Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. curl( k F) = k curl F
Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. curl( k F) = k curl F
Let k be a constant,
F
=
F(
x
,
y
,
z
)
,
G
=
G(
x
,
y
,
z
)
,
and
ϕ
=
ϕ
(
x
,
y
,
z
)
.
Prove the following identities, assuming that all derivatives involved exist and are continuous.
OW + OW = 0 for w = f(x, y), x = u – v, and y = v –- u and demonstrate the
ди ду
6. Show that
result for w = (x – y) sin (y – x).
Another derivative combination Let F = (f. g, h) and let u be
a differentiable scalar-valued function.
a. Take the dot product of F and the del operator; then apply the
result to u to show that
(F•V )u = (3
a
+ h
az
(F-V)u
+ g
+ g
du
+ h
b. Evaluate (F - V)(ry²z³) at (1, 1, 1), where F = (1, 1, 1).
University Calculus: Early Transcendentals (3rd Edition)
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY