Complex Variables Lecture Notes

Assorted notes from an undergrad complex variables class. Copied from lectures and incomplete, may have typos/broken LaTeX as they were written in a frenzy.

The textbook used is Complex Variables and Applications by Churchill and Brown (8th Ed.). The book is quite thorough with proofs, but not the easiest read despite its popularity as an undergrad textbook. I recommend the similiarly titled Complex Variables with Applications by A. David Wunch as a supplementary text. My analysis teacher graciously lended me his copy along with Schaums Outline of Theory and Problems of Complex Variables, which saved me many times when doing homework for this class. In general, I found Wunch’s explanations to be much clearer on most subjects. The Schaums book is good as a quick reference on theorems and properties. As a final recommendation, I suggest University of Washington professor Steve Brunton’s short video series on the subject. I generally do not like videos when studying, but his lecture style is very engaging and he covers a breadth of topics quite quickly – a good place to go if you are stuck. In fact, I would just start there if you want an applications level knowledge of complex variables.

Part 2