ABSTRACT
Part of the utility of conformal mappings is that they can be used to transform a problem on a given domain V to another domain U (see also Sections 7.1.1). Often we take U to be a standard domain such as the disc
D = {z ∈ C : |z| < 1} (8.1) or the upper half-plane
U = {z ∈ C : Im z > 0}. (8.2) Particularly in the study of partial differential equations, it is important to have an explicit conformal mapping between the two domains.
