What is mean by Lie group method?
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log into www.wikipedia.org and search for lie group...there is a detailed description and all the formulas as well and its free.
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I'm going to assume that you want a proof of Lagranges theorem in group theory which states that the number of elements of a subgroup divides the number of elements of the whole group. \n\nFirst, if G is a group and H is a subgroup, a collection gH={gh:h in H} is called a coset. It turns out the everything in the group is in exactly one coset and that every coset has the same number of elements as H does. If we write [G:H] for the number of cosets, we then get that the number of elements of G is [G:H] times the number of elements of H, hence the result.
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In mathematics, a symplectic manifold is a smooth manifold M equipped with a closed, nondegenerate, 2-form ω called the symplectic form. The study of symplectic manifolds is called symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds, e.g. in the Hamiltonian formulation of classical mechanics, which provides one of the major motivations for the field: The set of all possible configurations of a system is modelled as a manifold, and this manifold's cotangent bundle describes the phase space of the system.\n\nAny real-valued differentiable function H on a symplectic manifold can serve as an energy function or Hamiltonian. Associated to any Hamiltonian is a Hamiltonian vector field; the integral curves of the Hamiltonian vector field are solutions to the Hamilton-Jacobi equations. The Hamiltonian vector field defines a flow on the symplectic manifold, called a Hamiltonian flow or symplectomorphism. By Liouville's theorem, Hamiltonian flows preserve the volume form on the phase space.
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i am not sure with who came up with the concept, but this might be usefull \n\nhttp://en.wikipedia.org/wiki/Probability_Density_Function
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Take class in Numerical Methods, \n\nUniversity of Maryland offers these Graduate Level courses.\nNumerical Solution of Ordinary Differential Equations \nNumerical Methods in Partial Differential Equations
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DO YOU REFER TO CLASSICAL MECHANICS?\n\nIn classical Mechanics it may be useful to study changes from some generalized coordinates q_i and associated gen. momenta p_i to some other general coordinates Q_i and associated gen. momenta P_i. Most textbooks define a Transformation \n\n(q,p)->(Q(q,p,t),P(q,p,t)) (1) (where q is the "vector" of all q_i, etc.) as\n\nCanonical in the extended sense if and only if:\n\nFor any function H(p,q,t) fulfilling\n\ndq_i/dt=dH/dp_i and dp_i/dt= -dH/dq_i (partial derivatives on the right side)\n\nthere exists a Hamilton-function K(Q,P,t) full filling:\n\ndQ_i/dt=dK/dP_i and dP_i/dt= -dK/dQ_i (partial derivatives on the right side)\n\nIn other words: For any Hamiltonfct. of the p,q - Space there must exist a Hamiltonfct. of the P,Q- Space, (because Hamiltonfuncions of Systems  fulfill the relations above). Then and only then the transformation (1) is called canonical in ext. sense, because the form of Hamilton's equations is conserved.\n\nABOUT THE OTHER TRANSF. I DON'T KNOW ANYTHING. SEE THE LINK BELOW.
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It's called spectral analysis and you do this type of analysis on an operator on a Hilbert space. It is a generalization of the study of eigenvalues and eigenvectors of a matrix. If you are at a level where this question could come up, you should do the work yourself.
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http://mathworld.wolfram.com/HarmonicSeries.html
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you have to use the couchy schuartz method\nim nit sure on the spelling \nbasicly you take one vector (V1) and use it then you take the second vecter (U1) minous vi times(V1 interproduct U1)/(magnatude V1^2) and use that total as V2 then you do a simular thing for the third and fourth vector and up if you have them by subtrating V1<Ua,V1>/(mag V1)^2 plus V2<Ua,V2>/(mag V2)^2 .... till you have done that for each vector \nin other words every vector will have a term for all of the new previous vectors subtracted from it then finaly you take all the new vectors and devide them by their magnatude to get unit vectors and they will then all be orthOGANOL UNIT VECTORS
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it is a method to calculate atomic and molecular structure from first principles. the basis is the Schrodinger wave equation. without use of a computer it is a hopeless task.
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A wallpaper group (or plane crystallographic group) is a mathematical concept to classify repetitive designs on two-dimensional surfaces, such as walls, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The mathematical study of such patterns reveals that exactly 17 different types of patterns can occur.\n\nWallpaper groups are related to the simpler frieze groups, and to the more complex three-dimensional crystallographic groups (also called space groups).
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I hope this helps. here are a couple links to message boards discussing the Linden Method. the 3rd is a link to the Linden Method's website.
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finite element method\nit is used for systems identification , etc
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Formula for what?\nIn other words what is the subject or what is the problem?\nbelow are a few possibilities.
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What is the standard way to describe motion ?
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The idea is that the y_n form an orthonormal basis so every function can be expanded as a series of the form \nsum a_n y_n.\n\nHow is this known? Typically, the inverse operator of L can be shown to be a compact operator and the general theory of compact operators can be invoked. Some care may be needed with the convergence properties of the series you obtain. Only mean-square convergence (L_2) is guaranteed. \n\nIn any case, the fact that the y_n are eigenfunctions for L and that L is linear makes the determination of the A_n from the B_n much easier. The convergence details can either be ignored or dealt with separately.
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G=uys\nF=***\nE=verthing