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Book details
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Author : Stephen Abbott
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Pages : 312 pages
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Publisher : Springer 2016-08-22
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Language : English
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ISBN-10 : 1493927116
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ISBN-13 : 9781493927111
Book Synopsis
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 ?(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.