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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
    Technique Narrative
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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
    Modeling Scenario
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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.
    phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation
    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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    1-089-SpreadOfDisease-ModelingScenario
    In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with only a College Algebra background, can still enjoy differential equation...
    SIR modelProportionderivativedifference quotientSleeping Beautycontagious disease
    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
    Modeling Scenario
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    1-041-AirToTop-ModelingScenario
    One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using variable ascent rates.
    SCUBAascentair managementbreathingdivingunderwater
    Modeling Scenario
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    7-008-MachineReplacement-ModelingScenario
    Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
    Probabilityreplacement numberLaplace transformindustrial engineeringmachineconvolutiondistributiojstep functionderivative definition
    Technique Narrative
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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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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
    population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery