Advanced Calculus of Several Variables (Dover Books on Mathematics) [Paperback]

C. H. Edwards Jr. (Author)

Book Description

ISBN-10: 0486683362 | ISBN-13: 978-0486683362 | Publication Date: February 1, 1995 | Edition: Revised

Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

Product Details

• Paperback: 480 pages
• Publisher: Dover Publications; Revised edition (February 1, 1995)
• Language: English
• ISBN-10: 0486683362
• ISBN-13: 978-0486683362
• Product Dimensions: 9.2 x 6.2 x 0.9 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #281,760 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

46 of 46 people found the following review helpful:

5.0 out of 5 stars Excellent buy. Exceedingly clear presentation., May 12, 2006

By 

Henry Lenzi (Porto Alegre, RS Brazil) - See all my reviews
(REAL NAME)   

This review is from: Advanced Calculus of Several Variables (Dover Books on Mathematics) (Paperback)

Some people think Dover books, being cheap, ought to be bad. In fact, this Dover series specializes in "salvaging" great titles that went out of print and are of great intellectual/pedagogical value. Such is the case again for this title.
Very well written. Of course, C.H. Edwards is notorious for his book on the history of calculus.
Exceedingly clear. I started reading it while taking Calculus II, in search of some more elaborate perspectives. It is that clear.
Chapter 1 is a brief incursion in some topological aspects. Chapter 2 directional derivatives, differentials. Ch3. Chain rule. Ch.4 Critical points. Ch. 5 MANIFOLDS (patches ?! ) and Lagrange multipliers (and this is around a bit over page 100!). Ch 6 Taylor's in one and Ch. 7 several variables. Ch 8 Classification of critical points. Part III begins with Newton's method and contraction mappings. Then goes to Multivariable mean theorem, Inverse and Implicit Mapping Theorem. Ch 4 (III) is Manifolds in Rn and finishes with higher derivatives. Part IV is Multiple Integrals, n-dimensional integrals, Riemman sums, Fubini's theorem, Change of Variables, Improper Integrals, Path Lenght and Line Integrals, Green's theorem, some applied problems, Line and Surface Integrals. Book end with Differential Forms, Stoke;s theorem, Classical Theorems of Vector Analysis, Closed and Exact Forms, Normed Vectors Spaces, Variational Calculus the Isoperimetric problem.
Lots, lots of bangs for your bucks. Because of the breadth of the exposition, clarity and price, it's a must-have.
You can kind of draw a parallel between this and Hubbard's Vector Calculus, Linear Algebra and Differential Forms. Both kind of span the same space. Of course, being older, it doesn't have the same computational flavor as Hubbard's (but then again, it's not really about numerical methods, is it?).

54 of 55 people found the following review helpful:

5.0 out of 5 stars Older is better, August 28, 2000

By 

Mohammad - See all my reviews

This review is from: Advanced Calculus of Several Variables (Dover Books on Mathematics) (Paperback)

A lot of new books have a tendency to dilute the material with really nice computer generated graphics and so called "pedagogical" methods which really don't enhance intuitive and rigorous understanding. Moreover, there are books which use physics as a way around explaining the mathematics. This book is far above them. It is a MATH book, not a science book, and has no signs of pretention. The explanations require thought but once they are understood they contribute greatly to one's appreciation.

There is not doubt that a good course in algebra and calculus are required. It might even be advisable to have a some knowledge of multivariable calculus. With all these tools in hand, this volume gives much and simply asks for some patience and deligence from the student.

In short, this book is about teaching mathematics in a rigorous, and comprehensive style: all proofs are given (although some are "unique") and followed by discussion. Furthermore, the exercises really are at the heart of this book. To do them is to understand.

27 of 29 people found the following review helpful:

4.0 out of 5 stars Relatively user-friendly book on advanced calculus, October 24, 1999

By A Customer

This review is from: Advanced Calculus of Several Variables (Dover Books on Mathematics) (Paperback)

I have not yet finished the book, but I feel I have to express my disagreement with the reviewer from Florida. The book has nice linear algebra and calculus reviews (yes, he does assume that you have a good calculus background and that reviews are just, well, reviews. This is a book about ADVANCED calculus, after all!), effective diagrams, and plenty of exercises (hundreds of them).

Overall, it is somewhat easier to read than some celebrated classics like Spivak's "Calculus on Manifolds" or Munkres's "Analysis on Manifolds."