
2009NoakeSleighAirflowInfectionHospitalWards
29 Mar 2020  Contributor(s): Karen Bliss
2009NoakeSleighAirflowInfectionHospitalWardsNoakes, Catherine J. and P. Andrew Sleigh. 2009. Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards. J. R. Soc. Interface. 6: S791S800.Abstract: Understanding the risk of...

3067SRLCSeriesCircuit
28 Apr 2019  Modeling Scenarios  Contributor(s): Karen Bliss
In this validationoriented 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).

1986CookeLinear And Logistic Harvesting ModelsMath Modeling Journal
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Karen Bliss
Cook, K. L. and M. Witten. 1986. Onedimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301340.Abstract: Some of the results in the literature on simple onedimensional, density dependent, discrete and continuous modelswith and without harvestingare reviewed. Both...

LeakingBucket: Differential Equations in Engineering
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Karen Bliss
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...

2003RasmussenKeynesLinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Karen Bliss
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

1988StrogatzLoveAffairsAndDifferentialEquations
26 Nov 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
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

2015EastonMathematical models of health focusing on diabetes
11 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
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...

2013SlavikMixing Problems with Many Tanks
10 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806821.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,...

BobbingObjectInWater
09 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
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,...

FinioLinear Non Linear Springs Tutorial
06 Sep 2017  Potential Scenario Ideas  Contributor(s): Karen Bliss
Finio, Ben. Science Buddies – Linear & Nonlinear Springs Tutorial. https://www.sciencebuddies.org/sciencefairprojects/references/linearnonlinearspringstutorial#introduction . Accessed 5 September 2017.This tutorial provides a basic summary of linear and nonlinear...

Informed Conjecturing in a Modeling Context Differential Equations
29 Mar 2017  Articles and Publications  Contributor(s): Karen Bliss
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...

3030SSecondOrderIntro
22 Apr 2016  Modeling Scenarios  Contributor(s): Karen Bliss
SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODESPANISH.cls. Names will be xySTitleStudentVersionSpanish and xyTTitleTeacherVersionSpanish.

3060SDataToDifferentialEquation
24 Dec 2015  Modeling Scenarios  Contributor(s): Karen Bliss
Students use their knowledge of secondorder linear differential equations in conjunction with physical intuition of springmass 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...

Traffic Flow Modeling Using Second Order Ordinary Differential Equations
22 Jun 2015  Articles and Publications  Contributor(s): Karen Bliss
Mark McCartney.2004. Keep your distance! using secondorder ordinary differential equations to model traffic flow. International Journal of Mathematical Education in Science and Technology. 35(4): 588596,Article Abstract: A simple mathematical model for how ...