Calculus of Functions in Polar Coordinates

Abstract

Chapter 3 presents some basic mathematics. The importance of the rectangular or Cartesian coordinate system to the disciplines of geometry, trigonometry, and calculus and their applications cannot be overstated. These disciplines depend on the interplay between geometry and algebra that this coordinate system makes possible. The polar coordinate system makes this connection also. By identifying a location in the plane with respect to a fixed reference point and a ray that emanates from it, it provides a framework that is tailor-made for the analysis of the trajectory of any object that moves in response to a gravitational force. The chapter develops the essentials about the polar coordinate plane, the polar equations for the ellipse, parabola, and hyperbola, the calculus of polar functions, as well as the trigonometry needed along the way.