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Downloads
Views
Date
Relevance
Modeling Scenario
404
views
629
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
198
views
86
downloads
0
comments
1-144-HeatCool-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
temperature
Newton's Law of Cooling
cooling
Modeling Scenario
299
views
209
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
251
views
188
downloads
0
comments
1-064-TorricelliBox-ModelingScenario
The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.
groundwater flow
column of water
Torricelli's Law
water displacement
submerged box
Modeling Scenario
262
views
266
downloads
0
comments
1-079-HomeHeating-ModelingScenario
This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
Optimal Control Theory
temperature
heat
furnace
Newton's Law of Cooling
home heating
specific heat
Modeling Scenario
278
views
201
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
438
views
1069
downloads
0
comments
1-015-Torricelli-ModelingScenario
We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.
data
Spanish
tank
column of water
aperture
Torricelli's Law
Conservation of Energyt
Solver
water flow
Excel Solver
Modeling Scenario
1163
views
629
downloads
0
comments
3-065-UpDown-ModelingScenario
We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity
Newton's Second Law of Motion
velocity
motion
apex
Modeling Scenario
322
views
148
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
311
views
199
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
299
views
328
downloads
0
comments
1-088-RoomTemperature-ModelingScenario
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
environment
climate
temperature
Newton's Law of Cooling
cooling
periodic function
Modeling Scenario
302
views
183
downloads
0
comments
3-075-RLCCircuits-ModelingScenario
We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.
resistance
circuit
voltage
inductance
capacitance
current
Kirchhoff's Law
Modeling Scenario
795
views
373
downloads
1
comments
1-128-RocketFlight-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
resistance
Flight
Rocketry
mass
Newton's Second Law of Motion
thrust
Free Body Diagram
apex
rocket
Modeling Scenario
337
views
149
downloads
0
comments
1-105-AnimalFall-ModelingScenario
This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.
animal
Netwon's Second Law of Motion
falling body
terminal velocity
air resistance
Newton
air friction
fall
Modeling Scenario
450
views
908
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
Modeling Scenario
313
views
474
downloads
0
comments
6-070-BeerBubbles-ModelingScenario
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
molecular forensics
BEER
sphere
bubble
Newton' Second Law
Ideal Gas Law
drag force
Hadamard
Stokes
mole
Modeling Scenario
380
views
459
downloads
0
comments
1-011A-Kinetics-ModelingScenario
We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.
kinetics
Law of Mass Action
fitting
order of reaction
chemical reaction
Modeling Scenario
264
views
166
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
Modeling Scenario
268
views
387
downloads
0
comments
1-094-SteepingTea-ModelingScenario
We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration.
concentration
Surface Area
color
Newton's Law of Cooling
tea
sugar
Modeling Scenario
394
views
416
downloads
0
comments
1-102-CancerTumor-ModelingScenario
This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and...
optimization
logistic
prediction
data fitting
power law
Gompertz
cancer growth
eponential
Bertalanaffy
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