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    Modeling Scenario
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    6-024-DronePackageDelivery-ModelingScenario
    Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package.
    VectorsTrigonometryFlightdronesparametric curveImproved Euler MethodRunge-Kutta
    Modeling Scenario
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    3-035-StadiumDesign-ModelingScenario
    For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?
    projectile motionbaseballparametric equationstadiumhome runno reistantfairnessno resistance
    Modeling Scenario
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    3-029-FerrisWheelCatch-ModelingScenario
    We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.
    parametric equationsprojectile motioninitial velocityferris wheelcatchcollision
    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
    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
    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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    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
    Technique Narrative
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    195

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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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    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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    4-020-AnIEDBlast-ModelingScenario
    These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use the model to determine the results of a dynamical...
    applied mathematicsforcesFree Body DiagramImprovised Explosive Devicessum of forces
    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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    441

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    1-011A-Kinetics-ModelingScenario
    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.
    kineticsLaw of Mass Actionfittingorder of reactionchemical reaction
    Modeling Scenario
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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and...
    optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy
    Modeling Scenario
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    10-001-TilingHallway-ModelingScenario
    Students investigate difference equations through tiling hallways. They observe patterns in the tiling which lead to a difference equation. Solutions will be calculated by iteration. and the shift operator.
    Geometryiterationtilingrecurrenceshift operatorpatternsclosed formanalytic solution
    Modeling Scenario
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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
    population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts
    Modeling Scenario
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    9-005-InvasiveSpeciesModel-ModelingScenario
    This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion.
    Invasive Specieslogisticmigrationtraveling wavesdispersion
    Article or Presentation
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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
    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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    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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    1-032-WordPropagation-ModelingScenario
    This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
    Googleexponential growthlanguageword problemsetymologyNgrampropagationJumbo