The author once read a posting on an internet calculus reform newsgroup that claimed ``there are no real applications of the first year of calculus.'' We disagree. We believe that the applications in our course effectively combine theory, experiment, and ideas from the client disciplines so that the applications are interesting, thought-provoking, and as challenging for instructors and teaching assistants as they are for students. The labs provide a vehicle through which students investigate large-scale applications of the mathematics they have learned. These are not pseudo-applications about the maximum area that can be enclosed by a farmer with 100 feet of fencing and whose field borders a river shaped like a parabola. Instead, these are applications developed in collaboration with faculty outside of mathematics that touch on topics that many engineering students are likely to meet again in upper-division courses outside of mathematics.
In fact, so far the main drawback of the labs has been that instructors and TAs have sometimes been stumped by lab questions whose answers rely on physical or engineering concepts that are not part of the education of a typical mathematician. There is nothing wrong with an instructor not knowing the answer to a student's question, but it is important that the instructor is comfortable saying ``I don't know, but I will find out'' rather than confuse the students by giving a vague or misleading answer. Some people have suggested that a ``teacher's guide'' to the labs would be beneficial, but there is a danger in that approach, since it is inappropriate for an instructor to require students to work on a lab that the instructor has not completed. A more satisfactory (and more expensive!) solution would be an afternoon workshop at which instructors can learn the related engineering concepts.
A central focus of many calculus reform efforts is the introduction of interdisciplinary laboratory modules. At Minnesota, students work on these modules in teams to collect and analyze data, formulate and test conjectures, and communicate their ideas clearly and effectively in writing. As a group, the students submit a professionally-written lab report that summarizes their investigation. The four applications used for the 1995-96 sequence are described below: