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    1-090-EmptySphericalTank-ModelingScenario
    We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to...

    Keywords: VolumesphereTorricelli's Lawtimingspherical tankfluidempty

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    1-091-InvestigatingSlopeFields-ModelingScenario
    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss...

    Keywords: slope fieldspopulation

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    1-092-DashItAll-ModelingSenario
    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting...

    Keywords: datarunningsprintHill-Kellerworld recordOlympics

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    1-093-SucroseReaction-ModelingScenario
    We offer data on the hydrolysis of sucrose in the presence of catalyst sucrase. We present students with several models and ask which model is best. We ask students to estimate parameters for the...

    Keywords: kineticsMichaelis-Mentenhydrolysisreactionsucrose

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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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    1-098-NeuronDetection-ModelingScenario
    Students study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can help understand basics of neural dynamics. The modeling framework is known in ...

    Keywords: biologyneuroscienceneuron physiologyvoltageintegrate and firethrefholscoincidence detectionRC circuit

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    1-100-EngineeringDemographics-ModelingScenario
    Students show how models can be used to examine social issues. The students examine three different models and use numerical methods to apply each model to demographic data for the percentage of...

    Keywords: logisticpopulationImproved Euler MethodGompertzdemographicswomenautonomous

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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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    1-104-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.

    Keywords: infectionlogisticexponentialcovidcarrying capacity

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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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    1-110-TidePoolSnails-ModelingScenario
    Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the...

    Keywords: datasnailstemperatureNewton's Law of CoolingcoolingNewtonwarmingtital pooltide pool

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    1-111-SpreadOfInformation-ModelingScenario
    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with...

    Keywords: datalogisticracismprejudicemisinformationmemesspreaddisinformationinformationliesGoogle Trendscoinspennies

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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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    1-115-ModelingWithFirstOrderODEs-ModelingScenario
    Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.

    Keywords: bacteriafalling objectNewton's Law of Coolingdrugcoolingdrag

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    1-116-TropicalStormWindspeeds-ModelingScenario
    We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential...

    Keywords: hurricanedecaytropical stormcyclones

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    1-118-SolowEconomicGrowth-ModelingScenario
    Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a...

    Keywords: optimizationeconomicssteady stategrowthSolow-Swan modelcapitalproductionlaborGolden Rule of Economic Growth

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