Calculus of Variations

Calculus of Variations is a branch of mathematics that focuses on finding the best possible function or path that minimizes or maximizes a certain quantity, often called a functional. Imagine wanting to find the most efficient route or the shape that best balances certain constraints. Instead of dealing with specific numbers, it deals with functions and their behaviors. This approach is used in fields like physics, engineering, and economics to determine optimal solutions, such as the shortest path, least energy, or maximum profit, by analyzing how small changes in the functions affect the overall outcome.