# ADVICE on complex variables course needed:

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i'm sorry if this is the wrong area to be posting such a question, but im registered for a complex analysis course starting in the fall and I was wondering what i should review before starting this course?

I've had math coursework up through calculus, differential equations, linear algebra, and an introductory proof course.

I was just worried because i havent worked with complex numbers [imaginary number material] since algebra and that was a long while ago.

Should i review this old algebra material, and what else?

Thanks so much for any input, fellow mathematicians!
Amanda

You should post the course description so we can get a better idea. But, if you were able to register for it, then you probably have the pre-reqs already. I am planning on taking this class in the spring next year, and the only pre-req is calc 3. Ive only had up too the same background as you, minus the proof course, and I was reading through a complex variables book fine.

Review:
- complex numbers (obviously)
- partial and total derivatives
- line integrals (verrrrrrry important!!)
- power series

Thanks a lot, guys. I got an A in proof class, its just been a few quarters since ive been in calculus, and i was a bit nervous! I'll start reviewing immediately.

I had two courses, one called "Complex Variables" and one called "Complex Analysis" so I'm not sure which is more akin to the one you are taking but if you haven't had a course on complex variables before then I doubt it is like the complex analysis course that I took.

Assuming that is true then I second the suggestion of reviewing line integrals and basic properties of complex numbers and how to write them and manipulate them.

Complex numbers definitely lend a little quirkiness to the mathematics, but I think you will find that the skills you picked up so far will be very sufficient for success in the class.

In the parts I have learnt, I think Complex Analysis is one of the more beautiful branches of mathematics. Find out what textbook you will be using and do a little reading ahead. If it is something like Brown and Churchill (a common text for first courses), it will get you started if you look at the first few sections. If you are up to speed on your multivariable calculus, you should do fine.

If you want some supplementary reading, I would recommend Visual Complex Analysis by Tristan Needham:
https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20&tag=pfamazon01-20
or
http://www.bookdepository.com/Visual-Complex-Analysis-Tristan-Needham/9780198534464

It will be different from your textbook (and contain a wider range of material) but it has a lot of insight that is useful for properly understanding the subject.

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It might be a little late but I'm also planning to take Complex Analysis this year with your same pre-reqs except for intro to proofs. However, I've already taught myself some of it from Saff and Snider's book and the following online text:

http://people.math.gatech.edu/~cain/winter99/complex.html

It's a neat guideline with a simple introduction to most topics you might cover starting with complex numbers; that is if you're taking Complex Variables.

mathwonk
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here are some notes i wrote last time i taught the course.

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mathwonk
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heres a review of my whole course i wrote for the students studying for the final.

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the links and pdf files are extremely helpful, again, thank you! does anyone know the difference between a complex variable course and a complex analysis course?

the one im taking is complex variables.

the links and pdf files are extremely helpful, again, thank you! does anyone know the difference between a complex variable course and a complex analysis course?

the one im taking is complex variables.
Complex Variables and Complex Analysis are related in much the same way that Introductory Calculus and Real Analysis are related.

Introductory Calculus introduces the topic and theorems and rules and you spend your time learning how to apply them and manipulate them in order to find analytic/quantitative solutions to problems, with some proofs thrown in.

Real analysis takes you deeper down the rabbit hole and you study the rigor of those theorems and spend a lot of time focusing on the proofs.

At my university and with my professors, complex variables and complex analysis was separated in the same way.

I had "Complex Variables" as part of my ODE course, and a math grad student suggested using the Schaum's outline book with the same title (author: Spiegel). I found it very helpful. Really brief on the theory, but that's not what Schaum books are for.

thanks guys, all of the sources were very helpful. im doing extremely well in the class. its so interesting!