Date of Award

Spring 1954

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)



First Advisor

Pettit, Harvey

Second Advisor

Hanneken, C. B.


Geometrical representation of real functions of real variables is not merely a helpful means in the elementary interpretation of certain properties of these functions, but historically it gave birth to such important ideas a the definite integral of functions. On the contrary, the geometrical representation of functional analysis is the field of complex variables offers some real difficulties. Although there are geometrical representations of complex numbers (as the Argand diagram and the Riemann sphere), yet they are not extended to the representation of complex functions of complex variables. A geometrical representation of complex functions and a geometrical interpretation of such properties of complex functions as differential, integral and mapping will be attempted on the following pages.