現代分析及其套用教程

內容簡介

《現代分析及其套用教程（英文）》通過度量空間中序列的收斂性討論了完備性和緊性等問題，並給出了解決相關問題的方法，還闡述了現代分析中的另一種拓撲方法。

《現代分析及其套用教程（英文）》可套用到微分方程和積分方程、線性代數方程組、近似理論、數值分析和量子力學等領域，適合數學本科生、數學教師和其他需要學習一些數學分析知識用於其他領域的讀者參考使用。

Preface

1 Prelude to Modern Analysis

1．1 Introduction

1．2 Sets and numbers

1．3 Functions or mappings

1．4 Countability

1．5 Point sets

1．6 Open and closed sets

1．7 Sequences

1．8 Series

1．9 Functions of a real variable

1．10 Uniform convergence

1．11 Some linear algebra

1．12 Setting off

2 Metric Spaces

2．1 Definition of a metric space

2．2 Examples of metric spaces

2．3 Solved problems

2．4 Exercises

2．5 Convergence in a metric space

2．6 Examples on completeness

2．7 Subspace of a metric space

2．8 Solved problems

2．9 Exercises

3 The Fixed Point Theorem and its Applications

3．1 Mappings between metric spaces

3．2 The fixed point theorem

3．3 Applications

3．4 Perturbation mappings

3．5 Exercises

4 Compactness

4．1 Compact sets

4．2 Ascoli's theorem

4．3 Application to approximation theory