复分析（英文版·第3版）
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| 新书城图书编号：971 |
| 图书ISBN：7111134168 |
| 出版时间：2004-1-1 |
| 出版社：机械工业出版社 |
| 作者：[美]阿尔福斯 著 |
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市场价格：￥35 |
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普通会员：￥28
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80折 |
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VIP会员：￥26.25
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75折 |
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【图书简介】
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本书的诞生还是半个世纪之前的事情，但是，深贯其中的严谨的学术风范以及针对；不同时代所做出的切实改进使得它愈久弥新，成为复分析领域历经考验的一本经典教材。本书作者在数学分析领域声名卓著，多次荣获国际大奖，这也是本书始终保持旺盛的生命力的原因之一，本书适合用做数学专业本科高年级学生及研究生教材。
Lars V．Ahlfors生前是哈佛大学数学教授。他于1924年进入赫尔辛基大学学习，并在1930年于芬兰著名的土尔库大学获得博士学位。期间他还师从著名数学家Nevanlinna共同进行研究工作。1936年荣获菲尔茨奖。第二次世界大战结束后，辗转到哈佛大学从事教学工作。他又于1968年和1981年分别荣获Vihuri奖和Wolf奖。他的著述很多，除本书外，还著有《RiemannSurfaces》和《Conformal Invariants》等。
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【图书目录】
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Preface
CHAPTER 1 COMPLEX NUMBERS
The Algebra of Complex Numbers
1.1 Arithmetic Operations
1.2 Square Roots
1.3 Justification
1.4 Conjugation, Absolute Value
1.5 Inequalities
2 The Geometric Representation of Complex Numbers
2.1 Geometric Addition and Multiplication
2.2 The Binomial Equation
2.3 Analytic Geometry
2.4 The Spherical Representation
CHAPTER 2 COMPLEX FUNCTIONS
Introduction to the Concept of Analytic Function
1.1 Limits and Continuity
1.2 Analytic Functions
1.3 Polynomials
1.4 Rational Functions
2 Elementary Theory of Power Series
2.1 Sequences
2.2 Series
2.3 Uniform Convergence
2.4 Power Series
2.5 Abel's Limit Theorem
3 The Exponential and Trigonometric Functions
3.1 The Exponential
3.2 The Trigonometric Functions
3.3 The Periodicity
3.4 The Logarithm
CHAPTER 3 ANALYTIC FUNCTIONS AS MAPPINGS
I Elementary Point Set Topology
1.1 Sets and Elements
1.2 Metric Spaces
1.3 Connectedness
1.4 Compactness
1.5 Continuous Functions
1.6 Topological Spaces
2 Conformality
2.1 Arcs and Closed Curves
2.2 Analytic Functions in Regions
2.3 Conformal Mapping
2.4 Length and Area
Linear Transformations
3.1 The Linear Group
3.2 The Cross Ratio
3.3 Symmetry
3.4 Oriented Circles
3.5 Families of Circles
Elementary Conformal Mappings
4.1 The Use of Level Curves
4.2 A Survey of Elementary Mappings
4.3 Elementary Riemann Surfaces
CHAPTER 4 COMPLEX INTEGRATION
Fundamental Theorems
1.1 Line Integrals
1.2 Rectifiable Arcs
1.3 Line Integrals as Functions of Arcs
1.4 Cauchy's Theorem for a Rectangle
1.5 Cauchy's Theorem in a Disk
Cauchy' s Integral Formula
2.1 The Index of a Point with Respect to a Closed Curve
2.2 The Integral Formula
2.3 Higher Derivatives
Local Properties of Analytical Functions
3.1 Removable Singularities. Taylor's Theorem
3.2 Zeros and Poles
3.3 The Local Mapping
3.4 The Maximum Principle
The General Form of Cauchy's Theorem
4.1 Chains and Cycles
4.2 Simple Connectivity
4.3 Homology
4.4 The General Statement of Cauchy's Theorem
4.5 Proof of Cauchy's Theorem
4.6 Locally Exact Differentials
4.7 Multiply Connected Regions
The Calculus of Residues
5.1 The Residue Theorem
5.2 The Argument Principle
5.3 Evaluation of Definite Integrals
Harmonic Functions
6.1 Definition and Basic Properties
6.2 The Mean-value Property
6.3 Poisson's Formula
6.4 Schwarz's Theorem
6.5 The Reflection Principle
CHAPTER 5 SERIES AND PRODUCT DEVELOPMENTS
Power Series Expansions
1.1 Weierstrass's Theorem
1.2 The Taylor Series
1.3 The Laurent Series
Partial Fractions and Factorization
2.1 Partial Fractions
2.2 Infinite Products
2.3 Canonical Products
2.4 The Gamma Functio
2.5 Stirling's Formula
3 Entire Functions
3.1 Jensen's Formula
3.2 Hadamard's Theorem
The Riemann Zeta Function
4.1 The Product Development
4.2 Extension of (s) to the Whole Plane
4.3 The Functional Equation
4.4 The Zeros of the Zeta Function
Normal Families
5.1 Equicontinuity
5.2 Normality and Compactness
5.3 Arzela's Theorem
5.4 Families of Analytic Functions
5.5 The Classical Definition
CHAPTER 6 CONFORMAL MAPPING. DIRICHLET'S
PROBLEM
The Riemann Mapping Theorem
1.1 Statement and Proof
1.2 Boundary Behavior
1.3 Use of the Reflection Principle
1.4 Analytic Arcs
2 Conformal Mapping of Polygons
2.1 The Behavior at an Angle
2.2 The Schwarz-Christoffel Formula
2.3 Mapping on a Rectangle
2.4 The Triangle Functions of Schwarz
3 A Closer Look at Harmonic Functions
3.1 Functions with the Mean-value Property
3.2 Harnack's Principle
4 The Dirichlet Problem
4.1 Subharmonic Functions
4.2 Solution of Dirichlet's Problem,
5 Canonical Mappings of Multiply Connected Regions
5.1 Harmonic Measures
5.2 Green's Function
5.3 Parallel Slit Regions
CHAPTER 7 ELLIPTIC FUNCTIONS
Simply Periodic Functions
1.1 Representation by Exponentials
1.2 The Fourier Development
1.3 Functions of Finite Order
2 Doubly Periodic Functions
2.1 The Period Module
2.2 Unimodular Transformations
2.3 The Canonical Basis
2.4 General Properties of Elliptic Functions
3 The Weierstrass Theory
3.1 The Weierstrass p-function
3.2 The Functions (z) and (z)
3.3 The Differential Equation
3.4 The Modular Function ()
3.5 The Conformal Mapping by ()
CHAPTER 8 GLOBAL ANALYTIC FUNCTIONS
1 Analytic Continuation
1.1 The Weierstrass Theory
1.2 Germs and Sheaves
1.3 Sections and Riemann Surfaces
1.4 Analytic Continuations along Arcs
1.5 Homotopie Curves
1.6 The Monodromy Theorem
1.7 Branch Points
2 Algebraic Functions
2.1 The Resultant of Two Polynomials
2.2 Definition and Properties of Algebraic Functions
2.3 Behavior at the Critical Points
3 Picard's Theorem
3.1 Lacunary Values
Linear Differential Equations
4.1 Ordinary Points
4.2 Regular Singular Points
4.3 Solutions at Infinity
4.4 The Hypergeometric Differential Equation
4.5 Riemann's Point of View
Index
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