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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.

Mathematics. --- Global Analysis and Analysis on Manifolds. --- Differential Geometry. --- Calculus of Variations and Optimal Control; Optimization. --- Theoretical, Mathematical and Computational Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Global analysis. --- Global differential geometry. --- Mathematical optimization. --- Mathématiques --- Géométrie différentielle globale --- Optimisation mathématique --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Fiber spaces (Mathematics) --- Fibre spaces (Mathematics) --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential geometry. --- Calculus of variations. --- Physics. --- Gravitation. --- Algebraic topology --- Geometry, Differential --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical physics. --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Physical mathematics --- Isoperimetrical problems --- Variations, Calculus of --- Differential geometry --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Properties

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Differential invariants --- Invariants, Differential --- Continuous groups --- Differential invariants. --- Differential operators. --- Lie algebras. --- Lie groups. --- Geometry, Differential. --- Géométrie différentielle. --- Invariants différentiels. --- Géométrie différentielle. --- Invariants différentiels.

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514.75 --- Differential geometry in spaces with fundamental groups --- 514.75 Differential geometry in spaces with fundamental groups --- Geometry, Differential. --- Géometrie différentielle