Best Calculus one book I’m currently in my senior year of high-school. I’m planning to major in physics. I really enjoyed basic calculus but I really want to start studying it for real. I know university courses include calculus 1 2 3. I would like to start with calculus 1. I would like a suggestion for a book that would give me a thorough and deep understanding of calculus 1 and that would give me a head start in university, I want a hard book with many practice questions. Calculus is really interesting and I love it, I would really love to be fluent in it so I can easily understand the physics topics when I reach university. Any suggestion to what book is the best?
Good math books for physicists In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first thing to do is to learn to learn derivative, integral and algebra" (I don't know how much precise I'm being because I've read it in Portuguese). I would to know if there is some book that deals with math as Feynman did it in this lesson (respecting formalities, but teaching how to use the practical rules)? Also, someone have any recommendations for algebra book (college level)?
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$? We are asked the following:      let $f(x)$ be a continuous function on $[0, 1]$ such that   $$\int _ {0} ^ {1} \ f(y) dy = 1$$   prove that $f(x) = 1$ for some $x ∈ [0, 1]$   The question asks to take into account Rolle's Theorem and Mean Value Theorem.  I'm aware of the definitions, but I am really unsure how to answer this question and my tutors are not really responding till after easter.    Could someone please help? Why is there a "y" involved?  Thanks you