Green's third identity
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Green's third identity
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WebAug 26, 2015 · 1 Answer. Sorted by: 3. The identity follows from the product rule. d d x ( f ( x) ⋅ g ( x)) = d f d x ( x) g ( x) + f ( x) d g d x ( x). for two functions f and g. Noting that ∇ ⋅ ∇ = Δ we get. ∇ u ⋅ ∇ v + u ∇ ⋅ ∇ v = ∇ u ⋅ ∇ v + u Δ v. Applying the divergence theorem. WebEquation (9) is known as Green’s third identity. Notice that if ˚satis es Laplace’s equation the rst term on the right hand side vanishes and so we have (10) ˚(r o) = 1 4ˇ R @D 1 jr r …
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