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3-067-S-RLCSeriesCircuit
28 Apr 2019 | | Contributor(s):: Virgil Ganescu
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).
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1986-Cooke-Linear And Logistic Harvesting Models-Math Modeling Journal
09 Dec 2018 | | Contributor(s):: Brian Winkel
Cook, K. L. and M. Witten. 1986. One-dimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301-340.Abstract: Some of the results in the literature on simple one-dimensional, density dependent, discrete and continuous models-with and without harvesting-are reviewed. Both...
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LeakingBucket: Differential Equations in Engineering
03 Mar 2018 | | Contributor(s):: Unknown
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...
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2003-RasmussenKeynes-LinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018 | | Contributor(s):: Chris Rasmussen, Michael Keynes
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...
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1988-Strogatz-LoveAffairsAndDifferentialEquations
26 Nov 2017 | | Contributor(s):: Brian Winkel
Strogatz, Steven H. 1988. Love Affairs and Differential Equations. Mathematics Magazine. 61(7): 35.This is a system of differential equations to describe the love between Shakespeare’s Romeo and Juliet.Keywords: differential equation, system, linear, parameters
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2015-Easton-Mathematical models of health focusing on diabetes
11 Sep 2017 | | Contributor(s):: Brian Winkel
Easton, Jonathan. 2015. Mathematical models of health focusing on diabetes: Delay differential equations and data mining. Doctoral thesis, 186 pp. Northumbria University. http://nrl.northumbria.ac.uk/23582/ . Accessed 10 September 2017.This is an exhaustive study with very good...
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2013-Slavik-Mixing Problems with Many Tanks
10 Sep 2017 | | Contributor(s):: Brian Winkel
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806-821.Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix representation of the linear mixing model of differential equations. Keywords: tank, circula,...
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BobbingObjectInWater
09 Sep 2017 | | Contributor(s):: Brian Winkel
Introduction to Second Order Linear Equations- Bobbing Object in Water. 2 pp.This is a nice treatment of developing a model of a bobbing object in water from first principles with some nice additional questions which would make a nice Modeling Scenario.Keywords: buoyancy, bobbing, water,...
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Finio-Linear Non Linear Springs Tutorial
06 Sep 2017 | | Contributor(s):: Brian Winkel
Finio, Ben. Science Buddies – Linear & Nonlinear Springs Tutorial. https://www.sciencebuddies.org/science-fair-projects/references/linear-nonlinear-springs-tutorial#introduction . Accessed 5 September 2017.This tutorial provides a basic summary of linear and nonlinear...
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3-040-T-FirstPassageTime
07 Apr 2017 | | Contributor(s):: Brian Winkel
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time with several applications.
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Informed Conjecturing in a Modeling Context Differential Equations
29 Mar 2017 | | Contributor(s):: Brian Winkel
We examine two differential equations, (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 solution. We follow with...
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3-030-S-SecondOrderIntro
22 Apr 2016 | | Contributor(s):: Brian Winkel
SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODE-SPANISH.cls. Names will be x-y-S-Title-StudentVersion-Spanish and x-y--T-Title-TeacherVersion-Spanish.
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3-060-S-DataToDifferentialEquation
24 Dec 2015 | | Contributor(s):: Eric Sullivan, Kelly Cline
Students use their knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data. The data is presented as {%5Cit total distance traveled} instead of displacement so the...
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Traffic Flow Modeling Using Second Order Ordinary Differential Equations
22 Jun 2015 | | Contributor(s):: Mark McCartney
Mark McCartney.2004. Keep your distance! using second-order ordinary differential equations to model traffic flow. International Journal of Mathematical Education in Science and Technology. 35(4): 588-596,Article Abstract: A simple mathematical model for how ...