20. If F = F r ( r , θ) ˆ r + F θ ( r , θ) ˆ is conservative, then F = φ for some scalar field φ( r , θ) , and by Exercise 19, ∂φ ∂ r = F r , 1 r ∂φ ∂θ = F θ . For the equality of the mixed second partial derivatives of
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.