Manifolds, Tensors, and Forms

An Introduction for Mathematicians and Physicists

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics
Cover of the book Manifolds, Tensors, and Forms by Paul Renteln, Cambridge University Press
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Author: Paul Renteln ISBN: 9781107703131
Publisher: Cambridge University Press Publication: November 21, 2013
Imprint: Cambridge University Press Language: English
Author: Paul Renteln
ISBN: 9781107703131
Publisher: Cambridge University Press
Publication: November 21, 2013
Imprint: Cambridge University Press
Language: English

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.

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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.

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