Functional derivative
In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a Functional (a functional in this sense is a function that acts on functions) to a change in a function on which the functional depends. For example, consider the functional where f ′(x) ≡ df/dx. If f is varied by adding to it a function δf, and the resulting integrand L(x, f +δf, f '+δf ′) is expanded in powers of δf, then the change in the value of J to first order in δf can be expressed as follows:
Action (physics)Analytical mechanicsAsymptotic safety in quantum gravityBogoliubov causality conditionBretherton equationCalculus of variationsCanonical commutation relationDeWitt notationDelta (letter)Density functional theoryDerrick's theoremEffective actionEuler–Lagrange equationFinsler manifoldFirst variationFréchet derivativeFunctional (mathematics)Functional calculusFunctional deferentiationFunctional derivativeFunctional derivative(physics)Functional derivative operatorFundamental lemma of calculus of variationsGENERIC formalismGateaux derivativeGeneralizations of the derivativeGlossary of mathematical symbolsHamiltonian field theoryHamilton–Jacobi–Einstein equationIndex of physics articles (F)Iterated functionKarhunen–Loève theoremLagrangian (field theory)Lagrangian mechanicsList of variational topicsLoop algebraMaximum entropy probability distributionNehari manifoldNoether's second theoremNoether's theorem
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Functional derivative
In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a Functional (a functional in this sense is a function that acts on functions) to a change in a function on which the functional depends. For example, consider the functional where f ′(x) ≡ df/dx. If f is varied by adding to it a function δf, and the resulting integrand L(x, f +δf, f '+δf ′) is expanded in powers of δf, then the change in the value of J to first order in δf can be expressed as follows:
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Die Funktionalableitung ist ei ...... und der Feldtheorie verwendet.
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En las matemática y la física ...... al con respecto a una función.
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In matematica e in fisica, la ...... 'equazioni di Eulero-Lagrange:
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In the calculus of variations, ...... integration by parts was used.
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La dérivée fonctionnelle est u ...... tiabilité d'une fonctionnelle.
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В математике и теоретической ф ...... е они зачастую не различаются.
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Функціональна похідна є узагал ...... і вони часто не розрізняються.
@uk
在数学和理论物理中,泛函导数是方向导数的推广。后者对一个有限 ...... 微积分中导数的扩展。数学里专门研究泛函导数的分支是泛函分析。
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数学および理論物理学における汎函数微分(はんかんすうびぶん、 ...... いる。汎函数微分の数学的に厳密な取扱いは函数解析学に属する。
@ja
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title
Functional derivative
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comment
Die Funktionalableitung ist ei ...... und der Feldtheorie verwendet.
@de
En las matemática y la física ...... al con respecto a una función.
@es
In matematica e in fisica, la ...... simile alla derivata parziale.
@it
In the calculus of variations, ...... f can be expressed as follows:
@en
La dérivée fonctionnelle est u ...... r principe de moindre action).
@fr
В математике и теоретической ф ...... е они зачастую не различаются.
@ru
Функціональна похідна є узагал ...... і вони часто не розрізняються.
@uk
在数学和理论物理中,泛函导数是方向导数的推广。后者对一个有限 ...... 微积分中导数的扩展。数学里专门研究泛函导数的分支是泛函分析。
@zh
数学および理論物理学における汎函数微分(はんかんすうびぶん、 ...... いる。汎函数微分の数学的に厳密な取扱いは函数解析学に属する。
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label
Derivada funcional
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Derivata funzionale
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Dérivée fonctionnelle
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Functional derivative
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Funktionalableitung
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Функциональная производная
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Функціональна похідна
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汎函数微分
@ja
泛函导数
@zh