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  1. 9-020-T-HeatDiffusion

    14 Oct 2019 | Modeling Scenarios

    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. 9-020-S-HeatDiffusion

    14 Oct 2019 | Modeling Scenarios

    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...

  3. 1-111-T-SpreadOfInformation

    02 Sep 2019 | Modeling Scenarios

    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with a separable linear first order differential equation which can be compared to predicted data,...

  4. 1-111-S-SpreadOfInformation

    02 Sep 2019 | Modeling Scenarios

    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...

  5. 1-092-T-DashItAll

    01 Sep 2019 | Modeling Scenarios

    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...

  6. 1-092-S-DashItAll

    01 Sep 2019 | Modeling Scenarios

    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. 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...

  8. 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...

  9. 3-150-T-ItsABlastFurnace

    13 Aug 2019 | Modeling Scenarios

    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...

  10. 3-150-S-ItsABlastFurnace

    13 Aug 2019 | Modeling Scenarios

    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...

  11. 3-067-T-RLCSeriesCircuit

    28 Apr 2019 | Modeling Scenarios

    In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).

  12. 1-107-S-ClothDry

    27 Apr 2019 | Modeling Scenarios

    We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...

  13. 1-107-T-ClothDry

    27 Apr 2019 | Modeling Scenarios

    We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...

  14. 5090-T-SolidParticleErosion

    27 Mar 2019 | Modeling Scenarios

    By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface. Examination of the solution will yield a formula for the...

  15. 1-109-T-EmployeeAttrition

    25 Mar 2019 | Modeling Scenarios

    This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

  16. 5-005-Text-T-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives

    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

  17. 5-005-Text-S-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives

    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

  18. 3-009-T-BallDropInWater

    16 Dec 2018 | Modeling Scenarios

    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

  19. 1-053-T-SlimeSpread

    30 Aug 2018 | Modeling Scenarios

    We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

  20. 1-053-S-SlimeSpread

    30 Aug 2018 | Modeling Scenarios

    We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.