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    Potential Scenario
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    1975-Rodda-Sampson-Smith-The One-Compartment Open Model Parameter Estimation
    A new estimation procedure is proposed for estimating the parameters of the simplest pharmacokinetic model, the one-compartment open model.
    compartment modelpharmacokineticsnonlinear estimationone compartment model
    Article or Presentation
    180

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    63

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    2021-Brian_Winkel-Modelling_sublimation_of_carbon_dioxide
    We report results in our efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in our model.
    dataparameter estimationcarbon dioxidesublimationdry ice
    Modeling Scenario
    289

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    235

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    1-078-MonodGrowthModel-ModelingScenario
    Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
    bacterianutrient cyclesgrowthMonodconsumption
    Potential Scenario
    126

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    57

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    2007-Choisy-Guégan-Rohani-Mathematical Modeling of Infectious Diseases Dynamics
    After presenting general notions of mathematical modeling (Section 22.2) and the nature of epidemiological data available to the modeler (Section 22.3), we detail the very basic SIR epidemiological model (Section 22.5).
    stochasticSIR modeldeterministicincubationinfectives
    Modeling Scenario
    444

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    580

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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
    Modeling Scenario
    253

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    218

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    1-066-USCensusModeling-ModelingScenario
    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.
    datalogisticpopulationGompertzcensusgoodness of fit
    Potential Scenario
    154

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    59

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    1999-Meyer-Ausubel-Carrying Capacity-A Model with Logistically Varying Limits
    This paper extends the logistic equation to simple growth model with a logistically increasing carrying capacity. This is applied to human population situations in several countries with fits to data.
    population dynamicsparameter estimationlimited growthgrowthlogisitic
    Potential Scenario
    140

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    79

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    massoscillationspring\coupled springsperiodicfporcing
    Potential Scenario
    112

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    43

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    2001-Edwards-Buckmire-A differential equation model of North American cinematic box-office dynamics
    A new mathematical model is presented for the box-office dynamics of a motion picture released in North America.
    cinemamoviesbox-office
    Modeling Scenario
    211

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    239

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    4-036-AltitudeDependentGravity-ModelingScenario
    When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.
    agravityprojectilelinearizationltitufealtitude
    Modeling Scenario
    229

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    340

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    6-019-EnablingEpidemicExploration-ModelingScenario
    We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the data offered.
    Akaike Information CriterionMichaelis-Mentenepidemicsaturationgradientleast sum of square errors
    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
    Modeling Scenario
    432

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    1066

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    1-015-Torricelli-ModelingScenario
    We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.
    dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver
    Potential Scenario
    138

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    37

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    2014-Danielsen-Sørensen-Using authentic sources in teaching logistic growth
    This 12 page offering develops issues and questions about using historical materials to motivate mathematics study and develops 9 very rich exercises
    real datalogistichistorical materials
    Potential Scenario
    185

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    78

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    2014-Allen-EtAl-Perturbations in Epidemiological Models -When zombies attack we can survive
    In this paper, we investigate the existence of stability-changing bifurcations in epidemiological models used to study the spread of zombiism through a human population.
    epidemiologydynamical systemszombiesbifurcationperturbation
    Potential Scenario
    130

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    49

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    2012-Yuan_Yuan-A coupled plankton system with instantaneous and delayed predation
    We present two simple plankton population models: one has instantaneous predation, another has delayed predation.
    phytoplanktonbifurcationorbitsherbivorous zooplanktoneffect of fishmaturation time delay
    Potential Scenario
    157

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    72

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    2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus
    I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.
    in-class activityexperimentTorricelli's Lawcylinder of waterexpderiment
    Potential Scenario
    150

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    45

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    2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
    In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.
    logisticexponentialsigmoidtechnological innovationsasymptoticspread of innovation
    Potential Scenario
    191

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    44

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    2000-Dwayne-Anderson-Estimates of the future membership of the Church of Jesus Christ of Latter-Day Saints
    Thus, the purpose of this paper is to model the membership of the Church of the Latter Day Saints from the available data on membership from 1844 to 2000.
    population dynamicslogisticLatter-Day Saints
    Modeling Scenario
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    497

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    1-017-DiseaseSpread-ModelingScenario
    Using a grid and m&m candies, we simulate the spread of disease. Students conduct the simulation and collect data to estimate parameters (in several ways) in a differential equation model for the spread of the disease.