Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach

Several readers have complained about the lack of a student solution manual. One now exists, published by Matrix Editions. Errata for the book are posted on the book web site (URL given in the book). The most recent posting was Feb. 29, 2002. Readers who wish to be notified by e-mail when new errata are posted can sign up via the web site or e-mail the authors (address given in the book).

What's new in the second edition (the one with the pale yellow cover now being sold):

The main change is that we introduce a new approach to Lebesgue integration. In addition, the second edition has approximately 270 additional exercises and 50 additional examples. We have added pictures of mathematicians and more historical notes. There are now end-of-section exercises, as well as review exercises for Chapters 1--6. Some useful formulas are listed on the back cover.

More difficult material from Chapter 0 was moved to the Appendix. The inverse and implicit function theorems have been rewritten. In Chapter 3 we simplified the definition of a manifold, and we now begin with the general case and discuss curves and surfaces as examples. Similarly, in Chapter 5, we eliminated the separate sections on arc length and surface area; we now have one section on volume of manifolds.

In Chapter 6, we rewrote the discussion of orientation and changed the definition of a piece-with-boundary of a manifold, to make it both simpler and more inclusive.

Covers most of the standard topics in multivariate calculus, and a substantial part of a standard first course in linear algebra. Using a dual-presentation that is rigorous and comprehensive — yet exceptionally “reader-friendly” in approach, this book focuses on underlying ideas, integrates theory and applications, and features coverage of differential forms and an emphasis on numerical methods.

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