MATH 704 Texts and References
Lecture material will be based on A Course in Complex Analysis, a book
that I've been writing based on my previous courses at Penn and Stony Brook.
I will post chapters as they become available:
Chapters 1-3
Chapters 4-7
Chapter 3 (version of 3-19-2011)
Chapter 8 (version of 3-19-2011)
Note that this manuscript is work in progress, so your comments are certainly welcome.
Suggested textbooks:
There are several excellent complex analysis textbooks available on the market. Here is
a partial list in alphabetical order:
- L. Ahlfors, Complex Analysis, 3rd ed., McGraw-Hill, 1978.
- J. Conway, Functions of One Complex Variable I and II, Springer, 1995.
- T. Gamelin, Complex Analysis, Springer, 2001.
- R. Greene and S. Krantz, Function Theory of One Complex Variable, 3rd ed., AMS, 2006.
- E. Hille, Analytic Function Theory, vols. I and II, Chelsea, 1973.
- R. Narasimhan and Y. Nievergelt, Complex Analysis in One Variable, 2nd ed., Birkhauser, 2001.
- W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, 1987.
- E. Stein and R. Shakarchi, Complex Analysis, Princeton University Press, 2003.
Further readings:
There are also books which emphasize certain aspects of the theory. Some of these will be used for the upcoming course in the Spring.
- L. Ahlfors, Conformal Invariants, McGraw-Hill, 1973.
For the general version of the uniformization theorem.
- O. Forster, Lectures on Riemann surfaces, Springer, 1981.
The best introduction to the subject.
- S. Krantz, Complex Analysis: The Geometric Viewpoint, Carus Math
Monographs no. 23, MAA, 1990.
For conformal metrics, hyperbolicity, generalizations of 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. Especially useful are chapters on
infinite products and Riemann mapping theorem.
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Math 704