Fall 2021 - MATH 322 D100

Complex Variables (3)

Class Number: 1217

Delivery Method: Remote


  • Course Times + Location:

    Mo, We, Fr 1:30 PM – 2:20 PM

  • Exam Times + Location:

    Dec 9, 2021
    8:30 AM – 11:30 AM

  • Prerequisites:

    MATH 251 with a minimum grade of C-.



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.


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%


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


  • Access to internet reliable enough to upload and download exam materials
  • Ability to scan documents (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)



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.

Registrar Notes:


SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html


Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place.  Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.