Transformation of Selected Lines and Conics in the Z-Plane

Author

Lester Hornung, Fort Hays Kansas State College

Department

Math

Degree Name

Master of Arts (MA)

Abstract

The basic problem of this paper was to study the results of transforming selected conics under the transformations w = ez, w = sin z, and w = cos Z. The conic sections were limited to those that were symmetric to the origin, x or y axis. It was found that as the complexity of the curve to be transformed increased so did the complexity of the transformed curve. The other two factors of significance were found to be: 1) The effect of the periodicity of the sine and cosine function; 2) the rapidity by which the absolute values of ex, cosh x, and sinh x increase as x increases. The lone exception to the last statement is that as x approaches negative infinity the value of ex approaches zero.

Keywords

Mathematics, Functions of complex variables, Trigonometry, Analysis, Algebra, Equations

Advisor

Dr. Wilmont Toalson

Date of Award

Summer 1964

Document Type

Thesis - campus only access

DOI

10.58809/RDBM4871

Recommended Citation

Hornung, Lester, "Transformation of Selected Lines and Conics in the Z-Plane" (1964). Master's Theses. 857.
DOI: 10.58809/RDBM4871
Available at: https://scholars.fhsu.edu/theses/857

Rights

© The Author(s)

Comments

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