Real Analysis via Sequences and Series

  • Charles H.C. Little
  • Kee L. Teo
  • Bruce van Brunt

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 1-32
  3. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 33-108
  4. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 109-189
  5. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 191-214
  6. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 215-241
  7. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 243-332
  8. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 333-398
  9. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 399-421
  10. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 423-436
  11. Charles H. C. Little, Kee L. Teo, Bruce van Brunt
    Pages 437-469
  12. Back Matter
    Pages 471-476

About this book

Introduction

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 sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating  definitions, results, and proofs. Simple examples  are provided to  illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e, and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

Keywords

Airy function Airy's equation Baire's theorem Bolzano-Weierstrass theorem Cartesian product Cauchy condensation test Dirichlet's test Kummer-Jensen test Riemann integral Sequences infinite series integral test limits of functions real analysis text adoption sequence convergence

Authors and affiliations

  • Charles H.C. Little
    • 1
  • Kee L. Teo
    • 2
  • Bruce van Brunt
    • 3
  1. 1.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand
  2. 2.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand
  3. 3.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-2651-0
  • Copyright Information Springer Science+Business Media New York 2015
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-2650-3
  • Online ISBN 978-1-4939-2651-0
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • About this book