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Downloads
Views
Date
Relevance
Potential Scenario
140
views
58
downloads
0
comments
1999-McCartney-Carey-Modelling Traffic Flow Solving and Interpreting Differential EquationsÂ
A simple mathematical model for how traffic flows along a road is introduced.
traffic
traffic flow
Article or Presentation
179
views
70
downloads
0
comments
2004-Mark_McCartney-Using_second-order_ordinary_differential_equations_to_model_traffic_flow
A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted.
differential equations
traffic flow
vehicle follow
second order
Potential Scenario
184
views
51
downloads
0
comments
1975-DH_Griffel-Teaching the formation and solution of differential equations
This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.
parasites
Topography
population
epidemic
traffic flow
social interactions
fish weight
arms race
Modeling Scenario
310
views
196
downloads
0
comments
1-013-SleuthingWithDifferentialEquations-ModelingScenario
We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
projectile motion
acceleration
Newton's Law of Cooling
speeding
Modeling Scenario
443
views
879
downloads
0
comments
9-002-GroundWaterFlow-ModelingScenario
The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
s
groundwater flow
Darcy's Law
heat equation
aquifer
hydraulic head
Fourier's Law
sand tank
Article or Presentation
940
views
86
downloads
0
comments
SIMIODE Spring 2024 Webinars - Insightmaker
We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
modeling
simulation
Software
python
systems
InsightMaker
flow
Category Theory
stock
stock-flow
Potential Scenario
674
views
85
downloads
0
comments
2018-Franklin_Chen-Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model
This kinetics manual has been successfully implemented in Physical Chemistry at UW-Green Bay in the fall semester of 2017, with the students’ success rate greater than 80%.
kinetics
Physical Chemistry
Lotka Volterra equations
Berkeley Madonna platform
Potential Scenario
161
views
46
downloads
0
comments
1989-EY_Rodin-S_Jaques-Countercurrent Oxygen Exchange in the Swim Bladders of Deep-Sea Fish
Oxygen diffuses from lungs into blood, nutrients diffuse from intestinal tracts into blood and from blood into various cells, and waste products diffuse from cells back into blood.
fish
Cell Membrane
flow
blood
bladder
countercurrent
Potential Scenario
114
views
43
downloads
0
comments
1981-Geoffrey_Berresford-Differential Equations and Root Cellars
This is a classic module from UMAP in which the heat equation in one dimension is fully developed by using the standard technique of measuring the heat flow in and out of a small element of mass and equating them at equilibrium.
temperature
thermal conductivity
heat flow
thermal diffusivity
root cellar
Modeling Scenario
305
views
207
downloads
0
comments
1-051-OneTankSaltModel-ModelingScenario
A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...
compartment
salt
tank
mixing
flow
Modeling Scenario
297
views
206
downloads
0
comments
1-058-WaterClocks-ModelingScenario
We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out.
flow
Torricelli's Law
spigots
water clock
Modeling Scenario
306
views
232
downloads
0
comments
1-027-StochasticProcesses-ModelingScenario
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
Variance
Mean
stochastic
random
operations research
industrial engineering
Poisson process
traffic
Modeling Scenario
251
views
185
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
Potential Scenario
141
views
24
downloads
0
comments
2008-Duran-Caginalp-Parameter optimization for differential equations in asset price forecasting
The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days.
finance
inverse problem
numerical nonlinear optimization
asset flow
financial market dynamics
market return prediction algorithm
Potential Scenario
123
views
36
downloads
0
comments
1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange
A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.
mechanical ventilation
ventilation
carbon dioxide exchange
tracheal gas insufflation
alveolar ventilation
shunt
two-compartment model
Modeling Scenario
404
views
277
downloads
0
comments
1-029-ConeToCubeFlow-ModelingScenario
An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...
water
flow
Torricelli's Law
cone
cube
Modeling Scenario
262
views
162
downloads
0
comments
1-073-WaterExitBottle-ModelingScenario
We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container.
data
water
flow
Torricelli's Law
bottle
Potential Scenario
127
views
68
downloads
0
comments
2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics.
Torricelli's Law
Conservation of Energyt
Conservation of Mass
Bernoulli’s Theorem
Modeling Scenario
277
views
200
downloads
0
comments
1-074-BottleWaterFlow-ModelingScenario
We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow.
b
water
Torricelli's Law
bottle
Modeling Scenario
270
views
159
downloads
0
comments
6-012-RiverCrossing-ModelingScenario
Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order linear and a second order nonlinear differential...
dragon
Newton's Second Law of Motion
river crossin
river current
velocity profile
thrust
Free Body Diagram
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