Introduction to Integral Transforms

This note is the summary of a series of lectures presented for a number of years by the author to graduate students interested in Mathematical Modeling in Biology. Its aim is essentially practical; proofs are given when they help understanding the essence of a problem, otherwise the approach is mostly intuitive. The operational calculus is presented from an algebraic point of view; starting from the convolution integral, the extension from functions to operators is defined as analogous to the extension from natural numbers to rational numbers. Laplace and Fourier transforms are presented as special cases. The note concludes showing the connection between Fourier transforms and Fourier series.