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Field name	Details
Dewey Class	515
Title	The Laplace Transform ([EBook] :) : Theory and Applications / / by Joel L. Schiff.
Author	Schiff, Joel L.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York : : Imprint: Springer, , 1999.
Physical Details	XIV, 236 p. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9780387227573
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-387-22757-3
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Schiff, Joel L. . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 515 .

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The Laplace Transform: Theory and Applications /

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