Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Schriftenreihe: | Graduate Texts in Mathematics
214 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This textbook is intended for students who wish to obtain an introduction to the theory of partial differential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not offer a comprehensive overview of the whole field of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding question is how one can find a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for finding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting qualitative properties of a solution. Therefore, mathematical analysis has developed other, more powerful, approaches. (1) Solve a sequence of auxiliary problems that approximate the given one, and show that their solutions converge to a solution of that original problem. Differential equations are posed in spaces of functions, and those spaces are of infinite dimension |
| Beschreibung: | 1 Online-Ressource (XI, 325 p) |
| ISBN: | 9780387215952 9780387954288 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/b97312 |
Internformat
MARC
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| 500 | |a This textbook is intended for students who wish to obtain an introduction to the theory of partial differential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not offer a comprehensive overview of the whole field of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding question is how one can find a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for finding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting qualitative properties of a solution. Therefore, mathematical analysis has developed other, more powerful, approaches. (1) Solve a sequence of auxiliary problems that approximate the given one, and show that their solutions converge to a solution of that original problem. Differential equations are posed in spaces of functions, and those spaces are of infinite dimension | ||
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Datensatz im Suchindex
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| author | Jost, Jürgen |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b97312 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:03Z |
| institution | BVB |
| isbn | 9780387215952 9780387954288 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854344 |
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| series2 | Graduate Texts in Mathematics |
| spelling | Jost, Jürgen Verfasser aut Partial Differential Equations by Jürgen Jost New York, NY Springer New York 2002 1 Online-Ressource (XI, 325 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 214 0072-5285 This textbook is intended for students who wish to obtain an introduction to the theory of partial differential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not offer a comprehensive overview of the whole field of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding question is how one can find a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for finding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting qualitative properties of a solution. Therefore, mathematical analysis has developed other, more powerful, approaches. (1) Solve a sequence of auxiliary problems that approximate the given one, and show that their solutions converge to a solution of that original problem. Differential equations are posed in spaces of functions, and those spaces are of infinite dimension Mathematics Differential equations, partial Mathematical physics Physics Partial Differential Equations Mathematical and Computational Physics Numerical and Computational Methods Mathematik Mathematische Physik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s 1\p DE-604 Graduate Texts in Mathematics 214 (DE-604)BV035421258 214 https://doi.org/10.1007/b97312 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jost, Jürgen Partial Differential Equations Graduate Texts in Mathematics Mathematics Differential equations, partial Mathematical physics Physics Partial Differential Equations Mathematical and Computational Physics Numerical and Computational Methods Mathematik Mathematische Physik Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Partial Differential Equations |
| title_auth | Partial Differential Equations |
| title_exact_search | Partial Differential Equations |
| title_full | Partial Differential Equations by Jürgen Jost |
| title_fullStr | Partial Differential Equations by Jürgen Jost |
| title_full_unstemmed | Partial Differential Equations by Jürgen Jost |
| title_short | Partial Differential Equations |
| title_sort | partial differential equations |
| topic | Mathematics Differential equations, partial Mathematical physics Physics Partial Differential Equations Mathematical and Computational Physics Numerical and Computational Methods Mathematik Mathematische Physik Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematics Differential equations, partial Mathematical physics Physics Partial Differential Equations Mathematical and Computational Physics Numerical and Computational Methods Mathematik Mathematische Physik Partielle Differentialgleichung |
| url | https://doi.org/10.1007/b97312 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT jostjurgen partialdifferentialequations |