Theory of Functions of a Complex Variable I

Math 617--Fall 1997

Instructor: Dr. Francis J. Narcowich
Office: 302 Milner Hall
E-mail: fnarc@math.tamu.edu
Phone: 845-7369
URL: /~francis.narcowich/
Office Hours, Tuesday, 11-12, Wednesday and Friday, 12:40-1:40; and by appointment.

Prerequisites. MATH 410 or the equivalent.

Syllabus We will cover chapters I-VI in Conway's book. Topics will include: complex numbers, metric spaces and the topology of the complex plane, analytic functions, Moebius transformations, complex integration, Cauchy's theorem, Cauchy estimates, Liouville's theorem, power series representations, Rouche's theorem, the open mapping theorem, Goursat's theorem, singularities, residues, Laurent series, maximum modulus principle, Schwarz's lemma, and Hadamard's three circles theorem. We will also cover applications as we go along.

Required Text
  1. John B. Conway, Functions of One Complex Variable I, 2nd ed., Springer/Verlag Springer-Verlag, New York, 1978.
Supplementary Books
  1. Lars V. Ahlfors, Complex Analysis, 2nd ed., McGraw-Hill, New york, 1966.
  2. R. V. Churchill, Complex Variables and Applications, 2nd ed., McGraw-Hill, New York, 1960.
  3. E. T. Copson, Metric Spaces, Cambridge University Press, London, 1968.
  4. Walter Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New york, 1974.

Tests

Grading. Your grade will be based on homework, two in-class tests, and a final exam. The homework will count for 20% of your grade, each in-class test for 25%, and the final exam will count for the remaining 30%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, contact me immediately.