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1. 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. 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...

3. 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...

4. 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...

5. 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...

6. 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...

7. 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...

8. 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...

9. 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...

10. 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...

11. 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...

12. 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...

13. 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...

14. 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...

15. 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...

16. 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...

17. 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...

18. 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...

19. 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.

20. 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!