Philosophy of Math 3354 and Math 3355

In both quarters of the sequence, the emphasis will be on understanding the geometric ideas of multivariable calculus and linear algebra. The geometry will be used to understand, analyze, and compute the solutions to problems that involve functions of several variables, and systems of differential equations. The sequence will use several software packages to assist in the analysis, i.e., Matlab, Maple, and software for the numerical solution of differential equations. It is anticipated that by the end of this sequence the students will have a working familiarity with how to use technology to help analyze multivariable mathematics. They will be able to bring this skill to bear on problems in other classes, and on problems they encounter after graduation.

The course work is NOT in a lecture/recitation format. In many ways, it is lab-based, since a significant portion of the learning will occur in a "workshop setting" setting. The workshop component will allow students to work examples, discover patterns, and formulate conjectures. Group work is an essential part of the workshop, and collaboration is also encouraged on homework. The purpose of the lecture portion of the class is to introduce new material and to indicate how each subtopic fits into the larger context of the course.

The grade for each course will be primarily based on homework and lab reports. The lab reports are written answers to questions based on computer-based exploration of topics. The labs will be shorter than those in the first-year calculus courses, but there will be five or six of them in each course. Sample labs and topics are available at the URL

The instructor of these courses strongly believes that calculus is best learned in the context of applications, and that abstractions are best appreciated after meeting concrete examples. As a result, this sequence will integrate applications throughout the course, rather than isolating them into special sections. Similarly, concepts in linear algebra will be introduced as needed, rather than learned out of context.

The instructor for the course is Rick Wicklin (School of Mathematics) who has degrees in applied mathematics, pure mathematics, physics, and engineering. He has worked in the aerospace industry, in an industrial research and development setting, and has spent the last three years at the NSF Geometry Center at the University.

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Copyright: 1996 by the Regents of the University of Minnesota.
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Last modified: Sept 3 1996
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