Let u(x, y) be the harmonic function in the unit disk with the boundary values u(x,...

Let u(x, y) be the harmonic function in the unit disk with the boundary values u(x, y) = x^2 on {x^2 + y^2 = 1}. Find its Rayleigh–Ritz approximation of the form x^2 +C1*(1−x^2 −y^2).

Expert Solution

Colby Messinger answered 2 years ago

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3) S = {(x,y): 1 < x2 + y2 < 4}, u(x,y)= 5 (on outer circle) and = 7 (on inner circle) I have these two problems to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!

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Plot the contours of u(x,y)=xy and its harmonic conjugate v(x,y).

For the following u(x, y), show that it is harmonic and then find a corresponding v(x,...

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Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...

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