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Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.

Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Elliptic. --- Green's Function. --- Parabolic. --- Partial Differential Equation.

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This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions  and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

Green's functions. --- Quantum theory. --- Green's functions --- Finite element method --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Physics --- Physical Sciences & Mathematics --- Materials Science --- Applied Mathematics --- Atomic Physics --- Finite element method. --- Engineering. --- Computer mathematics. --- Continuum mechanics. --- Structural mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Computational Mathematics and Numerical Analysis. --- Structural Mechanics. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis