  Understanding Maxwell's equations in differential form is of great importance
when studying the electrodynamic phenomena discussed in advanced
electromagnetism courses. It is therefore necessary that students master the
use of vector calculus in physical situations. In this light we investigated
the difficulties second year students at KU Leuven encounter with the
divergence and curl of a vector field in mathematical and physical contexts. We
have found that they are quite skilled at doing calculations, but struggle with
interpreting graphical representations of vector fields and applying vector
calculus to physical situations. We have found strong indications that
traditional instruction is not sufficient for our students to fully understand
the meaning and power of Maxwell's equations in electrodynamics.
