
1083TFallingMeteorites
24 Aug 2019  Modeling Scenarios
After introducing the solution to the ordinary differential equation which models a falling object with drag (firstorder, nonlinear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

9010TTravelingWaves
21 Aug 2019  Modeling Scenarios
In this scenario, students will be taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation (PDE) model, after a change of variables, students are led quickly to an ordinary differential equation (ODE) model. Students...

1109TEmployeeAttrition
25 Mar 2019  Modeling Scenarios
This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a firstorder linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

1063TThreeHoleColumn
15 Dec 2018  Modeling Scenarios
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.

6003TSchoolFluEpidemic
28 Aug 2018  Modeling Scenarios
We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

6003SSchoolFluEpidemic
28 Aug 2018  Modeling Scenarios
We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

1118SSolowEconomicGrowth
22 Aug 2018  Modeling Scenarios

1118TSolowEconomicGrowth
22 Aug 2018  Modeling Scenarios
Students construct and analyze the celebrated SolowSwan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics, including elements of static optimization. Part one is...

1054TGrowthInFarmland
14 Aug 2018  Modeling Scenarios
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...

5026TEvictions
12 Aug 2018  Modeling Scenarios
In this project, students develop two SIS models to study eviction trends in a population of nonhomeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

1081STumorGrowth
09 Jun 2018  Modeling Scenarios
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...

1081TTumorGrowth
09 Jun 2018  Modeling Scenarios
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...

6018SExploringSIRModel
30 May 2018  Modeling Scenarios
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

6018TExploringSIRModel
30 May 2018  Modeling Scenarios
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
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...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
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...

2017AllaliMathModelingOfAdaptiveImmunieResponsesHBVInfection
07 Mar 2018  Potential Scenario Ideas
Karam Allali, Adil Meskaf, and Abdessamad Tridane. 2018. Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection. International Journal of Differential Equations. Volume 2017, Article ID 6710575, 13 pagesThis is an open access article distributed under the...

LeakingBucket: Differential Equations in Engineering
03 Mar 2018  Potential Scenario Ideas
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...

2015SivakumarRajendranKineticModelBananaWaste
03 Mar 2018  Potential Scenario Ideas
Sivakumar, Pavithra and Lakshmanan Rajendran. 2012. Approximate Analytical Expression of Concentrations in a Kinetic Model for Biogas Generation from Banana Waste. Applied Mathematics. 5(1): 714.Abstract: The initial value problem in a kinetic model for biogas generation from...

2011Gaff EtAlOptimalControlManagementTickBorneDisease
03 Mar 2018  Potential Scenario Ideas
Gaff, Holly D., Elsa Schaefer, and Suzanne Lenhart. 2011. Use of optimal control models to predict treatment time for managing tickborne disease. Journal of Biological Dynamics. 5(5): 517530Abstract: Tickborne diseases have been on the rise recently, and correspondingly, there is an...