ABSTRACT
As mentioned earlier, in conformal mapping we always try to determine a function f which maps a given region D ⊂ ℂ conformally onto another region G ⊂ ℂ. However such a function f does not always exist, and it is not always uniquely determined. Recall that the Riemann mapping theorem guarantees the existence and uniqueness of a conformal map of D onto the unit disk U under certain specific conditions. In this chapter the Schwarz-Christoffel transformations are presented. There are three types of equivalent definitions for this transformation, and they all lead to integral equations which are then solved as boundary value problems.
