數學(xué)分析原理（英文版·原書(shū)第3版·典藏版）簡(jiǎn)介，目錄書(shū)摘

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內容簡(jiǎn)介:　　《數學(xué)分析原理（英文版·原書(shū)第3版·典藏版）》是一部近代的數學(xué)名著(zhù)，一直受到數學(xué)界的推崇。該書(shū)作為分析學(xué)經(jīng)典著(zhù)作，在西方各國乃至我國有著(zhù)廣泛西深遠的影響，被許多高校用作數學(xué)分析課程的必選教材。
　　《數學(xué)分析原理（英文版·原書(shū)第3版·典藏版）》涵蓋了高等微積分學(xué)的豐富內容，精彩部分集中在基礎拓撲結構、函數序列與函數項級數、多元函數以及微分形式的積分等章節。第3版經(jīng)過(guò)增刪與修訂，更加符合學(xué)生的閱讀習慣和思考方式。
　　《數學(xué)分析原理（英文版·原書(shū)第3版·典藏版）》內容精練，結構簡(jiǎn)明，具有Rudin著(zhù)作的典型特色，堪稱(chēng)字典意義上的教科書(shū)。

作者簡(jiǎn)介:沃爾特·魯?。╓alter Rudin）1953年于杜克大學(xué)獲得數學(xué)博士學(xué)位. 曾先后執教于麻省理工學(xué)院、羅切斯特大學(xué)、威斯康星大學(xué)麥迪遜分校、耶魯大學(xué)等. 他的主要研究興趣集中在調和分析和復變函數. 除本書(shū)外，他還著(zhù)有《Functional Analysis》和《Real and Complex Analysis》等其他名著(zhù)，這些教材已被翻譯成十幾種語(yǔ)言，在世界各地廣泛使用.

目錄: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