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Date
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Technique Narrative
377
views
198
downloads
0
comments
1-030-RandomPerturbation-TechniqueNarrative
After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
random perturbation
Brownian motion
Langevin equation
Riemann-Steiltjes integral
Wiener process
Ito's calculus
Modeling Scenario
458
views
183
downloads
0
comments
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
372
views
910
downloads
0
comments
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
453
views
180
downloads
0
comments
1-039-StochasticPopModels-ModelingScenario
We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t.
Probability
population dynamics
Variance
Mean
stochastic
deterministic
Modeling Scenario
403
views
506
downloads
0
comments
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
364
views
162
downloads
0
comments
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
263
views
122
downloads
0
comments
1-084-GoingViral-ModelingScenario
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.
simulation
logistic
random
fitting
partial fractions
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