- #1
fluidistic
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Homework Statement
From a previous exercise (https://www.physicsforums.com/showthread.php?t=564520), I obtained [itex]u(r,\phi) = \frac{1}{2}A_{0} + \sum_{k = 1}^{\infty} r^{k}(A_{k}cos(k\phi) + B_{k}sin(k\phi))[/itex] which is the general form of the solution to Laplace equation in a disk of radius a.
I must find [itex]u(r, \phi )[/itex] for the Neumann's conditions ([itex]\frac{\partial u}{\partial n} \big | _c=f(\phi )[/itex]) where:
1)[itex]f(\phi )=A[/itex]
2)[itex]f(\phi )=Ax[/itex]
3)[itex]f(\phi )=A(x^2-y^2)[/itex]
4)[itex]f(\phi )=A \cos \phi +B[/itex]
5)[itex]f(\phi )=A \sin \phi +B \sin ^3 \phi[/itex]
Homework Equations
Already given I think.
The Attempt at a Solution
I don't know how to start. :/
What do they mean with the notation "_c"? Ah, in the contour I guess?