Download The Laplace Transform: Theory and Applications By Joel L. Schiff – 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 undergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace transform 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 transform 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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Book Contents
- Basic Principles
- Applications and Properties
- Complex Variable Theory
- Complex Inversion Formula
- Partial Differential Equations
About Author
Joel L. Schiff was born in Chicago and has a PhD in mathematics from the University of California, Los Angeles. He spent his career at the University of Auckland and has written three books on various mathematical subjects (published by Springer-Verlag and JW & Sons). He has also been a successful part-time asteroid hunter and was the founder/publisher of an international journal on Meteorites.
Having a life long interest in art, he is also an artist who paints in oils and in 2014 had a book published about the New Zealand/ Australian/British artist, Grace Joel. Research revealed that Ms Joel (no relation) studied at the well known Académie Julian in Paris and it was then that the author discovered another Julian student, Marie Bashkirtseff, one of the most fascinating individuals of the 19th century. His obsession with her led to the publication of the book: Portrait of Young Genius – The Life and Art of Marie Bashkirtseff, Vernon Press, 2017.
Other interests, such as orchid growing for more than 30 years has resulted in the book: Rare and Exotic Orchids (Springer – 2018). His pursuits in astronomy has compelled him to write a book on The Most Interesting Galaxies in the Universe to be published by IOP Science also in 2018.
Book Details
- Language: English
- ISBN-10: 0387986987
- ISBN-13: 978-0387986982
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