[按需印刷]復分析（英文版第3版） [美]Lars V.Ahlfors|15925 下載 mobi epub pdf 電子書 2024

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圖書介紹

店鋪：互動齣版網圖書專營店

齣版社：機械工業齣版社

ISBN：7111134168

商品編碼：26593707938

叢書名：經典原版書庫

齣版時間：2004-01-01

頁數：331

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書名：	復分析（英文版·第3版）[按需印刷]\|15925
圖書定價：	35元
圖書作者：	[美]Lars V.Ahlfors
齣版社：	機械工業齣版社
齣版日期：	2004/1/1 0:00:00
ISBN號：	7111134168
開本：	16開
頁數：	331
版次：	1-1

作者簡介

Lars V.Ahlfors生前是哈佛大學數學教授。他於1924年進入赫爾辛基大學學習，並在1930年於芬蘭著名的士爾庫大學獲得士學位。期間他還師從著名數學傢Nevanlinna共同進行研究工作。1936年榮獲菲爾茨奬。第二次世界大戰結束後，輾轉到哈佛大學從事教學工作。他又於1968年和1981年分彆榮獲Vihuri奬和Wolf奬。他的著述很多，除本書外，還著有《Riemann Surfaces》和《Conformal Invariants》等。

內容簡介

本書的誕生還是半個世紀之前的事情，但是，深貫其中的嚴謹的學術風範以及針對；不同時代所做齣的切實改進使得它愈久彌新，成為復分析領域曆經考驗的一本經典教材。本書作者在數學分析領域聲名卓著，多次榮獲國際大奬，這也是本書始終保持旺盛的生命力的原因之一，本書適閤用做數學專業本科高年級學生及研究生教材。
Lars V．Ahlfors生前是哈佛大學數學教授。他於1924年進入赫爾辛基大學學習，並在1930年於芬蘭著名的土爾庫大學獲得博士學位。期間他還師從著名數學傢Nevanlinna共同進行研究工作。1936年榮獲菲爾茨奬。第二次世界大戰結束後，輾轉到哈佛大學從事教學工作。他又於1968年和1981年分彆榮獲Vihuri奬和Wolf奬。他的著述很多，除本書外，還著有《RiemannSurfaces》和《Conformal Invariants》等。

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 [按需印刷]復分析（英文版第3版） [美]Lars V.Ahlfors|15925 下載 mobi epub pdf txt 電子書格式