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Manifolds, Tensors, and Forms

An Introduction for Mathematicians and Physicists

Paul Renteln (California State University, San Bernardino)

$124.95

Paperback

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English
Cambridge University Press
21 November 2013
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 www.cambridge.org/9781107042193.
By:  
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Dimensions:   Height: 246mm,  Width: 170mm,  Spine: 20mm
Weight:   770g
ISBN:   9781107042193
ISBN 10:   1107042194
Pages:   340
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Preface; 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; Appendixes; References; Index.

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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