Actually, the course I took was Numerical solution of the partial differential equation, rather than Partial Differential Equations. It is quilt different between these two courses, so please pay attention to it.
Numerical solution of the partial differential equation is one of the core courses of department of mathematics. It is a really hard course because of the large amount of calculation and abstract methods which is not easy to understand. There are always lots of steps in one methods and each step need calculating for a long time. And there are also many details should be remembered in every methods, include parameters, constant with special meaning, etc. Ah, also, you have to figure out exactly what types of PDE can use the methods.
It is the point for understanding that these methods about why they work and how they work. For example, the finite volume method in two-dimensional uses the knowledge and theories in mathematics analysis of Green formulas. If you can well understand these theories in mathematics analysis, you may comprehend the method quicker.
All right, this note is a functions and methods summary and the purpose of this note is to make me compare them and remember them easier. I marked the chapters of different methods and the exam formates about them. Hope these will be helpful for your revision.