The Geometry of Physics: An Introduction (Paperback, Revised)

Preface; Part I. Manifolds, Tensors and Exterior Forms: 1. Manifolds and vector fields; 2. Tensors and exterior forms; 3. Integration of differential forms; 4. The Lie derivative; 5. The Poincare Lemma and potentials; 6. Holonomic and non-holonomic constraints; Part II. Geometry and Topology: 7. R3 and Minkowski space; 8. The geometry of surfaces in R3; 9. Covariant differentiation and curvature; 10. Geodesics; 11. Relativity, tensors, and curvature; 12. Curvature and topology: Synge's theorem; 13. Betti numbers and De Rham's theorem; 14. Harmonic forms; Part III. Lie Groups, Bundles and Chern Forms: 15. Lie groups; 16. Vector bundles in geometry and physics; 17. Fiber bundles, Gauss?Bonnet, and topological quantization; 18. Connections and associated bundles; 19. The Dirac equation; 20. Yang?Mills fields; 21. Betti numbers and covering spaces; 22. Chern forms and homotopy groups; Appendix: forms in continuum mechanics.