The Laplace Transform: Theory and Applications

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9780387986982: The Laplace Transform: Theory and Applications

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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Book Description:

"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

Contenuti:

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.

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1.

Schiff, Joel L.
Editore: Springer-Verlag New York Inc., United States (1999)
ISBN 10: 0387986987 ISBN 13: 9780387986982
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Descrizione libro Springer-Verlag New York Inc., United States, 1999. Hardback. Condizione libro: New. 1999 ed.. 236 x 160 mm. Language: English . 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. Codice libro della libreria LIB9780387986982

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Descrizione libro Springer-Verlag New York Inc., 1999. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387986982

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Schiff, Joel L.
Editore: Springer-Verlag New York Inc., United States (1999)
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Descrizione libro Springer-Verlag New York Inc., United States, 1999. Hardback. Condizione libro: New. 1999 ed.. 236 x 160 mm. Language: English . 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. Codice libro della libreria LIB9780387986982

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Descrizione libro Springer, 1999. Condizione libro: New. Codice libro della libreria L9780387986982

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Descrizione libro Springer, 1999. Hardback. Condizione libro: NEW. 9780387986982 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0276822

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Descrizione libro Springer Okt 1999, 1999. Buch. Condizione libro: Neu. 235x155x20 mm. Neuware - 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. 236 pp. Englisch. Codice libro della libreria 9780387986982

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Descrizione libro Springer-Verlag New York Inc., 1999. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387986982

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Descrizione libro Springer, 1999. Hardcover. Condizione libro: New. 1999. This item is printed on demand. Codice libro della libreria DADAX0387986987

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Descrizione libro Springer, 1999. Hardcover. Condizione libro: New. book. Codice libro della libreria 0387986987

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Descrizione libro Springer Okt 1999, 1999. Buch. Condizione libro: Neu. 23.4x15.6x cm. Neuware - 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. 236 pp. Englisch. Codice libro della libreria 9780387986982

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