Prove the identity, where R is a simply connected region with boundary C. Assume that the required partial derivatives of the scalar functions ƒ and g are continuous. The expressions D_Nƒ and D_Ng are the derivatives in the direction of the outward normal vector N of C, and are defined by D_Nƒ = ∇ƒ ^. N, and D_Ng = ∇g ^. N.

Green’s first identity:

Transcribed Image Text:

ff (ƒV ²g + Vf • Vg) dA = - Sosi R. C fDng ds