On Conformal Mappings and Vector Fields

Abstract

We seek to extend the applicability of the tools of complex analysis that have been developed to deal with problems in two-dimensional harmonic field theory. In order to ease the reader who has only a basic understanding of complex analysis into a working knowledge of its relevant applications to field theory, this material is introduced through the use of vector fields as common ground. Opportunities for using the mathematical tools being developed to solve physical problems are also highlighted by examples in order to aid comprehension and foster intuition. Established techniques used in solving problems involving point sources are then generalized to handle those involving interval sources.