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*Complex Analysis*

A study of complex valued functions: Cauchy’s Theorem and residue theorem, Laurent series, and analytic continuation. Already have some experience in this area, but by no means extensive... and I'd like to know how useful it might be from a physicist's perspective.

*Topics in Differential Equations*

An introduction to the theory of ordinary differential equations. Existence and uniqueness theorems, global behavior of solutions, qualitative theory, numerical methods. This is being taught by an amazing guy, who told me today that much of the focus will be on different classes of problems such as PDEs in fluid dynamics and GR, classical formulations of the N-body problem, etc... Sounds cool, but one concern of mine is that I have already studied diffeqs in some depth, only not as rigorously as I'd like.

*Linear Algebra*

A brief introduction to field structures, followed by presentation of the algebraic theory of finite dimensional vector spaces. Geometry of inner product spaces is examined in the setting of real and complex fields. This is the usual course taken by people in my position here. That said, I am not sure it will be very illuminating beyond what I already know of linear (most of the practical stuff was addressed way back in sophomore year physics). But then again, I could use some practice, and I'm sure a rigorous treatment would be interesting as well.

What is your experience with courses of the nature of those listed above? I will likely cover everything else in grad school at some point, so I guess the prudent question is, "what will be most useful to get a head start on," and also, based on my interests, "what will help me the most in plasma physics research this summer?"

Thanks!