Date of Award
Master of Science (MS)
Dr. Emmet C. Stopher
The purpose of the problem was to investigate the behavior of curves under some simple complex transformations. The transformations used were limited tow,= z 2 w = z2 1 , , and w = -z • The curves considered were limited to straight lines and conic sections. However, the general cases of the conics were usually too complicated to be dealt with in the thesis. Therefore, most of the conics considered were special cases which were simpler and from which some indication of t he behavior of more general cases might be found. Some interesting special cases of the more complicated transformations were treated briefly, as were practical applications of complex transformations. Sketches were included showing the results of the transformations in graphic form. It was noted that, in general, subjection of a curve to a transformation complicated that curve. Cases in which the curve was simplified were less numerous, but usually had gr eater chance of application.
Deeter, Charles R., "Transformations of Lines and Conics in The Z-Plane" (1956). Master's Theses. 550.
Copyright 1956 Charles R. Deeter