The Laplace Transform: Theory and Applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York
Springer
[1999]
|
| Series: | Undergraduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | UBT01 BTU01 Volltext |
| Physical Description: | 1 Online-Ressource (XIV, 236 p) |
| ISBN: | 9780387227573 |
| DOI: | 10.1007/978-0-387-22757-3 |
Staff View
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042419107 | ||
| 003 | DE-604 | ||
| 005 | 20180208 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1999 |||| o||u| ||||||eng d | ||
| 020 | |a 9780387227573 |c Online |9 978-0-387-22757-3 | ||
| 024 | 7 | |a 10.1007/978-0-387-22757-3 |2 doi | |
| 035 | |a (OCoLC)704459473 | ||
| 035 | |a (DE-599)BVBBV042419107 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 |a DE-739 | ||
| 082 | 0 | |a 515 |2 23 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 000 |2 stub | ||
| 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 |
| 264 | 1 | |a New York |b Springer |c [1999] | |
| 300 | |a 1 Online-Ressource (XIV, 236 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Laplace-Transformation |0 (DE-588)4034577-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Laplace-Transformation |0 (DE-588)4034577-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-1-4757-7262-3 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 0-387-98698-7 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-0-387-22757-3 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027854524 | ||
| 966 | e | |u https://doi.org/10.1007/978-0-387-22757-3 |l UBT01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-0-387-22757-3 |l BTU01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
Record in the Search Index
| _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 |
| classification_rvk | SK 450 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03230nmm a2200493zc 4500</leader><controlfield tag="001">BV042419107</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180208 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1999 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387227573</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-387-22757-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-0-387-22757-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)704459473</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419107</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Schiff, Joel L.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)107410790X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Laplace Transform</subfield><subfield code="b">Theory and Applications</subfield><subfield code="c">Joel L. Schiff</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Springer</subfield><subfield code="c">[1999]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XIV, 236 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Undergraduate Texts in Mathematics</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Laplace-Transformation</subfield><subfield code="0">(DE-588)4034577-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Laplace-Transformation</subfield><subfield code="0">(DE-588)4034577-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-1-4757-7262-3</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">0-387-98698-7</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-0-387-22757-3</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027854524</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-0-387-22757-3</subfield><subfield code="l">UBT01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-0-387-22757-3</subfield><subfield code="l">BTU01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV042419107 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780387227573 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854524 |
| oclc_num | 704459473 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 DE-739 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 DE-739 |
| physical | 1 Online-Ressource (XIV, 236 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate Texts in Mathematics |
| 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 |