We present an empirical analysis of students' use of partial derivatives in the context of
problem solving in upper-division thermodynamics. Task-based individual interviews were …

APOS Theory is applied to study student understanding of the differential calculus of
functions of two variables, meaning by that, the concepts of partial derivative, tangent plane …

From literature, we know that making the connections between mathematics and physics is
not trivial for most students, even at the advanced level. In the specific context of partial …

This paper extends work in the areas of quantitative reasoning and covariational reasoning
at the undergraduate level. Task-based interviews were used to examine third-semester …

We describe an upper-division experiment in thermal physics where students measure the
tension of a rubber band as a function of temperature and length and use a Maxwell relation …

APOS Theory is applied to study student understanding of directional derivatives of functions
of two variables. A conjecture of mental constructions that students may do in order to come …

[This paper is part of the Focused Collection on Upper Division Physics Courses.] Partial
derivatives are used in a variety of different ways within physics. Thermodynamics, in …

Several studies in recent years have demonstrated that upper-division students struggle with
the mathematics of thermodynamics. This paper presents a task analysis based on several …

Abstract We use Action-Process-Object-Schema (APOS) theory to study students' geometric
understanding of partial derivatives of functions of two variables. This study contributes to …

This chapter discusses education research on the calculus concepts of derivatives and
integrals in relation to chemistry topics. Using the topics of chemical kinetics and …