Since this is our first formal contact with Mathematica, let us take the day to learn the syntax and commmands and apply them to functions on the list on page 12. You should first experiment with the one-dimensional version of these functions and then with the two dimensional version.
. This version of
the Gaussian has the property that its integral over the entire line
is 1 for all values of 
. The Dirac delta can be
represented by the limit of 
as 
.
for 
and 0
otherwise. The Dirac delta is the limit of 
as
approaches 0.
.
.
.
where a is a scalar.