Get Math Help

Vector Field

Illustration

Basic definition

A vector field is a function that assigns a vector to each point of Euclidean space. Vector fields arise in differential equations and differential geometry.

Detailed definition

$A vector field is a map f:R^n ↦R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its divergence and curl within a region and its normal component over the boundary, a result known as Helmholtz's theorem. Vector fields can be plotted in the Wolfram Language using VectorPlot[f, {x, xmin, xmax}, {y, ymin, ymax}]. Flows are generated by vector fields and vice versa. A vector field is a tangent bundle section of its tangent bundle.$

Related Wolfram Language symbol

VectorPlot

Educational grade level

college level

Why Club Z!?

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu.