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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...

    Keywords: retinal surgeryAkaike Information CriterionSpanishsum of square errorssurgeryretionaophthalmologyeyeintraocular gas bubble

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    1-005-OilSlick-ModelingScenario
    We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order,...

    Keywords: model fittingspreadsheetsSpanishderrame de petróleodatosexpansiónoil slick

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    3-019-ShuttleCockFalling-ModelingScenario
    We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and...

    Keywords: resistancegravityFree Body Diagramshuttlecockfallingc object

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    3-091-SpringModeling-ModelingScenario
    In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data.

    Keywords: datalaboratoryLoggerProVerniermass-spring systemmodel validationempirical modeltheoretical model

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    4-039-FallingDarts-ModelingScenario
    we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and...

    Keywords: optimizationresistanceterminal velocitymuzzle velocitydrag coefficientfree fallair drag

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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)...

    Keywords: vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension

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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...

    Keywords: optimizationsum of square errorsvector calculusLagrange multipliersline integrals

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    6-007-FunctionsAndDerivativesInSIRModels-ModelingScenario
    Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious...

    Keywords: epidemiologyspecies interactionsderivativesvisualizationinfectionSIR modelsLaw of Mass Action

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    6-019-EnablingEpidemicExploration-ModelingScenario
    We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the...

    Keywords: Akaike Information CriterionMichaelis-Mentenepidemicsaturationgradientleast sum of square errors

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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.

    Keywords: ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave

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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.

    Keywords: Probabilityreplacement numberLaplace transformindustrial engineeringmachineconvolutiondistributiojstep functionderivative definition

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    Working with plant phenology data and fitting a nonlinear model using least squares in R
    A participatory live-coding lesson on working with NEON phenology data and fitting a sine-wave model to determine when different species get and lose their leaves.

    Keywords: modelingRphenologyNEONRstatscodeparticipatory live-coding

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    Data from: Agent-based and Individual-based Modeling: A Practical Introduction, Chapter 5, Exercise 10 [Elevation]
    Supplemental data for ABM

    Keywords: elevationChapter 5exercise

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    Discovering Prokaryotic Gene Regulation by Building and Investigating a Computational Model of the lac Operon
    The ability to construct and reason through a biological system is an important skill to develop in science education. This level of understanding forces students to recognize the interrelatedness...

    Keywords: prokaryotesgene regulationLac Operoninducible operon

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    2017-Jun_Liu-Hammer Throwing parameters optimization model research based on flight dynamical differential equation
    With progress of times, sports techniques are also rapidly developing, in order to let Chinese hammer throwers more quickly improve themselves levels.

    Keywords: sportsprojectilehammer throwrelease angle

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    2017-Guy-Bart_Stan-Modelling in Biology
    This is a very rich set of notes, rich in examples and ideas for modeling. In almost all cases after a model is introduced in real context there is attention to stability analysis.

    Keywords: spring massbifurcationmass actionlimit cycles

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    2015-Just-Callender-Differential equation models of disease transmission
    The work give full analyses of standard epidemic model and then shows how to do it with differential equations and agent-based modeling. Then it compares the results.

    Keywords: disease transmissionSIR modelsepidemicagent-based

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    2015-Joshi-EtAl-Optimal control of an SIR model with changing behavior through an education campaign
    We study stability analysis and use optimal control theory on the system of differential equations to achieve the goal of minimizing the infected population (while minimizing the cost).

    Keywords: SIR modelsvaccinepopulationwater treatmentsusceptibleeducation campaignminimizing costinfected

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    2013-Antonin_Slavik-Mixing Problems with Many Tanks
    Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix representation of the linear mixing model of differential equations.

    Keywords: lineartankmixingcircularcascading

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    2012-Campbell-EtAl-Parameter estimation in differential equation models with constrained states
    We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non‐negative states.

    Keywords: chemical engineeringsmoothing-based relaxation method

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