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The Laplace Transform

Theory and Applications

  • Textbook
  • © 1999

Overview

Authors:
  1. Joel L. Schiff

    1. Department of Mathematics, The University of Auckland, Auckland, New Zealand

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Basic Principles

    • Joel L. Schiff
    Pages 1-39

  3. Applications and Properties

    • Joel L. Schiff
    Pages 41-114

  4. Complex Variable Theory

    • Joel L. Schiff
    Pages 115-150

  5. Complex Inversion Formula

    • Joel L. Schiff
    Pages 151-174

  6. Partial Differential Equations

    • Joel L. Schiff
    Pages 175-191

  7. Back Matter

    Pages 193-235
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Keywords

About this book

The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un­ dergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace trans­ form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + · · · + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A. 6)? Or, in many proofs it is required to take the limit inside an integral. This is always fraught with danger, especially with an improper integral, and not always justified. I have given complete details (sometimes in the Appendix) whenever this procedure is required. IX X Preface Furthermore, it is sometimes desirable to take the Laplace trans­ form of an infinite series term by term. Again it is shown that this cannot always be done, and specific sufficient conditions are established to justify this operation.

Reviews

"The book contains plenty of examples, exercises (with answers at the end) and a table of transforms.
The book is certainly a handsome introduction to the Laplae transform, by its clear representation well-suited for self-study."
Nieuw Archief voor Wiskunde, March 2001

"This clearly written undergraduate textbook can be recommended to students and teachers of this subject, both in a mathematial and engineering context."
Newsletter of the EMS, issue 42, December 2001

Authors and Affiliations

  • Department of Mathematics, The University of Auckland, Auckland, New Zealand

    Joel L. Schiff

Bibliographic Information

  • Book Title: The Laplace Transform

  • Book Subtitle: Theory and Applications

  • Authors: Joel L. Schiff

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-0-387-22757-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-387-98698-2Published: 14 October 1999

  • Softcover ISBN: 978-1-4757-7262-3Published: 25 April 2013

  • eBook ISBN: 978-0-387-22757-3Published: 05 June 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIV, 236

  • Topics: Analysis

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