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- DescriptionThe 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 t 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 t 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 cant always be done, and specific sufficient conditions are established to justify this operation.
- Author(s)Joel L. Schiff
- PublisherSpringer-Verlag New York Inc.
- Date of Publication25/04/2013
- Series TitleUndergraduate Texts in Mathematics
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight391 g
- Width155 mm
- Height235 mm
- Spine13 mm
- Edition StatementSoftcover reprint of the original 1st ed. 1999
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