**Calculus, Differential and Integral**, in mathematics, is the method
by which we discuss the properties of continuously varying quantities.
The nature of the method and the necessity for it may be indicated by a
simple example; *e. g*. the motion of a train in a track, or the motion
of a planet in its orbit. If we know the successive positions of the
moving body at successive short intervals of time, the rules of the
differential calculus enable us to calculate the speed, the change of
speed, the change of direction of motion (*i.e*. the curvature of the
path), and the effective force acting on the body. Conversely, given the
force at every point, and the initial position and velocity, the rules of
the integral calculus assist us in calculating the position and velocity
of the body at any future time. Expressed somewhat crudely, the
differential calculus has to do with the *differentials* (increments or
decrements) of varying quantities; while the integral calculus is a
process of summation or *integration* of these differentials.

Definition taken from
*The Nuttall Encyclopædia*,
edited by the Reverend James Wood (1907)

Calculus, Differential and Integral