Linear Integral Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1989
|
| Schriftenreihe: | Applied Mathematical Sciences
82 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equations of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also introduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equations. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory |
| Beschreibung: | 1 Online-Ressource (XI, 299p. 1 illus) |
| ISBN: | 9783642971464 9783642971488 |
| DOI: | 10.1007/978-3-642-97146-4 |
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| 500 | |a I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equations of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also introduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equations. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory | ||
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Datensatz im Suchindex
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-97146-4 |
| format | Electronic eBook |
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| id | DE-604.BV042423153 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642971464 9783642971488 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858570 |
| oclc_num | 863859479 |
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| physical | 1 Online-Ressource (XI, 299p. 1 illus) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Kress, Rainer Verfasser aut Linear Integral Equations by Rainer Kress Berlin, Heidelberg Springer Berlin Heidelberg 1989 1 Online-Ressource (XI, 299p. 1 illus) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 82 I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equations of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also introduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equations. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Integralgleichung (DE-588)4114426-0 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 s 1\p DE-604 Applied Mathematical Sciences 82 (DE-604)BV040244599 82 https://doi.org/10.1007/978-3-642-97146-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kress, Rainer Linear Integral Equations Applied Mathematical Sciences Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Integralgleichung (DE-588)4114426-0 gnd |
| subject_GND | (DE-588)4114426-0 |
| title | Linear Integral Equations |
| title_auth | Linear Integral Equations |
| title_exact_search | Linear Integral Equations |
| title_full | Linear Integral Equations by Rainer Kress |
| title_fullStr | Linear Integral Equations by Rainer Kress |
| title_full_unstemmed | Linear Integral Equations by Rainer Kress |
| title_short | Linear Integral Equations |
| title_sort | linear integral equations |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Integralgleichung (DE-588)4114426-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Integralgleichung |
| url | https://doi.org/10.1007/978-3-642-97146-4 |
| volume_link | (DE-604)BV040244599 |
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