Joel L. Schiff: The Laplace Transform

Cover: 9781475772623 | The Laplace Transform | Theory and Applications | Joel L. Schiff | xiv

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Preliminary Text. Do not use. The Laplace transform is a wonderful tool for solving ordinary and partial differential equations, and has enjoyed much success in this realm. But with its success, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. In the present text, the author brings to the subject a certain amount of mathematical correctness and makes it accessible to undergraduates.

Inhaltsverzeichnis

1 Basic Principles.- 2 Applications and Properties.- 3 Complex Variable Theory.- 4 Complex Inversion Formula.- 5 Partial Differential Equations.- References.- Tables.- Laplace Transform Operations.- Table of Laplace Transforms.- Answers to Exercises.

Erscheinungsjahr:	2013
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 236 S.
ISBN-13:	9781475772623
ISBN-10:	1475772629
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Schiff, Joel L.
Auflage:	Softcover reprint of the original 1st edition 1999
Hersteller:	Springer US Springer New York
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 14 mm
Von/Mit:	Joel L. Schiff
Erscheinungsdatum:	25.04.2013
Gewicht:	0,388 kg

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