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Ω
1
, Ω
2
ψ({(θ, ρ) : 0 < θ < 2π, ρ = 1})
N = 2 d = 2 ω = f dx + g dy
dω
=
∂f
∂y
dy
∧
dx
+
∂g
∂x
dx
∧
dy
=
µ
∂g
∂x
−
∂f
∂y
¶
dx
∧
dy,
Z
Ω
µ
∂g
∂x
−
∂f
∂y
¶
dx ∧ dy =
Z
∂Ω
f dx + g dy.
N = 3 d = 3 ω = P dx∧dy +Q dy ∧dz +R dz ∧dx
dω =
∂P
∂z
dz ∧ dx ∧ dy +
∂Q
∂x
dx ∧ dy ∧ dz +
∂R
∂y
dy ∧ dz ∧ dx =
µ
∂P
∂z
+
∂Q
∂x
+
∂R
∂y
¶
dx ∧ dy ∧ dz,
Z
Ω
µ
∂P
∂z
+
∂Q
∂x
+
∂R
∂y
¶
dx ∧ dy ∧ dz =
Z
∂Ω
P dx ∧ dy + Q dy ∧ dz + R dz ∧ dx.
