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Downloads
Views
Date
Relevance
Modeling Scenario
207
views
175
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
271
views
340
downloads
0
comments
1-165-FlushToilet-ModelingScenario
This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
julia
Diffusion
innovation
rate of innovation
Bass model
Solver
Modeling Scenario
295
views
211
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
330
views
238
downloads
0
comments
6-040-StruggleForExistence-ModelingScenario
We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters
competition
logistic
carrying capacity
paramecium
Technique Narrative
435
views
458
downloads
0
comments
1-005-NavigatingNumericalMethods-TechniqueNarrative
This technique narrative is a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor...
Euler's method
Taylor's Method
search and rescue
Coaast Guard
lost at sea
longitude
latitude
limit definition
Modeling Scenario
325
views
566
downloads
0
comments
1-155-CruiseControl-ModelingScenario
In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.
PID controller
feedback control
Control theory
cruise control
automobile
closed-loop control
input-ouput
block diagram
Potential Scenario
103
views
33
downloads
0
comments
1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange
A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.
mechanical ventilation
ventilation
carbon dioxide exchange
tracheal gas insufflation
alveolar ventilation
shunt
two-compartment model
Technique Narrative
456
views
485
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
404
views
510
downloads
0
comments
1-011-Kinetics-ModelingScenario
We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.
kinetics
chemistry
Law of Mass Action
chemical kinetics
order of reaction
chemical reaction
Modeling Scenario
229
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
Modeling Scenario
353
views
241
downloads
0
comments
5-076-LanchesterLaws-ModelingScenario
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
Lanchester's laws
sensitivity analysisanalysis
Modeling Scenario
316
views
171
downloads
0
comments
3-054-Relay-ModelingScenario
We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.
distance
projectile motion
relay
time
baseball
outfield
home plate
minimization
Modeling Scenario
284
views
128
downloads
0
comments
1-044-CollegeBound-ModelingScenario
Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.
interest rate
college saving
tuition
room and board
Modeling Scenario
130
views
48
downloads
0
comments
1-144-HeatCool-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
temperature
Newton's Law of Cooling
cooling
Potential Scenario
194
views
74
downloads
0
comments
2018-W_Hohenauer-Physical modelling based on first order ODEs
An introduction in techniques to solve first order ODE´s is given. Barometric formula, charging and discharging of a capacitor including its application for AMV, magnetic induction and growth effects are discussed.
discharge
capacitor
magnetic field
induction
magnetic induction
Potential Scenario
102
views
59
downloads
0
comments
2015-Goodnow-EtAl-Mathematical Models of Water Clocks
This is a historical tour of water clocks, known as clepsydra a Greek word meaning water thief. These devices were for telling time.
Torricelli's Law
water clock
Bernoulli's Law
clepsydra
Potential Scenario
123
views
44
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
Potential Scenario
124
views
67
downloads
0
comments
1992-John_Mathews-Bounded population growth-a curve fitting lesson
The purpose of this article is to present two methods for fitting the logistic curve to data supplied by the U. S. census bureau.
data
logistic
linearization
fitting
Potential Scenario
94
views
37
downloads
0
comments
1994-S_S_Everingham-C_Peter_Rydell-Modeling the Demand for Cocaine
This is a report prepared for the Office of National Drug Control Policy of the United States Army by the Rand Corporation. The report contains lots of data and builds a two compartment difference equation model.
drugs
two compartment
cocaine
demand
Modeling Scenario
1110
views
607
downloads
0
comments
3-065-UpDown-ModelingScenario
We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity
Newton's Second Law of Motion
velocity
motion
apex
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