or infinitesimal calculus, n. 1. the branch of mathematics, developed largely by Newton and, independently, by Leibniz, that was originally conceived in terms of the effects on a function of an infinitesimal change in the value of the independent variable, and is now understood in terms of limits of real functions. The differential calculus concerns the rate of change of the dependent variable, and so the slope of a curve; the integral calculus extends the notion of the sum of a finite number of discrete values of a function to a continuous function, and allows one to obtain the area under a curve. See also definite integral, indefinite integral, differential. 2. (Logic) an uninterpreted formal system, consisting of a vocabulary of primitive terms, and sets of formation rules and transformation rules. Compare formal language. 3. any formal theory or set of rules for calculation. In this sense one speaks of, for example, functional calculus, predicate calculus, and lambda calculus.