SIMIODE

5-015-T-RunnerSynchronize

13 Jan 2020 | Modeling Scenarios

In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena. The idea is that instead of describing these oscillatory systems with...

1-114-T-EarthClimate

09 Dec 2019 | Modeling Scenarios

In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth from solar radiation, emission of radiation to outer space, and Earth's...

2-005-Text-T-LinearizeItAll

09 Dec 2019 | Technique Narratives

Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained. A simple model using Torricelli's Law will compare the exact solution to the...

1-084-T-GoingViral

31 Aug 2019 | Modeling Scenarios

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-T-GearTrain

31 Aug 2019 | Modeling Scenarios

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-T-UnearthingTruth

28 Aug 2019 | Modeling Scenarios

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...

1-082-T-MirrorMirror

21 Aug 2019 | Modeling Scenarios

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...

5-002-T-PhasePortraitForRelationshipDynamics

15 Aug 2019 | Modeling Scenarios

The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....

1-068-T-WaterBottleCooling

14 Aug 2019 | Modeling Scenarios

This modeling scenario involves Newton's Law of Cooling and should be appropriate in the first week or even the first day of an introductory differential equations course. The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a...

1-001d-T-HotelPopulationDecay

03 Jul 2019 | Modeling Scenarios

We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

1-001c-T-PopulationDecayThenSome

18 Jun 2019 | Modeling Scenarios

This is an adaption of Modeling Scenario 1-001-S-MandMDeathAndImmigration  in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.