### Animated Demonstrations for Multivariable Calculus

John F. Putz

Mathematics and Computer Science Department

Alma College

Alma, MI 48801

Phone: (517) 463-7253

Fax: (517) 463-7277

E-mail: putz@alma.edu

#### ABSTRACT

With the ability of computer algebra systems to graph surfaces in
three dimensions, came a major leap in our capacity to convey the
ideas of multivariable calculus. Their facility for animation is
the next significant stride. Of all the methods I have tried,
animated demonstrations have been the most effective, particularly
for: quadric surfaces; level curves and level surfaces; velocity
and acceleration vectors; and directional derivative and gradient
vector. In this paper, I share ten animated demonstrations that
I have written using Maple V Release 4 to teach these topics.