基本信息
作者: （日）小平邦彥ISBN: 9787115178404
頁數: 404
定價: 59.0
出版社: 人民郵電出版社
叢書: 圖靈原版數學·統計學系列
裝幀: 平裝
出版年: 2008-6-1
圖書簡介
本書講述了複變函數的經典理論。作者用易於理解的方式嚴密介紹基礎理論，強調幾何觀點，避免了一些拓撲學難點。書中首先從拓撲上較簡單的情形論證了柯西積分公式，並引出連續可微函式的基本性質。然後闡述共形映射、解析延拓、黎曼映射定理、黎曼面及其結構，以及閉黎曼面上的解析函式等。書中包含大量的圖示和豐富的例子，並附有習題，可以幫助讀者增強對課程的理解。 本書可作為高等院校理工科專業複分析的入門教材，也可作為更高級學習研究的參考書。圖書目錄
1Holomorphic functions1.1Holomorphic functions
1.2Power series
1.3Integrals
1.4Properties ofholomorphic functions
2Cauchy's Theorem
2.1Piecewise smooth curves
2.2Cellular decomposition
2.3Cauchy's Theorem
2.4Differentiability and homology
3Conformal mappings
3.1Conformal mappings
3.2The Riemann sphere
3.3Linear fractional transformations
4Analytic continuation
4.1Analytic continuation
4.2Analytic continuation along curves
4.3Analytic continuation by integrals
4.4Cauchy's Theorem (continued)
5Riemann's Mapping Theorem
5.1Riemann's Mapping Theorem
5.2Correspondence of boundaries
5.3The principle of reflection
6Riemann surfaces
6.1Differential forms
6.2Riemann surfaces
6.3Differential forms on a Riemann surface
6.4Dirichlet's Principle
7The structure of Riemann surfaces
7.1Planar Riemann surfaces
7.2Compact Riemann surfaces
8Analytic functions on a closed Riemann surface
8.1Abelian differentials of the first kind
8.2Abelian differentials of the second and third kind
8.3The Riemann-Roch Theorem
8.4Abel's Theorem
Problems
Index
