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Downloads
Views
Date
Relevance
Modeling Scenario
353
views
223
downloads
0
comments
1-045-TimeOfDeath-ModelingScenario
Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.
body mass
temperature
death
Newton's Law of Cooling
body temperature
Modeling Scenario
429
views
331
downloads
0
comments
1-061-PotatoCooling-ModelingScenario
We model the cooling of a baked potato and compare it to student-collected data.
least sum of square errors
Newton's Law of Cooling
cooling
potato
Modeling Scenario
309
views
177
downloads
0
comments
1-071-NewtonWatson-ModelingScenario
Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis
temperature
death
Newton's Law of Cooling
time of death
Sherlock Holmes
Technique Narrative
401
views
206
downloads
0
comments
9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
Maternal-Fetal interface
heat equation
Conservation of Energyt
heat flux
Euler's forward method
central difference
skin burn
hyperthermia
thermal conductivity
layers
Modeling Scenario
308
views
291
downloads
0
comments
1-110-TidePoolSnails-ModelingScenario
Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the sun heats the water. Students model the tide pool's...
data
snails
temperature
Newton's Law of Cooling
cooling
Newton
warming
tital pool
tide pool
Modeling Scenario
296
views
322
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
306
views
282
downloads
0
comments
1-114-EarthClimate-ModelingScenario
In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
climate
energy
temperature
linearization
phase lines
energy balance model
root finding
Modeling Scenario
334
views
123
downloads
0
comments
1-131-CaffeineElimination-ModelingScenario
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
caffeine
elimination
pharmacokinetics
drug
Potential Scenario
153
views
45
downloads
0
comments
2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
time of death
Newton's aw of cooling
Modeling Scenario
336
views
537
downloads
0
comments
1-132-DigoxinElimination-ModelingScenario
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
nullclines
pharmacokinetics
digoxin
drug elimination
two compartment
Modeling Scenario
289
views
169
downloads
0
comments
3-009-BallDropInWater-ModelingScenario
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.
resistance
gravity
falling body
terminal velocity
buoyancy
Modeling Scenario
209
views
242
downloads
0
comments
5-020-ParacetamolAbsorption-ModelingScenario
We offer drug absorption data on paracetamol, an analgesic pain reliever, for two different sets of patients, vegetarian and non-vegetarian. Students build a two compartment model for plasma and non-plasma (tissue) compartments of human patients.
paracetamol
analgesic
vegetarian
non-vegetarian
Modeling Scenario
191
views
83
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
349
views
221
downloads
0
comments
1-043-CoolingUpAndDown-ModelingScenario
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.
temperature
oscillation
Newton's Law of Cooling
cooling
thermostat
air conditioner
Modeling Scenario
245
views
157
downloads
0
comments
1-068-WaterBottleCooling-ModelingScenario
Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
b
Newton's Law of Cooling
water bottle
autonomous
bottle
Modeling Scenario
259
views
265
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
477
views
196
downloads
0
comments
5-012-LipoproteinModeling-ModelingScenario
Data from a study on the amounts of low-density-lipoprotein (LDL), form of cholesterol, in blood plasma is presented. Students build, validate, and use a compartment model of the kinetic exchange of the LDL between body tissue and blood plasma.
wildlife
low-density-lipoprotein
tracer
compartment model
cholesterol
blood plasma
body tissue
Modeling Scenario
990
views
2110
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
Potential Scenario
115
views
44
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
236
views
592
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
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