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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0-486-65840-6 Publisher: Dover Pubns Pub. Date: 01 April, 1989 Format: Paperback Volumes: 1 List Price(USD): $15.95 |
Average Customer Rating: 4.4 (5 reviews)
Rating: 3
Summary: not so so rigorous
Comment: Lots of material for the price, but this is one of those maths book with a "physical approach", IMO. Definitions for instances, like the definition of a Tensor, aren't always enounced clearly.
This just make things look more complex and different than what they are for no gain.
I believe that the book "Tensor calculus on manifold", same editor, Goldberg/Bishop does a better job: more rigorous and more concise.
Rating: 5
Summary: Rigorous, yet informal enough to be a lot of fun.
Comment: Many years ago, this became the first book I had ever read about tensor calculus, differential geometry, or classical field theories, and I still have not found a better treatment of any of the three subjects anywhere else. I'm now not very far from a PhD in General Relativity theory, and I very rarely need to use any mathematics which I didn't first learn as a freshman undergraduate while reading this book independently. I owe a great debt to Lovelock and Rund, and could not recommend this book any more highly than I am right now.
Rating: 5
Summary: One of the best books ever
Comment: I don't know how they did it but, this is the book you want to buy if you're trying to learn differential geometry, especially if you're learning general relativity. It takes you from the concepts you are already familiar with into differential geometry faster than any other book I've ever tried (and I've tried many!). Before you know it, you are comfortable with covariant derivatives and Lie derivatives and.. well the list could go on. Do not be turned off by the reputation of Dover books-- "cheap and not worth it!" This is a gem.
For those of you learning GR: Buy this book and Schutz's "Geometrical Methods of Mathematical Physics." Read Lovelock and Rund first and then dive into Schutz's book. This will provide you with the necessary mathematical background to handle Wald's "General Relativity" with (some amount of) ease. You might want to try Schutz's "A First Course in General Relativity" before Wald's more advanced book.
I've read many glowing reviews on Amazon about books that I "must have" and, quite frankly, they turned out to be poor choices. But in this case I have to say you "must have" this book! It is that good. And it's cheap, so if you do not agree with me, it's not much money out of your pocket.
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Title: Tensor Analysis on Manifolds by Samuel I. Goldberg, Richard L. Bishop ISBN: 0486640396 Publisher: Dover Pubns Pub. Date: 01 December, 1980 List Price(USD): $12.95 |
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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: 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: Calculus of Variations by S. V. Fomin, I. M. Gelfand ISBN: 0486414485 Publisher: Dover Pubns Pub. Date: 16 October, 2000 List Price(USD): $9.95 |
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Title: Mathematics of Classical and Quantum Physics by Frederick W. Byron, W. Fuller Robert ISBN: 048667164X Publisher: Dover Pubns Pub. Date: 20 August, 1992 List Price(USD): $21.95 |
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