Math 591
Dr. Robert Smits
Complex Analysis
Fall 2009
New Mexico State University
Instructor:
Dr. Robert Smits
e-Mail: rsmits@nmsu.edu
phone: 505-646-4218
office: Science Hall 232
Class Location:
Science Hall 111 MWF 9:30-10:20
Textbook:
Functions of One Complex Variable: John Conway
Prerequisite:
Math 517 and Math 528 or consent of instructor
Catalog Description:
Rigorous treatment of complex differentiation and integration, properties of
analytic functions, series and Cauchy s integral representations.
Course Objectives:

Complex Differentiation and Integration: derivatives, antiderivatives, Cauchy-Goursat
Theorem, Morera's theorem, isolated singularities and residues, Cauchy's integral formula,
Rouché's theorem.

Properties of Analytic Functions: identity theorem, maximum modulus principle Liouville's
theorem, mapping properties of analytic functions.

Sequences of Analytic Functions: preservation of properties under normal convergence.

Series and Product Representations: Taylor and Laurent expansions, classification of
singularities, Blaschke and Weierstrass products, Mittag-Leffler's theorem.

Mapping in the Extended Plane: conformality, the Riemannian sphere, Möbius
transformations, chordal and hyperbolic metrics, Riemann mapping theorem.

Analytic Continuation: connectivity and multiple-valued functions, continuation by
rearrangement of series, singularities.
Drop Deadline
October 14
Homework Assignments:
 Homework will be assigned every class and will be collected the following lecture
 Make sure to write your name on all homework
 Students are encouraged to work in groups, however the final product must be in their
own thoughts. Homework is to be legible and stapled as necessary. Homework not meeting
these criteria will not be graded. (See make-up work policy below)
Office Hours & Outside Class Help:
 Office Hours: WF 10:30-11:20
 Questions can be posed via email at rsmits@nmsu.edu.
Midterm Tests:
September 28
November 2
Final Examination:
The Final Exam is cumulative and will be on December 7 from 8:00-10:00
Course Evaluation:
Homework
Tests 1-2 (25% each)
Final Exam
Total
15%
50%
35%
100%
Make-up work: For a university recognized absence, material including exams or homework can
be made up by appointment. If an illness prevents you from attending class, handing in work, etc.
you must either bring in a doctors note or in the case of a less severe illness or other excuse notify
me by phone or email before class. Student athletes should submit a complete calendar of excused
absences within the first two weeks of the semester to allow for planning on my part.
Academic Ethics:
Please refer to the 'Student Code of Conduct' in the NMSU Student Handbook Cheating on an
exam will result in a grade of zero for that exam.
Students with Disabilities. If you have or believe you have a disability and would benefit from any
accommodations, you may wish to self-identify by contacting the Services for Students with
Disabilities (SSD) Office located in Room 244 of Corbett Center (phone: 646-6840). If you have
already registered, please make sure that your instructor receives a copy of the accommodation
memorandum from SSD within the first two weeks of classes. It is your responsibility to inform
either your instructor or SSD representative in a timely manner if services/accommodations
provided are not meeting your needs.
If you have a condition which may affect your ability to exit safely from the premises in an
emergency or which may cause an emergency during class, you are encouraged to discuss any
concerns with the instructor and/or Ms. Jane Spinti, SSD Coordinator. Feel free to call Ms. Elva
Telles (EEO/ADA and Employee Relations Director) at 646-3333 with any questions about the
Americans with Disabilities Act (ADA) and/or Section 504 of the Rehabilitation Act of 1973. All
medical information will be treated confidentially