 Calculus of variations

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 $\mathbb{R}$.

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.