SIMIODE

5-010-S-MatrixExponential

12 Sep 2019 | Technique Narratives | Contributor(s): Kurt Bryan

The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to...

10-001-S-TilingHallway

12 Sep 2019 | Modeling Scenarios | 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...

1-111-S-SpreadOfInformation

02 Sep 2019 | Modeling Scenarios | Contributor(s): Jeff Pettit

Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model which can be compared to predicted data, measured data, and modeled data. Part 3 can require students to move from...

1-092-S-DashItAll

01 Sep 2019 | Modeling Scenarios | Contributor(s): Kurt Bryan

This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic Hill-Keller model for a...

1-084-S-GoingViral

31 Aug 2019 | Modeling Scenarios | Contributor(s): Bill Skerbitz

Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom).  Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.  Finally, students solve the...

3-064-S-GearTrain

31 Aug 2019 | Modeling Scenarios | Contributor(s): Lukasz Grabarek

In this scenario students will model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components. Students should have some...

9-015-S-UnearthingTruth

28 Aug 2019 | Modeling Scenarios | Contributor(s): Kurt Bryan

This project introduces electrical resistivity tomography, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical current. Specifically, a known electrical current is injected into an object (for example, the earth) and...

1-083-S-FallingMeteorites

24 Aug 2019 | Modeling Scenarios | Contributor(s): Lyle Clifford Smith

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...

1-082-S-MirrorMirror

21 Aug 2019 | Modeling Scenarios | Contributor(s): Kurt Bryan

This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

9-010-S-TravelingWaves

21 Aug 2019 | Modeling Scenarios | Contributor(s): Eric Stachura

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....