Differential Forms and Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This is a free translation of a set of notes published originally in Portuguese in 1971. They were translated for a course in the College of Differential Geome try, ICTP, Trieste, 1989. In the English translation we omitted a chapter on the Frobenius theorem and an appendix on the nonexistence of a complete hyperbolic plane in euclidean 3-space (Hilbert's theorem). For the present edition, we introduced a chapter on line integrals. In Chapter 1 we introduce the differential forms in Rn. We only assume an elementary knowledge of calculus, and the chapter can be used as a basis for a course on differential forms for "users" of Mathematics. In Chapter 2 we start integrating differential forms of degree one along curves in Rn. This already allows some applications of the ideas of Chapter 1. This material is not used in the rest of the book. In Chapter 3 we present the basic notions of differentiable manifolds. It is useful (but not essential) that the reader be familiar with the notion of a regular surface in R3. In Chapter 4 we introduce the notion of manifold with boundary and prove Stokes theorem and Poincare's lemma. Starting from this basic material, we could follow any of the possi ble routes for applications: Topology, Differential Geometry, Mechanics, Lie Groups, etc. We have chosen Differential Geometry. For simplicity, we re stricted ourselves to surfaces |
| Beschreibung: | 1 Online-Ressource (X, 118p. 18 illus) |
| ISBN: | 9783642579516 9783540576181 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-57951-6 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-57951-6 |
| format | Electronic eBook |
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| id | DE-604.BV042422695 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642579516 9783540576181 |
| issn | 0172-5939 |
| language | English |
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| physical | 1 Online-Ressource (X, 118p. 18 illus) |
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| publishDate | 1994 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Carmo, Manfredo P. Verfasser aut Differential Forms and Applications by Manfredo P. Carmo Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (X, 118p. 18 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 This is a free translation of a set of notes published originally in Portuguese in 1971. They were translated for a course in the College of Differential Geome try, ICTP, Trieste, 1989. In the English translation we omitted a chapter on the Frobenius theorem and an appendix on the nonexistence of a complete hyperbolic plane in euclidean 3-space (Hilbert's theorem). For the present edition, we introduced a chapter on line integrals. In Chapter 1 we introduce the differential forms in Rn. We only assume an elementary knowledge of calculus, and the chapter can be used as a basis for a course on differential forms for "users" of Mathematics. In Chapter 2 we start integrating differential forms of degree one along curves in Rn. This already allows some applications of the ideas of Chapter 1. This material is not used in the rest of the book. In Chapter 3 we present the basic notions of differentiable manifolds. It is useful (but not essential) that the reader be familiar with the notion of a regular surface in R3. In Chapter 4 we introduce the notion of manifold with boundary and prove Stokes theorem and Poincare's lemma. Starting from this basic material, we could follow any of the possi ble routes for applications: Topology, Differential Geometry, Mechanics, Lie Groups, etc. We have chosen Differential Geometry. For simplicity, we re stricted ourselves to surfaces Mathematics Global analysis (Mathematics) Global differential geometry Mathematical physics Differential Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Differentialform (DE-588)4149772-7 gnd rswk-swf Differentialform (DE-588)4149772-7 s 1\p DE-604 https://doi.org/10.1007/978-3-642-57951-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carmo, Manfredo P. Differential Forms and Applications Mathematics Global analysis (Mathematics) Global differential geometry Mathematical physics Differential Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Differentialform (DE-588)4149772-7 gnd |
| subject_GND | (DE-588)4149772-7 |
| title | Differential Forms and Applications |
| title_auth | Differential Forms and Applications |
| title_exact_search | Differential Forms and Applications |
| title_full | Differential Forms and Applications by Manfredo P. Carmo |
| title_fullStr | Differential Forms and Applications by Manfredo P. Carmo |
| title_full_unstemmed | Differential Forms and Applications by Manfredo P. Carmo |
| title_short | Differential Forms and Applications |
| title_sort | differential forms and applications |
| topic | Mathematics Global analysis (Mathematics) Global differential geometry Mathematical physics Differential Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Differentialform (DE-588)4149772-7 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Global differential geometry Mathematical physics Differential Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Differentialform |
| url | https://doi.org/10.1007/978-3-642-57951-6 |
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