Exterior Differential Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1991
|
| Schriftenreihe: | Mathematical Sciences Research Institute Publications
18 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object |
| Beschreibung: | 1 Online-Ressource (VII, 475p) |
| ISBN: | 9781461397144 9781461397168 |
| ISSN: | 0940-4740 |
| DOI: | 10.1007/978-1-4613-9714-4 |
Internformat
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| 100 | 1 | |a Bryant, Robert L. |d 1953- |e Verfasser |0 (DE-588)112659721 |4 aut | |
| 245 | 1 | 0 | |a Exterior Differential Systems |c by Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths |
| 264 | 1 | |a New York, NY |b Springer New York |c 1991 | |
| 300 | |a 1 Online-Ressource (VII, 475p) | ||
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| 337 | |b c |2 rdamedia | ||
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| 490 | 0 | |a Mathematical Sciences Research Institute Publications |v 18 |x 0940-4740 | |
| 500 | |a This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Bryant, Robert L. 1953- |
| author_GND | (DE-588)112659721 (DE-588)118520350 (DE-588)1089272758 (DE-588)136201695 (DE-588)131881434 |
| author_facet | Bryant, Robert L. 1953- |
| author_role | aut |
| author_sort | Bryant, Robert L. 1953- |
| author_variant | r l b rl rlb |
| building | Verbundindex |
| bvnumber | BV042420823 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-9714-4 |
| format | Electronic eBook |
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| id | DE-604.BV042420823 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461397144 9781461397168 |
| issn | 0940-4740 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856240 |
| oclc_num | 1184416140 |
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| physical | 1 Online-Ressource (VII, 475p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Mathematical Sciences Research Institute Publications |
| spelling | Bryant, Robert L. 1953- Verfasser (DE-588)112659721 aut Exterior Differential Systems by Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths New York, NY Springer New York 1991 1 Online-Ressource (VII, 475p) txt rdacontent c rdamedia cr rdacarrier Mathematical Sciences Research Institute Publications 18 0940-4740 This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Äußeres Differentialsystem (DE-588)4141545-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Äußeres Differentialsystem (DE-588)4141545-0 s 2\p DE-604 Chern, Shiing-shen 1911-2004 Sonstige (DE-588)118520350 oth Gardner, Robert B. 1939-1998 Sonstige (DE-588)1089272758 oth Goldschmidt, Hubert 1942- Sonstige (DE-588)136201695 oth Griffiths, Phillip 1938- Sonstige (DE-588)131881434 oth https://doi.org/10.1007/978-1-4613-9714-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bryant, Robert L. 1953- Exterior Differential Systems Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgleichung (DE-588)4012249-9 gnd Äußeres Differentialsystem (DE-588)4141545-0 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4141545-0 |
| title | Exterior Differential Systems |
| title_auth | Exterior Differential Systems |
| title_exact_search | Exterior Differential Systems |
| title_full | Exterior Differential Systems by Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths |
| title_fullStr | Exterior Differential Systems by Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths |
| title_full_unstemmed | Exterior Differential Systems by Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths |
| title_short | Exterior Differential Systems |
| title_sort | exterior differential systems |
| topic | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgleichung (DE-588)4012249-9 gnd Äußeres Differentialsystem (DE-588)4141545-0 gnd |
| topic_facet | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgleichung Äußeres Differentialsystem |
| url | https://doi.org/10.1007/978-1-4613-9714-4 |
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