Abstract

Citation

Researchers should cite this work as follows:

• McDill, J. M. (2023). 1994-JM_McDill-Bjorn_Felsager-The Lighter Side of Differential Equations. SIMIODE, QUBES Educational Resources. doi:10.25334/AYTV-R358

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Article Context

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McDill, J. M.  and Bjorn Felsager.  1994. The Lighter Side of Differential Equations. The College Mathematics Journal. 25(2): 448-452.

See https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-lighter-side-of-differential-equations . Accessed 23 March 2023.

First opening material in article,

“Although differential equations have many serious applications to the modeling of real-world problems, a few lighthearted problems can serve to motivate students and brighten their attitudes toward a computer-oriented course in differential equations. The following two scenarios are uninhibited by reality. The first problem involves a system of two coupled linear differential equations, which model the ups and downs of a love affair between Romeo and Juliet. In searching for the origins of the basic idea for this problem, we backtracked along an interesting trail and traced the source to Steven Strogatz of MIT. He contributed the problem to a Harvard final examination, although he had originated it during his college days (perhaps when Romeo-Juliet interactions were more compelling). He later wrote a brief article for Mathematics Magazine [7], and his use of the problem stimulated a column in 1988 by Clarence Peterson in the Chicago Tribune, `As Usual, Boy + Girl = Confusion’ [5].

More recently, Michael Radzicki of Worcester Polytechnic Institute described using a general version of the problem to teach system dynamics skills [6]. The problem has surfaced with many variations and is now passing into the folklore. We hope that the following variations are amusing (and original). The lab exercises described were very popular with students at Cornell and Cal Poly and contributed more than any others to the students' understanding of the relationships among the xy, tx, and ty graphs.”

This paper contains analysis of models of cannabalism

Keywords: love, Romeo and Juliet, model, system, differential equation, cannibalism, overcrowding, cooperation, harvesting