Vector Bundles and Their Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1998
|
| Schriftenreihe: | Mathematics and Its Applications
447 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In the last few years the use of geometrie methods has permeated many more branehes of mathematies and the seiences. Briefly its role may be eharaeterized as folIows. Whereas methods of mathematieal analysis deseribe phenomena 'in the sm all " geometrie methods eontribute to giving the picture 'in the large'. A seeond no less important property of geometrie methods is the eonvenienee of using its language to deseribe and give qualitative explanations for diverse mathematieal phenomena and patterns. From this point of view, the theory of veetor bundles together with mathematieal analysis on manifolds (global anal ysis and differential geometry) has provided a major stimulus. Its language turned out to be extremely fruitful: connections on prineipal veetor bundles (in terms of whieh various field theories are deseribed), transformation groups including the various symmetry groups that arise in eonneetion with physieal problems, in asymptotie methods of partial differential equations with small parameter, in elliptie operator theory, in mathematieal methods of classieal meehanies and in mathematieal methods in eeonomies. There are other eur rently less signifieant applieations in other fields. Over a similar period, uni versity edueation has ehanged eonsiderably with the appearanee of new courses on differential geometry and topology. New textbooks have been published but 'geometry and topology' has not, in our opinion, been wen eovered from a prae tieal applieations point of view |
| Beschreibung: | 1 Online-Ressource (VIII, 256 p) |
| ISBN: | 9781475769234 9781441948021 |
| DOI: | 10.1007/978-1-4757-6923-4 |
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| 500 | |a In the last few years the use of geometrie methods has permeated many more branehes of mathematies and the seiences. Briefly its role may be eharaeterized as folIows. Whereas methods of mathematieal analysis deseribe phenomena 'in the sm all " geometrie methods eontribute to giving the picture 'in the large'. A seeond no less important property of geometrie methods is the eonvenienee of using its language to deseribe and give qualitative explanations for diverse mathematieal phenomena and patterns. From this point of view, the theory of veetor bundles together with mathematieal analysis on manifolds (global anal ysis and differential geometry) has provided a major stimulus. Its language turned out to be extremely fruitful: connections on prineipal veetor bundles (in terms of whieh various field theories are deseribed), transformation groups including the various symmetry groups that arise in eonneetion with physieal problems, in asymptotie methods of partial differential equations with small parameter, in elliptie operator theory, in mathematieal methods of classieal meehanies and in mathematieal methods in eeonomies. There are other eur rently less signifieant applieations in other fields. Over a similar period, uni versity edueation has ehanged eonsiderably with the appearanee of new courses on differential geometry and topology. New textbooks have been published but 'geometry and topology' has not, in our opinion, been wen eovered from a prae tieal applieations point of view | ||
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Datensatz im Suchindex
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| author | Luke, Glenys |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-6923-4 |
| format | Electronic eBook |
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| isbn | 9781475769234 9781441948021 |
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| spelling | Luke, Glenys Verfasser aut Vector Bundles and Their Applications by Glenys Luke, Alexander S. Mishchenko Boston, MA Springer US 1998 1 Online-Ressource (VIII, 256 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 447 In the last few years the use of geometrie methods has permeated many more branehes of mathematies and the seiences. Briefly its role may be eharaeterized as folIows. Whereas methods of mathematieal analysis deseribe phenomena 'in the sm all " geometrie methods eontribute to giving the picture 'in the large'. A seeond no less important property of geometrie methods is the eonvenienee of using its language to deseribe and give qualitative explanations for diverse mathematieal phenomena and patterns. From this point of view, the theory of veetor bundles together with mathematieal analysis on manifolds (global anal ysis and differential geometry) has provided a major stimulus. Its language turned out to be extremely fruitful: connections on prineipal veetor bundles (in terms of whieh various field theories are deseribed), transformation groups including the various symmetry groups that arise in eonneetion with physieal problems, in asymptotie methods of partial differential equations with small parameter, in elliptie operator theory, in mathematieal methods of classieal meehanies and in mathematieal methods in eeonomies. There are other eur rently less signifieant applieations in other fields. Over a similar period, uni versity edueation has ehanged eonsiderably with the appearanee of new courses on differential geometry and topology. New textbooks have been published but 'geometry and topology' has not, in our opinion, been wen eovered from a prae tieal applieations point of view Mathematics Global analysis Operator theory Global differential geometry Distribution (Probability theory) Algebraic topology Algebraic Topology Global Analysis and Analysis on Manifolds Operator Theory Differential Geometry Probability Theory and Stochastic Processes Mathematik Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 s 1\p DE-604 Mishchenko, Alexander S. Sonstige oth https://doi.org/10.1007/978-1-4757-6923-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Luke, Glenys Vector Bundles and Their Applications Mathematics Global analysis Operator theory Global differential geometry Distribution (Probability theory) Algebraic topology Algebraic Topology Global Analysis and Analysis on Manifolds Operator Theory Differential Geometry Probability Theory and Stochastic Processes Mathematik Vektorraumbündel (DE-588)4187470-5 gnd |
| subject_GND | (DE-588)4187470-5 |
| title | Vector Bundles and Their Applications |
| title_auth | Vector Bundles and Their Applications |
| title_exact_search | Vector Bundles and Their Applications |
| title_full | Vector Bundles and Their Applications by Glenys Luke, Alexander S. Mishchenko |
| title_fullStr | Vector Bundles and Their Applications by Glenys Luke, Alexander S. Mishchenko |
| title_full_unstemmed | Vector Bundles and Their Applications by Glenys Luke, Alexander S. Mishchenko |
| title_short | Vector Bundles and Their Applications |
| title_sort | vector bundles and their applications |
| topic | Mathematics Global analysis Operator theory Global differential geometry Distribution (Probability theory) Algebraic topology Algebraic Topology Global Analysis and Analysis on Manifolds Operator Theory Differential Geometry Probability Theory and Stochastic Processes Mathematik Vektorraumbündel (DE-588)4187470-5 gnd |
| topic_facet | Mathematics Global analysis Operator theory Global differential geometry Distribution (Probability theory) Algebraic topology Algebraic Topology Global Analysis and Analysis on Manifolds Operator Theory Differential Geometry Probability Theory and Stochastic Processes Mathematik Vektorraumbündel |
| url | https://doi.org/10.1007/978-1-4757-6923-4 |
| work_keys_str_mv | AT lukeglenys vectorbundlesandtheirapplications AT mishchenkoalexanders vectorbundlesandtheirapplications |