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    Potential Scenario
    182

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    2012-Jambhekar-Breen-Extravascular Routes Of Drug Administration in Basic Pharamacokinetics
    This provides an excellent step-by-step of the physiology, construction of model, and notions like peak concentration as well as issues like lag time.
    concentrationphysiologydrugslag timeExtravascularPharamacokineticspeak time
    Potential Scenario
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    85

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    1975-David_Burghes-Population dynamics An introduction to differential equations
    In this paper a number of population models, which lead to differential equations, are derived. First-order variables separable equations are formulated from the Malthusian population model and its extension to include crowding effects.
    fishpredator-preylogisticpopulationdelaylag
    Potential Scenario
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    2005-Minna_Wedenberg-Pharmacokinetic modeling of gastric emptying
    The development of new drug substances is a complex, time consuming and expensive process. Reducing the time for drug development and avoiding late termination of candidate drugs are important challenges for the pharmaceutical industry.
    paracetamolpharmacokineticsstomachsmall intestinesulfapyridine
    Potential Scenario
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    1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation
    The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.
    kineticsnonlinear regressionsum of square errorsMonodlinearizemineralizationsubstratescarbonaceous
    Potential Scenario
    147

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    45

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    2011-Teleken-EtAl-Mathematical modeling of microbial growth in milk
    A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth.
    bacteriadairymilkfood safetymicrobilogy
    Potential Scenario
    120

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    61

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    2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
    A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
    delaytime delystep response
    Modeling Scenario
    429

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    330

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    1-061-PotatoCooling-ModelingScenario
    We model the cooling of a baked potato and compare it to student-collected data.
    least sum of square errorsNewton's Law of Coolingcoolingpotato
    Article or Presentation
    130

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    2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
    The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
    Newton's Law of Coolingtime of deathdouble exponentialcoroner
    Potential Scenario
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    1999-Leonid_Hanin-Which tank empties first
    Suppose that water towers like those shown in the opening are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first?
    tankTorricelli's Lawspherical tankemptyfrustrum of conecylinder
    Potential Scenario
    817

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    2019-Stender_EtAl-Recovery_Of_Differential_Equations_From_Impulse_Response
    In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation.
    time seriesregressionresponseimpulseoscillationsignal processingsparse regressionsystem identification
    Modeling Scenario
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    1-005-OilSlick-ModelingScenario
    We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.
    model fittingspreadsheetsSpanishderrame de petróleodatosexpansiónoil slick
    Modeling Scenario
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    123

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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
    Potential Scenario
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    2008-Brewer-EtAl-Fitting ordinary differential equations to short time course data
    In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters particularly suited to situations where noise levels are...
    time seriesEvaluation SPLINEgeneleast squaresbifurcation
    Modeling Scenario
    774

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    9-014-TurkeyCook-ModelingScenario
    The goal of this project is to investigate several models for the cooking time for a turkey based on weight, test these models with data obtained from heating curves for turkeys of various weights, and develop a new model to fit this data.
    sphereheat equationturkeyPanofskyradial symmetry
    Potential Scenario
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    2017-Anders_Kallen-Single species models in continuous time
    Part of a series of Lecture notes this lecture contains rich materials on logistic harvest models, spruce budworms, and chemostat.
    chemostatlogisticharvestspruce budworm
    Potential Scenario
    153

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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Potential Scenario
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    1999-F_Brauer-What Goes Up Must Come Down
    This paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces.
    projectilefrictionfalling timerising timemaximum height
    Article or Presentation
    272

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    79

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    2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick
    An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. Model this.
    differential equationssimulationparameter estimationdifference equation
    Modeling Scenario
    309

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    175

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    1-071-NewtonWatson-ModelingScenario
    Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis
    temperaturedeathNewton's Law of Coolingtime of deathSherlock Holmes
    Modeling Scenario
    429

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    119

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    6-067-LotkaVolterra-ModelingScenario
    This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities of R and R studio.
    time seriesdatacompetitionLotka-Volterramodel fittingpredictiongauseRexperimental