👉 Calculus of Variations (CRV), also known as the calculus of optimal curves, is a field that deals with finding functions that optimize certain integrals, often representing physical quantities like energy or work. It involves identifying functions that extremize (maximize or minimize) functionals, which are mappings from a space of functions to the real numbers. These functionals typically depend on both the function itself and its derivatives. CRV has applications in physics, engineering, and economics, where it helps solve problems like finding the path of least action in mechanics or determining optimal shapes for minimal material usage. The core techniques include setting up the Euler-Lagrange equations, which provide necessary conditions for a function to be an extremum of the given functional.
