THEORY OF FLUXIONS

The origin of the integral Calculus goes back to the early period of development of Mathematics .The great development of method of exhaustion in the early period was obtained in the worksof Eudoxus (440 B.C) and Archimedes(330 B.C).The theory of calculus began in the 17th century .In 1965,Newton began his work on the Calculus described by him as the theory of fluxions and used his theory in finding the tangent and radius of curvature at any point on a curve. Newton introduced the basic notion of inverse function called td by he antiderivative or the inverse method of tangents. The theory of calculus began in the 17th century.In 1665,Newton began his work on the calculus describe by him as the theory of fluxions and used his theory in finding the tangent and radius of curvature at any point on a curve.

The Theory of Fluxions is an early form of calculus developed by Sir Isaac Newton in the late 17th century. The term “fluxions” refers to what we now call “derivatives” or rates of change. Newton introduced this theory as a way to describe the motion of objects and how quantities change over time.

Concepts of the Theory of Fluxions:

Fluxion and Fluent:

• Fluent: This is a quantity that changes over time. For example, the position of a moving object or the amount of water flowing into a container.
• Fluxion: This is the rate of change of the fluent, analogous to what we now call the derivative. It represents how quickly the fluent changes at any given moment.

Instantaneous Rate of Change:

• Newton used the concept of fluxions to calculate the instantaneous rate of change, which is crucial in understanding the behavior of moving objects, among other things. For example, if a fluent represents the distance traveled by an object, its fluxion would represent the object’s velocity.

Geometrical Interpretation:

• Newton often described fluxions in geometric terms, where the fluxion of a curve represents the slope of the tangent line at any point on the curve.

Application to Physical Problems:

• The theory was applied to solve problems in physics, especially in mechanics and motion, such as calculating the area under curves, finding the center of mass, and understanding the dynamics of planetary motion.

Historical Context:

Newton developed the theory of fluxions around the same time that German mathematician Gottfried Wilhelm Leibniz was developing his own version of calculus, which he called differential calculus. While Newton’s approach was more geometric and rooted in the physical interpretation of motion, Leibniz’s method was more algebraic and analytical. Despite the differences, both approaches eventually converged into the modern form of calculus we use today.