MAT 295 and 296 is the first-year calculus sequence required of all science and
engineering majors at Syracuse University. The mathematical content of this program is typical
of most traditional first-year calculus courses. The concepts of limit, continuity, derivative, antiderivative,
and definite integral are developed in the usual way, and they are then applied to the
traditional collection of functions: polynomial, rational, trigonometric, and exponential, together
with their inverses, compositions, and algebraic combinations.
The results are then applied to a wide variety of problems from geometry, physics, and
other sciences. These include maximum and minimum problems, related rates, areas, volumes
and surfaces of revolution, arc length, work, fluid pressure, velocity and acceleration, and
exponential growth and decay.
Curve sketching is introduced at the very beginning and emphasized throughout, as we
believe strongly that this is an important skill for any calculus student to acquire. Graphing
calculators are a help here, since they contribute substantially to an understanding of the
functions being sketched. They are only a help, however; the calculators are not used as a
substitute for the skill itself.
During the course, students are introduced to progressively more sophisticated
programming techniques for the calculator. They are shown how to write programs first for the
evaluation and tabulation of functions and then for numerical evaluation of limits, derivatives,
and roots (the last by Newton’s Method). Students then learn to do finite sums, Riemann sums,
and finally numerical integration (by Simpson’s Rule). Programs are stored in the calculator as
they are written and are used throughout the course. This is a college course offered through
Syracuse University, and students paying the (discounted) fee for SU credit will receive a
Syracuse University transcript.