# Definition:Analysis

## Definition

**Analysis** is a branch of mathematics that studies continuous change.

It subsumes the fields of calculus, differential equations, the calculus of variations, power series, Fourier series, real analysis and complex analysis.

It is one of the main branches of mathematics, alongside geometry, number theory and algebra.

### Real Analysis

**Real analysis** is a branch of mathematics that studies real functions.

### Complex Analysis

**Complex analysis** is a branch of mathematics that studies complex functions.

## Also see

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

## Historical Note

The field of analysis was put into its modern shape by the work of Carl Friedrich Gauss, Niels Henrik Abel, Augustin Louis Cauchy and Karl Weierstrass.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**analysis** - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($1815$ – $1897$) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**analysis**