- 作 者：（德）费莱塔格著
- 出 版 社：北京/西安：世界图书出版公司
- 出版年份：2014
- ISBN：9787510077838
- 标注页数：533 页
- PDF页数：540 页
请阅读订购服务说明与试读!
订购服务说明
1、本站所有的书默认都是PDF格式，该格式图书只能阅读和打印，不能再次编辑。
2、除分上下册或者多册的情况下，一般PDF页数一定要大于标注页数才建议下单购买。【本资源540 ≥533页】
图书下载及付费说明
1、所有的电子图书为PDF格式，支持电脑、手机、平板等各类电子设备阅读；可以任意拷贝文件到不同的阅读设备里进行阅读。
2、电子图书在提交订单后一般半小时内处理完成,最晚48小时内处理完成。(非工作日购买会延迟)
3、所有的电子图书都是原书直接扫描方式制作而成。
Ⅰ Differential Calculus in the Complex Plane C 9
Ⅰ.1 Complex Numbers 9
Ⅰ.2 Convergent Sequences and Series 24
Ⅰ.3 Continuity 36
Ⅰ.4 Complex Derivatives 42
Ⅰ.5 The CAUCHY-RIEMANN Differential Equations 47
Ⅱ Integral Calculus in the Complex Plane C 69
Ⅱ.1 Complex Line Integrals 70
Ⅱ.2 The CAUCHY Integral Theorem 77
Ⅱ.3 The CAUCHY Integral Formulas 92
Ⅲ Sequences and Series of Analytic Functions,the Residue Theorem 103
Ⅲ.1 Uniform Approximation 104
Ⅲ.2 Power Series 109
Ⅲ.3 Mapping Properties of Analytic Functions 124
Ⅲ.4 Singularities of Analytic Functions 133
Ⅲ.5 LAURENT Decomposition 142
A Appendix to Ⅲ.4 and Ⅲ.5 155
Ⅲ.6 The Residue Theorem 162
Ⅲ.7 Applications of the Residue Theorem 170
Ⅳ Construction of Analytic Functions 191
Ⅳ.1 The Gamma Function 192
Ⅳ.2 The WEIERSTRASS Product Formula 210
Ⅳ.3 The MITTAG-LEFFLER Partial Fraction Decomposition 218
Ⅳ.4 The RIEMANN Mapping Theorem 223
A Appendix:The Homotopieal Version of the CAUCHY Integral Theorem 233
B Appendix:A Homological Version of the CAUCHY Integral Theorem 239
C Appendix:Characterizations of Elementary Domains 244
Ⅴ Elliptic Functions 251
Ⅴ.1 LIOUVILLE's Theorems 252
A Appendix to the Definition of the Period Lattice 259
Ⅴ.2 The WEIERSTRASS ？-function 261
Ⅴ.3 The Field of Elliptic Functions 267
A Appendix to Sect.Ⅴ.3:The Torus as an Algebraic Curve 271
Ⅴ.4 The Addition Theorem 278
Ⅴ.5 Elliptic Integrals 284
Ⅴ.6 ABEL's Theorem 291
Ⅴ.7 The Elliptic Modular Group 301
Ⅴ.8 The Modular Function j 309
Ⅵ Elliptic Modular Forms 317
Ⅵ.1 The Modular Group and Its Fundamental Region 318
Ⅵ.2 The k/12-formula and the Injectivity of the j-function 326
Ⅵ.3 The Algebra of Modular Forms 334
Ⅵ.4 Modular Forms and Theta Series 338
Ⅵ.5 Modular Forms for Congruence Groups 352
A Appendix to Ⅵ.5:The Theta Group 363
Ⅵ.6 A Ring of Theta Functions 370
Ⅶ Analytic Number Theory 381
Ⅶ.1 Sums of Four and Eight Squares 382
Ⅶ.2 DIRICHLET Series 399
Ⅶ.3 DIRICHLET Series with Functional Equations 408
Ⅶ.4 The RIEMANN ζ-function and Prime Numbers 421
Ⅶ.5 The Analytic Continuation of the ζ-function 429
Ⅶ.6 A TAUBERian Theorem 436
Ⅷ Solutions to the Exercises 449
Ⅷ.1 Solutions to the Exercises of Chapter Ⅰ 449
Ⅷ.2 Solutions to the Exercises of Chapter Ⅱ 459
Ⅷ.3 Solutions to the Exercises of Chapter Ⅲ 464
Ⅷ.4 Solutions to the Exercises of Chapter Ⅳ 475
Ⅷ.5 Solutions to the Exercises of Chapter Ⅴ 482
Ⅷ.6 Solutions to the Exercises of Chapter Ⅵ 490
Ⅷ.7 Solutions to the Exercises of Chapter Ⅶ 498
References 509
Symbolic Notations 519