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Downloads
Views
Date
Relevance
Modeling Scenario
240
views
163
downloads
0
comments
1-108-PoissonProcess-ModelingScenario
In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.
Probability
s
stochastic processes
Poisson process
waiting time
arrival
Modeling Scenario
412
views
317
downloads
0
comments
1-150-CancerTherapy-ModelingScenario
This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
population dynamics
phage therapy
exponential growth
cancer
water treatment
decay
surgery
Modeling Scenario
244
views
112
downloads
0
comments
1-084-GoingViral-ModelingScenario
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.
simulation
logistic
random
fitting
partial fractions
Modeling Scenario
1141
views
3669
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
Technique Narrative
458
views
490
downloads
0
comments
5-005-StiffDifferentialEquations-TechniqueNarrative
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.
Euler's method
explicit methods
implicit methods
stiff
sitffness
stiff differential equation
instability
Modeling Scenario
261
views
244
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
214
views
102
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
Modeling Scenario
193
views
155
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
209
views
184
downloads
0
comments
5-077-MandMAttritionWarfare-ModelingScenario
Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.
attrition
Lanchester model
predator-predator
N-square Law
Modeling Scenario
270
views
186
downloads
0
comments
6-011-HumansVsZombies-ModelingScenario
Students analyze the SIR differential equations model in the context of a zombie invasion of a human population. Students analyze a two equation system representing only two populations, humans and zombies and then recovered zombies.
zombies
infection
SIR models
Modeling Scenario
225
views
156
downloads
0
comments
6-023-DroneHeadingHome-ModelingScenario
We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.
drones
oursuit
flight path
change of variables
Modeling Scenario
537
views
400
downloads
0
comments
1-034-T-FishMixing-ModelingScenario
This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking and fishing plan in a lake.
simulation
fish
Fishing
mixing
restocking
Modeling Scenario
284
views
175
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
Modeling Scenario
210
views
85
downloads
0
comments
1-067-ModelingWithSigmoidCurves-ModelingScenario
The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape.
logistic
Gompertz
sigmoid
Verhulst-Pearl
Modeling Scenario
219
views
140
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
287
views
136
downloads
0
comments
1-111-SpreadOfInformation-ModelingScenario
Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with a separable linear first order differential...
data
logistic
racism
prejudice
misinformation
memes
spread
disinformation
information
lies
Google Trends
coins
pennies
Modeling Scenario
215
views
471
downloads
0
comments
3-076-CircuitBuilding-ModelingScenario
In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.
simulation
experiment
Multisim
circuit
inductance
capacitor
Kirchhoff's Voltage Law
resistor
Modeling Scenario
231
views
166
downloads
0
comments
1-095-RatingChessPlayers-ModelingScenarios
The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario.
simulation
chess
Elo's method
chess rating
Article or Presentation
902
views
72
downloads
0
comments
SIMIODE Spring 2024 Webinars - Insightmaker
We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
modeling
simulation
Software
python
systems
InsightMaker
flow
Category Theory
stock
stock-flow
Modeling Scenario
400
views
211
downloads
0
comments
6-005-InsectColonySurvivalOpt-ModelingScenario
We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
optimization
Optimal Control Theory
insect colony
optimal control
natural resources
Pointryagin's Maximum Principle
control variable
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