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## Resources

##### Includes clear efforts on Issues
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.
data Spanish tank column of water aperture Torricelli's Law Conservation of Energyt Solver water flow Excel 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.
linearization dimensional analysis time scale scaling dimensionless variables spatial scale
Modeling Scenario
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##### 1-025-MixingItUp-ModelingScenario
Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.
compartment salt tank mixing
Modeling Scenario
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##### 1-035-DotseroVolcanoEruption-ModelingScenario
In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
exponential decay half-life decay Euler's method carbon dating decay rate Carbon-14 Dotsero volcano volcano
Modeling Scenario
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##### 3-103-PullBackCars-ModelingScenario
This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.
modeling dynamics hands-on toy pull-back car pullback
Modeling Scenario
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##### 6-070-BeerBubbles-ModelingScenario
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
molecular forensics BEER sphere bubble Newton' Second Law Ideal Gas Law drag force Hadamard Stokes mole
Modeling Scenario
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##### 6-004-VillageEpidemic-ModelingScenario
Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they are to build a mathematical model.
SIR models epidemic susceptible infective removed Eyam English village
Modeling Scenario
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##### 1-001-MM-DeathAndImmigration-ModelingScenario
We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!
simulation immigration death Spanish dats Winkel Brian Winkel
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.
data physics dynamics data collection rolling slipping ripcord toy
Modeling Scenario
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##### 1-038-Ebola-ModelingScenario
Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
population dynamics data analysis exponential growth Ebola logistic epidemic
Modeling Scenario
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##### 1-128-RocketFlight-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
resistance Flight Rocketry mass Newton's Second Law of Motion thrust Free Body Diagram apex rocket
Modeling Scenario
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##### 9-014-TurkeyCook-ModelingScenario
The goal of this project is to investigate several models for the cooking time for a turkey based on weight, test these models with data obtained from heating curves for turkeys of various weights, and develop a new model to fit this data.
sphere heat equation turkey Panofsky radial symmetry
Modeling Scenario
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##### 1-078-MonodGrowthModel-ModelingScenario
Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
bacteria nutrient cycles growth Monod consumption
Modeling Scenario
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##### 3-030-SecondOrderIntro-ModelingScenario
We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
parameter estimation non-homogeneous Spanish frequency buoyancy inverse problem thrust underdamped first passage spring mash dashpot real complex homogeneous superposition parachute overdamped critically damped buoy quadratic equation roots rocket flight
Modeling Scenario
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