实数学分析（影印版）

出版时间：2009-2  出版社：高等教育出版社  作者：Charles Chapman Pugh  
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内容概要

本书是作者Pugh在伯克利大学讲授数学分析课程30多年之久的基础上编写而成，书中语言表述生动活泼、通俗易懂，引用了很多有价值的例子以及来自Dieudonne，Littlewood和Osserman等几位数学家的评论，还精心挑选了500多个精彩的练习题。本书内容包括实数、拓扑知识初步、实变函数、函数空间、多元微积分、Lebesgue积分理论等，其中多元微积分的讲法较为接近当前数学界常用的语言，将会对我国数学分析的教学产生积极的影响。

书籍目录

1  Real Numbers  1  Preliminaries  2  Cuts  3  Euclidean Space  4  Cardinality  5* Comparing Cardinalities  6* The Skeleton of Calculus  Exercises2  A Taste of Topology  1  Metric Space Concepts  2  Compactness  3  Connectedness  4  Coverings  5  Cantor Sets  6* Cantor Set Lore  7* Completion  Exercises3  Functions of a Real Variable  1  Differentiation  2  Riemann Integration  3  Series  Exercises4  Function Spaces  1  Uniform Convergence and C0[a, b]  2  Power Series  3  Compactness and Equicontinuity in CO  4  Uniform Approximation in Co  5  Contractions and ODE's  6* Analytic Functions  7* Nowhere Differentiable Continuous Functions   8* Spaces of Unbounded Functions  Exercises5  Multivariable Calculus  1  Linear Algebra  2  Derivatives  3  Higher derivatives  4  Smoothness Classes  5  Implicit and Inverse Functions  6* The Rank Theorem  7* Lagrange Multipliers  8  Multiple Integrals  9  Differential Forms  10  The General Stokes' Formula  11* The Brouwer Fixed Point Theorem  Appendix A: Perorations of Dieudonne  Appendix B: The History of Cavalieri's Principle  Appendix C: A Short Excursion into  the Complex Field  Appendix D: Polar Form  Appendix E: Determinants  Exercises6  Lebesgue Theory  1  Outer measure  2  Measurability  3  Regularity  4  Lebesgue integrals  5  Lebesgue integrals as limits  6  Italian Measure Theory  7  Vitali coverings and density points  8  Lebesgue's Fundamental Theorem of Calculus  9  Lebesgue's Last Theorem  Appendix A: Translations and Nonmeasurable sets  Appendix B: The Banach-Tarski Paradox  Appendix C: Riemann integrals as undergraphs  Appendix D: Littlewood's Three Principles  Appendix E: Roundness  Appendix F: Money  Suggested Reading  Bibliography  ExercisesIndex

用户评论 (总计6条)

•   評《實數學分析》在這部大學實分析的新引論中,作者採用了不同的寫法,即強調圖片在數學和難題中的重要性.其闡述是非正規的和輕鬆的,有很多有用的旁白,例子,和數學家的偶然間的評論.本書強調定理的理解而非正規的證明.本書包含500多個認真製作的練習,從簡單的練習到挑戰性的練習都有(因此本教材可用作實分析的例題和練習的資料書).
•   全英语的，看起来有点吃力，在努力中，感觉很可以的
•   　　此书内容上虽然跟国内实变函数教材有交集，但作者序言中说明此书的预期读者是“budding pure mathematician"(我译成”含苞待放的纯数学家“)，而且暗示先导课是普通的微积分，证明此书就是美国的”高等微积分“教材，应该译为”真正的数学分析“或者”数学分析当如此“lol..
•   数学分析当如此---
•   对这评论实在没法吐槽
•   楼主还是不要看这书了……