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Downloads
Views
Date
Relevance
Modeling Scenario
236
views
117
downloads
0
comments
3-040-FirstPassageTime-ModelingScenario
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
oscillator
damped
underdamped
first passage
first passage time
spring mash dashpot
Potential Scenario
113
views
59
downloads
0
comments
2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
delay
time dely
step response
Potential Scenario
143
views
44
downloads
0
comments
1999-Leonid_Hanin-Which tank empties first
Suppose that water towers like those shown in the opening are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first?
tank
Torricelli's Law
spherical tank
empty
frustrum of cone
cylinder
Potential Scenario
166
views
38
downloads
0
comments
1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.
plant
oscillation
delay
circumnutation
turning
Potential Scenario
177
views
49
downloads
0
comments
2012-Jambhekar-Breen-Extravascular Routes Of Drug Administration in Basic Pharamacokinetics
This provides an excellent step-by-step of the physiology, construction of model, and notions like peak concentration as well as issues like lag time.
concentration
physiology
drugs
lag time
Extravascular
Pharamacokinetics
peak time
Modeling Scenario
984
views
2099
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
168
views
63
downloads
0
comments
2016-Starling-EtAl-Local Brewery - A Project for Use in Differential Equations Courses
We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer.
BEER
Fermentation
brewery
Potential Scenario
269
views
54
downloads
0
comments
2012-Hassan_Moore-Using projects to stimulate learning in mathematics and engineering mathematics courses
Given that time is a premium in the academy and project creation is a time consumer, three original projects, which may be injected into any Calculus III, Differential Equations, or Engineering Mathematics course, have been created.
solutions
class projects
physical phenomenon
Modeling Scenario
1175
views
3679
downloads
0
comments
1-005-OilSlick-ModelingScenario
We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.
model fitting
spreadsheets
Spanish
derrame de petróleo
datos
expansión
oil slick
Modeling Scenario
420
views
327
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
Article or Presentation
197
views
76
downloads
0
comments
1994-Brian_Winkel-Ant_Tunnels_and_Calculus
A simple mathematical model describing the time it takes for an ant to construct a linear tunnel of length x is produced from five intuitively acceptable assumptions.
differential equations
difference equation
first order
derivative definition
ant tunnel
Potential Scenario
157
views
41
downloads
0
comments
1971-Boyes-Scott-Jebson-Godman-Julian-Lidocaine in Man
Plasma levels of lidocaine were measured in 5 normal male volunteers following both intravenous and oral administration of the drug.
p
Pharmacology
pharmacokinetics
lidocaine
Article or Presentation
121
views
53
downloads
0
comments
2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
Newton's Law of Cooling
time of death
double exponential
coroner
Article or Presentation
192
views
573
downloads
1
comments
2020-TeachingModule-ModelingFallingColumnOfWater
We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.
module
column of water
Torricelli's Law
Torricelli
Teaching Module
Potential Scenario
145
views
63
downloads
0
comments
2017-Anders_Kallen-Single species models in continuous time
Part of a series of Lecture notes this lecture contains rich materials on logistic harvest models, spruce budworms, and chemostat.
chemostat
logistic
harvest
spruce budworm
Potential Scenario
147
views
43
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
Article or Presentation
260
views
72
downloads
0
comments
2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick
An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. Model this.
differential equations
simulation
parameter estimation
difference equation
Technique Narrative
394
views
194
downloads
0
comments
2-001-NumericalMethodsComparisons-TechniqueNarrative
This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
Euler's method
improved Euler's method
RK3 methods
RK4 methods
order of accuracy
absolute error
CPU time
Modeling Scenario
214
views
221
downloads
0
comments
1-063-ThreeHoleColumnOfWater-ModelingScenario
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.
falling
column of water
Torricelli's Law
multiple spigots
spigots
Modeling Scenario
244
views
259
downloads
0
comments
1-090-EmptySphericalTank-ModelingScenario
We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...
Volume
sphere
Torricelli's Law
timing
spherical tank
fluid
empty
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