## Quick Reference

A series of mathematical techniques developed independently by Isaac Newton and Gottfried Leibniz (1646–1716). **Differential calculus** treats a continuously varying quantity as if it consisted of an infinitely large number of infinitely small changes. For example, the velocity *v* of a body at a particular instant can be regarded as the infinitesimal distance, written d*s*, that it travels in the vanishingly small time interval, d*t*; the instantaneous velocity *v* is then d*s*/d*t*, which is called the **derivative** of *s* with respect to *t*. If *s* is a known function of *t*, *v* at any instant can be calculated by the process of differentiation. The differential calculus is a powerful technique for solving many problems concerned with rate processes, maxima and minima, and similar problems.

**Integral calculus** is the opposite technique. For example, if the velocity of a body is a known function of time, the infinitesimal distance d*s* travelled in the brief instant d*t* is given by d*s* = *v*d*t*. The measurable distance *s* travelled between two instants *t*_{1} and *t*_{2} can then be found by a process of summation, called integration, i.e.*s*=∫*t*2*t*1*v*d*t*The technique is used for finding areas under curves and volumes and other problems involving the summation of infinitesimals.

**From:**
calculus
in
A Dictionary of Physics »

*Subjects:*
Physics.