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8 of 8 people found the following review helpful
4.0 out of 5 stars Complete for a mathematical axiomatic approach, 20 May 2001
This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)
This is a great title because it develops almost all the essential mathematical formalism of tensors and manifolds in a few pages (280). It is based on the "theorem-demostration-corollary" approach, and because of this, it has a lack of geometrical or physical point of view, skipping the 2D and 3D foundations of Advanced Calculus (I recommend Marsden, Tromba) and Classical Differential Geometry (I recommend Do Carmo). So it is great as a mathematical reference, like a compendium, very usefull when a physicist treats this subject briefly in a Classical Mechanics or General Relativity course, where you often ignore many of the algebraic and analytic foundations. It treats basically with:
- Basic Topology. - Theory of Manifolds. - Tensor algebra. - Tensor analysis on Manifolds. - Integration Theory. - Riemannian and Semi-Riemannian Manifolds. - Physical Applications (Hamiltonian Mechanics).
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5 of 5 people found the following review helpful
4.0 out of 5 stars good but terse, 28 Nov. 2000
This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)
Gives a thorough grounding in the topic, but the book's terseness makes it hard work sometimes. There needs to be more help for the reader in the transition from standard 3D geometry to the full manifold, explaining what assumptions are no longer valid, and why. Then the apparently bizarre stuff, like the definition of a tangent on a manifold, will make more sense.
You tend to end up with a lot of definitions, but not much feeling for them (eg knowing that a dual vector is a linear mapping from V to R, but having no real feel for what it actually signifies, or why it's important.)
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5 of 7 people found the following review helpful
5.0 out of 5 stars good introductory text, 22 July 1998
By A Customer
This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)
All of these dover books, this is the best one to learn differential geometry from (you can safely ignore just about any other dover text with the word "tensor" in the title). The authors keep the exposition very clear with good examples.
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1 of 2 people found the following review helpful
4.0 out of 5 stars good choice, 7 Oct. 2009
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S. Valentina (Padua, Italy) - See all my reviews
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This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)
Very specialistic book, suitable to in-depth studies. Probably too tough for starters in tensor analysis, but anyway incredibly interesting. Ideal size (very compact!), must have...!
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4.0 out of 5 stars Four Stars, 25 Aug. 2014
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This review is from: Tensor Analysis on Manifolds (Dover Books on Mathematics) (Paperback)
Perfect to the time
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Tensor Analysis on Manifolds (Dover Books on Mathematics)
Tensor Analysis on Manifolds (Dover Books on Mathematics) by Richard L. Bishop (Paperback - 17 Mar. 2003)
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