Selected topics in the geometrical study of differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Math. Soc.
2002
|
| Series: | Regional conference series in mathematics
96 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 115 S. Ill. |
| ISBN: | 0821826395 |
Staff View
MARC
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| 245 | 1 | 0 | |a Selected topics in the geometrical study of differential equations |c Niky Kamran |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 2002 | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Acknowledgments xiii
Chapter 1. Differential equations and their geometry 1
1. The Cauchy problem for first order partial differential equations 1
2. Hyperbolic equations integrable by the method of Darboux 3
3. External, internal and generalized symmetries 5
4. The inverse problem of the calculus of variations 6
5. Some important topics not covered in these lectures 7
Chapter 2. External and generalized symmetries 9
1. Jet bundles 9
2. Systems of differential equations 12
3. External symmetries 13
4. Classical symmetry reduction 15
5. Contact transformations and Backhand s Theorem 17
6. Generalized symmetries of differential equations 19
7. Generalized symmetries and conservation laws 22
Chapter 3. Internal, external and generalized symmetries 27
1. Internal symmetries 27
2. Normal systems of ordinary differential equations 28
3. Under determined systems of ordinary differential equations 29
4. Contact conditions for ordinary differential equations 32
5. Contact conditions for partial differential equations 35
Chapter 4. Transformations of surfaces 39
1. The method of Laplace 39
2. The Laplace transformation for surfaces 42
3. An application to the sfe Toda field theory 44
Chapter 5. Transformations of submanifolds 47
1. A multi dimensional geometric Laplace transformation 47
2. Transformations of systems of partial differential equations 51
Chapter 6. Hamiltonian systems of conservation laws 57
1. Systems of conservation laws and their local geometry 57
2. Strongly hyperbolic systems rich in conservation laws 60
3. The Laplace transformation for strongly hyperbolic systems 63
Chapter 7. The variational bi complex 67
viii CONTENTS
1. Jet bundles of infinite order 67
2. The tautological variational bi complex on J°° (E) 69
Chapter 8. The inverse problem of the calculus of variations 75
1. The local, global and equivariant inverse problems 75
2. Edge complexes and obstructions 78
3. Variational principles and symmetry reduction 81
Chapter 9. Conservation laws and Darboux integrability 83
1. Scalar hyperbolic partial differential equations in the plane 83
2. The constrained variational bi complex 85
3. Conservation laws 86
4. The generalized Laplace invariants 89
5. Vanishing theorems for conservation laws 92
6. Darboux integrability 93
7. Further applications 97
Chapter 10. Characteristic cohomology of differential systems 99
1. Exterior differential systems 99
2. Some existence theorems for integral manifolds 101
3. Involutive systems and the Cartan Kahler theorem 103
4. Characteristic cohomology 108
Bibliography 111
|
| any_adam_object | 1 |
| author | Kamran, Niky |
| author_facet | Kamran, Niky |
| author_role | aut |
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| classification_rvk | SI 195 |
| ctrlnum | (OCoLC)49531101 (DE-599)BVBBV014463184 |
| dewey-full | 515/.35 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515/.35 510 |
| dewey-search | 515/.35 510 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014463184 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:56Z |
| institution | BVB |
| isbn | 0821826395 |
| language | English |
| lccn | 2002066482 |
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| physical | XIV, 115 S. Ill. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Kamran, Niky Verfasser aut Selected topics in the geometrical study of differential equations Niky Kamran Providence, R.I. American Math. Soc. 2002 XIV, 115 S. Ill. txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 96 Differentiaaltopologie gtt EQUAÇÕES DIFERENCIAIS (ANÁLISE) larpcal MÉTODOS DE PFAFF larpcal Differential equations Geometry, Differential Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Regional conference series in mathematics 96 (DE-604)BV000004346 96 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009875941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kamran, Niky Selected topics in the geometrical study of differential equations Regional conference series in mathematics Differentiaaltopologie gtt EQUAÇÕES DIFERENCIAIS (ANÁLISE) larpcal MÉTODOS DE PFAFF larpcal Differential equations Geometry, Differential Differentialgleichung (DE-588)4012249-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4012248-7 |
| title | Selected topics in the geometrical study of differential equations |
| title_auth | Selected topics in the geometrical study of differential equations |
| title_exact_search | Selected topics in the geometrical study of differential equations |
| title_full | Selected topics in the geometrical study of differential equations Niky Kamran |
| title_fullStr | Selected topics in the geometrical study of differential equations Niky Kamran |
| title_full_unstemmed | Selected topics in the geometrical study of differential equations Niky Kamran |
| title_short | Selected topics in the geometrical study of differential equations |
| title_sort | selected topics in the geometrical study of differential equations |
| topic | Differentiaaltopologie gtt EQUAÇÕES DIFERENCIAIS (ANÁLISE) larpcal MÉTODOS DE PFAFF larpcal Differential equations Geometry, Differential Differentialgleichung (DE-588)4012249-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Differentiaaltopologie EQUAÇÕES DIFERENCIAIS (ANÁLISE) MÉTODOS DE PFAFF Differential equations Geometry, Differential Differentialgleichung Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009875941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT kamranniky selectedtopicsinthegeometricalstudyofdifferentialequations |