Using An Integrated Engineering Curriculum To Improve Freshman Calculus
S. A. Fulling, David L. Barrow
Abstract
This paper addresses the following question: What are some of the ways that the beginning calculus course for engineers can be improved, if it is part of an integrated curriculum that also includes physics, engineering, and chemistry courses? The authors have had the opportunity to participate in such an integrated curriculum at Texas A&M for the past two to four years. Several major changes were made in the first-year calculus sequence in order to present various topics at the times they were applied in other courses. We have found that these changes not only serve the needs of the partner disciplines, but also provide a more unified and coherent treatment of some topics from the point of view of mathematics itself. Vectors, parametric curves, line integrals, and especially centers of mass and moments of inertia are topics that students traditionally find difficult, unmotivated, or confusing because of inconsistent notation or terminology in different courses; covering them "early" actually improves their presentation. Other topics, such as multiple integrals, orthonormal bases, ordinary differential equations, and numerical approximation of derivatives and integrals, can be introduced in a motivated way in preparation for their more in-depth treatment in later years. Following "learning cycle" and "learning style" ideas, we have made an effort to provide more motivation and practice within the mathematics course; but the most effective and efficient motivators and practice fields are coordinated courses in other disciplines where the mathematics is actually used.