This class was the hardest I have ever taken in my entire life, not because of the prof. (who was fantastic) but the course material itself. There was one homework set due every week, each being real mind-benders that had me utterly dazed. Imagine using up an entire page, perhaps even two, for a single problem. Due to the manner in which PDE's are solved, that will often be the case (Most PDEs are solved iteratively by using Fourier series). And for the love of God, pay attention during the first three or four weeks because your comprehension of everything else presented in the class later down the road depends on how well you understand the first few things. Needless to say, the exams are all fast-paced and extremely difficult, but it's almost like that is to be expected from the APMA department, having already taken a whole bunch of previous math classes here. I'll proudly say that this class was the first one I ever got a C+ in at UVA, and I didn't want to do CR/NC (took this class spring '20) because I actually worked hard to achieve this grade. For mechanical/aerospace people taking this class: you do see partial differential equations in future classes (fluid mechanics and aerospace structures I believe, perhaps more), but you won't have to work with them in the same tedious way you'll solve PDE's in this class.