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 查看全文>>