Advanced Calculus of Several Variables

by Charles Henry Edwards

In this high-level treatment, the author provides a modern conceptual approach to 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, the book gives equal attention to the classical applications and computational methods responsible for much of the interest and importance of this subject.
Beginning with a discussion of Euclidean space and linear mappings, Professor Edwards (University of Georgia) follows with a thorough and detailed exposition of multivariable differential and integral calculus. Among the topics covered are the basics of single-variable differential calculus generalized to higher dimensions, the use of approximation methods to treat the fundamental existence theorems of multivariable calculus, iterated integrals and change of variable, improper multiple integrals and a comprehensive discussion, from the viewpoint of differential forms, of the classical material associated with line and surface integrals, Stokes' theorem, and vector analysis. The author closes with a modern treatment of some venerable problems of the calculus of variations.
Intended for students who have completed a standard introductory calculus sequence, the book includes many hundreds of carefully chosen examples, problems, and figures. Indeed, the author has devoted a great deal of attention to the 430 problems, mainly concrete computational ones, that will reward students who solve them with a rich intuitive and conceptual grasp of the material.

Genres: Mathematics, Reference, Textbooks, Calculus

478 pages, Paperback

First published January 1, 1973

About the author

Charles Henry Edwards
AKA C. Henry Edwards and C.H. Edwards

Reviews

[Kirk Peters · Rating 3 out of 5]

This book was difficult, and required for an Advanced Calculus uni course. Exercises can be really difficult to really easy. It felt dated, had unnecessary assumptions for some things. The defining of the Riemman integral was wonky. This was my first exposure to differential forms, and it was hard to make sense of, my professor sort of lectured from the book but also not really. I had a separate book Bachman's differential forms book, it was far clearer than this, but they muddle the other.
It's an okay book. I don't know that I would recommend it to anyone, especially if it's your only source.

[Jamison Thornton-Wright · Rating 2 out of 5]

Made me want to kill myself.

[Hannah Thomas · Rating 4 out of 5]

Being a huge math person and analyst, this is one of my favorite books! You do need to remember your Calculus methods to understand what is going on. It is definitely a book that needs a "helping hand" to review the equations and methods of Calculus.