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内容简介
本书是一部引进版的英文原版数学教材,是一套系列丛书中的一本。在第一卷中,着重于初级阶段,第1章介绍了多元微积分、逆函数定理、隐函数定理、 Riemann积分理论和变量变换定理；第2章讨论了光滑流形、余切丛以及 Stokes定理；第3章是 Riemann几何的介绍.给出了Levi-Civita连接,引入了测地线,讨论了 Jaco bi算子,证明了 Gauss-Bonnet定理。
目录
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
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’ Theorem
2．4 Applications of Stokes’ Theorem
3 Riemannian and Pseudo-Riemanruan 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 Iheorem
3．7 The Chern-Gauss-Bonnet Iheorem
Bibliography
Authors’ Biographies
Index
编辑手记