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1. 24 Aug 2019 | Modeling Scenarios

After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

2. 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...

3. 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 first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

4. 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.

5. 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.

6. 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.

7. 22 Aug 2018 | Modeling Scenarios

8. 22 Aug 2018 | Modeling Scenarios

Students construct and analyze the celebrated Solow-Swan 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...

9. 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...

10. 12 Aug 2018 | Modeling Scenarios

In this project, students develop two SIS models to study eviction trends in a population of non-homeowner 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...

11. 09 Jun 2018 | Modeling Scenarios

Students will transform, solve, and interpret a tumor growth scenario using non-linear 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...

12. 09 Jun 2018 | Modeling Scenarios

Students will transform, solve, and interpret a tumor growth scenario using non-linear 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...

13. 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...

14. 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...

15. 24 Apr 2018 | Modeling Scenarios

The goal of this project is to set up and numerically solve a first-order 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...

16. 24 Apr 2018 | Modeling Scenarios

The goal of this project is to set up and numerically solve a first-order 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...

17. 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...

18. 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...

19. 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): 7-14.Abstract: The initial value problem in a kinetic model for biogas generation from...

20. 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 tick-borne disease. Journal of Biological Dynamics. 5(5): 517-530Abstract:  Tick-borne diseases have been on the rise recently, and correspondingly, there is an...