You already figured out the units in your question.
1/2(5s)*5m = 12.5 ms
Apparently this is called absement. In ordinary kinematics I don't believe it has any physical or useful meaning. However there may be some theoretical use to the quantity in more advanced systems/problems.
Whichever is most interesting to you. At this level every one of these topics will be accessible to you (mathematically), so that shouldn't be a concern. Whichever topic interests you the most is the one you should take.
I do not mean that they copied the exact structure and progression course by course. I mean the structure of the Masters program itself is similar in style to Part III. Typical Masters programs take 2 years with concurrent courses and research spread out over the 2 years similar to undergraduate...
The Perimeter Institute models its Physics Masters program after the Mathematical Tripos III at Cambridge. So if you want a direct comparison then Cambridge's program is appropriate.
Ok, I'm not sure I'm following here. You have derived the correct expression, sure, but we can arrive at that just as easily by saying 1 - aV^{-1} = 1 in the second derivation. How come we're not allowed to do that when we have V^{N}(1-aV^{-1}) . I'm not sure I understand your comment about...
Homework Statement
I have come across a rather interesting conundrum. Given the configurational potential energy partition function for a non-ideal gas:
Z = Z_{internal}\frac{1}{N!}\left(\frac{2\pi m}{h^{2}\beta}\right)^{\frac{3N}{2}}(V^{N} - B_{2}(T)N^{2}V^{N-1})
where B_{2}(T) is the...
I've looked through Lebedev and he derives equation c) that I'm looking for first by using some recursion relations that I am not given in my text or notes. I'm first trying to doing only with what I'm given, but that book has been helpful so far.
Hm.. That disagrees with my text, I took a picture and uploaded it, no mistakes by me this time!
All the problem says is "Establish the recurrence relations (6.97) for the associated Legendre functions."
I figured the generating function would be the appropriate method to use.
When I physically write it down I don't make those mistakes, it's typing it out in latex after a long frustrating day of getting nowhere on the problem that caused the mistakes. Simple typos, that's all.
Ah, yes, my mistake. T should be T(\omega,s). Where \omega = cos(\theta). It's just a simplification that's made during the derivation. My prof used T(theta,phi) in class by mistake so that's just how I ended up writing it from my notes, it should be omega and s.
As for the summation, another...