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复分析 第2版PDF|Epub|txt|kindle电子书版本网盘下载
- （德）费莱塔格著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510077838
- 出版时间：2014
- 标注页数：533页
- 文件大小：52MB
- 文件页数：540页
- 主题词：复分析－教材－英文
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图书目录
Ⅰ Differential Calculus in the Complex Plane C9
Ⅰ.1 Complex Numbers9
Ⅰ.2 Convergent Sequences and Series24
Ⅰ.3 Continuity36
Ⅰ.4 Complex Derivatives42
Ⅰ.5 The CAUCHY-RIEMANN Differential Equations47
Ⅱ Integral Calculus in the Complex Plane C69
Ⅱ.1 Complex Line Integrals70
Ⅱ.2 The CAUCHY Integral Theorem77
Ⅱ.3 The CAUCHY Integral Formulas92
Ⅲ Sequences and Series of Analytic Functions,the Residue Theorem103
Ⅲ.1 Uniform Approximation104
Ⅲ.2 Power Series109
Ⅲ.3 Mapping Properties of Analytic Functions124
Ⅲ.4 Singularities of Analytic Functions133
Ⅲ.5 LAURENT Decomposition142
A Appendix to Ⅲ.4 and Ⅲ.5155
Ⅲ.6 The Residue Theorem162
Ⅲ.7 Applications of the Residue Theorem170
Ⅳ Construction of Analytic Functions191
Ⅳ.1 The Gamma Function192
Ⅳ.2 The WEIERSTRASS Product Formula210
Ⅳ.3 The MITTAG-LEFFLER Partial Fraction Decomposition218
Ⅳ.4 The RIEMANN Mapping Theorem223
A Appendix:The Homotopieal Version of the CAUCHY Integral Theorem233
B Appendix:A Homological Version of the CAUCHY Integral Theorem239
C Appendix:Characterizations of Elementary Domains244
Ⅴ Elliptic Functions251
Ⅴ.1 LIOUVILLE's Theorems252
A Appendix to the Definition of the Period Lattice259
Ⅴ.2 The WEIERSTRASS ？-function261
Ⅴ.3 The Field of Elliptic Functions267
A Appendix to Sect.Ⅴ.3:The Torus as an Algebraic Curve271
Ⅴ.4 The Addition Theorem278
Ⅴ.5 Elliptic Integrals284
Ⅴ.6 ABEL's Theorem291
Ⅴ.7 The Elliptic Modular Group301
Ⅴ.8 The Modular Function j309
Ⅵ Elliptic Modular Forms317
Ⅵ.1 The Modular Group and Its Fundamental Region318
Ⅵ.2 The k/12-formula and the Injectivity of the j-function326
Ⅵ.3 The Algebra of Modular Forms334
Ⅵ.4 Modular Forms and Theta Series338
Ⅵ.5 Modular Forms for Congruence Groups352
A Appendix to Ⅵ.5:The Theta Group363
Ⅵ.6 A Ring of Theta Functions370
Ⅶ Analytic Number Theory381
Ⅶ.1 Sums of Four and Eight Squares382
Ⅶ.2 DIRICHLET Series399
Ⅶ.3 DIRICHLET Series with Functional Equations408
Ⅶ.4 The RIEMANN ζ-function and Prime Numbers421
Ⅶ.5 The Analytic Continuation of the ζ-function429
Ⅶ.6 A TAUBERian Theorem436
Ⅷ Solutions to the Exercises449
Ⅷ.1 Solutions to the Exercises of Chapter Ⅰ449
Ⅷ.2 Solutions to the Exercises of Chapter Ⅱ459
Ⅷ.3 Solutions to the Exercises of Chapter Ⅲ464
Ⅷ.4 Solutions to the Exercises of Chapter Ⅳ475
Ⅷ.5 Solutions to the Exercises of Chapter Ⅴ482
Ⅷ.6 Solutions to the Exercises of Chapter Ⅵ490
Ⅷ.7 Solutions to the Exercises of Chapter Ⅶ498
References509
Symbolic Notations519