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1. 20 Jan 2020 | Presentations

Joint Mathematics Meetings 2020 MAA Minicourse #10Wall to Wall Modeling Scenarios for Differential EquationsWe offer up the materials from the Minicourse. The actual files are found in Supporting Docs.Part A – Thursday, 16 January 2020, 9:00 AM - 11:00 AM Room 704, Meeting Room...

2. 20 Jan 2020 | Presentations

We present the titles and abstracts as well as complete presentation for talks given at AMS Special Session on Wall to Wall Modeling Activities in Differential Equations Courses, Room 108, Meeting Room Level, Colorado Convention Center, held at JMM 2020, 18 January 2020, Denver CO...

3. 13 Jan 2020 | Modeling Scenarios

In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena. The idea is that instead of describing these oscillatory systems with...

4. 12 Jan 2020 | Technique Narratives

Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide. carbon dioxide is taken as a parameter and temperature is a function of time. For low values of carbon dioxide, there...

5. 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...

6. 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...

7. 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...

8. 07 Oct 2019 | Modeling Scenarios

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...

9. 12 Sep 2019 | Technique Narratives

The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to...

10. 12 Sep 2019 | Technique Narratives

The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to...

11. 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...

12. 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...

13. 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...

14. 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...

15. 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...

16. 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...

17. 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...

18. 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....

19. 15 Aug 2019 | Modeling Scenarios | Contributor(s): Karen Bliss

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....

20. 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...