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Preface

Manifolds, Tensors and Exterior Forms / Part I：

Manifolds and vector fields / 1：

Tensors and exterior forms / 2：

Integration of differential forms / 3：

The Lie derivative / 4：

The PoincarÃ© lemma and potentials / 5：

Holonomic and non-holonomic constraints / 6：

Geometry and Topology / Part II：

R3 and Minkowski space / 7：

The geometry of surfaces in R3 / 8：

Covariant differentiation and curvature / 9：

Geodesics / 10：

Relativity, tensors, and curvature / 11：

Curvature and topology: Synge's theorem / 12：

Betti numbers and de Rham's theorem / 13：

Harmonic forms / 14：

Lie Groups, Bundles and Chern Forms / Part III：

Lie groups / 15：

Vector bundles in geometry and physics / 16：

Fiber bundles, Gauss-Bonnet, and topological quantization / 17：

Connections and associated bundles / 18：

The Dirac equation / 19：

Yang-Mills fields / 20：

Betti numbers and covering spaces / 21：

Chern forms and homotopy groups / 22：

Forms in continuum mechanics / Appendix A：

Harmonic chains and Kirchhoff's circuit laws / Appendix B：

Symmetries, quarks, and meson masses / Appendix C：

Representations and hyperelastic bodies / Appendix D：

Orbits and Morse-Bott theory in compact Lie groups / Appendix E：

Preface

Manifolds, Tensors and Exterior Forms / Part I：

Manifolds and vector fields / 1：