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  1. 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).

  2. 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...

  3. 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...

  4. 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...

  5. 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 

  6. 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...

  7. 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,...

  8. 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,...

  9. 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...

  10. 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.

  11. 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...

  12. 3-030-S-SecondOrderIntro

    22 Apr 2016 | | Contributor(s):: Brian Winkel

  13. 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...

  14. 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 ...