Electronic Proceedings of the Eighth Annual International Conference on Technology in Collegiate MathematicsHouston, Texas, November 16-19, 1995Paper C016The CAS in Multivariable Calculus |
John F. PutzMathematics and Computer Science Department Alma College Alma, MI 48801 USA Phone: (517) 463-7253 Fax: (517) 463-7277 putz@alma.edu list of all papers by this author |
Click to access this paper: |
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