【文件属性】：
文件名称：Methods of Nonlinear Analysis
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更新时间：2021-11-08 05:02:03
FUNCTIONAL
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Preliminaries
1.1 Elements of Linear Algebra . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Normed Linear Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Properties of Linear and Nonlinear Operators
2.1 Linear Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.2 Compact Linear Operators . . . . . . . . . . . . . . . . . . . . . . 78
2.3 Contraction Principle . . . . . . . . . . . . . . . . . . . . . . . . . 93
3 Abstract Integral and Differential Calculus
3.1 Integration of Vector Functions . . . . . . . . . . . . . . . . . . . . 109
3.2 Differential Calculus in Normed Linear Spaces . . . . . . . . . . . . 126
3.2A Newton Method . . . . . . . . . . . . . . . . . . . . . . . . 144
4 Local Properties of Differentiable Mappings
4.1 Inverse Function Theorem . . . . . . . . . . . . . . . . . . . . . . . 149
4.2 Implicit Function Theorem . . . . . . . . . . . . . . . . . . . . . . 156
4.3 Local Structure of Differentiable Maps, Bifurcations . . . . . . . . 166
4.3A Differentiable Manifolds, Tangent Spaces and Vector
Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
4.3B Differential Forms . . . . . . . . . . . . . . . . . . . . . . . 207
4.3C Integration on Manifolds . . . .
. . . . . . . . . . . . . . . . 220