Complex Function Theory
Tuesday - Thursday 12:30-1:45 PM
Lippitt Hall 201

Instructor    Araceli Bonifant  
Office: Lippitt Hall 202 G
Phone: 874-4394

Office Hours:

Book: A Course in Complex Analysis by Saeed Zakeri (not published yet)

Course Description. An introduction to classical complex analysis with some emphasis on the geometric aspects of function theory in one variable.

Prerequisites. MTH 435-MTH 436 or MTH 437-MTH438 or permission of instructor.

Tentative List of Topics:

This syllabus will be modified according to the needs of the class

  • Definition of a holomorphic function, the Cauchy-Riemann equations
  • Complex integration, local Cauchy's theorem, Liouville's theorem, Morera's theorem
  • Power series representation of holomorphic functions
  • Local normal forms, the open mapping theorem
  • The maximum modulus principle

  • Covering properties of exp, lifting criteria
  • Winding numbers, cycles and homology
  • Homology version of Cauchy's theorem

  • Zeros, poles, and essential singularities
  • The Riemann sphere, meromorphic functions, Laurent series
  • Residue theorem, the argument principle, Rouche's theorem

  • Compact convergence, the Arzela-Ascoli theorem
  • Theorems of Weierstrass and Hurwitz
  • Normal families, theorems of Montel and Marty

  • If time permits, I would like to cover:

  • Elementary properties of the Moebius group
  • Classical version of the Schwarz lemma
  • Automorphism groups of the disk, plane, and sphere
  • Geometry in the hyperbolic plane, Pick's theorem

  • Recommended Reading:
    Complex Analysis - Lars V. Alfors, McGraw-Hill, 3rd edition, 1979
    Complex Analysis - Serge Lang, Springer, 4th edition,1999

    Homework will be posted here

    Evaluation Policy:

  • Homework              25%
  • Midterm                  35 %    Thursday March 5th
  • Final Exam              40 %     Tuesday May 5th,        11:30 AM - 2:30 PM
  • Standards of behaviour: Students are responsible for being familiar with and adhering to the published "Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook. If you must come in late, please do not disrupt the class. Please turn off all cell phones, pagers, or any electronic devices.

    Special Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.