My name is Ron Gordon, and since Dec ’12 or so I’ve been having a bit of fun posting solutions (and the occasional problem) on Mathematics Stack Exchange. I have a Ph.D. in Optics, a subject which really gave me a nice perspective on evaluating certain integrals, sums, and differential equations. I joined the work force as an engineer, mainly writing image simulation software for complex lithography systems. As the math involved became labor, I stopped doing problems for fun.
Years later, I changed careers to patent law, which I now practice. While I love my “new” career, my encounters with any significant math are rare. This has actually been somewhat of a blessing because I have found my passion for math as a hobby again. In the past year or so since I got sucked into the Stack Exchange community, I have honed my skills in certain areas better than I had done as an engineer/scientist. I decided that I should have a separate place for some of the problems I have solved from which I have learned something.
That place is here. I have given it a new name as residuetheorem.com, because I have solved roughly 2/3 of the problems here using some form of the residue theorem. What I have found is that being ready to use the residue theorem has provided me with a whole new set of tools that I didn’t have before. Integration, as I see it, is a form of pattern-matching; the way to evaluate an integral is to find a set of transformations that will deliver a form with which one can determine an answer. The residue theorem has brought me a whole new set of forms that let me determine an answer.
I hope that readers of this blog can profit from the material here. I find the expression of a solution to be even more important than the solution itself. Please write me in the comments, or send me an email, if a solution is anything less than crystal clear.
Northborough, MA USA