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### All Categories (21-36 of 36)

1. 19 May 2016 | | Contributor(s):: John Thomas Sieben

Divers, especially novice divers, have concerns about running out of breathing air while at depth.  One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using...

2. 26 Apr 2017 | | Contributor(s):: Kristin Burney, Lydia Kennedy, Audrey Malagon

Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...

3. 10 Feb 2016 | | Contributor(s):: Timothy Pennings

As captain of a barge, you need to determine how fast to transportyour barge up river against the current in order to minimize the expended energy.Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if...

4. 27 Nov 2016 | | Contributor(s):: Brian Winkel

We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

5. 27 Feb 2016 | | Contributor(s):: Brian Winkel

There are three videos associated with this Modeling Scenario and all are available on SIMIODE YouTube Channel: Capture-3 YouTube Version SlowMoCapture-1 YouTube Version SlowMoCapture-2 YouTubeVersion and as streaming videos or down loads in this Modeling Scenario under the Supporting Docs Tab...

6. 15 Jun 2020 | | Contributor(s):: Tracy Weyand

Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...

7. 04 Jun 2020 | | Contributor(s):: Brian Winkel

We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.

8. 11 Jun 2020 | | Contributor(s):: Tracy Weyand

Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are first-order ordinary differential equations (which...

9. 12 Sep 2019 | | Contributor(s):: Rob Krueger, Eric Stachura

Students will investigate difference equations through the context of tiling hallways. Students will observe patterns in the tiling which will lead to a difference equation model. Solutions will be calculated by iteration.  Then students will be introduced to the concept of the shift...

10. 22 Jul 2020 | | Contributor(s):: Brian Winkel

We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

11. 23 Nov 2016 | | Contributor(s):: Brian Winkel

We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters.

12. 12 Oct 2016 | | Contributor(s):: Brian Winkel

Two possible multiple dose drug administration regimens are offered for modeling. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus injections and the other involves steady drip flow over short periods of time....

13. 22 Aug 2018 | | 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.

14. 22 Aug 2018 | | 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.

15. 04 Jun 2015 | | Contributor(s):: Brian Winkel

Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields.

16. 22 Nov 2016 | | Contributor(s):: Gregg Waterman, Tiernan R Fogarty

This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions. Vertical deflection occurs as a result of the weight of the beam alone, with no compressive force at the ends or distributed...