A time dependent vector field on a manifold M is a map from an open subset on
such that for every, is an element of .
For every such that the set
is nonempty, is a vector field in the usual sense defined on the open set .
Read more about Time Dependent Vector Field: Associated Differential Equation, Integral Curve, Relationship With Vector Fields in The Usual Sense, Flow, Applications
Famous quotes containing the words time, dependent and/or field:
“Our fathers water’d with their tears
This sea of time whereon we sail,
Their voices were in all men’s ears
Who pass’d within their puissant hail.
Still the same ocean round us raves,
But we stand mute, and watch the waves.”
—Matthew Arnold (1822–1888)
“The mother whose self-image is dependent on her children places on those children the responsibility for her own identity, and her involvement in the details of their lives can put great pressure on the children. A child suffers when everything he or she does is extremely important to a parent; this kind of over-involvement can turn even a small problem into a crisis.”
—Grace Baruch (20th century)
“Mothers seem to be in subtle competition with teachers. There is always an underlying fear that teachers will do a better job than they have done with their child.... But mostly mothers feel that their areas of competence are very much similar to those of the teacher. In fact they feel they know their child better than anyone else and that the teacher doesn’t possess any special field of authority or expertise.”
—Sara Lawrence Lightfoot (20th century)