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An Introduction to Laplace Transforms and Fourier Series

  • Textbook
  • © 2014
  • Latest edition

Overview

Authors:
  1. Phil Dyke

    1. School of Computing and MathematicsPlymouth UniversityPlymouthUnited Kingdom

  • Provides an easy-to-read account of fourier serieswavelets and laplace transforms
  • Contains many examples
  • Provides solutions to all exercises
  • Includes supplementary material: sn.pub/extras

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

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About this book

In this bookthere is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets.

Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineeringphysics or mathematicsas well as for graduates in any discipline such as financial mathematicseconometrics and biological modelling requiring techniques for solving initial value problems.

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. The Laplace Transform

    • Phil Dyke
    Pages 1-12

  3. Further Properties of the Laplace Transform

    • Phil Dyke
    Pages 13-38

  4. Convolution and the Solution of Ordinary Differential Equations

    • Phil Dyke
    Pages 39-82

  5. Fourier Series

    • Phil Dyke
    Pages 83-122

  6. Partial Differential Equations

    • Phil Dyke
    Pages 123-143

  7. Fourier Transforms

    • Phil Dyke
    Pages 145-173

  8. Wavelets and Signal Processing

    • Phil Dyke
    Pages 175-208

  9. Complex Variables and Laplace Transforms

    • Phil Dyke
    Pages 209-237

  10. Back Matter

    Pages 239-318
    Download chapter PDF
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Authors and Affiliations

  • School of Computing and MathematicsPlymouth UniversityPlymouthUnited Kingdom

    Phil Dyke

About the author

Phil Dyke has over 40 years experience teaching at UK Universitiesand for the past 6 years has based a course on the subject of this book. He has also used Laplace transforms and Fourier methods in his research. He has been a professor of applied mathematics at Plymouth University for over 20 years.

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