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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.

    Keywords: Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous

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    3-100-Ripcord-Toys-ModelingScenario
    This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct...

    Keywords: dataphysicsdynamicsdata collectionrollingslippingripcordtoy

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    6-068-VisualizingPredator-PreyCycles
    In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be...

    Keywords: nullclinespredator-preyGeometrypredatorRunge-Kuttapreylimit cycle

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    1-024-MalariaControl-ModelingScenario
    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.

    Keywords: population dynamicsmalariaPolicyDecision-makingEuler's methodpharmacokineticsmosquitoimproved Euler's methodHuen's methodUS Army

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    3-110-MilitarySpringMassApplication-ModelingScenario
    The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation,...

    Keywords: dampingresonancebeatsspring-mass systemLaplace TransfomDirac Delta function

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    1-065-AlgalBlooms-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.

    Keywords: direction fieldstool:dfieldalgaeharmful algae bloomspopulationcompartmentLake Chapala

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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.

    Keywords: bNewton's Law of Coolingwater bottleautonomousbottle

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    3-072-EarthQuakePartI-ModelingScenario
    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.

    Keywords: earthquakevibrationamplituderesonanceundampedspring-mass system

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    4-020-AnIEDBlast-ModelingScenario
    These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use...

    Keywords: applied mathematicsforcesFree Body DiagramImprovised Explosive Devicessum of forces

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    9-125-BeamModeling-ModelingScenario
    This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam...

    Keywords: Fluid MechanicsbeamcantileverimpulseLaplace transformboundary conditionfourth order

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    6-067-LotkaVolterra-ModelingScenario
    This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities...

    Keywords: time seriesdatacompetitionLotka-Volterramodel fittingpredictiongauseRexperimental

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    5-002-RelationshipDynamics-ModelingScenario
    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed.

    Keywords: love affairRomeo and Juliet

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    1-062-BacteriaGrowth-ModelingScenario
    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches: exponential growth fit, difference equation, differential...

    Keywords: bacteriaexponentialgrowth

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    1-109-EmployeeAttrition-ModelingScenario
    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.

    Keywords: populationlinear growthdecayemployeeattrition

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    1-037-CommonColdSpread-ModelingScenario
    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more...

    Keywords: diseasecommon coldresidence hall

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    6-015-CombatingEbolaEpidemic-ModelingScenario
    This project offers students a chance to make a policy recommendation based on analysis of a nonlinear system of differential equations (disease model). The scenario is taken from the fall of 2014...

    Keywords: diseaseEbolaAnalysisPolicydecision

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    9-010-TravelingWave-ModelingScenario
    Students are taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation model, after a change of variables, students...

    Keywords: traveling wavesseepage velocityporous medium

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    3-103-PullBackCars-ModelingScenario
    This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and...

    Keywords: modelingdynamicshands-ontoypull-back carpullback

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    2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
    Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.

    Keywords: falling bodydimensional analysisdrag

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    1-003-CollegeSavings-ModelingScenario
    We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.

    Keywords: collegesavingsinterest ratecollege costsensitiviyty

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