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Title: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak ISBN: 0-8053-9021-9 Publisher: Westview Press Pub. Date: June, 1965 Format: Paperback Volumes: 1 List Price(USD): $44.00

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Average Customer Rating: 4 (14 reviews)

Rating: 5
Summary: Simply the best
Comment: This book is just the best monograph on the subject available. The author states his goal clearly since the beginning and includes the exact amount of fundamental material needed to get to the main result: Stoke's theorem. The approach is not as general or abstract as it could be, but obviously Dr. Spivak decided to sacrifice that to make the reading more comprehensible, because his goal was not an encycopaedic treaty of analysis and differential geometry, but a detailed explanation of how this important subject is understood by modern mathematicians.

Just a word of warning: this book is not for beginners. If you are a newcomer to multivariate calculus or if you are not in love with abstract mathematics then this book could give you a headache.

Rating: 5
Summary: A great little book
Comment: This book is really a great introduction to the concepts of multilinear algebra, and also works out the main theorems on advanced calculus.I believe that it will be a very helpfull introduction to those that want to study differential topology and geometry. A good place to find more material on the subject, and also a treatment of related topics on differential geometry, is do Carmo's book Differential Forms and Applications.

Rating: 3
Summary: Somewhat Terse
Comment: A useful companion to Spivak's big introduction to geometry book. I think the midpoint between that book and this one would be an excellent source for learning geometry. This book uses only equations, whereas in Spivak's bigger book, it's hard to figure out what rigorous mathematical concept he's trying to introduce, as everything is done with words and pictures.

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