Consider the steady state temperature problem over the disk of radius 3 centered at the origin. ▼²u(r, 0) = 0 subject to the following boundary condition: u(3,0) = f(0) = 4 sin³ (0) + 4 cos³ (0) (a) Find u(r, 0). Please go straight to the final formula for u(r, 0); do not show the separation of variables process. You need to show all details of integration or superposition (if it applies) for credit. (b) Approximate numerically u(3/2,π/4).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Consider the steady state temperature problem over the disk of radius 3 centered at
the origin.
▼²u(r, 0) = 0
subject to the following boundary condition:
u(3,0) = f(0) = 4 sin³ (0) + 4 cos³ (0)
(a) Find u(r, 0). Please go straight to the final formula for u(r, 0); do not show the
separation of variables process. You need to show all details of integration
or superposition (if it applies) for credit.
(b) Approximate numerically u(3/2,π/4).
Transcribed Image Text:Consider the steady state temperature problem over the disk of radius 3 centered at the origin. ▼²u(r, 0) = 0 subject to the following boundary condition: u(3,0) = f(0) = 4 sin³ (0) + 4 cos³ (0) (a) Find u(r, 0). Please go straight to the final formula for u(r, 0); do not show the separation of variables process. You need to show all details of integration or superposition (if it applies) for credit. (b) Approximate numerically u(3/2,π/4).
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