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(Solved): The 1 -form \psi =(udv-vdu)/(u^(2)+v^(2)) is well-defined on the plane R^(2) with the origin 0 remov ...
The 1 -form
\psi =(udv-vdu)/(u^(2)+v^(2))is well-defined on the plane
R^(2)with the origin
0removed. Show: (a)
\psi is closed but not exact on
R^(2)-0. (Hint: Integrate around the unit circle and use Ex. 3.) (b) The restriction of
\psi to, say, the right half-plane
u>0is exact.
