Applied/Pure Math PhD Coursework For the purpose of curiosity, I was wondering what set of courses undergraduate math students take if they're on the track to apply for a PhD in Pure Mathematics vs. Applied Mathematics? Let me try to elaborate as best as I can. I mean at my current university, I've known several people who have gone through the track of going for a PhD in Pure Math and they have taken lots of Grad level Math courses and gotten into top US universities for a PhD in Pure Math where research experience in relevant fields is a plus (I think). 

But my question is for undergraduate students trying to prepare for a PhD in Applied Math. What sort of coursework do they go through? I mean research experience (I believe) becomes important and taking graduate courses in Pure Mathematics is not so. I do not know much people who went for a PhD in applied math at my school. 

I would appreciate it if anyone who can comment on the relevance of pure math grad courses for such students who aspire or strive in applying for a PhD in applied math. Any other comments pertaining to this is welcomed ;)
It might be somewhat controversial for some here, but I don't think there is any one course that you should take in order to get in a particular graduate program. The reason behind my statement is that I believe the logic presented in the OP is rather backwards; one usually pursues graduate studies in a particular field that s/he is knowledgeable and interested in. In other words, you get your undergrad and Masters, and based on what you know and like, you apply to PhD programs in fields where you are competent. The other way around (deciding on a PhD program without have the undergrad and masters done, and choosing courses based on the desired PhD program) does not make much sense, in my humble opinion. 

Also consider that "a PhD in pure/applied maths" is really ill-defined. I can think of a hundred different projects that would have different requirements, with regards to previous courses. I would recommend deciding on a specific subject that you find interesting e.g. "elliptic curve cryptography" or "convex optimization" etc (not just pure/applied math).. then look for announced PhD programs based on projects focused on these subjects of interest. 

All that being said; I would think  advanced level courses in matrix theory (decompositions etc), functional and complex analysis, as well as  optimization theory would be useful in many different graduate programs at most maths departments.