1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: I am solving a PDE

  1. May 31, 2008 #1
    1. The problem statement, all variables and given/known data

    oh! after trying to re-solve a PDE I reached this:

    2. Relevant equations
    [tex]\sum\frac{4}{((2n-1)\pi)^2} (a+\frac{4(-1)^{n+1}}{(2n-1)\pi}) cos(\frac{2n-1}{2}\pi x) [/tex]

    n goes feom 1 to [tex]\infty[/tex] and "a" is a constant value.

    3. The attempt at a solution
    the solution i am trying to reach is:

    [tex]=\frac{1}{2} (1-x^{2}+(1-x)a)[/tex]

    but i don't know how?
    can anyone help please?
  2. jcsd
  3. May 31, 2008 #2


    User Avatar
    Science Advisor

    What is the Fourier series for [tex]\frac{1}{2} (1-x^{2}+(1-x)a)[/tex]?
  4. Jun 2, 2008 #3
    thanx for suggestion my buddy.
    u know the orginal problem is a heat equation - one dimentional and time dependent-


    j,c,b are constant and 0[tex]\leq[/tex]x[tex]\leq[/tex]1

    i solved the problem to here:

    [tex] T(x,t)= j^{2} \sum (\frac{1}{\lambda_{n}^{2}}) \times \frac{b}{cL}+ \frac {2 \times -1^{n+1}}{\lambda_{n} cos(\lambda_{n}x + j^{2} \sum \frac{-1}{(\lambda_{n})^{2}}(e)^{-\lambda_{n}t} \left[\frac{b}{cL}+ \frac {2\times -1^{n+1}}{\lambda_{n}\right] cos(\lambda_{n}x)[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook