Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v x = a cosh u cos v , y = a sinh u sin v , ( u and v are called elliptic cylinder coordinates).
Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v x = a cosh u cos v , y = a sinh u sin v , ( u and v are called elliptic cylinder coordinates).
Find the Jacobians
∂
x
,
y
/
∂
u
,
v
of the given transformations from variables
x
,
y
to variables
u
,
v
x
=
a
cosh
u
cos
v
,
y
=
a
sinh
u
sin
v
,
(
u
and
v
are called elliptic cylinder coordinates).
Calculate the directional derivative of g(x, y, z) = x ln (y+z) in the direction v = 5i - 4j+ 4k at the point P = (6, e, e).
Remember to use a unit vector in directional derivative computation.
(Use symbolic notation and fractions where needed.)
Dvg(6, e, e) =
Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).
Mathematics for Elementary Teachers with Activities (5th Edition)
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