Calculus, Differential and Integral

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)

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