Master's Theses

Department

Math

Degree Name

Master of Science (MS)

Abstract

The purpose of the problem was to investigate the behavior of curves under some simple complex transformations. The transformations used were limited to w = z 2, w = z1/2, and w = 1/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 that were simpler and from which some indication of the 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 greater chance of application.

Keywords

Mathematics, Geometry, Functions of complex variables, Z transformation, Analysis, Curves

Advisor

Dr. Emmet C. Stopher

Date of Award

Spring 1956

Document Type

Thesis - campus only access

Rights

© The Author(s)

Comments

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