Math 407
Complex Variables
Fall 2017
 Course description
 This threecredit course covers the elements of onedimensional
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 SpringerVerlag 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/4072017c/
 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, 9798457554.