Advanced Calculus of Several Variables (Dover Books on Mathematics) Revised Edition

So far, this text is an invaluable reference for me.It has the more theoretical bent that I desired, and is very reader-friendly in the following ways:(1) The book is compact yet includes full proofs, no-nonsense explanations, and interesting examples.(2) The organization is consistent---specific topic are easily found from the index or table of contents, and there is balanced depth from part to part.(3) The exercises are accessible, although there is no solution appendix, and elucidate the discussion.In short, this book would be helpful for anyone who is interested in theoretical mathematics, such as the student of Physics or Mathematics, who has a background of single-variable Calculus.Note: The newer /Multivariable Mathematics/ by Shifrin covers content similar to that of this book.However, the former is more wordy and self-conscious, which makes is more difficult to read.

This is a nice introduction to advanced calculus. I am using it to help teach myself theoretical physics. It is a nice text.

I don't know how good this book will be for someone who is not comfortable with proofs, because it takes a somewhat more abstract, less computational and visual approach to the subject. Nevertheless, if you already learned multivariable calculus in a computational/visual style in an early undergraduate class, and now find yourself more comfortable with the abstract approach of higher mathematics, this book will help you re-learn the concepts of multivariable calculus in the proper abstract setting. Everything clicks at reasonable reading speed so you don't need to spend a lot of time stopping to remind yourself of what he's doing. An easy, smooth read that will leave you with a good perspective on the subject. Highly recommended for the right kind of reader.

This is a wonderful book. The exercises are interesting and resolvable: you do not need to be a genius. In rigorous style, it covers differential manifolds, differential forms, etc.. Buy it!

Thank you.

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?).

This book can be used to supplement existing texts used for standard Advanced Calculus courses, and it includes all the essentials one would look for such as:Linear mappings (Ch. I), multivariable calculus (Ch. II), Multiple Integrals (Ch. IV), Line and suurface integrals (Ch. V) and calculus of variations (Ch. VI).My only quibble is the approach is somewhat dated, and also I thought it would have been nice to have at least one chapter on complex calculus - treating contour integration, Laurent series, and the residue theorem and applications to complex integration. Most Advanced Calc courses today include such fare, but again - if Edwards' text is just used as a supplement it's no biggie.The text is also very useful for self-study and if the student wants an additional text to cover complex calculus he can get 'Complex Variables and Applications' by James Ward Brown and Ruel V. Churchill (6th ed.)

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.