MAT 542 Texts and References
Lecture material will be based on the first
few chapters of A Course in (Quasi-)Conformal Analysis, a book
that I'm writing in my spare time.
I will try to give you copies of the relevant chapters as we go along.
Suggested textbooks:
There are many excellent graduate-level complex analysis textbooks. Here is
a partial list; our presentation will be closest in spirit to Rudin. Most of
these books are on reserve in the Math/Physics library.
- L. Ahlfors, "Complex Analysis," 3rd ed., McGraw-Hill, 1978.
- C. Bernstein and R. Gay, "Complex Variables: An Introduction,"
Springer-Verlag, 1991.
- 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.
- R. Remmert, "Theory of Complex Functions," Springer-Verlag, 1991.
- W. Rudin, "Real and Complex Analysis," 3rd ed., McGraw-Hill, 1987.
Further readings for selected topics:
- L. Ahlfors, "Conformal Invariants," McGraw-Hill, 1973.
For the general version of the uniformization theorem.
- O. Forster, "Lectures on Riemann surfaces," Springer-Verlag,
1981.
Mostly Chapter 1.
- 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-Verlag, 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 542