作者：（美）普雷姆·K.凯瑟
页数：912
出版社：哈尔滨工业大学出版社
出版日期：2024
ISBN：9787576709421
电子书格式：PDF
PDF下载地址
内容简介
本书是一部学习应用数学的工具书。本著作有许多其他书籍、手册或数学百科全书没有的特色。本书包括25章正文和10篇附录，在目录中详细列出了300多个共形映射，书中还包括了500多个插图，其中一些有多个图形.虽然本书并未自称详尽无遗，但本书编译和讨论的所有基本的共形映射都可以通过合成和链属性的过程生成其他共形映射，书中提供了一些这类映射的例子，本书被分为三个部分：(i)理论与共形映射，在它们的几何和代数性质上定义，贯穿全书，但主要在第1章到第7章中出现；(ii)解决各种作为共形映射的结果出现的积分方程的数值方法，涵盖了第8章到第15章；（ⅲ）第16章到第25章是应用。
目录
Preface
Notations, Definitions, and Acronyms
Part 1: Theory and Conformal Maps
1 Introduction
1.1 Historical Background
1.2 Modern Developments
1.3 In Retrospect
2 Conformal Mapping
2.1 Definitions
2.1.1 Analytic Functions
2.1.2 Integration
2.1.3 Fatou’s Lemma
2.2 Jordan Contour
2.2.1 HSlder Condition
2.3 Metric Spaces
2.4 Basic Theorems
2.4.1 Singularities
2.4.2 Residues
2.4.3 Boundary Values for Cauchy Integral
2.4.4 Argument Principle
2.4.5 Plemelj Formulas
2.5 Harmonic Functions
2.5.1 Harmonic Conjugate
2.5.2 Capacity
2.6 Univalent Functions
2.6.1 Conformality and Uniqueness
2.6.2 Conformal and Isogonal Mappings
2.6.3 Conformal Mapping of an Area Element
2.6.4 Analytic Continuation
2.6.5 Chain Property
2.6.6 Schwarz Reflection Principle
2.6.7 Conformal Equivalence
2.6.8 Riemann Sphere
2.6.9 Bieberbach Conjecture
2.6.10 Mercator’s Projection
2.7 Taylor Series Approximations
2.7.1 Interior of the Unit Circle
3 Linear and Bilinear Transformations
3.1 Definitions of Certain Curves
3.1.1 Line
3.1.2 Circle
3.1.3 Ellipse
3.1.4 Hyperbola
3.1.5 Rectangular Hyperbola
3.1.6 Parabola
3.1.7 Cassini’s Ovals and Lenmiscate
3.1.8 Cardioid and Lima~ons
3.2 Bilinear Transformations
3.2.1 Fixed Points
3.2.2 Linear Transformation
3.2.3 Composition of Bilinear Transformations
Map 3.1. Involutory Transformation
Map 3.2. Three Points onto Three Points
Map 3.3. Sequence of Bilinear Transformations
3.3 Cross-Ratio
3.3.1 Symmetric Points
3.3.2 Symmetry Principle
3.3.3 Special Cases
……
Part 2：Numerical Conformal Mapping
Part 3: Applications
Notations, Definitions, and Acronyms
Part 1: Theory and Conformal Maps
1 Introduction
1.1 Historical Background
1.2 Modern Developments
1.3 In Retrospect
2 Conformal Mapping
2.1 Definitions
2.1.1 Analytic Functions
2.1.2 Integration
2.1.3 Fatou’s Lemma
2.2 Jordan Contour
2.2.1 HSlder Condition
2.3 Metric Spaces
2.4 Basic Theorems
2.4.1 Singularities
2.4.2 Residues
2.4.3 Boundary Values for Cauchy Integral
2.4.4 Argument Principle
2.4.5 Plemelj Formulas
2.5 Harmonic Functions
2.5.1 Harmonic Conjugate
2.5.2 Capacity
2.6 Univalent Functions
2.6.1 Conformality and Uniqueness
2.6.2 Conformal and Isogonal Mappings
2.6.3 Conformal Mapping of an Area Element
2.6.4 Analytic Continuation
2.6.5 Chain Property
2.6.6 Schwarz Reflection Principle
2.6.7 Conformal Equivalence
2.6.8 Riemann Sphere
2.6.9 Bieberbach Conjecture
2.6.10 Mercator’s Projection
2.7 Taylor Series Approximations
2.7.1 Interior of the Unit Circle
3 Linear and Bilinear Transformations
3.1 Definitions of Certain Curves
3.1.1 Line
3.1.2 Circle
3.1.3 Ellipse
3.1.4 Hyperbola
3.1.5 Rectangular Hyperbola
3.1.6 Parabola
3.1.7 Cassini’s Ovals and Lenmiscate
3.1.8 Cardioid and Lima~ons
3.2 Bilinear Transformations
3.2.1 Fixed Points
3.2.2 Linear Transformation
3.2.3 Composition of Bilinear Transformations
Map 3.1. Involutory Transformation
Map 3.2. Three Points onto Three Points
Map 3.3. Sequence of Bilinear Transformations
3.3 Cross-Ratio
3.3.1 Symmetric Points
3.3.2 Symmetry Principle
3.3.3 Special Cases
……
Part 2：Numerical Conformal Mapping
Part 3: Applications