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    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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    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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    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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    3-033-S-TimeUpTimeDown-ModelingScenario
    We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.
    projectile motionapexvertical motion
    Modeling Scenario
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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
    Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous
    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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    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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    1-130-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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    3-009-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 velocity.
    resistancegravityfalling bodyterminal velocitybuoyancy
    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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    3-013-WhiffleBallFall-ModelingScenario
    We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.
    Akaike Information CriterionresistancegravityFree Body Diagramforcefalling objectWhiffle ball
    Modeling Scenario
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    3-026-SpringInverseProblem-ModelingScenario
    We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.
    datamassinverse problemspring\parameter estimate
    Modeling Scenario
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    3-035-StadiumDesign-ModelingScenario
    For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?
    projectile motionbaseballparametric equationstadiumhome runno reistantfairnessno resistance
    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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    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
    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
    General Resource
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    Instructor Solutions Second Edition SIMIODE Textbook HTML Version
    This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
    textbookhtmlSIMIODE textbookSecond Edition
    Modeling Scenario
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    3-130-MatterOfSomeGravity-ModelingScenario
    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
    gravityinverse problemacceleration
    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