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Manifolds, Tensors, and Forms
An Introduction for Mathematicians and Physicists

$74.99 (P)

  • Author: Paul Renteln, California State University, San Bernardino
  • Date Published: December 2013
  • availability: Available
  • format: Hardback
  • isbn: 9781107042193
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$ 74.99 (P)

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About the Authors
  • Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and degree theory. It also features over 250 detailed exercises, and a variety of applications revealing fundamental connections to classical mechanics, electromagnetism (including circuit theory), general relativity and gauge theory. Solutions to the problems are available for instructors at

    • Demonstrates how to use tensors and forms and how to apply them to problems in mathematics and physics
    • Bridges the gap between pure mathematics and applied science by explaining in detail the relationship between abstract and concrete approaches (theory and computations)
    • Requires minimal prerequisites and explains advanced concepts not usually taught at this level, providing an easier route to these subjects for mathematicians and scientists who are not experts in the field
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    Customer reviews

    24th Jan 2015 by Rengolin

    Very clear and succinct, shows the relationship between all representations of algebra, as well as a paced evolution of the concepts. Havent got far, yet, but Im finally getting tensors.

    Review was not posted due to profanity


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    Product details

    • Date Published: December 2013
    • format: Hardback
    • isbn: 9781107042193
    • length: 340 pages
    • dimensions: 246 x 170 x 20 mm
    • weight: 0.77kg
    • contains: 61 b/w illus. 271 exercises
    • availability: Available
  • Table of Contents

    1. Linear algebra
    2. Multilinear algebra
    3. Differentiation on manifolds
    4. Homotopy and de Rham cohomology
    5. Elementary homology theory
    6. Integration on manifolds
    7. Vector bundles
    8. Geometric manifolds
    9. The degree of a smooth map

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    Manifolds, Tensors, and Forms

    Paul Renteln

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  • Author

    Paul Renteln, California State University, San Bernardino
    Paul Renteln is Professor of Physics in the Department of Physics, California State University, San Bernardino, where he has taught a wide range of courses in physics. He is also Visiting Associate in the Department of Mathematics, California Institute of Technology, where he conducts research into combinatorics.

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