复分析

出版时间：2003-6  出版社：世界图书出版公司(此信息作废)  作者：S.lang  页数：485  
Tag标签：无  

内容概要

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra reading material for students on their own. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students.

书籍目录

Foreword Prerequisites PART ONE Basic Theory CHAPTER Ⅰ Complex Numbers and Functions   1. Definition   2. Polar Form   3. Complex Valued Functions   4. Limits and Compact Sets   5. Complex Differentiability   6. The Cauchy-Riemann Equations   7. Angles Under Holomorphic Maps CHAPTER Ⅱ Power Series   1. Formal Power Series   2. Convergent Power Series   3. Relations Between Formal and Convergent Series   4. Analytic Functions  5. Differentiation of Power Series  6. The Inverse and Open Mapping Theorems  7. The Local Maximum Modulus PrincipleCHAPTER Ⅲ Cauchy's Theorem,First Part  1. Holomorphic Functions on Connected Sets  2. Integrals Over Paths  3. Local Primitive for a Holomorphic Function  4. Local Primitive for a Holomorphic Function  5. The Homotopy Form of Cauchy's Theorem  6. Existence of Global Primitives.Definition of the Logarithm  7. The Local Cauchy FormulaCHAPTER Ⅳ Winding Numbers and Cauchy's TheoremCHAPTER Ⅴ Applications of Cauchy's Integral FormulaCHAPTER Ⅵ Calculus of ResiduesCHAPTER Ⅶ Conformal MappingsCHAPTER Ⅷ Harmonic FunctionsPART TWO Geometric Function TheoryCHAPTER Ⅸ Schwarz ReflectionCHAPTER Ⅹ The Riemann Mapping TheoremCHAPTER Ⅺ Analytic Continuation Along CurvesPART THREE Various Analytic TopicsCHAPTER Ⅻ Applications of the Maximum Modulus Principle and Jensen's FormulaCHAPTER ⅩⅢ Entire and Meromorphic FunctionsCHAPTER ⅩⅣ Elliptic FunctionsCHAPTER ⅩⅤ The Gamma and Zeta FunctionsCHAPTER ⅩⅥ The Prime Number TheoremAppendixBibliographyIndex

用户评论 (总计8条)

•   除了书页 诶 毕竟是影印版 内容是没的说~ 要学好复分析 必须人手一本
•   介绍的很详细，适合初学者
•   我是学这个专业的,这本书很好,我很满意,希望当当能提供更多的书,像函数空间,黎曼曲面,拟共形映照,复动力系统,亚纯函数等方面的书
•   才看到第二章，内容自然不错，不过有些习题的跳跃性也太大了。。。
•   需要一些分析基础,速度比较快
•   都是很喜欢读的书
•   应该适合研究生水平吧
•   其实对于英文版的数学著作我买的不多，整体还是蛮期待的。大家评论这本复分析写的不错，个人没有来得及细看，也相信书作者的水平。但是其封面上有明显污迹，看起来很不舒服，希望以后这样的情况不会发生。