Tensors and Manifolds: With Applications to Physics / Edition 2

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This book is a new edition of Tensors and Manifolds: With Applications to Mechanics and Relativity which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanses modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.
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Product Details

  • ISBN-13: 9780198510598
  • Publisher: Oxford University Press, USA
  • Publication date: 7/8/2004
  • Edition description: REV
  • Edition number: 2
  • Pages: 464
  • Product dimensions: 9.30 (w) x 6.20 (h) x 1.20 (d)

Meet the Author

Robert H. Wasserman is Professor Emeritus of Mathematics at Michigan State University, USA.

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Table of Contents

1 Vector spaces 1
2 Multilinear mappings and dual spaces 11
3 Tensor product spaces 25
4 Tensors 34
5 Symmetric and skew-symmetric tensors 46
6 Exterior (Grassmann) algebra 71
7 The tangent map of real cartesian spaces 84
8 Topological spaces 102
9 Differentiable manifolds 108
10 Submanifolds 131
11 Vector fields, 1-forms, and other tensor fields 136
12 Differentiation and integration of differential forms 153
13 The flow and the lie derivative of a vector field 168
14 Integrability conditions for distributions and for Pfaffian systems 186
15 Pseudo-Riemannian geometry 198
16 Connection 1-forms 212
17 Connections on manifolds 230
18 Mechanics 248
19 Additional topics in mechanics 268
20 A spacetime 282
21 Some physics on Minkowski spacetime 306
22 Einstein spacetimes 326
23 Spacetimes near an isolated star 339
24 Nonempty spacetimes 356
25 Lie groups 369
26 Fiber bundles 384
27 Connections on fiber bundles 394
28 Gauge theory 409
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