Math 407
Complex Variables
Fall 2017

Course description
This three-credit course covers the elements of one-dimensional complex analysis: the complex numbers (their algebra, geometry, and topology); analytic functions of a complex variable (definition, examples, properties); integration in the complex plane, particularly Cauchy’s integral formula and its consequences; infinite series of complex numbers and of complex variables, including Taylor series and Laurent series; the residue theorem and the computation of real integrals by complex methods; and conformal mapping.
Course objectives
By the end of the course, you should be able to
  • analyze functions of a complex variable using series expansions, using line integrals, using geometry, and using partial differential equations;
  • explain the major theorems that distinguish complex analysis from real analysis; and
  • apply complex analysis to compute geometric mappings and real integrals.
Prerequisite
The official prerequisite for this course is Math 221 (Several Variable Calculus).
Textbook
The required textbook is Complex Analysis by Theodore W. Gamelin, published by Springer-Verlag in 2001. Since the campus library subscribes to a collection of Springer books, TAMU students can download a copy of the textbook for free in either pdf or ePub format. (You may need your TAMU NetID and password to download the book.) From the same link, you can purchase a paper copy of the book for $24.99 (plus tax), much cheaper than the list price. (Look for the box headed “MyCopy Softcover Edition.”)
The course covers a subset of Chapters I–XI of the textbook.
Meeting time and place
The course meets 9:35–10:50 on Tuesday and Thursday mornings in BLOC 161.
Exams and grades
Grades are based on the standard scale (60% is passing, 70% or higher earns a C, 80% or higher earns a B, 90% or higher earns an A).
  • The two midterm exams are scheduled for September 28 (Thursday) and October 26 (Thursday). Each of these exams counts for 20% of the course grade.
  • The cumulative final examination, which has been scheduled by the Registrar for 12:30–2:30 on the afternoon of Friday, December 8, counts for 20% of the course grade.
  • Homework counts for 20% of the course grade.
  • Quizzes count for 20% of the course grade.
Course website
http://www.math.tamu.edu/~boas/courses/407-2017c/
Office hours
During the Fall 2017 semester, my regular office hour in Blocker 601L is on Monday and Wednesday afternoons from 2:00–3:00. Additionally, I am available by appointment.
The best way to contact me is via email to boas@tamu.edu. Telephone messages can be left at the Department of Mathematics, 979-845-7554.