World Population Growth -- Notes for the Instructor



This module works well as the last lab exercise in a first-semester calculus course, and it can also be used early in a second-semester course to stimulate interest as a striking example of very simple formal integration. Either way, there are strong messages about the importance of correct calculation, reinforced by obviously absurd answers that result from common errors. In particular, students find themselves in untenable positions if

a. they think that integrating "1 over something" always means take the log of "something," or,

b. they forget the constant of integration.

There are several modeling messages here as well, not all of which are made explicit in the module.

For students who do not encounter simple differential equations in their calculus course, the module could also be used early in a differential equations course -- to emphasize a modeling point of view and to review important calculus topics.

In addition to the references in the module, you will find more about the coalition model in David Smith's paper “Human Population Growth: Stability or Explosion?,” Mathematics Magazine 50 (1977), 186-197.

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