The geometry of physics an introduction
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included ar...
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| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
2012
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| Edition: | 3rd ed |
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| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Overview: an informal overview of Cartan's exterior differential forms, illustrated with an application to Cauchy's stress tensor
- t I. Part I: Manifolds and vector fields
- Tensors and exterior forms
- Integration of differential forms
- The Lie derivative
- The Poincare Lemma and potentials
- Holonomic and nonholonomic constraints
- Part II: Geometry and topology
- R3 and Minkowski space
- The geometry of surfaces in R3
- Covariant differentiation and curvature
- Geodesics
- Relativity, tensors, and curvature
- Curvature and topology: Synge's theorem
- Betti numbers and De Rham's theorem
- Harmonic forms
- Part III: Lie Groups
- Vector bundles in geometry and physics
- Fiber bundles, Gauss-Bonnet, and topological quantization
- Connections and associated bundles
- The Dirac equation
- Yang-Mills fields
- Betti numbers and covering spaces
- Chern forms and homotopy groups