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 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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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 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:
has abstract
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 ...... 'equazioni di Eulero-Lagrange:
@it
In the calculus of variations, ...... f the Euler-Lagrange equation,
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La dérivée fonctionnelle est u ...... fonction fournie en argument.
@fr
В математике и теоретической ф ...... е они зачастую не различаются.
@ru
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
subject
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 ...... o in potenze di , denotato con
@it
In the calculus of variations, ...... f can be expressed as follows:
@en
La dérivée fonctionnelle est u ...... fonction fournie en argument.
@fr
В математике и теоретической ф ...... е они зачастую не различаются.
@ru
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。
@ja
label
Derivada funcional
@es
Derivata funzionale
@it
Dérivée fonctionnelle
@fr
Functional derivative
@en
Funktionalableitung
@de
Функциональная производная
@ru
汎函数微分
@ja
泛函导数
@zh