Investigating Students’ Difficulties with Differential Equations in Physics

There are numerous cases in physics where the value of a quantity and changes in that quantity are related. For example, the speed of an object depends on its acceleration. Except in highly idealized settings, the analysis of these cases requires students to recognize, set up, and solve a differential equation (DE). In many universities, including DCU, DEs are studied in mathematics before they are applied in physics. However, the aims of mathematicians and physicists can be very different, leading to different emphases in instruction and consequently, difficulties for students in applying mathematical knowledge of DEs in the physics setting. Other potential reasons why DEs present a problem for physics students include gaps in students’ mathematical knowledge, conceptual issues with DEs, and educational transfer issues. The aim of this project is to identify and understand students’ difficulties with differential equations in physics, and to develop a pilot curriculum that seeks to resolve them.