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425 pages, 22Mb, February 17, 2010,

Abstract:

Hamiltonian Mechanics and Symplectic Geometry: Classical Mechanics and Geometry, vol.1-Introduction; =====================Copyright@2010 by Bci2.=================== CONTENTS: Classical mechanics Dynamical system (definition) Equations of motion Canonical transformations Generalized coordinates William Rowan Hamilton,Sir Hamilton's principle Hamiltonian mechanics Hamiltonian vector field Hamilton--Jacobi equations Lie bracket Euler--Lagrange equations Lagrangian mechanics Legendre transformations Legendre--Fenchel transformations Poisson bracket Poisson algebra Poisson manifold Vector space Differential Geometry and Molecular Mechanics Differential geometry Symplectic vector space Symplectic space Symplectic manifold Symplectic form Symplectic group Symplectic structure Symplectic matrix Symplectic representation Symplectic sum Symplectic geometry Symplectomorphisms Algebraic geometry Category theory Molecular Dynamics and Integrators Dynamical system Symplectic integrator Molecular dynamics Molecular modelling Relativity Theory Einstein--“Hilbert action General relativity Einstein field equations Solutions of the Einstein field equations Spherical coordinate system Maxwell's equations in curved spacetime Riemannian manifolds Pseudo--Riemannian manifolds Quantum Theory in Feynman's Formulation and Hamiltonian formalism inadequacies Quantum mechanics Commutators Canonical quantization Moyal bracket Path integral formulation in Quantum Theory Dirac bracket Quantum field theory Jacobi identity Lie algebra Lie groups Lie theory Lie groupoids Lie algebroids R-algebroid Algebraic topology Double groupoids Higher dimensional algebra Poisson superalgebra Quantum Symmetry and TQFT Symmetry Chiral symmetry Loop quantum cosmology Quantum cohomology Topological quantum field theory Standard Model Quantum anomalies Supersymmetry --SUSY Minimal Supersymmetric Standard Model -MSSM Statistical Physics and Quantum Theory Exchange symmetry Statistical physics Statistical mechanics Statistical field theory Ergodic theory

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Open access, GFDL: http://en.wikipedia.org/wiki/User:Bci2/Books/HamiltonianMechanicsAndSymplecticGeometry Copyright@2010 bci1 and Bci2, Edited and originated by Bci2- with several contributors listed before the License Statement by bci1 and Bci2: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version ;published by the Free Software Foundation, with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in ;the section entitled "GNU Free Documentation License". Edited by Bci2, with all contributors listed before the License statement.

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