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    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
    Potential Scenario
    191

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    59

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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.
    lineartankmixingcircularcascading
    Potential Scenario
    665

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    83

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    2018-Franklin_Chen-Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model
    This kinetics manual has been successfully implemented in Physical Chemistry at UW-Green Bay in the fall semester of 2017, with the students’ success rate greater than 80%.
    kineticsPhysical ChemistryLotka Volterra equationsBerkeley Madonna platform
    Potential Scenario
    147

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    31

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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
    TrigonometryTrigonometric Functionsparametric equationscirclesinecosinesquigonometryinverse function
    Potential Scenario
    133

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    39

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    2010-Randy_Boucher-Determining Dissolved Oxygen Levels
    This is a full module given to students and the article contains comments for instructors as well.
    Environmental Engineeringbiochemical oxygen demandoxygen level
    Potential Scenario
    197

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    70

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    1997-Jeff_Graham-Julia_Barnes-A Laboratory Experience for Students of Differential Equations Using RLC Circuits
    Acknowleging that applied mathematics courses rarely offer any hand-on experiences the authors constructed an RLC circuit from which they collected data and validated the differential equation of the RLC circuit.
    datacollectionslaboratorycircuitRLC
    Article or Presentation
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    376

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    2020-TeachingModule-SpringDesignToMeetSpecsAtMinimumCosts
    We discuss a Modeling Scenario in which students are asked to design a spring mass system at minimum costs give relative costs of features of the spring.
    moduleoptimizationspring massmassspring\costTeaching Moduleminimal cost
    Potential Scenario
    147

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    43

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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Potential Scenario
    194

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    64

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    2011-Brian_Winkel-Parameter Estimates in Differential Equation Models for Population Growth
    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models.
    logisticpopulationparameciaGausegradient search
    Potential Scenario
    232

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    54

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    1967-JG-Wagner-Computers in pharmacokinetics
    This is a seminal paper in pharmacokinetics in which the author introduces historic notions and approaches. As can be seen from the abstract there is a variety of material here.
    kineticscomputerspharmacokinetics
    Potential Scenario
    156

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    46

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    1969-Carl_Metzler-A mathematical model for the pharmacokinetics of LSD effect
    Contains data on performance scores vs. plasma levels of LSD in human tissues.
    LSDtestingpharmacokineticsperformanceplasma level
    Free Online Textbook
    135

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    66

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    2009-Eriksson- Estep-Hansho-Johnson-Computational Differential Equations
    Differential Equations and Advanced Computational Differential Equations, presents a unified approach to computational mathematical modeling using differential equations based on a principle of a fusion of mathematics and computation.
    Galerkin
    Technique Narrative
    388

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    198

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    9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
    The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
    Maternal-Fetal interfaceheat equationConservation of Energytheat fluxEuler's forward methodcentral differenceskin burnhyperthermiathermal conductivitylayers
    Modeling Scenario
    214

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    214

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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 second order differential equations to model a planet
    optimizationsum of square errorsvector calculusLagrange multipliersline integrals
    Article or Presentation
    929

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    79

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    SIMIODE Spring 2024 Webinars - Insightmaker
    We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
    modelingsimulationSoftwarepythonsystemsInsightMakerflowCategory Theorystockstock-flow
    Potential Scenario
    130

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    61

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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
    pendulumLotka Volterra equationsexistenceuniqueness
    Potential Scenario
    156

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    70

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    2014-Michael_Monagan-The Mortgage Payment Problem Approximating a Discrete Process with a Differential Equation
    In this article and a subsequent article I will give two non-standard examples that I've found helpful. The one presented here is a first order linear system. Second order systems and non-linear systems.
    compartmentheatinghouse
    Potential Scenario
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    87

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    2014-Hrydziuszko-EtAl-Mathematical Two-compartment Model of Human Cholesterol Transport
    We develop a two-compartment mathematical model to investigate cholesterol transport in the circulatory system and its de novo synthesis in the liver.
    metabolic syndromecompartmentcholesteroltwo-compartment modelcholesterol transport
    Article or Presentation
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    64

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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 as a rate of change.
    datafirst orderparameterAIDS
    Modeling Scenario
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    3-051-ProjectileMotions-ModelingScenario
    We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
    trajectorylaunching radiantprojectile motionprojectileno resistanceangle of launch