Experiences in a differential equations massive course

Abstract

This work describes a differential equations online course based on the solution of learning challenges, through mathematical modelling. This course has been developed on the OpenEdx platform. This course is built in order to provide engineering students with the abilities necessary to analyze and solve ordinary differential equations (ODE). The course consists of five units or modules: 1) first order ODE’s, 2) second order ODE’s, 3) Laplace transform, 4) Numerical methods and 5) Partial differential equations (PDE). On each module, the necessary theory is briefly explained through interactive videos. Besides this, our course includes: an e-Book, computational simulations using applications such as Mathematica and Python, an adaptive trainer for problems and exercises, a comprehensive activity about concepts and an evaluation activity. At the end of each module, the course offers a real life situation or a mathematical challenge to be solved in a collaborative way. The goal of this course is to develop the student’s abilities for mathematical modelling of systems through differential equations. Technology being implemented lets to give an individual following to each student. Finally, we show the results obtained recently by the students that took part in the course of differential equations, and we also show several examples with their answers to the proposed problems.