Maple demonstrations for teaching multivariable
calculus,
by Fr. Mike May, St. Louis University
At Saint Louis University, we are using graphing calculators
as the primary technology in teaching our introductory calculus courses.
However, as students advance to multivariable calculus,
the need to visualize in 3 dimensions makes Maple far more effective than
graphing calculators. Our Calculus III course is being taught in a computer
classroom where the students have access to Maple.
The strategy I have used for bringing Maple into the classroom
is to introduce it through carefully designed worksheets, which I use
as:
Lecture aids with the instructor running the worksheet
with a projection system.
Handouts for the students
Lab assignment that the class
will start together as a substitute for a lecture.
Supplemental homework assignments.
These worksheets include a significant amount of exploratory
text and exercises. The exercises ask the student to repeat the examples
in the worksheets with minor modification. I do not expect them to produce
the code, but rather to copy and modify a code template, focusing on the
results of the problems.
A fast handout explaining the syntax for dot
and cross product in Maple. The intent is to show the students how to use
Maple to check their work with vector computations.
Visualizing the definition that a function is
differentiable at a point if the graph near the point is locally approximated
by the tangent plane. The definition is used to understand the corresponding
delta-epsilon definition.
Demonstrates for the students the Maple commands
needed to do integration. It seems useful in this chapter where many of
the problems reduce to "and finish by evaluating the two or three integrals."
How to plot in coordinate systems other than
Cartesian. It also shows how to combine objects described in different coordinate
systems on a single plot.
The Riemann sum definition of double integrals.
It follows the usual pattern of the course by reviewing the definitions
in the one variable case, then generalizing.
This worksheet was done by the students in class.
It looks at setting up integrals in polar coordinates and switching between
rectangular and polar coordinates.
Parameterizing planetary motion under gravity.
This is a demonstration worksheet and was done after Chapter 17. It solves
for planetary motion with a flow line solution of a vector field in 4 dimensions.
The orbits of Mars and Halley's comet are studied as examples.
The procedure of setting up and evaluating a
flux integral through a surface. It is intended as a homework checker.
"This material is based upon work supported by
the National Science Foundation under Grant No. 9851405."
"Any opinions, findings and conclusions or recommendations expressed
in this material are those of the author(s) and do not necessarily reflect
the views of the National Science Foundation (NSF)."
