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  1. 1-092-T-DashItAll

    01 Sep 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  2. 1-092-S-DashItAll

    01 Sep 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  3. 1-083-T-FallingMeteorites

    24 Aug 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  4. 1-082-T-MirrorMirror

    21 Aug 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  5. Ice Coverage in the Arctic Climate over time

    17 Aug 2019 | Articles and Publications | Contributor(s): Jessica Libertini

    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...

  6. 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....

  7. 1-068-T-WaterBottleCooling

    14 Aug 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  8. 1-001d-T-HotelPopulationDecay

    03 Jul 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

  9. 1-001c-S-PopulationDecayThenSome

    18 Jun 2019 | Modeling Scenarios

    This is an adaption of Modeling Scenario 1-001-S-MandMDeathAndImmigration  in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.

  10. 1-107-T-ClothDry

    27 Apr 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  11. 7-011-Text-T-CoupledSystemLaplace

    31 Mar 2019 | Technique Narratives

    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

  12. 7-011-Text-S-CoupledSystemLaplace

    31 Mar 2019 | Technique Narratives

    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

  13. 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...

  14. 5-005-Text-T-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    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...

  15. 5-005-Text-S-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    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...

  16. 1-125-T-DiceyPopulations

    04 Mar 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    We offer students an opportunity to generate unique data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters and try to explain how the simulation...

  17. 1-077-T-RLMSimSeriesCircuit

    03 Mar 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

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

  18. 1-042-Kool-Aid Modeling Video

    24 Feb 2019 | General Resources | Contributor(s): Jessica Libertini

    This is a video which can be used with students after they have worked on the Modeling Scenario 1-042-KoolAid. Dina Yagodich, Frederick Community College, Frederick MD USA produced the video in support of her students who thoroughly enjoyed doing this Modeling Scenario.This video is only...

  19. 1-143-S-PopulationModelVariationsMATLAB

    17 Feb 2019 | Modeling Scenarios

    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations.  They will also work with other utilities...

  20. 1-003-T-Text-IntroNumericalMethods

    10 Jan 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    We develop elementary approaches to numerically solving first order differential equations with Euler's Method and Improved Euler's Method. We ask students to develop these geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different...