
10001STilingHallway
12 Sep 2019   Contributor(s):: Rob Krueger, Eric Stachura
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...

1092SDashItAll
01 Sep 2019   Contributor(s):: Kurt Bryan
This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic HillKeller model for a...

1001dSHotelPopulationDecay
03 Jul 2019   Contributor(s):: Dina Yagodich
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

1063SThreeHoleColumn
15 Dec 2018   Contributor(s):: Brian Winkel
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

1062SBacterialGrowth
15 Sep 2018   Contributor(s):: Arati Nanda Pati
We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

1053SSlimeSpread
30 Aug 2018   Contributor(s):: Brian Winkel
We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

7040STankInterruptMixing
22 Aug 2018   Contributor(s):: Norman Loney
We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

7020SThermometerInVaryingTempStream
22 Aug 2018   Contributor(s):: Norman Loney
We present a differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.

1138SInnerEarDrugDelivery
20 Aug 2018   Contributor(s):: Jue Wang
Hearing loss is difficult to treat due to the inner ear location and structure. Drawing from this challenging case, this scenario guides students to transform a treatment protocol into a mathematical model. Students engage in preclinical studies to examine local drug delivery to the cochlea. The...

1054SGrowthInFarmland
14 Aug 2018   Contributor(s):: Richard Spindler
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

1081STumorGrowth
09 Jun 2018   Contributor(s):: Randy Boucher, Ryan Edmund Miller
Students will transform, solve, and interpret a tumor growth scenario using nonlinear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

6070SBeerBubbles
24 Apr 2018   Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (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...

1115SModelingWithFirstOrderODEs
04 Sep 2017   Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model

1043SCoolingUpAndDown
26 Aug 2017   Contributor(s):: Brian Winkel
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.

1057SFiguringFluidFlow
15 Aug 2017   Contributor(s):: Brian Winkel
We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.

1042SKoolAid
26 Apr 2017   Contributor(s):: Kristin Burney, Lydia Kennedy, Audrey Malagon
Singlecompartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...

1014SDrainingContainers
17 Mar 2017   Contributor(s):: Brian Winkel
We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''

1037SCommonColdSpread
30 Nov 2016   Contributor(s):: Richard Corban Harwood
This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential...

1052SSaltWaterTanks
27 Nov 2016   Contributor(s):: Brian Winkel
We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

1058SWaterClocks
26 Nov 2016   Contributor(s):: Sania Qureshi, Brian Winkel
We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out. First, we review the principles and derivation of the applicable physics in...