-
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...
-
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...
-
9-020-T-HeatDiffusion
14 Oct 2019 | Modeling Scenarios
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...
-
9-020-S-HeatDiffusion
14 Oct 2019 | Modeling Scenarios
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...
-
10-001-T-TilingHallway
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...
-
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...
-
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...
-
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...
-
1-083-T-FallingMeteorites
24 Aug 2019 | Modeling Scenarios
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...
-
1-083-S-FallingMeteorites
24 Aug 2019 | Modeling Scenarios
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...
-
9-010-T-TravelingWaves
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...
-
3-011-T-EulerBallThrowing
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...
-
3-011-S-EulerBallThrowing
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...
-
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...
-
3-150-T-ItsABlastFurnace
13 Aug 2019 | Modeling Scenarios
This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...
-
3-150-S-ItsABlastFurnace
13 Aug 2019 | Modeling Scenarios
This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...
-
1-076-T-ClimateBifurcation
08 Aug 2019 | Modeling Scenarios
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...
-
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.
-
SCUDEM and COMAP MCM/ICM Talk at University of Nebraska - Lincoln
22 Apr 2019 | Competitions-SCUDEM
Elizabeth Carlson, holder of NSF Graduate Research Fellowship at the University of Nebraska - Lincoln, Lincoln NE USA, gave a talk in the spring 2018 to the mathematics club at her school on Math Modeling Competitions. Enjoy!