Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems; it consists of differential calculus and integral calculus, respectively used for the techniques of differentiation and integration. While some of the ideas of calculus had been developed earlier in Egypt, Greece, China, India, Iraq, Persia, and Japan, the modern use of infinitesimal calculus began in Europe, during the 17th century.

It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s: Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today. Further, John Wallis exploited an infinitesimal he denoted (1/infinity) in area calculations, preparing the ground for integral calculus. They drew on the work of such mathematicians as Isaac Barrow and René Descartes. Both Newton and Leibniz provided were the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series.

Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change, and many times in studying a problem we know one value and are trying to find the other.

In computer science, calculus is applied in various disciplines. Among others robotics, machine learning, programming and network analysis, analysis of queuing theory and analysis of algorithms commonly require use of calculus.