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  1. 9-020-S-HeatDiffusion

    14 Oct 2019 | Modeling Scenarios | Contributor(s):: Kimberly Spayd, James Puckett

    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...

  2. 1-087-S-ThanosPopulationDynamics

    07 Oct 2019 | Modeling Scenarios | Contributor(s):: Sarah Elizabeth Ritchey Patterson, Blain Patterson

    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 his...

  3. 5-010-S-MatrixExponential

    12 Sep 2019 | Technique Narratives | Contributor(s):: Kurt Bryan

    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...

  4. 10-001-S-TilingHallway

    12 Sep 2019 | Modeling Scenarios | Contributor(s):: Rob Krueger, Eric Stachura

    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...

  5. 1-111-S-SpreadOfInformation

    02 Sep 2019 | Modeling Scenarios | Contributor(s):: Jeff Pettit

    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model which can be compared to predicted data, measured data, and modeled data. Part 3 can require students to move from...

  6. 1-092-S-DashItAll

    01 Sep 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic Hill-Keller model for a...

  7. 1-084-S-GoingViral

    31 Aug 2019 | Modeling Scenarios | Contributor(s):: Bill Skerbitz

    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. 3-064-S-GearTrain

    31 Aug 2019 | Modeling Scenarios | Contributor(s):: Lukasz Grabarek

    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. 9-015-S-UnearthingTruth

    28 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    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...

  10. 1-083-S-FallingMeteorites

    24 Aug 2019 | Modeling Scenarios | Contributor(s):: Lyle Clifford Smith

    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. 1-082-S-MirrorMirror

    21 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    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...

  12. 9-010-S-TravelingWaves

    21 Aug 2019 | Modeling Scenarios | Contributor(s):: Eric Stachura

    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....

  13. 3-011-S-EulerBallThrowing

    19 Aug 2019 | Modeling Scenarios | Contributor(s):: Chris McCarthy

    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. Ice Coverage in the Arctic Climate over time

    17 Aug 2019 | Articles and Publications | Contributor(s):: Wisam Victor Yossif Bukaita, Kelcey Meaney, Angie Dimopulos

    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. 5-002-S-PhasePortraitForRelationshipDynamics

    15 Aug 2019 | Modeling Scenarios | Contributor(s):: Lawrence C Udeigwe

    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....

  16. 1-068-S-WaterBottleCooling

    14 Aug 2019 | Modeling Scenarios | Contributor(s):: Eli E Goldwyn

    The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room. The goal is for the students to understand...

  17. 3-150-S-ItsABlastFurnace

    13 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    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. 1-076-S-ClimateBifurcation

    08 Aug 2019 | Modeling Scenarios | Contributor(s):: Mayer Humi

    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. 9-005-S-InvasiveSpeciesModel

    08 Aug 2019 | Modeling Scenarios | Contributor(s):: Eric Stachura

    This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion. Students will explore various Mathematica modules...

  20. Moon and Mars Exploration

    07 Aug 2019 | General Resources | Contributor(s):: Frank Wattenberg

    Description to be provided by Dr. Frank Wattenberg, Department of Mathematical Sciences, United States Military Academy, West Point NY USA.Current materials can be found at the Moon and Mars Exploration web site.