Math 106 - Complex Analysis

This course provides an introduction to complex analysis. We will cover complex numbers, holomorphic functions, Cauchy's integral formula, Taylor expansions, meromorphic functions, Laurent expansions, residues and applications.

Instructor: Dragos Oprea, oprea "at", Room 382D (2nd floor).

Lectures: Tuesday, Thursday, 11am-12:15pm, Room 381T.

Office hours: Monday 2-4 and 6:30-7:30pm.

Course Assistant: Penka Georgieva, penkag "at", Room 381H.

Office hours: Mon 4-6:30, Thr 2:30-4, Fri 3:10-5:10pm.

Textbook: James Brown and Ruel Churchill - Complex Variables and Applications.

There are two copies of the textbook on reserve in the Math library, they circulate for a couple of hours. You can also buy cheaper copies from the internet (check the usual websites).

Prerequisites: Familiarity with multivariable calculus at the level of Math 52 will be assumed.


Problem Sets: There will be weekly problem sets, usually due on Tuesday in class. The problem sets will be posted online. Group work is encouraged, but you have to hand in your own write up of the homework problems.

Final Grades:

Important dates:

Tentative syllabus: PDF

Lecture Summaries

Homework 1

Due Tuesday, Oct 3, in class. Solve the following problems from the textbook:

Solutions (written by Penka): Page 1, Page 2, Page 3, Page 4, Page 5, Page 6.

Solutions 2: PDF

Solutions 3: PDF

Midterm 1: PDF

Practice Midterm: PDF

Solutions to Homework 3B: PDF

Solutions to Homework 4: PDF

Solutions to Homework 5: PDF

Midterm 2 due Friday, Nov 17, 4:30pm in my office. PDF

Solutions to Midterm 2: PDF

Solutions to Homework 6: PDF

Practice Final: PDF

Solutions: Page 1, Page 2, Page 3, Page 4, Page 5.

Final Exam: PDF