I finalize the discussion started in Part 1 with an example showing the behavior for a specific source, which is a simple Gaussian in space and in time. I comment on how to make sure the desired initial conditions are satisfied by adding a solution to the homogeneous equation. Video. Notes.
Category Archives: Green’s functions
Green’s function for diffusion in 1D. Part 1.
I solve for the Green’s function of the diffusion operator on the whole real line. To that end, I use Fourier transforms in space and time and contour integration (more on that later!).Video. Notes.
Green’s functions of the Laplacian: eigenfunction expansion.
Using the cartesian and spherical eigenfunctions of the Laplacian discussed in previous videos, we build the corresponding Green’s functions. What happens when we remove the boundaries? A step toward Fourier transforms and quantum field theory.Video. Notes.
A 1d Green’s function example two ways
A closer look at how to calculate a Green’s function in a 1D example, using a direct solution and a spectral representation. Video. Notes.