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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...
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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...
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2-005-Text-S-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...
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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...
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1-084-S-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...
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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...
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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...
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9-015-S-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...
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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...
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1-082-S-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...
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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...
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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....
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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...
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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.
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Exploring differential equation of HIV infection
21 Jun 2019 | Presentations
Exploring differential equation models of the HIV infectionPresentation by Rebecca L. Goulson Department of Mathematics Pacific Lutheran University Tacoma, WA, May, 2015. 67 SlidesModels presented and data analyzed to determine parameters.
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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.
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1-001c-S-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.
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3-067-T-RLCSeriesCircuit
28 Apr 2019 | Modeling Scenarios
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).
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1-107-T-ClothDry
27 Apr 2019 | Modeling Scenarios
We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...
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7-011-Text-T-CoupledSystemLaplace
31 Mar 2019 | Technique Narratives
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...