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    1-074-BottleWaterFlow-ModelingScenario
    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow.

    Keywords: bwaterTorricelli's Lawbottle

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    1-094-SteepingTea-ModelingScenario
    We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our...

    Keywords: concentrationSurface AreacolorNewton's Law of Coolingteasugar

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    1-095-RatingChessPlayers-ModelingScenarios
    The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario.

    Keywords: simulationchessElo's methodchess rating

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    1-096-OP-AMP-Differentiator-ModelingScenario
    The output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and compared with...

    Keywords: simulationMeasurementfeedbackMultisimcircuitvoltageoperational amplifiervalidationSPICE

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    1-101-ClassMMDeathImmigration-ModelingScenario
    We offer students an opportunity to generate unique data for their team on a death and immigration model using m&m's and then pass on the data to another student team for analysis with a model they...

    Keywords: simulationimmigrationdata collectiondeath

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including ...

    Keywords: optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy

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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including...

    Keywords: optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz

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    1-105-AnimalFall-ModelingScenario
    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

    Keywords: animalNetwon's Second Law of Motionfalling bodyterminal velocityair resistanceNewtonair frictionfall

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    1-114-EarthClimate-ModelingScenario
    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface...

    Keywords: climateenergytemperaturelinearizationphase linesenergy balance modelroot finding

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    1-124-WorldPopulation-ModelingScenario
    We build models of world population using data to estimate growth rate.

    Keywords: population dynamicshumangrowth ratevarying growth rate

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    1-138-InnerEarDrugDelivery-ModelingScenario
    Students examine local drug delivery to the cochlea. The delivery system is modeled as a liquid mixing problem. Students formulate the differential equation, and solve the equation using separation...

    Keywords: concentrationdrug deliveryinner earcochleahearing loss

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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and...

    Keywords: Lanchester's lawssensitivity analysisanalysis

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    1-141-MMGameRevisited-ModelingScenario
    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen...

    Keywords: Probabilitystochastic processesBayesian methodsprobability distribution

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    1-142-WaterBottles-ModelingScenario
    This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or...

    Keywords: data collectionexperimenthalf-lifeNewton's Law of Coolingwater bottle

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    1-160-HeartDeathRate-ModelingScenario
    Students simulate experience from a given data set which represents the heart death rate during the period 2000 - 2010 using several approaches to include exponential decay, difference equation,...

    Keywords: dataheart death rate

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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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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a...

    Keywords: juliaDiffusioninnovationrate of innovationBass modelSolver

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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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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.

    Keywords: phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation

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    3-009-BallDropInWater-ModelingScenario
    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...

    Keywords: resistancegravityfalling bodyterminal velocitybuoyancy

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