calculus (mathematics)

Branch of mathematics which uses the concept of a derivative to analyse the way in which the values of a function vary. Calculus is probably the most widely used part of mathematics. Many real-life problems are analysed by expressing one quantity as a function of another – position of a moving object as a function of time, temperature of an object as a function of distance from a heat source, force on an object as a function of distance from the source of the force, and so on – and calculus is concerned with such functions.

There are several branches of calculus. Differential and integral calculus, both dealing with small quantities which during manipulation are made smaller and smaller, compose the infinitesimal calculus. Differential equations relate to the derivatives of a set of variables and may include the variables. Many give the mathematical models for physical phenomena such as simple harmonic motion. Differential equations are solved generally by integration, depending on their degree. If no analytical processes are available, integration can be performed numerically. Other branches of calculus include calculus of variations and calculus of errors.