Line Integral

1. May 31, 2010

sebb1e

1. The problem statement, all variables and given/known data

http://www.maths.ox.ac.uk/system/files/private/active/0/b05.pdf [Broken]
Q8, last part

2. Relevant equations

3. The attempt at a solution

Essentially we are calculating the integral of -dG/dn*g(x,y) ds

I'm pretty sure G is (1/2Pi)log((x-e)^2+(y-m)^2) (using e,m instead of greek letters)

I can't get the integral to come out. Essentially I end up with the correct denominator but ((2x-2e)cost+(2y-2m)sint)g(cost,sint) as the numerator.

This can be rearranged to 2(1-ecost-msint)g, I seem to have picked up a factor of -2 and I need to convert this cost and sint to e and m respectively.

I've let x=cost y=sint and replaced ds by dt and integrating between 0 and 2Pi.

In working out dG/dn, I'm using dG/dn=dG/dxcost+dG/dysint

I don't know where I'm going wrong. I'm probably making a very basic error so even if you don't know what Green's functions are you may spot my mistake.

Thanks

Last edited by a moderator: May 4, 2017