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Vector bundles and their applicationsкнига
- Авторы: Luke Glenys, Mishchenko Alexander S.
- Год издания: 1998
- Место издания: Kluwer Academic Publishers Dordrecht
- Объём: 254 страниц
- ISBN: 0-7923-5154-1, 978-1-4419-4802-1, 978-1-4757-6923-4
- Монография
- DOI: 10.1007/978-1-4757-6923-4
- Аннотация: In the last few years the use of geometric methods has permeated many more branches of mathematics and the sciences. Briefly its role may be characterized as follows. Whereas methods of mathematical analysis describe phenomena ‘in the small’, geometric methods contribute to giving the picture ‘in the large’. A second no less important property of geometric methods is the convenience of using its language to describe and give qualitative explanations for diverse mathematical phenomena and patterns. From this point of view, the theory of vector bundles together with mathematical analysis on manifolds (global anal- ysis and differential geometry) has provided a major stimulus. Its language turned out to be extremely fruitful: connections on principal vector bundles (in terms of which various field theories are described), transformation groups including the various symmetry groups that arise in connection with physical problems, in asymptotic methods of partial differential equations with small parameter, in elliptic operator theory, in mathematical methods of classical mechanics and in mathematical methods in economics. There are other cur- rently less significant applications in other fields. Over a similar period, uni- versity education has changed considerably with the appearance of new courses on differential geometry and topology. New textbooks have been published but ‘geometry and topology’ has not, in our opinion, been well covered from a prac- tical applications point of view. Existing monographs on vector bundles have been mainly of a purely theoretical nature, devoted to the internal geometric and topological problems of the subject. Students from related disciplines have found the texts difficult to use. It therefore seems expedient to have a simpler book containing numerous illustrations and applications to various problems in mathematics and the sciences.
- Добавил в систему: Мищенко Александр Сергеевич