Analog Computer Techniques for Problems in Complex Variables

Abstract

By programming pairs of amplifiers to represent the real and imaginary parts of complex variables on an analog computer, techniques are developed which 1) permit the mechanization of the method of steepest descents, for finding roots of complex functions, in Cartesian coordinates; 2) allow the generation of complex functions utilizing the Cauchy integral theorem; 3) enable a programmer to scan the z plane efficiently when electronic mode control and track-and-hold circuitry are available. Examples are given which show that these techniques frequently provide more efficient programs, in terms of equipment, than previous methods.