Tensors and Manifolds: With Applications to Physics
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An advance undergraduate or beginning graduate textbook introducing the expanse of modern mathematics and its application in modern physics to students who are intending to go into pure mathematics, and may not otherwise be exposed to applications for a long time. It seeks to harmonize the two approaches that are variously termed classical, index or local on the one hand and modern, intrinsic, or global on the other. The 1992 edition has been corrected, expanded, and clarified and a few problems have been added. Annotation ©2004 Book News, Inc., Portland, OR
1Vector spaces12Multilinear mappings and dual spaces113Tensor product spaces254Tensors345Symmetric and skew-symmetric tensors466Exterior (Grassmann) algebra717The tangent map of real cartesian spaces848Topological spaces1029Differentiable manifolds10810Submanifolds13111Vector fields, 1-forms, and other tensor fields13612Differentiation and integration of differential forms15313The flow and the lie derivative of a vector field16814Integrability conditions for distributions and for Pfaffian systems18615Pseudo-Riemannian geometry19816Connection 1-forms21217Connections on manifolds23018Mechanics24819Additional topics in mechanics26820A spacetime28221Some physics on Minkowski spacetime30622Einstein spacetimes32623Spacetimes near an isolated star33924Nonempty spacetimes35625Lie groups36926Fiber bundles38427Connections on fiber bundles39428Gauge theory409
