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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 Functional derivative ： ウィキペディア英語版 Functional derivative In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional to a change in a function that the functional depends on. In the calculus of variations, functionals are usually expressed in terms of an integral of functions, their arguments, and their derivatives. In an integrand of a functional, if a function is varied by adding to it another function that is arbitrarily small, and the resulting integrand is expanded in powers of , the coefficient of in the first order term is called the functional derivative. For example, consider the functional :$J()\; =\; \backslash int\; \backslash limits\_a^b\; L(\backslash ,\; x,\; f(x),\; f\; \backslash ,\; \text{'}(x)\; \backslash ,)\; \backslash ,\; dx\; \backslash \; ,$ where . If is varied by adding to it a function , and the resulting integrand is expanded in powers of , then the change in the value of to first order in can be expressed as follows:〔〔According to , this notation is customary in physical literature.〕 :$\backslash delta\; J\; =\; \backslash int\_a^b\; \backslash frac\; \backslash ,\; dx\; \backslash ,\; .$ The coefficient of , denoted as , is called the functional derivative of with respect to at the point .〔.〕 For this example functional, the functional derivative is the left hand side of the Euler-Lagrange equation, :$\backslash frac\; =\; \backslash frac\; -\backslash frac\; \backslash frac\; \backslash ,\; .$ ==Definition== In this section, the functional derivative is defined. Then the functional differential is defined in terms of the functional derivative. 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「Functional derivative」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.