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Downloads
Views
Date
Relevance
Modeling Scenario
394
views
475
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
Modeling Scenario
291
views
154
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
214
views
214
downloads
0
comments
5-080-SpaceFlightRecolonize-ModelingScenario
This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of second order differential equations to model a planet
optimization
sum of square errors
vector calculus
Lagrange multipliers
line integrals
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
Modeling Scenario
633
views
373
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
217
views
161
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
263
views
416
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
Modeling Scenario
312
views
182
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
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
Modeling Scenario
286
views
163
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
235
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
281
views
190
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
217
views
228
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
Modeling Scenario
383
views
250
downloads
0
comments
1-097-SwimmingPool-ModelingScenario
This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.
concentration
c
chlorine
numerical error
swimming pool
horine
erreor
Potential Scenario
130
views
61
downloads
0
comments
2017-Adolfo_Rumbos-Differential Equations and modeling
The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
pendulum
Lotka Volterra equations
existence
uniqueness
Article or Presentation
168
views
38
downloads
0
comments
2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
vibration
resonance
tuned mass damper
peak frequency response
excitation
Modeling Scenario
302
views
206
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
Potential Scenario
177
views
72
downloads
0
comments
1996-D_Erdman-MM_Morelock-A Study of Kinetics
This paper introduces new and old features of the SAS System for the estimation and simulation of systems of first-order differential equations with emphasis on examples in kinetics.
simulation
kinetics
parameter estimation
Enzyme
substrate
savings
compartment
stomach
blood
ginseng
Potential Scenario
200
views
87
downloads
0
comments
1971-Carl_Metzler-Usefulness Of Two Compartment Open Model In Pharmacokinetics
Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism and excretion of a drug. In this article two applications of the two compartment open model are discussed.
LSD
compartment
pharmacokinetics
Modeling Scenario
219
views
456
downloads
0
comments
5-002-RelationshipDynamics-ModelingScenario
The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed.
love affair
Romeo and Juliet
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