- 数学分析原理(英文版原书第3版典藏版)/华章数学原版精品系列
- - 作者：(美)沃尔特·鲁丁
  - 出版社：机械工业
  - ISBN：9787111619543
  - 出版日期：2019/03/01
  - 页数：342
- 售价：27.6

内容大纲
    沃尔特·鲁丁著的《数学分析原理(英文版原书第3版典藏版)/华章数学原版精品系列》是一部近代的数学名著，一直受到数学界的推崇。本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。
    本书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。
    本书内容精练，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。
作者介绍
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上。除本书外，他还著有《Functional Analysis》（泛函分析）和《Principles of Mathematical Analysis》（数学分析原理）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。
目录
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 Theorem
  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

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作者介绍

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