Interactive Web-based Calculus Projects at Hollins University: Design of a Thrilling Roller Coaster

Trish Hammer

Department of Mathematics and Statistics
Hollins University
PO Box 9681
Roanoke, VA 24020
USA
Phone: (540) 362-6599
phammer@hollins.edu

list of all papers by this author

Click to access this paper: paper.pdf

ABSTRACT

In the mathematics and statistics curriculum at Hollins University and Virginia Western Community College, there is much emphasis on the application of concepts to real life problems. For this purpose, we have recently developed two interactive web-based calculus projects which use JAVA applets as well as downloadable Maple worksheets. These projects are original and exciting and have been well received by both students and colleagues.

In the Calculus I project, the emphasis is on application of derivatives. Students develop a more thorough understanding of slope, local maximum and minimum points, and points of inflection by applying these concepts to straight stretch roller coasters. Students use 'live' online images of real roller coasters to identify peak and valley points and also to determine the points of steepest ascent and descent. Then students determine the 'thrill' (as defined in the project) of these coasters. Student use downloadable Maple worksheets to design and mathematically build their own straight stretch coasters (given certain coaster restrictions) and to determine the corresponding thrill. Cubic polynomial functions and trigonometric functions are used to model the paths of these single drop and several drop coasters. As a project assignment, students are asked to mathematically design a coaster which satisfies the given restrictions and that has the maximum thrill. We will showcase this exciting project along with possible solutions.

Keyword(s): Maple, calculus