Prove the identity, assuming that F, σ , and G satisfy the hypotheses of the Divergence Theorem and that all necessary differentiability requirements for the functions f x , y , z and g x , y , z are met. ∬ σ ∇ f ⋅ n d S = ∭ G ∇ 2 f d V ∇ 2 f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2
Prove the identity, assuming that F, σ , and G satisfy the hypotheses of the Divergence Theorem and that all necessary differentiability requirements for the functions f x , y , z and g x , y , z are met. ∬ σ ∇ f ⋅ n d S = ∭ G ∇ 2 f d V ∇ 2 f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2
Prove the identity, assuming that F,
σ
, and G satisfy the hypotheses of the Divergence Theorem and that all necessary differentiability requirements for the functions
f
x
,
y
,
z
and
g
x
,
y
,
z
are met.
∬
σ
∇
f
⋅
n
d
S
=
∭
G
∇
2
f
d
V
∇
2
f
=
∂
2
f
∂
x
2
+
∂
2
f
∂
y
2
+
∂
2
f
∂
z
2
University Calculus: Early Transcendentals (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.