Designing a Telescope Mirror for Second-Semester Calculus Students

The purpose of this article is to present an interdisciplinary project, developed as a collaborative effort by the authors, involving the design of a telescope mirror as it was given to second semester calculus students. The goals of the project are to provide an applied setting for the topics typically covered in this type of course including the following: definite integration, partial fractions, volumes by cylindrical shells, applications of integrals, differentials, first order differential questions, separation of variables, and work. Additionally it motivates and uses the following topics that are not typical of a second semester calculus course: kinetic energy, angular velocity, vector addition, Stephan's Law of Cooling, and mathematical modeling, thereby serving as a springboard for future work in applied mathematics. Students working in groups of three were given two weeks to complete the project. Solutions and instructor notes follow the presentation of the project. (Contains 8 figures.)