Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on an infinite dimensional spaces.

The calculus of variations seeks to minimize or maximize an entire functional's worth of parameters instead of changing just one parameter. It achieves this by applying standard calculus techniques to the integral of a functional, thereby reducing $\mathbb R \to \mathbb R$ to just one parameter $\in\mathbb R$.

In symbols one considers $\max \int f(x) \ker(x) dx$ rather than $\max f(s)$.

Two famous applications of the calculus of variations are in regression analysis and deriving the catenary shape of a rope hanging between two poles.

history | excerpt history