Vector Fields and Velocity Flows in 2D
A vector field is a function that assigns a vector to each point in space.
A physical example of a two dimensional vector field is the surface velocity
of points on a smoothly flowing river. Given a velocity vector field,
particles of fluid will move along parametric curves in such a way that
the derivative of the parametric position function is the velocity at the
point. These paths are called flow lines.
Flow of Vector Fields
The next figure shows flow lines and the velocity vectors of a vector field.
You can see an animated Mathematica-computed flow of this vector
field by clicking the link below the figure.
![[Graphics:../Images/index_gr_78.gif]](index_gr_78.gif)
Given a vector field, we will want to find things like the amount of fluid
that crosses a boundary. Green's Theorem in the next section relates
the flow across a boundary to a certain derivative.
Converted by Mathematica
May 7, 2001