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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. 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...

5. 13 Jan 2020 | Modeling Scenarios

The goal is for students to practice finding and classifying equilibria of a one-variable system in this modeling context while also introducing variables defined on a restricted domain (the circle).

6. 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...

7. 20 Dec 2019 | Modeling Scenarios

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 in-class part we analyze the solutions found at...

8. 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...

9. 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...

10. 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...

11. 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...

12. 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...

13. 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...

14. 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...

15. 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...

16. 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...

17. 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...

18. 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...

19. 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...

20. 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...