[Math] A good graduate complex analysis textbook

Question

I'm about to teach a graduate level one-semester complex analysis course. The audience will be very good advanced undergraduate students and first year graduate students.

I don't want to use Lang or Ahlfors.

I was considering "Complex Analysis" by Elias Stein and Rami Shakarchi or possibly "Complex Analysis" by Eberhard Freitag and Rolf Busam. Does anyone have any experience teaching courses with those books, particularly for a one semester course with the audience I mentioned above?

Thanks,
Alan

Answer 1

Complex Made Simple by David C. Ullrich is excellent.

To quote from an MAA review:

This is an excellent book for a first-year graduate student doing a course in complex analysis. Instructors will like it as well, but students will enjoy and profit from Ullrich’s careful explanation of why the theorems work the way they do and also sometimes why seemingly nice ideas that promised to work do not (but often can be patched so that they do).