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    1-001a-MMDeathImmigration-Variation-ModelingScenario
    We model exponential death with m&m's as well as death with immigration.

    Keywords: simulationdatam&mimmigrationdeath

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    3-002-ModelsMotivatingSecondOrder-ModelingScenario
    Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because...

    Keywords: resistancespring massoscillationHooke's Lawdampening

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    3-006-Buoyancy-ModelingScenario
    We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body...

    Keywords: data collectionexperimentbuoyancyNewton's Second Law of Motion

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    3-011-EulerBallThrowing-ModelingScenario
    If a tennis ball is thrown through the air it will 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...

    Keywords: codingdragonVectorsEuler's methodball

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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle

    Keywords: Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error

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    4-039-FallingDarts-ModelingScenario
    we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and...

    Keywords: optimizationresistanceterminal velocitymuzzle velocitydrag coefficientfree fallair drag

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    5-012-LipoproteinModeling-ModelingScenario
    Data from a study on the amounts of low-density-lipoprotein (LDL), form of cholesterol, in blood plasma is presented. Students build, validate, and use a compartment model of the kinetic...

    Keywords: wildlifelow-density-lipoproteintracercompartment modelcholesterolblood plasmabody tissue

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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.

    Keywords: attritionLanchester modelpredator-predatorN-square Law

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    5-080-SpaceFlightRecolonize-ModelingScenario
    This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of...

    Keywords: optimizationsum of square errorsvector calculusLagrange multipliersline integrals

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    6-019-EnablingEpidemicExploration-ModelingScenario
    We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the...

    Keywords: Akaike Information CriterionMichaelis-Mentenepidemicsaturationgradientleast sum of square errors

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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of...

    Keywords: Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error

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    1-036-NeutralBuoyancy-ModelingScenario
    An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenon

    Keywords: DensitybuoyancyArchimedes’ Principlefloatneutral buoyance

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    1-009-ICUSpread-ModelingScenario
    We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

    Keywords: logisticsum of square errorsIntensive Care Unithospitalspread

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    4-035-ParEstSteadyState-ModelingScenario
    Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the...

    Keywords: driversteady statesum of square errors

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    3-150-ItsABlastFurnace-ModelingScenario
    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.

    Keywords: steady stateheat equationinverse problemfurnace

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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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    10-100-InsectOutbreaks-ModelingScenario
    We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.

    Keywords: ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

    Keywords: Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency

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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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    3-105-FrequencyResponse-ModelingScenario
    We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

    Keywords: transient dynamicscircuitspring massdriverfrequency responseamplitudesteady state

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