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

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

Paul Renteln (Author)

9781107042193, Cambridge University Press

Hardback, published 21 November 2013

340 pages, 61 b/w illus. 271 exercises
24.6 x 17 x 2 cm, 0.77 kg

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.

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.

Subject Areas: Mathematical physics [PHU], Physics [PH], Mathematics & science [P]