Here is the source of most of the problems I ask here, a majority of which I am currently unable to solve.
From responses to one of these questions I get the idea that there might not be a solution in the ordinary sense to some of these problems. For example, for (3) someone posted a helpful answer of how to get mathematica to solve it, and after staring at the solution I realized it was not in my capacity to have arrived at that answer using my method, or probably any method without a computer.
So I would ask if someone more experienced could give a quick look at the problems and tell me what analytical virtues the author demands and is trying to test, and hence deems essential? So that I can start working on those skill areas so that I know what mathphy minimum expects me to know.
Also a reference request at similar stuff would be good. It is aimed at physicists and as someone hoping to be a mathematical physicist, the premise of the question bank provoked me a little.