ABSTRACT
The strategy of choosing a particular coordinate system or frame to perform a calculation or to present a concept is ubiquitous in both mathematics and physics. For example, Newton’s equations of planetary motion are much easier to solve in polar coordinates than in Cartesian coordinates. In the differential geometry of curves, calculations of local properties are often simpler when carried out in the Frenet frame associated to the curve at a point. This chapter introduces general coordinate systems on Rn and the concept of variable frames in a consistent and general manner. With a solid foundation of coordinate systems, we conclude the chapter by introducing tensor notation in what one might call the physics style or the classical style.
