Math 650
Several Complex Variables
Fall 2013
 Course description
 This course is an introduction to the theory of functions of
several complex variables, emphasizing the part of the
theory that intersects with analysis and with partial differential
equations.
Here are some of the topics to be discussed.
 multivariable power series
 Reinhardt domains
 domains of convergence
 the Hartogs phenomenon
 entire functions
 integral representations
 the Cauchy integral
 the Bochner–Martinelli integral
 the Bergman kernel function
 notions of convexity
 linear convexity
 polynomial convexity
 holomorphic convexity
 pseudoconvexity
 the Levi problem
 the ∂ problem
 holomorphic mappings
 Course objectives

By the end of the course, you should be able to
 describe the similarities and the differences between
onedimensional function theory and multidimensional function
theory;
 explain the concept of domain of holomorphy;
 read the research literature on multidimensional
function theory.
 Prerequisites
 You should have some acquaintance at the firstyear graduate
level with both real analysis and (onevariable) complex analysis.
The official prerequisites for this course are Math 608 and
Math 618 (or equivalents).
 Textbook

There is no required textbook. I have asked the campus library to put hard copies of
the following books on reserve.
 Lars Hörmander, An introduction to complex analysis in
several variables, second edition, NorthHolland, 1973;
QA331 .H64 1973.
 Steven G. Krantz, Function theory of several complex
variables, second edition, American Mathematical Society,
2001; QA331.7 .K74 2001.
 R. Michael Range, Holomorphic functions and integral
representations in several complex variables, SpringerVerlag,
1986; QA331 .R355 1986.
Moreover, the indicated book by Range is
available in electronic form from computers on campus. Another
book that similarly is available electronically is Introduction to complex analysis in
several variables by Volker Scheidemann (Birkhäuser,
2005; QA331.7 .S34 2005).
 Meeting time and place

The course meets 11:10–12:25 on Tuesdays and Thursdays in room 624 of the Blocker building.
 Grading
 Grades will be based on class participation and homework. There
will be no examinations (in particular, no final examination).
 Course website

https://www.math.tamu.edu/~boas/courses/6502013c/
 Office hours

During the Fall 2013 semester, my office hour in Milner 202 is
2:00–3:00 in the afternoon on Tuesday, Wednesday, and Thursday; I am available also by appointment. The best way to contact me is via email to boas@tamu.edu. Telephone messages can be left at the Milner office of the Department of Mathematics, 9798457554.