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    1-170-CensusModeling-ModelingScenario
    Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in...

    Keywords: logistic growthexponentialpopulationU.S. Census DataassumptionGoogle SheetsUnites StatesGuatemala

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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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    3-017-StackedCoffeeFiltersFalling-ModelingScenario
    Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power....

    Keywords: dataresistancefalling bodycoffee filterstacked

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    3-019-ShuttleCockFalling-ModelingScenario
    We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and...

    Keywords: resistancegravityFree Body Diagramshuttlecockfallingc object

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    3-027-BobbingDropping-ModelingScenario
    We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law...

    Keywords: drug resistancedirectedbuoyancyfree fallstatic equilibriumdisplacement

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    3-076-CircuitBuilding-ModelingScenario
    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.

    Keywords: simulationexperimentMultisimcircuitinductancecapacitorKirchhoff's Voltage Lawresistor

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    3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
    Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.

    Keywords: massundampedFree Body Diagramspringstwo springsoscillationspring constantfixed ends

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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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    5-023-FakingGause-ModelingScenario
    We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competition in the 1930's studies of G. F. Gause in the...

    Keywords: competitionlogisticyeastGauseparameciumpoplulation

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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF)...

    Keywords: vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension

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    6-002-EulerCromerPendulum-ModelingScenario
    This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method...

    Keywords: pendulumsemi-implicit methodsEuler-Cromernumerical solvers

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    6-007-FunctionsAndDerivativesInSIRModels-ModelingScenario
    Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious...

    Keywords: epidemiologyspecies interactionsderivativesvisualizationinfectionSIR modelsLaw of Mass Action

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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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    6-023-DroneHeadingHome-ModelingScenario
    We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.

    Keywords: dronesoursuitflight pathchange of variables

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    6-024-DronePackageDelivery-ModelingScenario
    Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package.

    Keywords: VectorsTrigonometryFlightdronesparametric curveImproved Euler MethodRunge-Kutta

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    6-045-CholeraTranmission-ModelingScenario
    During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools.

    Keywords: infectious diseasecholeraendemicdisease-freetransmission ratewaterborne pathogen

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    6-028-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.

    Keywords: concentrationcomparmentsalttankmixing

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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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    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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