# Definition:Calculus

## Definition

**Calculus** is the branch of mathematics which studies change.

### Differential Calculus

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

### Integral Calculus

**Integral calculus** is a subfield of calculus which is concerned with the study of the rates at which quantities accumulate.

Equivalently, given the rate of change of a quantity **integral calculus** provides techniques of providing the quantity itself.

The equivalence of the two uses are demonstrated in the Fundamental Theorem of Calculus.

The technique is also frequently used for the purpose of calculating areas and volumes of curved geometric figures.

## Also known as

Archaic and historical sources may refer to **calculus** as **infinitesimal calculus**.

## Also see

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

## Historical Note

**Calculus** has been described as:

*the most powerful instrument ever invented for the mathematical exploration of the physical universe.*- -- 1937: Eric Temple Bell:
*Men of Mathematics*

- -- 1937: Eric Temple Bell:

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**calculus** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**calculus** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World: Calculus