Most Helpful Customer Reviews
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46 of 47 people found the following review helpful:
5.0 out of 5 stars
One of the best books ever, April 29, 2002
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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27 of 28 people found the following review helpful:
5.0 out of 5 stars
Rigorous, yet informal enough to be a lot of fun., August 8, 2003
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 much better treatment of any of these subjects anywhere else.
The notation is often very classical, in the sense that there are a lot of indices, usually referring to coordinate bases, and there is a lot of talk of "transformation laws." While this style can be distressing to more advanced students, those familiar with the beautiful methods of avoiding such structures, I think it is useful to younger students, especially physicists, who yearn for concrete examples. Also, for the one section in which a more formal approach is advantageous, such a treatment is included as an appendix.
The book is also wonderful for its breadth. It is not a "tensor calculus" book, or a "differential geometry" book. It is really best described as a "geometrical methods" book "with applications to theoretical physics." Yet unlike most examples of this now-cliched subject, the breadth of material is matched by a cohesion of style.
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50 of 59 people found the following review helpful:
5.0 out of 5 stars
THe Mathematics of General Relativity, September 15, 2000
The authors present a thorough development of TENSOR CALCULUS, from basic principals, such as ordinary three dimensional vector space. Tensors are generalizations of vectors to any number of dimensions (vectors are type (1,0) tensors, diff. forms are type (0,1) tensors). One of the key principles of General Relativity is that if physical laws are expressed in tensor form, then they are independent of local coordinate systems, and valid everywhere. Chap. 1: Preliminary Obs.-- Chap. 2: Affine Tensor Algebra in Euclidean Geometry-- Chap. 3: Tensor Analysis on Manifolds -- Chap. 4: Additional Topics from the Tensor Calculus -- Chap. 5: The Calculus of Differential Forms -- Chap. 6: Invariant Problems in the Calculus of Variations -- Chap. 7: Riemannian Geometry -- Chap. 8: Invariant Var. Principles and Phys. Field Theories - Chap. 8 covers a good deal of General Relativity. This book is a worthy addition to any mathematical library.
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