# Complex analysis vs. PDE class

Im a rising junior in the US starting my upper division physics classes.
I have an opening this quarter and want to take an applied math course, but cannot decide between these two:

In the mathematics department:
"Applied complex anlysis
Introduction to complex functions and their applications to engineering and science. Complex numbers, elementary functions; analytic functions; complex integration; power series; residue theory; conformal maps; applications."

In the mechanical engr department
"Introduction to Engineering Analysis
Analytical methods in engineering. Nonhomogeneous linear ordinary differential equations. Variable coefficient linear ordinary differential equations. Eigenfunction expansions. Laplace transforms. Introduction to Fourier transforms. Linear partial differential equations."

I havent decided on my research interest too much, but materials, spectroscopy and signal processing have caught my interest. I was thinking about taking an elemtary analysis course my senior year so I could study Fourier analysis a little more--something i know that would have relevance to both quantum and signal processing. I have no idea if i can handle the theorem-proof method of learning mathematics though.

If anyone has any input on which class they would recommend, please tell me. I cannot take both classes, unfortunately. It's possible I could take once class this year and the other one next year.

Also: the applied complex analysis course is a pre req for an upper div continuous signal processing class in the EE department (but not the discrete signal processing class).

EDIT: these are both upper division classes. i've already taken all my lower division math classes (linear algebra, differ eq, etc).

no one has ANY input on this subject?

Hi, flemmyd!

It's a tough choice you have to make :)

I'm not sure what the level of the complex analysis course you quoted above is, but since it's in the maths department I can assure you that almost all of what you'll be seeing there will consist of the 'theorem-proof method' (besides the chapters on residual calculus and Laurent series). However it says 'Applied cpx Analysis..' so this is something I'd strongly recommend you to check.

On the other hand, complex analysis is one of the most beautiful (i.e. mathematically simple) theories (in my personal opinion), so it's worth learning it anyway. I would say that it also requires Real Analysis in 2 dimensions and a tiny bit of linear algebra.

From the resume of the other course, I see it's mainly about mathematical tools for manipulating ODE's and simple PDE's. If you have already taken Classical Electrodynamics or Quantum Mechanics, then it will be kind of boring (in comparison to cpx. analysis). However, if not - practising this stuff will help you significantly to concentrate on the physics of the two fields later on (E-dynamics and QM). The topics of this course are routine techniques used permanently there.

Now, if you really want to understand where Fourier series (FS) and Transform (FT) come from and what they really mean and so on, you'd better consider visiting a Functional Analysis course. (this is a very hard but interesting course usually having as prereq's loads of real analysis and linear algebra and is purely mathematical, but then you know what FT is all about and also many more)

I'm sorry, but I'm not able to tell you to do one or the other. You have to weight up the advantages and the disadvantages by yourself. Nonetheless, I hope to have helped you a little bit towards your decision :)

with regards,
marin