Calculus (Latin, calculus, a small stone used for counting) is a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series, and which constitutes a major part of modern university education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of equations.

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient. Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus".

More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, and lambda calculus. The ancient period introduced some of the ideas of integral calculus, but does not seem to have developed these ideas in a rigorous or systematic way.

Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1820 BC), in which an Egyptian successfully calculated the volume of a pyramidal frustum. From the school of Greek mathematics, Eudoxus (c.

408−355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes while Archimedes (c. 287−212 BC) developed this idea further, inventing heuristics which resemble integral calculus. The method of exhaustion was later used in China by Liu Hui in the 3rd century AD in order to find the area of a circle.

In the 5th century AD, Zu Chongzhi used what would later be called Cavalieri's principle to find the volume of a sphere.

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