Manifolds, Tensors, and Forms

An Introduction for Mathematicians and Physicists

Paul Renteln (California State University, San Bernardino)

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English

Cambridge University Press
21 November 2013

Mathematics & Sciences; Differential & Riemannian geometry; Topology; Mathematical physics

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: Paul Renteln (California State University San Bernardino)
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: 21 November 2013
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.