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Article or Presentation
145
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
Potential Scenario
348
views
77
downloads
0
comments
2017-Varanis-Mereles-Mathematical Model of a Vehicle Crash A Case Study
The model proposed in this paper allows one to obtain the parameters of the system, and then compare them with the ones obtained experimentally to test the suitability of the model with the vehicle crash.
case study
Runge-Kutta
spring mass damper
vehicle crash
Modeling Scenario
262
views
100
downloads
0
comments
5-036-HalfCarVibration-ModelingScenario
Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF) including pitch and bounce of vehicle body on suspension...
vibration
vehicle
half-car model
finite element analysis
shock absorbers
suspension
Modeling Scenario
213
views
183
downloads
0
comments
3-105-FrequencyResponse-ModelingScenario
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
transient dynamics
circuit
spring mass
driver
frequency response
amplitude
steady state
Technique Narrative
838
views
110
downloads
0
comments
3-090-ChebyshevPolynomialSolution-TechniqueNarrative
The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
series soluotion
polynomial solutions
Chebyshev polynomials
Chebyshev differential equations
Modeling Scenario
232
views
119
downloads
0
comments
1-122-SpreadPEV-ModelingScenario
We present data on world sales data of plug-in electric vehicles (PEVs) and request a model on the rate of change in sales over time, leading to prediction as to number of PEVs in the future.
data
logistic
prediction
spread
plug-in vehicle
PEV
Modeling Scenario
211
views
405
downloads
0
comments
4-020-AnIEDBlast-ModelingScenario
These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use the model to determine the results of a dynamical...
applied mathematics
forces
Free Body Diagram
Improvised Explosive Devices
sum of forces
Article or Presentation
178
views
45
downloads
0
comments
2010-Scott_Carrell-James_West-Does_Professor_Quality_Matter-Evidence_from_Random_Assignment_of_Students_to_Professors
In the postsecondary environment, scores on student evaluations of professors are typically used to measure teaching quality. We possess unique data that allow us to measure relative student performance in mandatory follow-on classes.
teaching
evaluation
follow-on course
student achievement
Modeling Scenario
322
views
543
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
131
views
67
downloads
0
comments
2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
kinematics
curve design
highway exit
tangential acceleration
Article or Presentation
116
views
40
downloads
0
comments
2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
resistance
projectile motion
projectile
fluid
Mersenne
Modeling Scenario
213
views
348
downloads
0
comments
6-026-IsleRoyaleModeling-ModelingScenario
The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle.
ecology
optimization
predator-prey
population
vector calculus
Lagrange multipliers
least squares
Islel Royale
Potential Scenario
173
views
53
downloads
0
comments
2015-Valerie_Billard-Pharmacokinetic-pharmacodynamic relationship of anesthetic drugs - from modeling to clinical use
The purpose of this short review is to describe the basis of pharmacokinetics and modeling, the concentration-effects relationship, and drug interactions modeling to offer to anesthesiologists and non-anesthesiologists an overview of the rules to...
anesthesia
pharmacokinetics
pharmacodynamic
anesthetic
Article or Presentation
139
views
34
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
133
views
48
downloads
0
comments
2006-G_Ashline-J_Ellis-Monaghan-How high-fast-long-Modeling water rocket flight with calculus
We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts.
calculus
Flight
projectile
water rocket
Potential Scenario
143
views
41
downloads
0
comments
2003-Rasmussen-Keynes-Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations
The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant...
instructional design
eigenvalues
eigenvalue analysis
Article or Presentation
111
views
43
downloads
0
comments
1999-F_Brauer-What_Goes_Up_Must_Come_Down
It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces that are nonlinear functions of velocity.
resistance
falling
projectile
vertical projectile
Modeling Scenario
319
views
130
downloads
0
comments
1-001d-HotelPopulationDecay-ModelingScenario
You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel. Before you run the simulation in MATLAB, answer some questions.
simulation
logistic
exponential decay
fitting
Potential Scenario
112
views
31
downloads
0
comments
2008-Chernyshov-EtAl-The Problem of Modelling of Economic Dynamics in Differential Form
The authors have tried to analyze procedures of the construction of differential equations that are employed for modeling of macroeconomic processes. The results prove to be rather unexpected.
Fredholm integral equation of
Leontief’s model
macroeconomic processes
Potential Scenario
134
views
35
downloads
0
comments
1999-Kowalczyk-Hausknecht-Using DEs To Model Real World Data
With the increasing availability of easy to use interactive differential equation software, we convinced ourselves to completely redesign the way we teach differential equations.
circuit
Torricelli's Law
Hooke's Law
RC circuit
harmonic oscillator
glucose
glucose tolerance test
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