Differential topology and geometry with applications to physics:
Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Bristol, UK
IOP Publishing
[2018]
|
| Ausgabe: | Version: 20181201 |
| Schriftenreihe: | IOP expanding physics
|
| Schlagworte: | |
| Online-Zugang: | UBR01 URL des Erstveröffentlichers |
| Zusammenfassung: | Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | 1 Online-Ressource (verschiedene Seitenzählung) Illustrationen |
| ISBN: | 9780750320726 9780750320719 |
| DOI: | 10.1088/2053-2563/aadf65 |
Internformat
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| 245 | 1 | 0 | |a Differential topology and geometry with applications to physics |c Eduardo Nahmad-Achar, National Autonomous University of Mexico, Mexico City, Mexico |
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| 505 | 8 | |a 1. Synopsis of general relativity -- 2. Curves and surfaces in E3 -- 3. Elements of topology -- 4. Differentiable manifolds -- 5. Tangent vectors and tangent spaces -- 6. Tensor algebra -- 7. Tensor fields and commutators -- 8. Differential forms and exterior calculus -- 9. Maps between manifolds -- 10. Integration on manifolds -- 11. Integral curves and Lie derivatives -- 12. Linear connections -- 13. Geodesics -- 14. Torsion and curvature -- 15. Pseudo-Riemannian metric -- 16. Newtonian space-time and thermodynamics -- 17. Special relativity, electrodynamics, and the Poincar e group -- 18. General relativity -- 19. Gravitational radiation -- 20. Further reading | |
| 520 | |a Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics | ||
| 650 | 4 | |a SCIENCE / Physics / Mathematical & Computational / bisacsh | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Topology | |
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Datensatz im Suchindex
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| author | Nahmad-Achar, Eduardo |
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| contents | 1. Synopsis of general relativity -- 2. Curves and surfaces in E3 -- 3. Elements of topology -- 4. Differentiable manifolds -- 5. Tangent vectors and tangent spaces -- 6. Tensor algebra -- 7. Tensor fields and commutators -- 8. Differential forms and exterior calculus -- 9. Maps between manifolds -- 10. Integration on manifolds -- 11. Integral curves and Lie derivatives -- 12. Linear connections -- 13. Geodesics -- 14. Torsion and curvature -- 15. Pseudo-Riemannian metric -- 16. Newtonian space-time and thermodynamics -- 17. Special relativity, electrodynamics, and the Poincar e group -- 18. General relativity -- 19. Gravitational radiation -- 20. Further reading |
| ctrlnum | (OCoLC)1129928190 (DE-599)BVBBV046649832 |
| discipline | Physik |
| discipline_str_mv | Physik |
| doi_str_mv | 10.1088/2053-2563/aadf65 |
| edition | Version: 20181201 |
| format | Electronic eBook |
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| id | DE-604.BV046649832 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:16:09Z |
| indexdate | 2024-07-10T08:50:16Z |
| institution | BVB |
| isbn | 9780750320726 9780750320719 |
| language | English |
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| publishDate | 2018 |
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| publisher | IOP Publishing |
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| series2 | IOP expanding physics |
| spelling | Nahmad-Achar, Eduardo Verfasser (DE-588)1175124176 aut Differential topology and geometry with applications to physics Eduardo Nahmad-Achar, National Autonomous University of Mexico, Mexico City, Mexico Version: 20181201 Bristol, UK IOP Publishing [2018] 1 Online-Ressource (verschiedene Seitenzählung) Illustrationen txt rdacontent c rdamedia cr rdacarrier IOP expanding physics Includes bibliographical references 1. Synopsis of general relativity -- 2. Curves and surfaces in E3 -- 3. Elements of topology -- 4. Differentiable manifolds -- 5. Tangent vectors and tangent spaces -- 6. Tensor algebra -- 7. Tensor fields and commutators -- 8. Differential forms and exterior calculus -- 9. Maps between manifolds -- 10. Integration on manifolds -- 11. Integral curves and Lie derivatives -- 12. Linear connections -- 13. Geodesics -- 14. Torsion and curvature -- 15. Pseudo-Riemannian metric -- 16. Newtonian space-time and thermodynamics -- 17. Special relativity, electrodynamics, and the Poincar e group -- 18. General relativity -- 19. Gravitational radiation -- 20. Further reading Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics SCIENCE / Physics / Mathematical & Computational / bisacsh Geometry, Differential Topology Mathematical physics Erscheint auch als Druck-Ausgabe 978-0-7503-2070-2 https://doi.org/10.1088/2053-2563/aadf65 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Nahmad-Achar, Eduardo Differential topology and geometry with applications to physics 1. Synopsis of general relativity -- 2. Curves and surfaces in E3 -- 3. Elements of topology -- 4. Differentiable manifolds -- 5. Tangent vectors and tangent spaces -- 6. Tensor algebra -- 7. Tensor fields and commutators -- 8. Differential forms and exterior calculus -- 9. Maps between manifolds -- 10. Integration on manifolds -- 11. Integral curves and Lie derivatives -- 12. Linear connections -- 13. Geodesics -- 14. Torsion and curvature -- 15. Pseudo-Riemannian metric -- 16. Newtonian space-time and thermodynamics -- 17. Special relativity, electrodynamics, and the Poincar e group -- 18. General relativity -- 19. Gravitational radiation -- 20. Further reading SCIENCE / Physics / Mathematical & Computational / bisacsh Geometry, Differential Topology Mathematical physics |
| title | Differential topology and geometry with applications to physics |
| title_auth | Differential topology and geometry with applications to physics |
| title_exact_search | Differential topology and geometry with applications to physics |
| title_exact_search_txtP | Differential topology and geometry with applications to physics |
| title_full | Differential topology and geometry with applications to physics Eduardo Nahmad-Achar, National Autonomous University of Mexico, Mexico City, Mexico |
| title_fullStr | Differential topology and geometry with applications to physics Eduardo Nahmad-Achar, National Autonomous University of Mexico, Mexico City, Mexico |
| title_full_unstemmed | Differential topology and geometry with applications to physics Eduardo Nahmad-Achar, National Autonomous University of Mexico, Mexico City, Mexico |
| title_short | Differential topology and geometry with applications to physics |
| title_sort | differential topology and geometry with applications to physics |
| topic | SCIENCE / Physics / Mathematical & Computational / bisacsh Geometry, Differential Topology Mathematical physics |
| topic_facet | SCIENCE / Physics / Mathematical & Computational / bisacsh Geometry, Differential Topology Mathematical physics |
| url | https://doi.org/10.1088/2053-2563/aadf65 |
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