# differential calculus & integral calculus

**Calculus**, originally called **infinitesimal calculus** or “the calculus of infinitesimals”, is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves.

These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.

Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz.

Today, calculus has widespread uses in science, engineering, and economics.

In mathematics education, *calculus* denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits.