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partial differential operator

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  • Differential operator — In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning… …   Wikipedia

  • Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

  • Pseudo-differential operator — In mathematical analysis a pseudo differential operator is an extension of the concept of differential operator. Pseudo differential operators are used extensively in the theory of partial differential equations and quantum field theory.… …   Wikipedia

  • differential operator — Math. a function, usually expressed as a polynomial, that indicates linear combinations of the derivatives of the expression on which it operates. * * * In mathematics, any combination of derivatives applied to a function. It takes the form of a… …   Universalium

  • Hyperbolic partial differential equation — In mathematics, a hyperbolic partial differential equation is usually a second order partial differential equation (PDE) of the form :A u {xx} + 2 B u {xy} + C u {yy} + D u x + E u y + F = 0 with: det egin{pmatrix} A B B C end{pmatrix} = A C B^2 …   Wikipedia

  • Symbol of a differential operator — In mathematics, differential operators have symbols, which are roughly speaking the algebraic part of the terms involving the most derivatives.Formal definitionLet E 1, E 2 be vector bundles over a closed manifold X , and suppose: P: C^infty(E 1) …   Wikipedia

  • List of partial differential equation topics — This is a list of partial differential equation topics, by Wikipedia page. Contents 1 General topics 2 Specific partial differential equations 3 Numerical methods for PDEs 4 …   Wikipedia

  • Numerical partial differential equations — is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). Numerical techniques for solving PDEs include the following: The finite difference method, in which functions are represented by… …   Wikipedia

  • Parabolic partial differential equation — A parabolic partial differential equation is a type of second order partial differential equation, describing a wide family of problems in science including heat diffusion and stock option pricing. These problems, also known as evolution problems …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Differential ideal — In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior… …   Wikipedia

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