Transformation procedure of unit vectors to facilitate evaluation of vector potentials

A simple method is presented which details the process by which unit vectors in a source region are represented in terms of unit vectors of a field point. Since everything is done from the standpoint of the source unit vectors, this procedure differs slightly from equivalent treatments that transform distributions of source currents. The objective of this paper is to present this method in a systematic fashion which easily translates to a number of coordinate systems. Using the method of the gradient and a high-level language such as Mathematica, these conversions can be done with great ease This approach finds its greatest value when considering coordinate systems that are not used widely used.