Multivariable Mathematics, Fourth Edition

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Summary: A coherent view of multivariable mathematics
Review: For those with sufficient preparation (say, a good BC Calculus course and an enjoyment of mathematics), this text offers a very fine presentation of multivariable calculus. Certainly, some of the material is challenging and some of the exercises require insight, but after finishing this book, or substantial portions of it, you will have a coherent view of multivariable calculus, as well as some appreciation of significant, but elementary, applications of linear algebra. I particularly recommend this text to those who have learned multivariable calculus in one of the "fat" three semester calculus texts, and feel that, although they could solve all the problems, they don't really have any sense of what the subject is all about. This text has a distinguished history: it is the latest incarnation of a vector calculus text (Calculus of Vector Functions) first published in 1962 by Crowell and Williamson. Spivak described that text (and I hope Dover someday reissues the third edition) as "one of the first, and still one of the nicest, treatments of advanced calculus using linear algebra."

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Summary: Sometimes it takes a second read, or third, or fourth....
Review: I liked this book because it is written at a slightly more sophisticated level than most lower division math books. Admittedly, it is difficult to understand some of the proofs and examples on the first read. It just takes some time, after a second or third read, before the text begins to make sense. Then you'll realize the examples are presented quite well and you have everything you need to solve the problem sets. And you know you've learned the material well if you understand the text and you can do the problems, which are oriented more to make you think than compute.

Rating:
Summary: Naughty Book
Review: This book was used for a two-course introductory math series at Stanford in 1996-7 and 1997-8. The book drew so many complaints that it was abandoned after two years. Personally, I found it difficult to understand many of the formal proofs and explanations provided. Many shortcuts were taken in solving the example problems which made them difficult to follow. The answers to problems in the back of the book were frequently incorrect. This is a poorly written book for all students except those extremely insightful in mathematics.