Pedagogy of second order homogeneous differential equations: A holistic approach using a Matlab workbook

Abstract

A Matlab workbook is developed to facilitate a better understanding of the multiple approaches available to solve homogeneous second order differential equations with constant coefficients. With minimal input consisting of the coefficients and initial conditions, the workbook displays all aspects of the differential equation such the phase plane plot, state of the equilibrium, solutions based on roots of the characteristic equation, Laplace transforms and Runge-Kutta methods. The workbook format is such that it displays results as if the instructor is solving the differential equation on a blackboard with definitions, explanations, solution of unknown constants and comparison of solutions from multiple approaches. Several examples are provided which demonstrate the potential of the workbook in enhancing the pedagogy by letting instructors and students observe all aspects, thereby providing a holistic approach. The workbook (with examples and the Matlab script as a.p file) is available to all from the author's university website.