ABSTRACT
This chapter discusses conformal mappings on a given domain. Particularly in the study of partial differential equations, it is important to have an explicit conformal mapping between two domains. The chapter provides a useful and explicit compendium of conformal mappings. Steady-state heat distribution on a lens-shaped region is discussed along with incompressible fluid flow around a post. The chapter provides a set of exercises based on conformal mapping of the region of the flow to the upper halfplane. In practical applications, computer techniques for calculating conformal mappings have been shown to be decisive. A conformal self-map of the unit disc is completely determined once the images of three boundary points are known.
