ABSTRACT
The central problem in the theory of conformal mapping is to determine a function f which maps a given region D ⊂ ℂ conformally onto another region G ⊂ ℂ. The function f does not always exist, and it is not always uniquely determined. The Riemann mapping theorem (§2.6, Theorem 2.15) guarantees the existence and uniqueness of a conformal map of D onto the unit disk U under certain specific conditions. First, we will introduce definitions of certain curves, and some elementary mappings, before we will study linear and bilinear transformations.
