Overview
The calculus of variations was developed in order to find the maximum or minimum of functionals. (see below)
Functional
A functional is a function where the input to the function is a function itself. The canonical example of a functional is the integral of a function.
{% F[y(x)] = \int_a^b y(x)dx %}
{% F[y(x)] = \int_a^b L(y(x), y'(x), x) dx %}
{% \delta F[y] = F[y + \delta y] - F[y] %}
{% \delta F[y] = %}