Advanced Calculus

Learning can be tough from this book. I used it in conjunction with random advanced calculus books from the library. Folland's really concise and you definitely gotta use the errata list... but still. Once you manage to understand what he's saying it's a pretty awesome feeling. Like you've earned the knowledge and it's for keeps, not like you just borrowed it from some easier book so you could pass a test or do a homework. Then you do the practice problems and it feels even better. And sometimes you're doing a problem and there's a little error (there are lots of these) and you'll be like "wait... this doesn't make sense, because... it should be..." and so you check the errata list. And you were right! Hah, beat the cranky Folland at his own game. It feels good and kind of gives you some ulterior motivation to continue learning. Just to show that miserly Mr. Folland that he's not as clever as he may think. Good in those kinda-quirky regards, but at the end of the day it's an inefficient use of time. I like Taylor's "Advanced Calculus" more.

I was a T.A for a course for which this was the textbook. I found this book a joy to read. The proofs are very careful and rigorous, but they also omit details which would otherwise halt the flow of the text. The omissions are made only where the author has already prepared the reader to fill in the gaps. The nice flow allows the reader to catch the ideas behind the proofs. The author motivates the theorems and proofs very well, making clever ideas transparent and natural. This prepares the reader for future studies. The book includes very interesting sections on more advanced topics like the Gamma function, Stirling's formula and Fourier series. If you just want a good grade in your course, this may not be the best book for you, but if you really want to learn something, this book is perfect.