Math 4100 (Complex Analysis) Spring 2023

Instructor: Ching-Li Chai
Office: DRL 4N36, Ext. 8-8469.
Office Hours: MW 11:20-12:00, and by appointments.
Email: chai@math.upenn.edu

Grader: Junyu Ma
Office: DRL 3C5
Office Hours: Mondays 5:00-6:00 pm.
Email:junyuma@sas.upenn.edu

Homework Assignments

General Information

• Lectures: MW 1:45-3:14 am, Moor 212
  First meeting: Wednesday, January 11.
  
  
• Textbook:
  • Robert B. Ash and W. P. Novinger, Complex Variables, second edition, is the "official textbook". The digital version is free. A print version is published by Dover.
  • Lars Ahlfors, Complex Analysis, a classic, is a supplementary text.
  • Two other supplementary texts: Bak/Newman and Lang; see references below.
  
  
• Brief course description: Complex numbers, complex valued functions of a complex variable, the complex derivative, analytic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, residue theory, computation of definite integrals by residues, and elementary conformal mapping. Further topics such as Jensen's formula, the Riemann Mapping Theorem, Weierstrass products, special and harmonic functions might be covered, time permitting.
  
  
• Prerequisites: Math 2400 or its equivalent. Some knowledge of real analysis and writing proofs, such as the coursework in Math 3600/5080.
  
  
• Homework will be assigned every week, posted on the course website. Homework will be assigned on Fridays, and it will be due the following Friday at 4pm, either by uploading a pdf to Canvas, or a hard copy in your TA's mailbox. You will be allowed one week to complete each assignment. Collaboration between students is encouraged, but you must write your own solutions, understand them and give credit to your collaborators. (To be precise, put a list of the students with whom you collaborated on your homework.)
  Late homework will not be accepted. Your two lowest homework scores will be dropped.
  
  
• Exams: There will be three (3) in-class exams.
  
  
• Attendance and Course Notes: It is in your best interest to attend each lecture and take accurate notes. You will be tested on the material as it is covered in class. If you miss a lecture, make sure that you copy from a classmate and review the notes from that day.
  
  
• Evaluation: Your course grade is based on: your level of participation in class (10%), the homework (24%), as well as the in-class exams (22% each).
  
  

Important Dates:

• First day of classes: Wednesday, January 11
  
• MLK Jr. Day: Monday, January 16
  
• First in-class exam: Wednesday, February 15.
  
• Drop period ends: Monday, February 20
  
• Spring break: March 4 (Saturday)-12 (Sunday)
  
• Second in-class exam: Wednesday, March 22
  
• Last day to withdraw: Monday, March 27
  
• Third in-class exam: Wednesday, April 26
  
• Last day of classes: Wednesday, April 26
  

Some References and supplementary texts:

• Joseph Bak and Donald J. Newman, Complex Analysis is another supplementary text.
• Serge Lang, Complex Analysis, 3rd edition, is a standard textbook in complex analysis, comparable to Ahlfors.
• Edmund Landau, Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie, 2nd ed., 1929, 122 pp. G. H. Hardy said it is "probably Landau's most beautiful book".
• G. N. Watson, Complex Integration and Cauchy's Theorem, 1914, 79 pp. This thin book treats basics of complex analysis and include many interesting examples/exercises (in pp. 65-71).
• Whittaker and Watson, A Course of Modern Analysis, is a timeless classic. Part I contains basic complex analysis (and more), while Part II treats special functions.