Office: 330 Herman Brown Hall

Office Hours: 1--2:30 PM, Th or By appointment

Math
382 - Complex Analysis

Instructor: Arindam Roy

Office: 330 Herman Brown Hall

Office Hours: 1--2:30 PM, Th or By appointment

Office: 330 Herman Brown Hall

Office Hours: 1--2:30 PM, Th or By appointment

**Textbook:** *Complex Variables,* S.D. Fisher, Dover, 1999.

**Basic Plan:** Well go through the entire book, but well have to skip a few topics along the way. A tentative
plan is following:

(1) Complex numbers and functions.

(2) Analytic functions: Cauchy-Riemann equations, exponential, trigonometric, logarithm and
power functions, the Riemann surface for log z, harmonic functions.

(3) Complex integration: contour integration, the Cauchy integral theorem and Cauchy-Goursat theorem for
star-shaped regions, the Cauchy integral formula, Taylor’s series, uniqueness,
the maximum principle, isolated singularities, Laurent series.

(4) Residue theory: Simply connected domains, the residue theorem, integrals over the real
axis, improper integrals and principal values, integrands with branch points, principle of
the argument, Rouch ́e’s theorem.

(5) Conformal mapping, bilinear transformations, inverse mappings and univalent functions,
global mapping theorems, the Riemann mapping theorem.

(6) Uniform convergence for sequences and series, power series.

**Assignments:** There will be homework each week due on Monday in
class. You are allowed (and encouraged) to work with other students while
trying to understand the homework problems. However, the homework that you hand in should be your work alone. Late homework will not be accepted, but the lowest score will be dropped.

**Grading and Exams:** There will be two take home midterms and a takehome final. The
midterm exams will be given on February 10th and on March 30th. The date of the final exam is yet to be
determined
by the Registrar’s Office. The formula for the course grade is roughly as
follows:
Homework (35%), Midterms (40%), Final (25%).

**Disability Support:** Any student with a documented disability seeking academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All such discussions will remain as confidential as possible. Students with disabilities will need to also contact Disability Support Services in the Allen Center.