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    1-047-Condensation-ModelingScenario
    We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and...

    Keywords: simulationsum of square errorscondensationbest fit

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    1-052-SaltWaterTanks-ModelingScenario
    We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

    Keywords: salttankmixing

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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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    1-092-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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    1-096-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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    1-105-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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    1-116-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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    1-119-DairyFarming-ModelingScenario
    A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This...

    Keywords: population dynamicsdairyfarmers' marketsgrowthcow

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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the...

    Keywords: population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery

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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their...

    Keywords: undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation

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    4-065-GasInjection-ModelingScenario
    Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest...

    Keywords: Prandtl-Blasius equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN

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    6-026-IsleRoyaleModeling-ModelingScenario
    The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle.

    Keywords: ecologyoptimizationpredator-preypopulationvector calculusLagrange multipliersleast squaresIslel Royale

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    3-069-HeatInBar-ModelingScenario
    The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.

    Keywords: heat transferexperimentconductionconvectionboundary conditionsfinite volume method

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    3-070-FallingInWater-ModelingScenario
    We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and...

    Keywords: datawaterresistancefallingbuoyancymass

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    1-126-MarriageMath-ModelingScenario
    We will explore a model which describes the process of entry into marriage by an individual. In the model, rate of change in the fraction of the cohort already married will be investigated along...

    Keywords: marriageGompertz function

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    3-045-RampBounce-ModelingScenario
    Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile...

    Keywords: projectile motioninclined rampcoefficient of restitutionoptimal anglebounce

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    Dendroclimatology
    Dendroclimatologists can reconstruct climate records further into the past than written records, by examining tree rings. Students "reverse-engineer" this process by considering growth rates of a...

    Keywords: linear regressiongraphingdata visualizationstandardizationclimatetree ringsdendrochronology

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    Quantifying Uncertainty and Distinguishing Data Sets in Introductory Physics
    Physics labs are moving increasingly to open-ended experiments where students develop experimental physics skills, rather than verify textbook physics concepts. This sequence of activities sets the...

    Keywords: statisticsMeasurementlaboratoryuncertaintypendulumexperimental skills

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    Fitting Exponential and Logistic Growth Models to Bacterial Cell Count Data
    In this activity, students will model a noisy set of bacterial cell count data using both exponential and logistic growth models. For each model the students will plot the data (or a linear...

    Keywords: modelingdata analysislinear regressiongraphingExponentsoptimizationcalculusInterpreting GraphsFunctionsqbccCellular and Molecular BiologyChoosing modelsUnderstanding ratesConcepts in Statisticsmeasurementsmanipulating equationscreating graphsExponential and Logarithmic Functionsinterpreting tables

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    A How to Guide and Template for Designing a Puzzle Based Escape Room Game
    Educational games are one active and effective way of engaging students with material while also providing additional motivation to tackle challenging concepts. A particularly popular game concept...

    Keywords: Problem SolvingCollaborative WorkCorrect Misconceptions

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