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In this worksheet you will look at some vector fields and calculate their \
curls to get a feel for what the curl is geometrically.

Define and plot some vectors in 2-dimensions and calculate the curl of the \
vector.  Note: even though we are interested in looking at a 2-dimensional \
vector, we will define it to be a three component vector, where the \
z-component is zero.  This is done because the curl operation is expecting a \
three component vector.\
\>", "Text",
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You can calculate the curl of this function in your head...do you agree with \
Maple?\
\>", "Text",
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Imagine putting a paddle wheel in the plane of the plot, it will turn if the \
curl is non-zero.  If you put a paddle wheel in the center, what will happen? \
 Where is the curl positive?  Where is it negative? (Recall, in a right \
handed coordinate system, you can use the right hand rule to determine which \
direction is positive.  Is positive into or out of the page?) Where is the \
curl zero?  Which vector component of the curl are we examining?\
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Now define a \"2-d\" vector field of your own, plot it, and find its curl:\
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Define and plot some vectors in 3 dimensions.  Calculate the curl of these \
vector fields:\
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 "By changing the orientation of the plot, you can view the plot in the plane \
of the coordinate axis (i.e. ",
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 " plane).  Convince yourself that each component of the curl is zero.  Now, \
calculate the curl."
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Now choose your own 3-d vecor field, plot it, and find its curl:\
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Cell["\<\

by Corinne Manogue
Copyright 2004 Corinne Manogue\
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