Paulette Libermann, Charles-Michel Marle (auth.)9027724385, 9789027724380
Approach your problems from the right end It isn’t that they can’t see the solution. and begin with the answers. Then one day, It is that they can’t see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father ‘The Hermit Clad in Crane Feathers’ Brown ‘The point of a Pin’. in R. van Gulik’s The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the “tree” of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci ences has changed drastically in recent years: measure theory is used (non-trivially) in re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homo topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. |
Table of contents :
Front Matter….Pages i-xvi
Symplectic vector spaces and symplectic vector bundles….Pages 1-52
Semi-basic and vertical differential forms in mechanics….Pages 53-88
Symplectic manifolds and Poisson manifolds….Pages 89-184
Action of a Lie group on a symplectic manifold….Pages 185-274
Contact manifolds….Pages 275-340
Back Matter….Pages 341-526 |
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