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    1-031-CoolIt-ModelingScenario
    We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling...

    Keywords: SpanishNewton's Law of Coolingcooling

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    2020-TeachingModule-CarSuspension
    The modeling activity on car suspensions assumes that students have grappled with second order linear homogeneous differential equations with constant coefficients.

    Keywords: modulesuspensioncar suspensionsecond orderTeaching Module

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    2020-TeachingModule-ModelingSpreadOfOilSlick
    This is support material and video for teaching a Modeling Scenario using a first order ODE to model the spread of an oilslick with incomplete data.

    Keywords: moduleoil slickTeaching Module

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    2020-Teaching Module-Applying Separation Of Variables
    This is one of several Teaching Modules prepare by the Principal Investigates of SIMIODE’s National Science Foundation grant and offered in 2020. The material offered is a complete narrative of how...

    Keywords: modulesEbolaseparation of variablesTeaching ModulesSeparation

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    1-061-SingularPerturbation-TechniqueNarrative
    This paper introduces the basics of singular perturbation methods for solving ordinary differential equations. Interactive examples will show how the smallness of physical parameters can...

    Keywords: perturbationsingular perturbation

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    1-060-RegularPerturbation-TechniqueNarrative
    This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation...

    Keywords: perturbationregular perturbationasymptotic expansionsanalytical approximationBernoulli equation

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    1-104A-T-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions and comparing to actual...

    Keywords: regressioninfectionCOVID19carrying capacitylogistic equationexponential model

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    1-015-Torricelli-ModelingScenario
    We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the...

    Keywords: dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver

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    1-015-DimensionlessVariables-TechniqueNarrative
    This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to...

    Keywords: linearizationdimensional analysistime scalescalingdimensionless variablesspatial scale

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    2018-W_Hohenauer-Physical modelling based on first order ODEs
    An introduction in techniques to solve first order ODE´s is given. Barometric formula, charging and discharging of a capacitor including its application for AMV, magnetic induction and growth...

    Keywords: dischargecapacitormagnetic fieldinductionmagnetic induction

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    2018-Meredith_Greer-Ella_Livesay-Mathematical Epidemiology Goes to College
    In this article we present models that were inspired by two real-life outbreaks at a small residential college campus: H1N1 influenza in 2009 and, surprisingly, mumps in 2016.

    Keywords: epidemiologydiseaseH1N1Influenzaoutbreak

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    2018-LA_Peletier-Ordinary Differential Equations in Pharmacodynamics
    Good mix of theory, application, solution technique in a number of areas of applications of differential equations. Develops qualitative behavior issues. Exercises, but not about models, more about...

    Keywords: compartment modelpharmacokineticspharmacodynamicsorbitsturnover

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    2018-Joseph-EtAl-A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM
    In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from...

    Keywords: asthmatobacco smokeLiao’s Homotopy analysis Method (environmental pollutants

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    2018-David_Bourne-Pharmacokinetics – Source Material
    This is a rich source of pharmacokinetics modeling activities and data. These are syllabus notes with homework assignments listed.

    Keywords: boluspharmacokineticspharmacodynamicdrug distribution

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    2018-Akman-EtAl-Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization
    We demonstrate Particle Swarm Optimization efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.

    Keywords: epidemicParticle Swarm Optimizationoptimize parameters

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    2017-William_Bialek-Boxes and Arrows To Differential Equations
    This material uses pictures to build kinetic models of reactions and then offers analytic solutions.

    Keywords: Michaelis-MentenEnzymesubstrateDNA\kinetis

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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-Jean-Roux-Mathematical Models in Air Quality Problems
    Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.

    Keywords: air pollution effects on forest ecosystemsfinite volume methodboundary layerchemical kineticsfinite differenceemissionsdepositionsadvection

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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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    2017-Gilbert-Lewis-Harvesting of renewable natural resource
    This is a resource to accompany a commercial text book and has a tutorial nature with some analysis and several good exercises

    Keywords: logisticmaximum sustainable yieldwhaleharvestrenewable resourceconstant harvest

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