Identidades vectoriales Teoremas vectoriales

ANTENAS
ANEXO I
Identidades vectoriales
∇ ⋅ (∇ × A ) = 0
∇ × ∇ψ = 0
∇ ( φ + ψ ) = ∇ φ + ∇ψ
∇ (φψ ) = φ∇ψ + ψ∇φ
∇ ⋅ ( A + B) = ∇ ⋅ A + ∇ ⋅ B
∇ × ( A + B) = ∇ × A + ∇ × B
∇ ⋅ (ψ A ) = A ⋅∇ψ + ψ∇ ⋅ A
∇ × (ψ A ) = ∇ψ × A + ψ∇ × A
∇ ( A ⋅ B ) = ( A ⋅∇ ) B + ( B ⋅∇ ) A + A × ( ∇ × B ) + B × ( ∇ × A )
∇ ⋅ ( A × B ) = B ⋅∇ × A − A ⋅∇ × B
∇ × ( A × B ) = A∇ ⋅ B − B∇ ⋅ A + ( B ⋅∇ ) A − ( A ⋅∇ ) B
∇ × ∇ × A = ∇ (∇ ⋅ A ) − ∇2A
Teoremas vectoriales
v∫ A ⋅ dl = ∫∫ ( ∇ × A ) ⋅ ds
c
s
w
∫∫ A ⋅ ds = ∫∫∫ ( ∇ ⋅ A )dv
s
v
w
∫∫ ( nˆ × A )ds = ∫∫∫ ( ∇ × A )dv
s
v
w
∫∫ ψ ds = ∫∫∫ ∇ψ dv
s
v
v∫ ψ dl = ∫∫ nˆ × ∇ψ ds
c
s
© Miguel Ferrando, Alejandro Valero. Dep. Comunicaciones. Universidad Politécnica de Valencia
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