《现代分析及其应用教程（英文）》通过度量空间中序列的收敛性讨论了完备性和紧性等问题，并给出了解决相关问题的方法，还阐述了现代分析中的另一种拓扑方法。
　　《现代分析及其应用教程（英文）》可应用到微分方程和积分方程、线性代数方程组、近似理论、数值分析和量子力学等领域，适合数学本科生、数学教师和其他需要学习一些数学分析知识用于其他领域的读者参考使用。

　　This book offers an introduction to some basic aspects of modern analysis. It is designed for students who are majoring in some area of mathematics but who do not necessarily intend to continue their studies at a graduate level.
　　The choice of material and the method of presentation are both aimed at as wide a readership as possible. Future teachers of high school mathematics should be given an introduction to the mathematical future as much as they must be given some knowledge of the mathematical past; students of mathematical engineering， biology or finance may need to read current literature without desiring to contribute to it. These are perhaps the extremes in the type of student to whom this book is directed. At the same time， students who do need to go on to courses in measure theory and functional analysis will find this book an easy introduction to the initial concepts in those areas.

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
4．4 Solved problems
4．5 Exercises

5 Topological Spaces
5．1 Definitions and examples
5．2 Closed sets
5．3 Compact sets
5．4 Continuity in topological spaces
5．5 Homeomorphisms; connectedness
5．6 Solved problems
5．7 Exercises
……

6 Normed Vector Spaces
7 Mappings on Normed Spaces
8 Inner Product Spaces
9 Hilbert Space

Bibliography
Selected Solutions
Index
编辑手记