Math 4555 - Complex Variables

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

Instructor: Alina Marian, a.marian@neu.edu, office in 557 Lake Hall.

Lectures: Mon, Tues, Wed, Thurs 1:30-3:10 pm, Kariotis Hall, Room 110.

Office hours: Tuesday 3:30-4:30 pm and Wednesday 5-6 pm.

Math tutoring hours: Mon, Tues, Wed 11am-6pm, Thurs 11am-5pm, all in 540B Nightingale Hall.

Textbook: John Mathews and Russell Howell - Complex Analysis for Mathematics and Engineering, sixth edition.

Prerequisites: Familiarity with multivariable calculus at the level of Math 2321 (Calc 3).

Exams: There will be one midterm exam and one final exam. Occasional quizzes, to be weighed under "Homework", are not excluded.

Final Grades: Homework (25 percent), Midterm (25 percent), Final Exam (50 percent).

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

• Homework 1 (due May 9): Section 1.2 - exercises 2, 5; Section 1.3 - exercises 1, 3, 6, 10; Section 1.4 - exercises 3, 5; Section 1.5 - exercises 1, 5.
• Homework 2 (due May 16): Section 1.5 - exercises 8, 9; Section 2.1 - exercises 3, 10; Section 2.5 - exercises 1, 2, 3, 4, 6, 14; Section 3.1 - exercises 1, 2, 3, 11; Section 3.2 - exercises 1, 2, 3. Solutions
• Homework 3 (due May 23): Section 3.2 - exercises 7, 9, 15; Section 3.3 - exercises 1, 2, 5; Section 5.1 - exercises 4, 5, 6, 7, 8, 9, 13; Section 5.2 - exercises 1, 3; Section 5.3 - exercises 1, 2; Section 5.4 - exercises 1, 2, 5, 6; Section 4.3 - exercise 4. Solutions
• Homework 4 (due May 30): Section 4.3 - exercises 5; Section 4.4 - exercises 3, 6; Section 6.2 - exercises 7 b,c, 11, 13, 14. Solutions
• Homework 5 (due June 6): Section 6.3 - exercises 1, 2, 3, 4, 5, 6, 7, 9, 10. Solutions
• Homework 6 (due June 13): Section 6.5 - exercises 2, 4, 6, 8, 12, 16; Section 6.6 - exercises 1, 6, 10; Section 7.1 - exercises 3, 4; Section 7.2 - exercises 3ab, 4ab, 5; Section 7.3 - exercises 4, 5, 6. Solutions
• Homework 7 (due June 20): Section 7.4 - exercises 1dhk, 2bh, 3acdg, 5, 9; Section 8.1 - exercises 1adei, 3aefg, 8; Section 8.2 - exercises 4, 8, 14; Section 8.3 - exercises 6, 10; Section 8.4 - exercises 4, 10, 11; Section 8.6 - exercises 8, 14. Solutions