Tom Apostol - Calculus Vol 1 & 2 [English]

Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra
and
Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability

Tom M. Apostol

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

Product Details
Volume 1
Hardcover: 666 pages
Publisher: Wiley; 2nd edition (January 16, 1991)
Language: English
ISBN-10: 0471000051
ISBN-13: 978-0471000051

Volume 2
Hardcover: 673 pages
Publisher: Wiley; 2nd edition (June 20, 1969)
Language: English
ISBN-10: 0471000078
ISBN-13: 978-0471000075

User Review:

This book is extremely well-written and leaves you with the feeling that it couldn't have been better. A tribute to this fact is that it is still in its second edition from 66 and, though it is rather old, has kept its quality.

It has a good number of exercises (usually between 15-30 per section/topic), which is less than most standard calculus book, but the difference is that the quality of the exercises here is much higher, and you will be surprised when some months later, when tackling some problem for another course, you will remember having done the exercise in Apostol. It also has answers to all the exercises (except for the ones which require a proof, rather than a number as a result). The problems range from easy to very hard, but usually there won't be more than two problems per section that one won't be able to do upon first reading and a little thinking.

The writing of the book is very good and rigorous, and it covers some topics that are not present in most calculus books. For example it has a small section on partial derivatives, it covers the weighted mean-value theorem for integrals and rearrangements of series. There are many other topics that don't usually fit in a calculus course, but the introduction of these when you are still learning it makes the connection between the topics much clearer. After having read the book from cover to cover, it has now become a very useful reference that never leaves my table. Also, because it is rigorous and has a broad number of topics, if you learn this and vol. II now you will save a lot of time later in more advanced courses such as analysis, differential equations, linear algebra and to a lesser extent even differential geometry and probability.

Because of its nonstandard approach, I think that this book is unsuitable for most people learning calculus for the first time (especially if you are taking a course and not just studying at your own pace). However, it (along with vol. II) is mandatory reading for anyone who wants to study math, in my opinion.