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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 estimation non-homogeneous Spanish frequency buoyancy inverse problem thrust underdamped first passage spring mash dashpot real complex homogeneous superposition parachute overdamped critically damped buoy quadratic equation roots rocket flight
    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.
    LSD Spanish compartment pharmacokinetics lysergic acid diethylamide
    Modeling Scenario
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    7-011-CoupledSystemLaplace-ModelingScenario
    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
    transfer function polycarbonate baby heater coupled system heating
    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.
    design spring-mass-dashpot spring constant underdamping car suspension suspension tolerance static equilibrium
    Modeling Scenario
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    29

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    1-013-SleuthingWithDifferentialEquations-ModelingScenario
    We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
    projectile motion acceleration Newton's Law of Cooling speeding
    Modeling Scenario
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    58

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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.
    kinetics Law of Mass Action fitting order of reaction chemical reaction
    Modeling Scenario
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    18

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    1-005B-ChemDataCollection-ModelingScenario
    A chemistry graduate student is collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not note the times.
    kinetics laboratory order of reaction chemical reaction chemical data infusion
    Modeling Scenario
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    20

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    1-040-OutcomeSavings-ModelingScenario
    We ask students to build a model for a savings account and to determine the monthly deposit in a savings account in order meet a long term savings goal.
    Pop_Growth Pilot savings growth deposit g
    Modeling Scenario
    77

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    24

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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 mass temperature death Newton's Law of Cooling body temperature
    Modeling Scenario
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    23

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    1-005A-ChemDataCollection-ModelingScenario
    A student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting data. She only collects data at the start and end of a number of ten minute intervals and does not keep track of when the observations are...
    linear regression kinetics chemistry order of reaction chemical reaction chemical data infusion differencing
    Modeling Scenario
    82

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    52

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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.
    kinetics chemistry Law of Mass Action chemical kinetics order of reaction chemical reaction
    Modeling Scenario
    60

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    18

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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?
    concentration sum of square errors bolus drug rate constant administer
    Modeling Scenario
    50

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    18

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    1-086-MedicinalPill-ModelingScenario
    Administration of a medicinal pill in single and multiple doses is modeled.
    medicine spillover compartment bloodstream GIT-Track
    Modeling Scenario
    59

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    10

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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 dynamics dairy farmers' markets growth cow
    Modeling Scenario
    48

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    16

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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.
    pharmacokinetics drug aspirin