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    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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    1-011-Kinetics-ModelingScenario
    We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.
    kineticschemistryLaw of Mass Actionchemical kineticsorder of reactionchemical reaction
    Modeling Scenario
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    1-132-DigoxinElimination-ModelingScenario
    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    nullclinespharmacokineticsdigoxindrug eliminationtwo compartment
    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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    1-131-CaffeineElimination-ModelingScenario
    We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    caffeineeliminationpharmacokineticsdrug
    Modeling Scenario
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    1-084-GoingViral-ModelingScenario
    Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.
    simulationlogisticrandomfittingpartial fractions
    Modeling Scenario
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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 maximize the distance the ball lands from the...
    codingdragonVectorsEuler's methodball
    Modeling Scenario
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    3-030-SecondOrderIntro-ModelingScenario
    We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
    parameter estimationnon-homogeneousSpanishfrequencybuoyancyinverse problemthrustunderdampedfirst passagespring mash dashpotrealcomplexhomogeneoussuperpositionparachuteoverdampedcritically dampedbuoyquadratic equationrootsrocket flight
    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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    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
    Potential Scenario
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    2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics
    This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.
    projectileair resistancefree falldragharmonic oscillation
    Modeling Scenario
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    5-001-LSD-ModelingScenario
    We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature.
    LSDSpanishcompartmentpharmacokineticslysergic acid diethylamide
    Modeling Scenario
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    3-040-FirstPassageTime-ModelingScenario
    We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
    oscillatordampedunderdampedfirst passagefirst passage timespring mash dashpot
    Modeling Scenario
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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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    3-075-RLCCircuits-ModelingScenario
    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.
    resistancecircuitvoltageinductancecapacitancecurrentKirchhoff's Law
    Modeling Scenario
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    3-060-DataToDifferentialEquation-ModelingScenario
    Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.
    Association & Data Fittingmassspring-mass systemspring\total distancenumerical differentiation
    Modeling Scenario
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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, differential equation, and parameter estimation...
    dataheart death rate
    Modeling Scenario
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    3-095-ShotInWater-ModelingScenario
    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.
    projectile motionterminal velocityprojectilewater resistancereduction of orderfrictionair resistance
    Modeling Scenario
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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 ratio is not immediately intuitive.
    population dynamicsdairyfarmers' marketsgrowthcow
    Modeling Scenario
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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 exponential, power law, Bertalanffy, logistic, and...
    optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz