Date of Award
College of Science
Type of Degree
Bonita A. Lawrence
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.
Peterson, Molly Kathryn, "Mechanical Visualization of a Second Order Dynamic Equation on Varying Time Scales" (2014). Theses, Dissertations and Capstones. 826.