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Title: Differential Forms With Applications to the Physical Sciences by Harley Flanders ISBN: 0-486-66169-5 Publisher: Dover Publications Pub. Date: 01 January, 1990 Format: Paperback Volumes: 1 List Price(USD): $11.95 |
Average Customer Rating: 4 (4 reviews)
Rating: 3
Summary: Concise
Comment: As a survey of the applications of differential forms to various aspects of the physical sciences, this book works quite well. However, for the non-mathematician, there are more intuitive texts available, although it is unlikely that they will have the same scope. The exposition is extremely concise, far more so than, for example, Lovelock and Rund, and at times this makes the text somewhat heavy going. Having said that though, the reader with a reasonable level of mathematical maturity will find the book very rewarding. A reader who is mainly focussed on differential geometry though would probably be better off with Lovelock and Rund.
Rating: 3
Summary: Read on
Comment: Why is it that any book that contains the word "physics" or "physical" in its title feels free to be sloppy? Flander's book is sloppy. There are no shortcuts to understanding - if you want to know differential geometry you have to learn it right, not from Flander's book. For example: he devotes 3 pages to antisymmetrical tensors. The way he manages to do this is by avoiding precise definitions, or giving elaborate proofs. He does not even mention the word tensor! This is unacceptable for anyone who seeks to truly understand differential geometry. After all, if you intend to invest effort and time learning a subject, shouldn't you do it the right way?
I'm not saying Flander's book is without merit - especially the low price - which might make it worthwhile purchasing it is an additional source of information, but as a primary source it is, in my opinion, a very bad one.
There are many alternatives to Flander's book I suggest you check out before trying your luck with this one. The standard reference is Bishop & Goldberg's "Tensor analysis on manifolds". Another good book is "differential forms and connections" by Darling. A comprehensive book about diff. geometry is "Geometry and Physics" by Frankel. I'm sure others will have their personal favorites, but these are a good place to start.
Rating: 5
Summary: Generalize vector calculus for general relativity
Comment: This book covers the basic math behind the "geometric approach" to tensor calculus. The math required is not heavy, but it requires some considerable mathematical maturity. If talk of "the boundary of a boundary is zero" or "exterior derivative" confuses you, this is a good book. An intuitive approach, not a sea of indices. If you want really heavy stuff then Bishop & Goldberg is good.
Most Dover math books are first rate. This one is.
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Publications Pub. Date: 01 April, 1989 List Price(USD): $15.95 |
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Title: Tensor Analysis on Manifolds by Richard L Bishop, Samuel I. Goldberg ISBN: 0486640396 Publisher: Dover Publications Pub. Date: 01 September, 1981 List Price(USD): $12.95 |
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Title: Theory of Spinors by Elie Joseph Cartan ISBN: 0486640701 Publisher: Dover Publications Pub. Date: 01 June, 1981 List Price(USD): $10.95 |
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Title: Differential Forms and Connections by R. W. R. Darling ISBN: 0521468000 Publisher: Cambridge University Press Pub. Date: 22 September, 1994 List Price(USD): $32.00 |
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Title: Differential Geometry by Erwin Kreyszig ISBN: 0486667219 Publisher: Dover Publications Pub. Date: 01 June, 1991 List Price(USD): $14.95 |
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