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:
“To measure life learn thou betimes, and know
Toward solid good what leads the nearest way;
For other things mild Heaven a time ordains,
And disapproves that care, though wise in show,
That with superfluous burden loads the day,
And, when God sends a cheerful hour, refrains.”
—John Milton (1608–1674)
“Man is so muddled, so dependent on the things immediately before his eyes, that every day even the most submissive believer can be seen to risk the torments of the afterlife for the smallest pleasure.”
—Joseph De Maistre (1753–1821)
“But the old world was restored and we returned
To the dreary field and workshop, and the immemorial feud
Of rich and poor. Our victory was our defeat.”
—Sir Herbert Read (1893–1968)