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Views
Date
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Modeling Scenario
268
views
115
downloads
0
comments
3-085-SimplePendulum-ModelingScenario
Thestudent is asked to derive and solve a differential equation that gives the position (angle
Newton's Second Law of Motion
pendulum
kinetic energy
potential energy
Conservation of Energyt
initial conditions
small angle approximation
Taylor polynomial
percent error
Technique Narrative
424
views
206
downloads
0
comments
2-005-LinearizeItAll-TechniqueNarrative
Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
computation
error
Torricelli's Law
data fitting
linear approximation
Technique Narrative
399
views
195
downloads
0
comments
2-001-NumericalMethodsComparisons-TechniqueNarrative
This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
Euler's method
improved Euler's method
RK3 methods
RK4 methods
order of accuracy
absolute error
CPU time
Modeling Scenario
387
views
250
downloads
0
comments
1-097-SwimmingPool-ModelingScenario
This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.
concentration
c
chlorine
numerical error
swimming pool
horine
erreor
Modeling Scenario
223
views
255
downloads
0
comments
6-029-TumorGrowth-ModelingScenario
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
Pop_Growth Pilot
logistic
comparment
tumor
synthetic data
sum of squares error
Modeling Scenario
299
views
406
downloads
0
comments
1-165-FlushToilet-ModelingScenario
This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
julia
Diffusion
innovation
rate of innovation
Bass model
Solver
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