单复变函数 第2版

出版时间：2004-11  出版社：世界图书出版公司(此信息作废)  作者：John B.Conway  
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内容概要

This book is intended as a textbook for a first course in the theory offunctions of one complex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.

书籍目录

Preface Ⅰ. The Complex Number System   1. The real numbers   2. The field of complex numbers   3. The complex plane   4. Polar representation and roots of complex numbers   5. Lines and half planes in the complex plane   6. The extended plane and its spherical representation Ⅱ. Metric Spaces and the Topology of C   1. Definition and examples of metric spaces   2. Connectedness   3. Sequences and completeness   4. Compactness   5. Continuity   6. Uniform convergence Ⅲ. Elementary Properties and Examples of Analytic Functions   1. Power series   2. Analytic functions   3. Analytic functions as mappings， M6bius transformations Ⅳ. Complex Integration  1.Riemann-Stieltjes integrals  2.Power series representation of analytic functions  3.Zeros of an analytic function  4.The index of a closed curve  5.Cauchy's Theorem and Integral Formula  6.The homotopic version of Cauchy's Therorem and simple connectivity  7.Counting zeros;the Open Mapping Theorem  8.Goursat's TheoremⅤ.Singularities  1.Classification of singularities  2.Residues  3.The Argument PrincipleⅥ.Compactness and Convergence in the Ⅶ.Runge's TheoremⅧ.Analytic Continuation and Riemann SurfacesⅨ.Harmonic FunctionsⅩ.Entire FunctionsⅪ.The Range of an Analytic FunctionAppendix A:Calculus for Complex Complex Valued Functions of and IntervalAppendix B:Suggestions for Further Study and Bibliographical NotesReferencesIndexList of Symbols

用户评论 (总计5条)

•   单复变的经典之作
•   帮老师买的，应该是不错的书！
•   GTM丛书几乎本本经典，值得好好一读。
•   不错，经典书，老外写的书就是好！
•   等我细读之后再评