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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Monge equation ： ウィキペディア英語版 Monge equation In the mathematical theory of partial differential equations, a Monge equation, named after Gaspard Monge, is a first-order partial differential equation for an unknown function ''u'' in the independent variables ''x''1,...,''x''''n'' :$F\backslash left(u,x\_1,x\_2,\backslash dots,x\_n,\backslash frac,\backslash dots,\backslash frac\backslash right)=0$ that is a polynomial in the partial derivatives of ''u''. Any Monge equation has a Monge cone. Classically, putting ''u'' = ''x''0, a Monge equation of degree ''k'' is written in the form :$\backslash sum\_\; P\_(x\_0,x\_1,\backslash dots,x\_k)\; \backslash ,\; dx\_0^\; \backslash ,\; dx\_1^\; \backslash cdots\; dx\_n^=0$ and expresses a relation between the differentials ''dx''''k''. The Monge cone at a given point (''x''0, ..., ''x''''n'') is the zero locus of the equation in the tangent space at the point. The Monge equation is unrelated to the (second-order) Monge–Ampère equation. 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「Monge 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.