I need help with this problem. The problem is attached. Thanks
M meks0899 New member Joined Aug 27, 2009 Messages 17 Dec 9, 2009 #1 I need help with this problem. The problem is attached. Thanks Attachments Problem 4.jpg 17.7 KB · Views: 101
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Dec 9, 2009 #2 This appears to involve the Divergence Theorem. Try using the alternative form of Green's Theorem and the property div(fG)=f div(G)+∇f⋅G\displaystyle div(fG)=f \;\ div(G)+{\nabla}f\cdot Gdiv(fG)=f div(G)+∇f⋅G ∫R∫(f∇2g+∇f⋅∇g)ds\displaystyle \int_{R}\int (f{\nabla}^{2}g+{\nabla}f\cdot {\nabla}g)ds∫R∫(f∇2g+∇f⋅∇g)ds =∫R∫(f div(∇g)+∇f⋅∇g)ds\displaystyle =\int_{R}\int (f \;\ div({\nabla} g)+{\nabla}f\cdot\nabla g)ds=∫R∫(f div(∇g)+∇f⋅∇g)ds ∫R∫div(f∇g)ds\displaystyle \int_{R}\int div(f{\nabla}g)ds∫R∫div(f∇g)ds ∫C(f∇g⋅n)ds\displaystyle \int_{C}(f{\nabla}g\cdot n) ds∫C(f∇g⋅n)ds
This appears to involve the Divergence Theorem. Try using the alternative form of Green's Theorem and the property div(fG)=f div(G)+∇f⋅G\displaystyle div(fG)=f \;\ div(G)+{\nabla}f\cdot Gdiv(fG)=f div(G)+∇f⋅G ∫R∫(f∇2g+∇f⋅∇g)ds\displaystyle \int_{R}\int (f{\nabla}^{2}g+{\nabla}f\cdot {\nabla}g)ds∫R∫(f∇2g+∇f⋅∇g)ds =∫R∫(f div(∇g)+∇f⋅∇g)ds\displaystyle =\int_{R}\int (f \;\ div({\nabla} g)+{\nabla}f\cdot\nabla g)ds=∫R∫(f div(∇g)+∇f⋅∇g)ds ∫R∫div(f∇g)ds\displaystyle \int_{R}\int div(f{\nabla}g)ds∫R∫div(f∇g)ds ∫C(f∇g⋅n)ds\displaystyle \int_{C}(f{\nabla}g\cdot n) ds∫C(f∇g⋅n)ds
