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    1981-Geoffrey_Berresford-Differential Equations and Root Cellars
    This is a classic module from UMAP in which the heat equation in one dimension is fully developed by using the standard technique of measuring the heat flow in and out of a small element of mass...

    Keywords: temperaturethermal conductivityheat flowthermal diffusivityroot cellar

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    Uncovering Hidden Figures of Natural History Collections Using Digital Data Sleuthing & Storytelling
    In this presentation we will introduce a series of modules meant to train the next generation of scientists to be data sleuths and storytellers, engaging learners in authentic research experiences...

    Keywords: natural history museumssocial justicedigitized natural history collectionsLDC2023hidden figures

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    1972-Suresh_Sethi-Optimal Control of the Vidale-Wolfe Advertising Model
    This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market...

    Keywords: Optimal Control Theoryadvertisingsales

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    1968-Wagner-Aghajanian-Bing-Correlation of performance test scores with tissue concentration of lysergic acid diethylamide
    This paper offers a two compartment model of lysergic acid diethylamide (LSD) in volunteer students and through parameter estimation models the amount of LSD in the tissue after its initial...

    Keywords: LSDcorrelation coefficientcompartment modellysergic acid diethylamideperformancetest scoretissue concentration

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    2018-Robert_Phair-Differential_equation_methods_for_simulation_of_GFP_kinetics_in_non–steady_state_experiments
    Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological...

    Keywords: protein quality controlkineticsCellssteady statechemical kineticsfluouresencephotoactivationinytracellular

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    1992-Emelie_Kenney-Differential_equations_and_the_AIDS_epidemic
    This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative...

    Keywords: datafirst orderparameterAIDS

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    2011-Lorelei_Koss-Sustainability_in_a_differential_equations_course_case_study_of_Easter_Island
    Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to...

    Keywords: differential equationssustainabilitypopulationEaster Islandcollapseenvironmental collapse

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    2011-Richard_Fitzpatrick-Newtonian_Dynamics
    This 300 page text is packed with motivational physics. Indeed, Professor Fitzpatrick brings us to the origins of why differential equations are the dominant tools of mathematics in the study of...

    Keywords: modelingtextbookphysicsbifurcation

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    2014-Jiri_Lebl-Notes_on_Diffy_Qs_Differential_Equations_for_Engineers
    There is a pdf and html version of the text as well as a purchasable paperback version. The text has pretty much all the basics, but has only a few exercises and there is very little modeling.

    Keywords: differential equationstextbookengineering

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    2019-Fan_ Li_ Yin- Impact_of_environmental_tax_on_green_development-nonlinear_dynamical_system_analysis
    This study analyzes the impact of environmental tax on green development by using a four-dimension dynamical system.

    Keywords: environmentsystemequilibrium pointmodel chaoseconomic growthnonlinear

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    2019-Radulescu-Lundgren-A_pharmacokinetic_model_of_lead_absorption_and_calcium_competitive_dynamics
    We build and analyze a compartmental model of lead pharmacokinetics, focused specifically on addressing neurotoxicity.

    Keywords: QUBES Leadership Teamparametersabsorptionbifurcationpharmacokineticscalciumcognitive decline

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    2019-Banuelos_Danet_Flores_Ramos-Epidemiological_Math_Model_Approach_To_Political_System_with_Three_Parties
    A nonlinear compartmental model is derived to study the movement between classes of voters with the assumption of a constant population that is homogeneously mixed.

    Keywords: politicsparametersvotingcompartment modelepidemiological modelequilibriathree-party system

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    1-001-MM-DeathAndImmigration-ModelingScenario
    We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to...

    Keywords: simulationimmigrationdeathSpanishdatsWinkelBrian Winkel

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    The struggle is valid: Increasing student science identity and quantitative skills
    This poster outlines the approach to our research on science identity and quantitative skills. Our approach includes an established educational researcher to assure that our design, approach,...

    Keywords: data visualizationquantitative skillsSelf-Efficacyinclusive classroomsdiversity equity and inclusionscience identityBIOME 2022survey instruments

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    6-001-Epidemic-ModelingScenario
    This paper presents real-world data, a problem statement, and discussion of a common approach to modeling that data, including student responses. In particular, we provide time-series data on the...

    Keywords: datadifference equationsparameter estimationcontinuousepidemicdiscreteboarding school

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    3-043-BallisticModeling-SpongeDart-ModelingScenario
    The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.

    Keywords: projectile motionair resistanceballisticsdimensional analysisNewtonian mechanicssponge dartNerf gunNerf dartBuckingham's Theorem

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    3-064-GearTrain-ModelingScenario
    Students model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and...

    Keywords: frictiongearspur geargear traintorquegear ratioangular accelerationangular velocitymoment of inertiadouble reduction gear

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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their...

    Keywords: undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation

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    3-101-SpringMassFirstTry-NoResistance-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.

    Keywords: frequencymassoscillationundampedspring constantspring\Single Degree of Freedom System

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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...

    Keywords: Prandtl-Blasius equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN

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