Introduction to Smooth Manifolds (Hardcover, 2, 2013)

Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Lie Groups.- 7 Vector Fields.- 8 Integral Curves and Flows.- 9 Vector Bundles.- 10 Sard's Theorem.- 11 Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 Distributions and Foliations.- 18 The Exponential Map of a Lie Group.- 19 Quotient Manifolds.- 20 De Rham Cohomology.- 21 The de Rham Theorem.- 22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index