Definition:Analysis

Definition

Analysis is a branch of mathematics that studies continuous change, and the use of limits.

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): analysis
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): analysis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): analysis
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): analysis
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): analysis