## What's New:

### Modeling Scenarios feed

1. 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:...

2. 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...

3. 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 be...

4. 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...

5. 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.

6. 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...

7. 12 Aug 2018 | Modeling Scenarios | Contributor(s):: Meredith Greer

8. 12 Aug 2018 | Modeling Scenarios | Contributor(s):: Mary Vanderschoot

9. 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...

10. 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...

11. 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 SIR...

12. 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...

13. 24 Apr 2018 | Modeling Scenarios | Contributor(s):: Michael Karls

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...

14. 15 Apr 2018 | Modeling Scenarios | Contributor(s):: Brian Winkel

This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

15. 05 Apr 2018 | Modeling Scenarios | Contributor(s):: Kurt Bryan

This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene: Do bullets moving through water slow as dramatically as depicted in the movies, so that someone a few...

16. 30 Jan 2018 | Modeling Scenarios | Contributor(s):: Kurt Bryan

This project concerns the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return? Both scenarios are analyzed in a series of exercises.

17. 15 Sep 2017 | Modeling Scenarios | Contributor(s):: Jean Marie Linhart

The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled.

18. 12 Sep 2017 | Modeling Scenarios | Contributor(s):: Eric Sullivan, Jesica Bauer, Erica Wiens

In this activity, we provide photographs of the steeping process for a fruit tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration of the tea oils in...

19. 04 Sep 2017 | Modeling Scenarios | Contributor(s):: Ben Dill, Holly Zullo

Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves. In this activity, students are introduced to the concepts of...

20. 04 Sep 2017 | Modeling Scenarios | Contributor(s):: Michael Grayling

Several models using first order differential equations are offered with some questions on formulating a differential equations model