Math 421, Theory of Functions of a Complex Variable I

Short Description
We assume. familiarity with the basic notions of set theory and topology. For the latter, the material. covered in Math 417-418 is more than sufficient. …

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Content
Math 421, Theory of Functions
of a Complex Variable I
Fall 2003
Instructor: David Wright
Office: Room 114, Cupples I
Phone: 935-6781 (office)
E-mail: wright@einstein.wustl.edu
Office Hours: MWF 1:00-2:00
Class Meetings: MWF 10:00-11:00 in Cupples I, Rm 216
Text: Complex Analysis (Third Edition), by Lars Ahlfors
Prerequisites: Mastery of undergraduate differential and integral calculus. The
student should be completely comfortable with theorem and proof. We assume
familiarity with the basic notions of set theory and topology. For the latter, the material
covered in Math 417-418 is more than sufficient.
Content: This course is a study of the basic theorems and methods of modern
complex analysis. It will present a systematic introduction to the fields of complex
numbers, holomorphic and meromorphic functions, complex differentiation and
integration, harmonic functions, linear fractional transformations, elementary functions
such as the logarithm and exponential, power series and Laurant series, classification of
zeros and singularities, residues, simply connected domains, and basic results such as
Liouville’s Theorem, Cauchy’s Theorem, Runge’s Theorem, the Residue Theorem, and
Rouche’s Theorem.
Goals: 1. Cover the concepts and theorems of complex analysis which every
mathematician should know.
2. Prepare…