I ended up finishing this mathy stuff a bit ago. I realized I had no idea how to integrate secant, but I knew the answer had natural-log-of-tangent in it, so I derived natural-log-of-tangent and used the solution to that to connect everything. I guess I could probably use the derivative to natural-log-of-tangent to figure out the proper way to integrate secant. That might be interesting. I probably could have done all this easily back in college.
Also, at one point Jess was really considering doing NaNoWriMo, and I had some ideas that I wanted to work into a story, so I thought about trying to do it also. Then after about one and a half days I realized that I didn't enjoy writing enough to spend the four hours a day I'd need to spend to accomplish it. Still, I wrote a short chapter of stuff that was pretty OK. I realized as I was going that my three main characters were sort of like the three protagonists in The Big Lebowski, so I ended the chapter with a reference to that... and I'll put that in the next post.