**Guidelines for the Instructor**

In order to use the
textbook as the basis for a multivariable course, students must have access to
the internet, and the instructor should have a computer and projector available
in the classroom. Because the book is
online and free, we have begun requiring that students purchase the *Maple Adoption Kit* in lieu of having to purchase a
textbook.

students will need either access
to Maple on campus or access to a computer off campus that can run the student
version of Maple. We recommend Maple 9
Classic or lower be used except for machines with at least 512 mb ram and at least a 2.2 ghz
processor.

Once adequate
technological resources have been secured, the course delivery need differ only
slightly from the traditional lecture-homework-assessment model. Let’s describe the procedures in our course,
which is conducted in a 24 seat computer-based classroom with a white board and
an computer with projector.

**1.
****Lecture with
Maple:** Material is introduced based on the first part of the Maple
worksheet for that section.

**2.
****Exercises
and Tools: **Exercises are assigned after lecture along with some
activities with the tool for that section.
Both the exercises and the tools are discussed at the beginning of the
next class meeting.

**3.
****Maple
Applications: **After the
exercises and tools have been discussed, one or two exercises from the Maple
worksheet are assigned. These worksheet
assignments are periodically collected and receive a homework grade.

**4.
****Assessment**:
Tests are a mixture of pencil and paper calculations, simple proofs, and
Maple-based problems. Students must
“show their work,” except for the Maple problems which are typically
calculations that are too involved for pencil and paper calculation in a
restricted time setting.

In addition, we also assign longer projects based on Maple which tend
to be “implementation assignments.” We
typically assign 2-3 such projects each semester, with recent projects
including the gradient following algorithm, least squares curve fitting to a
given data set, the Gauss-Newton method, geodesics on unusual surfaces (such as
polyhedra), simple Monte Carlo Methods for multiple
integrals, and centroids of regions bounded by closed
curves using Green’s theorem.

There is one section
and parts of other sections that are marked “DIFF GEOM.” These sections are
topics from differential geometry—such as the curvature of a surface—that are
suitable for a general audience of multivariable calculus students but that are
traditionally considered exclusive to a differential geometry course.

Each semester we cover
all the material in the five chapters and finish somewhere within the capstone
material. Although we cover the DIFF
GEOM material, we do not always include the material in our assessments. The biggest obstacles to teaching the course
using the online format is in securing access to Maple, athough
the Maple adoption kit seems to have addressed that issue.