Winter 2019: Math 185A
You are welcome to email me with questions, at:
cooperjacob [AT] math [DOT] ucdavis [DOT] edu
web link to Professor Temple's webpage for Math 185A
Additional reference books on Complex Analysis.
Disclaimer: You are not required to read any of the additional reference books listed here; you need only read the required textbook for the class, which is Basic Complex Analysis by Jerrold Marsden and Michael Hoffman. In my opinion, this is an excellent book for introductory complex analysis; I especially like that it discusses the more general case of many results (whereas other introductory complex analysis books often only treat the simpler cases).
However, especially when I was a undergraduate, I found it very helpful to look through at least one other book in addition to reading the required text (of course, this is also in addition to carefully re-reading notes taken during the lectures). The following is a list (in alphabetical order) of other complex analysis books which I have found useful. The comments are based on my own observations and opinions (i.e., feel free to disagree with me).
1. Complex Analysis, by Lars Ahlfors.
This book is a mix of introductory and more advanced topics. Admittedly, I have not read very much of it, but, when confused on a particular topic, I often found it very useful to read the applicable discussion in this book, as an alternative approach.
2. Complex Variables and Applications, by Brown and Churchill.
This is the book I learned complex analysis from as an undergraduate, and I highly recommend it as an additional reference for extra examples and exercises to practice solving. The main drawback of this book is that it does not discuss the more general case of some of the results, which are covered in the Marsden and Hoffman text.
3. Visual Complex Analysis, by Tristan Needham.
This is a more advanced text than the Marsden and Hoffman text. As stated in the title, the explanations are quite visual, and the approach is from a much more geometric point of view. I initially found this book's explanations rather difficult to understand until I had learned the corresponding material from a more "standard" point of view; then, the explanations were much clearer, and they helped me to solidify my understanding by approaching it from another perspective.
4. Complex Analysis, by Elias Stein and Rami Shakarchi.
Technically, this is also a more advanced text. It is generally used in the UCD graduate class on Complex Analysis (205A), but, in my opinion, the first five chapters are certainly accessible after (!) you read the applicable sections in the Marsden and Hoffman text. Then, it goes on to cover some interesting topics which are not covered in 185A, such as the gamma function and the zeta function (which appear frequently in some areas of research-level mathematics), and conformal mappings.