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    Modeling Scenario
    179

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    167

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    9-152-HorizontalBeam-ModelingScenario
    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.
    Polynomial dynamical systembeamcantilever
    Modeling Scenario
    237

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    334

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    9-125-BeamModeling-ModelingScenario
    This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.
    Fluid MechanicsbeamcantileverimpulseLaplace transformboundary conditionfourth order
    Modeling Scenario
    235

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    592

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    9-020-HeatDiffusion-ModelingScenario
    This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
    laboratoryDiffusionheat
    Potential Scenario
    160

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    48

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    1969-Carl_Metzler-A mathematical model for the pharmacokinetics of LSD effect
    Contains data on performance scores vs. plasma levels of LSD in human tissues.
    LSDtestingpharmacokineticsperformanceplasma level
    Modeling Scenario
    305

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    207

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    1-051-OneTankSaltModel-ModelingScenario
    A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...
    compartmentsalttankmixingflow
    Modeling Scenario
    245

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    157

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    0

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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
    bNewton's Law of Coolingwater bottleautonomousbottle
    Potential Scenario
    208

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    89

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    1971-Carl_Metzler-Usefulness Of Two Compartment Open Model In Pharmacokinetics
    Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism and excretion of a drug. In this article two applications of the two compartment open model are discussed.
    LSDcompartmentpharmacokinetics
    Article or Presentation
    174

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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
    Article or Presentation
    200

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    76

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    1994-Brian_Winkel-Ant_Tunnels_and_Calculus
    A simple mathematical model describing the time it takes for an ant to construct a linear tunnel of length x is produced from five intuitively acceptable assumptions.
    differential equationsdifference equationfirst orderderivative definitionant tunnel
    Article or Presentation
    233

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    70

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    2009-Brian_Winkel-Population_modelling_with_MandMs
    Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented.
    simulationparameter estimationimmigrationdeathdifference equation
    Article or Presentation
    164

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    54

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    0

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    2009-Agnes_Rash-Brian_Winkel-Birth_and_Death_Process_Modeling_Leads_to_the_Poisson_Distribution
    In this paper there are details of development of the general birth and death process from which we can extract the Poisson process as a special case.
    ProbabilityMeanPoisson processbirth and death processinfinite number of differential equations
    Technique Narrative
    401

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    206

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    9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
    The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
    Maternal-Fetal interfaceheat equationConservation of Energytheat fluxEuler's forward methodcentral differenceskin burnhyperthermiathermal conductivitylayers
    Article or Presentation
    941

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    86

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    0

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    SIMIODE Spring 2024 Webinars - Insightmaker
    We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
    modelingsimulationSoftwarepythonsystemsInsightMakerflowCategory Theorystockstock-flow
    Potential Scenario
    165

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    45

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    1971-Boyes-Scott-Jebson-Godman-Julian-Lidocaine in Man
    Plasma levels of lidocaine were measured in 5 normal male volunteers following both intravenous and oral administration of the drug.
    pPharmacologypharmacokineticslidocaine
    Potential Scenario
    282

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    72

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    1968-Wagner-Aghajanian-Bing-Correlation of performance test scores with tissue concentration of lysergic acid diethylamide
    This paper offers a two compartment model of lysergic acid diethylamide (LSD) in volunteer students and through parameter estimation models the amount of LSD in the tissue after its initial administration through the plasma.
    LSDcorrelation coefficientcompartment modellysergic acid diethylamideperformancetest scoretissue concentration
    Potential Scenario
    294

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    47

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    2018-Robert_Phair-Differential_equation_methods_for_simulation_of_GFP_kinetics_in_non–steady_state_experiments
    Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes.
    protein quality controlkineticsCellssteady statechemical kineticsfluouresencephotoactivationinytracellular
    Potential Scenario
    295

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    51

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    2008-Claire_Vailance-Reaction_Kinetics-Course_Notes
    This is but one of several set of notes which may interest the reader on chemical kinetics.
    kineticsparametersrate constantchemical kineticsreactions
    Article or Presentation
    184

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    56

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    2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
    We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
    circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit
    Article or Presentation
    127

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    64

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    1992-Emelie_Kenney-Differential_equations_and_the_AIDS_epidemic
    This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative as a rate of change.
    datafirst orderparameterAIDS
    Modeling Scenario
    321

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    211

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    9-012-PDEGuitarTuning-ModelingScenario
    We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.
    extensionsine wavesfrequencyguitardampingFourierstringtuning