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Views
Date
Relevance
Modeling Scenario
392
views
594
downloads
0
comments
1-076-ClimateBifurcation-ModelingScenario
We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
energy balance
climate
energy
albedo
Hysteresis
bifurcation
ice-age
greenhouse
balance
Stefan Boltzmann Law
Modeling Scenario
393
views
610
downloads
0
comments
6-022-CannibalismPredatorPrey-ModelingScenario
The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time. In this module, we look at modifying this prey-predator model to consider the case when there is cannibalism in the predator species.
stability
predator-prey
equilibria
oscillations
cannibalism
phase planes
spiral sinks
Technique Narrative
373
views
197
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
245
views
141
downloads
0
comments
3-027-BobbingDropping-ModelingScenario
We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
drug resistance
directed
buoyancy
free fall
static equilibrium
displacement
Modeling Scenario
290
views
208
downloads
0
comments
3-044-DeepWell-ModelingScenario
We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.
gravity
projectile motion
falling body
speed of sound
Modeling Scenario
290
views
406
downloads
0
comments
1-037-CommonColdSpread-ModelingScenario
This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example.
disease
common cold
residence hall
Modeling Scenario
332
views
451
downloads
0
comments
3-099-PullBack-ModelingScenario
We guide students through the development of an empirical model for the velocity and distance traveled of a simple pull-back toy. Students can record videos and extract data using their own pull-back toy or use data included.
dynamics
pull-back toy
Modeling Scenario
398
views
176
downloads
0
comments
7-008-MachineReplacement-ModelingScenario
Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
Probability
replacement number
Laplace transform
industrial engineering
machine
convolution
distributioj
step function
derivative definition
Modeling Scenario
279
views
94
downloads
0
comments
10-001-TilingHallway-ModelingScenario
Students investigate difference equations through tiling hallways. They observe patterns in the tiling which lead to a difference equation. Solutions will be calculated by iteration. and the shift operator.
Geometry
iteration
tiling
recurrence
shift operator
patterns
closed form
analytic solution
Modeling Scenario
329
views
514
downloads
0
comments
5-005-Dialysis-ModelingScenario
We design a compartment model of a kidney dialysis machine and compare 3 and 9 compartments for the machine as well as determine the effect of change in one of the parameters in the model on the effectiveness to deliver quality dialysis.
countercurrent multiplier
kidney
dialysis
concurrent
compartment
Modeling Scenario
348
views
244
downloads
0
comments
5-007-ChemOpt-ModelingScenario
Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
optimization
p
Yield and sustainability
nonprofit management
Law of Mass Action
kinetic
reaction
Modeling Scenario
281
views
220
downloads
0
comments
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
774
views
2059
downloads
0
comments
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
285
views
189
downloads
0
comments
1-136-MarriageAge-ModelingScenario
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these...
messages
marriage
using social sciences in forecasting
directed
Modeling Scenario
220
views
526
downloads
0
comments
1-126-MarriageMath-ModelingScenario
We will explore a model which describes the process of entry into marriage by an individual. In the model, rate of change in the fraction of the cohort already married will be investigated along with two governing assumptions;.
marriage
Gompertz function
Modeling Scenario
321
views
210
downloads
0
comments
9-012-PDEGuitarTuning-ModelingScenario
We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.
extension
sine waves
frequency
guitar
damping
Fourier
string
tuning
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