nab - Nabla operator for use with tensor arithmetic.
Calling sequence:
nab(f)[i]
Parameters:
f - an expression or function depending on x,y,z.
Synopsis:
Examples:
> nab(u(x,y,z))[i];
nab(u(x, y, z))[i]
> nab(phi(x,y,z))[i] &t nab(u(x,y,z))[i] ;
/ d \ / d \ / d \ / d \
|---- phi(x, y, z)| |---- u(x, y, z)| + |---- phi(x, y, z)| |---- u(x, y, z)|
\ dx / \ dx / \ dy / \ dy /
/ d \ / d \
+ |---- phi(x, y, z)| |---- u(x, y, z)|
\ dz / \ dz /
> delta[i,j] &t nab( nab(u(x,y,z))[i] )[j];
/ 2 \ / 2 \ / 2 \
| d | | d | | d |
|----- u(x, y, z)| + |----- u(x, y, z)| + |----- u(x, y, z)|
| 2 | | 2 | | 2 |
\ dx / \ dy / \ dz /
> delta[i,j] &t nab( nab(u(x,y))[i] )[j];
/ 2 \ / 2 \
| d | | d |
|----- u(x, y)| + |----- u(x, y)|
| 2 | | 2 |
\ dx / \ dy /