Vibrating Circular Membranes - Partial Differential Equations | Lecture 31

In this lecture we apply our study of the Helmholtz equation in the previous lecture to the wave equation in two spatial dimensions. In particular, we solve the PDE of a vibrating circular membrane using separation of variables. Using polar coordinates, we show that the solution can be represented in terms of Bessel functions. Bessel functions are extremely important special functions that arise naturally when solving the Helmholtz equation in polar coordinates and are used through approximation theory and applied mathematics.
Learn more about Bessel functions: en.wikipedia.o...
ODE lecture on Bessel equation and series solutions: • Bessel's Equation - Or...
Lectures series on differential equations: • Welcome - Ordinary Dif...
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[@sschmachtel8963]

Not yet watched but beauty topic :-)

[@SpawnD1701]

r is always positive! So the only problems are the singularity at r=0 of q(r) and the condition at r=0.