# Definition:Calculus/Differential

## Definition

**Differential calculus** is a 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.

## Linguistic Note

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

## 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.

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

## 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 - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**differential calculus** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World: Calculus