9. Show that the Laplacian defined a2f , a2f V²f = dx² ' ðy² as is isotropic (invariant to rotation). You will need the following equations relating coordinates for axis rotation by an angle 0 x = x'cose – y'sin0 y = x'sine + y'cose
9. Show that the Laplacian defined a2f , a2f V²f = dx² ' ðy² as is isotropic (invariant to rotation). You will need the following equations relating coordinates for axis rotation by an angle 0 x = x'cose – y'sin0 y = x'sine + y'cose
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Transcribed Image Text:9. Show that the Laplacian defined
a2f , 02f
V²f :
as is isotropic (invariant to rotation). You will need the following equations relating
coordinates for axis rotation by an angle 0
х — хcos@ — у'sin®
y = x'sine + y'cos0
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