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    Potential Scenario
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    2002-Faia-Differential Equation Modeling as a Source of Theoretical Insight-Four Disparate Examples
    We explore differential equations involving alcoholism, social mobility, excess female mortality, and international arms competition.
    sociologyarms racesaccumulative advantagealcoholismPeter Principlefemale mortalitypopulation pressureoccupational mobilitysocial mobilityRichardson theory of war
    Modeling Scenario
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    1-155-CruiseControl-ModelingScenario
    In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.
    PID controllerfeedback controlControl theorycruise controlautomobileclosed-loop controlinput-ouputblock diagram
    Modeling Scenario
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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
    optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable
    Potential Scenario
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    2001-Smith-Moore-The SIR Model for Spread of Disease
    A multiple part tour of SIR Models freely available with Maple, Mathematics, and MatLab support files at MAA site.
    epidemicSIR modelEuler's methodherd immunityHong Kong flu
    Modeling Scenario
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    1-082-MirroMirror-ModelingScenario
    This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical...
    astronomymirror climate change mitigation ocean deacidificationopticstelescopelensFoucaultinterpolation
    Modeling Scenario
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    3-061-ChemEngApps-ModelingScenario
    Students go through a chemical engineering problem: calculate concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation; then analyze the concentration as the radius of the catalyst...
    Spanishporous mediumcatalyisiscyclohexenehydrogeldehydrogenationhyperbolic trig functions
    Modeling Scenario
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    6-040-StruggleForExistence-ModelingScenario
    We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters
    competitionlogisticcarrying capacityparamecium
    Modeling Scenario
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    3-072-EarthQuakePartI-ModelingScenario
    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.
    earthquakevibrationamplituderesonanceundampedspring-mass system
    Modeling Scenario
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    1-092-DashItAll-ModelingSenario
    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.
    datarunningsprintHill-Kellerworld recordOlympics
    Modeling Scenario
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    5-026-Evictions-ModelingScenario
    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .
    carrying capacitycompartmentevictionhomeownerSIS modelhomelessness
    Modeling Scenario
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    1-136-MarriageAge-ModelingScenario
    Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these...
    messagesmarriageusing social sciences in forecastingdirected
    Modeling Scenario
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    9-002-GroundWaterFlow-ModelingScenario
    The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
    sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank
    Modeling Scenario
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    1-088-RoomTemperature-ModelingScenario
    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
    environmentclimatetemperatureNewton's Law of Coolingcoolingperiodic function
    Free Online Textbook
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    2016-Rob_deBoer-Population Dynamics  A Graphical Approach
    This book is an introduction into modeling population dynamics in ecology. Because there are several good textbooks on this subject, the book needs a novel ecological niche to justify its existence.
    mathematical modelstabilitycompetitionSIRbifurcationconsumptionpopulation population dynamicsgeneral replicationnonlinear density dependenciesfunctional responsepersistencephase plan analysis
    Modeling Scenario
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    3-073-EarthQuakePartII-ModelingScenario
    Your goal here is to determine how much friction/damping should be designed into a building to keep the roof from moving too far (which would result in the entire building collapsing) when it undergoes minor vibrations from a small earthquake.
    earthquakevibrationdampingamplitudespring-mass systemsteady-state solutionunderdamped
    Potential Scenario
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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
    Modeling Scenario
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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 model to approximate the value of the spring...
    undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation
    General Resource
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    Instructor Solutions Second Edition SIMIODE Textbook HTML Version
    This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
    textbookhtmlSIMIODE textbookSecond Edition
    Potential Scenario
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    2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
    In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.
    regressionlogisticTorricelli's Lawgrowthperiodic process
    Technique Narrative
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    5-010-MatrixExponential-TechniqueNarrative
    The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and...
    matrix esponentialPutzer's Algorithmdiagonalizationeigenvalueseigenvectors