the branch of mathematics that deals with the problem of finding a curve or surface that maximizes or minimizes a given expression, usually with several restrictions placed on the desired curve.
calculus of variations Mathematical analysis of the maxima and minima of definite integrals, the integrands of which are functions of independent variables, dependent variables, and the derivatives of one or more dependent variables. Compare differential calculus, integral calculus.
branch of mathematics concerned with the problem of finding a function for which the value of a certain integral is either the largest or the smallest possible. Many problems of this kind are easy to state, but their solutions commonly involve difficult procedures of the differential calculus and differential equations.