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Help with heat equation dirac delta function?

  1. Oct 11, 2012 #1
    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 :

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

    after all that i get to

    [tex]1[\exp(\infty)-\exp(0)[/tex]

    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. jcsd
  3. Oct 11, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Show us what you tried. Surely, the first part should be simple.
     
  4. Oct 11, 2012 #3
    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?
     
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