
10001TTilingHallway
12 Sep 2019  Modeling Scenarios
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...

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...

1083TFallingMeteorites
24 Aug 2019  Modeling Scenarios
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...

1083SFallingMeteorites
24 Aug 2019  Modeling Scenarios
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...

9010TTravelingWaves
21 Aug 2019  Modeling Scenarios
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. Students...

3011TEulerBallThrowing
19 Aug 2019  Modeling Scenarios
If a tennis ball of mass $m$ is thrown through the air it will eventually hit the ground due to gravity. If you can throw a tennis ball 12 meters/second (about 26.8 mph) how far can you throw it; meaning how far away from you can you make it land? Assume that when the ball leaves your hand it...

3011SEulerBallThrowing
19 Aug 2019  Modeling Scenarios
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...

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...

5002TPhasePortraitForRelationshipDynamics
15 Aug 2019  Modeling Scenarios
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....

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...

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.

1001cSPopulationDecayThenSome
18 Jun 2019  Modeling Scenarios
This is an adaption of Modeling Scenario 1001SMandMDeathAndImmigration 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.

7011TextTCoupledSystemLaplace
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...

7011TextTCoupledSystemLaplace
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...

7011TextSCoupledSystemLaplace
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...

7011TextSCoupledSystemLaplace
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...

5090TSolidParticleErosion
27 Mar 2019  Modeling Scenarios
By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface. Examination of the solution will yield a formula for the...

1125TDiceyPopulations
04 Mar 2019  Modeling Scenarios
We offer students an opportunity to generate unique data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters and try to explain how the simulation...