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Article or Presentation
174
views
68
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
118
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
255
views
206
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
890
views
116
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
235
views
553
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
201
views
63
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
350
views
613
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
146
views
81
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
134
views
48
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
Potential Scenario
192
views
68
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
158
views
42
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
157
views
54
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
Potential Scenario
161
views
39
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
Free Online Textbook
148
views
45
downloads
0
comments
2010-Bruce-Conrad-Ordinary_Differential_Equations_A_Systems_Approach
This is an author posted second edition to the text which was originally published by Prentice Hall in 2003.
differential equations
textbook
Potential Scenario
425
views
85
downloads
0
comments
2020-Cline-EtAl-A Vision for Projects Across the Mathematics Curriculum
We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.
projects
technical writing
interdisciplinary skills
Free Online Textbook
139
views
51
downloads
0
comments
2014-William_Trench-Elementary_Differential_Equations-Books_and_Monographs
This is the most widely cited and referenced free online text for differential equations and is very complete. These two books are exactly what they say they are.
differential equations
textbook
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