数学分析原理（英文版·原书第3版·典藏版）
Preface
Chapter 1 The Real and Complex Number Systems
Introduction
Ordered Sets
Fields
The Real Field
The Extended Real Number System
The Complex Field
Euclidean Spaces
查看完整
Chapter 1 The Real and Complex Number Systems
Introduction
Ordered Sets
Fields
The Real Field
The Extended Real Number System
The Complex Field
Euclidean Spaces
查看完整
沃尔特·鲁丁（Walter Rudin）1953年于杜克大学获得数学博士学位. 曾先后执教于麻省理工学院、罗切斯特大学、威斯康星大学麦迪逊分校、耶鲁大学等. 他的主要研究兴趣集中在调和分析和复变函数. 除本书外，他还著有《Functional Analysis》和《Real and Complex Analysis》等其他名著，这些教材已被翻译成十几种语言，在世界各地广泛使用.
《数学分析原理（英文版·原书第3版·典藏版）》是一部近代的数学名著，一直受到数学界的推崇。该书作为分析学经典著作，在西方各国乃至我国有着广泛西深远的影响，被许多高校用作数学分析课程的必选教材。
《数学分析原理（英文版·原书第3版·典藏版）》涵盖了高等微积分学的丰富内容，精彩部分集中在基础拓扑结构、函数序列与函数项级数、多元函数以及微分形式的积分等章节。第3版经过增删与修订，更加符合学生的阅读习惯和思考方式。
《数学分析原理（英文版·原书第3版·典藏版）》内容精练，结构简明，具有Rudin著作的典型特色，堪称字典意义上的教科书。
《数学分析原理（英文版·原书第3版·典藏版）》涵盖了高等微积分学的丰富内容，精彩部分集中在基础拓扑结构、函数序列与函数项级数、多元函数以及微分形式的积分等章节。第3版经过增删与修订，更加符合学生的阅读习惯和思考方式。
《数学分析原理（英文版·原书第3版·典藏版）》内容精练，结构简明，具有Rudin著作的典型特色，堪称字典意义上的教科书。
Preface
Chapter 1 The Real and Complex Number Systems
Introduction
Ordered Sets
Fields
The Real Field
The Extended Real Number System
The Complex Field
Euclidean Spaces
Appendix
Exercises
Chapter 2 Basic Topology
Finite， Countable， and Uncountable Sets
Metric Spaces
Compact Sets
Perfect Sets
Connected Sets
Exercises
Chapter 3 Numerical Sequences and Series
Convergent Sequences
Subsequences
Cauchy Sequences
Upper and Lower Limits
Some Special Sequences
Series
Series of Nonnegative Terms
The Number e
The Root and Ratio Tests
Power Series
Summation by Parts
Absolute Convergence
Addition and Multiplication of Series
Rearrangements
Exercises
Chapter 4 Continuity
Limits of Functions
Continuous Functions
Continuity and Compactness
Continuity and Connectedness
Discontinuities
Monotonic Functions
Infinite Limits and Limits at Infinity
Exercises
Chapter 5 Differentiation
The Derivative of a Real Function
Mean Value Theorems
The Continuity of Derivatives
L'Hospital's Rule
Derivatives of Higher Order
Taylor's Theorem
Differentiation of Vector-valued Functions
Exercises
Chapter 6 The Riemann-Stieltjes Integral
Definition and Existence of the Integral
Properties of the Integral
Integration and Differentiation
Integration of Vector-valued Functions
Rectifiable Curves
Exercises
Chapter 7 Sequences and Series of Functions，
Discussion of Main Problem
Uniform Convergence
Uniform Convergence and Continuity
Uniform Convergence and Integration
Uniform Convergence and Differentiation
Equicontinuous Families of Functions
The Stone-Weierstrass Therem
Exercises
Chapter 8 Some Special Functions
Power Series
The Exponential and Logarithmic Functions
The Trigonometric Functions
The Algebraic Completeness of the Complex Field
Fourier Series
The Gamma Function
Exercises
Chapter 9 Functions of Several Variables
Linear Transformations
Differentiation
The Contraction Principle
The Inverse Function Theorem
The Implicit Function Theorem
The Rank Theorem
Determinants
Derivatives of Higher Order
Differentiation of Integrals
Exercises
Chapter 10 Integration of Differential Forms
Integration
Primitive Mappings
Partitions of Unity
Change of Variables
Differential Forms
Simplexes and Chains
Stokes' Theorem
Closed Forms and Exact Forms
Vector Analysis
Exercises
Chapter 11 The Lebesgue Theory
Set Functions
Construction of the Lebesgue Measure
Measure Spaces
Measurable Functions
Simple Functions
Integration
Comparison with the Riemann Integral
Integration of Complex Functions
Functions of Class [WTHT]L[WT]\+
Exercises
Bibliography
List of Special Symbols
Index
^ 收 起
Chapter 1 The Real and Complex Number Systems
Introduction
Ordered Sets
Fields
The Real Field
The Extended Real Number System
The Complex Field
Euclidean Spaces
Appendix
Exercises
Chapter 2 Basic Topology
Finite， Countable， and Uncountable Sets
Metric Spaces
Compact Sets
Perfect Sets
Connected Sets
Exercises
Chapter 3 Numerical Sequences and Series
Convergent Sequences
Subsequences
Cauchy Sequences
Upper and Lower Limits
Some Special Sequences
Series
Series of Nonnegative Terms
The Number e
The Root and Ratio Tests
Power Series
Summation by Parts
Absolute Convergence
Addition and Multiplication of Series
Rearrangements
Exercises
Chapter 4 Continuity
Limits of Functions
Continuous Functions
Continuity and Compactness
Continuity and Connectedness
Discontinuities
Monotonic Functions
Infinite Limits and Limits at Infinity
Exercises
Chapter 5 Differentiation
The Derivative of a Real Function
Mean Value Theorems
The Continuity of Derivatives
L'Hospital's Rule
Derivatives of Higher Order
Taylor's Theorem
Differentiation of Vector-valued Functions
Exercises
Chapter 6 The Riemann-Stieltjes Integral
Definition and Existence of the Integral
Properties of the Integral
Integration and Differentiation
Integration of Vector-valued Functions
Rectifiable Curves
Exercises
Chapter 7 Sequences and Series of Functions，
Discussion of Main Problem
Uniform Convergence
Uniform Convergence and Continuity
Uniform Convergence and Integration
Uniform Convergence and Differentiation
Equicontinuous Families of Functions
The Stone-Weierstrass Therem
Exercises
Chapter 8 Some Special Functions
Power Series
The Exponential and Logarithmic Functions
The Trigonometric Functions
The Algebraic Completeness of the Complex Field
Fourier Series
The Gamma Function
Exercises
Chapter 9 Functions of Several Variables
Linear Transformations
Differentiation
The Contraction Principle
The Inverse Function Theorem
The Implicit Function Theorem
The Rank Theorem
Determinants
Derivatives of Higher Order
Differentiation of Integrals
Exercises
Chapter 10 Integration of Differential Forms
Integration
Primitive Mappings
Partitions of Unity
Change of Variables
Differential Forms
Simplexes and Chains
Stokes' Theorem
Closed Forms and Exact Forms
Vector Analysis
Exercises
Chapter 11 The Lebesgue Theory
Set Functions
Construction of the Lebesgue Measure
Measure Spaces
Measurable Functions
Simple Functions
Integration
Comparison with the Riemann Integral
Integration of Complex Functions
Functions of Class [WTHT]L[WT]\+
Exercises
Bibliography
List of Special Symbols
Index
^ 收 起
沃尔特·鲁丁（Walter Rudin）1953年于杜克大学获得数学博士学位. 曾先后执教于麻省理工学院、罗切斯特大学、威斯康星大学麦迪逊分校、耶鲁大学等. 他的主要研究兴趣集中在调和分析和复变函数. 除本书外，他还著有《Functional Analysis》和《Real and Complex Analysis》等其他名著，这些教材已被翻译成十几种语言，在世界各地广泛使用.
《数学分析原理（英文版·原书第3版·典藏版）》是一部近代的数学名著，一直受到数学界的推崇。该书作为分析学经典著作，在西方各国乃至我国有着广泛西深远的影响，被许多高校用作数学分析课程的必选教材。
《数学分析原理（英文版·原书第3版·典藏版）》涵盖了高等微积分学的丰富内容，精彩部分集中在基础拓扑结构、函数序列与函数项级数、多元函数以及微分形式的积分等章节。第3版经过增删与修订，更加符合学生的阅读习惯和思考方式。
《数学分析原理（英文版·原书第3版·典藏版）》内容精练，结构简明，具有Rudin著作的典型特色，堪称字典意义上的教科书。
《数学分析原理（英文版·原书第3版·典藏版）》涵盖了高等微积分学的丰富内容，精彩部分集中在基础拓扑结构、函数序列与函数项级数、多元函数以及微分形式的积分等章节。第3版经过增删与修订，更加符合学生的阅读习惯和思考方式。
《数学分析原理（英文版·原书第3版·典藏版）》内容精练，结构简明，具有Rudin著作的典型特色，堪称字典意义上的教科书。
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