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# Interactive Calculus Problems in Biology

Joseph M. Mahaffy (San Diego State University)
Screen Shots | System Requirements

The Interactive Calculus Problems in Biology module provides a set of calculus problems that address some of the mathematical issues underlying the models and theories that students commonly encounter in their biology courses. The module consists of a series of labs developed for a two-semester “Calculus for Life Sciences” course in which students interested in biology, chemistry, medicine, and other fields use Maple™, a commercially available symbolic algebra system, to solve bioscience-oriented calculus problems.

In these problems, students are often asked to use their data to model a system in several different ways, for instance, by comparing exponential, logarithmic, and power functions. They may be asked to consider the biological implications of what they have learned, as in the problem below taken from an early first semester lab:

Other problems might ask students to

• explore the growth of a population of bacteria when modelled using the Malthusian growth model and to compare these results to the results obtained with a population of bacteria that satisfies the Logistic growth law.
• use trigonometric functions to study elliptical motion and annual rates of growth in populations with seasonal behavior.
• optimize (which involves differentiating a polynomial ) the oxygen consumption of the bug Triatoma phyllosoma after ingestion of a blood meal.
• given a dataset, develop a power rule (from island biogeography theory) to determine the number of species of herpeto-fauna as a function of island area.

Many of the mathematical formulations in this problem set provide an excellent background for the mathematics underlying other BioQUEST modules. For example, a problem which describes the modeling of action potentials, a single nerve firing, and a nerve cell that has a subcritical stimulation is directly relevant to the Axon simulation. Several problems are devoted to studying various population growth models. These are directly relevant to Biota.

### System Requirements

Macintosh or Power Macintosh

• System 7.1 or later.
• 4 - 5MB of available RAM; 16 - 35MB disk space.

Windows 3.1, Windows 95, or Windows NT

• Windows 3.1 or later, or Windows 95, or Windows NT 3.5 or later.
• 8MB of available RAM; 18 - 36MB disk space.

Requires a copy of Maple™, available from Waterloo Maple Inc. (519) 747-2373