Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2) [Hardcover]

Tom M. Apostol (Author)

Book Description

ISBN-10: 0471000078 | ISBN-13: 978-0471000075 | Publication Date: June 1969 | Edition: Volume 2

Now available in paperback! 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.

Editorial Reviews

From the Publisher

Now available in paperback! 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: 673 pages
• Publisher: Wiley; Volume 2 edition (June 1969)
• Language: English
• ISBN-10: 0471000078
• ISBN-13: 978-0471000075
• Product Dimensions: 7.1 x 1.3 x 10.1 inches
• Shipping Weight: 2.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #299,061 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

20 of 21 people found the following review helpful:

5.0 out of 5 stars A Calculus book for future Mathematicians, April 21, 1999

By A Customer

This review is from: Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2) (Hardcover)

Apostol's Calculus is the definitive book on Calculus for anyone who wants to be a mathematician. Historical notes, intuitive ideas, clear definitions, demonstrations, all is there, from natural numbers to Stokes' Theorem. His applications of linear algebra to multivariate calculus are among the best I have seen on calculus textbooks Better than this, only a book on Mathematical Analysis.

53 of 63 people found the following review helpful:

2.0 out of 5 stars Weak, August 24, 2004

By 

Raman (Chicago, IL USA) - See all my reviews

This review is from: Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2) (Hardcover)

Few books in the mathematical literature have given me so much pain as this one. Freshman year, I took a heavily theoretical linear algebra class with Tommy II as the textbook, and then the next term I took multivariable calculus out of this book as well. In either case, this book was my first experience with the material, though as an "introductory" text it should have done the job. Suffice it to say that neither experience was terribly positive.

My problem is that Apostol never seems to try to motivate ideas well, and he uses cumbersome, nonstandard, and occasionally inconsistent notation. His proofs can be inelegant and opaque at times. He is far too sparing on geometrical intuition as a way to understand the material, preferring to talk in symbols rather than pictures. (This is especially true in the first five chapters on linear algebra. His multivariable chapters are well-illustrated, but calculus on R^n seems to be trivial once calculus on R is under your belt from a good introductory book like Larson/Hostetler/Edwards at a high-school pace. Thus, the motivation is needed least where it is used most.) As a result, I feel that I still don't intuitively understand how operators work on inner-product spaces, even after trying to remedy my deficiencies for a year and a half now.

I attributed my lack of understanding to my stupidity, but then I found myself learning exterior forms from Arnol'd's excellent mathematical mechanics book and groups from Dummit/Foote's superb abstract algebra text - and understanding the exposition perfectly. And I started to feel that this book is the thing at fault.

If a prospective reader is prepared for the terseness and difficulty of Apostol, I recommend that s/he go straight to the real math rather than settling for this obfuscated treatment of inroductory subjects. It is no harder to learn the rudiments of metric topology than it is to learn Apostol's open balls, and it seems no more inspired to take on Halmos' linear algebra classic, with its intimations of Hilbert space, than it is to struggle through Apostol's treatment. (The former seems to combine considerable difficulty with terse, but wonderful, motivation, but don't take my work on that: I'm only forty pages into it!) But the books are more inspired, and the math is far more general and beautiful.

My recommendation: learn your calculus (and potentially your first linear algebra) patiently but thoroughly from a prosaic, worked-example-ridden, 1000-page monster, then go straight to the upper undergraduate/early graduate classics for the real fun. Tommy II, caught somewhere in the middle, has no place in this plan.

17 of 19 people found the following review helpful:

4.0 out of 5 stars Very thorough, but very dense, November 17, 2004

By 

Kate K (WI) - See all my reviews

This review is from: Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2) (Hardcover)

I'm currently taking an honors calculus sequence at the U of WI, and have used this book and the first volume for the past three semesters. Needless to say, you have to take Apostol with a grain of salt. Although the no-frills style and lack of worked examples is upsetting to many students who are used to pictures, thorough examples, and color, these volumes cover a lot of material in a small space. And also beware; my professor and others in the math department have found errors in definitions and theorems, and the archaic notation is off-setting at times. Basically, if you're looking for straighforward information (written by a mathematician, for a mathematician), you've found the perfect book. If you're looking for an easy-to-read and understand book, keep searching.