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Technique Narrative
228
views
359
downloads
0
comments
1-060-RegularPerturbation-TechniqueNarrative
This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation methods.
perturbation
regular perturbation
asymptotic expansions
analytical approximation
Bernoulli equation
Modeling Scenario
401
views
296
downloads
0
comments
1-102C-CancerGrowth-ModelingScenario
This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and...
optimization
cancer
logistic
exponential
prediction
tumor
growth
data fitting
power law
Bertanffy
Gompertz
Modeling Scenario
275
views
116
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
Modeling Scenario
238
views
604
downloads
0
comments
9-020-HeatDiffusion-ModelingScenario
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
laboratory
Diffusion
heat
Modeling Scenario
227
views
257
downloads
0
comments
3-069-HeatInBar-ModelingScenario
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
heat transfer
experiment
conduction
convection
boundary conditions
finite volume method
Modeling Scenario
275
views
430
downloads
0
comments
3-090-OneSpringMass-ModelingScenario
We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
undamped
sum of square errors
mass spring
Hooke's Law
oscilation
least-squares approximation
Modeling Scenario
399
views
258
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
299
views
790
downloads
0
comments
6-024-DronePackageDelivery-ModelingScenario
Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package.
Vectors
Trigonometry
Flight
drones
parametric curve
Improved Euler Method
Runge-Kutta
Modeling Scenario
297
views
586
downloads
0
comments
10-100-InsectOutbreaks-ModelingScenario
We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.
ecology
climate change
insect
insect outbreaks
insect outbreak
solitary wave
Modeling Scenario
285
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
245
views
103
downloads
0
comments
4-065-GasInjection-ModelingScenario
Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary...
Prandtl-Blasius equations
boundary layer
gas injection
esponential box scheme
uniform convergence
FORTRAN
Modeling Scenario
243
views
358
downloads
0
comments
5-090-SolidParticleErosion-ModelingScenario
By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.
classical mechanics
solid mechanics
Newton's Laws of Motion
rigid body
plasticity
pitting
ductile surface
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