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Aspects of Calculus

  • Gabriel Klambauer

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Gabriel Klambauer
    Pages 1-48
  3. Gabriel Klambauer
    Pages 49-101
  4. Gabriel Klambauer
    Pages 102-150
  5. Gabriel Klambauer
    Pages 151-245
  6. Gabriel Klambauer
    Pages 246-308
  7. Gabriel Klambauer
    Pages 309-378
  8. Gabriel Klambauer
    Pages 379-511
  9. Back Matter
    Pages 512-516

About this book

Introduction

This book is intended for students familiar with a beginner's version of differential and integral calculus stressing only manipulation offormulas and who are now looking for a closer study of basic concepts combined with a more creative use of information. The work is primarily aimed at students in mathematics, engineering, and science who find themselves in transition from elementary calculus to rigorous courses in analysis. In addition, this book may also be of interest to those preparing to teach a course in calculus. Instead of exposing the reader to an excess of premature abstractions that so easily can degenerate into pedantry, I felt it more useful to stress instruc­ tive and stimulating examples. The book contains numerous worked out examples and many of the exercises are provided with helpful hints or a solution in outline. For further exercises the interested reader may want to consult a problem book by the author entitled Problems and Propositions in Analysis (New York: Marcel Dekker, 1979). For the history of calculus I recommend the book by C. B. Boyer, The Concepts of the Calculus (New York: Dover, 1949).

Keywords

Abstraction Calc Logarithmus Riemann integral calculus convergence derivative differential equation exponential function history of mathematics information integral integration logarithm proposition

Authors and affiliations

  • Gabriel Klambauer
    • 1
  1. 1.Department of MathematicsUniversity of OttawaOttawaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9561-4
  • Copyright Information Springer-Verlag New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9563-8
  • Online ISBN 978-1-4613-9561-4
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site