Forms

Before we begin to discuss functions of vectors, we first need to learn how to specify a vector. And before we can answer that, we must first learn where vectors live. In Figure 4.1 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 TpC, the tangent space to C at the point p.