| 词条 | 小平邦彦复分析 |
| 释义 | 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 |
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