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Title: Tensor Analysis on Manifolds by Samuel I. Goldberg, Richard L. Bishop ISBN: 0-486-64039-6 Publisher: Dover Pubns Pub. Date: 01 December, 1980 Format: Paperback Volumes: 1 List Price(USD): $12.95 |
Average Customer Rating: 4.57 (7 reviews)
Rating: 4
Summary: The pros and cons of Bishop & Goldberg
Comment: 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 (a.) the notation is a bit outdated.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!
Rating: 4
Summary: A perfect starting point
Comment: 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.
Rating: 5
Summary: "Did you say relativity?" Find all the prerequisites here
Comment: This books is the perfect introduction to modern differential geometry, especially for people with a specific purpose in mind such as the study of relativity or analytical mechanics. This book is a very straight forward read. But that dosent mean it compromises on quality on the depth of the material presented. The exercises are great, as they illustrate the concepts just learned very nicely. One section leads very nicely to the other. As for the topology needed to study differentiable manifolds, it is developed in the beginnning, though its not the best "quick untro to topology" Ive seen. Of course you can skip some of the sections such as Paracompactness. The only consequence is that you might not be able to follow some of the proofs later on. The only other complaint is that in the few exercises on special relativity, they use the old "ict" coordinate system. Try to remember that this sysytem is frowned upon these days. But all in all an excellent read. And especially for the price you can buy this at.
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Pubns Pub. Date: 01 April, 1989 List Price(USD): $14.95 |
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Title: Differential Geometry by Erwin Kreyszig ISBN: 0486667219 Publisher: Dover Pubns Pub. Date: 01 June, 1991 List Price(USD): $14.95 |
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Title: Differential Forms with Applications to the Physical Sciences by Harley Flanders ISBN: 0486661695 Publisher: Dover Pubns Pub. Date: 01 December, 1989 List Price(USD): $11.95 |
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Title: General Relativity by Robert M. Wald ISBN: 0226870332 Publisher: University of Chicago Press Pub. Date: July, 1984 List Price(USD): $37.00 |
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Title: Tensor Calculus by J. L. Synge, A. Schild ISBN: 0486636127 Publisher: Dover Pubns Pub. Date: 01 July, 1978 List Price(USD): $14.95 |
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