Modeling the Real World
|A chance to work with
the top freshmen
The main theme of Fast-Track Calculus is modeling physical
situations with mathematics. The course begins by building on the
student's high school mathematics foundation. While reviewing the
concepts of graphing and the differentiation of functions of one
variable, we introduce the student to the world of laptop computers
and computer algebra systems (CAS) which are used in all Freshman
and Sophomore level mathematics courses at Rose-Hulman.
The course then relates the concepts learned in differential
calculus to functions of several variables (3-space). Topics in
polar coordinates; vectors and parametric equations in two and
three dimensions; partial and directional derivatives; maxima and
minima of functions of several variables are covered wi th an
emphasis on visual representations (computer generated graphics in
2 and 3 dimensions).
The course finishes with applications of integration which
include deriving and solving the differential equations which model
population growth, the movement of falling bodies, and the cooling
of a cup of cocoa; the Fundamental Theorem of Calculus; and
multiple integration to find the volume of a solid and center of
mass of two and three dimensional objects.