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## Resources

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Modeling Scenario
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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 offering three predator-prey models, each more complex...
nullclinespredator-preyGeometrypredatorRunge-Kuttapreylimit cycle
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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##### 1-026-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 mathematical model for the rate of change in the respective...
evaporationconealcoholPetri dish
Article or Presentation
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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
Article or Presentation
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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
moduleepidemicboarding schoolTeaching Module
Article or Presentation
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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.
moduleoil slickTeaching Module
Article or Presentation
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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.
modulecolumn of waterTorricelli's LawTorricelliTeaching Module
Article or Presentation
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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. The focus of this simulation is on the common cold.
Modeling Scenario
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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 of how drugs move in the body.
nullclinespharmacokineticsdigoxindrug eliminationtwo compartment
Article or Presentation
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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 should be familiar with using eigenvalues.
modulelinear systemsdigoxinTeaching Module
Article or Presentation
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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.
modulesuspensioncar suspensionsecond orderTeaching Module
Article or Presentation
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##### 2020-Teaching Module-Applying Separation Of Variables
This is one of several Teaching Modules prepare by the Principal Investigates of SIMIODEâ€™s National Science Foundation grant and offered in 2020. The material offered is a complete narrative of how a modeling activity can be offered including...
modulesEbolaseparation of variablesTeaching ModulesSeparation
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
Technique Narrative
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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 drastically change the nature of the solutions.
perturbationsingular perturbation
Technique Narrative
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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 methods.
perturbationregular perturbationasymptotic expansionsanalytical approximationBernoulli equation
Modeling Scenario
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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 disease data sets.
regressioninfectionCOVID19carrying capacitylogistic equationexponential model
Modeling Scenario
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##### 3-100-Ripcord-Toys-ModelingScenario
This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct experiments or use videos to collect data.
dataphysicsdynamicsdata collectionrollingslippingripcordtoy
Modeling Scenario
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##### 3-130-MatterOfSomeGravity-ModelingScenario
This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
gravityinverse problemacceleration
Modeling Scenario
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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 column.
dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver
Technique Narrative
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