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Modeling Scenarios feed

1. 28 Aug 2018 | Modeling Scenarios | Contributor(s):: Darrell Weldon Pepper

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.

2. 27 Aug 2018 | Modeling Scenarios | Contributor(s):: Mehdi Hakim-Hashemi

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

3. 27 Aug 2018 | Modeling Scenarios | Contributor(s):: Mehdi Hakim-Hashemi

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.

4. 22 Aug 2018 | Modeling Scenarios | Contributor(s):: Yuri Yatsenko

5. 22 Aug 2018 | Modeling Scenarios | 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.

6. 22 Aug 2018 | Modeling Scenarios | 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.

7. 20 Aug 2018 | Modeling Scenarios | 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 pre-clinical studies to examine local drug delivery to the cochlea....

8. 20 Aug 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important? Three cases are presented: shattering a wine glass, collapse of a suspension bridge, and crash of...

9. 18 Aug 2018 | Modeling Scenarios | Contributor(s):: Natali Hritonenko

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:...

10. 17 Aug 2018 | Modeling Scenarios | Contributor(s):: Therese Shelton

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...

11. 15 Aug 2018 | Modeling Scenarios | Contributor(s):: Therese Shelton

We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a 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...

12. 15 Aug 2018 | Modeling Scenarios | Contributor(s):: Therese Shelton

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. 15 Aug 2018 | Modeling Scenarios | Contributor(s):: Shinemin Lin

In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

14. 14 Aug 2018 | Modeling Scenarios | 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...

15. 12 Aug 2018 | Modeling Scenarios | Contributor(s):: Meredith Greer

16. 12 Aug 2018 | Modeling Scenarios | Contributor(s):: Mary Vanderschoot

17. 29 Jul 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...

18. 09 Jun 2018 | Modeling Scenarios | Contributor(s):: Ryan Miller, Randy Boucher

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...

19. 30 May 2018 | Modeling Scenarios | Contributor(s):: Stanley Florkowski, Ryan Miller

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...

20. 20 May 2018 | Modeling Scenarios | Contributor(s):: Steven Morse, Brian Allen, Stanley Florkowski

The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle. This setting allows us to also employ multivariable optimization as a means of model fitting and multivariable integration in the context of...