In a few weeks I will write an exam in Analysis 2, that pretty much covers everything more metric spaces to multi variable calculus, Fourier series and ODE.
I think I am pretty well prepared for the "practical" stuff related to those topics, saying: If there is something to compute, I can probably do it. I consider calculation and being able to do easy short proofs to be absolutely mandatory skills. There is really enough stuff for that to train on the Internet.
However there are always a few exercises in exams, that are "challenging" and require a solid and maybe deep understanding of the matter. I think, if really wants to become good or be one of the best, he/she has to work very hard, therefore I looked on the Internet for more difficult problems or material for further studying on those topics, but I didn't find much. So, does someone know maybe a good book, or website that collected many many different problems on those topics? I thought about something like the Analysis 1 written by Walther Rudin. Thx in advance.