Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

PDE wave equation

  1. Dec 2, 2012 #1
  2. jcsd
  3. Dec 5, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    Putting a countable infinity of A's and B's instead of only 2 values A and B is a standard technique in Fourier analysis, which is particulary well suited for linear ODE's/PDE's. That is you rightfully assume that, because the linear/vector space of solutions is infinite dimensional, there is one (generally different) coefficient for each basis vector of the solution space, hence the infinite summation.
  4. Dec 6, 2012 #3
    Which part of it do you not understand.
    This is how a homogenous linear PDE is usually solved:
    1.Seperate equation (possible for many of the usual PDEs)
    2.Solve the equations to get a "basis"
    3.Write an infinite sum with them
    4.Use the imposed initial/boundary conditions to solve for the coefficients of the linearly independent solutions with the generalized Fourier's trick

    If none of that made sense to you, then you are not ready for that book.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook