# Fall 2021 - MATH 322 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 1:30 PM – 2:20 PM
REMOTE LEARNING, Burnaby

• #### Exam Times + Location:

Dec 9, 2021
8:30 AM – 11:30 AM
REMOTE LEARNING, Burnaby

• #### Prerequisites:

MATH 251 with a minimum grade of C-.

## Description

#### CALENDAR DESCRIPTION:

Functions of a complex variable, differentiability, contour integrals, Cauchy's theorem, Taylor and Laurent expansions, method of residues. Students with credit for MATH 424 may not take this course for further credit. Quantitative.

#### COURSE DETAILS:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Complex numbers arise when the familiar arithmetic of the real number system is supplemented by the square root of minus one.  This course will be an introduction to complex analysis, which is a specialized calculus for functions that depend on a complex-valued variable.  At the heart of complex analysis is the class of "analytic" functions, which are defined by their differentiability properties.  The goal of this course is to understand the many amazing properties with which these complex-valued functions are endowed.

The highlights of the course will be: discussions and proofs of the elementary theorems of analytic function theory; series representations of functions; evaluation of complex contour integrals; and geometrical properties of conformal mappings.

The overlap between complex variable theory with other branches of mathematics includes:  geometry, topology, number theory, combinatorics, computer graphics and Fourier analysis. Various applications of complex analysis from these areas will be discussed throughout the course.

#### Course Delivery

•  Lecture: synchronous- lectures will be held at fixed times, on-line
•  Midterm(s): synchronous; date: TBA
•  Final exam: synchronous; date: TBA

• Assignments 50%
• Midterms (2) 20%
• Final Exam 30%

#### NOTES:

*Note: A student MUST obtain a passing grade on the final exam in order to pass the course*

#### REQUIREMENTS:

• Ability to scan documents (phone app acceptable)

## Materials

#### MATERIALS + SUPPLIES:

REQUIRED: Math 322 will use the Maple TA online assessment that connects through their Canvas class page. There is an access charge through a Maplesoft account (around \$25) that students must pay if they enroll in the course. Instructions on how to pay the charge will be explained in class at the start of the semester.

Complex Variables and Applications
Brown; Churchill; Churchill, Ruel V.; Brown, James Ward
9/E, McGraw-Hill
ISBN: 9780073383170

Other text materials will be supplied. Older editions of the book (from the 6th onward) are fine as a resource, though references in the lecture will be to this edition.