This tag line reserved for humor.  Once we find some.

### Today's Math Problem: Green's Functions

Ok, sharky, now you're ready for:

Consider a linear differential equation written in the general form

L(x)u(x)=f(x)

where L(x) is a linear, self-adjoint differential operator, u(x) is the unknown function, and f(x) is a known non-homogeneous term.

e.g. L(x) could be the Laplacian.

The solution can be written in integral form as:

http://www.boulder.nist.gov/div853/greenfn/pictures/Image15.gif

Where G(x;x') is the Green's Function, which satisfies

L(x)G(x;x')=delta(x-x')

(delta is the Dirac delta function, of course)

Returning to the example of L(x) being the laplacian operator, show that the Green's function for a 2-dimensional laplacian equation is:

G(x;x')= - ln(r) / 2 pi

Sorry, no part marks for work, answers due by 1pm Friday, no extensions!
Ward
September 29th, 2006 12:54am
Uh...are you the real Ward?

She should be doing her homework! (Like I suppose to work...)
Rick Tang
September 29th, 2006 1:02am
Ward has a master's degree.... in Science!

this entire thread is a farting dog.
hello.
September 29th, 2006 1:11am
> this entire thread is a farting dog.

IBS is a serious problem.
Rover the Foul
September 29th, 2006 1:12am
I'm not able to see the image linked above. I'm getting a connection timeout error. Is there an alternate link?
Senthilnathan N.S.
September 29th, 2006 1:20am
Yeah I'm the real Ward, Math 400 was my best mark in my last couple years at university.  Not saying much, my marks were terrible...

Anyway, the link is to an image that shows:

u(x) = integral from -infinity to +infinity
of G(x;x')f(x')dx'
Ward
September 29th, 2006 3:04am
So your math is better than your engineering physics! Who would have thought...
Rick Tang
September 29th, 2006 3:11am
I always hated Dirac's delta function, then again I hated all functions with infinite bits in them. As far as I'm aware, the delta function hated me right back.
The Harbour Master
September 29th, 2006 3:12am
I think the guy in charge of the Eng Phys program took pity on me and let me keep going even w/ lousy marks.

Ward
September 29th, 2006 3:19am
Delta functions are cool...

Integrate and you get one.  Integrate delta(x-a) and you get a step function w/ the step at a (good for control systems).
Ward
September 29th, 2006 3:20am
Computer Science.

I think I am made for it :)

My engineering physics friend beats me in every academic subject except C++ programming and CS classes :)
Rick Zeng/Tseng
September 29th, 2006 3:22am
"Ok, sharky, now you're ready for:"

No.  No I'm not.  I've never had a math course higher than sophomore college level.  I dropped Calc 3, and I'm retaking Calc II and then III if I make it past this current class.
sharkfish
September 29th, 2006 10:05am