复分析是数学*核心的学科之一，不但自身引人入胜、丰富多彩，而且在多种其他数学学科（纯数学和应用数学）中都非常有用。《单复变函数论（第三版 英文版）》的与众不同之处在于它从多变量实微积分中直接发展出复变量。每一个新概念引进时，它总对应了实分析和微积分中相应的概念，《单复变函数论（第三版 英文版）》配有丰富的例题和习题来印证此点。

作者有条不紊地将分析从拓扑中分离出来，从柯西定理的证明中可见一斑。《单复变函数论（第三版 英文版）》分几章讨论专题，如对特殊函数的完整处理、素数定理和Bergman核。作者还处理了Hp空间，以及共形映射边界光滑性的Painleve定理。

《单复变函数论（第三版 英文版）》是一本很吸引人且现代的复分析导引，可用作研究生一年级的复分析教材，它反映了作者们作为数学家和写作者的专业素质。

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

Acknowledgments

Chapter 1． Fundamental Concepts

1．1． Elementary Properties of the Complex Numbers

1．2． Further Properties of the Complex Numbers

1．3． Complex Polynomials

1．4． Holomorphic Functions， the Cauchy-Riemann Equations， and Harmonic Functions

1．5． Real and Holomorphic Antiderivatives

Exercises

Chapter 2． Complex Line Integrals

2．1． Real and Complex Line Integrals

2．2． Complex Differentiability and Conformality

2．3． Antiderivatives Revisited

2．4． The Cauchy Integral Formula and the Cauchy Integral Theorem

2．5． The Cauchy Integral Formula： Some Examples

2．6． An Introduction to the Cauchy Integral Theorem and the Cauchy Integral Formula for More General Curves

Exercises

Chapter 3． Applications of the Cauchy Integral

3．1． Differentiability Properties of Holomorphic Functions

3．2． Complex Power Series

3．3． The Power Series Expansion for a Holomorphic Function

3．4． The Cauchy Estimates and Liouville's Theorem

3．5． Uniform Limits of Holomorphic Functions

3．6． The Zeros of a Holomorphic Function

Exercises

Chapter 4． Meromorphic Functions and Residues

4．1． The Behavior of a Holomorphic Function Near an Isolated Singularity

4．2． Expansion around Singular Points

4．3． Existence of Laurent Expansions

4．4． Examples of Laurent Expansions

4．5． The Calculus of Residues

4．6． Applications of the Calculus of Residues to the Calculation of Definite Integrals and Sums

4．7． Meromorphic Functions and Singularities at Infinity

Exercises

Chapter 5． The Zeros of a Holomorphic Function

5．1． Counting Zeros and Poles

5．2． The Local Geometry of Holomorphic Functions

5．3． Further Results on the Zeros of Holomorphic Functions

5．4． The Maximum Modulus Principle

5．5． The Schwarz Lemma

Exercises

Chapter 6． Holomorphic Functions as Geometric Mappings

6．1． Biholomorphic Mappings of the Complex Plane to Itself

6．2． Biholomorphic Mappings of the Unit Disc to Itself

6．3． Linear Fractional Transformations

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