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    Modeling Scenario
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    9-152-HorizontalBeam-ModelingScenario
    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.
    Polynomial dynamical systembeamcantilever
    Modeling Scenario
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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle
    Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error
    Modeling Scenario
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    6-020-AlgaePopulationSelf-Replenishment-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. A
    algaepopulationMexicoqualitativecompartmentlinearizationJacobianlaknondimensionalizationpplane
    Modeling Scenario
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    435

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    5-002-RelationshipDynamics-ModelingScenario
    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed.
    love affairRomeo and Juliet
    Modeling Scenario
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    4-023-MysteryCircuit-ModelingScenario
    Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors.
    filterscircuitRLC circuitKirchhoffvoltagegaindriver
    Modeling Scenario
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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.
    attritionLanchester modelpredator-predatorN-square Law
    Modeling Scenario
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    5-080-SpaceFlightRecolonize-ModelingScenario
    This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of second order differential equations to model a planet
    optimizationsum of square errorsvector calculusLagrange multipliersline integrals
    Modeling Scenario
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    170

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    6-023-DroneHeadingHome-ModelingScenario
    We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.
    dronesoursuitflight pathchange of variables
    Modeling Scenario
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    208

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
    Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency
    Modeling Scenario
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    186

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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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    6-017-OncolyticViruses-ModelingScenario
    Students explore oncolytic virotherapy using systems of differential equations and numerical simulations.
    cancercancer-immune dynamicsimmune suppressor drugoncolytic virusvirotherapy
    Article or Presentation
    911

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    73

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    SIMIODE Spring 2024 Webinars - Insightmaker
    We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
    modelingsimulationSoftwarepythonsystemsInsightMakerflowCategory Theorystockstock-flow
    Article or Presentation
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    513

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    2020-TeachingModule-ModelingNonlethalInfluenzaEpidemic
    We discuss the modeling efforts and tools for success in modeling the spread of nonlethal influenza in an English boarding school
    moduleepidemicboarding schoolTeaching Module
    Modeling Scenario
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    151

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    5-025-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
    compartmentsalttanks
    Modeling Scenario
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    426

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    6-070-BeerBubbles-ModelingScenario
    The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
    molecular forensicsBEERspherebubbleNewton' Second LawIdeal Gas Lawdrag forceHadamardStokesmole
    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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    143

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    3-150-ItsABlastFurnace-ModelingScenario
    This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.
    steady stateheat equationinverse problemfurnace
    Modeling Scenario
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    10-100-InsectOutbreaks-ModelingScenario
    We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.
    ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave
    Modeling Scenario
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    5-090-SolidParticleErosion-ModelingScenario
    By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.
    classical mechanicssolid mechanicsNewton's Laws of Motionrigid bodyplasticitypittingductile surface
    Modeling Scenario
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    1-190-IntroClass-ModelingScenario
    Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a predator prey system.
    population dynamicspredator-preylogisticexponentialgraphical interpretationsqualitative analysis