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Radial Harmonic Functions
Автор: Mike, the Mathematician
Загружено: 2026-01-13
Просмотров: 119
Описание:
We continue our discussion of harmonic functions by asking which of these functions is radial. Writing the Laplacian in spherical coordinates, we isolate the radial derivatives. It turns out that there are only two terms with radial derivatives, so the resulting equation reduces to an ODE. We see that solutions in all dimensions have a singularity at the origin. This singularity will help us to understand the structure of solutions to the Poisson equation.
#mikethemathematician, #mikedabkowski, #profdabkowski, #pde, #harmonicfunction
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