I'm just starting my graduate studies in Analysis and PDE's and am a bit lost about what topics should I cover in order to do a good Phd program.
I`ve already done the usual undergrad courses, plus Real and complex analysis (graduate level), functional analysis and measure theory.
So, if you guys can recommend me which courses I should do, (I can get my university to open new courses as needed), and which books I should study, it'd make me really happy
Best Answer
Some interesting courses that can be done with a standard PDE course: (with exemplary lecture notes so you can have a look into these)
And some Analysis courses: