This chapter is concerned with applying calculus in the context of vector fields. A two-dimensional vector field is a function $f$ that maps each point $(x,y)$ in $\R^2$ to a two-dimensional vector $\langle u,v\rangle$, and similarly a three-dimensional vector field maps $(x,y,z)$ to $\langle u,v,w\rangle$. Since a vector has no position, we typically indicate a vector field in graphical form by placing the vector $f(x,y)$ with its tail at $(x,y)$. Figure 16.1.1 shows a representation of the vector field $f(x,y)=\langle -x/\sqrt{x^2+y^2+4},y/\sqrt{x^2+y^2+4}\rangle$. For such a graph to be readable, the vectors must be fairly short, which is accomplished by using a different scale for the vectors than for the axes. Such graphs are thus useful for understanding the sizes of the vectors relative to each other but not their absolute size.