Fall 2023 - MATH 322 D100
Complex Variables (3)
Class Number: 2026
Delivery Method: In Person
Course Times + Location:
Sep 6 – Dec 5, 2023: Mon, Wed, Fri, 1:30–2:20 p.m.
Oct 10, 2023: Tue, 1:30–2:20 p.m.
Exam Times + Location:
Dec 18, 2023
Mon, 3:30–6:30 p.m.
1 778 782-3339
1 778 782-4814
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.
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 10%
- Quiz 10%
- Midterm 20%
- Final 60%
*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.
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:
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