# UBC MATH 440 & 508

## Complex Analysis

### Winter 2015, Term 1

**Instructor:** Dr. Michael Lamoureux

**Office:** EOS 4136 (PIMS Offices)

**Phone:** 604-822-0406

**Email:** mikel@pims.math.ca

**Office hours:** Wednesdays 12:00-1:00 in LSK 300B

**Webpage:** www.math.ubc.ca/~mikel/Math440.html

**Text:** Complex Analysis by E. Stein and R. Shakarchi. The textbook is available at the UBC Bookstore, at Amazon, or online at the UBC library.

**Prerequisite:** MATH 300 or equivalent and a score of 68% or higher in MATH 320.

**Course outline:** The UBC course description states the topics covered will include:

- The residue theorem
- The argument principle
- Conformal mapping
- The maximum modulus principle
- Harmonic functions
- Representation of functions by integrals, series, and products
- Other topics at the discretion of the instructor.

From the text, we will review Chapter 2, then cover in depth Chapters 3, 5 and 8. Time permitting, additional topics may be covered. Chapter 1 contains material that the student would have mastered in the prerequisite courses.
**Lectures:** MWF 11:00-12:00 in the Mathematics Building, Room 105.

Lecture notes for September are posted here.

Lecture notes for October are posted here, updated regularly.

Brief notes on Fourier transforms are posted here.

Lecture notes for end of October are posted here.

Lecture notes for November are posted here.

Examples and notes on conformal maps are posted here.

Source code for the Sept lecture notes (in Jupyter) are here.

Source code for the Oct lecture notes are here.

Source code for the Nov lecture notes are here.

Source code for the conformal map examples are here.

Midterm solutions are posted here.

**Grading Policy:** Homework problems will be assigned regularly, distributed in class and posted on the course website. There will be an in-class midterm and a take-home final examination. The final grade will be based on a weighted average of the homework, midterm, and final exam marks, as follows:

- 40% Homework
- 20% Midterm (In class, Friday Oct 23)
- 40% Final exam (Take home, due Dec 17.)

Assignment 1 is due September 21.

Assignment 2 is due October 16.

Assignment 2 Solutions.

Assignment 3 is due November 6.

Assignment 3 Solutions.

Assignment 4 is due November 27. (Note: corrected version is posted.)