# Definition:Calculus/Differential

## Definition

**Differential calculus** is the subfield of calculus which is concerned with the study of the rates at which quantities change.

## Also see

- Results about
**differential calculus**can be found**here**.

## Historical Note

The technique used by Archimedes of Syracuse to find the Tangent to Archimedean Spiral at Point is often suggested as anticipating the **differential calculus**.

Pierre de Fermat had the basic idea of differential calculus in its modern form in about $1628$ or $1629$, but he did not publish these ideas until a decade or so later.

Much of the early work developing **differential calculus** was done by Isaac Newton.

His initial work on this was done during the years $1665$ to $1667$ when he was at home in Woolsthorpe.

He suggested that Isaac Barrow include his ideas in his *Lectiones Geometricae* of $1670$.

Newton referred to a function as a **fluent**, and its derivative as a **fluxion**.

At the same time that Newton was arranging his thesis, Gottfried Wilhelm von Leibniz was publishing many papers himself on the same subject.

H.T.H. Piaggio states that Leibniz first published his account of **differential calculus** in $1684$.

Newton, on the other hand, finally published his ideas in his *Philosophiae Naturalis Principia Mathematica* in $1687$.

## Linguistic Note

The term **differential calculus** is the Anglified version of the neo-Latin phrase **calculus differentialis**, coined by Gottfried Wilhelm von Leibniz.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**calculus** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**differential calculus** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**calculus** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**differential calculus** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World: Calculus