图书信息
图书目录
基础复分析：分析综合教程（第2A部分）（影印版）
暂无简介
作者：
Barry Simon
定价：
269.00元
出版时间：
2023-03-08
ISBN：
978-7-04-059300-6
物料号：
59300-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
分析
重点项目：
暂无
版面字数：
1060.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 前辅文
- Chapter 1. Preliminaries
- §1.1. Notation and Terminology
- §1.2. Complex Numbers
- §1.3. Some Algebra, Mainly Linear
- §1.4. Calculus on R and Rn
- §1.5. Differentiable Manifolds
- §1.6. Riemann Metrics
- §1.7. Homotopy and Covering Spaces
- §1.8. Homology
- §1.9. Some Results from Real Analysis
- Chapter 2. The Cauchy Integral Theorem: Basics
- §2.1. Holomorphic Functions
- §2.2. Contour Integrals
- §2.3. Analytic Functions
- §2.4. The Goursat Argument
- §2.5. The CIT for Star-Shaped Regions
- §2.6. Holomorphically Simply Connected Regions, Logs, and Fractional Powers
- §2.7. The Cauchy Integral Formula for Disks and Annuli
- Chapter 3. Consequences of the Cauchy Integral Formula
- §3.1. Analyticity and Cauchy Estimates
- §3.2. An Improved Cauchy Estimate
- §3.3. The Argument Principle and Winding Numbers
- §3.4. Local Behavior at Noncritical Points
- §3.5. Local Behavior at Critical Points
- §3.6. The Open Mapping and Maximum Principle
- §3.7. Laurent Series
- §3.8. The Classification of Isolated Singularities
- Casorati–Weierstrass Theorem
- §3.9. Meromorphic Functions
- §3.10. Periodic Analytic Functions
- Chapter 4. Chains and the Ultimate Cauchy Integral Theorem
- §4.1. Homologous Chains
- §4.2. Dixon’s Proof of the Ultimate CIT
- §4.3. The Ultimate Argument Principle
- §4.4. Mesh-Defined Chains
- §4.5. Simply Connected and Multiply Connected Regions
- §4.6. The Ultra Cauchy Integral Theorem and Formula
- §4.7. Runge’s Theorems
- §4.8. The Jordan Curve Theorem for Smooth Jordan Curves
- Chapter 5. More Consequences of the CIT
- §5.1. The Phragm´en–Lindel¨of Method
- §5.2. The Three-Line Theorem and the Riesz–Thorin Theorem
- §5.3. Poisson Representations
- §5.4. Harmonic Functions
- §5.5. The Reflection Principle
- §5.6. Reflection in Analytic Arcs
- §5.7. Calculation of Definite Integrals
- Chapter 6. Spaces of Analytic Functions
- §6.1. Analytic Functions as a Fr´echet Space
- §6.2. Montel’s and Vitali’s Theorems
- §6.3. Restatement of Runge’s Theorems
- §6.4. Hurwitz’s Theorem
- §6.5. Bonus Section: Normal Convergence of Meromorphic Functions and Marty’s Theorem
- Chapter 7. Fractional Linear Transformations
- §7.1. The Concept of a Riemann Surface
- §7.2. The Riemann Sphere as a Complex Projective Space
- §7.3. PSL(2,C)
- §7.4. Self-Maps of the Disk
- §7.5. Bonus Section: Introduction to Continued Fractions and the Schur Algorithm
- Chapter 8. Conformal Maps
- §8.1. The Riemann Mapping Theorem
- §8.2. Boundary Behavior of Riemann Maps
- §8.3. First Construction of the Elliptic Modular Function
- §8.4. Some Explicit Conformal Maps
- §8.5. Bonus Section: Covering Map for General Regions
- §8.6. Doubly Connected Regions
- §8.7. Bonus Section: The Uniformization Theorem
- §8.8. Ahlfors’ Function, Analytic Capacity and the Painlev´e Problem
- Chapter 9. Zeros of Analytic Functions and Product Formulae
- §9.1. Infinite Products
- §9.2. A Warmup: The Euler Product Formula
- §9.3. The Mittag-Leffler Theorem
- §9.4. The Weierstrass Product Theorem
- §9.5. General Regions
- §9.6. The Gamma Function: Basics
- §9.7. The Euler–Maclaurin Series and Stirling’s Approximation
- §9.8. Jensen’s Formula
- §9.9. Blaschke Products
- §9.10. Entire Functions of Finite Order and the Hadamard Product Formula
- Chapter 10. Elliptic Functions
- §10.1. A Warmup: Meromorphic Functions on C
- §10.2. Lattices and SL(2, Z)
- §10.3. Liouville’s Theorems, Abel’s Theorem, and Jacobi’s Construction
- §10.4. Weierstrass Elliptic Functions
- §10.5. Bonus Section: Jacobi Elliptic Functions
- §10.6. The Elliptic Modular Function
- §10.7. The Equivalence Problem for Complex Tori
- Chapter 11. Selected Additional Topics
- §11.1. The Paley–Wiener Strategy
- §11.2. Global Analytic Functions
- §11.3. Picard’s Theorem via the Elliptic Modular Function
- §11.4. Bonus Section: Zalcman’s Lemma and Picard’s Theorem
- §11.5. Two Results in Several Complex Variables: Hartogs’ Theorem and a Theorem of Poincar´e
- §11.6. Bonus Section: A First Glance at Compact Riemann Surfaces
- Bibliography
- Symbol Index
- Subject Index
- Author Index
- Index of Capsule Biographies
