9780387986982-0387986987-The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

ISBN-13: 9780387986982
ISBN-10: 0387986987
Edition: 1999
Author: Schiff, Joel L.
Publication date: 1999
Publisher: Springer
Format: Hardcover 250 pages
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Book details

ISBN-13: 9780387986982
ISBN-10: 0387986987
Edition: 1999
Author: Schiff, Joel L.
Publication date: 1999
Publisher: Springer
Format: Hardcover 250 pages

Summary

Acknowledged authors Schiff, Joel L. wrote The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics) comprising 250 pages back in 1999. Textbook and eTextbook are published under ISBN 0387986987 and 9780387986982. Since then The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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.

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