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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. 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...

6. 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...

7. 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...

8. 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...

9. 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...

10. 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...

11. 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

12. 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...

13. 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,...

14. 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,...

15. 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...

16. 04 Sep 2017 | Modeling Scenarios | Contributor(s): Karen Bliss

Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves. In this activity, students are introduced to the concepts of...

17. 17 Apr 2017 | Modeling Scenarios | Contributor(s): Karen Bliss

We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container. Source: Farmer, T and F. Gass. 1992. Physical demonstration in the calculus classroom.  The College...

18. 07 Apr 2017 | Modeling Scenarios | Contributor(s): Karen Bliss

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.

19. 30 Mar 2017 | Modeling Scenarios | Contributor(s): Karen Bliss

We introduce several basic, but substantial, approaches to modeling the motion of a spring mass system using a standard second order, linear, constant coefficient differential equation obtained from Newton's Second Law of Motion and a Free Body Diagram. We do this using a set of data...

20. 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...