Textbook
Lecture material will be based on
The book has an accompanying webpage containing notes and comments, 130+ additional problems, and an errata list.
Further Reading
Here is a partial list of supplementary references in alphabetical order:
- L. Ahlfors, Complex Analysis, 3rd ed., McGraw-Hill, 1978.
- T. Gamelin, Complex Analysis, Springer, 2001.
- R. Remmert, Theory of Complex Functions, Springer, 1991.
- W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, 1987.
- E. Stein and R. Shakarchi, Complex Analysis, Princeton University Press, 2003.
Special Topics
A few books that emphasize certain aspects of the theory (some are useful for your future complex analysis endeavors):
- O. Forster, Lectures on Riemann surfaces, Springer, 1981.
The best introduction to the subject.
- S. Krantz, Complex Analysis: The Geometric Viewpoint, 2nd ed., MAA, 2004.
For conformal metrics, hyperbolicity, generalizations of the Schwarz Lemma and its interpretation in terms of curvature.
- Z. Nehari, Conformal Mappings, Dover, 1990.
Excellent source for conformal mappings of simply and multiply connected domains, and many special functions.
- R. Remmert, Classical Topics in Complex Function Theory,
Springer, 1998.
A highly readable account of many classical topics, with great historical notes.
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