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    Modeling Scenario
    69

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    35

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    6-050-BowlingBallPath-ModelingScenario
    This modeling scenario examines the motion of a bowling ball with the goal of understanding how various aspects of the release affect ball placement and the entry angle to the pocket, each an important factor in the frequency of strikes.
    calculusphysicsdynamicssportsrollingslippingbowlingbowling ballrolling with slippingbowling lane
    General Resource
    1062

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    168

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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
    308

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    244

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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
    686

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    229

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    5-026-Evictions-ModelingScenario
    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .
    carrying capacitycompartmentevictionhomeownerSIS modelhomelessness
    Modeling Scenario
    320

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    238

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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
    353

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    246

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    5-007-ChemOpt-ModelingScenario
    Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
    optimizationpYield and sustainabilitynonprofit managementLaw of Mass Actionkineticreaction
    Modeling Scenario
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    911

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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
    425

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    397

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    3-100-Ripcord-Toys-ModelingScenario
    This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct experiments or use videos to collect data.
    dataphysicsdynamicsdata collectionrollingslippingripcordtoy
    Modeling Scenario
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    247

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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
    287

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    220

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    1-035-DotseroVolcanoEruption-ModelingScenario
    In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
    exponential decayhalf-lifedecayEuler's methodcarbon datingdecay rateCarbon-14Dotsero volcanovolcano
    Modeling Scenario
    1001

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    2112

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    3-030-SecondOrderIntro-ModelingScenario
    We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
    parameter estimationnon-homogeneousSpanishfrequencybuoyancyinverse problemthrustunderdampedfirst passagespring mash dashpotrealcomplexhomogeneoussuperpositionparachuteoverdampedcritically dampedbuoyquadratic equationrootsrocket flight
    Modeling Scenario
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    1189

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    3-061-ChemEngApps-ModelingScenario
    Students go through a chemical engineering problem: calculate concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation; then analyze the concentration as the radius of the catalyst...
    Spanishporous mediumcatalyisiscyclohexenehydrogeldehydrogenationhyperbolic trig functions
    Technique Narrative
    388

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    214

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    1-009-Bifurcation-TechniqueNarrative
    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
    bifurcationqualitative behaviorbifurcation diagram
    Modeling Scenario
    251

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    244

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    1-060-SalesMarketing-ModelingScenario
    We lead students through a sales forecasting model based on marketing principles first espoused by F. M. Bass with definitions, assumptions, equations, and data on sales over 15 year periods against which models may be tested.
    marketingBass modelsalesconsumer productsinnovatorsimitators
    Modeling Scenario
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    423

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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
    juliaDiffusioninnovationrate of innovationBass modelSolver
    Modeling Scenario
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    292

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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
    Modeling Scenario
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    103

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    4-065-GasInjection-ModelingScenario
    Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary...
    Prandtl-Blasius equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN
    Modeling Scenario
    316

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    125

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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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    413

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    5-040-TunedMassDampers-PartII-ModelingScenario
    Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring...
    structureresistancespring-mass-dashpotearthquakevibrationcontroldampingtuned mass damperstiffnessreduction of vibration
    Modeling Scenario
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    450

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    6-026-IsleRoyaleModeling-ModelingScenario
    The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle.
    ecologyoptimizationpredator-preypopulationvector calculusLagrange multipliersleast squaresIslel Royale