Conformal Mapping of the Unit Disk
Conformal Mapping of the Unit Disk
The famous Riemann mapping theorem states that any simply connected domain in the complex plane (other than the whole plane itself) is conformally equivalent to the unit disk. However, finding an explicit conformal map for a given domain can be a tedious task. This Demonstration plots the image of the unit disk under various conformal maps , normalized so that and . Each plot shows the images of concentric circles around the origin and radial lines emanating from the origin.
f
f(0)=0
f'(0)=1