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Article or Presentation
162
views
53
downloads
0
comments
2009-Agnes_Rash-Brian_Winkel-Birth_and_Death_Process_Modeling_Leads_to_the_Poisson_Distribution
In this paper there are details of development of the general birth and death process from which we can extract the Poisson process as a special case.
Probability
Mean
Poisson process
birth and death process
infinite number of differential equations
Modeling Scenario
284
views
211
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
306
views
229
downloads
0
comments
1-027-StochasticProcesses-ModelingScenario
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
Variance
Mean
stochastic
random
operations research
industrial engineering
Poisson process
traffic
Potential Scenario
178
views
66
downloads
0
comments
2016-Starling-EtAl-Local Brewery - A Project for Use in Differential Equations Courses
We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer.
BEER
Fermentation
brewery
Potential Scenario
136
views
80
downloads
0
comments
2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
pharmacokinetics
dynamic models
smoothing
spline
mixed-effects models
HiV combination therapy
Potential Scenario
360
views
61
downloads
0
comments
2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
dynamical systems
regulation
steady state
sales model
external stimulus
Potential Scenario
134
views
52
downloads
0
comments
2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.
Expected Value
Riemann sum
net change
Potential Scenario
155
views
72
downloads
0
comments
2005-Saifullah-Mathematical Modeling With Differential Equations
This article aims to provide the students some basic modeling skills, which will have applications to a wide variety of problems.
species interactions
word equation
interactive software
Potential Scenario
121
views
54
downloads
0
comments
2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.
regression
logistic
Torricelli's Law
growth
periodic process
Modeling Scenario
402
views
500
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
281
views
220
downloads
0
comments
1-035-DotseroVolcanoEruption-ModelingScenario
In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
exponential decay
half-life
decay
Euler's method
carbon dating
decay rate
Carbon-14
Dotsero volcano
volcano
Potential Scenario
140
views
65
downloads
0
comments
2017-Allali-EtAl-Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection
The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies.
logistic
HBV infection
adaptive immunie response
T-lymphocytes
Potential Scenario
110
views
49
downloads
0
comments
2015-Cano-EtAl-Bringing partial differential equations to life for students
This work describes how to use an authoring tool, Easy Java Simulations, to build interactive simulations using FreeFem++ (Hecht F 2012 J. Numer. Math. 20 251) as a PDE solver engine.
Java Simulation
FreeFem
authoring tools
authoring methods
physical modelling
classroom teaching
Potential Scenario
156
views
63
downloads
0
comments
2011-Kenny_Harwood-Modeling a RLC Circuit Current with Differential Equations
This paper gives an abbreviated description of the photovaltaic effect (solar power production process) and then a RLC circuit will be modeled that is powered by a photovaltaic panel.
tuning
frequency response
LC circuit
RLC
Potential Scenario
336
views
94
downloads
0
comments
2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics
We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.
kinetics
chemical kinetics
zeroth order reaction
first order reaction
second order reaction
Technique Narrative
373
views
192
downloads
0
comments
1-030-RandomPerturbation-TechniqueNarrative
After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
random perturbation
Brownian motion
Langevin equation
Riemann-Steiltjes integral
Wiener process
Ito's calculus
Modeling Scenario
266
views
375
downloads
0
comments
1-094-SteepingTea-ModelingScenario
We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration.
concentration
Surface Area
color
Newton's Law of Cooling
tea
sugar
Modeling Scenario
429
views
119
downloads
0
comments
6-067-LotkaVolterra-ModelingScenario
This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities of R and R studio.
time series
data
competition
Lotka-Volterra
model fitting
prediction
gauseR
experimental
Potential Scenario
145
views
64
downloads
0
comments
2017-Brandi-Garcia-Motivating engineering students to math classes - Practical experience teaching ODEs
In this paper we propose an approach to teaching-learning process of mathematical concepts to engineering students with a motivational factor: a practical problem to be modeled in which students must apply concepts seen in class, in particular...
computational tools
teaching
engineering students
practical problem
Potential Scenario
146
views
82
downloads
0
comments
2017-Zhang-Wang-Study on public opinion propagation in self media age based on time delay differential model
We establish the Logistic equation, introduce the operator time delay differential equation, and finally establish the improved delay differential equation, which can describe the propagation trend of network news from the self media.
propagation
pubic opinion
Network public opinion
propagation law
self-media
Xiongan New Area
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