Textbook
Lecture material will be based on
The book is scheduled to be published in October. In the meantime, I'll provide copies of the relevant chapters as we go along.
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 (mostly 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., Mathematical Association of America, 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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