Fall 2013

** Lectures: ** MWF 2:00PM-2:50PM at Thack 704

** Office hours (subject to change): **
MW 3:00-3:50 or by appointment,
held at Thackeray Hall 610.

** Content and Prerequisites: **
This course is an introduction to Complex Analysis.

** Textbook: ** Complex Analysis, (Graduate Texts in Mathematics);
by Serge Lang.

** Other reading resources: **
Complex Analysis; by Ahlfors

Harmonic Function Theory; by Axler, Bourdon an Ramey

** A tentative syllabus:**

Complex number system, Cauchy-Riemann conditions, harmonic functions and
harmonic conjugates, one variable analytic functions and their properties,
special analytic functions including linear fractional transformations,
roots, exponential, Log, trigonometric and hyperbolic functions of a complex
variable; Complex integration and line integrals, Cauchy's theorem, Cauchy
representation, conformal mapping, Taylor and Laurent Series expansions; the
calculus of residues and various applications; conformal mappings, Schwartz
lemma; Riemann mapping theorem and analytic continuation theorem.
We will also cover some topics in elementary harmonic analysis (Fourier
Transforms and Fourier series) and -if time permits- some harmonic function
theory (study of harmonic functions in higher dimensions)

** Grading: **
Homework (10%), 2 Midterms (25% each), Final Exam (40%).

** Homework:** They will appear weakly on this website and will be collected
on Mondays in class. ** They will NOT be returned to you so make a copy for
yourself before handing in your homework. **

Homework 1.

Homework 2.

Homework 3.

Homework 4.

Homework 5.

Homework 6.

Homework 7.

** Midterm Policy: ** There will be no make up midterm exams. If you miss
the midterm exam for a *documented* serious medical reason or similar tragedy,
your grade on it will be prorated on your other exam and homework grade. No Incompletes
will be accorded except in extreme circumstances. As for auditing
the course, you need to talk with me about it at the latest by the end of September.

** Midterm exams: ** They will be held in class on ** Friday Feb. 14 ** and ** Friday Mar. 28**.
** They will mostly consist of theorems of class and problems of the homework. **

** Final exam: ** Will be held on the last day of classes during the
undergraduate exam week. The exact date will be announced.