
5002TPhasePortraitForRelationshipDynamics
15 Aug 2019  Modeling Scenarios  Contributor(s): Karen Bliss
The different possible dynamics of a twoperson romantic relationship are modeled  as a linear two dimensional system of equations  and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....

1068TWaterBottleCooling
14 Aug 2019  Modeling Scenarios  Contributor(s): Karen Bliss
This modeling scenario involves Newton's Law of Cooling and should be appropriate in the first week or even the first day of an introductory differential equations course. The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a...

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).

3067TRLCSeriesCircuit
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).

1109TEmployeeAttrition
25 Mar 2019  Modeling Scenarios
This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a firstorder linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

1077TRLMSimSeriesCircuit
03 Mar 2019  Modeling Scenarios  Contributor(s): Karen Bliss
In this validationoriented setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using Multisim) of the circuit. This is compared...

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...

1054TGrowthInFarmland
14 Aug 2018  Modeling Scenarios  Contributor(s): Karen Bliss
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

5026TEvictions
12 Aug 2018  Modeling Scenarios  Contributor(s): Karen Bliss
In this project, students develop two SIS models to study eviction trends in a population of nonhomeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

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...

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
18 Jan 2018  Presentations
Incorporating a Modeling First Approach into a Traditional ODE Course by Mike Karls. Ball State University.A talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego CA, 913...

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,...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017  Potential Scenario Ideas
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 118.Abstract: Differential equation models for population dynamics are now standard fare in singlevariable calculus. Building on these ordinary differential equation (ODE)...

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,...

2002FayThePendulumEquation
08 Sep 2017  Potential Scenario Ideas
Fay, T. 2001.The Pendulum Equation. Int. J. Math. Educ. Sci. Technology. 33(4): 505519.Abstract:We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it. On the one hand, we suggest that the third and fifthorder Taylor series...

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...