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Modeling Scenario
283
views
188
downloads
0
comments
3-011-EulerBallThrowing-ModelingScenario
If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
coding
dragon
Vectors
Euler's method
ball
Modeling Scenario
184
views
147
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
171
views
194
downloads
0
comments
4-050-ResonanceBeats-ModelingScenario
We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
Spring 2020 workshop
vibration
tuning
driver
resonance
forced vibration
undamped
beats
naturl frequency
Article or Presentation
129
views
44
downloads
0
comments
1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom
The experiment consists of dropping a balloon from two different heights and recording the time it takes to hit the floor. The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick.
differential equations
resistance
gravity
free fall
acceleration
balloon
Potential Scenario
168
views
49
downloads
0
comments
2012-Augustus-Wali-Mathematical Modeling of Uganda Population Growth
The purpose of this paper focuses on the application of logistic equation to model the population growth of Uganda using data from 1980 to 2010 (inclusive).
population growth
logistic growth
Drug and Alcohol detoxification
carrying capacity
vital coefficients
Potential Scenario
131
views
37
downloads
0
comments
2009-Su-EtAl-Fitting Compartmental Models to Multiple Dose Pharmacokinetic Data using SAS
In the case of a multiple dose study where subjects experience different dosing times, a superposition principle can be used to recursively account for each additional dose.
SAS
superposition
pharmacokinetics
compartmental models
multiple dose
Article or Presentation
101
views
27
downloads
0
comments
2002-Patrick_Nelson-Alan_Perelson-Mathematical_analysis_of_delay_differential _equation_models_of_HIV-1_infection
Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays.
delay
HIV-1
T cells
combination antiviral therapy
Potential Scenario
100
views
44
downloads
0
comments
2007-Exben_Friis-Jensen-Modeling and Simulation of Glucose-Insulin Metabolism
In this thesis one of the models of diabetes, Bergman’s minimal model is described trough derivation and simulations.
Metabolism
insulin resistance
glucose
PID controller
intolerance
Potential Scenario
109
views
42
downloads
0
comments
1999-Meade-Struthers-Differential Equations in the New Millennium-The Parachute Problem
The parachute problem will be used to illustrate several essential features of the improved courses. In particular, it will be seen that the traditional version of the parachute problem is not very realistic.
resistance
free fall
parachute
jump
skydiving
Modeling Scenario
210
views
125
downloads
0
comments
3-042-CatapultLaunch-ModelingScenario
We maximize the range of a projectile by backing up an incline in the opposite direction of the range to give some initial lift. Find the position on the hill from which to launch the projectile to give the best lift.
projectile motion
catapult
uphill
launch angle
Modeling Scenario
212
views
327
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
245
views
145
downloads
0
comments
3-102-SpringMassDamped-ModelingScenario
Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.
frequency
mass
oscillation
stiffness
spring constant
spring\
damped
Single Degree of Freedom System
coefficient
Modeling Scenario
244
views
127
downloads
0
comments
3-063-FallingBuildingIce-ModelingScenario
We model the fall of a piece of ice which is falling from a high building in New York City.
resistance
falling
gravity
ice
terminal velocity
skyscrapers
Modeling Scenario
454
views
1067
downloads
0
comments
5-040-TunedMassDamper-Part-I-Modeling Scenario
We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original structure as a spring-mass-dashpot system.
structure
spring-mass-dashpot
spring mass
earthquake
vibration
tuned mass tuner
restoring force
control
dampe
Free Online Textbook
168
views
64
downloads
0
comments
2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology
I am often asked if it is OK to use these notes in courses at other universities. The answer is “of course!” though I strongly suggest that a link to my website be provided, so that students can always access the current version.
biology
textbook
systems
dyanmical system
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