- 分析学教程--第3卷测度与积分理论复变量的复值函数(英文)/国外优秀数学著作原版系列
- - 作者：(英)尼尔斯·雅各布//克里斯蒂安·P.埃文斯|责编:刘家琳
  - 出版社：哈尔滨工业大学
  - ISBN：9787576706130
  - 出版日期：2023/03/01
  - 页数：788
- 售价：47.2

内容大纲
本书是分析学课程著作的第三卷，涵盖了每个数学家都必须要研究的两个主题，讨论了勒贝格的积分理论和实变量的实值函数理论中的第一个结果，介绍了一个复变量的复值函数理论——习惯上简称为“函数理论”。实值函数、傅里叶分析、函数分析、动力系统理论、偏微分方程或变分法的高级理论等也都在本书中有所提及。
作者介绍
目录
Preface
Introduction
List of Symbols
Part 6: Measure and Integration Theory
  1 A First Look at a-Fields and Measures
  2 Extending Pre-Measures. CarathSodory's Theorem
  3 The Lebesgue-Borel Measure and Hausdorff Measures
  4 Measurable Mappings
  5 Integration with Respect to a Measure The Lebesgue Integral
  6 The Radon-Nikodym Theorem and the Transformation Theorem
  7 Almost Everywhere Statements, Convergence Theorems
  8 Applications of the Convergence Theorems and More
  9 Integration on Product Spaces and Applications
  10 Convolutions of Functions and Measures
  11 Differentiation Revisited
  12 Selected Topics
Part 7: Complex-valued Functions of a Complex Variable
  13 The Complex Numbers as a Complete Field
  14 A Short Digression: Complex-valued Mappings
  15 Complex Numbers and Geometry
  16 Complex-Valued Functions of a Complex Variable
  17 Complex Differentiation
  18 Some Important Functions
  19 Some More Topology
  20 Line Integrals of Complex-valued Functions
  21 The Cauchy Integral Theorem and Integral Formula
  22 Power Series, Holomorphy and Differential Equations
  23 Further Properties of Holomorphic Functions
  24 Meromorphic Functions
  25 The Residue Theorem
  26 The F-functions the (-function and Dirichlet Series
  27 Elliptic Integrals and Elliptic Functions
  28 The Riemaim Mapping Theorem
  29 Power Series in Several Variables
Appendices
  Appendix I: More on Point Set Topology
  Appendix II: Measure Theory, Topology and Set Theory
  Appendix III: More on M/Sbius Transformations
  Appendix IV: Bernoulli Numbers
Solutions to Problems of Part 6
Solutions to Problems of Part 7
References
Mathematicians Contributing to Analysis (Continued)
Subject Index
编辑手记

内容大纲

作者介绍

目录

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