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Introduction to the Laplace Transform

  • Book
  • © 1978

Overview

Authors:
  1. Peter K. F. Kuhfittig

    1. Milwaukee School of Engineering, Milwaukee, USA

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Part of the book series: Mathematical Concepts and Methods in Science and Engineering (MCSENG, volume 8)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Basic Properties and Applications

    • Peter K. F. Kuhfittig
    Pages 1-42

  3. Further Properties and Applications

    • Peter K. F. Kuhfittig
    Pages 43-92

  4. Sketch of Complex Variable Theory

    • Peter K. F. Kuhfittig
    Pages 93-103

  5. The Complex Inversion Formula

    • Peter K. F. Kuhfittig
    Pages 105-110

  6. Convolutions

    • Peter K. F. Kuhfittig
    Pages 111-127

  7. Transforms with Infinitely Many Singularities

    • Peter K. F. Kuhfittig
    Pages 129-143

  8. Applications to Partial Differential Equations

    • Peter K. F. Kuhfittig
    Pages 145-168

  9. Back Matter

    Pages 169-205
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Keywords

About this book

The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily. The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.

Authors and Affiliations

  • Milwaukee School of Engineering, Milwaukee, USA

    Peter K. F. Kuhfittig

Bibliographic Information

  • Book Title: Introduction to the Laplace Transform

  • Authors: Peter K. F. Kuhfittig

  • Series Title: Mathematical Concepts and Methods in Science and Engineering

  • DOI: https://doi.org/10.1007/978-1-4899-2201-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1978

  • Hardcover ISBN: 978-0-306-31060-7Published: 01 April 1978

  • Softcover ISBN: 978-1-4899-2203-8Published: 04 June 2013

  • eBook ISBN: 978-1-4899-2201-4Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: X, 206

  • Topics: Analysis

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