复分析导引（第二版）（影印版）

本书是复分析入门的首 选，既可以用作教材，也可 以用来自学。高年级本科生 、低年级研究生、熟悉高等 微积分或具备实分析入门知 识的读者均可阅读本书。除 幂级数、柯西定理、留数、 共形映射和调和函数等标准 材料外，本书还对同类书中 不常见的有趣的主题做了清 晰论述。附加的主题和应用 使本书既适用于一学期课程 ，也适用于全年课程。 详细的习题解答既可给 学生做示范，也可促进自学 。书中未包含解答的补充练 习则提供了一种额外的教学 工具。

Preface to the Second Edition Preface to the First Edition To the Student Chapter 1 From Complex Numbers to Cauchy's Theorem 1.Complex Numbers 2.Functions 3.Power Series 4.Some Elementary Functions 5.Curves and Integrals 6.Cauchy's Theorem Chapter 2 Applications of Cauchy's Theorem 7.Cauchy's Integral Formula 8.Isolated Singular Points 9.Evaluation of Definite Integrals 10.Logarithms and General Powers 11.Additional Definite Integrals 12.Zeros of Analytic Functions 13.Univalence and Inverses 14.Laurent Series 15.Combinations of Power Series and Laurent Series 16.The Maximum Principle Chapter 3 Analytic Continuation 17.The Idea of Analytic Continuation 18.Power Series on the Circle of Convergence Chapter 4 Harmonic Functions and Conformal Mapping 19.Harmonic Functions 20.Harmonic Functions in a Disk *21.Harmonic Functions and Fourier Series 22.Conformal Mapping 23.Some Applications of Conformal Mapping to Physics 24.Some Special Flows 25.Mobius Transformations 26.Further Examples of Transformations and Flows 27.Dirichlet Problems in General 28.The Riemann Mapping Theorem 29.Intuitive Riemann Surfaces Chapter 5 Miscellaneous Topics 30.A Non-Euclidean Geometry 31.Infinite Products 32.Rate of Growth Versus Number of Zeros 33.Generalizations of the Maximum Principle 34.Asymptotic Series 35.Univalent Functions in the Disk Solutions of Exercises References Index About the Authors