MathWorld classroom

Topics in a Complex Analysis Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

Analytic Continuation Analytic continuation is a way of extending the domain over which a complex function is defined.
Analytic Function An analytic function is a complex function that is complex differentiable at every point in a region.
Complex Analysis Complex analysis is the study of complex functions and their derivatives, manipulation, and other properties.
Conformal Mapping A conformal mapping is a transformation in the complex plane that preserves local angles.
Pole In comlpex analysis, a pole is a singularity of a complex function.
Riemann Sphere The Riemann sphere is a name given to the complex plane together with a point at infinity, which has the topology of a sphere.
Riemann Surface A Riemann surface is a surface that represents the domain of a multiple-valued complex function.
Singularity In mathematics, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points.