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）

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）

分享

作者: [英] 尼尔斯.雅各布

出版社: 哈尔滨工业大学出版社

出版时间: 2023-03

版次: 1

ISBN: 9787576706130

定价: 118.00

装帧: 其他

开本: 16开

纸张: 胶版纸

页数: 788页

字数: 890.000千字

分类: 自然科学

6人买过

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。 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
内容简介:
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。
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

查看详情

相关分类

农业/林业畜牧/养殖生物科学环境科学数学物理学力学化学天文学测绘学地球科学大气科学（气象学）地质学海洋学