Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1) [Hardcover]

Tom M. Apostol (Author)

Editorial Reviews

From the Publisher

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

• Hardcover: 666 pages
• Publisher: Wiley; Volume 1 edition (June 1967)
• Language: English
• ISBN-10: 0471000051
• ISBN-13: 978-0471000051
• Product Dimensions: 7.1 x 1.6 x 10.2 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (33 customer reviews)
• Amazon Best Sellers Rank: #290,036 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

55 of 56 people found the following review helpful:

5.0 out of 5 stars Value in Diversity, January 26, 2000

By 

Got'em All (Ottawa, Ontario) - See all my reviews

This review is from: Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1) (Hardcover)

Apostol's presentation differs from the standard order and content for a calculus course, but is the more useful for it. Introducing integration first is historically more accurate and sets the tone for the rest of the book. This is not a "plumbers" book but the examples inform the abstraction very well. This book does not bog down in the tedium of analytical geometry and figure recognition which is too often the case elsewhere.

I am using the book for self-study as a middle-aged adult and find the presentation makes sense of things from other sources. The intellectual level is demanding but not unreasonable--challenging without being overwelming. While the introduction of linear algebra may no longer be needed for introductory calculus students, presenting it in the context of the calculus ties thing together nicely.

44 of 45 people found the following review helpful:

5.0 out of 5 stars The best math book I have ever read, April 21, 2005

By 

matematik - See all my reviews

This review is from: Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1) (Hardcover)

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 seciton 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.

37 of 39 people found the following review helpful:

5.0 out of 5 stars There is but one Apostol, and he is Tom., August 11, 1997

By 

Zachary Strider McGregor-Dorsey (Superior, CO) - See all my reviews
(REAL NAME)   

This review is from: Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1) (Hardcover)

Perhaps the best description for Calculus, by Tom M. Apostol, is simply its title. This text is Calculus. Like no other calculus book I have seen, it devotes itself totally to its subject matter, never compromising itself for the sake of understanding. By doing this, the reader is permitted to learn calculus completely.

So many calculus texts in the current market have a sort of misguided focus. Instead of explaining the subject they claim, all they offer is the tools for solving the rote calculus problems of Advanced Placement tests and engineering. This is fine for someone who cares nothing of mathematics, but is not sufficient for their claim of teaching calculus. Apostol's Calculus cares little about explaining the applications of calculus or preparing someone for yet another standardized test. Uncluttered by fancy computer-aided graphics and pages and pages of redundant examples, Apostol offers the basics of calculus with the prrofs behind the theorums. Never once is the reader left with questions as to what exactly integrals are or why any two nonequal numbers must have another number between them. Everything necessary for the reader to solve any single variable calculus problem is presented in text. Apostol's rigor knows no bounds, begining first with the proof of the positive integers and continuing to the finest points of integral calculus.

This text is not for the faint-hearted. If you just want to be able to solve calculus problems, you would have little use for this text. But if you want the tools and justifications for all of calculus, this is the book for you. It is a necessity for all mathmaticians' libraries.

See also Calculus 2 by Tom M. Apostle for multivariable calculus.