4103  Complex Analysis
Monday, Wednesday, Friday 1:00pm  1:50pm, Lunt 102
Course website:
www.math.northwestern.edu/~tosatti/ca.html
Instructor:
Valentino Tosatti
Email:
tosatti@math.northwestern.edu
Office: Lunt 225
Office hours:
Tuesdays 2:00pm3:00pm
or by appointment
Teaching Assistant:
Sungyoon Cho 
sungyoon@math.northwestern.edu
Course Description:
This course is an introduction to the study of complex analysis in one complex variable. See the syllabus below for more detailed content information.
Textbook:
E.M. Stein, R. Shakarchi  Complex Analysis, Princeton University Press 2003.
Homework:
There will be weekly written assignments which can be found below along with the due date and time. Problem sets are due
on Mondays in class, except as marked below.
Grading and Final:
The class grades will be based on the weekly homework and on the final exam. The final exam date is Monday June 5 from 9:00am to 11:00am in Lunt 102.
Daily Schedule:
This is a tentative syllabus and it is likely to change as the course progresses.
Date 
Topics Covered 
Remarks 
Mar. 27, 29, 31 
Holomorphic functions 
Homework 1 Due April 3 in class 
Apr. 3, 5, 7 
Cauchy's Theorem and Integral Formula, normal families 
Homework 2 Due April 10 in class 
Apr. 10, 12, 14 
Isolated singularities, Residues 
Homework 3 Due April 17 in class 
Apr. 17, 21 
Argument principle, Rouche's Theorem 
No class on Apr. 19
Homework 4 Due April 24 in class 
Apr. 24, 26, 28 
Automorphisms, Schwarz Lemma, Riemann mapping theorem 
Homework 5 Due May 1 in class 
May 1, 3, 5 
Riemann zeta function 
Homework 6 Due May 8 in class 
May 8, 10, 12 
Jensen formula 
Homework 7 Due May 15 in class 
May 15, 17, 19 
Harmonic and subharmonic functions 
Homework 8 Due May 22 in class 
May 22, 24, 26 
Elliptic functions 

Jun. 5 
Final Exam, 9:00am11:00am Lunt 102 
Practice Final Solution of Practice Final 