Differential geometry for physicists and mathematicians :: moving frames and differential forms : from Euclid past Riemann /
This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Körperschaft: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2010.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative - almost like a story being told - that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter. In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose. |
| Beschreibung: | 1 online resource (xvii, 293 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 277-283) and index. |
| ISBN: | 9789814566407 9814566403 |
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| 245 | 1 | 0 | |a Differential geometry for physicists and mathematicians : |b moving frames and differential forms : from Euclid past Riemann / |c Jose G. Vargas. |
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| 505 | 0 | |a I. Introduction. 1. Orientations -- II. Tools. 2. Differential forms -- 3. Vector spaces and tensor products -- 4. Exterior differentiation -- III. Two Klein geometries. 5. Affine Klein geometry -- 6. Euclidean Klein geometry -- IV. Cartan connections. 7. Generalized geometry made simple -- 8. Affine connections -- 9. Euclidean connections -- 10. Riemannian spaces and pseudo-spaces -- V. The future? 11. Extensions of Cartan -- 12. Understand the past to imagine the future -- 13. A book of farewells. | |
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| author | Vargas, José G. |
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| contents | I. Introduction. 1. Orientations -- II. Tools. 2. Differential forms -- 3. Vector spaces and tensor products -- 4. Exterior differentiation -- III. Two Klein geometries. 5. Affine Klein geometry -- 6. Euclidean Klein geometry -- IV. Cartan connections. 7. Generalized geometry made simple -- 8. Affine connections -- 9. Euclidean connections -- 10. Riemannian spaces and pseudo-spaces -- V. The future? 11. Extensions of Cartan -- 12. Understand the past to imagine the future -- 13. A book of farewells. |
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| id | ZDB-4-EBA-ocn874213903 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:52Z |
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| isbn | 9789814566407 9814566403 |
| language | English |
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| physical | 1 online resource (xvii, 293 pages) : illustrations |
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| publishDateSearch | 2014 |
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| spelling | Vargas, José G. Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / Jose G. Vargas. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2010. 1 online resource (xvii, 293 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 277-283) and index. I. Introduction. 1. Orientations -- II. Tools. 2. Differential forms -- 3. Vector spaces and tensor products -- 4. Exterior differentiation -- III. Two Klein geometries. 5. Affine Klein geometry -- 6. Euclidean Klein geometry -- IV. Cartan connections. 7. Generalized geometry made simple -- 8. Affine connections -- 9. Euclidean connections -- 10. Riemannian spaces and pseudo-spaces -- V. The future? 11. Extensions of Cartan -- 12. Understand the past to imagine the future -- 13. A book of farewells. This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative - almost like a story being told - that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter. In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose. Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Physique mathématique. Géométrie différentielle. MATHEMATICS Geometry General. bisacsh Geometry, Differential fast Mathematical physics fast World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 Print version: 9789814566391 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=752614 Volltext |
| spellingShingle | Vargas, José G. Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / I. Introduction. 1. Orientations -- II. Tools. 2. Differential forms -- 3. Vector spaces and tensor products -- 4. Exterior differentiation -- III. Two Klein geometries. 5. Affine Klein geometry -- 6. Euclidean Klein geometry -- IV. Cartan connections. 7. Generalized geometry made simple -- 8. Affine connections -- 9. Euclidean connections -- 10. Riemannian spaces and pseudo-spaces -- V. The future? 11. Extensions of Cartan -- 12. Understand the past to imagine the future -- 13. A book of farewells. Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Physique mathématique. Géométrie différentielle. MATHEMATICS Geometry General. bisacsh Geometry, Differential fast Mathematical physics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082129 http://id.loc.gov/authorities/subjects/sh85054146 |
| title | Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / |
| title_auth | Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / |
| title_exact_search | Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / |
| title_full | Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / Jose G. Vargas. |
| title_fullStr | Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / Jose G. Vargas. |
| title_full_unstemmed | Differential geometry for physicists and mathematicians : moving frames and differential forms : from Euclid past Riemann / Jose G. Vargas. |
| title_short | Differential geometry for physicists and mathematicians : |
| title_sort | differential geometry for physicists and mathematicians moving frames and differential forms from euclid past riemann |
| title_sub | moving frames and differential forms : from Euclid past Riemann / |
| topic | Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Physique mathématique. Géométrie différentielle. MATHEMATICS Geometry General. bisacsh Geometry, Differential fast Mathematical physics fast |
| topic_facet | Mathematical physics. Geometry, Differential. Physique mathématique. Géométrie différentielle. MATHEMATICS Geometry General. Geometry, Differential Mathematical physics |
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