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.