Multivariable Calculus Online

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 a 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 using 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. 

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 via 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.