About a week ago I finally added those new extra exercises I’ve been promising on the webpage (almost 150 new exercises) to my differential equations book. These are now with solutions. I did not want to add solutions to existing exercises. I still feel that it’s better to not have solutions. But I guess having some exercises with solutions does make the students feel better. Plus it seems this was an argument against using my book in at least department (not enough exercises and no exercises with solutions). So there. Some of the new exercises are interesting, many are just simple plug and play exercises to get students going. I’ve added all of them as exercises numbered 101 and above so that I would not change existing numbers. I suppose the “even/odd” thing is the common theme, but this has the added advantage that I can have fewer exercises without solutions.
As for the real analysis book. After having taught with Rosenlicht at UCSD (because my book doesn’t have metric spaces), I decided I will use my book at Madison this coming fall. This requires that I write up some metric space stuff. So I will be adding a Chapter 7 to the book. It will probably not be completely polished by the fall, so I might keep it separate even for the fall and only add it once all the bugs are caught after teaching with it. The plan is to do first everything on the real line and then do metric spaces. I found that metric space stuff was a bit too abstract for the students if I jumped right in. It might be better to do first sequences and continuity with real numbers only. I will skip some other material such as series though, and cover other material more lightly, due to time constraints. As for other news on the book: It is now (in slightly modified form) the standard book at University of Pittsburg.