# The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

## Joel L. Schiff

3,8 valoración promedio
( 15 valoraciones por Goodreads )

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.

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Review:

"The book contains plenty of examples, exercises (with answers at the end) and a table of transforms.
The book is certainly a handsome introduction to the Laplae transform, by its clear representation well-suited for self-study."
Nieuw Archief voor Wiskunde, March 2001

"This clearly written undergraduate textbook can be recommended to students and teachers of this subject, both in a mathematial and engineering context."
Newsletter of the EMS, issue 42, December 2001

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## 1.Laplace Transform, The: Theory And Applications

ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Estado de conservación: New. This item is Print on Demand - Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería POD_9780387986982

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## 2.The Laplace Transform: Theory and Applications (Hardback)

Editorial: Springer-Verlag New York Inc., United States (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer-Verlag New York Inc., United States, 1999. Hardback. Estado de conservación: New. 1999 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. Nº de ref. de la librería LIE9780387986982

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## 3.The Laplace Transform

Editorial: Springer-Verlag New York Inc. (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer-Verlag New York Inc., 1999. HRD. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IP-9780387986982

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## 4.The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Editorial: Springer (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer, 1999. Estado de conservación: New. This item is printed on demand for shipment within 3 working days. Nº de ref. de la librería LP9780387986982

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## 5.The Laplace Transform : Theory and Applications

Editorial: Springer (2016)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780387986982_lsuk

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## 6.The Laplace Transform. Theory and Applications

Editorial: Springer (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer, 1999. Hardback. Estado de conservación: NEW. 9780387986982 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0276822

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## 7.The Laplace Transform

Editorial: Springer-Verlag New York Inc. (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer-Verlag New York Inc., 1999. HRD. Estado de conservación: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Nº de ref. de la librería IP-9780387986982

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## 8.The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Editorial: Springer (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer, 1999. Hardcover. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería INGM9780387986982

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## 9.The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Editorial: Springer (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer, 1999. Hardcover. Estado de conservación: New. 1999. This item is printed on demand. Nº de ref. de la librería DADAX0387986987

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## 10.The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Editorial: Springer (2017)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descripción Springer, 2017. Hardcover. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería 0387986987

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