| Course Content | | Review and some extensions of single variable complex analysis. Complex linearity and holomorphicity in several variables, Hartog's theorem, Weierstraß' preparation theorem, Riemann extension theorem, Weierstra&szlin;' division theorem, analytic Nullstellensatz, implicit and inverse function theorems, complex manifolds and analytic subvarieties, meromorphic maps. |
| Textbooks | | None required, but the following are recommended.
- J. Eschmeier, Funktionentheorie mehrerer Veränderlicher. Springer Verlag, 2018.
- R. C. Gunning, Introduction to Holomorphic Functions of Several Variables, I, II, and III. Wadsworth & Brooks/Cole, 1990.
- L. Hörmander, An Introduction to Complex Analysis in Several Variables. North Holland, 1990.
- S. G. Krantz, Function Theory of Several Complex Variables. AMS Chelsea Publishing, 2011.
- R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables. Springer Verlag, 1986.
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