Tensors and manifolds : with applications to physics /
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."--Jacket.
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford ; New York :
Oxford University Press,
2004.
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| Edition: | 2nd ed. |
| Subjects: | |
| Online Access: | Table of contents Publisher description |
Table of Contents:
- Vector spaces
- Multilinear mappings and dual spaces
- Tensor product spaces
- Tensors
- Symmetric and skew-symmetric tensors
- Exterior (Grassmann) algebra
- The tangent map of real Cartesian spaces
- Topological spaces
- Differentiable manifolds
- Submanifolds
- Vector fields, 1-forms and other tensor fields
- Differentiation and integration of differential forms
- The flow and the lie derivative of a vector field
- Integrability conditions for distributions and for Pfaffian Systems
- Pseudo-Riemannian manifolds
- Connection 1-forms
- Connection on manifolds
- Mechanics
- Additional topics in mechanics
- A spacetime
- Some physics on Minkowski spacetime
- Einstein spacetimes
- Spacetimes near an isolated star
- Nonempty spacetimes-- Lie groups.
- Fiber bundles
- Connections on fiber bundles
- Gauge theory.