This is a first rigorous course in the theory of functions of one complex variable. The basic objects to be studied are complex-analytic functions (also known as holomorphic functions). The course covers the representation of holomorphic functions by power series and by integrals; complex line integrals, Cauchy's integral formula, and some 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.
- Textbook
- No textbook needs to be purchased. I will follow the book Complex Variables by Robert B. Ash and W. P. Novinger, which is freely available online. I expect to cover most of the topics in Chapters 1–4.
- Prerequisites
- The official prerequisite for this course is Math 410 (Advanced Calculus II) or its equivalent. The essential background that you need is familiarity with the kind of analytic reasoning used in “ε–δ (epsilon–delta) proofs”. Math 617 and its sequel Math 618 form the basis for the PhD Qualifying Examination in Complex Analysis in the Department of Mathematics.
- Venue
- The course meets 2:20–3:35 pm on Tuesday and Thursday in room 006 in the basement of the Civil Engineering Building.
- Exams and grades
- There will be exams in class on September 30 (Thursday), October 28 (Thursday), and November 23 (Tuesday). The final exam is scheduled for 1:00–3:00 pm on December 15 (Wednesday). Each of the exams counts for 20% of the course grade. Homework counts for the remaining 20% of the course grade.
- Website
- http://www.math.tamu.edu/~boas/courses/617-2010c/
- Office hours
- 1:00–2:00 pm on Tuesday, Wednesday, and Thursday in Milner 202; also by appointment.