(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
(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
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc8007df-3aba-42ae-a673-364cd7cd0009%2Fcd8ac5e8-46aa-407b-b0ef-4b38ec279969%2F1syrhsgl_processed.jpeg&w=3840&q=75)
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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