《复函数论导论》由帕克所著，是一部介绍单复变函数解析理论本科生教程，内容体系十分严谨但又不失基础性。本书从最基本定义开始，徐徐展开，除了微积分基本知识，没有做任何铺垫，深入讲解复分析的观点，可以说达到了这门学科的制高点。并且将这些主要知识点：如柯西定理，黎曼射影定理、mittag-leffler定理讲述的十分明朗。本书重在强调几何，专门有一章讨论共形射影，相当于讲述复函数理论的简明教程。每章都有大量的精选练习，从简单直接计算到很具有启发性思想的都具有。

读者对象：数学专业的本科生，研究生和相关专业的科研人员。

preface

i the complex number system

1 the algebra and geometry of complex numbers

2 exponentials and logarithms of complex numbers

3 functions of a complex variable

4 exercises for chapter i

ii the rudiments of plane topology

1 basic notation and terminology

2 continuity and limits of functions

3 connected sets

4 compact sets

5 exercises for chapter ii

iii analytic functions

1 complex derivatives

2 the cauchy-riemann equations

3 exponential and trigonometric functions

4 branches of inverse functions

5 differentiability in the real sense

6 exercises for chapter iii

iv complex integration

1 paths in the complex plane

2 integrals along paths

3 rectifiable paths

4 exercises for chapter iv

v cauchy's theorem and its consequences

1 the local cauchy theorem

2 winding numbers and the local cauchy integral formula

3 consequences of the local cauchy integral formula

4 more about logarithm and power functions

5 the global cauchy theorems

6 simply connected domains

7 homotopy and winding numbers

8 exercises for chapter v

vi harmonic functions

1 harmonic functions

2 the mean value property

3 the dirichlet problem for a disk

4 exercises for chapter vi

vii sequences and series of analytic functions

1 sequences of functions

2 infinite series

3 sequences and series of analytic functions

4 normal families

5 exercises for chapter vii

viii isolated singularities of analytic functions

1 zeros of analytic functions

2 isolated singularities

3 the residue theorem and its consequences

4 function theory on the extended plane

5 exercises for chapter viii

ix conformed mapping

1 conformal mappings

2 msbius transformations

3 paemann's mapping theorem

4 the caratheodory-osgood theorem

5 conformal mappings onto polygons

6 exercises for chapter ix

x constructing analytic functions

1 the theorem of mittag-leffier

2 the theorem of weierstrass

3 analytic continuation

4 exercises for chapter x

appendix a background on fields

1 fields

2 order in fields

appendix b winding numbers revisited

1 technical facts about winding numbers

index