数学分析原理（英文版·原书第3版）

《数学分析原理（英文版·原书第3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。 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。

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

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.

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