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