8.3.1 Vector Fields on ${\mathbb{R}}^n$

This section revisits some basic concepts from introductory courses such as calculus, linear algebra, and differential equations. You may have learned most of these for ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$. We eventually want to describe velocities in ${\mathbb{R}}^n$ and on manifolds, and then use the notion of a vector field to express a feedback plan in Section 8.4.1.