
5015TRunnerSynchronize
13 Jan 2020  Modeling Scenarios
In this modeling scenario we practice finding and classifying equilibria of a onevariable 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...

1010TextTAtmosphericCO2Bifurcation
12 Jan 2020  Technique Narratives
Students are introduced to the concept of a bifurcation in a firstorder ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide. carbon dioxide is taken as a parameter and temperature is a function of time. For low values of carbon dioxide, there...

1114TEarthClimate
09 Dec 2019  Modeling Scenarios
In this modeling scenario, we investigate the Earth's climate using a zerodimensional 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...

2005TextTLinearizeItAll
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...

2005TextSLinearizeItAll
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...

1087TThanosPopulationDynamics
07 Oct 2019  Modeling Scenarios
In the end of the “Avengers Infinity War,” the villain Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species? Investigate the validity of...

5010SMatrixExponential
12 Sep 2019  Technique Narratives
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...

5010TMatrixExponential
12 Sep 2019  Technique Narratives
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...

1084TGoingViral
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...

1084SGoingViral
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...

3064TGearTrain
31 Aug 2019  Modeling Scenarios
In this scenario students will model an inputoutput mechanical system of gears with a second order, nonhomogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components. Students should have some...

9015TUnearthingTruth
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...

9015SUnearthingTruth
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...

1082TMirrorMirror
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...

Ice Coverage in the Arctic Climate over time
17 Aug 2019  Articles and Publications
In this paper, entitled Ice Coverage in the Arctic Climate, from two students, Angie Dimopulos and Kelcey Heaney, and their professor, Dr. Wisam Bukaita, ice coverage in the Arctic is modeled over time. We present their abstract here and include the paper itself.ABSTRACT The Arctic plays a...

1068TWaterBottleCooling
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...

3150TItsABlastFurnace
13 Aug 2019  Modeling Scenarios
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

3150SItsABlastFurnace
13 Aug 2019  Modeling Scenarios
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

1001dTHotelPopulationDecay
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.

2008LiDE Models For Interacting and Transgenic Mosquito Populations
21 Jun 2019  Potential Scenario Ideas
Article Review and AnnotationLi, Jai. 2008. Differential equations models for interacting wild and transgenic mosquito populations. Journal of Biological Dynamics. 2(3): 241258.Abstract: We formulate and study continuoustime models, based on systems of ordinary differential...