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 ∇ g − g ∇ f ⋅ n d S = ∭ G f ∇ 2 g − g ∇ 2 f d V
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 ∇ g − g ∇ f ⋅ n d S = ∭ G f ∇ 2 g − g ∇ 2 f d V
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
∇
g
−
g
∇
f
⋅
n
d
S
=
∭
G
f
∇
2
g
−
g
∇
2
f
d
V
Ex12. Let L:R5 → R4 be defined by
X
y
(ED
L
1 0
-1
1
0 0
2
0
-1
0 0 -1 1
-
325
2
-1
-1
-1
0
X
y
Z
V
a) Find ker L, basis for ker L, dim(ker L) and
determine if L one to one.
b) Find range L, basis for range L, dim(range L)
and determine if Lonto.
part D E
Linear Transformation
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (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.