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Downloads
Views
Date
Relevance
Modeling Scenario
311
views
316
downloads
0
comments
4-039-FallingDarts-ModelingScenario
we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined...
optimization
resistance
terminal velocity
muzzle velocity
drag coefficient
free fall
air drag
Modeling Scenario
178
views
183
downloads
0
comments
3-064-GearTrain-ModelingScenario
Students model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components.
friction
gear
spur gear
gear train
torque
gear ratio
angular acceleration
angular velocity
moment of inertia
double reduction gear
Potential Scenario
166
views
63
downloads
0
comments
2017-D_Goulet-Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments
In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The differential equations are typically nonlinear.
optimization
Biochemistry
sensitivity analysis
chromatography
mass action
cluster analysis
conservation laws
dimerization
estrogen receptor protein
Modeling Scenario
180
views
131
downloads
0
comments
3-095-ShotInWater-ModelingScenario
This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.
projectile motion
terminal velocity
projectile
water resistance
reduction of order
friction
air resistance
Potential Scenario
104
views
34
downloads
0
comments
2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
Walk through the cases in context of second order linear constant coefficient differential equation with driving function
driving function
viscous
mechanical system
Potential Scenario
116
views
61
downloads
0
comments
2016-Erno_Keszei-Chemical Kinetics for Beginners
The most important goal of kinetic research is the identification and characterisation of elementary molecular events which make possible the transformation of reactants into products.
kinetics
zeroth order reaction
first order reaction
second order reaction
reaction rates
third order reaction
Potential Scenario
99
views
54
downloads
0
comments
2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
delay
time dely
step response
Potential Scenario
227
views
43
downloads
0
comments
1989-EY_Rodin-K_Egan-Mathematics modelling of the rate of chemical reactions
The development of improved designs for chemical reactors as well as the prediction of optimal operating conditions in chemical production are based on an understanding of the rates at which chemical processes occur.
kinetics
first order
reaction
second order
zeroth order
Potential Scenario
146
views
42
downloads
0
comments
2012-Ogunrinde-Sunday-On some models based on second order differential equation
This paper presents some models based on second order differential equations. Such models include interaction between different kinds of species in an environment and pricing policy for optimum inventory level of a firm.
species interaction
pricing policy
optimal inventory
Article or Presentation
139
views
40
downloads
0
comments
2015-Brian_Winkel-Informed_Conjecturing_of_Solutions_for_Differential_Equations_In_a_Modeling_Contex
We examine (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their...
exponential growth
solutions
linear systems
decay
conjecture
Potential Scenario
129
views
38
downloads
0
comments
2014-Yahdi-EtAl-Modeling and Sensitivity Analysis of the Role of Biodiversity to Control Pest Damage in Agroecosystems
The paper provides a mathematical framework for cost-effective and environmentally safe strategies to minimize alfalfa damage from pests in alfalfa agroecosystems with optimal biodiversity levels.
sensitivity analysis
predator
steady state
alfalfa
Shannon diversity index
plant herbivore
Potential Scenario
128
views
54
downloads
0
comments
2011-Gaff-Lenhart-Use of optimal control models to predict treatment time for managing tick-borne disease
Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk.
disease
optimal control
TICK
tick mode
ehrlichiosis
bang bang control
Potential Scenario
116
views
39
downloads
0
comments
1998-K_H_Louie_Clark-P_C_D_Newton-Analysis of differential equation models in biology-clover meristem populations
A simple differential equation model (dynamical system) for clover, based on meristem numbers, is outlined and analysed mathematically.
sensitivity analysis
stability analysis
steady states
growing points
buds
meristems
Potential Scenario
649
views
39
downloads
0
comments
2000-Erdman-Morelock-A Study of Kinetics The Estimation and Simulation of Systems of First-Order Differential Equations
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.
kinetics
SAS
compartment
pharmacokinetics
Potential Scenario
312
views
84
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
Potential Scenario
151
views
61
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
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
Free Online Textbook
193
views
99
downloads
0
comments
2021-G_Nagy-Ordinary_Differential_Equations
This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations.
differential equations
textbook
Article or Presentation
150
views
62
downloads
0
comments
2004-Mark_McCartney-Using_second-order_ordinary_differential_equations_to_model_traffic_flow
A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted.
differential equations
traffic flow
vehicle follow
second order
Modeling Scenario
295
views
317
downloads
0
comments
5-040-TunedMassDampers-PartII-ModelingScenario
Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring...
structure
resistance
spring-mass-dashpot
earthquake
vibration
control
damping
tuned mass damper
stiffness
reduction of vibration
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