pdf (it, 2.898,97 KB, 25/01/13)

2π
0
cos θ sin θ dθ = 1
2
2π
0
cos 3 θ dθ =
=
=
2π
0
3π/2
−π/2
π/2
−π/2
1
−1
sin(2θ) dθ = 1
4
cos 3 θ dθ =
4π
0
3π/2
−π/2
(1 − sin 2 θ) cos θ dθ +
(1 − w 2 ) dw +
−1
1
sin w dw = 0.
(1 − sin 2 θ) cos θ dθ
3/2π
π/2
(1 − w 2 ) dw = 0.
Σ ⊂ R 3
(1 − sin 2 θ) cos θ dθ
ϕ(θ, z) = ( 1 + 2z 2 cos θ, 1 + 2z 2 sin θ, z), |θ| ≤ π/4, |z| ≤ 1,
F (x, y, z) = (1/ 1 + 2z 2 , 1/ 1 + 2z 2 , x 2 + y 2 )
Σ (1, 0, 0) (−1, 0, 0)
F = (F1, F2, F3)
div F (x, y, z) = ∂F1
∂x
+ ∂F2
∂y
+ ∂F3
∂z
F
S S ∪ Σ
C
θ ∈ [−π/4, π/4] z γ x = √ 1 + 2z 2
y = 0
Σ : ϕ(θ, z) = ( √ 1 + 2z 2 cos θ, √ 1 + 2z 2 sin θ, z) γ
x = √ 1 + 2z 2
S + θ ∈ [−π/4, π/4]
(0, 0, 1) ( √ 2, 0, 1) y = 0 z
= 0.
S + = {(r cos θ, r sin θ, 1) ∈ R 3 : 0 ≤ r ≤ √ 2, |θ| ≤ π/4}
C (0, 0, 1)