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PDE homework

  1. Sep 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Verify that, for any continuously differentiable function g and any constant c, the function

    u(x, t) = 1/(2c)∫(x + ct)(x - ct) g(z) dz ( the upper limit (x + ct) and lower limit (x - ct))

    is a solution to the PDE utt = c2uxx.

    Do not use the Leibnitz Rule, but instead review the

    Fundamental Theorem of Calculus.

    2. Relevant equations
    Fundamental Theorem of Calculus I & II.


    3. The attempt at a solution
    Not a clue but tried the first and second fundamental theorem of calculus (learned in calc I or II) but did not seem to get anywhere.
     
  2. jcsd
  3. Sep 3, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

    This question is simply about taking derivatives and solving the equation. If you can't recall the fundamental theorem, here's a nutshell version of it :

    $$\frac{d}{dx} \int_{a(x)}^{b(x)} f(t) dt = f(b(x))(b'(x)) - f(a(x))(a'(x))$$
     
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