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- Functional_derivative abstract "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 L of a functional, if a function f is varied by adding to it another function δf that is arbitrarily small, and the resulting L is expanded in powers of δf, the coefficient of δf in the first order term is called the functional derivative.For example, consider the functionalwhere 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:The coefficient of δf(x), denoted as δJ/δf(x), is called the functional derivative of J with respect to f at the point x. For this example functional, the functional derivative is the left hand side of the Euler-Lagrange equation,".
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- Functional_derivative wikiPageExternalLink 0486414485.html.
- Functional_derivative wikiPageExternalLink functional%20derivative.pdf.
- Functional_derivative wikiPageExternalLink UWEETR-2008-0001.pdf.
- Functional_derivative wikiPageID "301504".
- Functional_derivative wikiPageRevisionID "605681046".
- Functional_derivative hasPhotoCollection Functional_derivative.
- Functional_derivative subject Category:Calculus_of_variations.
- Functional_derivative subject Category:Differential_calculus.
- Functional_derivative subject Category:Differential_operators.
- Functional_derivative subject Category:Topological_vector_spaces.
- Functional_derivative subject Category:Variational_analysis.
- Functional_derivative type Abstraction100002137.
- Functional_derivative type Attribute100024264.
- Functional_derivative type DifferentialOperators.
- Functional_derivative type Function113783816.
- Functional_derivative type MathematicalRelation113783581.
- Functional_derivative type Operator113786413.
- Functional_derivative type Relation100031921.
- Functional_derivative type Space100028651.
- Functional_derivative type TopologicalVectorSpaces.
- Functional_derivative comment "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.".
- Functional_derivative label "Derivada funcional".
- Functional_derivative label "Derivata funzionale".
- Functional_derivative label "Dérivée fonctionnelle".
- Functional_derivative label "Functional derivative".
- Functional_derivative label "Функциональная производная".
- Functional_derivative label "汎函数微分".
- Functional_derivative label "泛函导数".
- Functional_derivative sameAs Derivada_funcional.
- Functional_derivative sameAs Dérivée_fonctionnelle.
- Functional_derivative sameAs Derivata_funzionale.
- Functional_derivative sameAs 汎函数微分.
- Functional_derivative sameAs m.01rytv.
- Functional_derivative sameAs Q2621220.
- Functional_derivative sameAs Q2621220.
- Functional_derivative sameAs Functional_derivative.
- Functional_derivative wasDerivedFrom Functional_derivative?oldid=605681046.
- Functional_derivative isPrimaryTopicOf Functional_derivative.