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Real Analysis

  • Textbook
  • © 2001

Overview

Authors:
  1. John M. Howie

    1. School of Mathematics and Statistics, Mathematical Institute, University of St Andrews, Fife, Scotland

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  • Offers a fresh approach to a core subject
  • Provides a gentle and clear introduction without sacrificing rigour or accuracy
  • Includes worked examples and exercises designed to reinforce the underlying concepts
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. Introductory Ideas

    • John M. Howie
    Pages 1-26

  3. Sequences and Series

    • John M. Howie
    Pages 27-62

  4. Functions and Continuity

    • John M. Howie
    Pages 63-98

  5. Differentiation

    • John M. Howie
    Pages 99-118

  6. Integration

    • John M. Howie
    Pages 119-163

  7. The Logarithmic and Exponential Functions

    • John M. Howie
    Pages 165-179

  8. Sequences and Series of Functions

    • John M. Howie
    Pages 181-216

  9. The Circular Functions

    • John M. Howie
    Pages 217-228

  10. Miscellaneous Examples

    • John M. Howie
    Pages 229-235

  11. Back Matter

    Pages 237-276
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Keywords

About this book

From the point of view of strict logic, a rigorous course on real analysis should precede a course on calculus. Strict logic, is, however, overruled by both history and practicality. Historically, calculus, with its origins in the 17th century, came first, and made rapid progress on the basis of informal intuition. Not until well through the 19th century was it possible to claim that the edifice was constructed on sound logical foundations. As for practicality, every university teacher knows that students are not ready for even a semi-rigorous course on analysis until they have acquired the intuitions and the sheer technical skills that come from a traditional calculus course. 1 Real analysis, I have always thought, is the pons asinorv.m of modern mathematics. This shows, I suppose, how much progress we have made in two thousand years, for it is a great deal more sophisticated than the Theorem of Pythagoras, which once received that title. All who have taught the subject know how patient one has to be, for the ideas take root gradually, even in students of good ability. This is not too surprising, since it took more than two centuries for calculus to evolve into what we now call analysis, and even a gifted student, guided by an expert teacher, cannot be expected to grasp all of the issues immediately.

Authors and Affiliations

  • School of Mathematics and Statistics, Mathematical Institute, University of St Andrews, Fife, Scotland

    John M. Howie

Bibliographic Information

  • Book Title: Real Analysis

  • Authors: John M. Howie

  • Series Title: Springer Undergraduate Mathematics Series

  • DOI: https://doi.org/10.1007/978-1-4471-0341-7

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2001

  • Softcover ISBN: 978-1-85233-314-0Published: 28 March 2001

  • eBook ISBN: 978-1-4471-0341-7Published: 06 December 2012

  • Series ISSN: 1615-2085

  • Series E-ISSN: 2197-4144

  • Edition Number: 1

  • Number of Pages: X, 276

  • Number of Illustrations: 13 b/w illustrations

  • Topics: Analysis, Real Functions

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