I'm a computer engineering student. We often use the convolution integral but in our engineering textbooks the problems are often toy examples that are best solved via graphical trickery. I would like a deeper understanding of the mathematics behind this integration technique. I tutor mathematics and have gone a bit further than my own course offerings to gain a deeper understanding of the techniques we've used and would like to do that here.
I've looked into a few books (ie Theory and applications of the convolution integral-Srivastava) and the only ones I've found assume I've taken a few semesters of real analysis which I haven't and sadly won't be able to. I've been told that differential equations books might cover the topic in a more rigorous way but none that I own do cover it.