00:44:49,090
+طيب الآن لحد الآن بعتبر أنه احنا بنحكي عن معطيات
+
+457
+00:44:49,090 --> 00:44:54,030
+حتى لو كنا استنتجنا جزء منها من بعض الآن بقوللي
+
+458
+00:44:54,030 --> 00:44:58,970
+اللي هو موضوعنا if f is differentiable at c if
+
+459
+00:44:58,970 --> 00:45:12,350
+الآن if if f is differentiable at c element in I
+
+460
+00:45:13,160 --> 00:45:17,380
+ماشي الحال يعني F differentiable عنده نقطة C
+
+461
+00:45:17,380 --> 00:45:24,600
+element وين؟ ن I بقول لك then طبعاً A و F prime of
+
+462
+00:45:24,600 --> 00:45:28,340
+C أشمالها لاتساوي صفر لأنه هيلزمنا القسم عليها
+
+463
+00:45:28,340 --> 00:45:32,420
+عشان هيك لازم اللي هو عشان نحكي عن الـ inverse لال
+
+464
+00:45:32,420 --> 00:45:34,880
+derivative تكون الـ F prime عند الـ C أشمالها
+
+465
+00:45:34,880 --> 00:45:42,730
+لاتساوي صفر الآن then اللي هي الـ G الـ G اللي
+
+466
+00:45:42,730 --> 00:45:47,810
+سميناها F inverse اللي سميناها F inverse الـ G is
+
+467
+00:45:47,810 --> 00:45:51,150
+differentiable
+
+468
+00:45:51,150 --> 00:46:00,490
+is differentiable at اللي هو F of C is
+
+469
+00:46:00,490 --> 00:46:04,610
+differentiable at إيش؟ at F of C اللي هو مسميها
+
+470
+00:46:04,610 --> 00:46:11,800
+إيش اسمها دي الآن الإعلان الواضح أنه لو كانت F
+
+471
+00:46:11,800 --> 00:46:15,960
+differentiable عند الـC و F' للـC لاتساوي صفر
+
+472
+00:46:15,960 --> 00:46:20,400
+هتكون الـF inverse differentiable عند مين؟ عند
+
+473
+00:46:20,400 --> 00:46:34,300
+الـF of C اه and .. and F inverse prime at F of C
+
+474
+00:46:35,750 --> 00:46:46,830
+At F of C هتساوي واحد على F prime لمين؟ Let's see
+
+475
+00:46:46,830 --> 00:46:59,390
+يعني وكأنه وكأنه بمجول F inverse prime لل Y بتساوي
+
+476
+00:46:59,390 --> 00:47:07,690
+واحد على F prime of X where العلاقة بين Y و X اللي
+
+477
+00:47:07,690 --> 00:47:16,070
+هي Y بتساوي F of X واضح، اه، الكلام واضح وسهل اللي
+
+478
+00:47:16,070 --> 00:47:21,190
+هي f prime of c بدي أكتبها طريقة ثانية بيساوي واحد
+
+479
+00:47:21,190 --> 00:47:30,010
+على f prime of الآن هو سمى الـ f of c أشمالها D يعني
+
+480
+00:47:30,010 --> 00:47:37,080
+الـ c بتساوي f inverse لـ D صح؟ يعني بمعنى آخر
+
+481
+00:47:37,080 --> 00:47:45,060
+هو بقول F inverse prime عند مين؟ عند الـ D بساوي واحد
+
+482
+00:47:45,060 --> 00:47:50,580
+على F prime مكان الـ C إيش بده يحط؟ F inverse
+
+483
+00:47:50,580 --> 00:48:01,420
+of D يعني واحد على F prime فلأ بكفي اللي هي ماشي
+
+484
+00:48:01,420 --> 00:48:07,720
+الحل G of D لأ لأ اللي هو كاتبها يعني لإنه كاتب هو
+
+485
+00:48:07,720 --> 00:48:15,000
+بدل الـ F inverse كاتب مين الـG واضح واضحة طبعا هذه
+
+486
+00:48:15,000 --> 00:48:22,200
+اللي هي اللي احنا بدنا نثبته نيجي للإثبات
+
+487
+00:48:27,580 --> 00:48:32,740
+بدنا نطبطب روحنا شوية عرفناش اننا نطبطب اه عشان اللي
+
+488
+00:48:32,740 --> 00:48:41,260
+خاطر امسح وبدأ أبدأ اشتغل من فوق النظرية
+
+489
+00:48:41,260 --> 00:48:45,720
+احفظناها اه او خلينا نقول هي موجودة يعني اه بس
+
+490
+00:48:45,720 --> 00:48:49,160
+بدنا نطلع عالميا على البرهان الـ proof
+
+491
+00:48:56,060 --> 00:49:04,920
+بدنا نثبت احنا اللي هو g prime of 
+
+492
+00:49:04,920 --> 00:49:14,460
+D بساوي واحد على F prime of C هاي اللي بدنا نثبته
+
+493
+00:49:14,460 --> 00:49:17,820
+او واحد على F prime .. الـ G prime هذا طالع من
+
+494
+00:49:17,820 --> 00:49:22,140
+اليمين الـ G عبارة عن F inverse ماشي؟ شوفي الآن
+
+495
+00:49:25,040 --> 00:49:33,140
+بدي أعرف ده اللي برضه مساعدة لان خد Y لا تساوي D و
+
+496
+00:49:33,140 --> 00:49:39,760
+Y طبعا وين موجودة؟ Y element in J في domain من الـ
+
+497
+00:49:39,760 --> 00:49:43,640
+F inverse متذكرين؟
+
+498
+00:49:43,640 --> 00:49:52,360
+الـ F من I لعند R و الـ G اللي هي الـ F inverse من F
+
+499
+00:49:52,360 --> 00:49:59,500
+of I اللي سمناها J لعند مين؟ لعند الـ I مظبوط؟ طيب
+
+500
+00:49:59,500 --> 00:50:10,320
+الآن هعرف الـ H of Y H of Y بتساوي اللي هو F F
+
+501
+00:50:10,320 --> 00:50:20,250
+inverse of Y اللي هي F of G of Y ماقص F of G of
+
+502
+00:50:20,250 --> 00:50:25,430
+مين؟ of D نحطها على جنب ايش اللي بنعني فيه F of C
+
+503
+00:50:25,430 --> 00:50:33,110
+بتساوي D أو G of D اللي هي F inverse استذكروا أن 
+
+504
+00:50:33,110 --> 00:50:36,390
+أنا الـ G هي مين هي F inverse عشان تسهل عليكم
+
+505
+00:50:36,390 --> 00:50:41,630
+عملية الحسابات إيش بتساوي؟ C ماشي الآن F of G of Y
+
+506
+00:50:41,630 --> 00:50:48,750
+ناقص F of G of D على G of Y ناقص G of D
+
+507
+00:50:51,950 --> 00:50:56,890
+معايا؟ واضح اه؟ الآن أنا مفترض أن الـ Y لا تساوي D
+
+508
+00:50:56,890 --> 00:51:01,290
+طبعا الـ functions سبعنا سواء الـ F أو الـ G تمتين
+
+509
+00:51:01,290 --> 00:51:05,870
+one to one مأكيد الـ G of Y إيش مالها لا تساوي G of 
+
+510
+00:51:05,870 --> 00:51:09,990
+D إذا إن أنا مرتاح أنا ماخد Y لا تساوي Z إذا إن
+
+511
+00:51:09,990 --> 00:51:13,450
+automatic هذه is well defined يعني G of Y إيش
+
+512
+00:51:13,450 --> 00:51:19,270
+مالها لا تساوي مين؟ G of D واضح اه؟ أي سؤال؟
+
+513
+00:51:22,880 --> 00:51:28,700
+الآن الـ H of Y اللي هي بتساوي اللي هو F of G of Y
+
+514
+00:51:28,700 --> 00:51:33,120
+ناقص F وكذا على G of Y minus G of D is اللي هي well
+
+515
+00:51:33,120 --> 00:51:38,640
+defined طبعا الآن اللي فوق بناء على ما كتبناه
+
+516
+00:51:38,640 --> 00:51:45,220
+المستعملينه هنا كرموز هذه نفسها ممكن نطلع إليها
+
+517
+00:51:45,220 --> 00:51:50,520
+كصيغة أخرى أفما هي inverse تبعدها دول فبصير عبارة
+
+518
+00:51:50,520 --> 00:51:57,980
+عن Y ناقص D صح ولا لأ على G of Y ناقص مين G of D
+
+519
+00:51:57,980 --> 00:52:04,840
+هذا نظرة أخرى لمين للـ H of Y اللي عندنا أي سؤال؟
+
+520
+00:52:04,840 --> 00:52:10,740
+طبعا الـH of Y واضح أنها مش صفر لأن الـY أشمالها
+
+521
+00:52:10,740 --> 00:52:15,500
+لاتساوي D لأن بعد شوية بدي أجسم عليها عشان هيك بدي
+
+522
+00:52:15,500 --> 00:52:22,000
+أكتد لكم أن الـY الـH of Y أشمالها لاتساوي صفر
+
+523
+00:52:22,000 --> 00:52:31,170
+واضح لحد الآن، ماشي الحال، الآن بدي أستخدم اللي هو
+
+524
+00:52:31,170 --> 00:52:35,090
+التعريف في الوصول الـ Epsilon Delta Definition في
+
+525
+00:52:35,090 --> 00:52:42,570
+الوصول للي بديه اللي هو G prime of D بيساوي limit G
+
+526
+00:52:42,570 --> 00:52:48,770
+of Y نقص G of D على Y minus D الـY بتروح للـD اللي
+
+527
+00:52:48,770 --> 00:52:51,490
+هو exist .. that .. that .. that .. that مثلك أنه
+
+528
+00:52:51,490 --> 00:52:54,470
+لكل يكبر من صفر يوجد Delta أو Gamma أو اللي هي
+
+529
+00:52:54,470 --> 00:52:58,490
+such that لما تكون مسافة بين Y و D أصغر من Delta
+
+530
+00:52:58,490 --> 00:53:01,900
+يعطينا هدف أصغر من مين؟ من إبسلون هذا كيف بده
+
+531
+00:53:01,900 --> 00:53:07,060
+يثبته؟ بالاستعانة به اللي هو أنا بعرف أن الـ F is
+
+532
+00:53:07,060 --> 00:53:10,320
+differentiable و بالاستعانة بتدلة اللي عندي هذه
+
+533
+00:53:10,320 --> 00:53:14,080
+السؤال أي سؤال حتى الآن حتى الآن احنا اللي أثبتنا
+
+534
+00:53:14,080 --> 00:53:17,540
+أن H و Y اللي ركّبناها دي إيش مالها لا تساوي صفر
+
+535
+00:53:17,540 --> 00:53:27,380
+الآن عندي since F is differentiable at مين معطيني؟
+
+536
+00:53:27,380 --> 00:53:34,100
+at C إذن then for every epsilon أكبر من صفر بتستخدم
+
+537
+00:53:34,100 --> 00:53:38,920
+على طول اللي هو limit واضح then for every epsilon
+
+538
+00:53:38,920 --> 00:53:42,660
+أكبر من صفر there exist نستخدم نفس التعبير دلتا
+
+539
+00:53:42,660 --> 00:53:47,840
+أكبر من صفر أو نفس الرموز such that X minus C أكبر
+
+540
+00:53:47,840 --> 00:53:54,020
+من صفر وأصغر من دلتا implies F of X ناقص F of C
+
+541
+00:53:54,020 --> 00:53:59,240
+على X minus C ناقص اللي هو الـ derivative اللي هي F
+
+542
+00:53:59,240 --> 00:54:06,500
+prime of C صح؟ أصغر من مين؟ من إبسلون وسمي هذه إيش
+
+543
+00:54:06,500 --> 00:54:17,000
+مسميها هو؟ همسميها 1 هذا سمي 1 واضح
+
+544
+00:54:17,000 --> 00:54:21,360
+اه؟ في معنى وكده الآن f is differentiable in c
+
+545
+00:54:21,360 --> 00:54:25,580
+than لكل y نقل المستقبل اللي يعني استخدمنا limit f
+
+546
+00:54:25,580 --> 00:54:30,470
+of x نقص f of c على x minus c سوى f prime of c طبعا
+
+547
+00:54:30,470 --> 00:54:34,630
+أنا بعيد على أساس اللي بتابعنا مش سواعب أنكم مش 
+
+548
+00:54:34,630 --> 00:54:42,350
+سواعبته واضح؟ ماشي الحاجة الآن بدنا نستخدم الـ
+
+549
+00:54:42,350 --> 00:54:47,410
+continuity لمين؟ لـ G G is continuous طبعا G is
+
+550
+00:54:47,410 --> 00:54:51,870
+differentiable أصلا G is differentiable عند مين؟
+
+551
+00:54:51,870 --> 00:54:56,690
+عند اللي هو D يعني G is differentiable عند F of C
+
+552
+00:54:56,690 --> 00:55:03,740
+إذا continuous مظبوط؟ إذا الآن since .. since G is
+
+553
+00:55:03,740 --> 00:55:12,540
+continuous at D بتساوي F of C إذا يعني صار عندي 
+
+554
+00:55:12,540 --> 00:55:24,060
+limit G of Y لما Y تروح لـ D بساوي مين؟ G of D اه
+
+555
+00:55:25,340 --> 00:55:29,760
+واضح ها؟ واضح .. واضح ها؟ خلّيني نعمل .. على أساس
+
+556
+00:55:29,760 --> 00:55:32,980
+ما نستخدم الرموز هذه نربطها باللي بقى بالها ..
+
+557
+00:55:32,980 --> 00:55:37,900
+بنغير بعدين معايا؟ طيب .. هذه إيش معناتها by
+
+558
+00:55:37,900 --> 00:55:41,460
+epsilon delta definition؟ أنه لكل .. الآن بدي
+
+559
+00:55:41,460 --> 00:55:45,780
+أستخدم الـ delta هذه لإن بدي أستخدم الاتنين مع بعض
+
+560
+00:55:45,780 --> 00:55:49,800
+الوصول للي بديها واضح؟ هذه لكل إبسلون في الدنيا،
+
+561
+00:55:49,800 --> 00:55:53,140
+أي إن كانت من ضمن إنترفالز الـDelta اللي لاجيناها،
+
+562
+00:55:53,140 --> 00:55:57,300
+واضح اللي بحكيه؟ الآن لكل إبسلون أكبر من 0، there 
+
+563
+00:55:57,300 --> 00:56:01,160
+exists Gamma اللي هي .. ابحثت إنه لما يكون Y minus
+
+564
+00:56:01,160 --> 00:56:05,100
+D أصغر من Gamma، يعطيني هذا أصغر، اللي هو من اللي
+
+565
+00:56:05,100 --> 00:56:08,180
+بديه .. من اللي بدي أن أناسك دموع، اللي هو
+
+566
+00:56:08,180 --> 00:56:16,030
+الـDelta، الآن continuous  كده then for every
+
+567
+00:56:16,030 --> 00:56:18,930
+إبسلون الابسلون اللي بده استخدمها اللي من ضمن
+
+568
+00:56:18,930 --> 00:56:21,290
+الإبسلون هي اللي بتنفع ايه اللي بتنفع على ال delta
+
+569
+00:56:21,290 --> 00:56:25,970
+هذه then for delta أكبر من صفر there exist gamma
+
+570
+00:56:25,970 --> 00:56:32,670
+أكبر من صفر such that لما y minus d يكون أكبر من 
+
+571
+00:56:32,670 --> 00:56:37,170
+صفر وأصغر من الجامعة اللي لجيتها هذا بيعطيني اللي 
+
+572
+00:56:37,170 --> 00:56:46,080
+هو ال Gof Y نقص الـ G of D يكون أصغر من مين من الـ
+
+573
+00:56:46,080 --> 00:56:51,820
+Epsilon اللي هي سميتها H Delta أي سؤال هذا بده
+
+574
+00:56:51,820 --> 00:57:01,100
+سميه H اسمه بده سميه اتنين اه هساخد من ال N طيب
+
+575
+00:57:01,100 --> 00:57:07,080
+شوفوا
+
+576
+00:57:07,080 --> 00:57:17,060
+الآن أنا في الآخر بدي اللي هو أصل لإنه اللي هي ال
+
+577
+00:57:17,060 --> 00:57:21,680
+derivative لل F prime اللي هو واحد ال F inverse
+
+578
+00:57:21,680 --> 00:57:29,840
+prime واحد على ال F prime ماشي طيب لما
+
+579
+00:57:29,840 --> 00:57:37,150
+تسيري الآن ال Y طبعا ال y .. ال .. ال .. ال .. ال
+
+580
+00:57:37,150 --> 00:57:37,190
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+581
+00:57:37,190 --> 00:57:37,210
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+582
+00:57:37,210 --> 00:57:37,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+583
+00:57:37,750 --> 00:57:37,770
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+584
+00:57:37,770 --> 00:57:38,230
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+585
+00:57:38,230 --> 00:57:46,550
+.. ال ..
+
+586
+00:57:46,550 --> 00:57:47,090
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+587
+00:57:47,090 --> 00:57:47,550
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+588
+00:57:47,550 --> 00:57:48,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+589
+00:57:48,510 --> 00:57:48,870
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+590
+00:57:48,870 --> 00:57:49,850
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+591
+00:57:49,850 --> 00:57:57,250
+ال ..
+
+592
+00:57:57,250 --> 00:57:58,030
+ال
+
+593
+00:58:03,070 --> 00:58:09,070
+إذا حيطلع عند الـ GY نقص GY دي إيش معلها؟ أقل من
+
+594
+00:58:09,070 --> 00:58:14,570
+مين؟ من دلتا اللي هي by using اتنين G of Y إيش
+
+595
+00:58:14,570 --> 00:58:19,730
+اسمها؟ اللي هي G of Y اللي هي Y إيش بتسوى F of X
+
+596
+00:58:19,730 --> 00:58:25,580
+عن G of Y بتسوى Xأه اللي هي عبارة عن X minus G of
+
+597
+00:58:25,580 --> 00:58:31,900
+D الـ D اللي هي عبارة عن مين؟ اللي هي F of C و الـ
+
+598
+00:58:31,900 --> 00:58:35,820
+G inverse للـ F إذا هتطلع عبارة عن مين؟ عن C أصغر
+
+599
+00:58:35,820 --> 00:58:45,140
+من مين؟ من دلتا واضح طبيعي وأكبر أكيد أكيد أكيد
+
+600
+00:58:45,140 --> 00:58:52,230
+أكيد واضح لحد الآن الان هذا بده يخليني أستخدم مين
+
+601
+00:58:52,230 --> 00:58:59,750
+أستخدم واحد إذا صار عندي then هذا متحقق الان then
+
+602
+00:58:59,750 --> 00:59:04,830
+بدي أربط هذا الكلام بمين باللي فوق اللي هو H of Y
+
+603
+00:59:04,830 --> 00:59:12,450
+H of Y ناقص F prime of C شوف كيف بده F مثلك الان
+
+604
+00:59:12,450 --> 00:59:19,780
+اللي هو بساوي H of Y مين؟ H of Y اللي هو عبارة عن Y
+
+605
+00:59:19,780 --> 00:59:27,960
+ناقص D على G of Y ناقص G of D، مظبوط؟ اللي هو بيه
+
+606
+00:59:27,960 --> 00:59:30,960
+عبارة عن مين؟ F of G of Y ناقص كده، إلى آخرين
+
+607
+00:59:30,960 --> 00:59:42,000
+بيصير بساوي اللي هو F of G of Y ناقص F of G of D
+
+608
+00:59:42,000 --> 00:59:52,730
+على Y على g of y ناقص g of d اللي هو ناقص f prime
+
+609
+00:59:52,730 --> 01:00:00,150
+of c أصغر من مين؟ من y عارفين ليش؟ لأن الـ g of y
+
+610
+01:00:00,150 --> 01:00:04,880
+مين هي؟ الـ x و الـ G of D اللي هي مين الـ C
+
+611
+01:00:04,880 --> 01:00:10,480
+فاهمين؟ أنا قصد أكتبها بالصورة هذه عشان أقولكم أيش
+
+612
+01:00:10,480 --> 01:00:14,580
+لو سُلتله H of I ناقص أفرو برايم of C بساوي هذا
+
+613
+01:00:14,580 --> 01:00:21,500
+المقدار ناقص هذا متحقق كمان مرة يا جماعة اللي
+
+614
+01:00:21,500 --> 01:00:26,220
+بيحقق هذا غصب عنه بيحقق هذا و اللي بيحقق هذا بيحقق
+
+615
+01:00:26,220 --> 01:00:31,240
+هذا ماشي الحال أنا الأن أخدت عندي Y element in J
+
+616
+01:00:31,920 --> 01:00:36,960
+والـ Y لا تساوي D واخدت هذا يكون أصغر من دولتا تحت
+
+617
+01:00:36,960 --> 01:00:41,320
+هذا الشرط الآن أنا بشتغل تحت هذا الشرط الآن هذا
+
+618
+01:00:41,320 --> 01:00:46,140
+أدالي حسب اللي هي اتنين ان هذا ناقص هذا أصغر من
+
+619
+01:00:46,140 --> 01:00:51,090
+دولتا هذا اللي هو X وهذا اللي هو mean الـC الآن
+
+620
+01:00:51,090 --> 01:00:54,790
+مادام أصغر من دلتا إذا أعطاني واحد إذا أعطاتني هذه
+
+621
+01:00:54,790 --> 01:00:59,510
+أصغر من هذه هذه في الواقع مين هي F of X هي عبارة
+
+622
+01:00:59,510 --> 01:01:03,830
+عن F of G of Y لأن G of Y هي ال X و C ليه F of D
+
+623
+01:01:03,830 --> 01:01:08,690
+صار هذا ناقص هذا أصغر من مين من إبسلون من جهة أخرى
+
+624
+01:01:08,690 --> 01:01:13,650
+هذا المقدار مين هو عبارة عن H of Y وهذا اللي هي F
+
+625
+01:01:13,650 --> 01:01:18,550
+prime of C إذا القالة اللي وصلت إليه أنه لكل إبسلون
+
+626
+01:01:18,550 --> 01:01:22,670
+أكبر من 0 وجدت Gamma لأن Gamma بين إيديا واجدتها
+
+627
+01:01:22,670 --> 01:01:27,050
+من الأصل إلى لكل إبسلون أكبر من 0 لجيت Gamma ابحث
+
+628
+01:01:27,050 --> 01:01:30,290
+أنه لما يكون هذه المسافة بينها أصغر من Gamma
+
+629
+01:01:30,290 --> 01:01:33,610
+يعطينا المسافة أصغر من إبسلون يعني المسافة هذه
+
+630
+01:01:33,610 --> 01:01:40,760
+أصغر من إبسلون أو بمعنى آخر limitH of Y لما الـ Y
+
+631
+01:01:40,760 --> 01:01:50,320
+تروح للـ D بساوة F prime of مين؟ of C تصيرنا 
+
+632
+01:01:50,320 --> 01:01:55,660
+جريبين من اللي بدنايا عند الـ H of Y limitها بساوة
+
+633
+01:01:55,660 --> 01:02:02,980
+limit هذا بساوة F prime of C هذا عبارة عن مين؟ عن
+
+634
+01:02:02,980 --> 01:02:10,910
+G prime مقلوق G prime إذا الآن خلصنا تقريبا نمسح
+
+635
+01:02:10,910 --> 01:02:16,130
+حده و نمسك
+
+636
+01:02:16,130 --> 01:02:28,150
+بهدي مع هدي صار عندي limit h of y لما ال y تقول
+
+637
+01:02:28,150 --> 01:02:34,960
+الى d limitH of Y لما Y تقول إلى D طلع عندي عبارة
+
+638
+01:02:34,960 --> 01:02:40,960
+عن F prime of C هي تحت من جهة أخرى هذا بيساوي مين؟
+
+639
+01:02:40,960 --> 01:02:48,720
+limit Y نقص D على G of Y نقص G of D لما Y تروح
+
+640
+01:02:48,720 --> 01:02:55,980
+لمين؟ للـ D صح؟ هذا عبارة عن limit أو واحد على
+
+641
+01:02:55,980 --> 01:03:03,130
+limitG of Y نقص G of D على Y minus D لما Y تروح لـ
+
+642
+01:03:03,130 --> 01:03:10,310
+D 1 على الـ limit هذا فهي
+
+643
+01:03:10,310 --> 01:03:16,390
+ساوية 1 على g prime of D إذا صارت عندي F prime of
+
+644
+01:03:16,390 --> 01:03:23,710
+C بساوية 1 على g prime of D أو بمعنى آخر F prime
+
+645
+01:03:23,710 --> 01:03:31,800
+of C بساوية 1 على F G prime اللي هي Finverse prime
+
+646
+01:03:31,800 --> 01:03:42,000
+of D أو بتعبير آخر F inverse prime of D بساوية
+
+647
+01:03:42,000 --> 01:03:55,700
+واحد على F of C وهو المطلوب طيب
+
+648
+01:04:01,020 --> 01:04:02,360
+خدّيني أجف عن نقطة
+
+649
+01:04:19,990 --> 01:04:25,110
+هي نفس اللي فوق بس كانت اللي فوق عنده نقطة هنا in
+
+650
+01:04:25,110 --> 01:04:29,510
+general الان لو كانت على كل ال domain يعني الان
+
+651
+01:04:29,510 --> 01:04:33,150
+بقولي لو كانت I subset من R بيه an interval and F
+
+652
+01:04:33,150 --> 01:04:37,510
+من I لعند R strictly monotone on I ماشي ..
+
+653
+01:04:37,510 --> 01:04:42,750
+strictly monotone و let J بيسوء F of I and let G
+
+654
+01:04:42,750 --> 01:04:47,410
+من I لعند R بيه the function inverse of F ماشي ..
+
+655
+01:04:47,980 --> 01:04:52,360
+لأن إذا كانت F as differential على الـ I كلها إذا
+
+656
+01:04:52,360 --> 01:04:55,860
+أكيد هتكون continuous على الـ I كلها مدام هتكون
+
+657
+01:04:55,860 --> 01:04:58,300
+continuous على الـ I كلها و strictly monotone
+
+658
+01:04:58,300 --> 01:05:02,180
+هتكون الـ G العجبالها برضه strictly monotone و
+
+659
+01:05:02,180 --> 01:05:06,870
+continuous إذا شروط اللي فوق اتحققت إذا الـ J ..
+
+660
+01:05:06,870 --> 01:05:10,030
+طبعا ال F' of X معطينيها إشمالها تسوى X على كل ال
+
+661
+01:05:10,030 --> 01:05:13,350
+I إذا أكيد حسب النظر اللي قبل شوية G is
+
+662
+01:05:13,350 --> 01:05:17,230
+differentiable على كل ال J و ال G' بساوية واحدة
+
+663
+01:05:17,230 --> 01:05:22,210
+على F' لإنه composite مين؟ composite G واضح؟ يعني
+
+664
+01:05:22,210 --> 01:05:28,130
+.. كمان مرة؟ إذا كانت ال F strictly monotone و
+
+665
+01:05:28,130 --> 01:05:32,890
+كانت اللي هي ال J بتساوي كل ال F of I وكانت الـ G
+
+666
+01:05:32,890 --> 01:05:37,310
+هي عبارة عن ال inverse للـ F وكانت ال F
+
+667
+01:05:37,310 --> 01:05:39,570
+differentiable على ال I مدام F differentiable على
+
+668
+01:05:39,570 --> 01:05:42,210
+ال I إذا صارت continuous على كل ال I مدام
+
+669
+01:05:42,210 --> 01:05:44,710
+continuous على ال I و strictly monotone هتكون ال
+
+670
+01:05:44,710 --> 01:05:47,710
+inverse سبعتها اللي هي ال G برضه continuous و
+
+671
+01:05:47,710 --> 01:05:51,700
+strictly monotone إذا انتحققت شروط النظرية السابقة
+
+672
+01:05:51,700 --> 01:05:55,680
+إذا هتكون ال F و طبعا ال F' طبعا لها تساوي صفر ع
+
+673
+01:05:55,680 --> 01:05:59,020
+كل ال I إذا صارت ال G ال differential بالع كل ال J
+
+674
+01:05:59,020 --> 01:06:02,220
+و العلاقة بين التنتين G' بسوء واحد على F'
+
+675
+01:06:02,680 --> 01:06:09,040
+composite مين؟ composite J أو زي ما بنقول G' of Y
+
+676
+01:06:09,040 --> 01:06:16,220
+بسوء واحد على F' of مين؟ of X تحت العلاقة X بتساوي
+
+677
+01:06:16,220 --> 01:06:25,320
+F of Y أو Y بس هوقف و فكس Y بس هوقف و فكس طبعا هذا
+
+678
+01:06:25,320 --> 01:06:32,220
+البرهان كله حكيناه ال remark اللي عندنا ال remark
+
+679
+01:06:32,220 --> 01:06:37,100
+اللي عندنا ال
+
+680
+01:06:37,100 --> 01:06:43,460
+remark
+
+681
+01:06:43,460 --> 01:06:51,180
+اللي عندنا هي اللي حكيتها الآن D'Y بسوء واحد عالميا
+
+682
+01:06:51,180 --> 01:06:53,660
+على F'X
+
+683
+01:06:57,210 --> 01:06:59,530
+التي قبل بشوية حكيناها جي برايم أو اي بيسوا واحد
+
+684
+01:06:59,530 --> 01:07:03,890
+على اف برايم كومبز الجي ماشي الحال الآن صارت عندي
+
+685
+01:07:03,890 --> 01:07:08,950
+هذه جي برايم كومبز كومبز اف of X بيسوا جي برايم اف
+
+686
+01:07:08,950 --> 01:07:12,290
+of X بيسوا واحد على اف برايم كومبز الجي أو اي
+
+687
+01:07:12,290 --> 01:07:15,470
+بياخد نظرية مرتين و يسوا واحد على اف برايم of X
+
+688
+01:07:15,470 --> 01:07:18,370
+التانيين مع بعض جي برايم بيسوا واحد على اف برايم
+
+689
+01:07:18,370 --> 01:07:24,310
+of X و المرة الجاهزة اللي بنكمل بنعيد هذا اللي إذا
+
+690
+01:07:24,310 --> 01:07:26,470
+كان حكيناها على السريع 
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eeec959b448e0cbdb4c0ecd0be08782f1047f6e5
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/gz91ZmeweRY_postprocess.srt
@@ -0,0 +1,1820 @@
+1
+00:00:05,030 --> 00:00:07,750
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,750 --> 00:00:10,710
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:10,710 --> 00:00:16,270
+أجمعين هذه هي المحاضرة رقم 26 مساق تحليل حقيقه 2
+
+4
+00:00:16,270 --> 00:00:20,290
+طلاب طالبات الجامعة الإسلامية قسم رياضيات كلية
+
+5
+00:00:20,290 --> 00:00:24,650
+العلوم اليوم هنكمل حديثنا في شطر 9 ولكن في section
+
+6
+00:00:24,650 --> 00:00:29,050
+جديد ال section هنبدأ فيه اللي هو tests for
+
+7
+00:00:29,050 --> 00:00:36,950
+absolute convergenceاختبارات الـ Series التي تحتوي
+
+8
+00:00:36,950 --> 00:00:40,490
+على الـ Positive Terms أو اللي هو بمفهوم الـ
+
+9
+00:00:40,490 --> 00:00:46,010
+Absolute Convergence نأتي الآن للأولاني المشهور
+
+10
+00:00:46,010 --> 00:00:51,130
+921بنسميه ال comparison test او اللي هو اختبار
+
+11
+00:00:51,130 --> 00:00:55,490
+المقارن ال let x يعني اللي بيكون عندنا فيه C ال
+
+12
+00:00:55,490 --> 00:00:58,910
+series و بنقارنها ب series أخرى بنعبجها عارفين
+
+13
+00:00:58,910 --> 00:01:02,930
+اللي هو converged ولا diverse وبناء عليه بنحكم على
+
+14
+00:01:02,930 --> 00:01:07,250
+ال series اللي بيبقى انقارنها اللي هي انها
+
+15
+00:01:07,250 --> 00:01:11,900
+converged او diverseLed X بيساوي XN وY بيساوي YN
+
+16
+00:01:11,900 --> 00:01:17,420
+بـReal Sequences Suppose that for some natural
+
+17
+00:01:17,420 --> 00:01:22,340
+numbers K اللي هو XN أكبر أو أصغر أو يساوي YN يعني
+
+18
+00:01:22,340 --> 00:01:26,400
+بمعنى آخر أننا بنحكي عن Sequence of Positive Terms
+
+19
+00:01:26,400 --> 00:01:32,160
+ماشي إذا هذه اللي هي عبارة عن Testلـ Series مكوّنة
+
+20
+00:01:32,160 --> 00:01:36,420
+الـ Terms تبعتها من Positive Terms for N أكبر و
+
+21
+00:01:36,420 --> 00:01:40,320
+ساوة و K then the convergence of summation yn
+
+22
+00:01:40,320 --> 00:01:44,320
+implies the convergence of xn and the divergence
+
+23
+00:01:44,320 --> 00:01:48,440
+of xn implies the divergence of summation yn اللي
+
+24
+00:01:48,440 --> 00:01:53,680
+أنا بقول ليه ال test بيقول بيحكيلي معايا ليه ان لو
+
+25
+00:01:53,680 --> 00:01:56,820
+كان في عندي two sequences xn و yn هم اللي بيكون
+
+26
+00:01:56,820 --> 00:02:01,920
+جسم اللي هو ال seriesباجي إذا كان عندي Xn أصغر
+
+27
+00:02:01,920 --> 00:02:05,700
+سواء و Yn لكل انه طبعا و اتنتين positive باجي بقول
+
+28
+00:02:05,700 --> 00:02:10,800
+إذا كان اللي هي الكبيرة اللي هي converts ال Yn
+
+29
+00:02:10,800 --> 00:02:14,280
+أكيد من باب أولى الصغيرة أشمالها converts يعني ال
+
+30
+00:02:14,280 --> 00:02:18,520
+convergence لل Yn بيعطي ال convergence لمن؟ لل Xn
+
+31
+00:02:19,050 --> 00:02:23,830
+إذا كانت الصغيرة diverges من باب أولاد كل كبيرة
+
+32
+00:02:23,830 --> 00:02:27,750
+إيش ما لها، diverges خلّينا نبرهن الآن Suppose
+
+33
+00:02:27,750 --> 00:02:33,730
+that yn is convergent، ماشي الحال؟suppose that
+
+34
+00:02:33,730 --> 00:02:37,090
+summation yn converges نفترض لكبير أنها converges
+
+35
+00:02:37,090 --> 00:02:41,050
+then for every ي أكبر من صفر there exists m of
+
+36
+00:02:41,050 --> 00:02:45,850
+epsilon element in n such that for every m أكبر من
+
+37
+00:02:45,850 --> 00:02:50,330
+n و أكبر من م يبسلون اللي هو ال الكوشي criterion
+
+38
+00:02:50,330 --> 00:02:55,530
+اللي هو y واحد زي ym ناقص y واحد زي yn أصغر من مين
+
+39
+00:02:55,530 --> 00:03:02,870
+من إبسلون ماشي الحال الان هذا الكلاماللي هو عندي
+
+40
+00:03:02,870 --> 00:03:06,710
+صحيح لكل N أكبر وسوء ASK يعني مش من بداية ال
+
+41
+00:03:06,710 --> 00:03:10,970
+sequence مش كتير مهم أنا عند بداية ال sequence ان
+
+42
+00:03:10,970 --> 00:03:12,950
+اللي بحكم على ال convergence و ال divergence اللي
+
+43
+00:03:12,950 --> 00:03:17,330
+هو mean اللي هو ال terms من عند حد إلى ما لنهاية
+
+44
+00:03:17,330 --> 00:03:20,630
+اللي هو اللي هيأثر على المجموع انه اللي هو موجود
+
+45
+00:03:20,630 --> 00:03:26,630
+او مش موجود طيب الآن هذه اللي هي صحيحة لكل N و M
+
+46
+00:03:26,630 --> 00:03:32,180
+أكبر من M اللي لجناهاوعندي هذه صحيحة لكل mean N
+
+47
+00:03:32,180 --> 00:03:37,840
+أكبر وساوة K عشان أستخدم واحد و أستخدم star لازم
+
+48
+00:03:37,840 --> 00:03:42,520
+أختار أقول from one and star we have for every
+
+49
+00:03:42,520 --> 00:03:46,480
+epsilon there exists N عشان أستخدم واحد و star بدي
+
+50
+00:03:46,480 --> 00:03:50,500
+أخد N هي ال maximum بين ال K و بين ال M of epsilon
+
+51
+00:03:50,500 --> 00:03:54,720
+such thatلما تكون ال M أكبر من N و أكبر من ال K
+
+52
+00:03:54,720 --> 00:03:58,140
+الماكسيموم معناته أكبر من K و أكبر من هذه معناته
+
+53
+00:03:58,140 --> 00:04:02,880
+هذه صحيحة و هذه صحيحة يعني بحج اللي الناس تخدمها
+
+54
+00:04:02,880 --> 00:04:09,920
+we have X1 زيد X2 زيد XM اللي هي ال partial sum ل
+
+55
+00:04:09,920 --> 00:04:17,290
+X و هذه ناقص اللي هي X1 لعند XNأترحى من بعض اللي
+
+56
+00:04:17,290 --> 00:04:21,670
+هو حيساوى الـ XM زائد واحد لعند الـ XM الـ XN زائد
+
+57
+00:04:21,670 --> 00:04:25,650
+واحد أكيد اللي هو أصغر أشهر من YN زائد واحد الـ XN
+
+58
+00:04:25,650 --> 00:04:28,150
+زائد اتنين أصغر من YN زائد اتنين لما أصل الـ XM
+
+59
+00:04:28,150 --> 00:04:33,770
+أصغر أشهر من الـ YMالان هذه عبارة عن مين؟ عن هذه
+
+60
+00:04:33,770 --> 00:04:38,470
+ناقص هذه اللي هي Y1 زي Ym ناقص Y1 زي Yn اللي هي
+
+61
+00:04:38,470 --> 00:04:42,610
+أصغر من وين من Y لإنه converges اللي هي ال Yn بناء
+
+62
+00:04:42,610 --> 00:04:49,190
+عليه اللي هو أثبتنا إن ال SM ناقص ال SN بالنسبة لل
+
+63
+00:04:49,190 --> 00:04:53,570
+X اللي هي satisfies كوشي كراي كتير إن أنا أصغر من
+
+64
+00:04:53,570 --> 00:04:58,510
+Y معناه تصميش لل XN إيش ما لها convergesالعنوان
+
+65
+00:04:58,510 --> 00:05:03,110
+الثاني هو Contrapositive للعنوان الأول لماذا؟ لأن
+
+66
+00:05:03,110 --> 00:05:09,870
+لو كانت الـ summation Xn مختلفة وليس مرتبطة، فأكيد
+
+67
+00:05:09,870 --> 00:05:14,390
+ستعطي الـ summation Yn أشمالها التي ليست مرتبطة
+
+68
+00:05:14,650 --> 00:05:19,810
+يعني diverse يعني الجزء الثاني هذا ما هو إلا عبارة
+
+69
+00:05:19,810 --> 00:05:23,650
+عن اللي هو الجزء الأول بس شماله موفود بال
+
+70
+00:05:23,650 --> 00:05:27,890
+contraposition يعني B implies Q يعني not Q implies
+
+71
+00:05:27,890 --> 00:05:32,730
+not B طيبالان نيجي هذا اللي هو الـ Comparison Test
+
+72
+00:05:32,730 --> 00:05:38,070
+اللي هو المقارنة المباشرة بين ال terms تبعات مين
+
+73
+00:05:38,070 --> 00:05:41,890
+تبعات اللي هو الـ sequences أحياناً عملياً هذه مش
+
+74
+00:05:41,890 --> 00:05:46,830
+كتير الناس بترغبها في test تاني comparison test
+
+75
+00:05:46,830 --> 00:05:50,530
+لكن هذا ال test اللي هو بنسميه limit comparison
+
+76
+00:05:50,530 --> 00:05:53,910
+test وهذا أسهل في الاستخدام وأوسع في الاستخدام
+
+77
+00:05:53,910 --> 00:05:59,310
+والناس بتنيل عادة لاستخدامهاماشي الحال الانصاب
+
+78
+00:05:59,310 --> 00:06:02,450
+both that X بالساوية XN وY بالساوية YN are
+
+79
+00:06:02,450 --> 00:06:07,570
+positive serial sequences if the relation limit XN
+
+80
+00:06:07,570 --> 00:06:12,730
+على YN لان limit XN على YN لا يساوي سفر يعني عبارة
+
+81
+00:06:12,730 --> 00:06:17,400
+عن عدد هذايعني عبارة عن عدد يعني سير ال XN و سير
+
+82
+00:06:17,400 --> 00:06:23,260
+ال YN جريب من بعض لما نقول بطلع عدد limit XN على
+
+83
+00:06:23,260 --> 00:06:29,000
+YN يعني سيرهم جريب من بعض لدرجة أنه في الآخر بطلع
+
+84
+00:06:29,000 --> 00:06:32,280
+عدد يعني لا هو طلع مالة نهاية نقول اللي فوق أسرع
+
+85
+00:06:32,280 --> 00:06:37,180
+كتير ولا طلع سفر نقول اللي تحت أسرع كتير لأ اللي
+
+86
+00:06:37,180 --> 00:06:42,770
+هو limit XN على YN طلعلي عدد عشان هيكلما هذا يحدث
+
+87
+00:06:42,770 --> 00:06:45,970
+if the relation limit xn على yn لا يساوي سفر hold
+
+88
+00:06:45,970 --> 00:06:51,570
+then ال summation xn is convergent if and only if
+
+89
+00:06:51,570 --> 00:06:56,650
+ال summation ال yn أشمال is convergent لأن سيرهما
+
+90
+00:06:56,650 --> 00:07:01,770
+متقارب عشان هيك بنقول يا التنتين converges يا
+
+91
+00:07:01,770 --> 00:07:08,570
+التنتين diverse لكن if the limit in two هنا is
+
+92
+00:07:08,570 --> 00:07:13,540
+zeroمعناته اللي تحت Star طير على المالة نهاية يعني
+
+93
+00:07:13,540 --> 00:07:18,400
+صار كله على إيش بساوي سفر فبكون الآن ال YN إذا
+
+94
+00:07:18,400 --> 00:07:22,840
+الكبير Convergent من باب أولى لصغير إيش ماله؟
+
+95
+00:07:22,840 --> 00:07:27,000
+Convergent لأنه هذا صار سفر معناته هذا أسرع من هذا
+
+96
+00:07:27,000 --> 00:07:32,340
+بكتير معناته لو كان اللي تحت Converged أكيد أكيد
+
+97
+00:07:32,340 --> 00:07:36,600
+أكيد أكيدهيكون اللي فوق اشمله convergence لأن اللي
+
+98
+00:07:36,600 --> 00:07:42,420
+فوق بيكون أبطأ أو أقل قيمة يعني نحو الكبر يعني
+
+99
+00:07:42,420 --> 00:07:46,040
+معناته انه اللي هو ال summation لل YN ال
+
+100
+00:07:46,040 --> 00:07:49,120
+convergence له على طول بيعطي اللي هو ال
+
+101
+00:07:49,120 --> 00:07:52,980
+convergence لل XN هذه حول اللي هو نص النظرية نيجي
+
+102
+00:07:52,980 --> 00:07:59,670
+الآنللبرهان نأتي لبرهان نثبت أنه نفترض ان ال
+
+103
+00:07:59,670 --> 00:08:02,810
+summation نثبت ان ال summation XN is convergent
+
+104
+00:08:02,810 --> 00:08:05,510
+فندهلي في ال summation YN اللي هو convergent الان
+
+105
+00:08:05,510 --> 00:08:09,790
+بدنا نأتي للبرهان قلنا عندي limit ال XN على ال YN
+
+106
+00:08:09,790 --> 00:08:13,430
+ايش بيساوي؟ بيساوي L لأ تساوي سفرإذاً حسب التعريف
+
+107
+00:08:13,430 --> 00:08:16,050
+الـ Epsilon Delta Definition أو الـ Epsilon K
+
+108
+00:08:16,050 --> 00:08:19,650
+Definition for Epsilon بساوة L على 2 أخدت لأي
+
+109
+00:08:19,650 --> 00:08:22,550
+Epsilon أخدت من ضمنها L على 2 للحسابات there
+
+110
+00:08:22,550 --> 00:08:27,210
+exists K such that اللي هو XN على YN ناقص L أصغر
+
+111
+00:08:27,210 --> 00:08:30,470
+من Epsilon اللي هي L على 2 لكل N أكبر أو يساوي K
+
+112
+00:08:30,470 --> 00:08:35,350
+خلّيني نفرضها هذه بيصير عند XN على YN أكبر من L
+
+113
+00:08:35,350 --> 00:08:40,280
+ناقص L على 2 وأصغر من L زائد من L على 2الان صار
+
+114
+00:08:40,280 --> 00:08:43,560
+عندى الان اللى هى ال .. ال .. ال .. ال .. ال .. ال
+
+115
+00:08:43,560 --> 00:08:44,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+116
+00:08:44,080 --> 00:08:44,380
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+117
+00:08:44,380 --> 00:08:44,700
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+118
+00:08:44,700 --> 00:08:45,400
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+119
+00:08:45,400 --> 00:08:45,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+120
+00:08:45,680 --> 00:08:45,940
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+121
+00:08:45,940 --> 00:08:46,620
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+122
+00:08:46,620 --> 00:08:47,900
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+123
+00:08:47,900 --> 00:08:48,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+124
+00:08:48,420 --> 00:08:50,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+125
+00:08:50,320 --> 00:08:59,540
+ال .. ال .. ال .. ال .. ال ..
+
+126
+00:08:59,540 --> 00:09:01,420
+ال .. ال ..
+
+127
+00:09:06,850 --> 00:09:11,550
+بال test اللي قبل بشوية إذا ال summation yn مش هذا
+
+128
+00:09:11,550 --> 00:09:16,790
+اللي هنستخدمه هنستخدم اللي هو xn أكبر من yn في L
+
+129
+00:09:16,790 --> 00:09:19,750
+على 2 إذا كانت هذي convergent هتكون هذي إيش مهلها
+
+130
+00:09:19,750 --> 00:09:24,410
+convergent وبما أن yn في L على 2 convergent هتطلع
+
+131
+00:09:24,410 --> 00:09:28,410
+عندي اللي هي ال summation yn إيش مهلها is
+
+132
+00:09:28,410 --> 00:09:34,660
+convergentماشي طيب الان conversely بدي افترض اللي
+
+133
+00:09:34,660 --> 00:09:39,480
+هو ال summation ل Yn ايش ماله is convergent ال
+
+134
+00:09:39,480 --> 00:09:41,920
+summation ل Yn is convergent مدام ال summation ل
+
+135
+00:09:41,920 --> 00:09:46,680
+Yn is convergent هيكون ال summation اللي هي
+
+136
+00:09:46,680 --> 00:09:50,500
+التلاتة في L على 2 في Yn is convergent لأن هذا
+
+137
+00:09:50,500 --> 00:09:54,000
+عبارة عن ثابتهذا لما انفرضنا الـ yn is summation
+
+138
+00:09:54,000 --> 00:09:57,320
+الـ yn convergent إذا هيكون ال summation الكبير
+
+139
+00:09:57,320 --> 00:10:00,940
+هذا convergent من باب أو لا ال summation للـ xn
+
+140
+00:10:00,940 --> 00:10:06,200
+إيش ماله is convergent يعني اتبعوا اللي حكيته هان
+
+141
+00:10:06,200 --> 00:10:14,030
+هذه اللي هي ال convergenceللـ Xn اللي هي الكبيرة
+
+142
+00:10:14,030 --> 00:10:17,850
+بيعطي ال convergence لهذه هو من ثم ال convergence
+
+143
+00:10:17,850 --> 00:10:22,710
+لهذه لأن في الجزء الثاني ال convergence لل Yn
+
+144
+00:10:22,710 --> 00:10:26,430
+بيعطي ال convergence لهذه ال convergence لهذه اللي
+
+145
+00:10:26,430 --> 00:10:31,930
+هو الكبير بيعطي ال convergence لمن؟ لل Xn طيب نيجي
+
+146
+00:10:31,930 --> 00:10:35,910
+الآن طبعا
+
+147
+00:10:35,910 --> 00:10:42,080
+ال .. ال .. ال .. المطلوب بي ..بدنا نفترض
+
+148
+00:10:44,730 --> 00:10:51,270
+suppose that limit xn على yn بساوة سفر ونفترض أن
+
+149
+00:10:51,270 --> 00:10:54,130
+الـ yn أشمالها is convergent بالذات بت الـ xn
+
+150
+00:10:54,130 --> 00:10:59,330
+أشمالها is convergent لأن شو معناه limit xn على yn
+
+151
+00:10:59,330 --> 00:11:03,230
+بساوة سفر لكل y أكبر من سفر؟ there exists k
+
+152
+00:11:03,230 --> 00:11:06,810
+element in n such that xn على yn أصغر من مين من
+
+153
+00:11:06,810 --> 00:11:10,810
+إبسلون لكل n أكبر وسوء k هذا اللي هو تعريف ال
+
+154
+00:11:10,810 --> 00:11:15,700
+limit لل xn على yn بساوة سفرومنه هذا دروب طرفين في
+
+155
+00:11:15,700 --> 00:11:20,680
+وسطين XN أصلا من YN في Y ن إحنا مفترضين أن ال YN
+
+156
+00:11:20,680 --> 00:11:24,240
+is convergent يعني ال Y في ال YN ثابتة ما هي ال Y
+
+157
+00:11:24,240 --> 00:11:27,620
+is convergent إذا كان الكبيرة convergent من باب
+
+158
+00:11:27,620 --> 00:11:32,680
+أولى الصماش لل XN إيش هتكون اللي هي is convergent
+
+159
+00:11:32,680 --> 00:11:39,020
+by اللي هو comparison test الأصليالان اذا خلصنا من
+
+160
+00:11:39,020 --> 00:11:42,300
+ال testين اللي هو ال comparison test وال limit
+
+161
+00:11:42,300 --> 00:11:45,880
+comparison test وكانت ال testين عبارة عن على
+
+162
+00:11:45,880 --> 00:11:50,520
+positive sequences الان بدنا نحكي عن حاجة اسمها
+
+163
+00:11:50,520 --> 00:11:53,700
+the root and the ratio test نشوف ال root و ال
+
+164
+00:11:53,700 --> 00:11:57,260
+ratio test ال test الأولان اللي هو ال root test
+
+165
+00:11:57,260 --> 00:12:03,010
+ايه؟ fx بسوي xnis a sequence in A and R and there
+
+166
+00:12:03,010 --> 00:12:07,410
+exists a positive number R أصغر من واحد and a
+
+167
+00:12:07,410 --> 00:12:11,590
+natural number K such that يعني الخاصية هذه بدوا
+
+168
+00:12:11,590 --> 00:12:16,590
+إياها X N أسواحد على N أصغر أو ساوي R تتحقق لكل N
+
+169
+00:12:16,590 --> 00:12:20,550
+أكبر أو يساوي K من عند K وطالع مش مشكلةلأن أنا
+
+170
+00:12:20,550 --> 00:12:22,670
+اللي في ال divergence و ال convergence مين اللي
+
+171
+00:12:22,670 --> 00:12:26,990
+بتحكم اللي هو ال terms اللي لما .. لإنها بتروح إلى
+
+172
+00:12:26,990 --> 00:12:29,890
+مالة نهاية يعني لو كان أول مليون term أو أول متين
+
+173
+00:12:29,890 --> 00:12:33,970
+مليون أو جد ما يكون في الأول اللي هو لا تحقق
+
+174
+00:12:33,970 --> 00:12:38,250
+الخاصية اللي بديها أنا بهم مني اللي فيما بعد يحقق
+
+175
+00:12:38,250 --> 00:12:40,550
+الخاصية اللي بديها اللي بدا تحكم على ال
+
+176
+00:12:40,550 --> 00:12:44,950
+convergence أو ال divergence إذن الآن لو كان عندي
+
+177
+00:12:44,950 --> 00:12:49,520
+X أقص .. X أقص واحد أنا الأصغر يستخدم Rلكل n أكبر
+
+178
+00:12:49,520 --> 00:12:51,020
+يساوي كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+179
+00:12:51,020 --> 00:12:53,220
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+180
+00:12:53,220 --> 00:13:03,200
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+181
+00:13:03,200 --> 00:13:05,720
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+182
+00:13:05,720 --> 00:13:15,340
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+183
+00:13:15,340 --> 00:13:22,200
+كتنفترض أنه تلاتة holes يعني نفترض أنه XN أسواحد
+
+184
+00:13:22,200 --> 00:13:26,500
+على N أصغر أو يساوي R لكل N أكبر أو يساوي K الان
+
+185
+00:13:26,500 --> 00:13:29,760
+منها هيكون عند ال absolute value XN أكبر أو يساوي
+
+186
+00:13:29,760 --> 00:13:35,680
+0 أصغر أو يساوي 100 RN لكل N أكبر أو يساوي K الان
+
+187
+00:13:37,230 --> 00:13:42,990
+الـ summation للـ R أُس عن R نحن ناخدها أصغر من
+
+188
+00:13:42,990 --> 00:13:45,950
+واحد و positive طبعاً أصغر من واحد معناته ال
+
+189
+00:13:45,950 --> 00:13:50,250
+summation للـ R أن converge مظبوط؟ مدام الـ R أن
+
+190
+00:13:50,250 --> 00:13:55,310
+converge فال summation لل XN is converge يعني
+
+191
+00:13:55,310 --> 00:13:58,150
+بمعنى أخر صارت ال summation لل XN is absolutely
+
+192
+00:13:58,150 --> 00:14:06,100
+convergent طيبsuppose that أربعة holds اللي هي مين
+
+193
+00:14:06,100 --> 00:14:10,840
+أربعة هذا أكبر أو ساوء واحد لأن لكل N أكبر أو ساوء
+
+194
+00:14:10,840 --> 00:14:17,920
+K معناته اللي هو ال XN اللي هي أس واحد على N لو
+
+195
+00:14:17,920 --> 00:14:23,700
+جيت أخدته limitها limit اللي هي ال XN هيكون عند ال
+
+196
+00:14:23,700 --> 00:14:28,600
+absolute value لل XNأكبر أو ساوء واحد يعني limit
+
+197
+00:14:28,600 --> 00:14:33,340
+ال absolute value ل Xn as n goes to infinity أكيد
+
+198
+00:14:33,340 --> 00:14:37,640
+أكبر أو ساوء واحد إذا exist يعني بتسويش سفر مدام
+
+199
+00:14:37,640 --> 00:14:41,920
+بتسويش سفر إذا نصممش لل Xn بال test اللي هو
+
+200
+00:14:41,920 --> 00:14:46,780
+الأولان اللي أخدناهالان مدام الـ summation xn الـ
+
+201
+00:14:46,780 --> 00:14:51,260
+absolute value xn does not converge to 0 إذا هتكون
+
+202
+00:14:51,260 --> 00:14:55,580
+الـ xn does not converge to 0 ومن ثم ال summation
+
+203
+00:14:55,580 --> 00:15:00,560
+للـ xn أشملها diverse حسب اللي هو اللي قلنا عنه ال
+
+204
+00:15:00,560 --> 00:15:03,420
+divergence test اللي هو ال summation للـ xn
+
+205
+00:15:03,420 --> 00:15:06,820
+converges بلاقاء ال limit للـ xn بساوة 0 لكن عندي
+
+206
+00:15:06,820 --> 00:15:11,360
+طلعت limit للـ xn لا تساوة 0 طيب corollary لللي
+
+207
+00:15:11,360 --> 00:15:15,870
+فوقالأن الـ Corollary بتقول ما هي ليه؟ let X
+
+208
+00:15:15,870 --> 00:15:20,230
+بيساوي Xn بيبقى Sequence اند R and let R بيساوي
+
+209
+00:15:20,230 --> 00:15:25,350
+Limit Xn أس واحدة لان هناك كانت اللي هي بتاخد ال
+
+210
+00:15:25,350 --> 00:15:29,830
+and roots لمن؟ لل terms و بتشوف اللي هنا إذا كان
+
+211
+00:15:29,830 --> 00:15:33,410
+ال and roots لل terms اللي هي أكبر أو يساوي R من
+
+212
+00:15:33,410 --> 00:15:43,630
+عند K و طالعالان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+213
+00:15:43,630 --> 00:15:48,470
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+214
+00:15:48,470 --> 00:15:48,530
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+215
+00:15:48,530 --> 00:15:48,750
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+216
+00:15:48,750 --> 00:15:49,210
+بتحكم ليه؟ الان بتحكم ليه؟ الان بتحكم ليه؟ الان
+
+217
+00:15:49,210 --> 00:15:53,220
+بتحكم ليه؟ الان بتحكم ليه؟نفترض إن Xn بيكون
+
+218
+00:15:53,220 --> 00:15:57,500
+سيكوينس في R وR بيسوى Limit Xn plus 1 لـ N نفترض
+
+219
+00:15:57,500 --> 00:16:02,840
+إن هذا الـ Limit موجود ثم الصممش للـ Xn هو
+
+220
+00:16:02,840 --> 00:16:10,360
+بالتأكيد مرتبط لما R أصغر من 1 وهو مرتبط عندما R
+
+221
+00:16:10,360 --> 00:16:13,140
+أكبر من 1 وهذا ال test انتوا عارفينه يعني بمعنى
+
+222
+00:16:13,140 --> 00:16:18,040
+آخر باجي بقول باخد Limit Xn
+
+223
+00:16:18,970 --> 00:16:23,270
+أُس واحدة لأن أس أن قصة infinity طلع عندي ايش
+
+224
+00:16:23,270 --> 00:16:28,550
+بيساوي بيساوي R احنا مفترضين ان ال limit exist اذا
+
+225
+00:16:28,550 --> 00:16:34,550
+R أكبر من واحد خلاص ال series xn divers اذا R أصغر
+
+226
+00:16:34,550 --> 00:16:39,030
+من واحد ال series ايش مالها converge و absolutely
+
+227
+00:16:39,030 --> 00:16:44,370
+convergentلكن إذا كانت R بتساوي واحد بنقول ال test
+
+228
+00:16:44,370 --> 00:16:47,650
+fail يعني ممكن يكون convergence وممكن تكون إيش ما
+
+229
+00:16:47,650 --> 00:16:53,650
+لها divergence وفيه أمثلة واضح؟ طيب الآن بدنا نيجي
+
+230
+00:16:53,650 --> 00:16:59,570
+للبرهان suppose that limit Xn أس واحد على N بساوي
+
+231
+00:16:59,570 --> 00:17:05,790
+R وR إيش ما لها أصغر من واحد نفترض إنه limit Xn أس
+
+232
+00:17:05,790 --> 00:17:07,670
+واحد على N بساوي R أصغر من واحد
+
+233
+00:17:10,860 --> 00:17:22,100
+طيب عندى لما اقول limit xn أس واحدة لان بساوى واحد
+
+234
+00:17:22,100 --> 00:17:29,260
+او بساوى R اللى هى أصغر من واحد ايش معناته هذا هذا
+
+235
+00:17:29,260 --> 00:17:35,490
+معناته لكل ي أكبر من سفرThere exist k element in N
+
+236
+00:17:35,490 --> 00:17:39,550
+such that for every N أكبر وسوء k اللي هو بيكون
+
+237
+00:17:39,550 --> 00:17:50,390
+عند X N أسواحدة ل N ناقص R ناقص R أصغر من مين؟ من
+
+238
+00:17:50,390 --> 00:17:58,340
+إبسلونأصغر من إبسلون خد الآن إبسلون إبسلون بتساوي
+
+239
+00:17:58,340 --> 00:18:02,780
+عند واحد ناقص R أكبر من سفر لغرض الحسابات بتاخد
+
+240
+00:18:02,780 --> 00:18:06,720
+إبسلون عبارة عن واحد ناقص R على اتنين واحد ناقص R
+
+241
+00:18:06,720 --> 00:18:09,640
+على اتنين أكيد أكبر من سفر إذا هتصير أصغر من واحد
+
+242
+00:18:09,640 --> 00:18:14,420
+ناقص R على اتنين على اتنين صار عندي الآن Xn أسواحد
+
+243
+00:18:14,420 --> 00:18:20,120
+على N أصغر من واحد ناقص R على اتنين زائد R وأكبر
+
+244
+00:18:20,120 --> 00:18:27,300
+منR ناقص .. اللي هو واحد ناقص R على مين؟ على اتنين
+
+245
+00:18:27,300 --> 00:18:32,080
+انا بتهيب من المنطقة هذه ماشي الحال صار عندى اللي
+
+246
+00:18:32,080 --> 00:18:40,540
+هو ال XL أسواحد على N أصغر من اللي هو واحد
+
+247
+00:18:42,070 --> 00:18:47,950
+1 الان هذه اتنين R اللي هي واحد زائد R على مين على
+
+248
+00:18:47,950 --> 00:18:52,210
+اتنين ماشي؟ لذا صارت ال Xn أسواحد على N absolute
+
+249
+00:18:52,210 --> 00:18:57,790
+value أصغر من واحد زائد R على اتنين لكل N أكبر أو
+
+250
+00:18:57,790 --> 00:19:06,720
+يساوي مين K لذا حصلت على هذه هذه سموليها R'R' أو
+
+251
+00:19:06,720 --> 00:19:20,880
+يسمونها R واحد هذي R واحد اكبر او
+
+252
+00:19:20,880 --> 00:19:30,580
+اكبر اكبر اكبر اكبر اكبر اكبر اكبر اكبر اكبر
+
+253
+00:19:30,580 --> 00:19:33,070
+اكبر اكبر اكبر اكبر اكبرR أصغر من واحد يعني عبارة
+
+254
+00:19:33,070 --> 00:19:38,010
+عن هدولة عبارة عن R يعني R واحد أصغر من مين من R
+
+255
+00:19:38,010 --> 00:19:44,070
+في نفس الوقت هتكون أصغر من واحداللي وصلتله انا
+
+256
+00:19:44,070 --> 00:19:48,030
+suppose that اللي مش مشروح انا شرحته هناك limit x
+
+257
+00:19:48,030 --> 00:19:51,070
+minus واحد على n بساوي R أصغر من واحد then there
+
+258
+00:19:51,070 --> 00:19:55,650
+exists R واحد such that R واحد أكبر من R وأصغر من
+
+259
+00:19:55,650 --> 00:20:02,090
+مين من واحد R واحد أكبر من R وأكيد أصغر من واحد
+
+260
+00:20:02,090 --> 00:20:07,590
+زائد واحد على اتنين ويساوي واحد اللي هي andاللي هو
+
+261
+00:20:07,590 --> 00:20:11,270
+إيش هيكون عنده a natural number K اللي لجيته such
+
+262
+00:20:11,270 --> 00:20:15,210
+that XN plus 1 الان أصغر يسوء R1 لكل N أكبر أو
+
+263
+00:20:15,210 --> 00:20:21,930
+يسوء K والها وهيني فصلتلكم إيها هان الان صار جاهز
+
+264
+00:20:21,930 --> 00:20:25,250
+اللي هو النظرية اللي احنا هتذكرولها لها ال
+
+265
+00:20:25,250 --> 00:20:30,990
+comparison test اللي هو عندي summation لل R1 هذه
+
+266
+00:20:30,990 --> 00:20:37,810
+صارت الآن XN plus 1 الان أصغر من R1 يعنيبمهادر تبه
+
+267
+00:20:37,810 --> 00:20:44,030
+عليها ده خلينا نعملها برضه أفصلها صار عندي الآن يا
+
+268
+00:20:44,030 --> 00:20:53,890
+جماعة عندي اللي هو x and هيها x and absolute value
+
+269
+00:20:53,890 --> 00:21:01,550
+other أو ساوي R واحد أس انماشي هذي الان ال R1 أصغر
+
+270
+00:21:01,550 --> 00:21:07,590
+من واحد مدام أصغر واحد وهذه ال series converts
+
+271
+00:21:07,590 --> 00:21:12,030
+الكبيرة إذا بقى بأول هذه ال series الشمالة تكون
+
+272
+00:21:12,030 --> 00:21:16,690
+converts then by comparison testالآن اللي هي
+
+273
+00:21:16,690 --> 00:21:21,350
+summation R1Rn converges implies بواسطة هذه ان ال
+
+274
+00:21:21,350 --> 00:21:26,350
+summation لل Xn is absolutely convergent الان لو
+
+275
+00:21:26,350 --> 00:21:30,530
+فرضنا ان limit Xn أس واحدة بساوي R أكبر من واحد
+
+276
+00:21:31,090 --> 00:21:34,410
+بنفس الطريقة اللى جيتها قبل بشوية بس هاخد الـY
+
+277
+00:21:34,410 --> 00:21:39,010
+اللى هو هستخدم الـY definition بس هاخد الـY R ناقص
+
+278
+00:21:39,010 --> 00:21:42,250
+واحد على اتنين و هطبّك زي ما طبّجت بالظبط قبل
+
+279
+00:21:42,250 --> 00:21:47,650
+بشوية هلاجي natural number K such that ال X أنقص
+
+280
+00:21:47,650 --> 00:21:52,490
+واحد على N أكبر من واحد ولا لأ أنا بلزمش حتىعلى
+
+281
+00:21:52,490 --> 00:21:56,150
+طول limit xn أسواه دلان اللي هو بسوء r أكبر من
+
+282
+00:21:56,150 --> 00:21:59,010
+واحد هيطلع عندي xn أسواه دلان أكبر من واحد فهو r
+
+283
+00:21:59,010 --> 00:22:03,290
+أكبر سواء k ومنه على طول بما أن هذه اللي هو أكبر
+
+284
+00:22:03,290 --> 00:22:05,590
+من واحد حسب ال test اللي قبل بشوية ال summation لل
+
+285
+00:22:05,590 --> 00:22:11,290
+xn is divergent وده ماعرفش أعمل أعملها زي ما
+
+286
+00:22:11,290 --> 00:22:15,830
+عملتها قبل بشوية أنا none no conclusion وهذا
+
+287
+00:22:15,830 --> 00:22:21,070
+حكيتها no conclusionWhen R بيساوي واحد either
+
+288
+00:22:21,070 --> 00:22:28,830
+convergence or divergence is possible في حالة لما
+
+289
+00:22:28,830 --> 00:22:32,730
+جينا .. أخدنا ال limit و لجينا ال limit لان
+
+290
+00:22:32,730 --> 00:22:36,750
+through ال test بيساوي واحد معناته انه يمكن يكون
+
+291
+00:22:36,750 --> 00:22:43,190
+convergence و ممكن يكون divergence طيب نيجي الآن
+
+292
+00:22:43,190 --> 00:22:49,470
+لل ratio test ال ratio test مشابهأخدنا اللي هو
+
+293
+00:22:49,470 --> 00:22:53,090
+الان comparison test بشقيه العادي و ال limit و
+
+294
+00:22:53,090 --> 00:22:55,890
+أخدنا الان through ال test بشقيه العادي و ال limit
+
+295
+00:22:55,890 --> 00:22:59,630
+العادي اللي هو اللي قصدنا فيه اللي هو X أنوس واحدة
+
+296
+00:22:59,630 --> 00:23:05,910
+أكبر من واحد اللي هو أو أصغر اللي كانت الأولى و
+
+297
+00:23:05,910 --> 00:23:08,350
+اللي بعدها limit comparison test نفس الأشياء أكبر
+
+298
+00:23:08,350 --> 00:23:13,440
+أو أصغر طيب ال ratio testFx بيساوي xn is a
+
+299
+00:23:13,440 --> 00:23:18,280
+sequence of non-zero terms هذه ميزتها إنها
+
+300
+00:23:18,280 --> 00:23:21,760
+بيلزمهاش طبعا زي اللي جابلها بيلزمها الأولى
+
+301
+00:23:21,760 --> 00:23:25,920
+بيلزمها ال comparison test بيلزمها تقارن بسيريز
+
+302
+00:23:25,920 --> 00:23:30,920
+أخرى الان الانثرويد test وال ratio test تقارن
+
+303
+00:23:30,920 --> 00:23:35,790
+بنفسهايعني من داخل نفسها بتقدر تعرف اللي هو ..
+
+304
+00:23:35,790 --> 00:23:38,810
+اللي هي بطريقة معينة تعرف إن هي converged ولا
+
+305
+00:23:38,810 --> 00:23:42,810
+diverse يعني الآن Fx بسوء Xn is a sequence of non
+
+306
+00:23:42,810 --> 00:23:43,910
+-zero elements
+
+307
+00:23:46,750 --> 00:23:51,010
+of R and there is a positive number R أصغر من واحد
+
+308
+00:23:51,010 --> 00:23:55,730
+and a natural number K such that Xn زائد واحد على
+
+309
+00:23:55,730 --> 00:23:59,950
+Xn أصغر سوء R for N أكبر سوء K then the summation
+
+310
+00:23:59,950 --> 00:24:04,030
+Xn is absolutely convergent يعني الآن جيت انت لجيت
+
+311
+00:24:04,030 --> 00:24:08,310
+Xn زائد واحد على Xnاللي جيتها دايماً أصغر أوي ساوي
+
+312
+00:24:08,310 --> 00:24:12,130
+R والـ R أصغر strictly من مين؟ من واحد يعني دايماً
+
+313
+00:24:12,130 --> 00:24:15,830
+ال ratio هذا اللي بعده على اللي جابله اللي بعد على
+
+314
+00:24:15,830 --> 00:24:19,870
+اللي جاب اللي جيته أصغر معناته أنه صارت اللي هي
+
+315
+00:24:19,870 --> 00:24:23,890
+أشمالها عمالها بتصغر ال sequence كل ما ماشيت قدام
+
+316
+00:24:23,890 --> 00:24:27,330
+بيصير اللي ورا ع اللي قدام أصغر من واحد اللي ورا ع
+
+317
+00:24:27,330 --> 00:24:31,570
+اللي قدام أصغر من واحد يعني واضح أنه في اللي هو في
+
+318
+00:24:31,570 --> 00:24:36,410
+ال submission للـ XN is absolutely convergentلأن
+
+319
+00:24:36,410 --> 00:24:39,570
+بيقول if there exists a natural number k such that
+
+320
+00:24:39,570 --> 00:24:44,650
+بعده بيصير تصرفها ان xn زي 1 على xn هيكون أكبر
+
+321
+00:24:44,650 --> 00:24:48,350
+ويسوء 1 مدام أكبر ويسوء 1 معناته صار اللي هو كل
+
+322
+00:24:48,350 --> 00:24:51,890
+مامشيت قدام ال term بيكبر مثلا بيكبر ال term نفسه
+
+323
+00:24:51,890 --> 00:24:55,170
+إذا ال limit مش هيروح للصفر إذا معناته انه صارت ال
+
+324
+00:24:55,170 --> 00:25:01,530
+series divergent طيب ال proof خلينا نبرهن ايهif 6
+
+325
+00:25:01,530 --> 00:25:06,550
+holds يعني لو هو كانت هذا متحقق then by induction
+
+326
+00:25:06,550 --> 00:25:12,590
+one can see that for M أكبر أوي ساوية واحد K X K M
+
+327
+00:25:12,590 --> 00:25:18,890
+أصغر أوي ساوية أرقص M X K بتصور مش صعب إثبات هذه
+
+328
+00:25:18,890 --> 00:25:24,370
+for عندي خد X ال induction عالميا for M أكبر أوي
+
+329
+00:25:24,370 --> 00:25:32,360
+ساوية واحد على Mاللي هان بيصير xk زائد واحد اللي
+
+330
+00:25:32,360 --> 00:25:37,820
+هو xk زائد واحد هنا لإنها بتتحقق من k وطالع k زائد
+
+331
+00:25:37,820 --> 00:25:45,920
+واحد بيصير على ال xk يعني أصغر ساوي R في xk درم
+
+332
+00:25:45,920 --> 00:25:52,980
+التفرق الطرفين في وسطين xk إذن هذه صحيحةR M في
+
+333
+00:25:52,980 --> 00:25:56,020
+حالة الواحد صحيحة في حالة ال M ساو واحد الان
+
+334
+00:25:56,020 --> 00:26:01,420
+suppose that this true for M بدا تبت صحيتها for me
+
+335
+00:26:01,420 --> 00:26:08,360
+in M زائد واحد X K زائد M زائد واحد بدا تبت صحيتها
+
+336
+00:26:08,360 --> 00:26:12,940
+في حالة ال M زائد واحد اللي هو حسب اللي هنا اللي
+
+337
+00:26:12,940 --> 00:26:21,080
+أصغر أو ساوي ال Rثمين في اللي هي هنا N زائد واحد S
+
+338
+00:26:21,080 --> 00:26:28,160
+زائد واحد K M K زائد M K زائد M اذا R في absolute
+
+339
+00:26:28,160 --> 00:26:34,280
+value X K زائد M ماشي لان و بما ان هذا true for M
+
+340
+00:26:34,280 --> 00:26:38,840
+يعني هذا متحققه اذا من هنا ب hypothesis induction
+
+341
+00:26:38,840 --> 00:26:47,440
+بيصير R في R أس Mفي XK Y ساوية R أقصى M زايد واحد
+
+342
+00:26:47,440 --> 00:26:54,500
+في XK يعني صارت هذه صحيحة for M زايد واحد إذا صارت
+
+343
+00:26:54,500 --> 00:26:59,440
+صحيحة لكل M إذا هذه دائما صحيحة لأي M أكبر وساوية
+
+344
+00:26:59,440 --> 00:27:03,120
+واحد في ضوء العلاقة اللي هي 6 صحيحة
+
+345
+00:27:06,690 --> 00:27:13,130
+إذاً هذا لكل M أكبر أو يساوي واحد عندي لكل N أكبر
+
+346
+00:27:13,130 --> 00:27:17,350
+أو يساوي K الان
+
+347
+00:27:17,350 --> 00:27:27,330
+شيلي ال K زائد M وحط مكانها N يعني N بتساوي K زائد
+
+348
+00:27:27,330 --> 00:27:36,860
+M بصير هذه X Nأثر أو يساوي الـ M بتساوي N ناقص K و
+
+349
+00:27:36,860 --> 00:27:42,100
+X K زي ما هي X K لأنه شيلت ال N و حطيت مكانها K
+
+350
+00:27:42,100 --> 00:27:46,100
+زائد M و ال N طبعا اللي هي بتساوي K زائد M أكيد
+
+351
+00:27:46,100 --> 00:27:50,400
+أكبر أو يساوي K إذن هذه اللي هي صحيحة إذن صار عندي
+
+352
+00:27:50,400 --> 00:27:56,340
+الآن اللي عشان بعد شوية هتستخدمها صار عندي الآن ال
+
+353
+00:27:56,340 --> 00:28:03,180
+absolute valueللـ Xn أصغر أو يساوي R أُس N ناقص K
+
+354
+00:28:03,180 --> 00:28:10,180
+في X K ماشي الحال هذا لكل N أكبر أو يساوي إيش K
+
+355
+00:28:10,180 --> 00:28:19,740
+طيب نكمل للبرهان الـ N summation لل R أُس N
+
+356
+00:28:19,740 --> 00:28:20,660
+converts
+
+357
+00:28:23,610 --> 00:28:29,250
+لأن الار مالها بين صفر و واحد مادام هذي متغيرت
+
+358
+00:28:29,250 --> 00:28:33,450
+طبعا هذا term مجرد عدد يعنى term لأنه عند ك كهذا
+
+359
+00:28:33,450 --> 00:28:37,390
+هو اشي fixed يعني هو عبارة عن عدد والمتغير من الان
+
+360
+00:28:37,390 --> 00:28:44,510
+هذه اللي أنا ال summation لها للار الناقص كيعني بس
+
+361
+00:28:44,510 --> 00:28:48,670
+بنشيل K من ال terms مش مشكلة بتضل اللي هو converge
+
+362
+00:28:48,670 --> 00:28:52,270
+اللي هي summation R أُس N converge ثم summation
+
+363
+00:28:52,270 --> 00:28:56,430
+أُس R N ناقص K كيفيكس number عبارة عن converge ثم
+
+364
+00:28:56,430 --> 00:28:59,530
+صارت هذه ال series converge من باب أولى لل series
+
+365
+00:28:59,530 --> 00:29:02,670
+اللي أصغر منها اللي هتكون converge ثم صارت عندي
+
+366
+00:29:02,670 --> 00:29:05,070
+summation absolute value converge او بمعنى اخر
+
+367
+00:29:05,070 --> 00:29:12,450
+summation XN is absolutely convergent الان نيجيلأ
+
+368
+00:29:12,450 --> 00:29:18,050
+الجزء الثاني الان إذا كانت اللي هي سبعة holes سبعة
+
+369
+00:29:18,050 --> 00:29:21,970
+هي سبعة شايفينها هي سبعة اللي هو ال XN زائد واحد
+
+370
+00:29:21,970 --> 00:29:28,990
+على XN أكبر أو ساوى واحد لكل N أكبر أو ساوى مين
+
+371
+00:29:28,990 --> 00:29:36,420
+أكبر أو ساوى K كلام مشابهكلام مشابه if 7 holds
+
+372
+00:29:36,420 --> 00:29:41,900
+then by induction one can see that xkm أكبر أو
+
+373
+00:29:41,900 --> 00:29:46,880
+يساوي xk for m بساوي واحد و بعدين it is true for m
+
+374
+00:29:46,880 --> 00:29:49,480
+then it is true for m زائد واحد و زي ما عملت قبل
+
+375
+00:29:49,480 --> 00:29:54,170
+بشوية هتلاجوها بكل سهولة تطلعالان خد ال limit هذا
+
+376
+00:29:54,170 --> 00:29:58,690
+الان هذا صحيح لكل M أكبر أو يساوي واحد الان خد ال
+
+377
+00:29:58,690 --> 00:30:01,630
+limit as M goes to infinity بيصير أكبر أو يساوي
+
+378
+00:30:01,630 --> 00:30:05,090
+اللي هو المقدار هذا والمقدار هذا strictly أكبر من
+
+379
+00:30:05,090 --> 00:30:09,970
+100 من 0 لأن ال terms اللي عندي كلها لاتساوي 0 من
+
+380
+00:30:09,970 --> 00:30:14,930
+عند K وطالع اذا انتر عندي اللي هو limit ال Xn اللي
+
+381
+00:30:14,930 --> 00:30:20,490
+هو أكبر من 0 and so summation لل Xn is divergent
+
+382
+00:30:21,110 --> 00:30:26,670
+طيب، نريد الان لإيه الـ Corollary الأخيرة في
+
+383
+00:30:26,670 --> 00:30:32,050
+محاضرة اليوم اللي هي بتقول ليت X بسوء XN بيه
+
+384
+00:30:32,050 --> 00:30:36,790
+Sequence in R and Setواضح انه بيعطي اللي هو عادي و
+
+385
+00:30:36,790 --> 00:30:38,990
+بعدين limit عادي و بعدين limit و في ال ratio test
+
+386
+00:30:38,990 --> 00:30:42,410
+نفس الاشي بده ياخد limit ال exant زائد واحد على ال
+
+387
+00:30:42,410 --> 00:30:47,410
+exant بساوي R و الناس هتميل في الحلول في معظمها
+
+388
+00:30:47,410 --> 00:30:51,270
+اللي هي limits whenever the limit exist إذا كانت
+
+389
+00:30:51,270 --> 00:30:55,230
+ال limit هذه exist بنيجيthen the series summation
+
+390
+00:30:55,230 --> 00:30:58,630
+xn converges أو absolutely convergent إذا كان آر
+
+391
+00:30:58,630 --> 00:31:02,210
+أصغر من واحد وdivergent إذا كانت يشملها أكبر من
+
+392
+00:31:02,210 --> 00:31:06,110
+واحد يعني بناخد limit xn زائد واحد على xn absolute
+
+393
+00:31:06,110 --> 00:31:09,110
+value طبعا إذا كانت positive terms على طول بدون
+
+394
+00:31:09,110 --> 00:31:13,780
+absolute values طلع أن دي limit موجودما دام اطلع
+
+395
+00:31:13,780 --> 00:31:18,300
+ال limit موجود في عندي حكم إذا كان اللي هو أكبر من
+
+396
+00:31:18,300 --> 00:31:21,780
+واحد diverse إذا كان أصغر من واحد converge إذا
+
+397
+00:31:21,780 --> 00:31:26,220
+بيساوي واحد معناته the test fails وبنبحث اللي عن
+
+398
+00:31:26,220 --> 00:31:30,440
+test آخر طيب الآن suppose that limit xn زاد واحد
+
+399
+00:31:30,440 --> 00:31:33,300
+على xn as n goes to infinity بيساوي R أصغر من مين
+
+400
+00:31:33,300 --> 00:31:38,410
+من واحدبنفس الطريقة اللي عملناها قبل بشوية في
+
+401
+00:31:38,410 --> 00:31:44,230
+الأول let R1 satisfies R1 أكبر من R أصغر من 1 then
+
+402
+00:31:44,230 --> 00:31:48,810
+اللي هو لأن طبيعي between any two real numbers فيه
+
+403
+00:31:48,810 --> 00:31:53,770
+real number سميته مين؟ R1 الآن بما أن ال limit هذا
+
+404
+00:31:53,770 --> 00:31:57,370
+بيساوي R يدل كل إيبسلون أكبر من 0 من ضمن مين
+
+405
+00:31:57,370 --> 00:32:02,760
+الإيبسلون اللي بدأ أخدها؟ R1-RThen for epsilon
+
+406
+00:32:02,760 --> 00:32:07,280
+بساوة R واحد ناقص R أكبر من سفر there exists K
+
+407
+00:32:07,280 --> 00:32:10,260
+elements in N such that ال absolute value لهذا
+
+408
+00:32:10,260 --> 00:32:13,160
+ناقص هذا أصغر من مين من ال epsilon هي R واحد ناقص
+
+409
+00:32:13,160 --> 00:32:18,180
+مين ناقص R هذا صحيح لكل مين لكل N أكبر أو ساوة K
+
+410
+00:32:18,800 --> 00:32:23,600
+الآن نفردها هذه بس بتاخد الجهة اللي على اليمين هي
+
+411
+00:32:23,600 --> 00:32:27,420
+اللي بتمنى اللي هو صار عندى xn زائد واحد على xn
+
+412
+00:32:27,420 --> 00:32:31,540
+أصغر من r واحد ناقص r ولمّا تجيب هذا على الجهة
+
+413
+00:32:31,540 --> 00:32:34,240
+الثانية بعد ما فكرا absolute value بصير r ويساوي
+
+414
+00:32:34,240 --> 00:32:39,400
+ايش بتساوي؟ ويساوي بساوي r واحدالان و تساوي R واحد
+
+415
+00:32:39,400 --> 00:32:44,620
+اذا اللي هي .. اللي هيكون عندى اللي بال ..
+
+416
+00:32:44,620 --> 00:32:47,480
+بالنظرية اللي هي تسعة اتنين خمسها هتطلع عندى
+
+417
+00:32:47,480 --> 00:32:51,280
+الاصابيش ال absolute value اكسن اشمالها is
+
+418
+00:32:51,280 --> 00:32:56,110
+absolutely convergentهيطلع عندي summation للـ xn
+
+419
+00:32:56,110 --> 00:32:59,350
+is absolutely convergent اللي هي من نظرية تسعة
+
+420
+00:32:59,350 --> 00:33:02,450
+اتنين خمسة لإنه صار عندي ال absolute value لـ xn
+
+421
+00:33:02,450 --> 00:33:07,750
+زائد واحد على xn أصغر من رقم أصغر من واحد لكل n
+
+422
+00:33:07,750 --> 00:33:11,710
+أكبر سوى k من عند k وطالع بمعنى آخر صار عندي اللي
+
+423
+00:33:11,710 --> 00:33:15,530
+هي ال series is convergent لإنه هذا أصلا corollary
+
+424
+00:33:15,530 --> 00:33:21,830
+للي جابلها الآنودناخد اللي هو الجزء الثاني من اللي
+
+425
+00:33:21,830 --> 00:33:25,470
+هي ال .. ال .. ال .. البرهان اللي هو اللي بتعلق في
+
+426
+00:33:25,470 --> 00:33:28,330
+الجزء الثاني من ال Corollary بدنا نفترض انه limit
+
+427
+00:33:28,330 --> 00:33:33,390
+لل Xn زائد واحد ع ال Xn اللي هو بساوي R أكبر من
+
+428
+00:33:33,390 --> 00:33:37,910
+واحد وبدنا نشوف اللي هو كيف diverse يعني بدأ افترض
+
+429
+00:33:37,910 --> 00:33:40,670
+انه limit limit
+
+430
+00:33:42,720 --> 00:33:46,740
+Xn زائد واحد على Xn as n جثه infinity اللي هو
+
+431
+00:33:46,740 --> 00:33:51,940
+إجماله عبارة عن رقم اللي هو أكبر من واحد نسميها R
+
+432
+00:33:51,940 --> 00:33:58,260
+يساوي R أكبر من واحد ونشوف كيف أن هو عندي اللي هي
+
+433
+00:33:58,260 --> 00:34:04,040
+diverse الآنخد الـ Epsilon حلو خد Epsilon for
+
+434
+00:34:04,040 --> 00:34:09,560
+Epsilon for Epsilon بساوي R ناقص واحد أكبر من سفر
+
+435
+00:34:09,560 --> 00:34:13,220
+there exists K element in N such that for every N
+
+436
+00:34:13,220 --> 00:34:19,000
+أكبر وسوء K بطلع عنده هو XN زائد واحد على XN
+
+437
+00:34:19,510 --> 00:34:25,650
+absolute value ناقص الـ R أكبر من أصغر من مين من
+
+438
+00:34:25,650 --> 00:34:30,190
+إبسلون اللي هي عبارة عن R ناقص واحد هي ال إبسلون
+
+439
+00:34:30,190 --> 00:34:33,130
+اللي أخدت R ناقص واحد أو زي ما هو عاملها هان أصغر
+
+440
+00:34:33,130 --> 00:34:36,550
+من هيها أصغر من R minus واحد اللي هي الإبسلون اللي
+
+441
+00:34:36,550 --> 00:34:40,570
+هان فوق فوق اللي هان مش بيهمنيش الجهة اللي هان
+
+442
+00:34:40,570 --> 00:34:43,850
+بيهمني الجهة الثانية عكس اللي أولانياللي عن حيط
+
+443
+00:34:43,850 --> 00:34:47,790
+لعندي xn زائد واحد على xn أكبر من واحد اللي هي r
+
+444
+00:34:47,790 --> 00:34:50,870
+ناقص r minus واحد اللي هي ايش بتطلع واحد صار هذا
+
+445
+00:34:50,870 --> 00:34:54,030
+المقدار أكبر من واحد و بال test اللي قبل بشوية ال
+
+446
+00:34:54,030 --> 00:34:57,790
+theorem تسعة اتنين خمسة بما أنه صار هذا من عند n
+
+447
+00:34:57,790 --> 00:35:01,670
+أكبر يساوي k وطالع من عند k وطالع طلع عندي هذا
+
+448
+00:35:01,670 --> 00:35:05,050
+أكبر من واحد معناته صارت ال information هذه is
+
+449
+00:35:05,050 --> 00:35:10,340
+divergentوطبعا اللي دايما بنقولها دايما اللي هي no
+
+450
+00:35:10,340 --> 00:35:14,320
+conclusion و ال R بتساوي واحد اللي هو ممكن تكون
+
+451
+00:35:14,320 --> 00:35:17,080
+conversion و ممكن تكون diversion عشان هذا الأساس
+
+452
+00:35:17,080 --> 00:35:22,160
+بنقول ال test fail في حالة ال R بتساوي واحد و نبحث
+
+453
+00:35:22,160 --> 00:35:26,900
+عن test آخر و الآن بنيجي ل اللي هو المرة الجاية ان
+
+454
+00:35:26,900 --> 00:35:30,440
+شاء الله بناخد ال integral test و إلى لقاء آخر
+
+455
+00:35:30,440 --> 00:35:31,400
+والسلام عليكم و رحمه الله
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/rKngzYKfO2U_postprocess.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/rKngzYKfO2U_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a09f05fedfb0e4f455c826b0adeb2bea6ca636d9
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/rKngzYKfO2U_postprocess.srt
@@ -0,0 +1,2600 @@
+1
+00:00:05,150 --> 00:00:09,890
+بسم الله الرحمن الرحيم اليوم ان شاء الله عندنا
+
+2
+00:00:09,890 --> 00:00:15,270
+اللي هو المحاضرة رقم عشرة في مساق تحليل حقيقه
+
+3
+00:00:15,270 --> 00:00:21,130
+اتنين لطلبة الجامعة الإسلامية كلية العلوم قسم
+
+4
+00:00:21,130 --> 00:00:27,370
+الرياضيات اليوم ان شاء الله هنبدأ في chapter سبعة
+
+5
+00:00:28,110 --> 00:00:33,150
+اللي هو الجزء الثاني من المادة أو العصب الثاني
+
+6
+00:00:33,150 --> 00:00:37,130
+للمادة اللي هو حكينا عن ال derivatives اليوم نحكي
+
+7
+00:00:37,130 --> 00:00:42,170
+عن اللي هو the reman integral أو تكامل رمان هيتم
+
+8
+00:00:42,170 --> 00:00:45,730
+الحديث اليوم ان شاء الله في ال section الأول هنحكي
+
+9
+00:00:45,730 --> 00:00:51,450
+عن ال reman integrability أو قابلية تكامل الدالة
+
+10
+00:00:51,450 --> 00:00:56,270
+على اللي هو بالنسبة لرمانفي البداية هنحكي عن بعض
+
+11
+00:00:56,270 --> 00:01:00,410
+التعريف اللي هتوصلنا للي بدناياه في الموضوع اللي
+
+12
+00:01:00,410 --> 00:01:03,910
+هو الـ Riemann Integrability الان هاخدلنا function
+
+13
+00:01:03,910 --> 00:01:11,090
+F F من some interval I نفترض ان الدالة اللي عند F
+
+14
+00:01:11,090 --> 00:01:18,850
+من A و B لعند R is a bounded function الان
+
+15
+00:01:18,850 --> 00:01:22,050
+بدنا نعرف بعض التعريفات اللي بتخودنا الى الـ
+
+16
+00:01:22,050 --> 00:01:26,950
+Riemann Integrabilityأول اشي بدنا نعرف شو معناه
+
+17
+00:01:26,950 --> 00:01:30,750
+partition لو كانت هذه الدانلة مثلا هي Y بالساوية F
+
+18
+00:01:30,750 --> 00:01:36,170
+of X على الفترة المذكورة وكانت من A ل B اللي هو ال
+
+19
+00:01:36,170 --> 00:01:41,650
+domain بدنا الآن نيجي نجزق المنطقة اللي هي الفترة
+
+20
+00:01:41,650 --> 00:01:47,210
+من A ل B اللي هو خلّي نسمي هذا X noteهذا نسميه x1
+
+21
+00:01:47,210 --> 00:01:51,750
+هذا نسميه x2 لعند ما أصل للفترة النموذجية اللي
+
+22
+00:01:51,750 --> 00:01:58,270
+بتسميها xk-1 لعند ال xk وهذا أسميها اللي هي xn
+
+23
+00:01:58,270 --> 00:02:06,110
+الان الفترة من a لb أنا جزقتها بx0 وx1 وx2 لعند xn
+
+24
+00:02:06,110 --> 00:02:13,370
+هذه التجزية بتحطها في 6 وسميها بي بتساوي x0و X1 و
+
+25
+00:02:13,370 --> 00:02:19,410
+X2 لعند Xn هذا اللي بسميه is a partition of the
+
+26
+00:02:19,410 --> 00:02:26,510
+interval A و B إذا عندي I subset من R closed
+
+27
+00:02:26,510 --> 00:02:30,430
+bounded interval ال ordered set هذه اللي حكيتها
+
+28
+00:02:30,430 --> 00:02:34,410
+كتبتها ان هي عبارة عن X0 و X1 لعند Xn بنسميها a
+
+29
+00:02:34,410 --> 00:02:39,390
+partition of I بحيث انه A X0 أصغر من X1 لعند ما
+
+30
+00:02:39,390 --> 00:02:45,060
+أقول أصغر من Xnالان الـ function عندى F من I لعند
+
+31
+00:02:45,060 --> 00:02:49,980
+R bounded function on I الان بدى أعرف بعض
+
+32
+00:02:49,980 --> 00:02:54,660
+التعريفات اللى هتلزمني برضه في اللى هو الوصول إلى
+
+33
+00:02:54,660 --> 00:02:59,160
+الـ Remain Integrability أول تعريف بدى أخد الآن
+
+34
+00:02:59,160 --> 00:03:07,000
+أسمي M1 هو عبارة عن الـ supremum للـ function في
+
+35
+00:03:07,000 --> 00:03:12,990
+المنطقة هذهالـ M1 بدي أسميه عبارة عن الـ Supremum
+
+36
+00:03:12,990 --> 00:03:16,810
+للدالة F of X والـ Supremum موجودة لأن الـ F
+
+37
+00:03:16,810 --> 00:03:21,870
+أشمالها is bounded السوب للـ F of X حيث الـ X
+
+38
+00:03:21,870 --> 00:03:29,310
+موجودة في الفترة من X note لعند X1 هذه اللي هي بدي
+
+39
+00:03:29,310 --> 00:03:34,570
+أسميها M1 Capital M1 Small اللي هي عبارة عن ال
+
+40
+00:03:34,570 --> 00:03:38,960
+Infimumلـ .. لـ الـ function hand اللي عبارة عن
+
+41
+00:03:38,960 --> 00:03:45,400
+الـ infimum لـ F of X حيث X تنتمي إلى الفترة X
+
+42
+00:03:45,400 --> 00:03:50,440
+naught و X واحد in general .. in general في الفترة
+
+43
+00:03:50,440 --> 00:03:55,280
+النموذجية بدي أسمي M K هي عبارة عن .. الآن في
+
+44
+00:03:55,280 --> 00:03:59,850
+الفترة هذهعالفترة هذه الـ supremum للـ function
+
+45
+00:03:59,850 --> 00:04:06,170
+هنا بدي اسميها M K K بسوء F of X such that X
+
+46
+00:04:06,170 --> 00:04:13,030
+element in X K minus واحد لعند X K و ال M small K
+
+47
+00:04:13,030 --> 00:04:19,330
+هسميها اللي هي بنفس اللي هسميت X واحد اللي هي ال
+
+48
+00:04:19,330 --> 00:04:23,370
+infimum لل F of X في الفترة من X K minus واحد لعند
+
+49
+00:04:23,370 --> 00:04:30,300
+X K على سبيل المثالالـ M K يعني هيها هذا اللي هي M
+
+50
+00:04:30,300 --> 00:04:36,340
+K Small والـ M K Capital على سبيل المثال هيها
+
+51
+00:04:36,340 --> 00:04:42,640
+هيقبتها هذا الـ M K Capital إذن الآن عندي سميت
+
+52
+00:04:42,640 --> 00:04:45,560
+اللي هي الـ M K Capital هي الـ Supremum والـ M K
+
+53
+00:04:45,560 --> 00:04:49,740
+Small هي عبارة عن الـ Infimum وهلجيت حنشوف إيش
+
+54
+00:04:49,740 --> 00:04:55,560
+دواعي هذه التسمية أو ليش سمينا هيكالان بدنا نعرف
+
+55
+00:04:55,560 --> 00:05:00,380
+اللي هو .. بدنا
+
+56
+00:05:00,380 --> 00:05:04,380
+نعرف الآن اللي هو حاجة اسمها lower sum و حاجة
+
+57
+00:05:04,380 --> 00:05:12,540
+اسمها ايش ال upper sum الان لو جيت بعد ما عملت ال
+
+58
+00:05:12,540 --> 00:05:21,020
+partition اللي عندي هذا و جيت أخدت اللي هي
+
+59
+00:05:28,550 --> 00:05:32,770
+أخدت الـ partition B اللي عندي هذا هذا ال
+
+60
+00:05:32,770 --> 00:05:40,110
+partition B هو عبارة عن X0 X1 X2 اللي عند XN جيت
+
+61
+00:05:40,110 --> 00:05:44,590
+أنا أخدت اللي هو الـ supremum للدالة في هذه
+
+62
+00:05:44,590 --> 00:05:51,550
+المنطقة والتي تكون طبعا هنا شكلها اللي هي سميتها
+
+63
+00:05:51,550 --> 00:06:02,170
+M1 في X1 نقص X0و جيت ضفت لها برضه ال supremum
+
+64
+00:06:02,170 --> 00:06:08,030
+للدالة في المنطقة هذه اللي هي زائد M2 سميت ال
+
+65
+00:06:08,030 --> 00:06:15,230
+supremum اللي هو M2 في X2-X0 لما نوصلت لآخر واحدة
+
+66
+00:06:15,230 --> 00:06:20,750
+بنفس الأسلوب أخدت اللي هو ال supremum اللي هي ال
+
+67
+00:06:20,750 --> 00:06:26,870
+supremum طبعا M1 عندىالتي هي طول الريانج اللي عندى
+
+68
+00:06:26,870 --> 00:06:32,850
+مضروب في مين اللي هو x1-x0 فبتطلع هذه المنطقة
+
+69
+00:06:32,850 --> 00:06:41,710
+بالظبط مساحة اللي عندى الان بضل أجمع بنفس الأسلوب
+
+70
+00:06:41,710 --> 00:06:45,830
+بجمحن بنفس الأسلوب عندى
+
+71
+00:06:53,690 --> 00:06:58,050
+هذا المجموع اللي بالازرق هو اللي بنسميه هسميه ال
+
+72
+00:06:58,050 --> 00:07:03,170
+other sum هذا ال other sum اللي هو ال other لل F
+
+73
+00:07:03,170 --> 00:07:08,090
+للدالة F بواسطة
+
+74
+00:07:08,090 --> 00:07:12,830
+مين ال partition B إذا ال other sum هذا اللي هو
+
+75
+00:07:12,830 --> 00:07:17,830
+عبارة عن اللي هو لل function بواسطة ال partition B
+
+76
+00:07:17,830 --> 00:07:20,410
+يعني ال other sum هذا يعتمد على ال F ويعتمد على
+
+77
+00:07:20,410 --> 00:07:25,690
+مين؟ على ال partition اللي عنديالأن similarly بدي
+
+78
+00:07:25,690 --> 00:07:31,190
+آجي أعرف اللي هو ال lower sum إذا ال upper sum
+
+79
+00:07:31,190 --> 00:07:38,890
+بيساوي ال summation ل X K نقص X K minus واحد مضروب
+
+80
+00:07:38,890 --> 00:07:43,950
+في ال M K capital K من عند واحد لعند N هذه اللي
+
+81
+00:07:43,950 --> 00:07:48,930
+بيسميها ال upper sum similarly بدي أعرف مين اللي
+
+82
+00:07:48,930 --> 00:07:56,170
+هو ال lower sumللـ F و لل D هيساوي الآن بدل ما أخد
+
+83
+00:07:56,170 --> 00:07:59,330
+اللي هو ال suprem أعلى قيمة بتاخد اللي هو ال
+
+84
+00:07:59,330 --> 00:08:05,390
+infimum بيصير عندي اللي هو summation X K minus X K
+
+85
+00:08:05,390 --> 00:08:10,790
+minus واحد في ال M K small K من عند واحد لعند N
+
+86
+00:08:10,790 --> 00:08:15,050
+هذا اللي هو عبارة عن ال lower sum في الواقع هو
+
+87
+00:08:15,050 --> 00:08:21,350
+هيكون المنطقة اللي بالأحمر هذهبناء على إني باخد
+
+88
+00:08:21,350 --> 00:08:27,670
+أنا اللي هو الارتفاع هو عبارة عن ال M K Small اللي
+
+89
+00:08:27,670 --> 00:08:33,410
+هو ال minimum لقيمة الدالة على كل المنطقة وهكذا
+
+90
+00:08:33,410 --> 00:08:38,030
+لما أصل لآخر واحدة فبصير عندى هذا ال summation
+
+91
+00:08:38,030 --> 00:08:43,890
+لهذه اللي هي المستطيلات
+
+92
+00:08:43,890 --> 00:08:51,510
+بناء على ال partition اللي عندىهي عبارة عن مين؟ عن
+
+93
+00:08:51,510 --> 00:08:56,190
+اللي هو اللا وارسم طبعا ناخد الدالة اللي هي في
+
+94
+00:08:56,190 --> 00:09:00,670
+منطقة موجة بأساس إنه اللي هي يكون أكثر توضيحا طبعا
+
+95
+00:09:00,670 --> 00:09:04,650
+لو منطقة سالبة برضه باخد نفس الأسلوب لكن بيصير
+
+96
+00:09:04,650 --> 00:09:08,810
+اللي هو بديل مساحة بيصير سالب مساحة أو مخلوطة بين
+
+97
+00:09:08,810 --> 00:09:13,070
+مساحة موجة مساحة سالبة و بت cancel بعض إلى أن أنا
+
+98
+00:09:13,070 --> 00:09:16,350
+أخدتها على فترة موجة بأساس اللي هو تسهل مسعملية
+
+99
+00:09:16,820 --> 00:09:22,620
+اللي هي التوضيح الآن خلينا تحت شوية إذا اللي حكيته
+
+100
+00:09:22,620 --> 00:09:28,420
+الآن أعرفت ال lower sum زي ما أنتوا شايفين عند ال
+
+101
+00:09:28,420 --> 00:09:32,780
+lower sum هيه هذا ال lower sum يعتمد في مجموعه على
+
+102
+00:09:32,780 --> 00:09:37,300
+ال M K اللي هي عبارة عن ال infimum لدالة على
+
+103
+00:09:37,300 --> 00:09:43,960
+الفترة X K minus واحد لعند X Kو-xk-1 هي عبارة عن
+
+104
+00:09:43,960 --> 00:09:49,040
+قيم ال partition اللي عندي إذا ال lower sum أو حتى
+
+105
+00:09:49,040 --> 00:09:53,820
+ال upper sum التمتين باعتمدين عالميا على اللي هو
+
+106
+00:09:53,820 --> 00:09:57,940
+ال partition وعلى الدالة اللي بنعملها أو لو وجدلها
+
+107
+00:09:57,940 --> 00:10:03,160
+ال lower sum و ال upper sum الهن واضح أن ال lower
+
+108
+00:10:03,160 --> 00:10:09,780
+sum ال lower sum واضح أنه اللي هو دائمااللي هو لل
+
+109
+00:10:09,780 --> 00:10:13,480
+partition المعين هيكون أصغر من مين من ال upper sum
+
+110
+00:10:13,480 --> 00:10:21,380
+واضح أه؟ الان اللي بنحكي if F من I ل R is bounded
+
+111
+00:10:21,380 --> 00:10:27,520
+and B is any partition of I then ال lower sum لل B
+
+112
+00:10:27,520 --> 00:10:32,020
+و ال F أصغر سوى ال upper sum لل B و ال F وبرهانه
+
+113
+00:10:32,020 --> 00:10:39,830
+سهل وسريعلو جئنا و أخذنا الـ bi-partition x0 x1
+
+114
+00:10:39,830 --> 00:10:40,550
+عند xn
+
+115
+00:10:43,460 --> 00:10:48,540
+وقررنا بين الـMK والـMK Capital أكيد الـMK Small
+
+116
+00:10:48,540 --> 00:10:50,540
+أصغر من الـMK Capital لإنه هذا عبارة عن
+
+117
+00:10:50,540 --> 00:10:54,820
+الـSupremum للفункشن على الفترة أو الـSubinterval
+
+118
+00:10:54,820 --> 00:10:59,780
+XK minus 1 عند XK وهذا الـSupremum للفункشن، هذا
+
+119
+00:10:59,780 --> 00:11:02,860
+الـInfimum وهذا الـSupremum فأكيد هذا أكبر أو
+
+120
+00:11:02,860 --> 00:11:07,080
+يساوي ما هو الـMK Small وهذا الكلام صحيح على كل
+
+121
+00:11:07,080 --> 00:11:11,380
+الـSubintervals يعني صحيح لكل K من 1 إلى 2 عند N
+
+122
+00:11:11,490 --> 00:11:14,650
+وفي نفس الوجهة الـ xk هو الـ xk minus واحد أكبر من
+
+123
+00:11:14,650 --> 00:11:18,610
+سفر إذا بيصير عندي حاصل ضرب هادي فى طول الفترة
+
+124
+00:11:18,610 --> 00:11:22,570
+وهادي فى طول الفترة بتظل ال inequality صحيحة لإنه
+
+125
+00:11:22,570 --> 00:11:26,730
+طول الفترة موجبة فبصير mk فى هذا المقدار أصغر ساوى
+
+126
+00:11:26,730 --> 00:11:29,950
+mk capital فى هذا المقدار بنعمل summation على الكل
+
+127
+00:11:29,950 --> 00:11:32,770
+وهذا ال summation على الكل بيصير عندى هذا هو عبارة
+
+128
+00:11:32,770 --> 00:11:36,150
+عن ال upper sum وهذا ال lower sum يعني اللى وصلنا
+
+129
+00:11:36,150 --> 00:11:44,110
+إلى انه دائما ال lower sumلأن ال lower sum هو أسفل
+
+130
+00:11:44,110 --> 00:11:48,230
+من ال upper sum في القيام فبكون أكيد ال lower sum
+
+131
+00:11:48,230 --> 00:11:56,870
+أصغر أو يساوي ال upper sum اطلع لفهم الان احنا لو
+
+132
+00:11:56,870 --> 00:12:01,590
+اجينا لو
+
+133
+00:12:01,590 --> 00:12:06,170
+اجينا اعرفنا .. بنعرف حاجة اللي في عندي P is a
+
+134
+00:12:06,170 --> 00:12:10,890
+partitionلو ضفت على الـ partition أي قيمة جديدة
+
+135
+00:12:10,890 --> 00:12:15,370
+بالاضافة للقيم الموجودة بيصير عندى هذا ال .. ال ..
+
+136
+00:12:15,370 --> 00:12:20,710
+ال .. الجديد عبارة عن refinement لمين للـ B يعني
+
+137
+00:12:20,710 --> 00:12:26,290
+تحسين لل partition يعني الآن بنقول عن أن الـ B الـ
+
+138
+00:12:26,290 --> 00:12:30,190
+Q is a refinement of B إذا كانت الـ B subset من
+
+139
+00:12:30,190 --> 00:12:34,990
+مين؟ من الـ Q طيب، الآن نشوف إيش اللي بنقوله
+
+140
+00:12:45,570 --> 00:12:57,310
+الأن لو أخدنا الفترة اللي هي A وB و جزّقناها X0 X1
+
+141
+00:12:57,310 --> 00:13:03,460
+لعند XNوالفترة النموذجية اللي نشرع عليها xk minus
+
+142
+00:13:03,460 --> 00:13:08,640
+واحد أو ال sub interval لعند مين لعند xk الان ال b
+
+143
+00:13:08,640 --> 00:13:13,520
+هذا هو عبارة عن ال partition x naught x واحد لعند
+
+144
+00:13:13,520 --> 00:13:17,400
+ال xn وهذا ordered يعني نكتبها على صورة ordered
+
+145
+00:13:17,400 --> 00:13:20,640
+لما نكتبها على هذا متفقين على انه ايش اللي هو احنا
+
+146
+00:13:20,640 --> 00:13:25,380
+نعمله ordered ال order بالنسبة له ايش ماله مهم لأن
+
+147
+00:13:25,380 --> 00:13:28,080
+هذا معناه تبدأ بال x naught وبعدين x واحد بعدين
+
+148
+00:13:28,080 --> 00:13:35,240
+اللي هو ال xnلو جينا أخدنا اللي هو أضفنا أي نقطة
+
+149
+00:13:35,240 --> 00:13:39,060
+هنا طبعاً أضفنا أي نقطة أو أي رقم بين الـA و بين
+
+150
+00:13:39,060 --> 00:13:45,320
+مين الـB الرقم المضاف اللي هو أضفنا لهذه وسميناها
+
+151
+00:13:45,320 --> 00:13:50,930
+Q فبكون الـQ هي عبارة عن refinement للـBيعني بمعنى
+
+152
+00:13:50,930 --> 00:13:55,030
+اخر اكيو refinement ل ال B معناته انه في اكيو فيها
+
+153
+00:13:55,030 --> 00:14:02,790
+نقاط اللي هي زيادة عن نقطة B واسمه تحسين لانه فعلا
+
+154
+00:14:02,790 --> 00:14:08,870
+بحسن وضع ال lower sum و ال upper sum الان ال lower
+
+155
+00:14:08,870 --> 00:14:14,250
+sum عرفناه لل B و ال F قلنا بعتمد عليهم بسوء ال
+
+156
+00:14:14,250 --> 00:14:22,130
+summationاللي هو xk ناقص xk minus واحد في ال mk
+
+157
+00:14:22,130 --> 00:14:25,090
+اللي هي mk small هي عبارة عن قلنا اللي هي عبارة عن
+
+158
+00:14:25,090 --> 00:14:29,050
+ال infimum لدى العهد الفترة k من عند واحد لعند n
+
+159
+00:14:29,050 --> 00:14:34,770
+والان ال upper sum ب U, B وF اللي هو بساوى ال
+
+160
+00:14:34,770 --> 00:14:40,890
+summation لل xk minus xk minus واحد mk capital k
+
+161
+00:14:40,890 --> 00:14:47,930
+من عند واحد لعند nوقلنا إن الـ lower للـ B و الـ F
+
+162
+00:14:47,930 --> 00:14:52,390
+دايما أصغر سوى ال upper للـ B و الـ F فده اللي حتى
+
+163
+00:14:52,390 --> 00:14:58,470
+الآن اللي حكيناه الآن نيجي ناخد الملاحظة اللي عندي
+
+164
+00:14:58,470 --> 00:15:04,510
+if Q above is a refinement of B لو قلنا إن Q عبارة
+
+165
+00:15:04,510 --> 00:15:09,390
+عن إيه شمالها؟ refinement of Brefinement معناته
+
+166
+00:15:09,390 --> 00:15:14,690
+اضفت اللي هو نقطة او اكتر من نقطة لنقاط ال
+
+167
+00:15:14,690 --> 00:15:20,810
+partition اللي عندى اذا اي فترة اي فترة اللي هي xk
+
+168
+00:15:20,810 --> 00:15:27,550
+minus واحد لعند xk اللي هو في ال partition بيه
+
+169
+00:15:27,550 --> 00:15:34,060
+هقدر اكتبها على صورة ميناللي هو yj-1 yj اتحاد ال
+
+170
+00:15:34,060 --> 00:15:37,940
+yj yj زاد 1 اتحاد ده ما اصل عند اتحاد yn نقص 1
+
+171
+00:15:37,940 --> 00:15:44,040
+لعند مين لعند ال yn ماشي الحال طبعا الان هذول عدد
+
+172
+00:15:44,040 --> 00:15:47,740
+الفترات على حسب الإضافة اللي هنالو ضفنا نقطة واحدة
+
+173
+00:15:47,740 --> 00:15:52,240
+بين هذول التنتين معناته هيصير عندى من الـ yj-1 هي
+
+174
+00:15:52,240 --> 00:15:56,460
+عبارة عن xk-1 والنقطة المضافة اتحاده النقطة
+
+175
+00:15:56,460 --> 00:15:59,780
+المضافة اللي هي مع مين مع النقطة هذه بيكون عندى بس
+
+176
+00:15:59,780 --> 00:16:03,690
+فترة تانية لو كان فيه عندىنقطين مضافات بيصير عندي
+
+177
+00:16:03,690 --> 00:16:06,710
+اللي هو للنقطة الأولى و بعدين من النقطة الأولى
+
+178
+00:16:06,710 --> 00:16:12,030
+لنقطة ثانية و بعدين من النقطة الثانية لـ XK فبيصير
+
+179
+00:16:12,030 --> 00:16:16,030
+عندي أكم فترة انضاف تلت .. بيصير تلت فترات و هكذا
+
+180
+00:16:16,030 --> 00:16:19,970
+إذن و لو مافيش إضافة في هذه الفترة بالمرة بيصير
+
+181
+00:16:19,970 --> 00:16:24,460
+عندي بس اللي هي ال interval الأولىأه إذا صار عندى
+
+182
+00:16:24,460 --> 00:16:29,640
+الآن في حالة اللى هو الـQ refinement للـB أي فترة
+
+183
+00:16:29,640 --> 00:16:35,040
+في الـB الأصلية بقدر أكتبها على صورة اللى هى هذا
+
+184
+00:16:35,040 --> 00:16:40,000
+الاتحاد وهذا الاتحاد يحتمل اللى هو الفترة الحاله
+
+185
+00:16:40,000 --> 00:16:44,460
+أو فترتين أو تلاته إلى آخره على حسب اللى هو النقاط
+
+186
+00:16:44,460 --> 00:16:50,060
+المضافة واضح اللى ما اللى هي سبعة واحد اتنينif f
+
+187
+00:16:50,060 --> 00:16:53,960
+من I عند R is bounded and B is any partition of I
+
+188
+00:16:53,960 --> 00:16:57,680
+and Q is a refinement of B فرضنا ان Q ايش ما هي
+
+189
+00:16:57,680 --> 00:17:03,180
+refinement لـ B إذا ال lower sum الاعتماد على
+
+190
+00:17:03,180 --> 00:17:06,820
+partition B و ال function F أصغر يساوي ال lower
+
+191
+00:17:06,820 --> 00:17:12,780
+sum لـ Q و ال F و ال U ال Q و ال F أصغر يساوي ال U
+
+192
+00:17:12,780 --> 00:17:17,900
+و ال B و ال F هو أصلا واقعا ال refinement هو فعلا
+
+193
+00:17:17,900 --> 00:17:25,250
+تحسين أصلاأحنا لما نجينا دربنا المثال في الأول و
+
+194
+00:17:25,250 --> 00:17:28,690
+رسمنا الرسمة على سبيل المثال هذه الرسمة اللي عندي
+
+195
+00:17:28,690 --> 00:17:36,290
+و أخدنا من a لعند b مثلا اللي هو الفترة و كان في
+
+196
+00:17:36,290 --> 00:17:42,150
+عندي اللي هو اللي عملنا تجزء x note x1 الاخره x2
+
+197
+00:17:42,150 --> 00:17:49,420
+x3 لعند الاخيرة xn مثلاعلى سبيل المثال واخدنا
+
+198
+00:17:49,420 --> 00:17:52,860
+القبر صم القبر صم هيكون عبارة عن المنطقة هذه
+
+199
+00:17:52,860 --> 00:17:57,240
+والقبر صم عبارة عن المنطقة هذه والقبر صم بيكون هذه
+
+200
+00:17:57,240 --> 00:18:02,150
+المنطقة كلها اللي بالأزرقالآن لما نزيد اللي هو
+
+201
+00:18:02,150 --> 00:18:07,210
+نقاط الـ Partition اللي هو هذا اللي هي النقاط
+
+202
+00:18:07,210 --> 00:18:12,630
+بتجلل الجزء الزائد فالآن فعلًا بيكون تحسين على
+
+203
+00:18:12,630 --> 00:18:15,330
+الأولاني لأنه أصلا أنا بعد شوية هتلاقي غاية في
+
+204
+00:18:15,330 --> 00:18:21,140
+الوصول أن أصل اللي هو اللي هو أصغر واحدفي ال upper
+
+205
+00:18:21,140 --> 00:18:25,720
+sums يصير زي أكبر واحد في ال lower sums يوم ما
+
+206
+00:18:25,720 --> 00:18:29,820
+يلتجوا مع بعض بيكون فعلا اللي هو ال upper sum وال
+
+207
+00:18:29,820 --> 00:18:35,000
+lower sum اللي هو تجاوزا بيصير بساوي بالظبط اللي
+
+208
+00:18:35,000 --> 00:18:40,080
+هو المساحة تحت المنحنة أو المنطقة اللي هنسميها في
+
+209
+00:18:40,080 --> 00:18:43,340
+حينه ان هي عبارة عن remen integral بل وقيمة ال
+
+210
+00:18:43,340 --> 00:18:47,660
+remen integral هو عبارة عن هذه المنطقة اللي صارتمن
+
+211
+00:18:47,660 --> 00:18:53,540
+اللي هو انه ناخد نزغر اللي هو الأبر و نرفع ال
+
+212
+00:18:53,540 --> 00:18:57,540
+lower و نشوف كيف بنزغر الأبر و كيف بنرفع ال lower
+
+213
+00:18:57,540 --> 00:19:01,580
+اللي هو معنى اللي هيوصل لنا معنى ال integrability
+
+214
+00:19:02,250 --> 00:19:06,710
+إذا الـ Refinement فعلاً Refinement تحسين لما أقول
+
+215
+00:19:06,710 --> 00:19:13,390
+أن بي إي كيو زادت عن هذه الـ Q إيش هتعمل؟ هتتجللل
+
+216
+00:19:13,390 --> 00:19:19,630
+الجزء الزائد في الـ Upper لما أزيد النقاط و هتزيد
+
+217
+00:19:19,630 --> 00:19:24,950
+للجزء المفقود وين في ال lowerماشي الحال ففعلا
+
+218
+00:19:24,950 --> 00:19:28,310
+هيكون ايه بقى عبارة عن refinement او تحسين انت
+
+219
+00:19:28,310 --> 00:19:32,470
+نشوف الآن نشوف لمتنا اللي عندنا اللي هو معنى اللي
+
+220
+00:19:32,470 --> 00:19:38,350
+بقوله انا انه عندي لو كانت Q refinement لل B بكون
+
+221
+00:19:38,350 --> 00:19:43,790
+الlower لجديدعليه أكبر أو يساوي الـ Lower القديم
+
+222
+00:19:43,790 --> 00:19:48,390
+يعني بمعنى آخر اقترب إلى اللي بدناهي اللي متوقعين
+
+223
+00:19:48,390 --> 00:19:53,110
+انه يكون هو التحسين النهائي اللي هنسميه اللي هو ال
+
+224
+00:19:53,110 --> 00:19:58,670
+integration ماشي؟ وال Upper هنا Upper UQ واضح انه
+
+225
+00:19:58,670 --> 00:20:03,510
+بصغر اللي هو عن الأصل لأنه صار فيه تحسين واقترب من
+
+226
+00:20:03,510 --> 00:20:08,070
+الحقيقة اقترب من اللي هو القيمة اللي احنا هنسميها
+
+227
+00:20:08,070 --> 00:20:12,370
+في النهاية integrationطيب، بدنا نثبت الكلام هذا،
+
+228
+00:20:12,370 --> 00:20:16,810
+شوف كيف بدنا نثبته، اللي أنا عندي بيأخدت I اللي هو
+
+229
+00:20:16,810 --> 00:20:21,290
+ال partition ال arbitrary واخدت اللي هو sigma I،
+
+230
+00:20:21,290 --> 00:20:26,310
+بد أشتغل على إضافة نقطة ومن ثم أقول إضافة النقطة
+
+231
+00:20:26,310 --> 00:20:31,340
+تؤدي إلى اللي هو باقي النقطة، نشوف إيش بقولعند بي
+
+232
+00:20:31,340 --> 00:20:35,080
+هي اللي هو الـ partition أخدت z element in I و الـ
+
+233
+00:20:35,080 --> 00:20:39,100
+z هذي و أنا بدأ أحطها في الفترة xk minus واحد لعند
+
+234
+00:20:39,100 --> 00:20:42,640
+مين لعند الـ xk يعني الآن ال partition اللي بي
+
+235
+00:20:42,640 --> 00:20:51,200
+عندي هو عبارة عن x naught لعند xn xk minus واحد xk
+
+236
+00:20:51,200 --> 00:20:55,620
+indeed في المنطقة هذه ضفت نقطة وسميت بيها prime و
+
+237
+00:20:55,620 --> 00:21:03,380
+عبارة عن x naught xk minus واحدZ X K وظل الخلايت
+
+238
+00:21:03,380 --> 00:21:07,720
+كله زي ما هو لعد مين لعد X بس اللي غيرت فيه او
+
+239
+00:21:07,720 --> 00:21:12,420
+اللي ضفتله بس ضفت نقطة هنا اسمها Z بدى اشوف تأثير
+
+240
+00:21:12,420 --> 00:21:16,640
+هذا النقطة ايش بده يعمل بين ال partition القديم
+
+241
+00:21:16,640 --> 00:21:20,520
+وال partition الجديد ومن ثم نستنتج اي refinement
+
+242
+00:21:20,520 --> 00:21:26,990
+على اللي هو ال B القديمةالأمر سهل ان شاء الله الان
+
+243
+00:21:26,990 --> 00:21:30,290
+ال .. ال .. ال .. الاضافة الجديدة صار عند بي برايم
+
+244
+00:21:30,290 --> 00:21:35,870
+ايش هو X Note X واحد وهي ال Z ضفتهان اللي اختلف عن
+
+245
+00:21:35,870 --> 00:21:43,640
+فوق بس ال Z اللي هان بناء عليه الان ال M Kالـ mk'
+
+246
+00:21:43,860 --> 00:21:49,020
+هي عبارة عن الـ supremum للـ function f وين في
+
+247
+00:21:49,020 --> 00:21:58,920
+المنطقة بين zk-1 و مين و z الآن في الفترة بين xk-1
+
+248
+00:21:58,920 --> 00:22:04,800
+و بين xk ضفت z الآن الـ z اللي ضفت هنا هذه المنطقة
+
+249
+00:22:04,800 --> 00:22:11,150
+بدي أسميه ال supremum اللي فيها mk' اللي هنااللي
+
+250
+00:22:11,150 --> 00:22:16,190
+ضالت نسميها إيش مالها MK double prime مع العلم إنه
+
+251
+00:22:16,190 --> 00:22:19,890
+الـ supremum الأصلية في ال partition الأصلي على كل
+
+252
+00:22:19,890 --> 00:22:23,250
+الفترة من XK minus واحد عند XK اسمها إيش مسمينا
+
+253
+00:22:23,250 --> 00:22:31,130
+احنا MK capital باشي الحال طيب ركزوا معاياالآن
+
+254
+00:22:31,130 --> 00:22:34,970
+عندي الـ MK' هي الـ supremum على اللي هو الـ
+
+255
+00:22:34,970 --> 00:22:39,610
+subinterval هذه الـ MKW' هي ال supremum على اللي
+
+256
+00:22:39,610 --> 00:22:43,910
+هي ال subinterval اللي جنبها اللي هي من Z لعند XK
+
+257
+00:22:43,910 --> 00:22:49,890
+واضح أن ال supremum على الكبيرة هذه من XK minus 1
+
+258
+00:22:49,890 --> 00:22:53,790
+لعند XK أكيد أكبر أو يساوي ال supremum على الصغيرة
+
+259
+00:22:54,620 --> 00:22:58,580
+لأن هذه أشملها جزء من 100 من هذه كلها فال supremum
+
+260
+00:22:58,580 --> 00:23:01,940
+لل function عالي كبيرة أكبر أو يساوي ال supremum
+
+261
+00:23:01,940 --> 00:23:06,020
+على مين؟ على الصغيرة و similarly للتانية إذا ال MK
+
+262
+00:23:06,020 --> 00:23:12,180
+أكبر أو يساوي MK' Similarly MK أكبر يساوي MKW' لأن
+
+263
+00:23:12,180 --> 00:23:15,220
+هذه عبارة عن ال supremum على الجزء الثاني منها
+
+264
+00:23:15,220 --> 00:23:20,520
+اللي إلى جاي، واضح؟إذا صار عندي therefore الآن بدأ
+
+265
+00:23:20,520 --> 00:23:24,840
+أصل لحاجة معينة اللي هي mk في xk ناقص xk minus
+
+266
+00:23:24,840 --> 00:23:31,310
+واحددربت اللي هي Mk في هذا هذه الفترة طبعا اللي هي
+
+267
+00:23:31,310 --> 00:23:40,730
+بتساوي Zk-Zk-Xk-1 زائد Xk-Zk الان صارت هذه Mk في
+
+268
+00:23:40,730 --> 00:23:45,410
+المقدار هذا بساوي Mk في هذه زائد هذه ماشي الحال
+
+269
+00:23:45,410 --> 00:23:50,820
+الان ال Mkأكبر أو يساوي mean mk' إذا انصار المقدار
+
+270
+00:23:50,820 --> 00:23:58,780
+هذا أكبر أو يساوي mk' في zk z ناقص xk minus واحد و
+
+271
+00:23:58,780 --> 00:24:04,820
+هذه ال mk برضه أكبر أو يساوي mk double prime of xk
+
+272
+00:24:04,820 --> 00:24:10,380
+ناقص z ماشي الحالة الآن احنا بين ال two partitions
+
+273
+00:24:10,380 --> 00:24:14,580
+اللي حدث بس تغيير واحد زي ما قلنا بس على المنطقة
+
+274
+00:24:14,580 --> 00:24:23,090
+هذه لاحظ انتالان ال lower sum ال lower sum لل b و
+
+275
+00:24:23,090 --> 00:24:30,350
+ال f ال b prime و ال f بساوي لو حسبنا للأولاني أول
+
+276
+00:24:30,350 --> 00:24:38,350
+إشي هو عبارة عن m1 في x0 او x1 نقص x0 زاد لما أصل
+
+277
+00:24:38,350 --> 00:24:51,620
+عند mk في xK-XK-1 زائد لما أصل لعند MN في XN-XN-1
+
+278
+00:24:51,620 --> 00:24:57,800
+هذا إيش هو يا جماعة؟ هو عبارة عن الأبرثان الأبرثان
+
+279
+00:24:57,800 --> 00:25:03,120
+لمن؟ لـB و لـF متفجر، ماشي الحالة على مين؟ على ال
+
+280
+00:25:03,120 --> 00:25:12,270
+partition B الآن هذا بساويم1 في x1 ناقص x0 زائد
+
+281
+00:25:12,270 --> 00:25:18,010
+الان هذه جزئناها جزئين بعد شوية زائد زائد هذا نفسه
+
+282
+00:25:18,010 --> 00:25:25,690
+ماتغيرش هذا اللي هو عبارة عن mk لسه xk ناقص z
+
+283
+00:25:25,690 --> 00:25:34,850
+مظبوط زائد اللي هو mk خليني اقول ال
+
+284
+00:25:34,850 --> 00:25:46,170
+mkاللي هو Z ناقص كحسابات ناقص X كمينوس واحد صحيح؟
+
+285
+00:25:46,170 --> 00:25:53,130
+باضح زائد الباقي زي ما هو زائد M N في X N ناقص X N
+
+286
+00:25:53,130 --> 00:26:00,980
+ناقص واحد الآن هذا ماتغيرش نفسهزائد هذا الـ N هو
+
+287
+00:26:00,980 --> 00:26:05,540
+اللي اتغير وهنا في ال inequality هنا لقنا عبارة عن
+
+288
+00:26:05,540 --> 00:26:12,220
+هذا المقدار اللي هو أكبر أو يساوي اللي هو اللي ما
+
+289
+00:26:12,220 --> 00:26:15,420
+اتغيرش هذا نسميه اللي هو M1
+
+290
+00:26:18,760 --> 00:26:25,640
+معايا يا شباب زائد اللي هو mk شرطة في xk ناقص z
+
+291
+00:26:25,640 --> 00:26:31,520
+زائد mk شرطين في z ناقص xk ماينوس واحد زائدة دا
+
+292
+00:26:31,520 --> 00:26:38,570
+كما تتغيرش زي ما هو mn في xnنقص XN نقص 1 هذا في
+
+293
+00:26:38,570 --> 00:26:42,690
+الواقع مين هو أصلاً هذا هو عبارة عن اللي هو ال
+
+294
+00:26:42,690 --> 00:26:48,510
+upper sum لل partition مين ال B' هو بساوي ال upper
+
+295
+00:26:48,510 --> 00:26:55,270
+sum لل B' والFيعني اللي لجناه أنه لما نضفنا اللي
+
+296
+00:26:55,270 --> 00:26:59,830
+هو نقطة على اللي هو الـ partition صار عند الـ
+
+297
+00:26:59,830 --> 00:27:03,590
+partition اللي هو الأبر للـ partition الجديد أصغر
+
+298
+00:27:03,590 --> 00:27:08,360
+أو يساوي الأبر للـ partition من القديمالان اللي
+
+299
+00:27:08,360 --> 00:27:11,760
+حدث على نقطة ممكن يحدث على نقطين يعني الان ممكن
+
+300
+00:27:11,760 --> 00:27:15,640
+نقطة مثلا انضافت هنا ممكن انضافت كمان مرة هنا كمان
+
+301
+00:27:15,640 --> 00:27:20,560
+نقطة هيصير لجديد بنفس الأسلوب أكبر ويساوي تلت نقاط
+
+302
+00:27:20,560 --> 00:27:24,040
+بيصير أكبر ويساوي أربع نقاط بيصير أكبر ويساوي يعني
+
+303
+00:27:24,040 --> 00:27:29,500
+in general مدام ال refinement UQ اللي محتوي بيه في
+
+304
+00:27:29,500 --> 00:27:34,820
+النهاية عدد الإضافات finiteإذا حيكون اللي هو كل
+
+305
+00:27:34,820 --> 00:27:39,300
+مرة بعدد الإضافات بيصير sub intervals بنفس الأسلوب
+
+306
+00:27:39,300 --> 00:27:43,940
+اللي هان حيصير عنده القبر القديم أكبر أو يساوي
+
+307
+00:27:43,940 --> 00:27:48,620
+القبر الجديد يعني بمعنى أخر in general القبر للـB
+
+308
+00:27:48,620 --> 00:27:54,080
+والـF هيكون أكبر أو يساوي القبر للـQ ال refinement
+
+309
+00:27:54,080 --> 00:27:59,160
+وMain والـFوطبعا زي ما قلنا هذا عبارة عن تحسين لإن
+
+310
+00:27:59,160 --> 00:28:03,960
+القبر هذا بيصير يصغر يقترب من المساحة الحقيقية
+
+311
+00:28:03,960 --> 00:28:08,360
+اللي تحت المنحنة في حالة اللي هو الدل ايش الموجبة
+
+312
+00:28:08,360 --> 00:28:15,860
+واضح طيب الان similarly for lower الان الlower
+
+313
+00:28:15,860 --> 00:28:20,940
+بيصير اللي هوفي الـ lower بدل ما يصير عندي لو كان
+
+314
+00:28:20,940 --> 00:28:25,700
+عندي بنحكي عن ال lower احنا ال L بيوقف و بنحكي عن
+
+315
+00:28:25,700 --> 00:28:30,220
+ال M 1 small و ال M 2 small و M K small و M N
+
+316
+00:28:30,220 --> 00:28:36,660
+small بيصير عندي M 1 small و M K small و M KSmall
+
+317
+00:28:36,660 --> 00:28:44,520
+ومكSmall ومنSmall بيصير الان اللي هي المن هنا بدل
+
+318
+00:28:44,520 --> 00:28:49,680
+ما هي أكبر إيش هتصير على إيش أصغر لإنه بيحكي عن ال
+
+319
+00:28:49,680 --> 00:28:54,810
+infimum منأيش صغير على أيش صغير إلى infimum على
+
+320
+00:28:54,810 --> 00:28:59,570
+أيش أيش اللي هو أصغر فمعناته أيش صار عنده بيصير له
+
+321
+00:28:59,570 --> 00:29:04,910
+infimum اللي هو ال M1 أصغر من ال M1' أو ال Mk
+
+322
+00:29:04,910 --> 00:29:11,730
+Small أصغر أو يساوي ال Mk' Small واضح أه؟ ومنه
+
+323
+00:29:11,730 --> 00:29:17,870
+بنستنتج أنه هيكون عند ال LBF أصغر أو يساوي
+
+324
+00:29:21,260 --> 00:29:28,950
+الـ LBF هنصل أصغر و ساويالـ QF وفعلًا أيضًا هذا هو
+
+325
+00:29:28,950 --> 00:29:35,410
+تحسين لإنه اللي هي زاد اللي هو ال lower sum بحيث
+
+326
+00:29:35,410 --> 00:29:41,550
+إنه بده يصل أو يروح ناحية مين اللي هو المساحة
+
+327
+00:29:41,550 --> 00:29:46,310
+الحقيقية تحت المنحنة في حالة التقاء الجهتين بيصير
+
+328
+00:29:46,310 --> 00:29:52,670
+عندي اللي هو إنه القيمة إذا يعني أخدنا بمعنى أخر
+
+329
+00:29:52,670 --> 00:29:58,540
+ندخل للموضوع مدام هيكإنه لو أخدنا اللي هو صار عندى
+
+330
+00:29:58,540 --> 00:30:03,140
+ال lower يبدأ يكبر يعني لو أخدتله ال suprem لكل ال
+
+331
+00:30:03,140 --> 00:30:06,960
+lowers على كل ال partitions اللي في الدنيا و أخدت
+
+332
+00:30:06,960 --> 00:30:10,980
+ال infimum على كل كبار اللي هو و اتساون مع بعض ال
+
+333
+00:30:10,980 --> 00:30:14,820
+infimum يعني عالمين على ال upper sums بيصير ال
+
+334
+00:30:14,820 --> 00:30:17,500
+suprem مع ال lower sums و ال infimum مع ال lower
+
+335
+00:30:17,500 --> 00:30:22,780
+sums يوم ما يتساونهو اللي بنسميه اللي هو الـ
+
+336
+00:30:22,780 --> 00:30:26,920
+Remain Integrable وبنسمي اللي هي الـ Remain
+
+337
+00:30:26,920 --> 00:30:30,440
+Integrable في هذه الحالة بساوي هذه القيمة المشتركة
+
+338
+00:30:30,440 --> 00:30:35,720
+اللي أصبحت متساوية نيجي لللمة اللي عندي هذه، لمة
+
+339
+00:30:35,720 --> 00:30:40,720
+برضه يعني برهانها سهل، نشوف إيش بتقول اللمة، اللمة
+
+340
+00:30:40,720 --> 00:30:45,610
+بتقول let F from I to R be boundedif B1 وB2 are
+
+341
+00:30:45,610 --> 00:30:49,470
+any two partitions يعني مش نفس ال partition على أي
+
+342
+00:30:49,470 --> 00:30:54,090
+two partitions دائما اللاور على أي partition في
+
+343
+00:30:54,090 --> 00:30:57,150
+الدنيا أصغر أو يساوي الأبر على أي partition تاني
+
+344
+00:30:57,150 --> 00:30:59,970
+مش مشكلة إيش هو في الأول قلنا على نفس ال partition
+
+345
+00:30:59,970 --> 00:31:05,510
+arbitrarily و الإثبات هنستخدم اللمّة الأولى و
+
+346
+00:31:05,510 --> 00:31:09,010
+اللمّة الثانية اللي أخدناها و هنصلي هذه بكل سهولة
+
+347
+00:31:09,010 --> 00:31:13,760
+شوف كدهخلّينا ناخد الـ Q ايش بتساوي بي واحد اتحاد
+
+348
+00:31:13,760 --> 00:31:17,240
+دي اتنين صارت الـ Q هذه refinement للأولى و
+
+349
+00:31:17,240 --> 00:31:21,420
+refinement لمين؟ للتانية تحسين للتانتين بناء عليه
+
+350
+00:31:21,420 --> 00:31:25,380
+.. بناء على اللي هي اللمّة اللي أخدناها سبعة واحد
+
+351
+00:31:25,380 --> 00:31:28,660
+واحد وسبعة واحد اتنين احنا حصول على ناية ليه
+
+352
+00:31:28,660 --> 00:31:33,000
+احسبلي ال بي واحد و أف صار refinement مزام صار ..
+
+353
+00:31:33,000 --> 00:31:37,620
+صار له refinement او تحسين بده يكبر اللاور صار
+
+354
+00:31:37,620 --> 00:31:42,750
+أصغر أو ساوي ال Q Fمن جهة أخرى قبل بشوية أثبتنا أن
+
+355
+00:31:42,750 --> 00:31:48,310
+الـQF أصغر يساوي UQF for any اللي هو specific mean
+
+356
+00:31:48,310 --> 00:31:53,070
+الـQ لنفس الـQ لأن برضه اللي هو الـQ refinement
+
+357
+00:31:53,070 --> 00:31:57,790
+لمين؟ للـB2 مازال refinement إذا الـQ بدي يصير
+
+358
+00:31:57,790 --> 00:32:03,050
+أصغر أو يساوي مين الـUB2F زي اللي بواسطة أثبتناها
+
+359
+00:32:03,050 --> 00:32:07,470
+قبل بشوية يعني in generalin general الـ B1 و F
+
+360
+00:32:07,470 --> 00:32:15,810
+أصغر أو ساوي و B2 و F بدون يعني بغض النظر عن B1 و
+
+361
+00:32:15,810 --> 00:32:21,130
+B2 أنهم كونوا زي بعض أو مختلفات لأي two partitions
+
+362
+00:32:21,130 --> 00:32:26,370
+of the interval I طيب الـ definition الآن اللي
+
+363
+00:32:26,370 --> 00:32:28,830
+حكيناها قبل شوية قولناها قبل شوية بدنا نعرف حاجة
+
+364
+00:32:28,830 --> 00:32:33,940
+اسمها lower integralالـ Lower Integral وحاجة اسمها
+
+365
+00:32:33,940 --> 00:32:38,760
+الـ Upper Integral أخدنا
+
+366
+00:32:38,760 --> 00:32:42,740
+الـ function F bounded طبعا معروف ليش bounded عشان
+
+367
+00:32:42,740 --> 00:32:47,880
+يكون الـ M1 و الـ M2 و الـ Mn كلهم موجودات سواء
+
+368
+00:32:47,880 --> 00:32:51,040
+الـ M capital أو الـ M small عشان هما عبارة عن
+
+369
+00:32:51,040 --> 00:32:54,260
+supremum و infimum فلازم تكون bounded ال function
+
+370
+00:32:54,260 --> 00:32:58,280
+الآن فرضنا الـ F عبارة عن bounded function على ال
+
+371
+00:32:58,280 --> 00:33:01,520
+close bounded interval اللي عندى هذهبنعرف الـ
+
+372
+00:33:01,520 --> 00:33:06,320
+lower integral of F on I اللي هو المعتمد عالميا
+
+373
+00:33:06,320 --> 00:33:11,680
+على ال lower sums ال lower sums قولنا انحسن انحسن
+
+374
+00:33:11,680 --> 00:33:16,960
+انحسن انحسن احسن تحسين اذا جهز التعبير اللي هو ال
+
+375
+00:33:16,960 --> 00:33:21,640
+supremum لكل مين لكل ال lower sums على كل ال
+
+376
+00:33:21,640 --> 00:33:25,040
+partitions اللي في الدنيا هذول ايه الشمال اللي
+
+377
+00:33:25,040 --> 00:33:31,260
+بنسميه L of F اللي بنسميه lower sumأخد الـ
+
+378
+00:33:31,260 --> 00:33:35,400
+supremum هي ال lower sums تحت المنحنة لما أخد اللي
+
+379
+00:33:35,400 --> 00:33:40,220
+هنا ال supremum اللي هو هذا ال supremum بدي أسميه
+
+380
+00:33:40,220 --> 00:33:46,300
+ال lower integral الآن ال upper sums بدي أخد اللي
+
+381
+00:33:46,300 --> 00:33:52,020
+هنا ال infimum يعني بدي أزغرهن اللي هو و أسميه ال
+
+382
+00:33:52,020 --> 00:33:57,760
+upper integral إذا صار عندي lowerIntegral هو عبارة
+
+383
+00:33:57,760 --> 00:34:02,080
+عن الـ Supremum للـ Lower Sums و ال .. واضح يا
+
+384
+00:34:02,080 --> 00:34:06,060
+عيسى و ال Upper Integral هو عبارة عن ال Infimum
+
+385
+00:34:06,060 --> 00:34:10,620
+لمن؟ لل Upper Sums متوقع أنه يقول لنا أنه احنا
+
+386
+00:34:10,620 --> 00:34:16,810
+بنقول عنهافوق الصفحة التانية متوقع يقولنا انه عنا
+
+387
+00:34:16,810 --> 00:34:20,970
+الآن بنسميها remain integrable اذا تساوت ايش
+
+388
+00:34:20,970 --> 00:34:26,130
+اتجهتين ماشي جابيه لبس خلينا نبرهن او نتطلع على
+
+389
+00:34:26,130 --> 00:34:33,430
+هذه اللي أمامنا برضه ملاحظة سهلة الملاحظة بتقولي
+
+390
+00:34:33,430 --> 00:34:42,780
+لو الان جيناسمّينا الـ M I small عبارة عن الـ
+
+391
+00:34:42,780 --> 00:34:49,860
+infimum للدالة على الفترة كلها الـ infimum يعني
+
+392
+00:34:49,860 --> 00:34:57,460
+الـ M I سماها عبارة عن الـ infimum للدالة F of X
+
+393
+00:34:57,460 --> 00:35:02,860
+حيث X موجودة على I وكأنه في الواقع أخذ الـ
+
+394
+00:35:02,860 --> 00:35:07,520
+partition هو عبارة عن نقطيناللي عبارة عن a و مين و
+
+395
+00:35:07,520 --> 00:35:12,800
+b ال partition بس a و b في هذا الحلق و جالك اللي
+
+396
+00:35:12,800 --> 00:35:18,020
+هو .. ليش .. هلجيت تشوفوا ال mi capital عبارة عن
+
+397
+00:35:18,020 --> 00:35:21,860
+ال supreme لل f of x such that x element in I
+
+398
+00:35:21,860 --> 00:35:27,780
+بقولك الآن إذن .. إذن mi ال mi small مضروبة في طول
+
+399
+00:35:27,780 --> 00:35:32,120
+الفترة يعني ال partition واحد لأن ال partition a و
+
+400
+00:35:32,120 --> 00:35:39,750
+b بس أصغر أو يساوياللي هو اللوفاف طبيعي طبيعي لأن
+
+401
+00:35:39,750 --> 00:35:45,570
+هذا واحد من مين من ال lower sums، بظبط؟ وهذا أصلا
+
+402
+00:35:45,570 --> 00:35:49,170
+ال supremum لل lower sums فهيكون ال supremum أكبر
+
+403
+00:35:49,170 --> 00:35:52,670
+يساوي مين؟ واحد منهم، هذا زي ما أقول أنها lower
+
+404
+00:35:52,670 --> 00:35:58,450
+sum على partition في A و BSimilarly, M I في الـ B
+
+405
+00:35:58,450 --> 00:36:03,590
+minus A أكبر أو ساوي ال other sum of F، ليه؟ لأن
+
+406
+00:36:03,590 --> 00:36:07,470
+هذا عبارة عن واحد من ال other sums و هذا عبارة عن
+
+407
+00:36:07,470 --> 00:36:10,210
+ال N في المملكة و ليه ال other sums فطبيعي هيكون
+
+408
+00:36:10,210 --> 00:36:14,260
+ال U of F أكبر أو ساوي B minus Ato be more
+
+409
+00:36:14,260 --> 00:36:18,360
+specific for every B element in B of I نحن لدينا M
+
+410
+00:36:18,360 --> 00:36:22,140
+I في B minus A أصغر أو يساوي L, B و F لأن هذا واحد
+
+411
+00:36:22,140 --> 00:36:28,800
+من ال partitions قلنا اللي هي لفترة I نفس الشيء
+
+412
+00:36:28,800 --> 00:36:34,800
+فبصير عند ال L of B و A F أصغر أو يساوي اللي هو ال
+
+413
+00:36:34,800 --> 00:36:40,060
+U, B و F أصغر أو يساوي M I في B minus Aمعروف هذا
+
+414
+00:36:40,060 --> 00:36:43,580
+أنا مش حاجة لزمنه أصلاً فبصير mi أصغر سواء ل و بف
+
+415
+00:36:43,580 --> 00:36:48,060
+و ل و بف أصغر سواء mi في ال b-a اللي وضحته هناك
+
+416
+00:36:48,060 --> 00:36:54,640
+أوضح من اللي مكتوب هناك واضح أه نيجي لنظرية اللي
+
+417
+00:36:54,640 --> 00:37:00,630
+عندى هذهTheorem بتقول لت I بساوة A وB and لت F من
+
+418
+00:37:00,630 --> 00:37:05,490
+I لR بيه bounded function وفهمنا ليش احنا بنقول
+
+419
+00:37:05,490 --> 00:37:08,410
+bounded then the lower integral L of F and the
+
+420
+00:37:08,410 --> 00:37:12,090
+upper integral U of F on I exist moreover ال L of
+
+421
+00:37:12,090 --> 00:37:15,330
+F أشمالها أصغر ساوية U of F طبعا ال existence سبب
+
+422
+00:37:15,330 --> 00:37:18,650
+ال existence كله اللي هو انه ال function bounded
+
+423
+00:37:18,650 --> 00:37:21,110
+مثلا bounded كل اللي هنا الحسابات اللي على أساس ال
+
+424
+00:37:21,110 --> 00:37:25,350
+supernormal information موجودةلأن اللي قال الـ U
+
+425
+00:37:25,350 --> 00:37:29,170
+of F أصغر ساوي مين؟ U بقى، U of F كلام سهل، شوف
+
+426
+00:37:29,170 --> 00:37:32,210
+إيش بدنا ناخد بتاخد بي واحد و بي اتنين بي أي two
+
+427
+00:37:32,210 --> 00:37:36,210
+partitions of I، ماشي؟ لأن then by لمّا اللي حكينا
+
+428
+00:37:36,210 --> 00:37:40,150
+قبل شوية عنها، اللي قال بي واحد و أف أصغر ساوي U
+
+429
+00:37:40,150 --> 00:37:44,350
+بي اتنين of F، ماشي الحال؟ لأي two partitions،
+
+430
+00:37:44,350 --> 00:37:48,270
+ثبتلي واحدة منهم الآن، خلّي اللي هو بي اتنين of is
+
+431
+00:37:48,270 --> 00:37:52,560
+fixedماشي صارت هذه .. هذه القيمة صارت .. بنحكي عن
+
+432
+00:37:52,560 --> 00:37:56,980
+عدد محدد ماشي بـ 2 arbitrarily صح لكن الان انا بدي
+
+433
+00:37:56,980 --> 00:38:01,020
+ثابته وهذه المتغيرة صار عند الان ال U B 2 و F
+
+434
+00:38:01,020 --> 00:38:07,940
+عبارة عن upper bound of the set of all اللي هي مين
+
+435
+00:38:07,940 --> 00:38:13,790
+ال B I و F على أي partitionطيب هذا upper bound
+
+436
+00:38:13,790 --> 00:38:19,270
+فبنقله في قفل هذه اللي هو ال minimum الهن ال
+
+437
+00:38:19,270 --> 00:38:22,470
+supremum الهن مظبوط اللي هو ال least upper bound
+
+438
+00:38:22,470 --> 00:38:26,350
+إذا ال least upper bound أكيد أصغر أو شومين ال
+
+439
+00:38:26,350 --> 00:38:32,340
+upper bound كمان مرةطيب، الآن therefore U B 2 و F
+
+440
+00:38:32,340 --> 00:38:37,820
+is an upper bound of هذه الست ماشي؟ و هذه الست ال
+
+441
+00:38:37,820 --> 00:38:42,500
+supremum لها إيش اسمه؟ L of F إذا أكيد اللي هو ال
+
+442
+00:38:42,500 --> 00:38:45,220
+supremum اللي هو ال least upper bound اللي هو ال L
+
+443
+00:38:45,220 --> 00:38:51,620
+of F أصغر أو يساوي واحد من ال upper bounds، مظبوط؟
+
+444
+00:38:51,620 --> 00:38:58,990
+أي سؤال؟واضح ها؟ الان خلصها من هذه الان similarly
+
+445
+00:38:58,990 --> 00:39:04,390
+since B2 was arbitrarily partition of I صارت الان
+
+446
+00:39:04,390 --> 00:39:10,230
+عند L of F أصغر أو يساوي UB2 of F يعني صارت هذه
+
+447
+00:39:10,230 --> 00:39:17,530
+عدد أصغر أو يساوي ال UB2 of F for any partition B2
+
+448
+00:39:18,500 --> 00:39:22,560
+الان صارت هذه عبارة عن lower bound لها لهذه ال
+
+449
+00:39:22,560 --> 00:39:26,200
+collection lower bound لها اذا هذه lower bound
+
+450
+00:39:26,200 --> 00:39:30,160
+اصغر او يساوي ال greatest lower bound مين ال
+
+451
+00:39:30,160 --> 00:39:35,200
+greatest lower bound لهدول اللي هو ال L اللي هو ال
+
+452
+00:39:35,200 --> 00:39:45,700
+U of F اذا صار عند ال L of F اصغر او يساوي U of F
+
+453
+00:39:45,700 --> 00:39:48,360
+اي سؤال؟
+
+454
+00:39:51,810 --> 00:39:56,530
+واضحة؟ ان في سؤال كان في ريال واحد زي هيك بنحل على
+
+455
+00:39:56,530 --> 00:39:59,690
+هيك اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+456
+00:39:59,690 --> 00:40:00,510
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+457
+00:40:00,510 --> 00:40:01,130
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+458
+00:40:01,130 --> 00:40:01,850
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+459
+00:40:01,850 --> 00:40:06,550
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+460
+00:40:06,550 --> 00:40:13,540
+اربع اتنين اربع اعدد هذا هو اللي هو اللي اللي اللي
+
+461
+00:40:13,540 --> 00:40:17,340
+اللي المتغير صار عند العدد هذا أصغر أو شاوي كل
+
+462
+00:40:17,340 --> 00:40:22,080
+اللي هو أعضاء العائلة اللي بتحكي عنها إذا صار الآن
+
+463
+00:40:22,080 --> 00:40:27,580
+هذا الالوفاف عبارة عن lower bound ofthe collection
+
+464
+00:40:27,580 --> 00:40:32,600
+of all U, P, T و F عالميا على ال partitions هذه
+
+465
+00:40:32,600 --> 00:40:36,260
+مادام هذا صار عبارة عن lower bound إذا هذا lower
+
+466
+00:40:36,260 --> 00:40:40,580
+bound أصغر أو يساوي ال greatest lower bound اللي
+
+467
+00:40:40,580 --> 00:40:43,860
+هو اللي بنسميه ال infimum إذا صارت ال L و F أصغر
+
+468
+00:40:43,860 --> 00:40:47,000
+أو يساوي ال infimum لهدول ال infimum لهدول مين هو
+
+469
+00:40:47,000 --> 00:40:52,940
+ال U و Fالـ U of F هو الـ infimum لكل الـ U, B, T,
+
+470
+00:40:53,280 --> 00:40:58,040
+2 و F such that B2 element in the set of all
+
+471
+00:40:58,040 --> 00:41:07,220
+partitions نيجي الآن لبعده الـ Definition الان ..
+
+472
+00:41:07,220 --> 00:41:16,080
+الان احنا زغرنا ال other sums و كبرنا ال other
+
+473
+00:41:16,080 --> 00:41:22,680
+sumsيوم مالتجهن مع بعض بنسمي اللي هو الالتقاء هذا
+
+474
+00:41:22,680 --> 00:41:26,320
+أو الرقم اللي التقن فيه هو قيمة الـ Remain
+
+475
+00:41:26,320 --> 00:41:30,800
+Integral للفункشن F على الفترة المذكورة وهذا هو
+
+476
+00:41:30,800 --> 00:41:35,040
+التعريف let I بسوء A و B and let F من I لعند R be
+
+477
+00:41:35,040 --> 00:41:39,060
+a bounded function then F is said to be Remain
+
+478
+00:41:39,060 --> 00:41:46,480
+Integrable on I if L of Fاللي هو عبارة عن الـ
+
+479
+00:41:46,480 --> 00:41:54,140
+Supremum للـ Lower Bounds للـ Lower Sums بساوي ال
+
+480
+00:41:54,140 --> 00:42:00,320
+Infimum لل Upper Sums يوم ما يتساون هذولة بنسمي
+
+481
+00:42:00,320 --> 00:42:03,780
+الـ Function is Remain Integrable وفي هذه الحالة
+
+482
+00:42:03,780 --> 00:42:06,860
+بيكون القيمة المشتركة هذه هي اللي بنسميها الـ
+
+483
+00:42:06,860 --> 00:42:13,740
+Integration من A ل B F of X D of Xدكتور ان الملحنة
+
+484
+00:42:13,740 --> 00:42:17,420
+احنا بدنا نجيب مساحة كذا كذا احنا ال .. المساحة
+
+485
+00:42:17,420 --> 00:42:21,480
+إذا كان فوق الآن إذا كان تحت بيكون سالب المساحة
+
+486
+00:42:21,480 --> 00:42:24,680
+إذا كان مخلوط بيصير .. إذا كان فوق و تحت معناته
+
+487
+00:42:24,680 --> 00:42:28,180
+بيصير جزء مساحة و جزء سالب مساحة عشان نجد مساحته
+
+488
+00:42:28,180 --> 00:42:30,980
+بالظبط تاخد ال absolute بتقطع لذاك و تاخد ال
+
+489
+00:42:30,980 --> 00:42:34,340
+absolute value اللي بيطلع اللي هو المساحة عشان
+
+490
+00:42:34,340 --> 00:42:39,580
+نجيبوا مساحته و نجسم الملحنة هذا لمستطيلة صح؟
+
+491
+00:42:41,500 --> 00:42:46,400
+كمستطيل و بيجيبوا مجموع مستطلاق بدين المنحنى بديك
+
+492
+00:42:46,400 --> 00:42:51,760
+مساحة تحت المنحنى لما تاخد ال upper sums و ال
+
+493
+00:42:51,760 --> 00:42:55,260
+lower sums و تاخد ال supremum و تاخد ال infimum و
+
+494
+00:42:55,260 --> 00:42:59,080
+يكون ال supremum بساوي ال infimum بتلح هو المساحة
+
+495
+00:42:59,080 --> 00:43:04,990
+تحت المنحنى في حالة ال positive functionsفي حالة
+
+496
+00:43:04,990 --> 00:43:08,710
+الـ negative المخلوق بيصير integration بيصير قيمة
+
+497
+00:43:08,710 --> 00:43:12,170
+integration قيمة ال integration لا تعبر عن المساحة
+
+498
+00:43:12,170 --> 00:43:16,670
+اللي هو بالضبط إلا في حالة ال other إلا في حالة ال
+
+499
+00:43:16,670 --> 00:43:19,970
+positive ال function في حالة ال negative بتعبر على
+
+500
+00:43:19,970 --> 00:43:24,170
+سلب المساحة في حالة إشي فوج و إشي تحت بيصير اللي
+
+501
+00:43:24,170 --> 00:43:26,950
+هو .. لأ المساحات بت cancel بعضها و بيصير قيمة
+
+502
+00:43:26,950 --> 00:43:30,930
+integrationبيدك المساحات من وسط ال integration
+
+503
+00:43:30,930 --> 00:43:33,110
+انها تستخدم ال integration في إيجاد المساحة
+
+504
+00:43:33,110 --> 00:43:37,570
+بتجزئها لإيش إلى أجزاء وين بتقطع محور السينات يعني
+
+505
+00:43:37,570 --> 00:43:40,550
+بتحدد وين موجبة و وين سالبة بتاخد ال absolute
+
+506
+00:43:40,550 --> 00:43:43,410
+value حتى لو ماكنشت يعرف مين الموجبة ومين السالبة
+
+507
+00:43:43,410 --> 00:43:46,570
+وبيطلع اللي هو عن طريق ال integration بتوجد قيمة
+
+508
+00:43:46,570 --> 00:43:52,290
+مين المساحة لكن في حالة الدالة موجبة على كل الفترة
+
+509
+00:43:52,290 --> 00:43:59,410
+ال integration هو بالظبط المساحة طيبصلى على النبي
+
+510
+00:43:59,410 --> 00:44:01,990
+عليه الصلاة والسلام عرفنا الـ Romantic Grability
+
+511
+00:44:01,990 --> 00:44:06,470
+وقلنا اللي هو .. اللي هو الاشياء المشتركة اللي
+
+512
+00:44:06,470 --> 00:44:11,290
+حصلنا عليها الآن بنعرف برضه كتعريف من A ل B F of X
+
+513
+00:44:11,290 --> 00:44:15,930
+DX بساوي ناقص من B ل A F of X DX وبنعرف كتعريف أن
+
+514
+00:44:15,930 --> 00:44:19,830
+ال integration من A ل A F of X DX H بساوي سفر اطلع
+
+515
+00:44:19,830 --> 00:44:25,120
+فوق خليني أخد مثال وننهي بهذا المثالالآن .. و هذا
+
+516
+00:44:25,120 --> 00:44:30,080
+المثال احنا .. يعني .. كنا ناخد .. نفس المثال اللي
+
+517
+00:44:30,080 --> 00:44:33,760
+ناخده في ال calculus خلّينا نحكي عنه بالتفصيل الان
+
+518
+00:44:33,760 --> 00:44:37,480
+example show that g of x بساوة x is integrable on
+
+519
+00:44:37,480 --> 00:44:41,700
+0 و 1 بدنا نثبت أنه الدالة اللي هي g of x اللي
+
+520
+00:44:41,700 --> 00:44:45,220
+بنعرفها اللي هي المثال البسيط بساوة x عبارة عن
+
+521
+00:44:45,220 --> 00:44:52,130
+integrable عالميا على اللي هو الفترة 0 و 1الان انا
+
+522
+00:44:52,130 --> 00:44:56,270
+لتسهيل عملية الحسابات هاخد عائلة من ال partitions
+
+523
+00:44:56,270 --> 00:45:03,050
+معينة هذه العائلة بتسهيل الحسابات طب بنفع في ضوء
+
+524
+00:45:03,050 --> 00:45:07,910
+العلاقات اللي هنشوفها كيف توصلنا بالظبط ان ال L of
+
+525
+00:45:07,910 --> 00:45:12,830
+F بساوة ال U of F و لخصوصية الحسابات ده نشوف كيف
+
+526
+00:45:12,830 --> 00:45:21,760
+عندى ال F of X بساوة Xعنديها بديها من 0 لعند مين؟
+
+527
+00:45:21,760 --> 00:45:28,580
+لعند 1 هذه y بساوة x على الفترة 0 و 1 ايش بدنا
+
+528
+00:45:28,580 --> 00:45:34,580
+نسوي؟ بدنا نيجي اللي هو ان نعمل partition بين هذا
+
+529
+00:45:34,580 --> 00:45:39,540
+ال partition بديه يسهل الإحسابات فأسهل شيء بدي
+
+530
+00:45:39,540 --> 00:45:44,640
+أجزء هذه الفترة من 0 ل1 لN من الأجزاء و بديها تكون
+
+531
+00:45:44,640 --> 00:45:49,430
+كلها متساويةبنفع، أه، هينفع، هتشوف كيف اللي هو هذا
+
+532
+00:45:49,430 --> 00:45:52,650
+نفع في ضوء العلاقات بين اللي هو الـ Supremum و
+
+533
+00:45:52,650 --> 00:45:57,050
+الانفموع المجموعة الأكبر و المجموعة الأصغر و أيضًا
+
+534
+00:45:57,050 --> 00:46:01,130
+في ضوء ال limits المعينة اللي هان اللي هتيجي تخلي
+
+535
+00:46:01,130 --> 00:46:05,010
+اللي هو علاقة توصّل إلى اللي بدنيها، تفهم علش؟
+
+536
+00:46:05,010 --> 00:46:10,610
+ماقولهم كده، هذا صار عندي، هذا Zeroأما ده بدأت
+
+537
+00:46:10,610 --> 00:46:13,510
+تجزئها طولها واحد تجزئها الان من الفتراء sub
+
+538
+00:46:13,510 --> 00:46:16,130
+intervals إذا كل واحدة واحدة على الان هذا التاني
+
+539
+00:46:16,130 --> 00:46:20,130
+اتنين على الان التالتة تلاتة على الان تلاتة على
+
+540
+00:46:20,130 --> 00:46:24,770
+الان لما نصل للفترة النموذجية xk اللي هي تلقى k
+
+541
+00:46:24,770 --> 00:46:30,610
+minus واحد على ان وk على ان هذا اللي هي xk minus
+
+542
+00:46:30,610 --> 00:46:36,670
+واحد وهذا ال xk وهذا xنوت و اد اكس واحد الى اخرى
+
+543
+00:46:36,670 --> 00:46:39,790
+لان ما اصل الاخر واحدة اللى هى n على n اللى هى
+
+544
+00:46:39,790 --> 00:46:45,150
+واحدة ماشي الحالة هذا اللى عندى اللى .. لو اجيت
+
+545
+00:46:45,150 --> 00:46:48,190
+حسبت الان مدى احسب هذا ال partitions اللى صار عندى
+
+546
+00:46:48,190 --> 00:46:53,930
+عبارة عن zero و الواحدة الان و اتنين على n لما اصل
+
+547
+00:46:53,930 --> 00:46:58,490
+لعند ال n على n اللى هى ايش الواحدة هذه عائلة ال
+
+548
+00:46:58,490 --> 00:47:04,620
+partitions اللى اختارتها ماشي شوفوا عليها ال nلو
+
+549
+00:47:04,620 --> 00:47:09,460
+جيت حسبت اللي هو طول الـ interval واحدة لان لو بده
+
+550
+00:47:09,460 --> 00:47:16,960
+أحسب الآن L لل partition هذا اللي هو مين هو L ال F
+
+551
+00:47:16,960 --> 00:47:23,840
+عندي و ال P N هتساوي عبارة عن ال summation عارفين
+
+552
+00:47:23,840 --> 00:47:29,780
+انتوا ال summation اللي هو M small K في X K ناقص X
+
+553
+00:47:29,780 --> 00:47:36,290
+K minus واحد K من عند واحد عند N ويساويالان ال MK
+
+554
+00:47:36,290 --> 00:47:41,890
+في الفترة الأولى ايش هيكون عنده؟ صفر في الفترة
+
+555
+00:47:41,890 --> 00:47:47,430
+التانية ايش هيكون؟ واحدة على الانكريزين جدا اللي
+
+556
+00:47:47,430 --> 00:47:50,150
+بعدها اتنين على انواع و هكذا
+
+557
+00:47:52,920 --> 00:47:57,520
+الـ Mk in general إيش هيصير عنده الـ Mk وإيش
+
+558
+00:47:57,520 --> 00:48:03,020
+المساحة هي K minus واحد على مين على هذا اللي هو
+
+559
+00:48:03,020 --> 00:48:08,280
+طول تبع مين الـ Mk واضحة؟ لأن الـ infimum على
+
+560
+00:48:08,280 --> 00:48:12,760
+الفترة هذه النموذجية اللي هو ال .. ال .. ال
+
+561
+00:48:12,760 --> 00:48:17,920
+infimum عليها اللي هو أول واحدة لإنها increasing
+
+562
+00:48:17,920 --> 00:48:22,630
+واضحة تصورفلان هذه ثابتة أنا اختارتها أصلا ثابتة
+
+563
+00:48:22,630 --> 00:48:26,430
+طول الفترة ثابتة اللي هو 1 على n بيصير هذا إيش n
+
+564
+00:48:26,430 --> 00:48:32,670
+تربيع كامل عند واحد لعند مين لعند n واضح أه ويساوي
+
+565
+00:48:32,670 --> 00:48:38,110
+1 على n تربيع فيه ال summation هذا اللي هو عبارة
+
+566
+00:48:38,110 --> 00:48:42,830
+عن بيبدأ من 0 زائد 1 ولمّا يصل لعند مين لعند n
+
+567
+00:48:42,830 --> 00:48:49,760
+ناقص 1هذا بعرف ما هو مجموعه ويساوي 1 الان تربيع في
+
+568
+00:48:49,760 --> 00:48:54,760
+هذا ان لما نكون من واحد لعند ان ان فان زاد واحد
+
+569
+00:48:54,760 --> 00:48:58,440
+الان على اتنين الان هذا من وين واحد لعند ان ناقص
+
+570
+00:48:58,440 --> 00:49:03,540
+واحد فان ناقص واحد لكل عالمين يا جماعة على اتنين
+
+571
+00:49:03,540 --> 00:49:09,580
+ويساوي الان اعملي هذا بيطلع نص عندي ويساوي نص في
+
+572
+00:49:09,580 --> 00:49:15,150
+اللي هو ان تربيع ناقص من انعلى أن تربيعه بيصير
+
+573
+00:49:15,150 --> 00:49:22,650
+واحد ناقص واحدة لان صح ولا لأ طيب similarly for me
+
+574
+00:49:22,650 --> 00:49:29,430
+لأن لما بدي أخد اللي قاله و أفله اه ال .. ال ..
+
+575
+00:49:29,430 --> 00:49:36,930
+بعدين شوف عليهم الآن القبر للأف و بي أن بنفس
+
+576
+00:49:36,930 --> 00:49:44,250
+السلوب بيصير عندي عبارة عن summation mkفي xk-xk-1
+
+577
+00:49:44,250 --> 00:49:49,630
+k من عند 1 لعند n الان ال mk ال m واحد هيه لان
+
+578
+00:49:49,630 --> 00:49:54,010
+المتنين هيه إذا ال mk هي عبارة عن مين؟ k على n
+
+579
+00:49:54,010 --> 00:49:59,070
+لأنه increasing زي ما قلنا ويساوي صماشen k على n
+
+580
+00:49:59,070 --> 00:50:04,800
+في 1 على nK من عند واحد لعند ان ويساوي summation
+
+581
+00:50:04,800 --> 00:50:07,640
+واحدة لان تربية في summation لK من واحد لان لان
+
+582
+00:50:07,640 --> 00:50:12,800
+اللي ان فان زائد واحد الان هو الكل مكسوب على اتنين
+
+583
+00:50:12,800 --> 00:50:17,400
+ويساوي نص في اللي هو بطلع عندي هذا عبارة عن واحد
+
+584
+00:50:17,400 --> 00:50:23,920
+زائد واحدة لان، مظبوط؟ طيب إذا انصار عندي الآن
+
+585
+00:50:23,920 --> 00:50:28,410
+حصلت على التاليزي ما شوفنا حسابيا جميعا من هنا
+
+586
+00:50:28,410 --> 00:50:34,530
+اطلع لفوق صار عندى الان LPNG او F عبارة عن نصف
+
+587
+00:50:34,530 --> 00:50:40,230
+واحد نقص واحدة الان UPNJ ايش بيساوي نصف واحد زائد
+
+588
+00:50:40,230 --> 00:50:48,330
+واحد على مين على الان واضح الان الان اه الان الان
+
+589
+00:50:48,330 --> 00:50:53,100
+الان انت بي .. عندى ال collection هذهالـ
+
+590
+00:50:53,100 --> 00:50:57,280
+collection هذه partitions B1 is a partition اللي
+
+591
+00:50:57,280 --> 00:51:03,740
+هو عبارة عن Zero و واحد B2 Zero نص و واحد B3 Zero
+
+592
+00:51:03,740 --> 00:51:09,160
+و تلت و تلتين و واحد و هكذا إذا هذه عائلة من ال
+
+593
+00:51:09,160 --> 00:51:14,060
+partitionsجزء من مين؟ من الـ partitions العامة
+
+594
+00:51:14,060 --> 00:51:17,100
+يعني ال .. ال part .. هي the set of all partitions
+
+595
+00:51:17,100 --> 00:51:22,220
+هذه أكيد جزئية من the set of all partitions لمين؟
+
+596
+00:51:22,220 --> 00:51:25,980
+لل I اللي عنده اللي هي الفترة من مين؟ من 01 إذا
+
+597
+00:51:25,980 --> 00:51:31,500
+هذه مجموعة جزئية من هذه، مظبوط؟ طيب، الآن لو أجينا
+
+598
+00:51:31,500 --> 00:51:35,820
+أخدنا اللي هو ال set of partitions هذه أكيد ال
+
+599
+00:51:35,820 --> 00:51:39,580
+supreme على هذهالان ال .. ال .. ال .. ال .. ال ..
+
+600
+00:51:39,580 --> 00:51:44,820
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+601
+00:51:44,820 --> 00:51:45,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+602
+00:51:45,160 --> 00:51:48,400
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+603
+00:51:48,400 --> 00:51:48,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+604
+00:51:48,420 --> 00:51:50,120
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+605
+00:51:50,120 --> 00:51:50,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+606
+00:51:50,220 --> 00:51:50,340
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+607
+00:51:50,340 --> 00:51:59,480
+.. ال .. ال .. ال .. ال .. ال ..
+
+608
+00:51:59,480 --> 00:52:02,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+609
+00:52:02,920 --> 00:52:09,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..such that
+
+610
+00:52:09,060 --> 00:52:14,120
+N element in N هذه اللي هي main ال collection of
+
+611
+00:52:14,120 --> 00:52:19,260
+all partitions ال B1 وB2 وB3 عند BN لو جينا أخدنا
+
+612
+00:52:19,260 --> 00:52:24,740
+ال supremumلكل القيم هذه هيكون أصغر أو يساوي الـ
+
+613
+00:52:24,740 --> 00:52:32,320
+Supremum لمين لل L of F و B such that B element in
+
+614
+00:52:32,320 --> 00:52:36,620
+B and B of I لأن collection of all partitions هذه
+
+615
+00:52:36,620 --> 00:52:41,940
+اللي هو تحتوى ال partitions هدولة واضح الحمد الله
+
+616
+00:52:41,940 --> 00:52:45,500
+الان ال Supremum على القيم هذه اللي هي مين القيم
+
+617
+00:52:45,500 --> 00:52:51,230
+كانت عندهاللي هو عبارة عن نص في واحد ناقص ميل واحد
+
+618
+00:52:51,230 --> 00:52:55,590
+علان ال supremum لهذه عبارة عن zero إذن بتظل هي
+
+619
+00:52:55,590 --> 00:53:00,590
+إيش بتساوي نص ال supremum للنص في واحد ناقص واحد
+
+620
+00:53:00,590 --> 00:53:05,070
+علان معايا؟
+
+621
+00:53:05,070 --> 00:53:16,470
+أي سؤال؟ طيب إذا هذا مين هو؟ هذا عبارة عن الأو ما
+
+622
+00:53:16,470 --> 00:53:21,170
+فاهم ولا لأ إذا صار عند ال L و ال F مثبتها هذه ال
+
+623
+00:53:21,170 --> 00:53:29,390
+L و ال F هيصير أكبر أو يساوي النص نحك طيب
+
+624
+00:53:29,390 --> 00:53:35,650
+similarly for me and for you الآن عندي حصلت على ال
+
+625
+00:53:35,650 --> 00:53:41,970
+U, F و B أن لهذه العائلة الان الان the set of all
+
+626
+00:53:41,970 --> 00:53:50,880
+U, F و B أنsuch that N element in N هذه العائلة
+
+627
+00:53:50,880 --> 00:53:53,900
+مجموعة جزئية من العائلة الكبيرة الـ B of I الـ
+
+628
+00:53:53,900 --> 00:54:00,940
+partitions للـ I إذن هذه الـ infimum لها هيصير
+
+629
+00:54:00,940 --> 00:54:10,580
+أكبر أو يساوي الـ infimum لـ U, F و B such that B
+
+630
+00:54:10,580 --> 00:54:18,550
+element in B of Iالـ collection هذه أصغر من الـ
+
+631
+00:54:18,550 --> 00:54:21,730
+collection هذه، بظبط؟ إذا صار الـ infimum على هذه
+
+632
+00:54:21,730 --> 00:54:25,610
+أكبر و ساوي الـ infimum على هذه الـ infimum لهذه
+
+633
+00:54:25,610 --> 00:54:27,470
+الـ collection و اللي هو الـ infimum في الواقع
+
+634
+00:54:27,470 --> 00:54:31,110
+لمين؟ الـ infimum لهذه الـ infimum لهذه ليش
+
+635
+00:54:31,110 --> 00:54:35,910
+هيساوي؟ نص فبصير عندي نص أكبر و ساوي الـ infimum
+
+636
+00:54:35,910 --> 00:54:38,430
+هذا اللي هو أكبر و ساوي هذا اللي هو هذا اللي هو
+
+637
+00:54:38,430 --> 00:54:44,010
+مين؟ الـ U of F إذا حصلنا على كمان حاجة إن الـ U
+
+638
+00:54:44,010 --> 00:54:52,790
+of Fأصغر أو يساوي نص اللخص المعلومتين هدولة ونحصل
+
+639
+00:54:52,790 --> 00:54:57,810
+على اللي بدناه من المعلومتين من المعلومتين اللي
+
+640
+00:54:57,810 --> 00:55:06,860
+صار عندى اللي هو L of Fاللي هو اكبر او يساوي نص
+
+641
+00:55:06,860 --> 00:55:10,920
+وانا بعرف ان دائما ال الوف ايش ماله اصغر او يساوي
+
+642
+00:55:10,920 --> 00:55:15,180
+ال يوف اف و ال يوف اف ايش حصلته اصغر او يساوي من
+
+643
+00:55:15,180 --> 00:55:20,360
+نص اذا هذا اللي خلى اللي هو ال partition اللي عندى
+
+644
+00:55:20,360 --> 00:55:23,540
+اللي سهل اللي اخترته او ال set of partitions انها
+
+645
+00:55:23,540 --> 00:55:28,580
+توصلني للنتيجة اللي بديها بيصير عندى ال الوف اصغر
+
+646
+00:55:28,580 --> 00:55:33,220
+او يساوي ال يوف اف و هذا بين النص التنتين اذا الوف
+
+647
+00:55:33,220 --> 00:55:40,650
+افبساوية وف اف بساوية نص وهذا معناه ان ال function
+
+648
+00:55:40,650 --> 00:55:45,770
+is reversible and integrable and ال integration من
+
+649
+00:55:45,770 --> 00:55:52,650
+zero ل واحد لل x dx بساوية نص و الله يعطيك العافية
+
+650
+00:55:52,650 --> 00:55:54,590
+و المرة القادمة نكملها
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/rKngzYKfO2U_raw.srt b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/rKngzYKfO2U_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1336de6334f1983fce3687e08cbc9d07799932da
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/rKngzYKfO2U_raw.srt
@@ -0,0 +1,2616 @@
+1
+00:00:05,150 --> 00:00:09,890
+بسم الله الرحمن الرحيم اليوم ان شاء الله عندنا
+
+2
+00:00:09,890 --> 00:00:15,270
+اللي هو المحاضرة رقم عشرة في مساق تحليل حقيقه
+
+3
+00:00:15,270 --> 00:00:21,130
+اتنين لطلبة الجامعة الإسلامية كلية العلوم قسم
+
+4
+00:00:21,130 --> 00:00:27,370
+الرياضيات اليوم ان شاء الله هنبدأ في chapter سبعة
+
+5
+00:00:28,110 --> 00:00:33,150
+اللي هو الجزء الثاني من المادة أو العصب الثاني
+
+6
+00:00:33,150 --> 00:00:37,130
+للمادة اللي هو حكينا عن ال derivatives اليوم نحكي
+
+7
+00:00:37,130 --> 00:00:42,170
+عن اللي هو the reman integral أو تكامل رمان هيتم
+
+8
+00:00:42,170 --> 00:00:45,730
+الحديث اليوم ان شاء الله في ال section الأول هنحكي
+
+9
+00:00:45,730 --> 00:00:51,450
+عن ال reman integrability أو قابلية تكامل الدالة
+
+10
+00:00:51,450 --> 00:00:56,270
+على اللي هو بالنسبة لرمانفي البداية هنحكي عن بعض
+
+11
+00:00:56,270 --> 00:01:00,410
+التعريف اللي هتوصلنا للي بدناياه في الموضوع اللي
+
+12
+00:01:00,410 --> 00:01:03,910
+هو الـ Riemann Integrability الان هاخدلنا function
+
+13
+00:01:03,910 --> 00:01:11,090
+F F من some interval I نفترض ان الدالة اللي عند F
+
+14
+00:01:11,090 --> 00:01:18,850
+من A و B لعند R is a bounded function الان
+
+15
+00:01:18,850 --> 00:01:22,050
+بدنا نعرف بعض التعريفات اللي بتخودنا الى الـ
+
+16
+00:01:22,050 --> 00:01:26,950
+Riemann Integrabilityأول اشي بدنا نعرف شو معناه
+
+17
+00:01:26,950 --> 00:01:30,750
+partition لو كانت هذه الدانلة مثلا هي Y بالساوية F
+
+18
+00:01:30,750 --> 00:01:36,170
+of X على الفترة المذكورة وكانت من A ل B اللي هو ال
+
+19
+00:01:36,170 --> 00:01:41,650
+domain بدنا الآن نيجي نجزق المنطقة اللي هي الفترة
+
+20
+00:01:41,650 --> 00:01:47,210
+من A ل B اللي هو خلّي نسمي هذا X noteهذا نسميه x1
+
+21
+00:01:47,210 --> 00:01:51,750
+هذا نسميه x2 لعند ما أصل للفترة النموذجية اللي
+
+22
+00:01:51,750 --> 00:01:58,270
+بتسميها xk-1 لعند ال xk وهذا أسميها اللي هي xn
+
+23
+00:01:58,270 --> 00:02:06,110
+الان الفترة من a لb أنا جزقتها بx0 وx1 وx2 لعند xn
+
+24
+00:02:06,110 --> 00:02:13,370
+هذه التجزية بتحطها في 6 وسميها بي بتساوي x0و X1 و
+
+25
+00:02:13,370 --> 00:02:19,410
+X2 لعند Xn هذا اللي بسميه is a partition of the
+
+26
+00:02:19,410 --> 00:02:26,510
+interval A و B إذا عندي I subset من R closed
+
+27
+00:02:26,510 --> 00:02:30,430
+bounded interval ال ordered set هذه اللي حكيتها
+
+28
+00:02:30,430 --> 00:02:34,410
+كتبتها ان هي عبارة عن X0 و X1 لعند Xn بنسميها a
+
+29
+00:02:34,410 --> 00:02:39,390
+partition of I بحيث انه A X0 أصغر من X1 لعند ما
+
+30
+00:02:39,390 --> 00:02:45,060
+أقول أصغر من Xnالان الـ function عندى F من I لعند
+
+31
+00:02:45,060 --> 00:02:49,980
+R bounded function on I الان بدى أعرف بعض
+
+32
+00:02:49,980 --> 00:02:54,660
+التعريفات اللى هتلزمني برضه في اللى هو الوصول إلى
+
+33
+00:02:54,660 --> 00:02:59,160
+الـ Remain Integrability أول تعريف بدى أخد الآن
+
+34
+00:02:59,160 --> 00:03:07,000
+أسمي M1 هو عبارة عن الـ supremum للـ function في
+
+35
+00:03:07,000 --> 00:03:12,990
+المنطقة هذهالـ M1 بدي أسميه عبارة عن الـ Supremum
+
+36
+00:03:12,990 --> 00:03:16,810
+للدالة F of X والـ Supremum موجودة لأن الـ F
+
+37
+00:03:16,810 --> 00:03:21,870
+أشمالها is bounded السوب للـ F of X حيث الـ X
+
+38
+00:03:21,870 --> 00:03:29,310
+موجودة في الفترة من X note لعند X1 هذه اللي هي بدي
+
+39
+00:03:29,310 --> 00:03:34,570
+أسميها M1 Capital M1 Small اللي هي عبارة عن ال
+
+40
+00:03:34,570 --> 00:03:38,960
+Infimumلـ .. لـ الـ function hand اللي عبارة عن
+
+41
+00:03:38,960 --> 00:03:45,400
+الـ infimum لـ F of X حيث X تنتمي إلى الفترة X
+
+42
+00:03:45,400 --> 00:03:50,440
+naught و X واحد in general .. in general في الفترة
+
+43
+00:03:50,440 --> 00:03:55,280
+النموذجية بدي أسمي M K هي عبارة عن .. الآن في
+
+44
+00:03:55,280 --> 00:03:59,850
+الفترة هذهعالفترة هذه الـ supremum للـ function
+
+45
+00:03:59,850 --> 00:04:06,170
+هنا بدي اسميها M K K بسوء F of X such that X
+
+46
+00:04:06,170 --> 00:04:13,030
+element in X K minus واحد لعند X K و ال M small K
+
+47
+00:04:13,030 --> 00:04:19,330
+هسميها اللي هي بنفس اللي هسميت X واحد اللي هي ال
+
+48
+00:04:19,330 --> 00:04:23,370
+infimum لل F of X في الفترة من X K minus واحد لعند
+
+49
+00:04:23,370 --> 00:04:30,300
+X K على سبيل المثالالـ M K يعني هيها هذا اللي هي M
+
+50
+00:04:30,300 --> 00:04:36,340
+K Small والـ M K Capital على سبيل المثال هيها
+
+51
+00:04:36,340 --> 00:04:42,640
+هيقبتها هذا الـ M K Capital إذن الآن عندي سميت
+
+52
+00:04:42,640 --> 00:04:45,560
+اللي هي الـ M K Capital هي الـ Supremum والـ M K
+
+53
+00:04:45,560 --> 00:04:49,740
+Small هي عبارة عن الـ Infimum وهلجيت حنشوف إيش
+
+54
+00:04:49,740 --> 00:04:55,560
+دواعي هذه التسمية أو ليش سمينا هيكالان بدنا نعرف
+
+55
+00:04:55,560 --> 00:05:00,380
+اللي هو .. بدنا
+
+56
+00:05:00,380 --> 00:05:04,380
+نعرف الآن اللي هو حاجة اسمها lower sum و حاجة
+
+57
+00:05:04,380 --> 00:05:12,540
+اسمها ايش ال upper sum الان لو جيت بعد ما عملت ال
+
+58
+00:05:12,540 --> 00:05:21,020
+partition اللي عندي هذا و جيت أخدت اللي هي
+
+59
+00:05:28,550 --> 00:05:32,770
+أخدت الـ partition B اللي عندي هذا هذا ال
+
+60
+00:05:32,770 --> 00:05:40,110
+partition B هو عبارة عن X0 X1 X2 اللي عند XN جيت
+
+61
+00:05:40,110 --> 00:05:44,590
+أنا أخدت اللي هو الـ supremum للدالة في هذه
+
+62
+00:05:44,590 --> 00:05:51,550
+المنطقة والتي تكون طبعا هنا شكلها اللي هي سميتها
+
+63
+00:05:51,550 --> 00:06:02,170
+M1 في X1 نقص X0و جيت ضفت لها برضه ال supremum
+
+64
+00:06:02,170 --> 00:06:08,030
+للدالة في المنطقة هذه اللي هي زائد M2 سميت ال
+
+65
+00:06:08,030 --> 00:06:15,230
+supremum اللي هو M2 في X2-X0 لما نوصلت لآخر واحدة
+
+66
+00:06:15,230 --> 00:06:20,750
+بنفس الأسلوب أخدت اللي هو ال supremum اللي هي ال
+
+67
+00:06:20,750 --> 00:06:26,870
+supremum طبعا M1 عندىالتي هي طول الريانج اللي عندى
+
+68
+00:06:26,870 --> 00:06:32,850
+مضروب في مين اللي هو x1-x0 فبتطلع هذه المنطقة
+
+69
+00:06:32,850 --> 00:06:41,710
+بالظبط مساحة اللي عندى الان بضل أجمع بنفس الأسلوب
+
+70
+00:06:41,710 --> 00:06:45,830
+بجمحن بنفس الأسلوب عندى
+
+71
+00:06:53,690 --> 00:06:58,050
+هذا المجموع اللي بالازرق هو اللي بنسميه هسميه ال
+
+72
+00:06:58,050 --> 00:07:03,170
+other sum هذا ال other sum اللي هو ال other لل F
+
+73
+00:07:03,170 --> 00:07:08,090
+للدالة F بواسطة
+
+74
+00:07:08,090 --> 00:07:12,830
+مين ال partition B إذا ال other sum هذا اللي هو
+
+75
+00:07:12,830 --> 00:07:17,830
+عبارة عن اللي هو لل function بواسطة ال partition B
+
+76
+00:07:17,830 --> 00:07:20,410
+يعني ال other sum هذا يعتمد على ال F ويعتمد على
+
+77
+00:07:20,410 --> 00:07:25,690
+مين؟ على ال partition اللي عنديالأن similarly بدي
+
+78
+00:07:25,690 --> 00:07:31,190
+آجي أعرف اللي هو ال lower sum إذا ال upper sum
+
+79
+00:07:31,190 --> 00:07:38,890
+بيساوي ال summation ل X K نقص X K minus واحد مضروب
+
+80
+00:07:38,890 --> 00:07:43,950
+في ال M K capital K من عند واحد لعند N هذه اللي
+
+81
+00:07:43,950 --> 00:07:48,930
+بيسميها ال upper sum similarly بدي أعرف مين اللي
+
+82
+00:07:48,930 --> 00:07:56,170
+هو ال lower sumللـ F و لل D هيساوي الآن بدل ما أخد
+
+83
+00:07:56,170 --> 00:07:59,330
+اللي هو ال suprem أعلى قيمة بتاخد اللي هو ال
+
+84
+00:07:59,330 --> 00:08:05,390
+infimum بيصير عندي اللي هو summation X K minus X K
+
+85
+00:08:05,390 --> 00:08:10,790
+minus واحد في ال M K small K من عند واحد لعند N
+
+86
+00:08:10,790 --> 00:08:15,050
+هذا اللي هو عبارة عن ال lower sum في الواقع هو
+
+87
+00:08:15,050 --> 00:08:21,350
+هيكون المنطقة اللي بالأحمر هذهبناء على إني باخد
+
+88
+00:08:21,350 --> 00:08:27,670
+أنا اللي هو الارتفاع هو عبارة عن ال M K Small اللي
+
+89
+00:08:27,670 --> 00:08:33,410
+هو ال minimum لقيمة الدالة على كل المنطقة وهكذا
+
+90
+00:08:33,410 --> 00:08:38,030
+لما أصل لآخر واحدة فبصير عندى هذا ال summation
+
+91
+00:08:38,030 --> 00:08:43,890
+لهذه اللي هي المستطيلات
+
+92
+00:08:43,890 --> 00:08:51,510
+بناء على ال partition اللي عندىهي عبارة عن مين؟ عن
+
+93
+00:08:51,510 --> 00:08:56,190
+اللي هو اللا وارسم طبعا ناخد الدالة اللي هي في
+
+94
+00:08:56,190 --> 00:09:00,670
+منطقة موجة بأساس إنه اللي هي يكون أكثر توضيحا طبعا
+
+95
+00:09:00,670 --> 00:09:04,650
+لو منطقة سالبة برضه باخد نفس الأسلوب لكن بيصير
+
+96
+00:09:04,650 --> 00:09:08,810
+اللي هو بديل مساحة بيصير سالب مساحة أو مخلوطة بين
+
+97
+00:09:08,810 --> 00:09:13,070
+مساحة موجة مساحة سالبة و بت cancel بعض إلى أن أنا
+
+98
+00:09:13,070 --> 00:09:16,350
+أخدتها على فترة موجة بأساس اللي هو تسهل مسعملية
+
+99
+00:09:16,820 --> 00:09:22,620
+اللي هي التوضيح الآن خلينا تحت شوية إذا اللي حكيته
+
+100
+00:09:22,620 --> 00:09:28,420
+الآن أعرفت ال lower sum زي ما أنتوا شايفين عند ال
+
+101
+00:09:28,420 --> 00:09:32,780
+lower sum هيه هذا ال lower sum يعتمد في مجموعه على
+
+102
+00:09:32,780 --> 00:09:37,300
+ال M K اللي هي عبارة عن ال infimum لدالة على
+
+103
+00:09:37,300 --> 00:09:43,960
+الفترة X K minus واحد لعند X Kو-xk-1 هي عبارة عن
+
+104
+00:09:43,960 --> 00:09:49,040
+قيم ال partition اللي عندي إذا ال lower sum أو حتى
+
+105
+00:09:49,040 --> 00:09:53,820
+ال upper sum التمتين باعتمدين عالميا على اللي هو
+
+106
+00:09:53,820 --> 00:09:57,940
+ال partition وعلى الدالة اللي بنعملها أو لو وجدلها
+
+107
+00:09:57,940 --> 00:10:03,160
+ال lower sum و ال upper sum الهن واضح أن ال lower
+
+108
+00:10:03,160 --> 00:10:09,780
+sum ال lower sum واضح أنه اللي هو دائمااللي هو لل
+
+109
+00:10:09,780 --> 00:10:13,480
+partition المعين هيكون أصغر من مين من ال upper sum
+
+110
+00:10:13,480 --> 00:10:21,380
+واضح أه؟ الان اللي بنحكي if F من I ل R is bounded
+
+111
+00:10:21,380 --> 00:10:27,520
+and B is any partition of I then ال lower sum لل B
+
+112
+00:10:27,520 --> 00:10:32,020
+و ال F أصغر سوى ال upper sum لل B و ال F وبرهانه
+
+113
+00:10:32,020 --> 00:10:39,830
+سهل وسريعلو جئنا و أخذنا الـ bi-partition x0 x1
+
+114
+00:10:39,830 --> 00:10:40,550
+عند xn
+
+115
+00:10:43,460 --> 00:10:48,540
+وقررنا بين الـMK والـMK Capital أكيد الـMK Small
+
+116
+00:10:48,540 --> 00:10:50,540
+أصغر من الـMK Capital لإنه هذا عبارة عن
+
+117
+00:10:50,540 --> 00:10:54,820
+الـSupremum للفункشن على الفترة أو الـSubinterval
+
+118
+00:10:54,820 --> 00:10:59,780
+XK minus 1 عند XK وهذا الـSupremum للفункشن، هذا
+
+119
+00:10:59,780 --> 00:11:02,860
+الـInfimum وهذا الـSupremum فأكيد هذا أكبر أو
+
+120
+00:11:02,860 --> 00:11:07,080
+يساوي ما هو الـMK Small وهذا الكلام صحيح على كل
+
+121
+00:11:07,080 --> 00:11:11,380
+الـSubintervals يعني صحيح لكل K من 1 إلى 2 عند N
+
+122
+00:11:11,490 --> 00:11:14,650
+وفي نفس الوجهة الـ xk هو الـ xk minus واحد أكبر من
+
+123
+00:11:14,650 --> 00:11:18,610
+سفر إذا بيصير عندي حاصل ضرب هادي فى طول الفترة
+
+124
+00:11:18,610 --> 00:11:22,570
+وهادي فى طول الفترة بتظل ال inequality صحيحة لإنه
+
+125
+00:11:22,570 --> 00:11:26,730
+طول الفترة موجبة فبصير mk فى هذا المقدار أصغر ساوى
+
+126
+00:11:26,730 --> 00:11:29,950
+mk capital فى هذا المقدار بنعمل summation على الكل
+
+127
+00:11:29,950 --> 00:11:32,770
+وهذا ال summation على الكل بيصير عندى هذا هو عبارة
+
+128
+00:11:32,770 --> 00:11:36,150
+عن ال upper sum وهذا ال lower sum يعني اللى وصلنا
+
+129
+00:11:36,150 --> 00:11:44,110
+إلى انه دائما ال lower sumلأن ال lower sum هو أسفل
+
+130
+00:11:44,110 --> 00:11:48,230
+من ال upper sum في القيام فبكون أكيد ال lower sum
+
+131
+00:11:48,230 --> 00:11:56,870
+أصغر أو يساوي ال upper sum اطلع لفهم الان احنا لو
+
+132
+00:11:56,870 --> 00:12:01,590
+اجينا لو
+
+133
+00:12:01,590 --> 00:12:06,170
+اجينا اعرفنا .. بنعرف حاجة اللي في عندي P is a
+
+134
+00:12:06,170 --> 00:12:10,890
+partitionلو ضفت على الـ partition أي قيمة جديدة
+
+135
+00:12:10,890 --> 00:12:15,370
+بالاضافة للقيم الموجودة بيصير عندى هذا ال .. ال ..
+
+136
+00:12:15,370 --> 00:12:20,710
+ال .. الجديد عبارة عن refinement لمين للـ B يعني
+
+137
+00:12:20,710 --> 00:12:26,290
+تحسين لل partition يعني الآن بنقول عن أن الـ B الـ
+
+138
+00:12:26,290 --> 00:12:30,190
+Q is a refinement of B إذا كانت الـ B subset من
+
+139
+00:12:30,190 --> 00:12:34,990
+مين؟ من الـ Q طيب، الآن نشوف إيش اللي بنقوله
+
+140
+00:12:45,570 --> 00:12:57,310
+الأن لو أخدنا الفترة اللي هي A وB و جزّقناها X0 X1
+
+141
+00:12:57,310 --> 00:13:03,460
+لعند XNوالفترة النموذجية اللي نشرع عليها xk minus
+
+142
+00:13:03,460 --> 00:13:08,640
+واحد أو ال sub interval لعند مين لعند xk الان ال b
+
+143
+00:13:08,640 --> 00:13:13,520
+هذا هو عبارة عن ال partition x naught x واحد لعند
+
+144
+00:13:13,520 --> 00:13:17,400
+ال xn وهذا ordered يعني نكتبها على صورة ordered
+
+145
+00:13:17,400 --> 00:13:20,640
+لما نكتبها على هذا متفقين على انه ايش اللي هو احنا
+
+146
+00:13:20,640 --> 00:13:25,380
+نعمله ordered ال order بالنسبة له ايش ماله مهم لأن
+
+147
+00:13:25,380 --> 00:13:28,080
+هذا معناه تبدأ بال x naught وبعدين x واحد بعدين
+
+148
+00:13:28,080 --> 00:13:35,240
+اللي هو ال xnلو جينا أخدنا اللي هو أضفنا أي نقطة
+
+149
+00:13:35,240 --> 00:13:39,060
+هنا طبعاً أضفنا أي نقطة أو أي رقم بين الـA و بين
+
+150
+00:13:39,060 --> 00:13:45,320
+مين الـB الرقم المضاف اللي هو أضفنا لهذه وسميناها
+
+151
+00:13:45,320 --> 00:13:50,930
+Q فبكون الـQ هي عبارة عن refinement للـBيعني بمعنى
+
+152
+00:13:50,930 --> 00:13:55,030
+اخر اكيو refinement ل ال B معناته انه في اكيو فيها
+
+153
+00:13:55,030 --> 00:14:02,790
+نقاط اللي هي زيادة عن نقطة B واسمه تحسين لانه فعلا
+
+154
+00:14:02,790 --> 00:14:08,870
+بحسن وضع ال lower sum و ال upper sum الان ال lower
+
+155
+00:14:08,870 --> 00:14:14,250
+sum عرفناه لل B و ال F قلنا بعتمد عليهم بسوء ال
+
+156
+00:14:14,250 --> 00:14:22,130
+summationاللي هو xk ناقص xk minus واحد في ال mk
+
+157
+00:14:22,130 --> 00:14:25,090
+اللي هي mk small هي عبارة عن قلنا اللي هي عبارة عن
+
+158
+00:14:25,090 --> 00:14:29,050
+ال infimum لدى العهد الفترة k من عند واحد لعند n
+
+159
+00:14:29,050 --> 00:14:34,770
+والان ال upper sum ب U, B وF اللي هو بساوى ال
+
+160
+00:14:34,770 --> 00:14:40,890
+summation لل xk minus xk minus واحد mk capital k
+
+161
+00:14:40,890 --> 00:14:47,930
+من عند واحد لعند nوقلنا إن الـ lower للـ B و الـ F
+
+162
+00:14:47,930 --> 00:14:52,390
+دايما أصغر سوى ال upper للـ B و الـ F فده اللي حتى
+
+163
+00:14:52,390 --> 00:14:58,470
+الآن اللي حكيناه الآن نيجي ناخد الملاحظة اللي عندي
+
+164
+00:14:58,470 --> 00:15:04,510
+if Q above is a refinement of B لو قلنا إن Q عبارة
+
+165
+00:15:04,510 --> 00:15:09,390
+عن إيه شمالها؟ refinement of Brefinement معناته
+
+166
+00:15:09,390 --> 00:15:14,690
+اضفت اللي هو نقطة او اكتر من نقطة لنقاط ال
+
+167
+00:15:14,690 --> 00:15:20,810
+partition اللي عندى اذا اي فترة اي فترة اللي هي xk
+
+168
+00:15:20,810 --> 00:15:27,550
+minus واحد لعند xk اللي هو في ال partition بيه
+
+169
+00:15:27,550 --> 00:15:34,060
+هقدر اكتبها على صورة ميناللي هو yj-1 yj اتحاد ال
+
+170
+00:15:34,060 --> 00:15:37,940
+yj yj زاد 1 اتحاد ده ما اصل عند اتحاد yn نقص 1
+
+171
+00:15:37,940 --> 00:15:44,040
+لعند مين لعند ال yn ماشي الحال طبعا الان هذول عدد
+
+172
+00:15:44,040 --> 00:15:47,740
+الفترات على حسب الإضافة اللي هنالو ضفنا نقطة واحدة
+
+173
+00:15:47,740 --> 00:15:52,240
+بين هذول التنتين معناته هيصير عندى من الـ yj-1 هي
+
+174
+00:15:52,240 --> 00:15:56,460
+عبارة عن xk-1 والنقطة المضافة اتحاده النقطة
+
+175
+00:15:56,460 --> 00:15:59,780
+المضافة اللي هي مع مين مع النقطة هذه بيكون عندى بس
+
+176
+00:15:59,780 --> 00:16:03,690
+فترة تانية لو كان فيه عندىنقطين مضافات بيصير عندي
+
+177
+00:16:03,690 --> 00:16:06,710
+اللي هو للنقطة الأولى و بعدين من النقطة الأولى
+
+178
+00:16:06,710 --> 00:16:12,030
+لنقطة ثانية و بعدين من النقطة الثانية لـ XK فبيصير
+
+179
+00:16:12,030 --> 00:16:16,030
+عندي أكم فترة انضاف تلت .. بيصير تلت فترات و هكذا
+
+180
+00:16:16,030 --> 00:16:19,970
+إذن و لو مافيش إضافة في هذه الفترة بالمرة بيصير
+
+181
+00:16:19,970 --> 00:16:24,460
+عندي بس اللي هي ال interval الأولىأه إذا صار عندى
+
+182
+00:16:24,460 --> 00:16:29,640
+الآن في حالة اللى هو الـQ refinement للـB أي فترة
+
+183
+00:16:29,640 --> 00:16:35,040
+في الـB الأصلية بقدر أكتبها على صورة اللى هى هذا
+
+184
+00:16:35,040 --> 00:16:40,000
+الاتحاد وهذا الاتحاد يحتمل اللى هو الفترة الحاله
+
+185
+00:16:40,000 --> 00:16:44,460
+أو فترتين أو تلاته إلى آخره على حسب اللى هو النقاط
+
+186
+00:16:44,460 --> 00:16:50,060
+المضافة واضح اللى ما اللى هي سبعة واحد اتنينif f
+
+187
+00:16:50,060 --> 00:16:53,960
+من I عند R is bounded and B is any partition of I
+
+188
+00:16:53,960 --> 00:16:57,680
+and Q is a refinement of B فرضنا ان Q ايش ما هي
+
+189
+00:16:57,680 --> 00:17:03,180
+refinement لـ B إذا ال lower sum الاعتماد على
+
+190
+00:17:03,180 --> 00:17:06,820
+partition B و ال function F أصغر يساوي ال lower
+
+191
+00:17:06,820 --> 00:17:12,780
+sum لـ Q و ال F و ال U ال Q و ال F أصغر يساوي ال U
+
+192
+00:17:12,780 --> 00:17:17,900
+و ال B و ال F هو أصلا واقعا ال refinement هو فعلا
+
+193
+00:17:17,900 --> 00:17:25,250
+تحسين أصلاأحنا لما نجينا دربنا المثال في الأول و
+
+194
+00:17:25,250 --> 00:17:28,690
+رسمنا الرسمة على سبيل المثال هذه الرسمة اللي عندي
+
+195
+00:17:28,690 --> 00:17:36,290
+و أخدنا من a لعند b مثلا اللي هو الفترة و كان في
+
+196
+00:17:36,290 --> 00:17:42,150
+عندي اللي هو اللي عملنا تجزء x note x1 الاخره x2
+
+197
+00:17:42,150 --> 00:17:49,420
+x3 لعند الاخيرة xn مثلاعلى سبيل المثال واخدنا
+
+198
+00:17:49,420 --> 00:17:52,860
+القبر صم القبر صم هيكون عبارة عن المنطقة هذه
+
+199
+00:17:52,860 --> 00:17:57,240
+والقبر صم عبارة عن المنطقة هذه والقبر صم بيكون هذه
+
+200
+00:17:57,240 --> 00:18:02,150
+المنطقة كلها اللي بالأزرقالآن لما نزيد اللي هو
+
+201
+00:18:02,150 --> 00:18:07,210
+نقاط الـ Partition اللي هو هذا اللي هي النقاط
+
+202
+00:18:07,210 --> 00:18:12,630
+بتجلل الجزء الزائد فالآن فعلًا بيكون تحسين على
+
+203
+00:18:12,630 --> 00:18:15,330
+الأولاني لأنه أصلا أنا بعد شوية هتلاقي غاية في
+
+204
+00:18:15,330 --> 00:18:21,140
+الوصول أن أصل اللي هو اللي هو أصغر واحدفي ال upper
+
+205
+00:18:21,140 --> 00:18:25,720
+sums يصير زي أكبر واحد في ال lower sums يوم ما
+
+206
+00:18:25,720 --> 00:18:29,820
+يلتجوا مع بعض بيكون فعلا اللي هو ال upper sum وال
+
+207
+00:18:29,820 --> 00:18:35,000
+lower sum اللي هو تجاوزا بيصير بساوي بالظبط اللي
+
+208
+00:18:35,000 --> 00:18:40,080
+هو المساحة تحت المنحنة أو المنطقة اللي هنسميها في
+
+209
+00:18:40,080 --> 00:18:43,340
+حينه ان هي عبارة عن remen integral بل وقيمة ال
+
+210
+00:18:43,340 --> 00:18:47,660
+remen integral هو عبارة عن هذه المنطقة اللي صارتمن
+
+211
+00:18:47,660 --> 00:18:53,540
+اللي هو انه ناخد نزغر اللي هو الأبر و نرفع ال
+
+212
+00:18:53,540 --> 00:18:57,540
+lower و نشوف كيف بنزغر الأبر و كيف بنرفع ال lower
+
+213
+00:18:57,540 --> 00:19:01,580
+اللي هو معنى اللي هيوصل لنا معنى ال integrability
+
+214
+00:19:02,250 --> 00:19:06,710
+إذا الـ Refinement فعلاً Refinement تحسين لما أقول
+
+215
+00:19:06,710 --> 00:19:13,390
+أن بي إي كيو زادت عن هذه الـ Q إيش هتعمل؟ هتتجللل
+
+216
+00:19:13,390 --> 00:19:19,630
+الجزء الزائد في الـ Upper لما أزيد النقاط و هتزيد
+
+217
+00:19:19,630 --> 00:19:24,950
+للجزء المفقود وين في ال lowerماشي الحال ففعلا
+
+218
+00:19:24,950 --> 00:19:28,310
+هيكون ايه بقى عبارة عن refinement او تحسين انت
+
+219
+00:19:28,310 --> 00:19:32,470
+نشوف الآن نشوف لمتنا اللي عندنا اللي هو معنى اللي
+
+220
+00:19:32,470 --> 00:19:38,350
+بقوله انا انه عندي لو كانت Q refinement لل B بكون
+
+221
+00:19:38,350 --> 00:19:43,790
+الlower لجديدعليه أكبر أو يساوي الـ Lower القديم
+
+222
+00:19:43,790 --> 00:19:48,390
+يعني بمعنى آخر اقترب إلى اللي بدناهي اللي متوقعين
+
+223
+00:19:48,390 --> 00:19:53,110
+انه يكون هو التحسين النهائي اللي هنسميه اللي هو ال
+
+224
+00:19:53,110 --> 00:19:58,670
+integration ماشي؟ وال Upper هنا Upper UQ واضح انه
+
+225
+00:19:58,670 --> 00:20:03,510
+بصغر اللي هو عن الأصل لأنه صار فيه تحسين واقترب من
+
+226
+00:20:03,510 --> 00:20:08,070
+الحقيقة اقترب من اللي هو القيمة اللي احنا هنسميها
+
+227
+00:20:08,070 --> 00:20:12,370
+في النهاية integrationطيب، بدنا نثبت الكلام هذا،
+
+228
+00:20:12,370 --> 00:20:16,810
+شوف كيف بدنا نثبته، اللي أنا عندي بيأخدت I اللي هو
+
+229
+00:20:16,810 --> 00:20:21,290
+ال partition ال arbitrary واخدت اللي هو sigma I،
+
+230
+00:20:21,290 --> 00:20:26,310
+بد أشتغل على إضافة نقطة ومن ثم أقول إضافة النقطة
+
+231
+00:20:26,310 --> 00:20:31,340
+تؤدي إلى اللي هو باقي النقطة، نشوف إيش بقولعند بي
+
+232
+00:20:31,340 --> 00:20:35,080
+هي اللي هو الـ partition أخدت z element in I و الـ
+
+233
+00:20:35,080 --> 00:20:39,100
+z هذي و أنا بدأ أحطها في الفترة xk minus واحد لعند
+
+234
+00:20:39,100 --> 00:20:42,640
+مين لعند الـ xk يعني الآن ال partition اللي بي
+
+235
+00:20:42,640 --> 00:20:51,200
+عندي هو عبارة عن x naught لعند xn xk minus واحد xk
+
+236
+00:20:51,200 --> 00:20:55,620
+indeed في المنطقة هذه ضفت نقطة وسميت بيها prime و
+
+237
+00:20:55,620 --> 00:21:03,380
+عبارة عن x naught xk minus واحدZ X K وظل الخلايت
+
+238
+00:21:03,380 --> 00:21:07,720
+كله زي ما هو لعد مين لعد X بس اللي غيرت فيه او
+
+239
+00:21:07,720 --> 00:21:12,420
+اللي ضفتله بس ضفت نقطة هنا اسمها Z بدى اشوف تأثير
+
+240
+00:21:12,420 --> 00:21:16,640
+هذا النقطة ايش بده يعمل بين ال partition القديم
+
+241
+00:21:16,640 --> 00:21:20,520
+وال partition الجديد ومن ثم نستنتج اي refinement
+
+242
+00:21:20,520 --> 00:21:26,990
+على اللي هو ال B القديمةالأمر سهل ان شاء الله الان
+
+243
+00:21:26,990 --> 00:21:30,290
+ال .. ال .. ال .. الاضافة الجديدة صار عند بي برايم
+
+244
+00:21:30,290 --> 00:21:35,870
+ايش هو X Note X واحد وهي ال Z ضفتهان اللي اختلف عن
+
+245
+00:21:35,870 --> 00:21:43,640
+فوق بس ال Z اللي هان بناء عليه الان ال M Kالـ mk'
+
+246
+00:21:43,860 --> 00:21:49,020
+هي عبارة عن الـ supremum للـ function f وين في
+
+247
+00:21:49,020 --> 00:21:58,920
+المنطقة بين zk-1 و مين و z الآن في الفترة بين xk-1
+
+248
+00:21:58,920 --> 00:22:04,800
+و بين xk ضفت z الآن الـ z اللي ضفت هنا هذه المنطقة
+
+249
+00:22:04,800 --> 00:22:11,150
+بدي أسميه ال supremum اللي فيها mk' اللي هنااللي
+
+250
+00:22:11,150 --> 00:22:16,190
+ضالت نسميها إيش مالها MK double prime مع العلم إنه
+
+251
+00:22:16,190 --> 00:22:19,890
+الـ supremum الأصلية في ال partition الأصلي على كل
+
+252
+00:22:19,890 --> 00:22:23,250
+الفترة من XK minus واحد عند XK اسمها إيش مسمينا
+
+253
+00:22:23,250 --> 00:22:31,130
+احنا MK capital باشي الحال طيب ركزوا معاياالآن
+
+254
+00:22:31,130 --> 00:22:34,970
+عندي الـ MK' هي الـ supremum على اللي هو الـ
+
+255
+00:22:34,970 --> 00:22:39,610
+subinterval هذه الـ MKW' هي ال supremum على اللي
+
+256
+00:22:39,610 --> 00:22:43,910
+هي ال subinterval اللي جنبها اللي هي من Z لعند XK
+
+257
+00:22:43,910 --> 00:22:49,890
+واضح أن ال supremum على الكبيرة هذه من XK minus 1
+
+258
+00:22:49,890 --> 00:22:53,790
+لعند XK أكيد أكبر أو يساوي ال supremum على الصغيرة
+
+259
+00:22:54,620 --> 00:22:58,580
+لأن هذه أشملها جزء من 100 من هذه كلها فال supremum
+
+260
+00:22:58,580 --> 00:23:01,940
+لل function عالي كبيرة أكبر أو يساوي ال supremum
+
+261
+00:23:01,940 --> 00:23:06,020
+على مين؟ على الصغيرة و similarly للتانية إذا ال MK
+
+262
+00:23:06,020 --> 00:23:12,180
+أكبر أو يساوي MK' Similarly MK أكبر يساوي MKW' لأن
+
+263
+00:23:12,180 --> 00:23:15,220
+هذه عبارة عن ال supremum على الجزء الثاني منها
+
+264
+00:23:15,220 --> 00:23:20,520
+اللي إلى جاي، واضح؟إذا صار عندي therefore الآن بدأ
+
+265
+00:23:20,520 --> 00:23:24,840
+أصل لحاجة معينة اللي هي mk في xk ناقص xk minus
+
+266
+00:23:24,840 --> 00:23:31,310
+واحددربت اللي هي Mk في هذا هذه الفترة طبعا اللي هي
+
+267
+00:23:31,310 --> 00:23:40,730
+بتساوي Zk-Zk-Xk-1 زائد Xk-Zk الان صارت هذه Mk في
+
+268
+00:23:40,730 --> 00:23:45,410
+المقدار هذا بساوي Mk في هذه زائد هذه ماشي الحال
+
+269
+00:23:45,410 --> 00:23:50,820
+الان ال Mkأكبر أو يساوي mean mk' إذا انصار المقدار
+
+270
+00:23:50,820 --> 00:23:58,780
+هذا أكبر أو يساوي mk' في zk z ناقص xk minus واحد و
+
+271
+00:23:58,780 --> 00:24:04,820
+هذه ال mk برضه أكبر أو يساوي mk double prime of xk
+
+272
+00:24:04,820 --> 00:24:10,380
+ناقص z ماشي الحالة الآن احنا بين ال two partitions
+
+273
+00:24:10,380 --> 00:24:14,580
+اللي حدث بس تغيير واحد زي ما قلنا بس على المنطقة
+
+274
+00:24:14,580 --> 00:24:23,090
+هذه لاحظ انتالان ال lower sum ال lower sum لل b و
+
+275
+00:24:23,090 --> 00:24:30,350
+ال f ال b prime و ال f بساوي لو حسبنا للأولاني أول
+
+276
+00:24:30,350 --> 00:24:38,350
+إشي هو عبارة عن m1 في x0 او x1 نقص x0 زاد لما أصل
+
+277
+00:24:38,350 --> 00:24:51,620
+عند mk في xK-XK-1 زائد لما أصل لعند MN في XN-XN-1
+
+278
+00:24:51,620 --> 00:24:57,800
+هذا إيش هو يا جماعة؟ هو عبارة عن الأبرثان الأبرثان
+
+279
+00:24:57,800 --> 00:25:03,120
+لمن؟ لـB و لـF متفجر، ماشي الحالة على مين؟ على ال
+
+280
+00:25:03,120 --> 00:25:12,270
+partition B الآن هذا بساويم1 في x1 ناقص x0 زائد
+
+281
+00:25:12,270 --> 00:25:18,010
+الان هذه جزئناها جزئين بعد شوية زائد زائد هذا نفسه
+
+282
+00:25:18,010 --> 00:25:25,690
+ماتغيرش هذا اللي هو عبارة عن mk لسه xk ناقص z
+
+283
+00:25:25,690 --> 00:25:34,850
+مظبوط زائد اللي هو mk خليني اقول ال
+
+284
+00:25:34,850 --> 00:25:46,170
+mkاللي هو Z ناقص كحسابات ناقص X كمينوس واحد صحيح؟
+
+285
+00:25:46,170 --> 00:25:53,130
+باضح زائد الباقي زي ما هو زائد M N في X N ناقص X N
+
+286
+00:25:53,130 --> 00:26:00,980
+ناقص واحد الآن هذا ماتغيرش نفسهزائد هذا الـ N هو
+
+287
+00:26:00,980 --> 00:26:05,540
+اللي اتغير وهنا في ال inequality هنا لقنا عبارة عن
+
+288
+00:26:05,540 --> 00:26:12,220
+هذا المقدار اللي هو أكبر أو يساوي اللي هو اللي ما
+
+289
+00:26:12,220 --> 00:26:15,420
+اتغيرش هذا نسميه اللي هو M1
+
+290
+00:26:18,760 --> 00:26:25,640
+معايا يا شباب زائد اللي هو mk شرطة في xk ناقص z
+
+291
+00:26:25,640 --> 00:26:31,520
+زائد mk شرطين في z ناقص xk ماينوس واحد زائدة دا
+
+292
+00:26:31,520 --> 00:26:38,570
+كما تتغيرش زي ما هو mn في xnنقص XN نقص 1 هذا في
+
+293
+00:26:38,570 --> 00:26:42,690
+الواقع مين هو أصلاً هذا هو عبارة عن اللي هو ال
+
+294
+00:26:42,690 --> 00:26:48,510
+upper sum لل partition مين ال B' هو بساوي ال upper
+
+295
+00:26:48,510 --> 00:26:55,270
+sum لل B' والFيعني اللي لجناه أنه لما نضفنا اللي
+
+296
+00:26:55,270 --> 00:26:59,830
+هو نقطة على اللي هو الـ partition صار عند الـ
+
+297
+00:26:59,830 --> 00:27:03,590
+partition اللي هو الأبر للـ partition الجديد أصغر
+
+298
+00:27:03,590 --> 00:27:08,360
+أو يساوي الأبر للـ partition من القديمالان اللي
+
+299
+00:27:08,360 --> 00:27:11,760
+حدث على نقطة ممكن يحدث على نقطين يعني الان ممكن
+
+300
+00:27:11,760 --> 00:27:15,640
+نقطة مثلا انضافت هنا ممكن انضافت كمان مرة هنا كمان
+
+301
+00:27:15,640 --> 00:27:20,560
+نقطة هيصير لجديد بنفس الأسلوب أكبر ويساوي تلت نقاط
+
+302
+00:27:20,560 --> 00:27:24,040
+بيصير أكبر ويساوي أربع نقاط بيصير أكبر ويساوي يعني
+
+303
+00:27:24,040 --> 00:27:29,500
+in general مدام ال refinement UQ اللي محتوي بيه في
+
+304
+00:27:29,500 --> 00:27:34,820
+النهاية عدد الإضافات finiteإذا حيكون اللي هو كل
+
+305
+00:27:34,820 --> 00:27:39,300
+مرة بعدد الإضافات بيصير sub intervals بنفس الأسلوب
+
+306
+00:27:39,300 --> 00:27:43,940
+اللي هان حيصير عنده القبر القديم أكبر أو يساوي
+
+307
+00:27:43,940 --> 00:27:48,620
+القبر الجديد يعني بمعنى أخر in general القبر للـB
+
+308
+00:27:48,620 --> 00:27:54,080
+والـF هيكون أكبر أو يساوي القبر للـQ ال refinement
+
+309
+00:27:54,080 --> 00:27:59,160
+وMain والـFوطبعا زي ما قلنا هذا عبارة عن تحسين لإن
+
+310
+00:27:59,160 --> 00:28:03,960
+القبر هذا بيصير يصغر يقترب من المساحة الحقيقية
+
+311
+00:28:03,960 --> 00:28:08,360
+اللي تحت المنحنة في حالة اللي هو الدل ايش الموجبة
+
+312
+00:28:08,360 --> 00:28:15,860
+واضح طيب الان similarly for lower الان الlower
+
+313
+00:28:15,860 --> 00:28:20,940
+بيصير اللي هوفي الـ lower بدل ما يصير عندي لو كان
+
+314
+00:28:20,940 --> 00:28:25,700
+عندي بنحكي عن ال lower احنا ال L بيوقف و بنحكي عن
+
+315
+00:28:25,700 --> 00:28:30,220
+ال M 1 small و ال M 2 small و M K small و M N
+
+316
+00:28:30,220 --> 00:28:36,660
+small بيصير عندي M 1 small و M K small و M KSmall
+
+317
+00:28:36,660 --> 00:28:44,520
+ومكSmall ومنSmall بيصير الان اللي هي المن هنا بدل
+
+318
+00:28:44,520 --> 00:28:49,680
+ما هي أكبر إيش هتصير على إيش أصغر لإنه بيحكي عن ال
+
+319
+00:28:49,680 --> 00:28:54,810
+infimum منأيش صغير على أيش صغير إلى infimum على
+
+320
+00:28:54,810 --> 00:28:59,570
+أيش أيش اللي هو أصغر فمعناته أيش صار عنده بيصير له
+
+321
+00:28:59,570 --> 00:29:04,910
+infimum اللي هو ال M1 أصغر من ال M1' أو ال Mk
+
+322
+00:29:04,910 --> 00:29:11,730
+Small أصغر أو يساوي ال Mk' Small واضح أه؟ ومنه
+
+323
+00:29:11,730 --> 00:29:17,870
+بنستنتج أنه هيكون عند ال LBF أصغر أو يساوي
+
+324
+00:29:21,260 --> 00:29:28,950
+الـ LBF هنصل أصغر و ساويالـ QF وفعلًا أيضًا هذا هو
+
+325
+00:29:28,950 --> 00:29:35,410
+تحسين لإنه اللي هي زاد اللي هو ال lower sum بحيث
+
+326
+00:29:35,410 --> 00:29:41,550
+إنه بده يصل أو يروح ناحية مين اللي هو المساحة
+
+327
+00:29:41,550 --> 00:29:46,310
+الحقيقية تحت المنحنة في حالة التقاء الجهتين بيصير
+
+328
+00:29:46,310 --> 00:29:52,670
+عندي اللي هو إنه القيمة إذا يعني أخدنا بمعنى أخر
+
+329
+00:29:52,670 --> 00:29:58,540
+ندخل للموضوع مدام هيكإنه لو أخدنا اللي هو صار عندى
+
+330
+00:29:58,540 --> 00:30:03,140
+ال lower يبدأ يكبر يعني لو أخدتله ال suprem لكل ال
+
+331
+00:30:03,140 --> 00:30:06,960
+lowers على كل ال partitions اللي في الدنيا و أخدت
+
+332
+00:30:06,960 --> 00:30:10,980
+ال infimum على كل كبار اللي هو و اتساون مع بعض ال
+
+333
+00:30:10,980 --> 00:30:14,820
+infimum يعني عالمين على ال upper sums بيصير ال
+
+334
+00:30:14,820 --> 00:30:17,500
+suprem مع ال lower sums و ال infimum مع ال lower
+
+335
+00:30:17,500 --> 00:30:22,780
+sums يوم ما يتساونهو اللي بنسميه اللي هو الـ
+
+336
+00:30:22,780 --> 00:30:26,920
+Remain Integrable وبنسمي اللي هي الـ Remain
+
+337
+00:30:26,920 --> 00:30:30,440
+Integrable في هذه الحالة بساوي هذه القيمة المشتركة
+
+338
+00:30:30,440 --> 00:30:35,720
+اللي أصبحت متساوية نيجي لللمة اللي عندي هذه، لمة
+
+339
+00:30:35,720 --> 00:30:40,720
+برضه يعني برهانها سهل، نشوف إيش بتقول اللمة، اللمة
+
+340
+00:30:40,720 --> 00:30:45,610
+بتقول let F from I to R be boundedif B1 وB2 are
+
+341
+00:30:45,610 --> 00:30:49,470
+any two partitions يعني مش نفس ال partition على أي
+
+342
+00:30:49,470 --> 00:30:54,090
+two partitions دائما اللاور على أي partition في
+
+343
+00:30:54,090 --> 00:30:57,150
+الدنيا أصغر أو يساوي الأبر على أي partition تاني
+
+344
+00:30:57,150 --> 00:30:59,970
+مش مشكلة إيش هو في الأول قلنا على نفس ال partition
+
+345
+00:30:59,970 --> 00:31:05,510
+arbitrarily و الإثبات هنستخدم اللمّة الأولى و
+
+346
+00:31:05,510 --> 00:31:09,010
+اللمّة الثانية اللي أخدناها و هنصلي هذه بكل سهولة
+
+347
+00:31:09,010 --> 00:31:13,760
+شوف كدهخلّينا ناخد الـ Q ايش بتساوي بي واحد اتحاد
+
+348
+00:31:13,760 --> 00:31:17,240
+دي اتنين صارت الـ Q هذه refinement للأولى و
+
+349
+00:31:17,240 --> 00:31:21,420
+refinement لمين؟ للتانية تحسين للتانتين بناء عليه
+
+350
+00:31:21,420 --> 00:31:25,380
+.. بناء على اللي هي اللمّة اللي أخدناها سبعة واحد
+
+351
+00:31:25,380 --> 00:31:28,660
+واحد وسبعة واحد اتنين احنا حصول على ناية ليه
+
+352
+00:31:28,660 --> 00:31:33,000
+احسبلي ال بي واحد و أف صار refinement مزام صار ..
+
+353
+00:31:33,000 --> 00:31:37,620
+صار له refinement او تحسين بده يكبر اللاور صار
+
+354
+00:31:37,620 --> 00:31:42,750
+أصغر أو ساوي ال Q Fمن جهة أخرى قبل بشوية أثبتنا أن
+
+355
+00:31:42,750 --> 00:31:48,310
+الـQF أصغر يساوي UQF for any اللي هو specific mean
+
+356
+00:31:48,310 --> 00:31:53,070
+الـQ لنفس الـQ لأن برضه اللي هو الـQ refinement
+
+357
+00:31:53,070 --> 00:31:57,790
+لمين؟ للـB2 مازال refinement إذا الـQ بدي يصير
+
+358
+00:31:57,790 --> 00:32:03,050
+أصغر أو يساوي مين الـUB2F زي اللي بواسطة أثبتناها
+
+359
+00:32:03,050 --> 00:32:07,470
+قبل بشوية يعني in generalin general الـ B1 و F
+
+360
+00:32:07,470 --> 00:32:15,810
+أصغر أو ساوي و B2 و F بدون يعني بغض النظر عن B1 و
+
+361
+00:32:15,810 --> 00:32:21,130
+B2 أنهم كونوا زي بعض أو مختلفات لأي two partitions
+
+362
+00:32:21,130 --> 00:32:26,370
+of the interval I طيب الـ definition الآن اللي
+
+363
+00:32:26,370 --> 00:32:28,830
+حكيناها قبل شوية قولناها قبل شوية بدنا نعرف حاجة
+
+364
+00:32:28,830 --> 00:32:33,940
+اسمها lower integralالـ Lower Integral وحاجة اسمها
+
+365
+00:32:33,940 --> 00:32:38,760
+الـ Upper Integral أخدنا
+
+366
+00:32:38,760 --> 00:32:42,740
+الـ function F bounded طبعا معروف ليش bounded عشان
+
+367
+00:32:42,740 --> 00:32:47,880
+يكون الـ M1 و الـ M2 و الـ Mn كلهم موجودات سواء
+
+368
+00:32:47,880 --> 00:32:51,040
+الـ M capital أو الـ M small عشان هما عبارة عن
+
+369
+00:32:51,040 --> 00:32:54,260
+supremum و infimum فلازم تكون bounded ال function
+
+370
+00:32:54,260 --> 00:32:58,280
+الآن فرضنا الـ F عبارة عن bounded function على ال
+
+371
+00:32:58,280 --> 00:33:01,520
+close bounded interval اللي عندى هذهبنعرف الـ
+
+372
+00:33:01,520 --> 00:33:06,320
+lower integral of F on I اللي هو المعتمد عالميا
+
+373
+00:33:06,320 --> 00:33:11,680
+على ال lower sums ال lower sums قولنا انحسن انحسن
+
+374
+00:33:11,680 --> 00:33:16,960
+انحسن انحسن احسن تحسين اذا جهز التعبير اللي هو ال
+
+375
+00:33:16,960 --> 00:33:21,640
+supremum لكل مين لكل ال lower sums على كل ال
+
+376
+00:33:21,640 --> 00:33:25,040
+partitions اللي في الدنيا هذول ايه الشمال اللي
+
+377
+00:33:25,040 --> 00:33:31,260
+بنسميه L of F اللي بنسميه lower sumأخد الـ
+
+378
+00:33:31,260 --> 00:33:35,400
+supremum هي ال lower sums تحت المنحنة لما أخد اللي
+
+379
+00:33:35,400 --> 00:33:40,220
+هنا ال supremum اللي هو هذا ال supremum بدي أسميه
+
+380
+00:33:40,220 --> 00:33:46,300
+ال lower integral الآن ال upper sums بدي أخد اللي
+
+381
+00:33:46,300 --> 00:33:52,020
+هنا ال infimum يعني بدي أزغرهن اللي هو و أسميه ال
+
+382
+00:33:52,020 --> 00:33:57,760
+upper integral إذا صار عندي lowerIntegral هو عبارة
+
+383
+00:33:57,760 --> 00:34:02,080
+عن الـ Supremum للـ Lower Sums و ال .. واضح يا
+
+384
+00:34:02,080 --> 00:34:06,060
+عيسى و ال Upper Integral هو عبارة عن ال Infimum
+
+385
+00:34:06,060 --> 00:34:10,620
+لمن؟ لل Upper Sums متوقع أنه يقول لنا أنه احنا
+
+386
+00:34:10,620 --> 00:34:16,810
+بنقول عنهافوق الصفحة التانية متوقع يقولنا انه عنا
+
+387
+00:34:16,810 --> 00:34:20,970
+الآن بنسميها remain integrable اذا تساوت ايش
+
+388
+00:34:20,970 --> 00:34:26,130
+اتجهتين ماشي جابيه لبس خلينا نبرهن او نتطلع على
+
+389
+00:34:26,130 --> 00:34:33,430
+هذه اللي أمامنا برضه ملاحظة سهلة الملاحظة بتقولي
+
+390
+00:34:33,430 --> 00:34:42,780
+لو الان جيناسمّينا الـ M I small عبارة عن الـ
+
+391
+00:34:42,780 --> 00:34:49,860
+infimum للدالة على الفترة كلها الـ infimum يعني
+
+392
+00:34:49,860 --> 00:34:57,460
+الـ M I سماها عبارة عن الـ infimum للدالة F of X
+
+393
+00:34:57,460 --> 00:35:02,860
+حيث X موجودة على I وكأنه في الواقع أخذ الـ
+
+394
+00:35:02,860 --> 00:35:07,520
+partition هو عبارة عن نقطيناللي عبارة عن a و مين و
+
+395
+00:35:07,520 --> 00:35:12,800
+b ال partition بس a و b في هذا الحلق و جالك اللي
+
+396
+00:35:12,800 --> 00:35:18,020
+هو .. ليش .. هلجيت تشوفوا ال mi capital عبارة عن
+
+397
+00:35:18,020 --> 00:35:21,860
+ال supreme لل f of x such that x element in I
+
+398
+00:35:21,860 --> 00:35:27,780
+بقولك الآن إذن .. إذن mi ال mi small مضروبة في طول
+
+399
+00:35:27,780 --> 00:35:32,120
+الفترة يعني ال partition واحد لأن ال partition a و
+
+400
+00:35:32,120 --> 00:35:39,750
+b بس أصغر أو يساوياللي هو اللوفاف طبيعي طبيعي لأن
+
+401
+00:35:39,750 --> 00:35:45,570
+هذا واحد من مين من ال lower sums، بظبط؟ وهذا أصلا
+
+402
+00:35:45,570 --> 00:35:49,170
+ال supremum لل lower sums فهيكون ال supremum أكبر
+
+403
+00:35:49,170 --> 00:35:52,670
+يساوي مين؟ واحد منهم، هذا زي ما أقول أنها lower
+
+404
+00:35:52,670 --> 00:35:58,450
+sum على partition في A و BSimilarly, M I في الـ B
+
+405
+00:35:58,450 --> 00:36:03,590
+minus A أكبر أو ساوي ال other sum of F، ليه؟ لأن
+
+406
+00:36:03,590 --> 00:36:07,470
+هذا عبارة عن واحد من ال other sums و هذا عبارة عن
+
+407
+00:36:07,470 --> 00:36:10,210
+ال N في المملكة و ليه ال other sums فطبيعي هيكون
+
+408
+00:36:10,210 --> 00:36:14,260
+ال U of F أكبر أو ساوي B minus Ato be more
+
+409
+00:36:14,260 --> 00:36:18,360
+specific for every B element in B of I نحن لدينا M
+
+410
+00:36:18,360 --> 00:36:22,140
+I في B minus A أصغر أو يساوي L, B و F لأن هذا واحد
+
+411
+00:36:22,140 --> 00:36:28,800
+من ال partitions قلنا اللي هي لفترة I نفس الشيء
+
+412
+00:36:28,800 --> 00:36:34,800
+فبصير عند ال L of B و A F أصغر أو يساوي اللي هو ال
+
+413
+00:36:34,800 --> 00:36:40,060
+U, B و F أصغر أو يساوي M I في B minus Aمعروف هذا
+
+414
+00:36:40,060 --> 00:36:43,580
+أنا مش حاجة لزمنه أصلاً فبصير mi أصغر سواء ل و بف
+
+415
+00:36:43,580 --> 00:36:48,060
+و ل و بف أصغر سواء mi في ال b-a اللي وضحته هناك
+
+416
+00:36:48,060 --> 00:36:54,640
+أوضح من اللي مكتوب هناك واضح أه نيجي لنظرية اللي
+
+417
+00:36:54,640 --> 00:37:00,630
+عندى هذهTheorem بتقول لت I بساوة A وB and لت F من
+
+418
+00:37:00,630 --> 00:37:05,490
+I لR بيه bounded function وفهمنا ليش احنا بنقول
+
+419
+00:37:05,490 --> 00:37:08,410
+bounded then the lower integral L of F and the
+
+420
+00:37:08,410 --> 00:37:12,090
+upper integral U of F on I exist moreover ال L of
+
+421
+00:37:12,090 --> 00:37:15,330
+F أشمالها أصغر ساوية U of F طبعا ال existence سبب
+
+422
+00:37:15,330 --> 00:37:18,650
+ال existence كله اللي هو انه ال function bounded
+
+423
+00:37:18,650 --> 00:37:21,110
+مثلا bounded كل اللي هنا الحسابات اللي على أساس ال
+
+424
+00:37:21,110 --> 00:37:25,350
+supernormal information موجودةلأن اللي قال الـ U
+
+425
+00:37:25,350 --> 00:37:29,170
+of F أصغر ساوي مين؟ U بقى، U of F كلام سهل، شوف
+
+426
+00:37:29,170 --> 00:37:32,210
+إيش بدنا ناخد بتاخد بي واحد و بي اتنين بي أي two
+
+427
+00:37:32,210 --> 00:37:36,210
+partitions of I، ماشي؟ لأن then by لمّا اللي حكينا
+
+428
+00:37:36,210 --> 00:37:40,150
+قبل شوية عنها، اللي قال بي واحد و أف أصغر ساوي U
+
+429
+00:37:40,150 --> 00:37:44,350
+بي اتنين of F، ماشي الحال؟ لأي two partitions،
+
+430
+00:37:44,350 --> 00:37:48,270
+ثبتلي واحدة منهم الآن، خلّي اللي هو بي اتنين of is
+
+431
+00:37:48,270 --> 00:37:52,560
+fixedماشي صارت هذه .. هذه القيمة صارت .. بنحكي عن
+
+432
+00:37:52,560 --> 00:37:56,980
+عدد محدد ماشي بـ 2 arbitrarily صح لكن الان انا بدي
+
+433
+00:37:56,980 --> 00:38:01,020
+ثابته وهذه المتغيرة صار عند الان ال U B 2 و F
+
+434
+00:38:01,020 --> 00:38:07,940
+عبارة عن upper bound of the set of all اللي هي مين
+
+435
+00:38:07,940 --> 00:38:13,790
+ال B I و F على أي partitionطيب هذا upper bound
+
+436
+00:38:13,790 --> 00:38:19,270
+فبنقله في قفل هذه اللي هو ال minimum الهن ال
+
+437
+00:38:19,270 --> 00:38:22,470
+supremum الهن مظبوط اللي هو ال least upper bound
+
+438
+00:38:22,470 --> 00:38:26,350
+إذا ال least upper bound أكيد أصغر أو شومين ال
+
+439
+00:38:26,350 --> 00:38:32,340
+upper bound كمان مرةطيب، الآن therefore U B 2 و F
+
+440
+00:38:32,340 --> 00:38:37,820
+is an upper bound of هذه الست ماشي؟ و هذه الست ال
+
+441
+00:38:37,820 --> 00:38:42,500
+supremum لها إيش اسمه؟ L of F إذا أكيد اللي هو ال
+
+442
+00:38:42,500 --> 00:38:45,220
+supremum اللي هو ال least upper bound اللي هو ال L
+
+443
+00:38:45,220 --> 00:38:51,620
+of F أصغر أو يساوي واحد من ال upper bounds، مظبوط؟
+
+444
+00:38:51,620 --> 00:38:58,990
+أي سؤال؟واضح ها؟ الان خلصها من هذه الان similarly
+
+445
+00:38:58,990 --> 00:39:04,390
+since B2 was arbitrarily partition of I صارت الان
+
+446
+00:39:04,390 --> 00:39:10,230
+عند L of F أصغر أو يساوي UB2 of F يعني صارت هذه
+
+447
+00:39:10,230 --> 00:39:17,530
+عدد أصغر أو يساوي ال UB2 of F for any partition B2
+
+448
+00:39:18,500 --> 00:39:22,560
+الان صارت هذه عبارة عن lower bound لها لهذه ال
+
+449
+00:39:22,560 --> 00:39:26,200
+collection lower bound لها اذا هذه lower bound
+
+450
+00:39:26,200 --> 00:39:30,160
+اصغر او يساوي ال greatest lower bound مين ال
+
+451
+00:39:30,160 --> 00:39:35,200
+greatest lower bound لهدول اللي هو ال L اللي هو ال
+
+452
+00:39:35,200 --> 00:39:45,700
+U of F اذا صار عند ال L of F اصغر او يساوي U of F
+
+453
+00:39:45,700 --> 00:39:48,360
+اي سؤال؟
+
+454
+00:39:51,810 --> 00:39:56,530
+واضحة؟ ان في سؤال كان في ريال واحد زي هيك بنحل على
+
+455
+00:39:56,530 --> 00:39:59,690
+هيك اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+456
+00:39:59,690 --> 00:40:00,510
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+457
+00:40:00,510 --> 00:40:01,130
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+458
+00:40:01,130 --> 00:40:01,850
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+459
+00:40:01,850 --> 00:40:01,850
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+460
+00:40:01,850 --> 00:40:06,550
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+461
+00:40:06,550 --> 00:40:13,540
+اربع اتنين اربع اعدد هذا هو اللي هو اللي اللي اللي
+
+462
+00:40:13,540 --> 00:40:17,340
+اللي المتغير صار عند العدد هذا أصغر أو شاوي كل
+
+463
+00:40:17,340 --> 00:40:22,080
+اللي هو أعضاء العائلة اللي بتحكي عنها إذا صار الآن
+
+464
+00:40:22,080 --> 00:40:27,580
+هذا الالوفاف عبارة عن lower bound ofthe collection
+
+465
+00:40:27,580 --> 00:40:32,600
+of all U, P, T و F عالميا على ال partitions هذه
+
+466
+00:40:32,600 --> 00:40:36,260
+مادام هذا صار عبارة عن lower bound إذا هذا lower
+
+467
+00:40:36,260 --> 00:40:40,580
+bound أصغر أو يساوي ال greatest lower bound اللي
+
+468
+00:40:40,580 --> 00:40:43,860
+هو اللي بنسميه ال infimum إذا صارت ال L و F أصغر
+
+469
+00:40:43,860 --> 00:40:47,000
+أو يساوي ال infimum لهدول ال infimum لهدول مين هو
+
+470
+00:40:47,000 --> 00:40:52,940
+ال U و Fالـ U of F هو الـ infimum لكل الـ U, B, T,
+
+471
+00:40:53,280 --> 00:40:58,040
+2 و F such that B2 element in the set of all
+
+472
+00:40:58,040 --> 00:41:07,220
+partitions نيجي الآن لبعده الـ Definition الان ..
+
+473
+00:41:07,220 --> 00:41:16,080
+الان احنا زغرنا ال other sums و كبرنا ال other
+
+474
+00:41:16,080 --> 00:41:22,680
+sumsيوم مالتجهن مع بعض بنسمي اللي هو الالتقاء هذا
+
+475
+00:41:22,680 --> 00:41:26,320
+أو الرقم اللي التقن فيه هو قيمة الـ Remain
+
+476
+00:41:26,320 --> 00:41:30,800
+Integral للفункشن F على الفترة المذكورة وهذا هو
+
+477
+00:41:30,800 --> 00:41:35,040
+التعريف let I بسوء A و B and let F من I لعند R be
+
+478
+00:41:35,040 --> 00:41:39,060
+a bounded function then F is said to be Remain
+
+479
+00:41:39,060 --> 00:41:46,480
+Integrable on I if L of Fاللي هو عبارة عن الـ
+
+480
+00:41:46,480 --> 00:41:54,140
+Supremum للـ Lower Bounds للـ Lower Sums بساوي ال
+
+481
+00:41:54,140 --> 00:42:00,320
+Infimum لل Upper Sums يوم ما يتساون هذولة بنسمي
+
+482
+00:42:00,320 --> 00:42:03,780
+الـ Function is Remain Integrable وفي هذه الحالة
+
+483
+00:42:03,780 --> 00:42:06,860
+بيكون القيمة المشتركة هذه هي اللي بنسميها الـ
+
+484
+00:42:06,860 --> 00:42:13,740
+Integration من A ل B F of X D of Xدكتور ان الملحنة
+
+485
+00:42:13,740 --> 00:42:17,420
+احنا بدنا نجيب مساحة كذا كذا احنا ال .. المساحة
+
+486
+00:42:17,420 --> 00:42:21,480
+إذا كان فوق الآن إذا كان تحت بيكون سالب المساحة
+
+487
+00:42:21,480 --> 00:42:24,680
+إذا كان مخلوط بيصير .. إذا كان فوق و تحت معناته
+
+488
+00:42:24,680 --> 00:42:28,180
+بيصير جزء مساحة و جزء سالب مساحة عشان نجد مساحته
+
+489
+00:42:28,180 --> 00:42:30,980
+بالظبط تاخد ال absolute بتقطع لذاك و تاخد ال
+
+490
+00:42:30,980 --> 00:42:34,340
+absolute value اللي بيطلع اللي هو المساحة عشان
+
+491
+00:42:34,340 --> 00:42:39,580
+نجيبوا مساحته و نجسم الملحنة هذا لمستطيلة صح؟
+
+492
+00:42:41,500 --> 00:42:46,400
+كمستطيل و بيجيبوا مجموع مستطلاق بدين المنحنى بديك
+
+493
+00:42:46,400 --> 00:42:51,760
+مساحة تحت المنحنى لما تاخد ال upper sums و ال
+
+494
+00:42:51,760 --> 00:42:55,260
+lower sums و تاخد ال supremum و تاخد ال infimum و
+
+495
+00:42:55,260 --> 00:42:59,080
+يكون ال supremum بساوي ال infimum بتلح هو المساحة
+
+496
+00:42:59,080 --> 00:43:04,990
+تحت المنحنى في حالة ال positive functionsفي حالة
+
+497
+00:43:04,990 --> 00:43:08,710
+الـ negative المخلوق بيصير integration بيصير قيمة
+
+498
+00:43:08,710 --> 00:43:12,170
+integration قيمة ال integration لا تعبر عن المساحة
+
+499
+00:43:12,170 --> 00:43:16,670
+اللي هو بالضبط إلا في حالة ال other إلا في حالة ال
+
+500
+00:43:16,670 --> 00:43:19,970
+positive ال function في حالة ال negative بتعبر على
+
+501
+00:43:19,970 --> 00:43:24,170
+سلب المساحة في حالة إشي فوج و إشي تحت بيصير اللي
+
+502
+00:43:24,170 --> 00:43:26,950
+هو .. لأ المساحات بت cancel بعضها و بيصير قيمة
+
+503
+00:43:26,950 --> 00:43:30,930
+integrationبيدك المساحات من وسط ال integration
+
+504
+00:43:30,930 --> 00:43:33,110
+انها تستخدم ال integration في إيجاد المساحة
+
+505
+00:43:33,110 --> 00:43:37,570
+بتجزئها لإيش إلى أجزاء وين بتقطع محور السينات يعني
+
+506
+00:43:37,570 --> 00:43:40,550
+بتحدد وين موجبة و وين سالبة بتاخد ال absolute
+
+507
+00:43:40,550 --> 00:43:43,410
+value حتى لو ماكنشت يعرف مين الموجبة ومين السالبة
+
+508
+00:43:43,410 --> 00:43:46,570
+وبيطلع اللي هو عن طريق ال integration بتوجد قيمة
+
+509
+00:43:46,570 --> 00:43:52,290
+مين المساحة لكن في حالة الدالة موجبة على كل الفترة
+
+510
+00:43:52,290 --> 00:43:59,410
+ال integration هو بالظبط المساحة طيبصلى على النبي
+
+511
+00:43:59,410 --> 00:44:01,990
+عليه الصلاة والسلام عرفنا الـ Romantic Grability
+
+512
+00:44:01,990 --> 00:44:06,470
+وقلنا اللي هو .. اللي هو الاشياء المشتركة اللي
+
+513
+00:44:06,470 --> 00:44:11,290
+حصلنا عليها الآن بنعرف برضه كتعريف من A ل B F of X
+
+514
+00:44:11,290 --> 00:44:15,930
+DX بساوي ناقص من B ل A F of X DX وبنعرف كتعريف أن
+
+515
+00:44:15,930 --> 00:44:19,830
+ال integration من A ل A F of X DX H بساوي سفر اطلع
+
+516
+00:44:19,830 --> 00:44:25,120
+فوق خليني أخد مثال وننهي بهذا المثالالآن .. و هذا
+
+517
+00:44:25,120 --> 00:44:30,080
+المثال احنا .. يعني .. كنا ناخد .. نفس المثال اللي
+
+518
+00:44:30,080 --> 00:44:33,760
+ناخده في ال calculus خلّينا نحكي عنه بالتفصيل الان
+
+519
+00:44:33,760 --> 00:44:37,480
+example show that g of x بساوة x is integrable on
+
+520
+00:44:37,480 --> 00:44:41,700
+0 و 1 بدنا نثبت أنه الدالة اللي هي g of x اللي
+
+521
+00:44:41,700 --> 00:44:45,220
+بنعرفها اللي هي المثال البسيط بساوة x عبارة عن
+
+522
+00:44:45,220 --> 00:44:52,130
+integrable عالميا على اللي هو الفترة 0 و 1الان انا
+
+523
+00:44:52,130 --> 00:44:56,270
+لتسهيل عملية الحسابات هاخد عائلة من ال partitions
+
+524
+00:44:56,270 --> 00:45:03,050
+معينة هذه العائلة بتسهيل الحسابات طب بنفع في ضوء
+
+525
+00:45:03,050 --> 00:45:07,910
+العلاقات اللي هنشوفها كيف توصلنا بالظبط ان ال L of
+
+526
+00:45:07,910 --> 00:45:12,830
+F بساوة ال U of F و لخصوصية الحسابات ده نشوف كيف
+
+527
+00:45:12,830 --> 00:45:21,760
+عندى ال F of X بساوة Xعنديها بديها من 0 لعند مين؟
+
+528
+00:45:21,760 --> 00:45:28,580
+لعند 1 هذه y بساوة x على الفترة 0 و 1 ايش بدنا
+
+529
+00:45:28,580 --> 00:45:34,580
+نسوي؟ بدنا نيجي اللي هو ان نعمل partition بين هذا
+
+530
+00:45:34,580 --> 00:45:39,540
+ال partition بديه يسهل الإحسابات فأسهل شيء بدي
+
+531
+00:45:39,540 --> 00:45:44,640
+أجزء هذه الفترة من 0 ل1 لN من الأجزاء و بديها تكون
+
+532
+00:45:44,640 --> 00:45:49,430
+كلها متساويةبنفع، أه، هينفع، هتشوف كيف اللي هو هذا
+
+533
+00:45:49,430 --> 00:45:52,650
+نفع في ضوء العلاقات بين اللي هو الـ Supremum و
+
+534
+00:45:52,650 --> 00:45:57,050
+الانفموع المجموعة الأكبر و المجموعة الأصغر و أيضًا
+
+535
+00:45:57,050 --> 00:46:01,130
+في ضوء ال limits المعينة اللي هان اللي هتيجي تخلي
+
+536
+00:46:01,130 --> 00:46:05,010
+اللي هو علاقة توصّل إلى اللي بدنيها، تفهم علش؟
+
+537
+00:46:05,010 --> 00:46:10,610
+ماقولهم كده، هذا صار عندي، هذا Zeroأما ده بدأت
+
+538
+00:46:10,610 --> 00:46:13,510
+تجزئها طولها واحد تجزئها الان من الفتراء sub
+
+539
+00:46:13,510 --> 00:46:16,130
+intervals إذا كل واحدة واحدة على الان هذا التاني
+
+540
+00:46:16,130 --> 00:46:20,130
+اتنين على الان التالتة تلاتة على الان تلاتة على
+
+541
+00:46:20,130 --> 00:46:24,770
+الان لما نصل للفترة النموذجية xk اللي هي تلقى k
+
+542
+00:46:24,770 --> 00:46:30,610
+minus واحد على ان وk على ان هذا اللي هي xk minus
+
+543
+00:46:30,610 --> 00:46:36,670
+واحد وهذا ال xk وهذا xنوت و اد اكس واحد الى اخرى
+
+544
+00:46:36,670 --> 00:46:39,790
+لان ما اصل الاخر واحدة اللى هى n على n اللى هى
+
+545
+00:46:39,790 --> 00:46:45,150
+واحدة ماشي الحالة هذا اللى عندى اللى .. لو اجيت
+
+546
+00:46:45,150 --> 00:46:48,190
+حسبت الان مدى احسب هذا ال partitions اللى صار عندى
+
+547
+00:46:48,190 --> 00:46:53,930
+عبارة عن zero و الواحدة الان و اتنين على n لما اصل
+
+548
+00:46:53,930 --> 00:46:58,490
+لعند ال n على n اللى هى ايش الواحدة هذه عائلة ال
+
+549
+00:46:58,490 --> 00:47:04,620
+partitions اللى اختارتها ماشي شوفوا عليها ال nلو
+
+550
+00:47:04,620 --> 00:47:09,460
+جيت حسبت اللي هو طول الـ interval واحدة لان لو بده
+
+551
+00:47:09,460 --> 00:47:16,960
+أحسب الآن L لل partition هذا اللي هو مين هو L ال F
+
+552
+00:47:16,960 --> 00:47:23,840
+عندي و ال P N هتساوي عبارة عن ال summation عارفين
+
+553
+00:47:23,840 --> 00:47:29,780
+انتوا ال summation اللي هو M small K في X K ناقص X
+
+554
+00:47:29,780 --> 00:47:36,290
+K minus واحد K من عند واحد عند N ويساويالان ال MK
+
+555
+00:47:36,290 --> 00:47:41,890
+في الفترة الأولى ايش هيكون عنده؟ صفر في الفترة
+
+556
+00:47:41,890 --> 00:47:47,430
+التانية ايش هيكون؟ واحدة على الانكريزين جدا اللي
+
+557
+00:47:47,430 --> 00:47:50,150
+بعدها اتنين على انواع و هكذا
+
+558
+00:47:52,920 --> 00:47:57,520
+الـ Mk in general إيش هيصير عنده الـ Mk وإيش
+
+559
+00:47:57,520 --> 00:48:03,020
+المساحة هي K minus واحد على مين على هذا اللي هو
+
+560
+00:48:03,020 --> 00:48:08,280
+طول تبع مين الـ Mk واضحة؟ لأن الـ infimum على
+
+561
+00:48:08,280 --> 00:48:12,760
+الفترة هذه النموذجية اللي هو ال .. ال .. ال
+
+562
+00:48:12,760 --> 00:48:17,920
+infimum عليها اللي هو أول واحدة لإنها increasing
+
+563
+00:48:17,920 --> 00:48:22,630
+واضحة تصورفلان هذه ثابتة أنا اختارتها أصلا ثابتة
+
+564
+00:48:22,630 --> 00:48:26,430
+طول الفترة ثابتة اللي هو 1 على n بيصير هذا إيش n
+
+565
+00:48:26,430 --> 00:48:32,670
+تربيع كامل عند واحد لعند مين لعند n واضح أه ويساوي
+
+566
+00:48:32,670 --> 00:48:38,110
+1 على n تربيع فيه ال summation هذا اللي هو عبارة
+
+567
+00:48:38,110 --> 00:48:42,830
+عن بيبدأ من 0 زائد 1 ولمّا يصل لعند مين لعند n
+
+568
+00:48:42,830 --> 00:48:49,760
+ناقص 1هذا بعرف ما هو مجموعه ويساوي 1 الان تربيع في
+
+569
+00:48:49,760 --> 00:48:54,760
+هذا ان لما نكون من واحد لعند ان ان فان زاد واحد
+
+570
+00:48:54,760 --> 00:48:58,440
+الان على اتنين الان هذا من وين واحد لعند ان ناقص
+
+571
+00:48:58,440 --> 00:49:03,540
+واحد فان ناقص واحد لكل عالمين يا جماعة على اتنين
+
+572
+00:49:03,540 --> 00:49:09,580
+ويساوي الان اعملي هذا بيطلع نص عندي ويساوي نص في
+
+573
+00:49:09,580 --> 00:49:15,150
+اللي هو ان تربيع ناقص من انعلى أن تربيعه بيصير
+
+574
+00:49:15,150 --> 00:49:22,650
+واحد ناقص واحدة لان صح ولا لأ طيب similarly for me
+
+575
+00:49:22,650 --> 00:49:29,430
+لأن لما بدي أخد اللي قاله و أفله اه ال .. ال ..
+
+576
+00:49:29,430 --> 00:49:36,930
+بعدين شوف عليهم الآن القبر للأف و بي أن بنفس
+
+577
+00:49:36,930 --> 00:49:44,250
+السلوب بيصير عندي عبارة عن summation mkفي xk-xk-1
+
+578
+00:49:44,250 --> 00:49:49,630
+k من عند 1 لعند n الان ال mk ال m واحد هيه لان
+
+579
+00:49:49,630 --> 00:49:54,010
+المتنين هيه إذا ال mk هي عبارة عن مين؟ k على n
+
+580
+00:49:54,010 --> 00:49:59,070
+لأنه increasing زي ما قلنا ويساوي صماشen k على n
+
+581
+00:49:59,070 --> 00:50:04,800
+في 1 على nK من عند واحد لعند ان ويساوي summation
+
+582
+00:50:04,800 --> 00:50:07,640
+واحدة لان تربية في summation لK من واحد لان لان
+
+583
+00:50:07,640 --> 00:50:12,800
+اللي ان فان زائد واحد الان هو الكل مكسوب على اتنين
+
+584
+00:50:12,800 --> 00:50:17,400
+ويساوي نص في اللي هو بطلع عندي هذا عبارة عن واحد
+
+585
+00:50:17,400 --> 00:50:23,920
+زائد واحدة لان، مظبوط؟ طيب إذا انصار عندي الآن
+
+586
+00:50:23,920 --> 00:50:28,410
+حصلت على التاليزي ما شوفنا حسابيا جميعا من هنا
+
+587
+00:50:28,410 --> 00:50:34,530
+اطلع لفوق صار عندى الان LPNG او F عبارة عن نصف
+
+588
+00:50:34,530 --> 00:50:40,230
+واحد نقص واحدة الان UPNJ ايش بيساوي نصف واحد زائد
+
+589
+00:50:40,230 --> 00:50:48,330
+واحد على مين على الان واضح الان الان اه الان الان
+
+590
+00:50:48,330 --> 00:50:53,100
+الان انت بي .. عندى ال collection هذهالـ
+
+591
+00:50:53,100 --> 00:50:57,280
+collection هذه partitions B1 is a partition اللي
+
+592
+00:50:57,280 --> 00:51:03,740
+هو عبارة عن Zero و واحد B2 Zero نص و واحد B3 Zero
+
+593
+00:51:03,740 --> 00:51:09,160
+و تلت و تلتين و واحد و هكذا إذا هذه عائلة من ال
+
+594
+00:51:09,160 --> 00:51:14,060
+partitionsجزء من مين؟ من الـ partitions العامة
+
+595
+00:51:14,060 --> 00:51:17,100
+يعني ال .. ال part .. هي the set of all partitions
+
+596
+00:51:17,100 --> 00:51:22,220
+هذه أكيد جزئية من the set of all partitions لمين؟
+
+597
+00:51:22,220 --> 00:51:25,980
+لل I اللي عنده اللي هي الفترة من مين؟ من 01 إذا
+
+598
+00:51:25,980 --> 00:51:31,500
+هذه مجموعة جزئية من هذه، مظبوط؟ طيب، الآن لو أجينا
+
+599
+00:51:31,500 --> 00:51:35,820
+أخدنا اللي هو ال set of partitions هذه أكيد ال
+
+600
+00:51:35,820 --> 00:51:39,580
+supreme على هذهالان ال .. ال .. ال .. ال .. ال ..
+
+601
+00:51:39,580 --> 00:51:44,820
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+602
+00:51:44,820 --> 00:51:45,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+603
+00:51:45,160 --> 00:51:48,400
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+604
+00:51:48,400 --> 00:51:48,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+605
+00:51:48,420 --> 00:51:50,120
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+606
+00:51:50,120 --> 00:51:50,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+607
+00:51:50,220 --> 00:51:50,340
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+608
+00:51:50,340 --> 00:51:59,480
+.. ال .. ال .. ال .. ال .. ال ..
+
+609
+00:51:59,480 --> 00:52:02,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+610
+00:52:02,920 --> 00:52:02,920
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+611
+00:52:02,920 --> 00:52:02,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+612
+00:52:02,920 --> 00:52:02,920
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+613
+00:52:02,920 --> 00:52:09,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..such that
+
+614
+00:52:09,060 --> 00:52:14,120
+N element in N هذه اللي هي main ال collection of
+
+615
+00:52:14,120 --> 00:52:19,260
+all partitions ال B1 وB2 وB3 عند BN لو جينا أخدنا
+
+616
+00:52:19,260 --> 00:52:24,740
+ال supremumلكل القيم هذه هيكون أصغر أو يساوي الـ
+
+617
+00:52:24,740 --> 00:52:32,320
+Supremum لمين لل L of F و B such that B element in
+
+618
+00:52:32,320 --> 00:52:36,620
+B and B of I لأن collection of all partitions هذه
+
+619
+00:52:36,620 --> 00:52:41,940
+اللي هو تحتوى ال partitions هدولة واضح الحمد الله
+
+620
+00:52:41,940 --> 00:52:45,500
+الان ال Supremum على القيم هذه اللي هي مين القيم
+
+621
+00:52:45,500 --> 00:52:51,230
+كانت عندهاللي هو عبارة عن نص في واحد ناقص ميل واحد
+
+622
+00:52:51,230 --> 00:52:55,590
+علان ال supremum لهذه عبارة عن zero إذن بتظل هي
+
+623
+00:52:55,590 --> 00:53:00,590
+إيش بتساوي نص ال supremum للنص في واحد ناقص واحد
+
+624
+00:53:00,590 --> 00:53:05,070
+علان معايا؟
+
+625
+00:53:05,070 --> 00:53:16,470
+أي سؤال؟ طيب إذا هذا مين هو؟ هذا عبارة عن الأو ما
+
+626
+00:53:16,470 --> 00:53:21,170
+فاهم ولا لأ إذا صار عند ال L و ال F مثبتها هذه ال
+
+627
+00:53:21,170 --> 00:53:29,390
+L و ال F هيصير أكبر أو يساوي النص نحك طيب
+
+628
+00:53:29,390 --> 00:53:35,650
+similarly for me and for you الآن عندي حصلت على ال
+
+629
+00:53:35,650 --> 00:53:41,970
+U, F و B أن لهذه العائلة الان الان the set of all
+
+630
+00:53:41,970 --> 00:53:50,880
+U, F و B أنsuch that N element in N هذه العائلة
+
+631
+00:53:50,880 --> 00:53:53,900
+مجموعة جزئية من العائلة الكبيرة الـ B of I الـ
+
+632
+00:53:53,900 --> 00:54:00,940
+partitions للـ I إذن هذه الـ infimum لها هيصير
+
+633
+00:54:00,940 --> 00:54:10,580
+أكبر أو يساوي الـ infimum لـ U, F و B such that B
+
+634
+00:54:10,580 --> 00:54:18,550
+element in B of Iالـ collection هذه أصغر من الـ
+
+635
+00:54:18,550 --> 00:54:21,730
+collection هذه، بظبط؟ إذا صار الـ infimum على هذه
+
+636
+00:54:21,730 --> 00:54:25,610
+أكبر و ساوي الـ infimum على هذه الـ infimum لهذه
+
+637
+00:54:25,610 --> 00:54:27,470
+الـ collection و اللي هو الـ infimum في الواقع
+
+638
+00:54:27,470 --> 00:54:31,110
+لمين؟ الـ infimum لهذه الـ infimum لهذه ليش
+
+639
+00:54:31,110 --> 00:54:35,910
+هيساوي؟ نص فبصير عندي نص أكبر و ساوي الـ infimum
+
+640
+00:54:35,910 --> 00:54:38,430
+هذا اللي هو أكبر و ساوي هذا اللي هو هذا اللي هو
+
+641
+00:54:38,430 --> 00:54:44,010
+مين؟ الـ U of F إذا حصلنا على كمان حاجة إن الـ U
+
+642
+00:54:44,010 --> 00:54:52,790
+of Fأصغر أو يساوي نص اللخص المعلومتين هدولة ونحصل
+
+643
+00:54:52,790 --> 00:54:57,810
+على اللي بدناه من المعلومتين من المعلومتين اللي
+
+644
+00:54:57,810 --> 00:55:06,860
+صار عندى اللي هو L of Fاللي هو اكبر او يساوي نص
+
+645
+00:55:06,860 --> 00:55:10,920
+وانا بعرف ان دائما ال الوف ايش ماله اصغر او يساوي
+
+646
+00:55:10,920 --> 00:55:15,180
+ال يوف اف و ال يوف اف ايش حصلته اصغر او يساوي من
+
+647
+00:55:15,180 --> 00:55:20,360
+نص اذا هذا اللي خلى اللي هو ال partition اللي عندى
+
+648
+00:55:20,360 --> 00:55:23,540
+اللي سهل اللي اخترته او ال set of partitions انها
+
+649
+00:55:23,540 --> 00:55:28,580
+توصلني للنتيجة اللي بديها بيصير عندى ال الوف اصغر
+
+650
+00:55:28,580 --> 00:55:33,220
+او يساوي ال يوف اف و هذا بين النص التنتين اذا الوف
+
+651
+00:55:33,220 --> 00:55:40,650
+افبساوية وف اف بساوية نص وهذا معناه ان ال function
+
+652
+00:55:40,650 --> 00:55:45,770
+is reversible and integrable and ال integration من
+
+653
+00:55:45,770 --> 00:55:52,650
+zero ل واحد لل x dx بساوية نص و الله يعطيك العافية
+
+654
+00:55:52,650 --> 00:55:54,590
+و المرة القادمة نكملها
+
diff --git a/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_raw.json b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..161fd9660da40193822583527186577c3d2a0a14
--- /dev/null
+++ b/PL9fwy3NUQKwavFmspRNWAhbDWNXQPDNlH/uaBBi7JsFSQ_raw.json
@@ -0,0 +1 @@
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higher", "probability": 0.890625}, {"start": 247.01, "end": 247.47, "word": " derivative", "probability": 0.94921875}, {"start": 247.47, "end": 247.59, "word": " و", "probability": 0.34326171875}, {"start": 247.59, "end": 248.09, "word": " هتحللنا", "probability": 0.89697265625}, {"start": 248.09, "end": 248.51, "word": " المشاكل", "probability": 0.9930419921875}, {"start": 248.51, "end": 248.65, "word": " اللي", "probability": 0.97119140625}, {"start": 248.65, "end": 248.91, "word": " كانت", "probability": 0.968017578125}, {"start": 248.91, "end": 249.39, "word": " ماتتحللاش", "probability": 0.7806222098214286}, {"start": 249.39, "end": 249.75, "word": " جامعي", "probability": 0.60504150390625}, {"start": 249.75, "end": 249.93, "word": " اللي", "probability": 0.94873046875}, {"start": 249.93, "end": 250.05, "word": " هي", "probability": 0.888671875}, {"start": 250.05, "end": 250.29, "word": " second", "probability": 0.65771484375}, {"start": 250.29, "end": 250.69, "word": " 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differentiable و أشهر منه و مثال مشهور وسهل اللي هو F of X بسوء ال absolute value لل X F of X بسوء ال absolute value لل X هذا اللي هو", "tokens": [40228, 22653, 3714, 43020, 13672, 1829, 39896, 2423, 4386, 2423, 4386, 2423, 4386, 1975, 5016, 8315, 13672, 1829, 10874, 16758, 8315, 12174, 36150, 13412, 2407, 10632, 13672, 1829, 10874, 1829, 3555, 8315, 11296, 32748, 6027, 3660, 39896, 3714, 5016, 15040, 11296, 8978, 16472, 3794, 1829, 16758, 4032, 41185, 819, 72, 2310, 4032, 2423, 2099, 5551, 3615, 23942, 9154, 2423, 4386, 9154, 32748, 6027, 3660, 8717, 36178, 11296, 4032, 9122, 3215, 3224, 4032, 2423, 2445, 819, 9364, 44381, 23758, 2423, 28820, 10943, 37893, 11778, 47302, 15042, 11331, 33546, 1211, 16472, 3224, 2423, 42432, 2445, 6055, 30544, 819, 9364, 4032, 5551, 8592, 3224, 2288, 9154, 3224, 4032, 50113, 6027, 37893, 3224, 13063, 46952, 3224, 1211, 13672, 1829, 31439, 479, 295, 1783, 4724, 3794, 2407, 38207, 2423, 8236, 2158, 24976, 1783, 479, 295, 1783, 4724, 3794, 2407, 38207, 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F prime of X not في X واحد نقص X not زائد مين الآن ال remainder زائد ال remainder ال remainder إيش هو F double prime عند ال C واحد اللي لاجيناها في X minus X not الكل تربيع على 2 فكتوريا", "tokens": [6027, 20292, 31439, 479, 295, 1783, 406, 30767, 16373, 3215, 479, 5835, 295, 1783, 406, 8978, 1783, 36764, 24401, 8717, 4587, 9381, 1783, 406, 30767, 16373, 3215, 3714, 9957, 6024, 48506, 2423, 29837, 30767, 16373, 3215, 2423, 29837, 2423, 29837, 11933, 1829, 8592, 31439, 479, 3834, 5835, 43242, 2423, 383, 36764, 24401, 13672, 1829, 5296, 26108, 1829, 8315, 11296, 8978, 1783, 3175, 1783, 406, 2423, 28820, 6055, 2288, 21292, 3615, 15844, 568, 6156, 4117, 2655, 13063, 25528], "avg_logprob": -0.2309695474612407, "compression_ratio": 1.697142857142857, "no_speech_prob": 4.351139068603516e-06, "words": [{"start": 2052.67, "end": 2052.97, "word": "اللي", "probability": 0.7578125}, {"start": 2052.97, "end": 2053.33, "word": " هو", "probability": 0.96630859375}, {"start": 2053.33, "end": 2054.17, 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between x2 and x0 such that", "tokens": [10721, 9381, 17082, 2288, 9154, 13672, 1829, 31439, 14138, 456, 2514, 269, 17, 39894, 9566, 3555, 4587, 11296, 15844, 2031, 16, 15844, 2031, 17, 4032, 2031, 15, 456, 2514, 257, 269, 17, 1296, 2031, 17, 293, 2031, 15, 1270, 300], "avg_logprob": -0.3048780487804878, "compression_ratio": 1.140495867768595, "no_speech_prob": 6.967782974243164e-05, "words": [{"start": 2080.65, "end": 2081.17, "word": "أصغر", "probability": 0.82147216796875}, {"start": 2081.17, "end": 2081.39, "word": " من", "probability": 0.9609375}, {"start": 2081.39, "end": 2081.71, "word": " اللي", "probability": 0.5706787109375}, {"start": 2081.71, "end": 2081.87, "word": " هو", "probability": 0.978515625}, {"start": 2081.87, "end": 2082.73, "word": " similarly", "probability": 0.282470703125}, {"start": 2082.73, "end": 2085.13, "word": " there", "probability": 0.24267578125}, {"start": 2085.13, "end": 2085.77, "word": " exist", "probability": 0.58984375}, {"start": 2085.77, 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