Skip to Main Content
Powered by QUBES

Resources

Text Search:
Applied Filters
    Article or Presentation
    163

    views

    54

    downloads

    0

    comments

    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
    Potential Scenario
    178

    views

    66

    downloads

    0

    comments

    2016-Starling-EtAl-Local Brewery - A Project for Use in Differential Equations Courses
    We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer.
    BEERFermentationbrewery
    Modeling Scenario
    348

    views

    244

    downloads

    0

    comments

    5-007-ChemOpt-ModelingScenario
    Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
    optimizationpYield and sustainabilitynonprofit managementLaw of Mass Actionkineticreaction
    Potential Scenario
    136

    views

    80

    downloads

    0

    comments

    2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
    When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
    pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy
    Potential Scenario
    360

    views

    62

    downloads

    0

    comments

    2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
    This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
    dynamical systemsregulationsteady statesales modelexternal stimulus
    Modeling Scenario
    399

    views

    153

    downloads

    0

    comments

    1-001s-StochasticMDeathImmigration-ModelingScenario
    We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.
    simulationdatalogisticimmigrationstochasticdeathfitting
    Potential Scenario
    123

    views

    55

    downloads

    0

    comments

    2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
    In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.
    regressionlogisticTorricelli's Lawgrowthperiodic process
    Modeling Scenario
    403

    views

    506

    downloads

    0

    comments

    1-047a-CondensationOptimization-ModelingScenario
    We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
    simulationdataoptimizationenergycondensationbest fitcostsum of scquare errors
    Modeling Scenario
    281

    views

    220

    downloads

    0

    comments

    1-035-DotseroVolcanoEruption-ModelingScenario
    In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
    exponential decayhalf-lifedecayEuler's methodcarbon datingdecay rateCarbon-14Dotsero volcanovolcano
    Potential Scenario
    336

    views

    95

    downloads

    0

    comments

    2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics
    We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.
    kineticschemical kineticszeroth order reactionfirst order reactionsecond order reaction
    Modeling Scenario
    266

    views

    387

    downloads

    0

    comments

    1-094-SteepingTea-ModelingScenario
    We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration.
    concentrationSurface AreacolorNewton's Law of Coolingteasugar
    Modeling Scenario
    429

    views

    119

    downloads

    0

    comments

    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
    Potential Scenario
    132

    views

    47

    downloads

    0

    comments

    2007-Ramsay-Hooker-Campbell-Cao-Parameter estimation for differential equations-a generalized smoothing approach
    We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations.
    estimating equationfunctional data analysisGauss–Newton methodparameter cascadeprofiled estimationdynamic system
    Potential Scenario
    294

    views

    51

    downloads

    0

    comments

    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
    Modeling Scenario
    1180

    views

    4065

    downloads

    0

    comments

    1-038-Ebola-ModelingScenario
    Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
    population dynamicsdata analysisexponential growthEbolalogisticepidemic
    Modeling Scenario
    298

    views

    179

    downloads

    0

    comments

    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
    Potential Scenario
    135

    views

    51

    downloads

    0

    comments

    2007-Zenker-Rubin-Clermont-From inverse problems in mathematical physiology to quantitative differential diagnoses
    The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making.
    physiologyinverse problem
    Potential Scenario
    143

    views

    46

    downloads

    0

    comments

    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
    Article or Presentation
    130

    views

    54

    downloads

    0

    comments

    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
    Modeling Scenario
    458

    views

    183

    downloads

    0

    comments

    1-046-GoingViral-ModelingScenario
    Students participate in a simulation of the spread of a viral disease in the classroom and model the process with a logistic differential equation. The simulation uses random numbers and the entire class participates.
    simulationmathematical modeldatalogisticrandom number generatorfittingrandom process