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Vision and Change Core Competencies - Ability

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Modeling Scenario

123

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1-001s-StochasticMDeathImmigration-ModelingScenario

We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.

simulation data logistic immigration stochastic death fitting

Modeling Scenario

132

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1-001d-HotelPopulationDecay-ModelingScenario

You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel. Before you run the simulation in MATLAB, answer some questions.

simulation logistic exponential decay fitting

Modeling Scenario

118

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1-046-GoingViral-ModelingScenario

Students participate in a simulation of the spread of a viral disease in the classroom and model the process with a logistic differential equation. The simulation uses random numbers and the entire class participates.

simulation mathematical model data logistic random number generator fitting random process

Modeling Scenario

103

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1-001c-PopulationDecayThenSome-ModelingScenario

You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel.

simulation occupancy population hotel

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113

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1-047a-CondensationOptimization-ModelingScenario

We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.

simulation data optimization energy condensation best fit cost sum of scquare errors

Modeling Scenario

158

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360

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1-047-Condensation-ModelingScenario

We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and data is offered for modeling with a differential...

simulation sum of square errors condensation best fit

Modeling Scenario

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1-050-BargingAhead-ModelingScenario

As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.

optimization kinetics energy trophic efficiency work river terminal velocity friction current force barge worlk speed

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1-001B-DeathImmigrationMystery-ModelingScenario

We describe a classroom activity in which students use M\&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice

m&m Mystery Novels immigration experiment death

Modeling Scenario

112

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1-011-Kinetics-ModelingScenario

We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.

kinetics chemistry Law of Mass Action chemical kinetics order of reaction chemical reaction

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1-051-OneTankSaltModel-ModelingScenario

A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...

compartment salt tank mixing flow

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1-052-SaltWaterTanks-ModelingScenario

We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

salt tank mixing

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1-054-GrowthInFarmland-ModelingScenario

An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple...

fitting farm farmland

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1-055-WaterFallingInCone-ModelingScenario

We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.

Torricelli's Law discharge coefficient cone contraction coefficient

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1-057-FiguringFluidFlow-ModelingScenario

We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.

discharge tank Torricelli's Law Conservation of Energy fluid flow height liquid

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1-058-WaterClocks-ModelingScenario

We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out.

flow Torricelli's Law spigots water clock