MATH 704 Texts and References
Main reference
Lecture material will be based on A Course in Complex Analysis, a book that I've written based on my previous courses at Penn, Stony Brook, and CUNY. I'll provide copies of the relevant chapters as we go along.
Suggested textbooks
There are several excellent complex analysis textbooks on the market. Here is a partial list 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.
Further reading
Here are a few suggested books that emphasize certain aspects of the theory:
- O. Forster, Lectures on Riemann surfaces, Springer, 1981.
The best introduction to the subject. Chapter 1 is particularly relevant.
- 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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Math 704