I've been reading up on these three recently, and wondered if anyone could confirm what I think they do. I'm not 100% I understand these.(adsbygoogle = window.adsbygoogle || []).push({});

del [tex](\bigtriangleup)[/tex], when applied to a scalar, creates a vector with that scalar as each of the XYZ values. eg

[tex]\bigtriangleup . x = (x,x,x)[/tex]

[tex]\bigtriangleup . 3 = (3,3,3)[/tex]

divergence is applied to a vector, and sums the components of the vector into a scalar. eg

[tex]\bigtriangleup . (x,y,z) = x+y+z [/tex]

[tex]\bigtriangleup . (1,2,3) = 1+2+3 = 6 [/tex]

finally, laplacian. This is the one I'm not as sure about. It's applied to a scalar I think?

[tex]\bigtriangleup ^2 = \bigtriangleup(\bigtriangleup) [/tex]

[tex]\bigtriangleup ^2 . x = \bigtriangleup(\bigtriangleup . x) [/tex]

[tex]= \bigtriangleup((x,x,x)) [/tex]

[tex] = 3x [/tex]

That doesn't seem right (I think I'm meant to end up with a vector). Can laplacian be broken up like that or does it have a special rule?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Del, divergence, laplacian

**Physics Forums | Science Articles, Homework Help, Discussion**