what is the best book for calculus? I am looking for the best calculus book to use it to teach myself calculus. I have already had a bit of a search and these are what I have come up so far, But I have no idea which one is truly the best bet here and of more value in terms of being good at a self-study manner with lots of explanations and charts for every concepts and chapters. Here is the list i have so far:     James stewart calculus 7e Calculus -Richard A. Silverman The Calculus 7: Louis Leithold   Update: I am a Computer Science student and i need it for my courses and carrier, so please consider this in your answers. If there is any better book please mention it since i have no idea on these books. Thanks in advance
Calculus book recommendations (for complete beginner) Well I have not started calculus yet but I am really keen to. I would love if you suggest some books.  Points to be noted:   I really don't like the way textbooks are written so please no "textbooks"  I am COMPLETELY beginner in calculus. I know a little bit of trigonometry and what functions are but not really in depth.The book should start from the base, I mean really from the base. I may require a precalculus book too if the books don't cover that. I would really love if the book shows how calculus was developed, why it was developed and things like that.   Well,thanks in advance!
Why can partial derivatives be exchanged? In the   post in this stack exchange, one of the answers to the questions of do partial derivatives commute is: Second order partial derivatives commute if f is $C^2$ (i.e. all the second partial derivatives exist and are continuous). This is sometimes called Schwarz's Theorem or Clairaut's Theorem. This theorem is in my textbooks, yet I cannot seem to find the proof in them. I have tried proving the theorem yet I have gotten stuck. So, what is the proof of Clairaut's Theorem, or why do partial derivatives commute? If the proof is too long, a link to the proof with an intuitive explanation will be sufficient.