Davide Cervone and Frederick Wicklin, designed and taught a new course in multivariable calculus and linear analysis. The course emphasized a geometric approach to multivariable mathematics and incorporated laboratory-based learning in a fundamental way. Though the course covered most of the standard topics in a third semester calculus course, the geometric approach led to an increased emphasis on tangent vectors, tangent planes, linear transformations, and the geometry of differential equations and vector fields. At the end of the course, some students created on-line projects that explored some of these ideas.
Half of the course was spent in the classroom; the other half of the course took place in a computer lab. The class-time was itself a mixture of lectures interspersed with small-group activities and discussions. In the lab, the students primarily used Maple as a symbolic and graphical toolkit, although they also used public-domain dynamical systems software during the differential equations portion of the course. The labs were written in a hypertext format and included hyperlinks to definitions, examples, historical information, and on-line documentation of software. Students can also launch software from within hypertext documents, making this format substantially more powerful and interactive than a worksheet written on a piece of paper.
As an example of some of the activities that took place, we highlight two labs: one concerning the center of the state of Minnesota, the other concerning the geometry of fluid flow.
Author: Frederick J. Wicklin <email@example.com>
Comments to: firstname.lastname@example.org
Created: Fri Aug 18 1995 --- Last modified: Jul 21 1996
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