I'm supposed to prove the laplacian in cylindrical coord. is what it is. I tried tackling the problem in two ways and none work! I have no idea what's the matter. The first way is to calculate d²f/dr² , d²f/dO² and d²f/dz² and isolate d²f/dx² , d²f/dy² and d²f/dz². In cylindrical coord.,(adsbygoogle = window.adsbygoogle || []).push({});

x=rcosO

y=rsinO

z=z

(I'm not writting partial derivatives cuz in latex it's a pain in the @)

[tex]df/dr = df/dx dx/dr + df/dy dy/dr[/tex]

[tex]\Rightarrow d^2f/dr^2 = d^2f/dx^2 dx/dr + df/dx d^2x/dr^2 + d^2f/dy^2 dy/dr + df/dy d^2y/dr^2[/tex]

[tex]d^2f/dr^2 = d^2f/dx^2 cos^2\theta +d^2f/dy^2 sin^2\theta[/tex]

In the same way,

[tex]d^2f/d\theta^2 = r^2 (d^2f/dx^2 d^2f/dx^2)[/tex]

Hence, it would seem that the laplacian in cylindrical is just (1/r²)d²f/dO² + d^2f/dz^2.

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# Homework Help: Wild Laplacian!

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