I'm looking for a specific recommendation for a textbook on complex analysis. I very much like the outline of Bruce Palka's An Introduction to Complex Function Theory. The textbook is an ideal resource which can be used for an upper-level undergraduate course/beginning graduate course. Some of the topics that catch my eye:
- Chapter 1: The Complex Number System,
- Chapter 2: The Rudiments of Plane Topology
- Chapter 3: Analytic Functions
- Chapter 4: Complex Integration
- Chapter 5: Cauchy's Theorem and its Consequences
- Chapter 6: Harmonic Functions
- Chapter 7: Sequences and Series of Analytic Functions
- Chapter 8: Isolated Singularities of Analytic Functions
- Chapter 9: Conformal Mapping
The textbook, however, is quite verbose, and chatty. I don't mind reading such textbook, but I suppose reading Palka's textbook will consume a lot of time. Moreover, there are a very large number of interdependent exercises, and it would be very hard to do all of them.
Therefore, I'm looking for alternative books that covers all the aforementioned topics in detail and has good exercises. Please note that I'm looking for such books as Brown and Churchill's Complex Variables and Applications.