A Computer for Algebraic Functions of a Complex Variable

Citation

Morgan, Merle Loren (1954) A Computer for Algebraic Functions of a Complex Variable. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/19YT-MN23. https://resolver.caltech.edu/CaltechETD:etd-01232004-135703

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Any rational algebraic function of a complex variable, and certain irrational functions, can be factored in either of the equivalent forms: [...] or [...]. In these expressions, F is a function of the complex variable z; each m represents a positive or negative constant, and the other letters represent complex constants. A theory is developed for computers for such functions, in which voltages proportional to the logarithmic components of each factor are obtained from the electrical potential distributions on a pair of uniform resistive sheets. The electrical summation of the voltages representing the factors then yields readings of the logarithmic components of the function. An actual computer, built to test and demonstrate the theory, is described. This computer accepts information in the form of the magnitude (absolute value, modulus) and the phase (angle, argument, amplitude) of each constant and of z in either of the above expressions, and yields answers in the form of the magnitude and phase of the function F. The computer is useful for applications requiring the evaluation of F at a large number of values of z; it is even more valuable for the inverse problem--that of determining by trial (by root locus tracing) the values of z (the roots) for a given value of F.

Thesis Files