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    Modeling Scenario
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    1-091-InvestigatingSlopeFields-ModelingScenario
    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves.
    slope fieldspopulation
    Modeling Scenario
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    135

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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
    Potential Scenario
    161

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    69

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    1972-R_C_Rothermel-A Mathematical Model for Predicting Fire Spread in Wildland Fuels
    The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and demonstration of results to hypothetical fuel models.
    predictionforest firefire managementfire spreadfuel
    Modeling Scenario
    280

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    167

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    3-045-RampBounce-ModelingScenario
    Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile motion model of the ball bouncing off the ramp.
    projectile motioninclined rampcoefficient of restitutionoptimal anglebounce
    Potential Scenario
    197

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    57

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    2006-Michelle_LeMasurier-Nonstandard Topics for Student Presentations in Differential Equations
    An interesting and effective way to showcase the wide variety of fields to which differential equations can be applied is to have students give short oral presentations on a specific application.
    Presentationstudent presentation
    Potential Scenario
    318

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    53

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    1999-Lomen-Lovelock-Data Sets from text Differential Equations Graphics-Models-Data
    Data selected by field is presented, e.g., chemistry, electricity, growth, motion, population, miscellaneous.
    dataEstimate
    Technique Narrative
    761

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    224

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    7-006-LaplaceTransformBirth-TechniqueNarrative
    We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
    Transformationspower series
    Modeling Scenario
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    475

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    1-065-AlgalBlooms-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.
    direction fieldstool:dfieldalgaeharmful algae bloomspopulationcompartmentLake Chapala
    Potential Scenario
    137

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    65

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    2013-Michael-Evans-Growth and Decay
    Sometimes, we can describe processes of growth and decay—whether physical, chemical, biological or sociological—by mathematical models.
    exponential growthexponential decayisotopespopulationsresource depletion
    Potential Scenario
    186

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    74

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    1996-D_Erdman-MM_Morelock-A Study of Kinetics
    This paper introduces new and old features of the SAS System for the estimation and simulation of systems of first-order differential equations with emphasis on examples in kinetics.
    simulationkineticsparameter estimationEnzymesubstratesavingscompartmentstomachbloodginseng
    Technique Narrative
    420

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    858

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    8-002-TrigSumRepresentation-TechniqueNarrative
    Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.
    estimationTrigonometryTrigonometric Functionssum of square errorsfinite sumFourier seriesFouriere sumspectrumapproximatiopn
    Modeling Scenario
    268

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    554

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    6-065-InternetPlatformUsers-ModelingScenario
    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system.
    dynamicsflowconservedfixed pointscycletinternet platformdiverghenceJacobianattractingrepellingnodesstablesaddlespiral
    Free Online Textbook
    190

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    56

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    2012-Vivek_Patel-Chemical Kinetics
    The book is designed to help the reader, particularly students, researchers, research scholars, scientists, chemists and industry fraternity of chemistry and allied fields; understand the mechanics and reactions rates.
    kineticschemistryreaction
    Free Online Textbook
    213

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    57

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    2017-Andrew_Lewis-Introduction_to_Differential_Equations_for_Smart_Kids
    The author addresses the question, "If I do not teach all of the usual techniques and tricks for solving differential equations, what do I replace it with?" in a number of wonderful ways.
    differential equationsmodelingtextbook