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Title: Differential Forms and Connections by R. W. R. Darling ISBN: 0-521-46800-0 Publisher: Cambridge University Press Pub. Date: 22 September, 1994 Format: Paperback Volumes: 1 List Price(USD): $32.00 |
Average Customer Rating: 4.4 (5 reviews)
Rating: 2
Summary: Not for everyone, flawed in basic ways
Comment: I disagree with reviewers who found this book useful for self-study. I would not recommend it for individuals first learning this material. The book is frankly contradictory in places, and frustratingly repetitive in others. In the early chapters it assumes concepts not yet explained, and introduces terminology and symbols that are nowhere defined.
If you already know quite a bit, you may find this approach enlightening. But if you're just beginning to master these concepts, I suggest you look elsewhere.
I also suggest that much tighter editing would do this book a world of good. Go with Kreiszig, or Lovelock and Rund instead.
Rating: 5
Summary: Excellent book
Comment: This is a very modern, very concise, and very efficient book. By using vector bundles the curvature forms on semi-Riemannian manifolds are introduced. Definitions are given clearly and intuitively. Without spending tons of pages on digression to minimal surfaces, Hopf-Rinow thm, Gauss-Bonnet thm, etc., the book builds enough machinery to describe the gauge field theory in the last chapter. Most other differential geometry books either throw in too many applications to waste reader's time or give vague definitions (too bluntly abstract or not self-contained) to confuse the reader.
All exercise problems are interesting and important. Hints are given to some of them.
I found Warner's "Foundations of Differentiable Manifolds and Lie Groups" is a good complement to address the algebraic and topological side of differential geometry.
Rating: 5
Summary: The ONLY book really suited for self study
Comment: I would just like to point out that Darling's book is the only book I've encountered which is suited for self study. It resembles someone's classroom notes - i.e., nothing fancy, no glossy color 3-d graphics or such - but it is very neatly organized, with many examples and helpful problems, and it is really, really suited for someone trying to study the subject by him/herself (me ... ). It is not very physically oriented - not many physical examples are provided throughout the text, and it is mathematical in nature, but don't let that deter you! In fact, the sharp distinction between mathematics and physics is pedagogically wise.
Another good thing about this book is that it does not begin with completely abstract definitions. First of all it develops exterior calculus and diff. manifolds in ordinary Euclidian space. This is a must for anyone studying on their own, believe me! No matter how mathematically mature you are, those things just don't make sense unless you've seen how they work in familiar settings. You don't have to worry, though - Darling keeps his notation clean; Darling tries as hard as he can to keep everything in pure geometrical language, referring to a specific basis only when absolutely necessary (or when it helps one understand).
I cannot say how good a classroom text this is, but do yourself a favor and check it out if you're thinking of studying this on your own! Darling is a clear and (equally important!) responsible teacher.
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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): $15.95 |
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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: 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: 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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