Students' Understanding of Stokes' Theorem in Vector Calculus

This study investigates the challenges faced by second-year undergraduate engineering students in understanding Stokes' theorem in vector calculus, focusing on the misconceptions found in interconnected concepts that form its foundation. Stokes' theorem involves the application of line integrals, surface integrals, the curl of a vector field, and the flux of a vector field, which are essential for a thorough understanding of the theorem. This article reports on a study conducted to identify these misconceptions through the qualitative and quantitative analysis of the test papers from 47 students at the University of Cape Town who were studying vector calculus. The results reveal difficulties in grasping line integrals, curve parametrization, vectors, curl of a force field, and the projection factor in surface integrals. Our study concludes that proficiency in these underlying concepts is crucial for students to effectively understand Stokes' theorem, highlighting the need for targeted teaching approaches that address these known difficulties.