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    Modeling Scenario
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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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    1-059-ContainerShapeFallingWater-ModelingScenario
    We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.
    containersTorricelli's Lawshapedischarge coefficient
    Modeling Scenario
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    6-045-CholeraTranmission-ModelingScenario
    During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools.
    infectious diseasecholeraendemicdisease-freetransmission ratewaterborne pathogen
    Modeling Scenario
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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
    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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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Modeling Scenario
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    5-030-AirshedSulphur-ModelingScenario
    Temperature inversions and low wind speeds trap air pollutants in a mountain valley for a period of time. Gaseous sulfur compounds are a significant air pollution problem. We offer a model for analysis to predict long-term levels of levels of...
    sulphurpollutionairshedhydrogen sulfidesulfur dioxide
    Modeling Scenario
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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
    Modeling Scenario
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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
    Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error
    Modeling Scenario
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    1-119-DairyFarming-ModelingScenario
    A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.
    population dynamicsdairyfarmers' marketsgrowthcow
    Modeling Scenario
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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
    population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery