## Animating Calculus with Multimedia

### Patricia A. Clark

Rebecca E. Hill

Thomas C. Upson

Rochester Institute of Technology

85 Lomb Memorial Drive

Rochester, NY 14623
pacsma@rit.edu,
rehsma@rit.edu,
tcusma@rit.edu

*Grant Number*: DUE: 9650246

Multimedia software, such as Authorware, allows pictures, photos, paintings,
maps, movies and music to be imported into mathematics presentations.
Teaching can be enhanced by the addition of historical notes that might not
otherwise be possible. These additions enrich the learning experience.

Multimedia software interfaces with symbolic computation systems, such as
Mathematica or Maple. Graphs and computations can be carried out in
Mathematica and the results presented, interpreted, and discussed with all
segments unified under the user-friendly interface of Authorware.

Multimedia permits the development of presentations that can be used with
students at different levels. Students only need to visit the portions of the
presentations for their particular level. For example, the predator-prey
presentation that incorporates shark and food fish data from the Adriatic Sea
during World War I can be used in a freshman mathematics seminar or more
advanced courses in numerical analysis or differential equations. The
freshman seminar introduces first year majors to several different areas of
math and statistics. The use of multimedia to include historical background
reminds students of the intellectual struggles behind present-day textbook
order.

In our presentation on the solution of the cubic equation, we found that the
students were strongly motivated by the intriguing lives of the mathematicians
who studied the problem and contributed to its solution. How could one's
imagination not be captured by the story of a mathematician of the sixteenth
century, Cardano, who was the first to publish an algebraic solution of the
cubic and who also worked as an astrologer and was imprisoned for heresy
because he published a horoscope of Christ's life?

Equally interesting is the story of an Italian biologist, D'Ancona, of the
early twentieth century who was studying the competition of species. In
attempting to analyze fishing data, he was unable to explain the variation
of the ratio of sharks to food fish. Consequently he called upon the
expertise of his father-in-law, the famous mathematician Volterra, who then
developed a mathematical model which explained the variation of the data.
This detail adds life to the study of periodic solutions of nonlinear
equations.

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