A printable version of the first-day handout is available in .pdf format.
This is a first rigorous course in the theory of functions of one complex variable. The basic objects studied in the course are holomorphic (complex analytic) functions. The course covers the representation of holomorphic functions by power series and by integrals; complex line integrals, Cauchy's integral formula, and some of its applications; singularities of holomorphic functions, Laurent series, and computation of definite integrals by residues; the maximum principle and Schwarz's lemma; conformal mapping; and harmonic functions.
The required textbook is Function Theory of One Complex Variable by Robert E. Greene and Steven G. Krantz, Wiley, 1997. We will cover chapters 1-7.
The official prerequisite for this course is Math 410 (Advanced Calculus II) or its equivalent. The essential background you need is familiarity with the kind of analytic reasoning used in "epsilon-delta proofs". Math 617 and its successor Math 618 form the basis for the Mathematics Department Qualifying Examination in Complex Analysis.
The course meets 12:40-13:30 Monday, Wednesday, and Friday in ZACH 105D.
Dr. Harold P. Boas
322 Milner Hall
14:00-15:00 Monday, Wednesday, and Friday; and by appointment
409-845-7269
Friday, October 9
Friday, November 20
Final examination: originally scheduled for 10:30-12:30, Monday, December 14, it will now be a take-home examination distributed in class on Friday, December 4 and due at the beginning of class on Monday, December 7.
The final examination and the homework each count for 30% of the course grade. The two mid-term examinations each count for 20% of the course grade. Final letter grades will be based on the standard scale: you need an average of 90 for an A, 80 for a B, 70 for a C, 60 for a D.