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1. 15 Aug 2019 | Modeling Scenarios | Contributor(s): Karen Bliss

The different possible dynamics of a two-person 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....

2. 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...

3. 28 Apr 2019 | Modeling Scenarios | Contributor(s): Karen Bliss

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).

4. 28 Apr 2019 | Modeling Scenarios | Contributor(s): Karen Bliss

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).

5. 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 first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

6. 03 Mar 2019 | Modeling Scenarios | Contributor(s): Karen Bliss

In this validation-oriented 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...

7. 09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Karen Bliss

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...

8. 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...

9. 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 non-homeowner 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...

10. 24 Apr 2018 | Modeling Scenarios

The goal of this project is to set up and numerically solve a first-order 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...

11. 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...

12. 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): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

13. 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, Two-Year College, Four-Year Institution at Joint Mathematics Meetings, San Diego CA, 9-13...

14. 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

15. 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...

16. 10 Sep 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss

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,...

17. 10 Sep 2017 | Potential Scenario Ideas

Kerckhove, Michael.  2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 1-18.Abstract: Differential equation models for population dynamics are now standard fare in single-variable calculus. Building on these ordinary differential equation (ODE)...

18. 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,...

19. 08 Sep 2017 | Potential Scenario Ideas

Fay, T. 2001.The Pendulum Equation.  Int. J. Math. Educ. Sci. Technology.  33(4): 505-519.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 fifth-order Taylor series...

20. 06 Sep 2017 | Potential Scenario Ideas | Contributor(s): Karen Bliss

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...