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    Technique Narrative
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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
    Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time
    Modeling Scenario
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    9-030-WaterHammer-ModelingScenario
    We develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs) that describes the time evolution of the water hammer phenomenon.
    Stock and Flow modelhyperbolic equationsfinite differenceswater hammerhydrodynamicscompressibilitywave celerity
    Modeling Scenario
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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF) including pitch and bounce of vehicle body on suspension...
    vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension
    Modeling Scenario
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    3-069-HeatInBar-ModelingScenario
    The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
    heat transferexperimentconductionconvectionboundary conditionsfinite volume method
    Technique Narrative
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    107

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    3-090-ChebyshevPolynomialSolution-TechniqueNarrative
    The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
    series soluotionpolynomial solutionsChebyshev polynomialsChebyshev differential equations
    Technique Narrative
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    8-002-TrigSumRepresentation-TechniqueNarrative
    Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.
    estimationTrigonometryTrigonometric Functionssum of square errorsfinite sumFourier seriesFouriere sumspectrumapproximatiopn
    Modeling Scenario
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    9-002-GroundWaterFlow-ModelingScenario
    The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
    sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank
    Modeling Scenario
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    1-031-CoolIt-ModelingScenario
    We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...
    SpanishNewton's Law of Coolingcooling
    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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    1-005-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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    1-004-MicroorganismImmigration-ModelingScenario
    We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.
    continuousimmigrationpopulationdeathdiscrete
    Article or Presentation
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    SIMIODE Spring 2024 Webinars - WikiModel
    WikiModel is cloud-based application and requires no installation and is run via a web-browser to facilitate rapid implementation. Equations are typed in as they appear in a textbook. ODEs are automatically integrated via Runge-Kutta methods.
    modelingSoftwaretoolapplicationWikiModelmodeling cycle
    Modeling Scenario
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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
    optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable
    Modeling Scenario
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    6-003-SchoolFluEpidemic-ModelingScenario
    We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.
    infectionepidemicSIR modelflupeakschool children
    Modeling Scenario
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    1-026-Evaporation-ModelingScenario
    We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective...
    evaporationconealcoholPetri dish
    Modeling Scenario
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    1-019-RocksInTheHead-Modeling Scenario
    We describe an experiment with data on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. Students use the logistic differential equation as a reasonable model and estimate parameters.
    logistic growthparameter estimationexperiment
    Modeling Scenario
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    6-008-PursuitModels-Modeling Scenario
    Students are prompted to build systems of nonlinear differential equations to model pursuit-evader activities in which a pursuer attempts to follow, perhaps track down and come close to, an evader without knowledge of the evader's intentions, just...