Forms

Abstract

Before we begin to discuss functions of vectors, we first need to learn how to specify a vector. Before we can answer that, we must first learn where vectors live. In Figure 3.1 we see a curve, C, and a tangent line to that curve. The line can be thought of as the set of all tangent vectors at the point p. We denote that line as T _p C, the tangent space to C at the point p.