Curl, are my notes wrong?!

breadmonkey

The notes I have define a vector field as

v = Mi + Nj + Pk

They then define the curl as the determinent of the matrix

*Note that the d/dx etc should be partial derivatives (I coulnd't find the symbol). Sorry about the dots in the matrix, it jams all together otherwise! (It's a 3x3).

i.........j.............k
d/dx...d/dy......d/dz
M........N............P

Which they say is equal to

(dP/dy - dN/dz)i + (dP/dx - dM/dz)j + (dN/dx - dM/dy)k

Should the plus sign in bold not be a -?

Son Goku

breadmonkey wrote:

Should the plus sign in bold not be a -?

It should be a plus. Although the cross notation is confusing.

breadmonkey

I thought the determinant of a 3x3 has a minus there.

I checked wikipedia and came across this link. Scroll down a bit.
http://www.sosmath.com/matrix/determ1/determ1.html

Son Goku

breadmonkey wrote:

I thought the determinant of a 3x3 has a minus there.

I checked wikipedia and came across this link. Scroll down a bit.
http://www.sosmath.com/matrix/determ1/determ1.html

Ah jaysus, I'm a moron, yes your notes have a misprint.

In this case we have, looking only at the j component:

-j|d/dx d/dz|
...| M ... P |

Which gives:
-j (d/dx P - d/dzM)

= (d/dzM - d/dxP)j

So you are right.

breadmonkey

Thanks