Real Analysis via Sequences and Series

Real Analysis via Sequences and Series

This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisti...

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Bibliographic Details
Published in:Springer eBooks
Main Authors: Little, Charles H.C (Author), Teo, Kee L. (Author), van Brunt, Bruce (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2015.
Series:Undergraduate Texts in Mathematics,
Subjects:
mathematics.
Functions of real variables.
Sequences (Mathematics).
Mathematics.
Real Functions.
Sequences, Series, Summability.
Online Access:http://dx.doi.org/10.1007/978-1-4939-2651-0
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Table of Contents:
  • Preface
  • 1. Introduction
  • 2. Sequences
  • 3. Series
  • 4. Limits of Functions
  • 5. Continuity
  • 6. Differentiability
  • 7. The Riemann Integral
  • 8. Taylor Polynomials and Taylor Series
  • 9. The Fixed Point Problem
  • 10. Sequences of Functions
  • Bibliography
  • Index.

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