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Correcting the errors: Green's functions for the 1D Helmholtz and Laplacian operators.

[Click here for a PDF version of this post, and others in this series] The following recent posts explored 1D Green’s functions for the Helmholtz and Laplacian operators. There was a sign error (wrong residue sign for a negatively oriented contour) that I made near the beginning that caused a lot of trouble. Having found the error, I’ve now reworked all that exploratory content into a more…

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#absolute value #contour integral #convolution #delta function #driving function #Green&039;s function #Heavyside Theta #Helmholtz operator #incoming wave #infinite semicircle #limit #outgoing wave #pole #residue #sign function #test function #wave equation

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