具体描述
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.
Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.
用户评价
##复习数分
评分##适合入门读
评分##启发式教学，当作参考书挺好的，但别指望拿它当教材。
评分##09/2017 - 12/2017 學完前半部分，比某本一星的垃圾實分析教材好多了
评分##这本书作为我的第一本数分教材，里面的内容实在让我难以下咽。 对于知识的叙述比较混乱，一些很重要的定理甚至没有出现在课文讲解中而是以习题形式出现。 作者本意应该是想引导读者进行探索式学习，但貌似效果并不好......
评分##09/2017 - 12/2017 學完前半部分，比某本一星的垃圾實分析教材好多了
评分##复习数分
评分##09/2017 - 12/2017 補標，學完前半部分，比某本一星的垃圾實分析教材好多了
评分##启发式教学，当作参考书挺好的，但别指望拿它当教材。
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