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  1. JMM 2020 MAA Minicourse #10 Wall to Wall Modeling Scenarios for Differential Equations

    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. JMM 2020 AMS Special Session on Wall to Wall Modeling Activities in Differential Equations Courses

    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. 5-015-T-RunnerSynchronize

    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. 5-015-T-RunnerSynchronize

    13 Jan 2020 | Modeling Scenarios | Contributor(s): Brian Winkel

    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. 1-010-Text-T-AtmosphericCO2Bifurcation

    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...

  6. 1-114-T-EarthClimate

    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...

  7. 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...

  8. 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. 1-087-T-ThanosPopulationDynamics

    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...

  10. 5-010-S-MatrixExponential

    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. 5-010-T-MatrixExponential

    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...

  12. 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...

  13. 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...

  14. 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...

  15. 9-015-T-UnearthingTruth

    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. 9-015-S-UnearthingTruth

    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...

  17. 1-082-T-MirrorMirror

    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...

  18. 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...

  19. 5-002-T-PhasePortraitForRelationshipDynamics

    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....

  20. 5-002-T-PhasePortraitForRelationshipDynamics

    15 Aug 2019 | Modeling Scenarios | Contributor(s): Brian Winkel

    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....