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Downloads
Views
Date
Relevance
Modeling Scenario
404
views
506
downloads
0
comments
1-047a-CondensationOptimization-ModelingScenario
We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
simulation
data
optimization
energy
condensation
best fit
cost
sum of scquare errors
Potential Scenario
146
views
51
downloads
0
comments
1991-JR_Lobry-P_Flandois-Comparison of Monod's Growth Model Parameters from the Same Data Set
The paper obtains the parameters in Monod's Growth model using a minimization of the sum of square errors with a given data set and obtains confidence intervals
Confidence intervals
sum of square errors
linearization
growth
Modo Growth model
Technique Narrative
420
views
858
downloads
0
comments
8-002-TrigSumRepresentation-TechniqueNarrative
Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.
estimation
Trigonometry
Trigonometric Functions
sum of square errors
finite sum
Fourier series
Fouriere sum
spectrum
approximatiopn
Modeling Scenario
296
views
158
downloads
0
comments
3-015-StyrofoamBallFall-ModelingScenario
We are given data on a falling Styrofoam ball and we seek to model this motion.
football
resistance
gravity
falling body
sum of square errors
Newton's Second Law of Motion
sum of forces
styrofoam
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
651
views
398
downloads
0
comments
5-011-ModelingIbuprofren-ModelingScenario
We consider modeling of data from a clinical experiment administered as oral doses of 400 mg ibuprofen, an analgesic pain reliever. Concentrations of ibuprofen in the serum/plasma of the subjects were recorded after the initial ingestion of the...
data
AIC
Akaike Information Criterion
absorption
sum of square errors
compartment model
ibuprofen
delay
Modeling Scenario
221
views
130
downloads
0
comments
1-009-ICUSpread-ModelingScenario
We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.
logistic
sum of square errors
Intensive Care Unit
hospital
spread
Modeling Scenario
1272
views
979
downloads
0
comments
1-030-EyeModel-ModelingScenario
We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina.
retinal surgery
Akaike Information Criterion
Spanish
sum of square errors
surgery
retiona
ophthalmology
eye
intraocular gas bubble
Modeling Scenario
222
views
168
downloads
0
comments
4-035-ParEstSteadyState-ModelingScenario
Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the parameters and estimate these parameters
driver
steady state
sum of square errors
Modeling Scenario
229
views
340
downloads
0
comments
6-019-EnablingEpidemicExploration-ModelingScenario
We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the data offered.
Akaike Information Criterion
Michaelis-Menten
epidemic
saturation
gradient
least sum of square errors
Modeling Scenario
310
views
231
downloads
0
comments
1-085-DrugBolus-ModelingScenario
Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?
concentration
sum of square errors
bolus
drug
rate constant
administer
Modeling Scenario
372
views
910
downloads
0
comments
1-047-Condensation-ModelingScenario
We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and data is offered for modeling with a differential...
simulation
sum of square errors
condensation
best fit
Modeling Scenario
268
views
418
downloads
0
comments
3-090-OneSpringMass-ModelingScenario
We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
undamped
sum of square errors
mass spring
Hooke's Law
oscilation
least-squares approximation
Potential Scenario
140
views
49
downloads
0
comments
2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.
falling body
dimensional analysis
drag
Modeling Scenario
320
views
191
downloads
0
comments
3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy
mass-spring system
kinetic energy
potential energy
total energy
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
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
242
views
553
downloads
0
comments
4-020-AnIEDBlast-ModelingScenario
These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use the model to determine the results of a dynamical...
applied mathematics
forces
Free Body Diagram
Improvised Explosive Devices
sum of forces
Modeling Scenario
289
views
195
downloads
0
comments
3-130-MatterOfSomeGravity-ModelingScenario
This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
gravity
inverse problem
acceleration
Modeling Scenario
223
views
259
downloads
0
comments
6-029-TumorGrowth-ModelingScenario
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
Pop_Growth Pilot
logistic
comparment
tumor
synthetic data
sum of squares error
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