# Math 301

## Applied Complex Analysis

Instructor: Omer Angel
email: angel@math.ubc.ca (please specify "MATH 100" in the subject).
Location: Tu,Th 11:00-12:00 at LSK 460.
Office hours: Math Annex 1210, Monday after class, Friday 9:00-9:50 or by appointment.

### News

Midterm information: Midterm 1 will cover singularities and residue theory, Cauchy's residue theory and it's application for computing integrals over the reals, multi-valued functions, branch points and branches, and integrals involving multi-valued functions. The relevant sections are 6.1 to 6.6, and 3.3 for some multi-valued functions. Sample midterm hints actual Midterm solutions

Midterm 2 will cover conformal maps: sections 7.1,7.2,7.3,7.4. Older material may be needed, but will not be central. Sample midterm hints actual Midterm solutions

Additional notes on Branch points and branch cuts.

due date problems template solutions
Not due Homework 0 template PDF LaTeX
Jan. 15 Homework 1 template PDF LaTeX
Jan. 22 Homework 2 template PDF LaTeX
Jan. 29 Homework 3 template PDF LaTeX
Feb. 5 Homework 4 template PDF LaTeX
Not due Homework 5 template PDF LaTeX
Feb. 26 Homework 6 template PDF LaTeX
Mar. 5 Homework 7 template PDF LaTeX
Mar. 14 Homework 8 template PDF LaTeX
Not due Homework 9 template PDF LaTeX
Mar. 26 Homework 10 template PDF LaTeX
Apr. 2 Homework 11 template PDF LaTeX
not due Homework 12 template PDF LaTeX

Additional example for section 6.2: Integration of forms involving trigonometric functions.

### Course Outline

• Complex integration - 1 week
• Multivalued functions, branch points and branch cuts - 1.5 weeks
• Integrals involving multivalued functions - 1.5 weeks
• Conformal mappings and applications - 3 weeks
• Poles and zeros of complex functions - 1 week
• Laplace transform - 2 weeks
• Fourier analysis - 2 weeks

### Textbook

Fundamentals of Complex Analysis by Saff and Snider (Third Edition). We may cover some material not in the textbook.

### Evaluation:

The final mark will be based on homework (15%), two mid-terms (35%) and the final exam (50%).

Homework: Weekly assignments will be given. These are due at the beginning of class on the due date, normally each Wed. Answers will be posted online on the due date, and late assignments will not be accepted. The single lowest assignment will be ignored. All submitted assignments must be typeset (see some suggestions and tips). Due dates for assignments: Jan. 15,22,29; Feb. 5,26; Mar. 5,12,26; Apr. 2.

Mid-terms: Mid-terms will take place during the regularly scheduled class on Wednesday, February 12 and March 19.

Midterm 1 will cover singularities and residue theory, Cauchy's residue theory and it's application for computing integrals over the reals, multi-valued functions, branch points and branches, and integrals involving multi-valued functions. The relevant sections are 6.1 to 6.6, and 3.3 for some multi-valued functions. Sample midterm

Final Examination: will take place on April 30, at 12:00 (the last possible date).

Missed mid-terms and assignments will normally receive a zero grade. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must be notified as soon as possible (preferably before the test), and presented with a doctor's note immediately upon the student's return to UBC. When an exception is granted for a missed test, there is no make-up test, and the final exam mark will be used.