We return to the Dirichlet problem (2.13) in the unit disc. By switching to polar coordinates we obtain for u = u(r, 0). 22 и Ər² + 1 ди + r ər u(1,0) = g(0), 1 8² u r2 მ02 =0, 0
We return to the Dirichlet problem (2.13) in the unit disc. By switching to polar coordinates we obtain for u = u(r, 0). 22 и Ər² + 1 ди + r ər u(1,0) = g(0), 1 8² u r2 მ02 =0, 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 47RE
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![We return to the Dirichlet problem (2.13) in the unit disc. By switching to
polar coordinates we obtain
[02
u
Ər²
for u = u(r,0).
+
1 ди
+
1 0² u
r² 00²
= 0, 0<r<1, −¬≤0<¬,
2,11
r Or
u(1,0)= g(0), −¬≤0<л,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F882ce437-6984-48a2-b1c1-0c70a26630a5%2Fa1e76f02-e563-45a9-872d-6ae974cce22c%2Fit7myf_processed.png&w=3840&q=75)
Transcribed Image Text:We return to the Dirichlet problem (2.13) in the unit disc. By switching to
polar coordinates we obtain
[02
u
Ər²
for u = u(r,0).
+
1 ди
+
1 0² u
r² 00²
= 0, 0<r<1, −¬≤0<¬,
2,11
r Or
u(1,0)= g(0), −¬≤0<л,
![Problem 1: Give a formula for the solution of the Dirichlet problem in Section 2.11
when g(t) = 1².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F882ce437-6984-48a2-b1c1-0c70a26630a5%2Fa1e76f02-e563-45a9-872d-6ae974cce22c%2Frvizscj_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1: Give a formula for the solution of the Dirichlet problem in Section 2.11
when g(t) = 1².
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