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Mathematica already knows quite a lot about functional derivatives. In particular, you can do variational derivatives. That is, you have to give it the ...

that is an integral over the function f with a fixed weight function w(x). ... functional derivative corresponds to the second order total differential,.

I have a question about functional derivatives. I know there was a ... I am not experienced enough in Mathematica nor in xAct to do any of those two steps.

05.06.2020 · Volterra derivative. One of the first concepts of a derivative in an infinite-dimensional space. Let $ I ( y) $ be some functional of a continuous function of one variable $ y ( x) $; let $ x _ {0} $ be some interior point of the segment $ [ x _ {1} , x _ {2} ] $; let $ y _ {1} ( x) = y _ {0} ( x) + \delta y ( x) $, where the variation $ \delta y ( x) $ is different from zero in a small ...

returns the variational derivative of the integral with respect to u[x], where the integrand f is a function of u, its derivatives, and x. VariationalD[f,u[x,y ...

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 a…

In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a Functional ...

The object f' in Mathematica is the result of applying the differentiation functional to the function f. The full form of f' is in fact Derivative[1][f].

You can think of Derivative as a functional operator which acts on functions to give derivative functions. Derivative is generated when you apply D to functions whose derivatives the Wolfram Language does not know. The Wolfram Language attempts to convert Derivative [n] [f] and so on to pure functions.

17.12.2021 · Functional Derivative. The functional derivative is a generalization of the usual derivative that arises in the calculus of variations . In a functional derivative, instead of differentiating a function with respect to a variable, one differentiates a functional with respect to a function. The definition for the univariate case is.

Mathematica already knows quite a lot about functional derivatives. In particular, you can do variational derivatives.That is, you have to give it the functional and the function (I would strongly suspect that your problem can be written so as to use the VariationalD function). To get started, have a look at the tutorial for the Variational Methods package.