Tensor Analysis on Manifolds (Dover Books on Mathematics) [Paperback]

Richard L. Bishop (Author), Samuel I. Goldberg (Author), Mathematics (Author)

Book Description

ISBN-10: 0486640396 | ISBN-13: 978-0486640396 | Publication Date: December 1, 1980

Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.

Product Details

• Paperback: 288 pages
• Publisher: Dover Publications (December 1, 1980)
• Language: English
• ISBN-10: 0486640396
• ISBN-13: 978-0486640396
• Product Dimensions: 8.3 x 5.6 x 0.6 inches
• Shipping Weight: 11.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #194,869 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

87 of 89 people found the following review helpful:

4.0 out of 5 stars The pros and cons of Bishop & Goldberg, January 12, 2002

By 

Assaf Tal (Israel) - See all my reviews

This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)

I will briefly list the pros and cons of this book.
The pros are (a.) its price, (b.) the amount of material it manages to cover, (c.) it is quite complete - everything is formulated and proven within the text rigorously, and it covers a lot of ground (manifolds, tensors, differentiation and integration on manifolds, connections and Riemmanian manifolds) (d.) it does not require much background - nothing more than point-set topology and calculus. It even develops all the linear algebra it needs in a single chapter - quite admirable. (e.) the exercises are nice and instructive. (f.) It makes a good reference and supplement. (g.) It has a special chapter on Riemannian manifolds - quite good for relativity courses.
Now for the cons. (a.) the notation is a bit outdated. (b.) it does not treat infinite dimensional or complex manifolds. (c.) It sometimes leaves certain results for the reader to verify, which might annoy readers who simply want to get to a certain result as quick as possible. (d.) It is a bit dry. (e.) It lacks in concrete examples - that is not to say it doesn't have any examples, just that more would be much better, (f.) and this is chiefly aimed at physicits - it does not really focus on calculating things, which is what physics is all about, at the end.
Having said that, I honestly say that one can learn all about basic differential geometry from this book. I don't think seeing manifolds in R^n is a basic prerequisite for studying abstract diff. geometry. This book would be a good place to start - despite its age it manages to remain very relevant today. Finally, the reader is assured that the authors won't pull off any "dirty tricks" (since this is basically a mathematical book) - it's very important for the reader to be able to trust the book he's reading. And the price is fantastic!

39 of 41 people found the following review helpful:

5.0 out of 5 stars Terse, clear, modern introduction to tensors and forms, July 14, 1998

By 

henrique fleming - See all my reviews

This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)

The best introductory book on its subject. Being a physicist, not a mathematician, I particularly appreciated its self-contained and down-to-earth, though fully rigorous, style. The very good chapter on integration of forms shows mastery of the authors both in the topic and in the technique of exposition. Terse, yet very clear: a rare combination that reminds one of the best books by Halmos.

22 of 23 people found the following review helpful:

4.0 out of 5 stars A perfect starting point, October 30, 2001

By 

"dpapaioa" (California, USA) - See all my reviews

This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)

This is a great book for an introduction to differential geometry. The only real prerequisite is calculus and some topology, making this book accessible to undergraduate students interested in Mathematics or Physics. The book covers a wide variety of topics and there are plenty of examples and exercises.
I guess the two reasons why I don't give this book five stars are (1)the notation in not entirely modern and (2) I have not managed to effectively use it as a primary textbook but as a supplument to a textbook.
It is certainly a great value for the price.