Meeting Abstract
Students who have lived a winter in Utah are familiar through first hand experience with the fact that temperature inversions trap pollution. And temperature gradients in lakes are also familiar to outdoor enthusiasts who enjoy a summer swim or fishing trip, but are they aware of how climate change may influence lake ecology? Even less familiar is how to model or study such systems mathematically. As part of our undergraduate curriculum development project: Laboratory Experiences in Mathematical Biology, we have developed a lab that introduces students quantitatively to atmospheric temperature inversions, and basic limnology while addressing mathematical topics from multivariable calculus. In this laboratory, students work in groups to gather temperature data from a glass in which a fixed volume of cool milk is inserted beneath an approximately equal volume of hot coffee. The purpose of the lab is to give students a hands on experience with a function of two independent variables (time and space), expose them to the challenges of making mathematical models of real life phenomena including the process of discretizing continuous variables and making measurements, as well as to introduce/strengthen student experience with the following mathematical technical notions: functions of two variables, graphs of surfaces, contour maps of surfaces, level curves, limits of multivariable functions, and partial derivatives. In the presentation, I will share the results of our trials of this lab with students, as well as the current state of our resources for implementing the lab.
