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## Resources

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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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##### 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 the analysis and solution of ODE's.
linearizationdimensional analysistime scalescalingdimensionless variablesspatial scale
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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##### 2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
Potential Scenario
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##### 2020-Cline-EtAl-A Vision for Projects Across the Mathematics Curriculum
We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.
projectstechnical writinginterdisciplinary skills
Potential Scenario
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##### 2018-W_Hohenauer-Physical modelling based on first order ODEs
An introduction in techniques to solve first order ODEÂ´s is given. Barometric formula, charging and discharging of a capacitor including its application for AMV, magnetic induction and growth effects are discussed.
dischargecapacitormagnetic fieldinductionmagnetic induction
Potential Scenario
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##### 2023-TechShareNotes. Differential Equations Modeling
TechShareNotes is a web site with rich differential equation modeling html pages and this one is about mixing in one, two, and three tanks, with interesting questions and problems as well as excellent diagrams and explanations.
population dynamicspredator-preycircuitreactionspring masspharmacokineticscooling
Potential Scenario
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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.
epidemiologydiseaseH1N1Influenzaoutbreak
Potential Scenario
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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 the mathematics only.
compartment modelpharmacokineticspharmacodynamicsorbitsturnover
Potential Scenario
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##### 2018-Kovacs-Insperger-Retarded neutral and advanced differential equation models for balancing using an accelerometer
It is shown that slight modeling differences lead to significant qualitative change in the behavior of the system, which is demonstrated by means of the stability diagrams for the different models.
feedbackAccelerometersfunctional differential equationssemi-discretizationD-subdivision method
Potential Scenario
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16

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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 smokers in different type of population.
asthmatobacco smokeLiaoâ€™s Homotopy analysis Method (environmental pollutants
Potential Scenario
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16