User:Colette

Colette
Catastrophe Magnet Forum Profile
Characters
Kaiserin Siri Dr. Liang Admiral Fleur
Factions
Trattoria

Colette is the creator of the Trattorian Empire, obnoxious nerd of all things science and math, and resident sociopath of the BrikWars forums. Despite bragging about his rigorous high-school AP schedule, he still finds the time to participate on the forums, host the occasional battle, and play politics. His obsession with Model UN explains his advocacy of the Allied Nations.

Colette is a male, but through a series of unfortunate events got stuck with his current username. He serves the BrikWars forums in the capacity of New People moderator.

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

---

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

---

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

---

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