  The Dirac delta function is a standard mathematical tool used in multiple
topical areas in the undergraduate physics curriculum. While Dirac delta
functions are usually introduced in order to simplify a problem mathematically,
students often struggle to manipulate and interpret them. To better understand
student difficulties with the delta function at the upper-division level, we
examined responses to traditional exam questions and conducted think-aloud
interviews. Our analysis was guided by an analytical framework that focuses on
how students activate, construct, execute, and reflect on the Dirac delta
function in physics. Here, we focus on student difficulties using the delta
function to express charge distributions in the context of junior-level
electrostatics. Challenges included: invoking the delta function spontaneously,
constructing two- and three-dimensional delta functions, integrating novel
delta function expressions, and recognizing that the delta function can have
units.
