Teach Yourself Calculus

I used the 3rd edition of Loomis when I took Calculus. The book explains the material so well that I taught myself reading the book. The examples are numerous and particularly good in showing both easy and difficult problems. (Some books only show the easy problems or insufficient variety of them.) If anyone has a trouble with this book, serious review of algebra 2 is recommended. As for some of the previous reviews, there is no section 5.1.1 or 5.1.2, unless they are talking about a previous edition, which I have not seen. There is no mistake in section 5.1 or 5.2. But there are some mistakes in the answers in the back. Looking back at the book now, I prefer what Swokowski did with the series chapter much better (Loomis has interesting discussions on irrational numbers etc, but at the expense of losing the focus.). But Loomis does one of the best job in introducing vectors and functions of several variables. The chapter on Green's theorem is very nice, too. The chapter on multiple integral starts out by stating that it is only an introduction (like any other book at this level). What I realize now is that one has to go on to "advanced calculus" or vector calculus to master those things. I like Shuey's vector calculus, and after mastering that book, Buck's advanced calculus.

I liked the book. It was accesible and unpedantic. I had tried a couple of other sources before this one, and they all had a general tendency to be unapproachable. But it explained things clearly and concisely. It has many examples, and they're almost always clearly worked. The only two things to which I take exception are in section 5.1.2, in which a careless error is made that did in fact leave me saying "what the...", and the lack of creative sort of excercises thoughout the book. To be honest though, I never really did any of the exercises, and I understood calculus very well after reading this book. As one more plus, contrary to most academic books, this one is very cheap. Give it a try!