The CAS in Multivariable Calculus

John F. Putz

Mathematics and Computer Science Department
Alma College
Alma, MI 48801
USA
Phone: (517) 463-7253
Fax: (517) 463-7277
putz@alma.edu

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ABSTRACT

Over the past three years, we have been working to incorporate CAS technology into our calculus program at Alma College. Our guiding principle has been that we would try to find ways to use the technology to help students understand the concepts of calculus better; we would not use it to supplant hand computation. To accomplish this, we have been developing laboratory assignments which the students carry out cooperatively in groups of two or three. The CAS is Maple V.

Of the sixteen topics in calculus we have used a CAS to teach, I have found that those which are enhanced the most by the technology are the multivariable ones. In this paper, I discuss some of these topics and share the laboratory activities we have used to teach them. For example, the concept of limit in multivariable calculus entails the complication of path-independence. Typically, calculus text books include limit problems in which a function nears the same value along all lines of approach, but it tends to a different value along some curve of approach. The student is supposed to find such a curve by inspection. While this is a valid activity, another way is to use the graphics capability of a CAS to help find such a curve of approach or, at least, to determine that there is one to be found. This method has the advantage of giving the student a very concrete way to visualize what is happening.

I also share results of student surveys we have conducted about our project.

Keyword(s): computer algebra systems, calculus, multivariable calculus, Maple, limits