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Is Cancer going to post the test here for our benefit? It's been a long time since I failed Physics 400.

I'm on an iPad at the moment so I can't simply upload the PDF, but...

 

Estimate how many ways you can partition 10^24 stars into 10^12 galaxies each of 10^12 stars. (I gave them the formula for C(n, r); the point is to play with Stirling's approximation for n!)

 

Must a force that is strictly radial in direction and dependent only on distance necessarily be conservative?

 

Find the Fourier series expansion for f(x) = abs(sin x) on the interval -pi to +pi.

 

Find the general solution for the steady state temperature distribution in a solid sphere of radius 1, i.e. doing the separation of variables and getting the general solution. Then find the first three terms of the specific solution for a specific set of boundary conditions (no dependence on azimuth, only of the polar angle theta, specifically T(r=1, theta) = T0 * (cos theta - cos^3 theta). Note that most of that first part ought to have been on the page of notes they were allowed.

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Well, like I said, the fourth one is two parts, one of which is the set-up of the PDE and doing the separation of variables, and I gave them broad hints that something like that was coming. The other part is a series solution in Legendre polynomials (and again I gave them the polynomials on the exam).

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