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1. 30 Aug 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

2. 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.

3. 27 Aug 2018 | Modeling Scenarios

In this project students will learn to find a probability distribution using the classical M&M game in SIMIODE.

4. 27 Aug 2018 | Modeling Scenarios

In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

5. 22 Aug 2018 | Modeling Scenarios

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.

6. 22 Aug 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

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.

7. 22 Aug 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

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.

8. 20 Aug 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

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 pre-clinical studies to examine local drug delivery to the cochlea. The...

9. 18 Aug 2018 | Technique Narratives | Contributor(s): Jessica Libertini

It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

10. 18 Aug 2018 | Modeling Scenarios

The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape. The assignment contains two opposite, but related tasks:...

11. 17 Aug 2018 | Modeling Scenarios

We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

12. 15 Aug 2018 | Modeling Scenarios

We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

13. 14 Aug 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

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...

14. 29 Jul 2018 | Free Online Texts

In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...

15. 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...

16. 09 Jun 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

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...

17. 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 SIR...

18. 24 Apr 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

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...

19. 07 Mar 2018 | Potential Scenario Ideas

Hays, Marguerite. 1984. Compartmental Models for Human Iodine Metabolism. Mathematical  Biosciences. 73: 317-335.ABSTRACT: Compartmental models for the various aspects of human iodine metabolism are reviewed, emphasizing the role of Mones Berman in the development of this field. The review...

20. 07 Mar 2018 | Potential Scenario Ideas

Imane Agmour, Meriem Bentounsi, Naceur Achtaich, and Youssef El Foutayeni. 2017. Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest. International Journal of Differential Equations. Volume 2017, Article ID 3157294, 17...