Question

. In his development of the calculus, Newton used the idea of the fluent and the fluxion. Describe what these are and how they are related to calculus.

Answer 1

Fluent is a time varrying quantity or function. The Fluxion of the Fluent is its instantaneous rate of change or gradient at a given point. Fluxions were introduced by Isaac Newton to describe his form of a time derivative . Fluxions and Fluent made up Newton's early calculus.

Relation of Fluxions and Fluents to the Calculus :

For example ,

If the Fluent y is defined as y = t² , where t is the time then Fluxion ( derivative) at t =2 is

y'= y/t = [(2+o)²-2²]÷[(2+o)-2]

= [4+4o+o²-4]÷[2+o-2]

= 4+o

Here o is infinitely small amount of time and according to Newton , we can ignor it because of its infinite smallness. He justified the use of o as non zero quantity by stating that Fluxions were a consequence of movement by an object.