The Laplace Transform: Theory and Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
[1999]
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | UBT01 BTU01 Volltext |
| Beschreibung: | 1 Online-Ressource (XIV, 236 p) |
| ISBN: | 9780387227573 |
| DOI: | 10.1007/978-0-387-22757-3 |
Internformat
MARC
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| 100 | 1 | |a Schiff, Joel L. |e Verfasser |0 (DE-588)107410790X |4 aut | |
| 245 | 1 | 0 | |a The Laplace Transform |b Theory and Applications |c Joel L. Schiff |
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| 490 | 0 | |a Undergraduate Texts in Mathematics | |
| 505 | 8 | |a 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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Datensatz im Suchindex
| _version_ | 1804153089365639168 |
|---|---|
| any_adam_object | |
| author | Schiff, Joel L. |
| author_GND | (DE-588)107410790X |
| author_facet | Schiff, Joel L. |
| author_role | aut |
| author_sort | Schiff, Joel L. |
| author_variant | j l s jl jls |
| building | Verbundindex |
| bvnumber | BV042419107 |
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| contents | 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 |
| ctrlnum | (OCoLC)704459473 (DE-599)BVBBV042419107 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-387-22757-3 |
| format | Electronic eBook |
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| spelling | Schiff, Joel L. Verfasser (DE-588)107410790X aut The Laplace Transform Theory and Applications Joel L. Schiff New York Springer [1999] 1 Online-Ressource (XIV, 236 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 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 Mathematics Global analysis (Mathematics) Analysis Mathematik Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-4757-7262-3 Erscheint auch als Druck-Ausgabe 0-387-98698-7 https://doi.org/10.1007/978-0-387-22757-3 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Schiff, Joel L. 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 Mathematics Global analysis (Mathematics) Analysis Mathematik Laplace-Transformation (DE-588)4034577-4 gnd |
| subject_GND | (DE-588)4034577-4 |
| title | The Laplace Transform Theory and Applications |
| title_auth | The Laplace Transform Theory and Applications |
| title_exact_search | The Laplace Transform Theory and Applications |
| title_full | The Laplace Transform Theory and Applications Joel L. Schiff |
| title_fullStr | The Laplace Transform Theory and Applications Joel L. Schiff |
| title_full_unstemmed | The Laplace Transform Theory and Applications Joel L. Schiff |
| title_short | The Laplace Transform |
| title_sort | the laplace transform theory and applications |
| title_sub | Theory and Applications |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Laplace-Transformation (DE-588)4034577-4 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Laplace-Transformation |
| url | https://doi.org/10.1007/978-0-387-22757-3 |
| work_keys_str_mv | AT schiffjoell thelaplacetransformtheoryandapplications |