Vector Field

Topics: Calculus

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(definition)

A vector field is a function $F:{\mathbb{R}}^n\to V_n$ ($V_n$ a vector space of dimension $n$).

Example

Let $F:D\subseteq {\mathbb{R}}^2\to V_2$ be given by:

$$F(x,y)=⟨2x+y,\frac{1}{x+y}⟩$$

$F$ is a vector field whose domain is $D=\{x\in {\mathbb{R}}^2\mid y=-x\}$.

A conservative vector field is a vector field with potential functions.