University of Notre Dame

Honors Mathematics II

Course Number: MATH 10460
Instructor: Christopher Schommer-Pries

The course starts with the central aspects of Newton’s Principia Mathematica, arguably, along with Darwin’s Origin of Species, the most influential book of science ever written. The course pursues Newton’s study of centripetal force and, following his thoughts, develops the fundamental equations of planetary motion. Calculus is present, but it is hidden within Newton’s geometric approach. A quick overview of conventional differential calculus follows next as preparation for a detailed look at polar coordinates, polar functions, and polar calculus. The course concludes with the application of polar calculus to planetary motion. This modern elementary look at Newton’s account provides the students with a paradigmatic example of an application of mathematics to the study of the physical universe.