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Books > Science & Mathematics > Mathematics > Topology
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Vector Bundles and Their Applications (Hardcover, 1998 ed.)
Loot Price: R3,075
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Vector Bundles and Their Applications (Hardcover, 1998 ed.)
Series: Mathematics and Its Applications, 447
Expected to ship within 9 - 15 working days
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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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