The Laplace transform : theory and applications
 Author/Creator
 Schiff, Joel L.
 Language
 English.
 Imprint
 New York : Springer, c1999.
 Physical description
 xiv, 233 p. : ill. ; 25 cm.
 Series
 Undergraduate texts in mathematics.
Access
Available online

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QA432 .S33 1999

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QA432 .S33 1999
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 207208) and index.
 Contents

 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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) + anlY(nl) + * * * + 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.
(source: Nielsen Book Data)  Supplemental links

Publisher description
Table of contents only
Subjects
Bibliographic information
 Publication date
 1999
 Responsibility
 Joel L. Schiff.
 Series
 Undergraduate texts in mathematics
 ISBN
 0387986987 (alk. paper)
 9780387986982 (alk. paper)