 Calculus of variations

Calculus of variations is a field of mathematical analysis that deals with optimizing functionals, which are mappings from a set of functions to the real numbers. In simpler terms, it involves finding a function that minimizes or maximizes a specific quantity defined as an integral (or sometimes an infinite series) of a function and its derivatives. ### Key Concepts: 1. **Functional**: A functional is typically an integral that represents some physical quantity, such as energy or action.

Calculus of variations is the field that searches for maxima and minima of Functionals, rather than the more elementary case of functions from $\mathbb{R}$ to $\mathbb{R}$.