Questions about Laplace's equation and Green's functions etc. Watch

gangsta316
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Report Thread starter 7 years ago
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http://workspace.imperial.ac.uk/math...M2AA2-2010.PDF

3(iii)

So here we "guess" that the solution is f = f(r) (f for phi). Then we just have to solve an ODE. But the mark scheme says that we get
1/r^2 * d/dr (r^2 *df/dr) = 1
Why?
The Laplacian is
http://en.wikipedia.org/wiki/Laplace...Two_dimensions
that.
So wouldn't we get
1/r *d/dr (r* df/dr) = 1?



3(iv)

How is this question done? I know that, with the method of images, we want to solve grad^2 = Dirac delta function, and we extend it to the whole of R^3. Then we solve it and appeal to uniqueness to show that it's the solution for y>0. What would we do here?
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gangsta316
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Report Thread starter 7 years ago
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Can anyone help? I'm frightfully confused about the first one.
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