“Calculus” by Tom Apostol (Book Review)

In deciding that I needed to brush up on my math, I recently went looking for a good calculus / general math book, and came across this classic calculus text (comprised of two volumes) by Tom Apostol.  I found it by going to MIT’s Open Courseware site (http://ocw.mit.edu/), which has full information for many courses which have been taught at MIT, including syllabi (syllabuses?), reading lists, and lecture notes, and often exams.

I like this text because it explains the concepts fully in their “full-strength” versions.  I’ve found many textbooks seem to assume that the reader won’t understand the “real material”, and so they water it down in an attempt to make it easier to understand, which (at least for me) sometimes ends up making it harder to understand.

On the other side of the coin, it also gives explanations of why the material is important and how it fits into the bigger mathematical picture, instead of jumping right into the details without a discussion of the larger context.

Finally, the scope is very broad, teaching many basic mathematical topics that could be helpful to someone trying to get a basic math foundation, in addition to strictly “calculus” topics.  For example, it covers vector algebra, linear algebra, complex numbers, and basic real number axioms.

You can find the two volumes on Amazon here:

http://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051/

http://www.amazon.com/Calculus-Vol-Multi-Variable-Algebra-Applications/dp/0471000078/