In the study of any special issue in mathematics, two things may be of importance, namely, subjects and order of them. I just wrote down a plan to study the theory of partial differential equations in a treatise manner. My program is as follows, considering the subjects and their order based on the prerequisites and logical relationships between them:
Calculus of Variations
Classical Theory of Ordinary Differential Equations (ODEs)
Classical Theory of Partial Differential Equations (PDEs)
I am not sure that I have chosen the proper order for self-studying and also there may be things that I even don't know about to cover. So please tell me subjects that I should cover based on what you think and the ideal order of learning them.
It will be really nice if you suggest just one reading in each subject that you prefer is the best for a theoretical study.
How much time does it take to do the whole thing? 1, 2, 3 or 4 years?
Any other plan or thought you have is welcome. Please write whatever you think as answers not comments! :)