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**Final Exam / Problem 3**

« **on:**December 20, 2012, 01:32:15 PM »

Use separation of variables to solve the Dirichlet problem for the Laplacian on the unit disk $\mathbb{D} = \{ (x,y) \in \mathbb{R}^2: x^2 + y^2 < 1\}$ with boundary condition $u(1, \theta) = \cos \theta.$

(The boundary condition is described in polar coordinates $(r, \theta) \rightarrow u(r, \theta)$ along $r=1$).

hopeful solution attached! (since djirar is posting all the solutions right away after 13:30..)

(The boundary condition is described in polar coordinates $(r, \theta) \rightarrow u(r, \theta)$ along $r=1$).

hopeful solution attached! (since djirar is posting all the solutions right away after 13:30..)