Green's functions, F/Laplace Transforms, and Boundary conditions

[quantum13]

I'm having a ton of trouble understanding how to solve diff eqs by using Fourier or laplace transforms to solve for the green's function, with boundary conditions included. I can understand the basics of green's function solutions, especially if transforms are not needed, but my textbook seems like its spitting out voodoo magic whenever it uses transforms. I can't find many clear online resources either. Could anyone point me to some online resource that explains this and hopefully has some really basic examples, because right now I don't even know where to start.

 

[fluidistic]

I'm having a ton of trouble understanding how to solve diff eqs by using Fourier or laplace transforms to solve for the green's function, with boundary conditions included. I can understand the basics of green's function solutions, especially if transforms are not needed, but my textbook seems like its spitting out voodoo magic whenever it uses transforms. I can't find many clear online resources either. Could anyone point me to some online resource that explains this and hopefully has some really basic examples, because right now I don't even know where to start.

I'm in the same boat as you. Green function methods to solve PDE is a total blackout for me. I don't even know if using a Fourier or Laplace transform can solve a PDE that involves the Laplacian operator (in 2 or 3 dimensions). So I'll be following this thread.