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| E-Books | Biblioteca da FCTUNL | Não Ficção | QA614.8. FCT 96620 (Browse shelf) | 1 | Available |
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| QA614.8 FCT 95806 Sign-changing critical point theory | QA614.8. FCT 95923 Vector analysis versus vector calculus | QA614.8. FCT 96541 Differential topology | QA614.8. FCT 96620 Introduction to global variational geometry | QA614.8. FCT 96893 Analysis and Geometry | QA614.8 FCT 97043 Noether's theorems | QA614.8. FCT 97199 Quantum isometry groups |
Colocação: Online
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational sequence theory and its consequences for the global inverse problem (cohomology conditions)- examples of variational functionals of mathematical physics. Complete formulations and proofs of all basic assertions are given, based on theorems of global analysis explained in the Appendix.
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