While mathematical modeling is an integral process in applied mathematics, students rarely encounter genuine modeling opportunities in their calculus courses. Here we introduce a laboratory experience as a natural starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to ﬁt the data. We require students to write a report about their findings. This article includes details about the class activity conducted in two different college settings and provides our assessment of student interaction with the lab, and how the lab informs student understanding of multivariable functions.
Bruder, Andrea and Kohler, Brynja R., "Coffee to Go! Modeling Thermoclines in Multivariable Calculus" (2005). Mathematics and Statistics Faculty Publications. Paper 207.