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Qué (quién) es variational derivative - definición

CONCEPT IN CALCULUS OF VARIATION

Functional derivative(physics); Variational derivative; Functional deferentiation; Functional derivative operator

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.

https://en.wikipedia.org/wiki/Functional_derivative

Underlying

FINANCIAL INSTRUMENT WHOSE VALUE IS BASED ON ONE OR MORE UNDERLYING ASSETS

Underlying instrument; Underlying; Derivative securities; Derivatives analysis; Financial derivative; Derivatives trading; Finanical derivative; Derivative (security); Underlying instruments; Derivative products; Derivative contract; Derivative security; Derivatives pricing; Financial derivatives; Macro derivative; Underlying asset; Insurance derivatives; Financial Derivatives; Financial Derivative; Derivative (business); Macro derivatives; Embedded derivative; Derivative financial product

·adj Lying under or beneath; hence, fundamental; as, the underlying strata of a locality; underlying principles.

Derivative (finance)

FINANCIAL INSTRUMENT WHOSE VALUE IS BASED ON ONE OR MORE UNDERLYING ASSETS

Underlying instrument; Underlying; Derivative securities; Derivatives analysis; Financial derivative; Derivatives trading; Finanical derivative; Derivative (security); Underlying instruments; Derivative products; Derivative contract; Derivative security; Derivatives pricing; Financial derivatives; Macro derivative; Underlying asset; Insurance derivatives; Financial Derivatives; Financial Derivative; Derivative (business); Macro derivatives; Embedded derivative; Derivative financial product

In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying".

https://en.wikipedia.org/wiki/Derivative_(finance)

Wikipedia

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.

In the calculus of variations, functionals are usually expressed in terms of an integral of functions, their arguments, and their derivatives. In an integral L of a functional, if a function f is varied by adding to it another function δf that is arbitrarily small, and the resulting integrand is expanded in powers of δf, the coefficient of δf in the first order term is called the functional derivative.

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: where the variation in the derivative, δf ′ was rewritten as the derivative of the variation (δf) ′, and integration by parts was used.

https://en.wikipedia.org/wiki/Functional derivative