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

Autor Paul Renteln
en Limba Engleză Hardback – 20 noi 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.
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Specificații

ISBN-13: 9781107042193
ISBN-10: 1107042194
Pagini: 340
Ilustrații: 61 b/w illus. 271 exercises
Dimensiuni: 170 x 246 x 20 mm
Greutate: 0.77 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States

Cuprins

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.

Notă biografică


Descriere

Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.