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  • © 2004

Examples and Theorems in Analysis

  • Adopts a clear and practical approach, using an abundance of interesting and diverse examples to illustrate both the usefulness and the limitations of the results

  • A selection of exercises, with varying degrees of difficulty, is provided at the end of each chapter to test understanding

  • Hints and solutions to exercises are provided in an appendix

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eBook USD 54.99
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  • ISBN: 978-0-85729-380-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 69.99
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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
  2. Sequences

    • Peter Leslie Walker
    Pages 1-30
  3. Functions and Continuity

    • Peter Leslie Walker
    Pages 31-66
  4. Differentiation

    • Peter Leslie Walker
    Pages 67-101
  5. Constructive Integration

    • Peter Leslie Walker
    Pages 103-123
  6. Improper Integrals

    • Peter Leslie Walker
    Pages 125-139
  7. Series

    • Peter Leslie Walker
    Pages 141-194
  8. Applications

    • Peter Leslie Walker
    Pages 195-247
  9. Back Matter

    Pages 249-287

About this book

Examples and Theorems in Analysis takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. The results are introduced and motivated by reference to examples which illustrate their use, and further examples then show how far the assumptions may be relaxed before the result fails.

A number of applications show what the subject is about and what can be done with it; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems.

Written primarily for first- and second-year undergraduates in mathematics, this book features a host of diverse and interesting examples, making it an entertaining and stimulating companion that will also be accessible to students of statistics, computer science and engineering, as well as to professionals in these fields.

Keywords

  • Analysis
  • Calculus
  • Derivative
  • Distribution
  • Fourier series
  • Fourier-Analysis
  • Undergraduate Level
  • differential equation

Reviews

From the reviews:

"This book is a unique and very practical contribution to the teaching of calculus … . The aim of this book is to try to give the subject concreteness and immediacy by giving the well-chosen examples equal status with the theorems. … this excellent book is written primarily for first- and second-year undergraduates in mathematics; but it will also be of interest to students of statistics, computer science and engineering … . We warmly recommend it as an entertaining and stimulating companion …" (Ferenc Móricz, Acta Scientiarum Mathematicarum, 71, 2005)

"This book takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. … A number of applications show what the subject is about, and what can be done with it … . Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems." (L'enseignement mathématique, 50:1-2, 2004)

"The author presents a book on analysis in which theorems and examples are equally important. … It is a good textbook for students … to obtain a more complete picture of the material and to master basic methods of work in mathematical analysis." (EMS Newsletter, March, 2005)

Authors and Affiliations

  • College of Arts and Science, American University of Sharjah, Sharjah, United Arab Emirates

    Peter Leslie Walker

Bibliographic Information

  • Book Title: Examples and Theorems in Analysis

  • Authors: Peter Leslie Walker

  • DOI: https://doi.org/10.1007/978-0-85729-380-0

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2004

  • Softcover ISBN: 978-1-85233-493-2

  • eBook ISBN: 978-0-85729-380-0

  • Edition Number: 1

  • Number of Pages: X, 287

  • Topics: Analysis, Fourier Analysis, Real Functions

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-0-85729-380-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 69.99
Price excludes VAT (USA)