We present the titles and abstracts as well as complete presentation for talks given at AMS Special Session on Wall to Wall Modeling Activities in Differential Equations Courses, Room 108, Meeting Room Level, Colorado Convention Center, held at JMM 2020, 18 January 2020, Denver CO USA.
Complete Presentations of those submitted can be found in Supporting Docs.
Therese Shelton, Southwestern University
Brian Winkel, SIMIODE
Eye Surgery Problems, Dry Ice Does a Job, and How Water Cooling while Room Heats Up -- Modeling with Differential Equations.
Brian J Winkel*, Director, SIMIODE, Cornwall NY USA
ABSTRACT: We will engage the audience in modeling scenarios we have used with students in modeling with differential equations using data. In retinal surgery inert gas is injected into the eye and doctors need to model the gas’s diffusion out of the eye before permitting patients to fly. Otherwise bad things could happen! Dry ice sublimates, but how can we model it, and how should we not model it? Hot water cools in a room, but the room is heating up. What happens? All of these are readily available at www.simiode.org.
Thanos Population Dynamics.
Sarah Patterson*, Virginia Military Institute and Blain Patterson, Virginia Military Institute
ABSTRACT: In the end of the “Avengers Infinity War,” the villain Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long-term behavior of various species? Investigate the validity of his claim by modeling various population dynamics such as unconstrained and constrained growth, competing species, and predator-prey. In this talk, we will provide instructors with an engaging way for students to analyze the behavior of various population models.
Lost at Sea: Introduction to Numerical Methods through Navigation.
Corban Harwood*, George Fox University
ABSTRACT: In this talk, we will discuss a two part modeling activity which guides two simultaneous discovery-based approaches to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor method. These methods are motivated by dead reckoning applied graphically to the velocity field over two dimensions to locate a ship lost at sea. We also provide a guide for planning, facilitating, and assessing the two simultaneous activities which require groups to compare their results from different perspectives to conclude whether or not the ship is found.
Sometimes Predicting the Future is Easier than Deciphering the Past and Other Aspects of Modeling the Draining of a Bottle.
John F McClain*, University of New Hampshire
ABSTRACT: I will share an activity focused on modeling the height of a fluid being drained from a bottle, adapted from one available on SIMIODE.org to work in my class of roughly 200 students, partly in the large lecture and partly in smaller recitations ( 20 students). I will also share the results of a student survey on modeling activities. This activity includes data collection from video (from SIMIODE), development of a regression model, derivation of a differential equation, solution of the differential equation, and interpretation of results. It ends with a commonsense model verification that leads to a discussion of piecewise-defined solutions and lack of uniqueness for initial value problems corresponding to empty bottles. I emphasize the robustness of the differential equation to changing parameters in contrast to the regression model. I have found that the students appreciate the use of physical principles and geometric analysis in deriving the equation, however, they struggle with the use of the limit definition of derivative. Also, this model gives a physical example of an initial value problem without a unique solution: if the initial condition has height zero at time t¬ 0, any solution describing a bottle emptying before t_0 also satisfies the initial condition.
SCUDEM Update: Students' Expected and Measured Gains.
Jennifer A Czocher*, Texas State University and Elizabeth Roan, Texas State University
ABSTRACT: We present an update on student gains from participation in SCUDEM. We will first offer a synthesis of pre- and post-competition survey data from 3 rounds of the competition to describe the expectations students held going into the competition, the extent to which they were met, and how their expectations compared to those of other stakeholders. Results show that students, researchers, and designers held differing expectations. We explore implications of this finding for broadening participation. In addition, we will give preliminary results of a study linking gains in student self-efficacy to gains in modeling competencies
Tiling an n by 3 Hallway with 1 by 2 Tiles: An Interactive Presentation.
Robert Krueger*, Concordia University, St. Paul and Eric Stachura, Kennesaw State University
ABSTRACT: Students will investigate difference equations through the context of tiling hallways. Students will observe patterns in the tiling which will lead to a difference equation model. Solutions will be calculated by iteration. Then students will be introduced to the concept of the shift operator which will enable them to solve for a closed form solution. The session will be an interactive presentation of how this modeling scenario could be used in a differential equations classroom. This work was recently published here: https://www.simiode.org/resources/6417. This was joint work completed along with Eric Stachura as part of the DEMARC Fellowship sponsored by SIMIODE and the National Science Foundation
Modeling Bubbles of Beer.
Michael A. Karls*, Ball State University
ABSTRACT: The goal of this project is to set up and numerically solve a first-order nonlinear ODE system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify the model via data collected from a bubble rising in a glass of beer.
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