= Euler–Lagrange equation
{wiki=Euler–Lagrange_equation}
The Euler–Lagrange equation is a fundamental equation in the calculus of variations, which is a field of mathematics that deals with optimizing functionals. A functional is typically an integral that depends on a function and its derivatives. In particular, the Euler–Lagrange equation is used to find the function (or functions) that will minimize (or maximize) a certain integral, usually representing some physical quantity, such as action in physics.
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