Love Affairs and Differential Equations

Summary

Editors' Note: Professor Strogatz teaches in the Department of Theoretical and Applied Mechanics at Cornell University. His undergraduate education was at Princeton, with graduate work at Cambridge and Harvard. The present article was written at Harvard while he was on a postdoctoral NSF appointment. After reading this piece we are not surprised to learn that while teaching subsquently at MIT Strogatz won their highest teaching award, the E. M. Baker Award for Excellence in Undergraduate Teaching. He also won a Presidential Young Investigator Award from the National Science Foundation. His research is in nonlinear dynamics and chaos applied to physics, engineering, and biology.

The purpose of this note is to suggest an unusual approach to the teaching of some standard material about systems of coupled ordinary differential equations. The approach relates the mathematics to a topic that is already on the minds of many college students: the time-evolution of a love affair between two people. Students seem to enjoy the material, taking an active role in the construction, solution, and interpretation of the equations.

The essence of the idea is contained in the following example.

Juliet is in love with Romeo, but in our version of this story, Romeo is a fickle lover. The more Juliet loves him, the more he begins to dislike her. But when she loses interest, his feelings for her warm up. She, on the other hand, tends to echo him: her love grows when he loves her, and turns to hate when he hates her.