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Suppose you have a metal washer of the form {(r,θ) : 1 ≤ r ≤ 2}....

Suppose you have a metal washer of the form {(r,θ) : 1 ≤ r ≤ 2}. The inside circle is heated to a fixed temperature distribution f(θ), and the outside circle is heated to a fixed temperature distribution g(θ). (a) Find the general formula for the steady-state temperature function u(r,θ) on the washer. (b) Find u when f(θ) = cos(θ) and g(θ) = sin(θ). (c) Find u when f(θ)=1 and g(θ)=2.

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