Elementary Analysis: The Theory of Calculus

  • Kenneth A. Ross

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Kenneth A. Ross
    Pages 1-23
  3. Kenneth A. Ross
    Pages 24-86
  4. Kenneth A. Ross
    Pages 87-128
  5. Kenneth A. Ross
    Pages 129-154
  6. Kenneth A. Ross
    Pages 155-183
  7. Kenneth A. Ross
    Pages 184-232
  8. Back Matter
    Pages 233-264

About this book

Introduction

Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

Keywords

Differentialrechnung Elementary Analysis Integralrechnung calculus differential equation

Authors and affiliations

  • Kenneth A. Ross
    • 1
  1. 1.Department of MathematicsUniversity of OregonEugeneUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3971-8
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2811-5
  • Online ISBN 978-1-4757-3971-8
  • Series Print ISSN 0172-6056
  • About this book