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Conservative vector field
From Mathematics Is A Science
Revision as of 14:12, 6 November 2012 by imported>WikiSysop
Recall a vector field is a function $f: {\bf R}^2 \rightarrow {\bf R}^2$. It is called conservative if it is a gradient of a scalar function: $F = {\bf \hspace{3pt} grad \hspace{3pt}} f$.
Theorem. Suppose
Then $F$ is conservative provided $D$ is simply connected.
It is also path-independent.