Integrating Calculus and Physics Courses

Phillip Zenor, Department of Mathematics, Auburn University, Auburn, AL 36849
Dave Johnson, Department of Mathematics, Diablo Valley College, Pleasant
       Hill, CA  94549
Martin Jackson, Department of Mathematics and Computer Science,
       University of Puget Sound, Tacoma, WA  98416

The ongoing reform of mathematics undergraduate curricula has, among
other things, resulted in greater emphasis on applications of
mathematics within other disciplines.  Physics naturally comes to mind
as a discipline in which mathematics is applied.  Many students,
including prospective mathematics, physics, and engineering majors,
take separate calculus and physics courses concurrently.  We have been
part of a growing movement to integrate introductory calculus and
physics courses into a unified curriculum.

Each of the authors had been part of a separate program to design and
team teach an integrated calculus/physics course.  Our courses were
developed at three different types of institutions--a community
college, a liberal arts college, and a state university with a large
engineering component.  Despite the differences in our programs and
institutions, we have found a major common feature:  An early
treatment of vector calculus that coincides with the introduction of
mechanics greatly facilitates student understanding of both subjects.

In this paper, we will discuss the three programs we have separately
developed.  We will highlight those features that are common to all
three and should be portable to other institutions.

Auburn University is a large full service state university in Alabama
with a large engineering school.  Its four quarter integrated
calculus/physics course ran for 12 years.  The first quarter was a
mathematics course that introduced vector algebra and the derivative
of real-valued and vector-valued functions.  The remaining three
quarters was a well integrated, team-taught calculus/physics sequence
that presented the material as a single subject with mutually
reinforcing and motivating topics.  The early introduction to vector
calculus is applied to mechanics in a multi-dimensional setting from
the beginning.  Text materials and class notes were generated for the
course.  Part of these materials have been expanded into a text that
is currently being used in a stand alone calculus course that presents
vector-calculus from the beginning.  This calculus course is the
foundation for plans to expand the initial calculus/physics course
into a two year pre-engineering sequence that will integrate the
topics commonly covered in calculus, differential equations, linear
algebra, physics, and engineering mechanics, circuits, and electricity
and magnetism courses.

Diablo Valley College is a large community college in the San Francisco
bay area.  Its Special Intensive Program for Scientists and Engineers has
been in operation for 4 years and has significantly increased the success
rate in the physics and calculus sequences without decreasing content or
expectations.  For two semesters, students attend a single team-taught
course that combines calculus and physics:  semester one combines
Calculus I course with a new introductory physics course of our own
design, and semester two combines vector calculus with mechanics.  While
standard texts are used, topics are radically resequenced so that the two
subjects mesh.  Students collaborate in regular study groups that are
integral to the program.

The University of Puget Sound is a four year liberal arts school.
The program at Puget Sound targets first year students who have had
calculus in high school and are ready for our second semester calculus
course.  Our combined course begins with a review of basic concepts
(limit, continuity, derivative) in a context familiar to the students,
namely scalar-valued functions, and in a context new to the students,
namely vector-valued functions.  We concurrently develop the concepts
of mechanics first in one dimension and then in two and three
dimensions.