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: 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


    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 :

    $$\frac{d}{dx} \int_{a(x)}^{b(x)} f(t) dt = f(b(x))(b'(x)) - f(a(x))(a'(x))$$
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted