(9) If f(z) is analytic function expressed in polar form, show that both u and v satisfy Laplace equation in two dimensions given by: d'u 1 ди 1 d'u + dr² rər r²00² = 0, and d²v 1 dv + dr² + rdr rər 1 8²v r.²00² 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(9) If f(z) is analytic function expressed in polar form, show that both u and v
satisfy Laplace equation in two dimensions given by:
1 ди 1 №²u
+
r²00²
d²u
+
Or² rər
= 0, and
=
d²v 1 dv
+
dr²
r dr
+
1 d²v
r.² 80²
= 0
Transcribed Image Text:(9) If f(z) is analytic function expressed in polar form, show that both u and v satisfy Laplace equation in two dimensions given by: 1 ди 1 №²u + r²00² d²u + Or² rər = 0, and = d²v 1 dv + dr² r dr + 1 d²v r.² 80² = 0
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