University of Rhode Island      Department of Mathematics

MTH 562  Complex Analysis

TuTh 2-3:15pm Lippitt 204


Instructor  Dr. Mark Comerford
Office  Lippitt 102 F
Phone  874 5984
Email  mcomerford@math.uri.edu
Office Hours
  Wed 2 - 4 pm
or by appointment
Text John B. Conway
Functions of one Complex Variable,
Second Edition,
Springer Verlag,
ISBN 0-387-90328-3
Prerequisites  Mth 435 and Mth 436 or
Mth 437 and Math 438 or equivalent

Sylllabus


Chapter 1    Complex Numbers and their Basic Properties
Chapter 2    Differentiability
Chapter 3    The Cauchy-Riemann Equations
Chapter 4    Power Series - Radius of Convergence, Term-by-Term
                   Differentiation and Integration, the Exponential, Sine and
                   Cosine functions, the Logarithm
Chapter 5    Line Integrals along Piecewise Smooth Curves
Chapter 6    Cauchy's theorem for a Rectangle, Primitives on a Disc
Chapter 7    Cauchy's Integral Formula in a disc, Taylor's theorem,
                   Cauchy's Estimates, Morera's theorem,
                   Goursat's theorem, Liouville's theorem,
                   The Fundamental Theorem of Algebra
Chapter 8    Identity Principle, Mean Value Theorem,
                   Maximum and Minimum Modulus Theorems,
                   Open Mapping Theorem, Schwarz Lemma
Chapter 9    Integration along Continuous Paths, Homotopy
                   The Homotopic Form of Cauchy's Theorem,
                   Simple Connectivity
Chapter 10   Winding Numbers
Chapter 11   Homology and the Homological Form of
                    Cauchy's Theorem
Chapter 12   Counting Zeroes - a First Version of the
                    Argument Principle
Chapter 13   Isolated Singularities, Laurent Series Development
Chapter 14   Using the Laurent Series to Classify
                    Isolated Singularities
Chapter 15   Residues and the Residue Theorem
Chapter 16   Contour Integration - Using the Residue Theorem to
                    Evaluate Integrals and Sum Series
Chapter 17   The Argument Principle and Rouche's Theorem


Here is a link to Ben Salisbury's notes from 2007.

If there is additional time, we will consider other topics such as the Riemann mapping theorem or some elementary complex dynamics.


Exams


Midterm  Thursday March 8, 2012
Final  11:30am - 2:30pm, Thursday May 10, 2012 (in Lippitt 204)

 

Evaluation


Homework   30%
Midterm   30%
Final   40%


Homework

Homework will be assigned bi-weekly and selected problems will be graded.

Homework 1 Due February 7, 2012.

Homework 2 Due February 21, 2012.

Homework 3 Due March 6, 2012.

Homework 4 Due March 27, 2012.

Homework 5 Due April 10, 2012.

Homework 6 Due May 1, 2012.


Policies

You are expected to abide by the University's civility policy:

"The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class."

Cell phones, IPods, beepers and any electronic device must be turned off in class.

You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. Use of unauthorized aids such as cheat sheets or information stored in calculator memories, will be considered cheating. The Mathematics Department and the University strongly promote academic integrity.


H1N1 Flu Pandemic - Special Announcement

The H1N1 Flu Pandemic may impact classes this semester. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify your instructor by phone or by email of your status. Your instructor will communicate by email or by phone with you. In this way you and your instructor will work together to ensure that course instruction and work is completed for the semester.

The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view http://www.cdc.gov/flu/protect/habits.htm

URI information on the H1N1 will be posted on the URI website at http://www.uri.edu/news/h1n1, with links to the http://www.cdc.gov site.

Special Accommodations

Students who need special accomodations and who have documentation from Disability Services should make arrangements with me as soon as possible. Students should conact Disability Services for Students, Office of Student Life, 330 Memorial Union, 874-2098.