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These brief lecture notes are intended mainly for undergraduate students inengineering or physics or mathematics who have met or will soon be meeting theDirac delta function and some other objects related to it. These students mighthave already felt - or might in the near future feel - not entirely comfortablewith 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 andrigorous way, and this also means a more useful and reliable way, to definethese objects and the operations performed upon them. This can be done withoutany prior knowledge of functional analysis or of Lebesgue integration. Readersof these notes are assumed to only have studied basic courses in linearalgebra, and calculus of functions of one and two variables, and anintroductory course about the Fourier transform of functions of one variable.  Most of the results and proofs presented here are in the setting of the spaceof tempered distributions introduced by Laurent Schwartz. But there are alsosome very brief mentions of other approaches to distributions or generalizedfunctions.

A quick description for engineering students of distributions (generalized functions) and their Fourier transforms