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Tensor Analysis on Manifolds (Paperback)

by Richard L. Bishop (Author), Samuel I. Goldberg (Author)

4.2 out of 5 stars See all reviews (4 customer reviews)

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Product details

Paperback: 288 pages
Publisher: Dover Publications Inc. (1 Jul 1981)
Language English
ISBN-10: 0486640396
ISBN-13: 978-0486640396
Product Dimensions: 21.3 x 15 x 1.5 cm

Average Customer Review: 4.2 out of 5 stars See all reviews (4 customer reviews)

Amazon.co.uk Sales Rank: 381,878 in Books (See Bestsellers in Books)
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#45 in Books > Science & Nature > Mathematics > Calculus & Mathematical Analysis > Vector & Tensor Analysis

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Customer Reviews

4 Reviews

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4 star:		(3)
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4.2 out of 5 stars (4 customer reviews)

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4 of 4 people found the following review helpful:

4.0 out of 5 stars Complete for a mathematical axiomatic approach, 20 May 2001

By	Javier A. Vizoso (Europe) - See all my reviews (REAL NAME)

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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3 of 3 people found the following review helpful:

4.0 out of 5 stars good but terse, 28 Nov 2000

By	davem@fdgroup.co.uk (Sheffield. England) - See all my reviews

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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4 of 5 people found the following review helpful:

5.0 out of 5 stars good introductory text, 22 Jul 1998

By A Customer

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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Most Recent Customer Reviews

4.0 out of 5 stars good choice
Very specialistic book, suitable to in-depth studies. Probably too tough for starters in tensor analysis, but anyway incredibly interesting. Ideal size (very compact! Read more

Published 1 month ago by S. Valentina

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