Vector Fields

$$\vec{F}:{\mathbb{R}}^n\to {\mathbb{R}}^m$$

Assigns a unique vector $\vec{F}(\vec{r})$ to every position vector $\vec{r}$ in the domain

$$\vec{F}(\vec{r})=⟨F_1(x,y,\dots ),F_2(x,y,\dots ),\dots ⟩$$

Uses

1. Velocity Vector Field (ex: velocity)
2. Force Fields (ex: gravity and electric forces)

Visualizing

• Arrows
  • Can draw the vectors at select points
  • Same as slope fields in previous classes
• Flow Lines
  • Draw the lines that the vectors are tangential to