Given a distribution a vector field in is called horizontal.
In particular, is a vector field along the curve itself.
Thus, one must know both vector fields in an open neighborhood.
This model is illustrated by the vector field pictured in Figure 7a.
The relevant vector field for this example is the velocity of the moving air at a point.
This will follow if we show that the vector field is curl free.
A differential equation then can be read off the global vector field.
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.
This is often the case with the flows of vector fields.
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