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    Modeling Scenario
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    6-002-EulerCromerPendulum-ModelingScenario
    This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.
    pendulumsemi-implicit methodsEuler-Cromernumerical solvers
    Modeling Scenario
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    466

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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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    3-011-EulerBallThrowing-ModelingScenario
    If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
    codingdragonVectorsEuler's methodball
    Potential Scenario
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    77

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    2001-Smith-Moore-The SIR Model for Spread of Disease
    A multiple part tour of SIR Models freely available with Maple, Mathematics, and MatLab support files at MAA site.
    epidemicSIR modelEuler's methodherd immunityHong Kong flu
    Potential Scenario
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    37

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    2010-Shaza_Hussein-Predator-Prey Modeling
    The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible.
    population dynamicspredator-preylogistic equationEndangered Catsdecreasing populationrabbitsfoxes
    Modeling Scenario
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    196

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    9-125-BeamModeling-ModelingScenario
    This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.
    Fluid MechanicsbeamcantileverimpulseLaplace transformboundary conditionfourth order
    Technique Narrative
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    472

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    5-005-StiffDifferentialEquations-TechniqueNarrative
    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.
    Euler's methodexplicit methodsimplicit methodsstiffsitffnessstiff differential equationinstability
    Modeling Scenario
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    1-097-SwimmingPool-ModelingScenario
    This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.
    concentrationcchlorinenumerical errorswimming poolhorineerreor
    Modeling Scenario
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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
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    138

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    1-100-EngineeringDemographics-ModelingScenario
    Students show how models can be used to examine social issues. The students examine three different models and use numerical methods to apply each model to demographic data for the percentage of engineering degrees awarded to women in the United...
    logisticpopulationImproved Euler MethodGompertzdemographicswomenautonomous
    Free Online Textbook
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    39

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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.
    differential equationsmodelingtextbook
    Potential Scenario
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    2015-Sebesyen-Farago-Invasive Species Model with Linear Rat Harvesting on Easter Island
    In this paper we suggest a natural modification of this model. Namely, we will investigate the case where the amount of the rats is decreased due to some external factor, e.g., exterminations by the people.
    carrying capacityharvestEaster Islandinvasie especiesratsRoughgarden theorem.
    Technique Narrative
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    403

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    1-005-NavigatingNumericalMethods-TechniqueNarrative
    This technique narrative is a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor...
    Euler's methodTaylor's Methodsearch and rescueCoaast Guardlost at sealongitudelatitudelimit definition