In particular, is a vector field along the curve itself.

Thus, one must know both vector fields in an open neighborhood.

This is often the case with the flows of vector fields.

Given a distribution a vector field in is called horizontal.

This will follow if we show that the vector field is curl free.

The relevant vector field for this example is the velocity of the moving air at a point.

A differential equation then can be read off the global vector field.

This model is illustrated by the vector field pictured in Figure 7a.

Vector field reconstruction has several applications, and many different approaches.

However, a uniform 1D vector field has this symmetry group.

For this reason, a line integral of a conservative vector field is called path independent.

A vector field is complete if its flow curves exist for all time.

A vector field is an arrangement of vectors over an area.

Every left-invariant vector field on a Lie group is complete.

A magnetic field can't be more complicated than the wind because they're both just vector fields.

The curl is a form of differentiation for vector fields.

These have important applications in physics, as when dealing with vector fields.

The curl measures how much "rotation" a vector field has near a point.

The product is called the rotational curl of the vector field.

They describe society in terms of forces acting in a vector field.

More abstractly, a conservative vector field is an exact 1-form.

It is defined to be the contraction of a differential form with a vector field.

The potential function for the vector field is chosen to be:

A closely related idea is that of Hamiltonian vector fields.

Being Lie vector fields, these form a left-invariant basis for the group action.