or variational calculus, n. the extension of calculus concerned with the maxima or minima of definite integrals, and hence with finding functions that maximize or minimize a given function of those functions; this is analogous to the differential calculus, in which values of a function are found that maximize or minimize a given function of those values. In the simplest form, one attempts to minimizeover a class of piece-wise smooth arcs, the values at the endpoints of which are fixed or that satisfy other relevant constraints. For example, a typical problem seeks the shortest distance between two points on some surface. The calculus of variations was first developed by Euler in 1744, although both Newton and Jakob Bernoulli had solved problems involving variational methods; it has since become one of the major branches of analysis. See also control theory, Euler-Lagrange equations, optimization theory, brachistochrone problem.