DiffyQ-Live: A Pedagogical Tool - Version 1.0

Biological dynamics are frequently modeled using differential equations, yet students in the life sciences generally do not get a chance to develop an intuitive feel for how these equations behave. DiffyQ-Live is a command-line tool that addresses this problem by introducing students to three related differential equations that are commonly used in biology and medicine. The tool provides instruction and an environment for exploring how changes to parameters and initial conditions affect plotted solutions. Specifically, it starts out by introducing students to the simple equation for unrestrained exponential growth and decay. It then uses this as the basis for understanding two equations that model the constraint of runaway behavior: the equation for logistic growth, which is used as a model for population dynamics, and exponential decay with replacement, which is used as a model for drug dosing with constant infusion. The package has been structured so that it is straightforward for educators to customize, with linear code, identifiable equations, and easily editable text files. Note that students using DiffyQ-Live should have had enough calculus to understand what a derivative is.