# Help with heat equation dirac delta function?

1. Oct 11, 2012

### fredfuchs

1. The problem statement, all variables and given/known data
The question was way too long so i took a snap shot of it
http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc7/397320_358155177605479_1440801198_n.jpg [Broken]

2. Relevant equations
The equations are all included in the snapshot

3. The attempt at a solution
So for question A i've done what the question said:

so g(x)^2 :

$$= 1/(\sqrt(2\pi)\delta)^2\iint\exp(-(x^2+y^2)/2\delta^2) dxdy$$
so i simplified to:
$$1/(\sqrt(2\pi)\delta)^2\iint\exp(-(r^2)/2\delta^2) rdrd\theta (0<\theta<2\pi) (0<r<inifity)$$
so i let z= r/2\delta^2

after all that i get to

$$1[\exp(\infty)-\exp(0)$$

its suppose to = 1, but i got -1 instead
i know it's wrong, but i dont know here, and the next 2 questions i don't have a clue how to start, can you help me?

Last edited by a moderator: May 6, 2017
2. Oct 11, 2012

### HallsofIvy

Show us what you tried. Surely, the first part should be simple.

3. Oct 11, 2012

### fredfuchs

I just added into what i did
sorry i did't know how to post mathematical equations untill i looked it up before...
yeah, after that I pretty much have no clue.....
Can you give me a few hints how to start the next few questions?