Variational principles

Variational principles are mathematical concepts used in various fields such as physics, calculus of variations, and optimization. They involve finding extrema (maximum or minimum values) of functional quantities, which are mappings from a space of functions to the real numbers. These principles often rely on the idea that the optimal solution can be found by analyzing the behavior of these functionals under certain conditions. ### Key Concepts: 1. **Functional**: A functional is a rule that assigns a real number to a function.