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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 Exact differential equation ： ウィキペディア英語版 Exact differential equation In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering. ==Definition== Given a simply connected and open subset ''D'' of R2 and two functions ''I'' and ''J'' which are continuous on ''D'' then an implicit first-order ordinary differential equation of the form : $I(x,\; y)\backslash ,\; \backslash mathrmx\; +\; J(x,\; y)\backslash ,\; \backslash mathrmy\; =\; 0,\; \backslash ,\backslash !$ is called an exact differential equation if there exists a continuously differentiable function ''F'', called the potential function, so that :$\backslash frac\; =\; I$ and :$\backslash frac\; =\; J.$ The nomenclature of "exact differential equation" refers to the exact derivative of a function. For a function $F(x\_0,\; x\_1,...,x\_,x\_n)$, the exact or total derivative with respect to $x\_0$ is given by :$\backslash frac=\backslash frac+\backslash sum\_^\backslash frac\backslash frac.$ 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「Exact differential 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.