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Downloads
Views
Date
Relevance
Modeling Scenario
213
views
141
downloads
0
comments
3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.
mass
undamped
Free Body Diagram
springs
two springs
oscil
lation
spring constant
fixed ends
Modeling Scenario
276
views
192
downloads
0
comments
1-059-ContainerShapeFallingWater-ModelingScenario
We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.
containers
Torricelli's Law
shape
discharge coefficient
Modeling Scenario
382
views
197
downloads
0
comments
1-040-OutcomeSavings-ModelingScenario
We ask students to build a model for a savings account and to determine the monthly deposit in a savings account in order meet a long term savings goal.
Pop_Growth Pilot
savings
growth
deposit
g
Free Online Textbook
269
views
95
downloads
0
comments
2017-Thomas_Judson-The_Ordinary_Differential_Equations_Project
This text is intended for a one-semester undergraduate course in ordinary differential equations. There are additional exercises or computer projects at the ends of many of the chapters.
projects
mathematical model
textbook
techniques
free
proofs
sage
Theory
Modeling Scenario
234
views
577
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
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
Modeling Scenario
316
views
144
downloads
0
comments
1-014-DrainingContainers
Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?
containers
tank
flow
Torricelli's Law
draining
fixed volume
Modeling Scenario
250
views
193
downloads
0
comments
5-014-TwoSpringMass-ModelingScenario
We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.
mass
spring mass damper
springs
Modeling Scenario
300
views
152
downloads
0
comments
5-030-AirshedSulphur-ModelingScenario
Temperature inversions and low wind speeds trap air pollutants in a mountain valley for a period of time. Gaseous sulfur compounds are a significant air pollution problem. We offer a model for analysis to predict long-term levels of levels of...
sulphur
pollution
airshed
hydrogen sulfide
sulfur dioxide
Modeling Scenario
265
views
549
downloads
0
comments
6-065-InternetPlatformUsers-ModelingScenario
A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system.
dynamics
flow
conserved
fixed points
cyclet
internet platform
diverghence
Jacobian
attracting
repelling
nodes
stable
saddle
spiral
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
Potential Scenario
126
views
57
downloads
0
comments
2007-Choisy-Guégan-Rohani-Mathematical Modeling of Infectious Diseases Dynamics
After presenting general notions of mathematical modeling (Section 22.2) and the nature of epidemiological data available to the modeler (Section 22.3), we detail the very basic SIR epidemiological model (Section 22.5).
stochastic
SIR model
deterministic
incubation
infectives
Modeling Scenario
399
views
153
downloads
0
comments
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
178
views
165
downloads
0
comments
9-152-HorizontalBeam-ModelingScenario
This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.
Polynomial dynamical system
beam
cantilever
Potential Scenario
224
views
74
downloads
0
comments
2018-Arden_Baxter-Modeling Public Opinion
In this paper, we adapt the epidemiological models to model the dynamics of public opinion. Public opinion is any view prevalent among the general public. Our model considers any topic or issue in which the public has two decisive and opposing...
epidemiology
population
public opinion
Potential Scenario
136
views
80
downloads
0
comments
2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
pharmacokinetics
dynamic models
smoothing
spline
mixed-effects models
HiV combination therapy
Potential Scenario
156
views
41
downloads
0
comments
2014-Brun-EtAl-An introduction to the mechanics of the lasso
Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane.
bifurcation
motion
lasso
rod model
rodeo
Modeling Scenario
989
views
2108
downloads
0
comments
3-030-SecondOrderIntro-ModelingScenario
We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
parameter estimation
non-homogeneous
Spanish
frequency
buoyancy
inverse problem
thrust
underdamped
first passage
spring mash dashpot
real
complex
homogeneous
superposition
parachute
overdamped
critically damped
buoy
quadratic equation
roots
rocket flight
Technique Narrative
377
views
208
downloads
0
comments
1-009-Bifurcation-TechniqueNarrative
We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
bifurcation
qualitative behavior
bifurcation diagram
Modeling Scenario
251
views
183
downloads
0
comments
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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