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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.

    Keywords: Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous

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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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    6-022-CannibalismPredatorPrey-ModelingScenario
    The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time. In this module, we look at modifying this prey-predator model to consider the case when...

    Keywords: stabilitypredator-preyequilibriaoscillationscannibalismphase planesspiral sinks

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    5-007-ChemOpt-ModelingScenario
    Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.

    Keywords: optimizationpYield and sustainabilitynonprofit managementLaw of Mass Actionkineticreaction

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    3-034-CarSuspension-ModelingScenario
    We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'',...

    Keywords: designspring-mass-dashpotspring constantunderdampingcar suspensionsuspension tolerancestatic equilibrium

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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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    6-068-VisualizingPredator-PreyCycles
    In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be...

    Keywords: nullclinespredator-preyGeometrypredatorRunge-Kuttapreylimit cycle

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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.

    Keywords: sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank

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    1-026-Evaporation-ModelingScenario
    We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a...

    Keywords: evaporationconealcoholPetri dish

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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.

    Keywords: moduleoptimizationspring massmassspring\costTeaching Moduleminimal cost

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    2020-TeachingModule-ModelingNonlethalInfluenzaEpidemic
    We discuss the modeling efforts and tools for success in modeling the spread of nonlethal influenza in an English boarding school

    Keywords: moduleepidemicboarding schoolTeaching 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-TeachingModule-ModelingFallingColumnOfWater
    We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.

    Keywords: modulecolumn of waterTorricelli's LawTorricelliTeaching Module

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    2020-TeachingModule-SpreadOfCommonColdSimulation
    This simulation is meant to introduce the idea of a differential equation model and investigate the impact of heightened hygiene and decreased interactions on the spread of an infectious disease....

    Keywords: simulationmoduleinfectious diseasediseasespreadTeaching Modulespread of disease

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    1-132-DigoxinElimination-ModelingScenario
    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study...

    Keywords: nullclinespharmacokineticsdigoxindrug eliminationtwo compartment

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    2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling
    This module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students...

    Keywords: modulelinear systemsdigoxinTeaching 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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    1-155-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...

    Keywords: PID controllerfeedback controlControl theorycruise controlautomobileclosed-loop controlinput-ouputblock diagram

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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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