Preface
Acknowledgments
1 Basic Notions and Concepts
1.1 Metric Spaces
1.2 Linear Algebra
1.3 The Derivative
1.4 The Inverse and Implicit Function Theorems
1.5 The Riemann Integral
1.6 Improper Integrals
1.7 The Change of Variable Theorem
2 Manifolds
2.1 Smooth Manifolds
2.2 The Tangent and Cotangent Bundles
2.3 Stokes' Iheorem
2.4 Applications of Stokes' Theorem
3 Riemannian and Pseudo-Riemannian Geometry
3.1 The Pseudo-Riemannian Measure
3.2 Connections
3.3 The Levi-Civita Connection
3.4 Geodesics
3.5 The Jacobi Operator
3.6 The Gauss-Bonnet Theorem
3.7 The Chern-Gauss-Bonnet Theorem
Bibliography
Authors' Biographies
Index
编辑手记
