Newbie question about filters

Hi,

I'm trying to teach myself GIS and found Ilwis (www.ilwis.org). (I
would post this question on the Ilwis forum, but it is locked at the
moment.)

In their help files thei explain how to create an aspect map, that is,
a map that charts the directions of the slopes on a DEM.

The first step is to find the changes in the x direction, and they
have a built-in linear filter to do so. The filter is a 1x5 (rxc)
filter with the following values: 1, -8, 0, 8, -1. The gain for the
filter is 1/12 (0.8).

I understand why the filter has only one row but I would like to know
why these particular values and why this particular gain value? What
other options would there be? My question is: why these particular
values?

Also, what happens right at the edge of the map? Is the first pixel to
be changed in r1c3?

I'd be grateful for any help.

Ping