Let \(V\) be a finitely dimensional vectorspace over the field of real numbers and let \(I\subseteq \mathbb {R}\) be a real interval and \(U\subseteq V\) an open set. Then the function \[f\colon \cases{I\times U\longrightarrow V,\cr(t,v)\longmapsto f(t,v)}\] is called a vector field (on \(U\)).
