The geometry of jet bundles /:
The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1989.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
142. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality. The book includes a proof of the local exactness of the variational bicomplex. A knowledge of differential geometry is assumed by the author, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. Coordinate-free techniques are used throughout, although coordinate representations are often used in proofs and when considering applications. |
| Beschreibung: | 1 online resource (293 pages) |
| Bibliographie: | Includes bibliographical references (pages 286-287) and index. |
| ISBN: | 9781107361560 1107361567 9780511526411 0511526415 |
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| 245 | 1 | 4 | |a The geometry of jet bundles / |c D.J. Saunders. |
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| 504 | |a Includes bibliographical references (pages 286-287) and index. | ||
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| 520 | |a The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality. The book includes a proof of the local exactness of the variational bicomplex. A knowledge of differential geometry is assumed by the author, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. Coordinate-free techniques are used throughout, although coordinate representations are often used in proofs and when considering applications. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Introduction; 1 Bundles; 1.1 Fibred Manifolds and Bundles; 1.2 Sections; 1.3 Bundle Morphisms; 1.4 New Bundles From Old; 2 Linear Bundles; 2.1 Vector Bundles; 2.2 Vector Bundle Morphisms; 2.3 Duality and Tensor Products; 2.4 Affine Bundles; 3 Linear Operations on General Bundles; 3.1 Tangent and Cotangent Vectors; 3.2 Vector Fields; 3.3 Differential Forms; 3.4 Derivations; 3.5 Connections; 4 First-order Jet Bundles; 4.1 First-order Jets; 4.2 Prolongations of Morphisms; 4.3 Total Derivatives and Contact Forms; 4.4 Prolongations of Vector Fields | |
| 505 | 8 | |a 4.5 The Contact Structure4.6 Jet Fields; 4.7 Vertical Lifts; 5 Second-order Jet Bundles; 5.1 Second-order Jets; 5.2 Repeated Jets; 5.3 Integrability and Semi-holonomic Jets; 5.4 Second-order Jet Fields; 5.5 The Cartan Form; 6 Higher-order Jet Bundles; 6.1 Multi-index Notation; 6.2 Higher-order Jets; 6.3 The Contact Structure; 6.4 Vector Fields and their Prolongations; 6.5 The Higher-order Cartan Form; 7 Infinite Jet Bundles; 7.1 Preliminaries; 7.2 Infinite Jets; 7.3 The Infinite Contact System; 7.4 The Inverse Problem; Bibliography; Glossary of Symbols; Index | |
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| 650 | 0 | |a Differential equations. |0 http://id.loc.gov/authorities/subjects/sh85037890 | |
| 650 | 0 | |a Calculus of variations. |0 http://id.loc.gov/authorities/subjects/sh85018809 | |
| 650 | 6 | |a Équations différentielles. | |
| 650 | 6 | |a Calcul des variations. | |
| 650 | 6 | |a Fibrés des jets (Mathématiques) | |
| 650 | 6 | |a Géométrie différentielle. | |
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| adam_text | |
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| author | Saunders, D. J., 1964- |
| author_GND | http://id.loc.gov/authorities/names/nr89010887 |
| author_facet | Saunders, D. J., 1964- |
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| contents | Cover; Title; Copyright; Contents; Introduction; 1 Bundles; 1.1 Fibred Manifolds and Bundles; 1.2 Sections; 1.3 Bundle Morphisms; 1.4 New Bundles From Old; 2 Linear Bundles; 2.1 Vector Bundles; 2.2 Vector Bundle Morphisms; 2.3 Duality and Tensor Products; 2.4 Affine Bundles; 3 Linear Operations on General Bundles; 3.1 Tangent and Cotangent Vectors; 3.2 Vector Fields; 3.3 Differential Forms; 3.4 Derivations; 3.5 Connections; 4 First-order Jet Bundles; 4.1 First-order Jets; 4.2 Prolongations of Morphisms; 4.3 Total Derivatives and Contact Forms; 4.4 Prolongations of Vector Fields 4.5 The Contact Structure4.6 Jet Fields; 4.7 Vertical Lifts; 5 Second-order Jet Bundles; 5.1 Second-order Jets; 5.2 Repeated Jets; 5.3 Integrability and Semi-holonomic Jets; 5.4 Second-order Jet Fields; 5.5 The Cartan Form; 6 Higher-order Jet Bundles; 6.1 Multi-index Notation; 6.2 Higher-order Jets; 6.3 The Contact Structure; 6.4 Vector Fields and their Prolongations; 6.5 The Higher-order Cartan Form; 7 Infinite Jet Bundles; 7.1 Preliminaries; 7.2 Infinite Jets; 7.3 The Infinite Contact System; 7.4 The Inverse Problem; Bibliography; Glossary of Symbols; Index |
| ctrlnum | (OCoLC)839304386 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839304386 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107361560 1107361567 9780511526411 0511526415 |
| language | English |
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| publishDateSearch | 1989 |
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| publisher | Cambridge University Press, |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Saunders, D. J., 1964- https://id.oclc.org/worldcat/entity/E39PCjt3GGqHyhX8vvGJjMrXV3 http://id.loc.gov/authorities/names/nr89010887 The geometry of jet bundles / D.J. Saunders. Cambridge ; New York : Cambridge University Press, 1989. 1 online resource (293 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 142 Includes bibliographical references (pages 286-287) and index. Print version record. The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality. The book includes a proof of the local exactness of the variational bicomplex. A knowledge of differential geometry is assumed by the author, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. Coordinate-free techniques are used throughout, although coordinate representations are often used in proofs and when considering applications. Cover; Title; Copyright; Contents; Introduction; 1 Bundles; 1.1 Fibred Manifolds and Bundles; 1.2 Sections; 1.3 Bundle Morphisms; 1.4 New Bundles From Old; 2 Linear Bundles; 2.1 Vector Bundles; 2.2 Vector Bundle Morphisms; 2.3 Duality and Tensor Products; 2.4 Affine Bundles; 3 Linear Operations on General Bundles; 3.1 Tangent and Cotangent Vectors; 3.2 Vector Fields; 3.3 Differential Forms; 3.4 Derivations; 3.5 Connections; 4 First-order Jet Bundles; 4.1 First-order Jets; 4.2 Prolongations of Morphisms; 4.3 Total Derivatives and Contact Forms; 4.4 Prolongations of Vector Fields 4.5 The Contact Structure4.6 Jet Fields; 4.7 Vertical Lifts; 5 Second-order Jet Bundles; 5.1 Second-order Jets; 5.2 Repeated Jets; 5.3 Integrability and Semi-holonomic Jets; 5.4 Second-order Jet Fields; 5.5 The Cartan Form; 6 Higher-order Jet Bundles; 6.1 Multi-index Notation; 6.2 Higher-order Jets; 6.3 The Contact Structure; 6.4 Vector Fields and their Prolongations; 6.5 The Higher-order Cartan Form; 7 Infinite Jet Bundles; 7.1 Preliminaries; 7.2 Infinite Jets; 7.3 The Infinite Contact System; 7.4 The Inverse Problem; Bibliography; Glossary of Symbols; Index Jet bundles (Mathematics) http://id.loc.gov/authorities/subjects/sh85070153 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Differential equations. http://id.loc.gov/authorities/subjects/sh85037890 Calculus of variations. http://id.loc.gov/authorities/subjects/sh85018809 Équations différentielles. Calcul des variations. Fibrés des jets (Mathématiques) Géométrie différentielle. MATHEMATICS Geometry Differential. bisacsh Differential equations fast Calculus of variations fast Geometry, Differential fast Jet bundles (Mathematics) fast Jetbündel gnd http://d-nb.info/gnd/4498250-1 Jatos (geometria diferencial) larpcal Print version: Saunders, D.J., 1964- Geometry of jet bundles. Cambridge ; New York : Cambridge University Press, 1989 0521369487 (DLC) 89148500 (OCoLC)19412821 London Mathematical Society lecture note series ; 142. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552518 Volltext |
| spellingShingle | Saunders, D. J., 1964- The geometry of jet bundles / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Introduction; 1 Bundles; 1.1 Fibred Manifolds and Bundles; 1.2 Sections; 1.3 Bundle Morphisms; 1.4 New Bundles From Old; 2 Linear Bundles; 2.1 Vector Bundles; 2.2 Vector Bundle Morphisms; 2.3 Duality and Tensor Products; 2.4 Affine Bundles; 3 Linear Operations on General Bundles; 3.1 Tangent and Cotangent Vectors; 3.2 Vector Fields; 3.3 Differential Forms; 3.4 Derivations; 3.5 Connections; 4 First-order Jet Bundles; 4.1 First-order Jets; 4.2 Prolongations of Morphisms; 4.3 Total Derivatives and Contact Forms; 4.4 Prolongations of Vector Fields 4.5 The Contact Structure4.6 Jet Fields; 4.7 Vertical Lifts; 5 Second-order Jet Bundles; 5.1 Second-order Jets; 5.2 Repeated Jets; 5.3 Integrability and Semi-holonomic Jets; 5.4 Second-order Jet Fields; 5.5 The Cartan Form; 6 Higher-order Jet Bundles; 6.1 Multi-index Notation; 6.2 Higher-order Jets; 6.3 The Contact Structure; 6.4 Vector Fields and their Prolongations; 6.5 The Higher-order Cartan Form; 7 Infinite Jet Bundles; 7.1 Preliminaries; 7.2 Infinite Jets; 7.3 The Infinite Contact System; 7.4 The Inverse Problem; Bibliography; Glossary of Symbols; Index Jet bundles (Mathematics) http://id.loc.gov/authorities/subjects/sh85070153 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Differential equations. http://id.loc.gov/authorities/subjects/sh85037890 Calculus of variations. http://id.loc.gov/authorities/subjects/sh85018809 Équations différentielles. Calcul des variations. Fibrés des jets (Mathématiques) Géométrie différentielle. MATHEMATICS Geometry Differential. bisacsh Differential equations fast Calculus of variations fast Geometry, Differential fast Jet bundles (Mathematics) fast Jetbündel gnd http://d-nb.info/gnd/4498250-1 Jatos (geometria diferencial) larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85070153 http://id.loc.gov/authorities/subjects/sh85054146 http://id.loc.gov/authorities/subjects/sh85037890 http://id.loc.gov/authorities/subjects/sh85018809 http://d-nb.info/gnd/4498250-1 |
| title | The geometry of jet bundles / |
| title_auth | The geometry of jet bundles / |
| title_exact_search | The geometry of jet bundles / |
| title_full | The geometry of jet bundles / D.J. Saunders. |
| title_fullStr | The geometry of jet bundles / D.J. Saunders. |
| title_full_unstemmed | The geometry of jet bundles / D.J. Saunders. |
| title_short | The geometry of jet bundles / |
| title_sort | geometry of jet bundles |
| topic | Jet bundles (Mathematics) http://id.loc.gov/authorities/subjects/sh85070153 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Differential equations. http://id.loc.gov/authorities/subjects/sh85037890 Calculus of variations. http://id.loc.gov/authorities/subjects/sh85018809 Équations différentielles. Calcul des variations. Fibrés des jets (Mathématiques) Géométrie différentielle. MATHEMATICS Geometry Differential. bisacsh Differential equations fast Calculus of variations fast Geometry, Differential fast Jet bundles (Mathematics) fast Jetbündel gnd http://d-nb.info/gnd/4498250-1 Jatos (geometria diferencial) larpcal |
| topic_facet | Jet bundles (Mathematics) Geometry, Differential. Differential equations. Calculus of variations. Équations différentielles. Calcul des variations. Fibrés des jets (Mathématiques) Géométrie différentielle. MATHEMATICS Geometry Differential. Differential equations Calculus of variations Geometry, Differential Jetbündel Jatos (geometria diferencial) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552518 |
| work_keys_str_mv | AT saundersdj thegeometryofjetbundles AT saundersdj geometryofjetbundles |