The Geometry of Physics: An Introduction Book

	Preface to the Second Edition
	Preface to the Revised Printing
	Preface to the First Edition
1	Manifolds and Vector Fields	3
2	Tensors and Exterior Forms	37
3	Integration of Differential Forms	95
4	The Lie Derivative	125
5	The Poincare Lemma and Potentials	155
6	Holonomic and Nonholonomic Constraints	165
7	R[superscript 3] and Minkowski Space	191
8	The Geometry of Surfaces in R[superscript 3]	201
9	Covariant Differentiation and Curvature	241
10	Geodesics	269
11	Relativity, Tensors, and Curvature	291
12	Curvature and Topology: Synge's Theorem	323
13	Betti Numbers and De Rham's Theorem	333
14	Harmonic Forms	361
15	Lie Groups	391
16	Vector Bundles in Geometry and Physics	413
17	Fiber Bundles, Gauss-Bonnet, and Topological Quantization	451
18	Connections and Associated Bundles	475
19	The Dirac Equation	491
20	Yang-Mills Fields	523
21	Betti Numbers and Covering Spaces	561
22	Chern Forms and Homotopy Groups	583
App. A	Forms in Continuum Mechanics	617
App. B	Harmonic Chains and Kirchhoff's Circuit Laws	636
App. C	Symmetries, Quarks, and Meson Masses	648
App. D	Representations and Hyperelastic Bodies	660
App. E	Orbits and Morse-Bott Theory in Compact Lie Groups	670
	References	679
	Index	683