小平邦彦复分析(英文版)
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图灵原版数学统计学系列

小平邦彦复分析(英文版)

Kunihiko Kodaira (作者)
终止销售
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。
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出版信息

  • 书  名小平邦彦复分析(英文版)
  • 系列书名图灵原版数学统计学系列
  • 执行编辑关于本书的内容有任何问题,请联系 傅志红
  • 出版日期2008-05-12
  • 书  号978-7-115-17840-4
  • 定  价59.00 元
  • 页  数412
  • 开  本16开
  • 出版状态终止销售
  • 原书名Complex Analysis
  • 原书号0-521-80937-1

同系列书

目录

1 Holomorphic functions
1.1 Holomorphic functions
a. The complex plane
b. Functions of a complex variable
c. Holomorphic functions
1.2 Power series
a. Series whose terms are functions
b. Power series
1.3 Integrals
a. Curves
b. Integrals
c. Cauchy's integral formula for circles
d. Power series expansions
1.4 Properties ofholomorphic functions
a. mth-order derivatives
b. Limits of sequences of holomorphic fimctions
c. The Mean Value Theorem and the maximum principle
d. Isolated singularities
e. Entire functions
2 Cauchy's Theorem
2.1 Piecewise smooth curves
a. Smooth Jordan curves
b. Boundaries of bounded closed regions
2.2 Cellular decomposition
a. Calls
b. Cellular decomposition
2.3 Cauchy's Theorem
a. Cauchy's Theorem
b. Cauchy's integral formula
c. Residues
d. Evaluation of definite integrals
2.4 Differentiability and homology
3 Conformal mappings
3.1 Conformal mappings
3.2 The Riemann sphere
a. The Riemann sphere
b. Holomorphic functions with an isolated singularity at c~
c. Local coordinates
d. Homogeneous coordinates
3.3 Linear fractional transformations
a. Linear fractional transformations
b. Cross ratio
c. Elementary conformal mappings
4 Analytic continuation
4.1 Analytic continuation
a. Analytic continuation
b. Analytic continuation by expansion in power series
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
a. The principle of reflection
b. Modular functions
c. Picard's Theorem
d. The Schwarz-Christoffel formula
6 Riemann surfaces
6.1 Differential forms
a. Differential forms
b. Line integrals
c. Harmonic forms
d. Harmonic functions
6.2 Riemann surfaces
a. Hausdorff spaces
b. Definition of Riemann surfaces
6.3 Differential forms on a Riemann surface
a. Differential forms
b. Line integrals
c. Locally finite open coverings
d. Partition of unity
e. Green's Theorem
6.4 Dirichlet's Principle
a. Inner product and norm
b. Dirichlet's Principle
c. Analytic fimctions
7 The structure of Riemann surfaces
7.1 Planar Riemann surfaces
a. Planar Riemann surfaces
b. Simply connected Riemann surfaces
c. Multiply connected regions
7.2 Compact Riemann surfaces
a. Cohomology groups
b. Structure of compact Riemann surfaces
c. Homology groups
8 Analytic functions on a closed Riemann surface
8.1 Abelian differentials of the first kind
a. Harmonic 1-forms of the first kind
b. Abelian differential of the first kind
8.2 Abelian differentials of the second and third kind
a. Meromorphic functions
b. Abelian differentials of the second and third kind
8.3 The Riemann-Roch Theorem
a. Existence Theorem
b. The Riemann-Roch Theorem
8.4 Abel's Theorem
a. Existence Theorem
b. Abel's Theorem
Problems
References
Index
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