Date of Award


Degree Name



College of Science

Type of Degree


Document Type


First Advisor

Bonita A. Lawrence

Second Advisor

Clayton Brooks

Third Advisor

John Drost

Fourth Advisor

Ralph Oberste-Vorth


In this work, we give an introduction to Time Scales Calculus, the properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equation of second order. Time Scales Calculus was introduced by Stefan Hilger in 1988. It brings together the theories of difference and differential equations into one unified theory. By using the properties of the delta derivative and the delta anti-derivative, we analyze the behavior of a second order linear homogeneous dynamic equation on various time scales. After the analytical discussion, we will graphically evaluate the second order dynamic equation in Marshall’s Differential Analyzer Lab. Differential analyzers (DA) are mechanical machines designed to solve differential equations through a process called mechanical integration. The DA can be used to demonstrate to students and science educators a mechanical visualization of integration, specifically, Riemann sums. The DA can be used to solve nonlinear differential equations of interest to mathematics researchers in the broad field of dynamic equations on time scales.


Differential calculus.

Differential-difference equations.