
3071SWirelessTelegraphy
20 Dec 2019  Modeling Scenarios  Contributor(s):: Gabriel Nagy
This project has three parts, the first part to be done at home, the last two parts in class. In the home part we recall how to solve second order, linear, differential equations with constant coefficients and simple source functions. In the first inclass part we analyze the solutions found at...

1114SEarthClimate
09 Dec 2019  Modeling Scenarios  Contributor(s):: Terrance Pendleton
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...

3087SThanosPopulationDynamicsInteractingSpecies
06 Dec 2019  Modeling Scenarios  Contributor(s):: Blain Patterson, Sarah Elizabeth Ritchey Patterson
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 his...

3061SChemEng
27 Nov 2019  Modeling Scenarios  Contributor(s):: Eric Stachura, Tamara Lozano
Chemical and biomedical applications of differential equationsSPANISH LANGUAGE VERSION We have placed in Supporting Docs a Spanish version of this Student Modeling Scenario. Name will be xySTitleStudentVersionSpanish.

9020SHeatDiffusion
14 Oct 2019  Modeling Scenarios  Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

1087SThanosPopulationDynamics
07 Oct 2019  Modeling Scenarios  Contributor(s):: Sarah Elizabeth Ritchey Patterson, Blain Patterson
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 his...

10001STilingHallway
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...

1111SSpreadOfInformation
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...

1092SDashItAll
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 HillKeller model for a...

1084SGoingViral
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...

3064SGearTrain
31 Aug 2019  Modeling Scenarios  Contributor(s):: Lukasz Grabarek
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...

9015SUnearthingTruth
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...

1083SFallingMeteorites
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 (firstorder, nonlinear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

1082SMirrorMirror
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...

9010STravelingWaves
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....

3011SEulerBallThrowing
19 Aug 2019  Modeling Scenarios  Contributor(s):: Chris McCarthy
If a tennis ball is thrown through the air it will eventually hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the thrower taking into account air...

5002SPhasePortraitForRelationshipDynamics
15 Aug 2019  Modeling Scenarios  Contributor(s):: Lawrence C Udeigwe
The different possible dynamics of a twoperson 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....

1068SWaterBottleCooling
14 Aug 2019  Modeling Scenarios  Contributor(s):: Eli E Goldwyn
The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room. The goal is for the students to understand...

3150SItsABlastFurnace
13 Aug 2019  Modeling Scenarios  Contributor(s):: Kurt Bryan
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...

1076SClimateBifurcation
08 Aug 2019  Modeling Scenarios  Contributor(s):: Mayer Humi
In this paper we present (for educational purposes) simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations from the present Earth climate to an ice age or a ``Venus type of climate.'' The models are accompanied by Matlab.