Francisco Javier Gonzalez (Mexico), Alfonsa Garcia*, Francisco Garcia,
Alvaro Franco, Pedro Franco, Agustin de la Villa, Sara Hoya, Gerardo Rodriguez
(Spain),  garcial@eui.upm.es, avilla@dmc.icai.upco.es, gerardo@gugu.usal.es

Learning Calculus of Several Variables with New Technologies

In this paper, the authors, teachers of different universities working as a
team, show how they have been working with Computer Algebra Systems (CAS) such
as Mathematica or Maple, focussing them to analyze different topics of calculus
of several variables.

Applying the power of computers to make calculations and facilitate the
understanding of problems through their visualization, we emphasize concepts
like limit, partial differentiation, derivative, integration, etc.  We have
prepared two different kinds of documents for each topic: The first one, easy
to follow and understand, includes instructions written on paper on how to use
the CAS in order to learn calculus.  The second is an interactive file,
including experiments and different functions specially developed for the CAS
used, in order to solve mathematical problems.  This one requires a deeper
knowledge of the CAS used, Mathematica or Maple.  We try to offer a different
point of view from that presented previously in books and electronic material.
This work is specially suited for students majoring in physics or engineering.
We like to show trough several examples, realized with Maple or Mathematica,
the main goals, the advantages and disadvantages of this kind of tools.