Fall 2022 - MATH 322 D100
Complex Variables (3)
Class Number: 4117
Delivery Method: In Person
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.
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.
- 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*
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 ofmarks.
Please pay careful attention to the options discussed in class at the beginning of the semester.
This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).
Complex Variables and Applications
Brown; Churchill; Churchill, Ruel V.; Brown, James Ward
9/E, McGraw-Hill ISBN: 9780073383170
Purchaing this text is not required. A number of different online resources will be consulted. Other text materials will be supplied.
Older editions of the book (from the 6th onward) are fine as a resource, though referece will be made to the 9E.
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
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