  These brief lecture notes are intended mainly for undergraduate students in
engineering or physics or mathematics who have met or will soon be meeting the
Dirac delta function and some other objects related to it. These students might
have already felt - or might in the near future feel - not entirely comfortable
with the usual intuitive explanations about how to "integrate" or
"differentiate" or take the "Fourier transform" of these objects.
  These notes will reveal to these students that there is a precise and
rigorous way, and this also means a more useful and reliable way, to define
these objects and the operations performed upon them. This can be done without
any prior knowledge of functional analysis or of Lebesgue integration. Readers
of these notes are assumed to only have studied basic courses in linear
algebra, and calculus of functions of one and two variables, and an
introductory course about the Fourier transform of functions of one variable.
  Most of the results and proofs presented here are in the setting of the space
of tempered distributions introduced by Laurent Schwartz. But there are also
some very brief mentions of other approaches to distributions or generalized
functions.
