@SillyGoose most courses I had didn't even really use one specific book - they usually said something like "we're mostly following X, but here's a bunch of other resources that are also relevant"

yes, in the best case they had their own notes. When they do follow a book closely, it's because their notes have been published as a book. Of all the courses I took, I think a couple followed (a subset of) a book closely and the author was not the lecturer/previous lecturer at the same uni

Same for me. It was curious that the recommended books were quite different from the courses but there were non-recommended books that were so alike

Following a book closely is something students can do on their own

Side note about books: I hate when math books are ill-formatted and you see these huge walls of text

some lecture notes i have received so far (not many years to be fair) have seemed incomplete--so i end up just working through a book on the subject xD. would like to experience exceptional lecture notes one day

I'm not sure I understand the question :P

both are applicable to exactly those situations that are cylindrically or spherically symmetric, where does opinion enter into this?

@ACuriousMind Can you help me understand this paper? arxiv.org/pdf/0804.1377.pdf

Mainly some basic conceptual issues

That are more to do with the background knowledge required