This lab first presents data representing rates of change of
carbon-dioxide in aquatic systems
[Beyers]. The integration of this
data gives limnologists an idea about whether a lake or river is
healthy, or whether it is susceptible to algae blooms. After
integrating a set of given data, the students are asked to generate
their own data: each team of students gets in a car and drives around town
while recording their speed and mileage at a series of times. Upon
returning to campus, each team numerically integrates their velocity
data (using an interactive ``data integrator'' that is part of their
lab) and compares it to the total distance the team traveled. This
experiment sparks fascinating discussions about sampling frequency,
the assumptions that go into estimating (modeling) functions *
between* data points, and the realization that there is never an
absolute answer to the question ``what is the integral of this set of
data?''

The lab also introduces (but does not pursue) ideas such as cubic splines, Fourier polynomials, error estimation, and ``functions of best fit.'' The data integrator associated with this lab has been used by many experimentalists from outside the University and outside of mathematics because of its ease-of-use and versatility.

Frederick J. Wicklin <

Last modified: Fri Nov 29 12:28:11 1996