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Introduction to Mathematical Analysis

  • C. R. J. Clapham

Part of the Library of Mathematics book series (LIMA)

Table of contents

  1. Front Matter
    Pages ii-vii
  2. C. R. J. Clapham
    Pages 1-17
  3. C. R. J. Clapham
    Pages 18-26
  4. C. R. J. Clapham
    Pages 27-35
  5. C. R. J. Clapham
    Pages 36-44
  6. C. R. J. Clapham
    Pages 45-53
  7. C. R. J. Clapham
    Pages 54-77
  8. C. R. J. Clapham
    Pages 78-79
  9. Back Matter
    Pages 81-83

About this book

Introduction

I have tried to provide an introduction, at an elementary level, to some of the important topics in real analysis, without avoiding reference to the central role which the completeness of the real numbers plays throughout. Many elementary textbooks are written on the assumption that an appeal to the complete­ ness axiom is beyond their scope; my aim here has been to give an account of the development from axiomatic beginnings, without gaps, while keeping the treatment reasonably simple. Little previous knowledge is assumed, though it is likely that any reader will have had some experience of calculus. I hope that the book will give the non-specialist, who may have considerable facility in techniques, an appreciation of the foundations and rigorous framework of the mathematics that he uses in its applications; while, for the intending mathe­ matician, it will be more of a beginner's book in preparation for more advanced study of analysis. I should finally like to record my thanks to Professor Ledermann for the suggestions and comments that he made after reading the first draft of the text.

Keywords

Riemann integral calculus continuous function derivative differential equation limit of a function mathematical analysis mean value theorem

Authors and affiliations

  • C. R. J. Clapham
    • 1
  1. 1.Department of MathematicsUniversity of AberdeenUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-6572-3
  • Copyright Information Springer Science+Business Media B.V. 1973
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-7100-7529-1
  • Online ISBN 978-94-011-6572-3
  • Buy this book on publisher's site