| Time Scale Calculus, introduced by Dr. Stefan Hilger in 1988, combines the study of differential and difference equations into a single topic. We begin with an introduction of sets used in this field, time scales, and build up to the definition of the exponential function on a time scale. The main focus of this work is a study of the solutions of a particular logistic dynamic equation on varying time scales. We study both the analytical and graphical solutions of this equation. Analytical solutions are worked out using theorems from Time Scale Calculus, including properties of the exponential function. Graphical solutions are obtained using the Marshall University Differential Analyzer (DA), fondly known as Art. Differential analyzers, such as Art, are machines that perform mechanical integration to solve differential equations. Both the analytical and graphical solutions offer the same conclusions about the convergence of solutions as the time scales converge. |
