Understanding Analysis – Stephen Abbott – 2nd Edition

Description

This lively introductory text exposes the to the rewards of a rigorous study of functions of a real . In each chapter; informal discussions of questions that give 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 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.

Provides a polished and tuned-up version of the same core text that has proved successful with and instructors for 15 years Includes around 150 new exercises; in addition to around 200 of the best exercises from the first edition; and an accompanying manual for instructors. Presents three new self-guided projects exploring Euler’s sum; the factorial function and the Weierstrass Approximation Theorem.

Investigations of Euler’s 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 of analysis.

Table of Contents

The Real Numbers
Sequences and Series
Basic Topology of R
Functional Limits and Continuity
The Derivative
Sequences and Series of Functions
The Riemann Integral
Additional Topics

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