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:
“I see this is the time that the unjust man doth thrive.”
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“In the quilts I had found good objects—hospitable, warm, with soft edges yet resistant, with boundaries yet suggesting a continuous safe expanse, a field that could be bundled, a bundle that could be unfurled, portable equipment, light, washable, long-lasting, colorful, versatile, functional and ornamental, private and universal, mine and thine.”
—Radka Donnell-Vogt, U.S. quiltmaker. As quoted in Lives and Works, by Lynn F. Miller and Sally S. Swenson (1981)