ABSTRACT
In this chapter the concept of conformal mapping is introduced and full plane conformal mappings are developed. With the use of conformal mapping, a known solution can be used to generate solutions for new geometries. A section on boundary condition modifications due to conformal mapping is included. The Möbius transformation is the first full plane conformal mapping developed. It is developed by first considering the special cases of translation, magnification, rotation, and complex inversion. Since most of the interesting properties of the Mobius transformation stem from inversion, a detailed treatment of inversion is given. The logarithm transformation is also developed in this chapter. When performing a full plane transformation, how to transform charge located at infinity must be considered. A detailed discussion on transforming charge at infinity is given.
