Definition

1. Noun:
   • The part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential. This is the historical term used by Sir Isaac Newton for what is now commonly called differential calculus.

Usage

• The term method of fluxions is primarily used in historical or academic contexts to refer to Newton's original formulation of calculus. It describes the mathematical framework for analyzing rates of change and slopes of curves.

Examples

• Noun:
  • Isaac Newton developed his method of fluxions in the late 17th century.
  • Studying the history of mathematics, we learn that the method of fluxions was Newton's term for differential calculus.

Advanced Usage

• Historical Context: The term is used to distinguish Newton's approach and terminology from that of his contemporary, Gottfried Wilhelm Leibniz, who developed the notation and concepts more familiar in modern calculus (e.g., ).
  • The priority dispute between Newton and Leibniz centered on the invention of calculus, known as the method of fluxions in England.

Variants and Related Words

• Fluxion (n): In Newton's system, a fluxion is the instantaneous rate of change, or derivative, of a continuously changing quantity (a "fluent").
  • Newton considered a curve as generated by the motion of a point, with its coordinates as fluents and their velocities as fluxions.
• Differential Calculus (n): The modern term for the branch of calculus encompassing the concepts Newton called the method of fluxions.
• Infinitesimal Calculus (n): A broader historical term encompassing both differential and integral calculus.

Synonyms

• Differential Calculus: The contemporary synonym.
• Calculus of Fluxions: A less common, synonymous historical phrase.

Related Phrases

• The Calculus Controversy: A historical phrase referring to the dispute over whether Newton (with his method of fluxions) or Leibniz invented calculus first.

Noun

1. the part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential