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III - Convergence: Continuous variables
df = f~·dx + f~.dy
and differentiates the relations x = r cos (), y = r sin ():
dx = cos ().dr - r sin ().d(),
dy = sin ().dr + rcos().d().
Hence
df = f~·dr + f".d()
with
f~
cos ()f~ + sin ()f~,
f"
-rsin()f~ + rcos()f~.