First, for background information:
I'm at the end of my sophomore year (Australia), planning to take a course in Partial Differential Equations next semester. I have enrolled into a Real Analysis course this semester, almost through. I've been also studying (web courses) what I believe will be the prerequisites to do an audit of a PDEs web course this summer.

Now, please, take your time and read carefully:
I need a detailed list with the prerequisites to study Partial Differential Equations.
I need a detailed list with the titles of each of courses I should be taking (along with their core topics).
Before you answer, please take a look at the PDEs web course here. The topics are at the title of each lecture.
I understand I'll need something like Calculus with complex variables and complex analysis, but what else?

Please don't just type in a random textbook or something along the lines of "maybe you should..".
I need a detailed list with the titles of each of courses I should be taking along with their core topics.
Also please give a quick review of the lectures I've posted, how far they would take me into solving PDEs analytically/numerically (both in terms of theory and methods).

Tks in advance.