Simon Fraser University
Engaging the World

Course Outlines

Fall 2024 - MATH 322 D100

Complex Variables (3)

Class Number: 3937

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2024: Mon, Wed, Fri, 1:30–2:20 p.m.
    Burnaby

    Oct 15, 2024: Tue, 1:30–2:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 9, 2024
    Mon, 12:00–3:00 p.m.
    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:

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.

Grading

  • Participation 35%
  • Midterm 25%
  • Final 40%

NOTES:

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

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

REQUIRED READING:

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

Older editions of the book (from the 6th onward) are fine as a resource, though referece will be made to the 9E.

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website 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

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.