nab(f)[i]

Parameters:

f - an expression or function depending on x,y,z.

• nab(f)[i] returns the i-th component of the gradient of the argument f. f is assumed to depend on x,y and/or z.

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          /