User:Colette

Colette is the creator of the Trattorian Empire

In the meanwhile, have some math:

∇(fg) = f∇g + g∇f

∫c(f∇g)⋅dr = ∫c(∇(fg) - g∇f)⋅dr

∫c(f∇g)⋅dr=fg|∂c - ∫c(g∇f)⋅dr

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curl(gF) = g∇×F + ∇g×F

g∇×F = curl(gF) - ∇g×F

∬s(g∇×F)⋅dS= ∬s(curl(gF))⋅dS - ∬s(∇g×F)⋅dS

∬s(g∇×F)⋅dS=∮(∂s)gF⋅dr - ∬s(∇g×F)⋅dS

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div(gF) = g*div(F) + F⋅∇g

div(gF) = g(∇⋅F) + F⋅∇g

∭v(div(gF))dV = ∭v(g(∇⋅F) + F⋅∇g)dV

∯(∂v)gF⋅dS = ∭v(g(∇⋅F))dV + ∭v(F⋅∇g)dV

∭v(g(∇⋅F))dV=∯(∂v)gF⋅dS - ∭v(F⋅∇g)dV

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div(F×G) = G⋅(∇×F) - F⋅(∇×G)

∭v(div(F×G))dV = ∭v(G⋅(∇×F) - F⋅(∇×G))dV

∯(∂v)(F×G)⋅dS = ∭v(G⋅(∇×F))dV - ∭v(F⋅(∇×G))dV

∭v(G⋅(∇×F))dV = ∯(∂v)(F×G)⋅dS + ∭v(F⋅(∇×G))dV