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    Modeling Scenario
    269

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    115

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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle
    Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error
    Article or Presentation
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    40

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    2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
    We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
    vibrationresonancetuned mass damperpeak frequency responseexcitation
    Modeling Scenario
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    1-011A-Kinetics-ModelingScenario
    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.
    kineticsLaw of Mass Actionfittingorder of reactionchemical reaction
    Modeling Scenario
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    1-016-DogDrugs-ModelingScenario
    We offer a problem to determine the necessary drug administration in order to keep a dog sedated with specific information on half-life for an exponentially decaying presence of the drug in the body.
    wild_dogsdrug discoveryhalf-lifepentobarbital sodiumanesthesia
    Modeling Scenario
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    179

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    5-010-DNADegradation-ModelingScenario
    We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process.
    DNA\kinetisplasmaratpharmacokinetis
    Modeling Scenario
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    3-110-MilitarySpringMassApplication-ModelingScenario
    The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation, solve, and interpret the results.
    dampingresonancebeatsspring-mass systemLaplace TransfomDirac Delta function
    Modeling Scenario
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    4-060-CircuitTuner-ModelingScenario
    We present essential definitions and laws for the study of simple RLC electrical circuits and build a differential equation model using these notions. We describe how such a circuit can be used to tune a radio to a certain input frequency.
    resistanceciircuittuned mass tunerfrequencyKirchhoffvoltagegainfrequency responseamplitudes Voltage LawinductancecapacitorI am currently working in redesining an existing microbiology course. I would like to be part of ed
    Modeling Scenario
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    1-086-MedicinalPill-ModelingScenario
    Administration of a medicinal pill in single and multiple doses is modeled.
    medicinespillovercompartmentbloodstreamGIT-Track
    Modeling Scenario
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    292

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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 use data included in the student version.
    data collectionexperimenthalf-lifeNewton's Law of Coolingwater bottle
    Modeling Scenario
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    394

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    5-011-ModelingIbuprofren-ModelingScenario
    We consider modeling of data from a clinical experiment administered as oral doses of 400 mg ibuprofen, an analgesic pain reliever. Concentrations of ibuprofen in the serum/plasma of the subjects were recorded after the initial ingestion of the...
    dataAICAkaike Information Criterionabsorptionsum of square errorscompartment modelibuprofendelay
    Modeling Scenario
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    179

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    3-051-ProjectileMotions-ModelingScenario
    We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
    trajectorylaunching radiantprojectile motionprojectileno resistanceangle of launch
    Modeling Scenario
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    1-144-HeatCool-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
    temperatureNewton's Law of Coolingcooling
    Modeling Scenario
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    1-045-TimeOfDeath-ModelingScenario
    Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.
    body masstemperaturedeathNewton's Law of Coolingbody temperature
    Modeling Scenario
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    1-085-DrugBolus-ModelingScenario
    Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?
    concentrationsum of square errorsbolusdrugrate constantadminister
    Article or Presentation
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    70

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    2004-Mark_McCartney-Using_second-order_ordinary_differential_equations_to_model_traffic_flow
    A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted.
    differential equationstraffic flowvehicle followsecond order
    Modeling Scenario
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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 B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Modeling Scenario
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    3-034-CarSuspension-ModelingScenario
    We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.
    designspring-mass-dashpotspring constantunderdampingcar suspensionsuspension tolerancestatic equilibrium
    Modeling Scenario
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    1-130-AspirinAbsorption-ModelingScenario
    We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    pharmacokineticsdrugaspirin
    Modeling Scenario
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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
    energymass-spring systemkinetic energypotential energytotal energy
    Modeling Scenario
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    5-022-ColdPill-ModelingScenario
    A model for the flow of a cold pill drug through the gastrointestinal compartment to the bloodstream compartment of a human subject is proposed. Students solve the system of differential equation model, use known parameter values, and plot solutions.
    ratesmedicinedrug discoverycompartmentcold pillgastrointestinalbloodstream