Ebook: The geometry of physics : an introduction

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 Nonholonomic Constraints -- 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 -- 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