翻訳と辞書 Words near each other ・ Poisson kernel ・ Poisson limit theorem ・ Poisson manifold ・ Poisson number ・ Poisson point process ・ Poisson random measure ・ Poisson regression ・ Poisson ring ・ Poisson sampling ・ Poisson scatter theorem ・ Poisson summation formula ・ Poisson superalgebra ・ Poisson supermanifold ・ Poisson Volant ・ Poisson wavelet ・ Poisson's equation ・ Poisson's ratio ・ Poisson, Saône-et-Loire ・ Poissonia ・ Poissonnière (Paris Métro) ・ Poissons ・ Poisson–Boltzmann equation ・ Poisson–Lie group ・ Poissy ・ Poisvilliers ・ Poisy ・ Poitea ・ Poitea carinalis ・ Poitevin ・ Poitevin (dog) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poisson's equation ： ウィキペディア英語版 Poisson's equation In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics. It is used, for instance, to describe the potential energy field caused by a given charge or mass density distribution. The equation is named after the French mathematician, geometer, and physicist Siméon Denis Poisson. ==Statement of the equation== Poisson's equation is :$\backslash Delta\backslash varphi=f$ where $\backslash Delta$ is the Laplace operator, and ''f'' and ''φ'' are real or complex-valued functions on a manifold. Usually, ''f'' is given and ''φ'' is sought. When the manifold is Euclidean space, the Laplace operator is often denoted as ∇2 and so Poisson's equation is frequently written as :$\backslash nabla^2\; \backslash varphi\; =\; f.$ In three-dimensional Cartesian coordinates, it takes the form :$$ \left( \frac + \frac + \frac \right)\varphi(x,y,z) = f(x,y,z). When $f\; =0$ we retrieve Laplace's equation. Poisson's equation may be solved using a Green's function; a general exposition of the Green's function for Poisson's equation is given in the article on the screened Poisson equation. There are various methods for numerical solution. The relaxation method, an iterative algorithm, is one example. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poisson's equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.