小平邦彦复分析

基本信息作者: （日）小平邦彦

ISBN: 9787115178404

页数: 404

定价: 59.0

出版社: 人民邮电出版社

丛书: 图灵原版数学·统计学系列

装帧: 平装

出版年: 2008-6-1

图书简介本书讲述了复变函数的经典理论。作者用易于理解的方式严密介绍基础理论，强调几何观点，避免了一些拓扑学难点。书中首先从拓扑上较简单的情形论证了柯西积分公式，并引出连续可微函数的基本性质。然后阐述共形映射、解析延拓、黎曼映射定理、黎曼面及其结构，以及闭黎曼面上的解析函数等。书中包含大量的图示和丰富的例子，并附有习题，可以帮助读者增强对课程的理解。 本书可作为高等院校理工科专业复分析的入门教材，也可作为更高级学习研究的参考书。

图书目录1 Holomorphic functions

1.1 Holomorphic functions

1.2 Power series

1.3 Integrals

1.4 Properties ofholomorphic functions

2 Cauchy's Theorem

2.1 Piecewise smooth curves

2.2 Cellular decomposition

2.3 Cauchy's Theorem

2.4 Differentiability and homology

3 Conformal mappings

3.1 Conformal mappings

3.2 The Riemann sphere

3.3 Linear fractional transformations

4 Analytic continuation

4.1 Analytic continuation

4.2 Analytic continuation along curves

4.3 Analytic continuation by integrals

4.4 Cauchy's Theorem (continued)

5 Riemann's Mapping Theorem

5.1 Riemann's Mapping Theorem

5.2 Correspondence of boundaries

5.3 The principle of reflection

6 Riemann surfaces

6.1 Differential forms

6.2 Riemann surfaces

6.3 Differential forms on a Riemann surface

6.4 Dirichlet's Principle

7 The structure of Riemann surfaces

7.1 Planar Riemann surfaces

7.2 Compact Riemann surfaces

8 Analytic functions on a closed Riemann surface

8.1 Abelian differentials of the first kind

8.2 Abelian differentials of the second and third kind

8.3 The Riemann-Roch Theorem

8.4 Abel's Theorem

Problems

Index