Let V : R³ → R³ be given by (x(r, ¢,0)\ y(r, ø, 0) \z(r, 4, 0), r cos 0 cos O V (r, ø, 0): r cos 0 sin ø (1) r sin 0 where (r, ø, 0) E R³ are the coordinates of the domain, and (x, y, z) are the components of the function V.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please kindly proof and show this function is differentiable everywhere in R^3

Let V : R³ → R³ be given by
a (r, ф, 0)
y(r, ø, 0)
z(r, ø, 0)
r cos 0 cos Ø
Ψ(7, φ, θ) =
r cos 0 sin O
(1)
r sin 0
3
where (r, ø, 0) E R³ are the coordinates of the domain, and (x, y, z) are the components
of the function V.
Transcribed Image Text:Let V : R³ → R³ be given by a (r, ф, 0) y(r, ø, 0) z(r, ø, 0) r cos 0 cos Ø Ψ(7, φ, θ) = r cos 0 sin O (1) r sin 0 3 where (r, ø, 0) E R³ are the coordinates of the domain, and (x, y, z) are the components of the function V.
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