variational calculus

The calculus of variations is a generalization of the usual calculus that seeks to find the path, curve, surface, etc., for which a given function has a stationary value (which, in physical problems, is usually a minimum or maximum).

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a stationary value (which, in physical problems, is usually a minimum or maximum). Mathematically, this involves finding stationary values of integrals of the form I = integral_b^a f(y, y^., x) d x. I has an extremum only if the Euler-Lagrange differential equation is satisfied, i.e., if (df)/(dy) - d/(d x)((df)/(dy^.)) = 0.

Beltrami identity | Bolza problem | brachistochrone problem | catenary | envelope theorem | Euler-Lagrange differential equation | isoperimetric problem | isovolume problem | Lindelöf's theorem | line line picking | Morse theory | Plateau's problem | roulette | skew quadrilateral | sphere with tunnel | surface of revolution | unduloid | Weierstrass-Erdman corner condition

college level