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    Article or Presentation
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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
    Modeling Scenario
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    232

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    1-027-StochasticProcesses-ModelingScenario
    We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
    VarianceMeanstochasticrandomoperations researchindustrial engineeringPoisson processtraffic
    Modeling Scenario
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    1-001d-HotelPopulationDecay-ModelingScenario
    You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel. Before you run the simulation in MATLAB, answer some questions.
    simulationlogisticexponential decayfitting
    Modeling Scenario
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    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
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    1-122-SpreadPEV-ModelingScenario
    We present data on world sales data of plug-in electric vehicles (PEVs) and request a model on the rate of change in sales over time, leading to prediction as to number of PEVs in the future.
    datalogisticpredictionspreadplug-in vehiclePEV
    Modeling Scenario
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    1-084-GoingViral-ModelingScenario
    Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.
    simulationlogisticrandomfittingpartial fractions
    Modeling Scenario
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    1-047-Condensation-ModelingScenario
    We simulate 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. Animations are produced and data is offered for modeling with a differential...
    simulationsum of square errorscondensationbest fit
    Technique Narrative
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    1-001-SepartionOfVariables-TechniqueNarrative
    We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
    solutionsstrategymethodapplications
    Potential Scenario
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    69

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    2019-Ekici_Plyley. Inquiry-Based_Modeling_of_Population_Dynamics_With_Logistic_Differential_and_Difference_Equations
    Inquiry-based learning activities on modeling and controlling the growth of locally relevant species, such as lionfish or sea turtles, are developed by the authors.
    population dynamicslogisticInquiry-based modelingIBL
    Modeling Scenario
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    1-054-GrowthInFarmland-ModelingScenario
    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple...
    fittingfarmfarmland
    General Resource
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    Instructor Solutions Second Edition SIMIODE Textbook HTML Version
    This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
    textbookhtmlSIMIODE textbookSecond Edition
    Modeling Scenario
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    1-104-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.
    infectionlogisticexponentialcovidcarrying capacity
    Modeling Scenario
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    1-104A-T-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions and comparing to actual disease data sets.
    regressioninfectionCOVID19carrying capacitylogistic equationexponential model
    Modeling Scenario
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    1-143-PopulationModelVariationsMATLAB-ModelingScenario
    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.
    population dynamicsecologylogistic growthbifurcation theoryslope fieldsextinctionharvestingqualitative analysisstocking
    Modeling Scenario
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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
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    1-030-EyeModel-ModelingScenario
    We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina.
    retinal surgeryAkaike Information CriterionSpanishsum of square errorssurgeryretionaophthalmologyeyeintraocular gas bubble
    Modeling Scenario
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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and...
    optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz
    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
    Article or Presentation
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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
    Modeling Scenario
    368

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    221

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    1-005C-OilSlick-ModelingScenario
    We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate.
    Problem Solvingoil slickspreadfittinglineassumptions