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  1. 1-082-T-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...

  2. 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...

  3. 9-010-T-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. Students...

  4. 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....

  5. 3-011-T-EulerBallThrowing

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

    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...

  6. 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...

  7. 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...

  8. 5-002-T-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....

  9. 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....

  10. 1-068-T-WaterBottleCooling

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

    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...

  11. 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...

  12. 3-150-T-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...

  13. 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...

  14. 1-076-T-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...

  15. 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.

  16. 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...

  17. 9-005-T-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...

  18. 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. 

  19. 3-130-T-MatterOfSomeGravity

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

    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation. The theme of the project is that one often has a physical model for a system but in which the model contains unknown parameters or...

  20. 3-130-S-MatterOfSomeGravity

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

    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation. The theme of the project is that one often has a physical model for a system but in which the model contains unknown parameters or...