MATH 485/585 - Intro to Complex Variables

Last updated on Jan 26, 2023 current
Photo by Toa Heftiba on Unsplash

Syllabus

Course Meeting Times

Tuesday and Thursday 9:30AM - 10:45AM; Gordon Palmer Hall 151

Prerequisites

C- or higher in MATH 227 or C- or higher in MATH 247

Description

Some basic notions in complex analysis. Topics include analytic functions, complex integration, infinite series, contour integration, and conformal mappings.

Textbook

Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (3rd Edition) by E. B. Saff and A. D. Snider. Pearson. ISBN 978-0139078743

Quizzes and Exams

  1. Homework Assignments: Suggested homework problems will be given after each section, but will not be graded. Students are encouraged to work on the suggested problems with others in the class and to ask questions about the problems during office hours.

  2. Quizzes: Short weekly quizzes will be administered to the class every Thursday. These quizzes will be based on the examples discussed in class and the suggested homework assignments from the material covered the preceding week. These quizzes are meant to keep students faithful to the material on a regular basis. Your three lowest quiz scores will be dropped when final grades are computed. All quizzes are to be weighted the same.

  3. Exams: There will be three take-home exams during the semester and a comprehensive final exam. Mid-term exams will contain a blend of theoretical and calculation intensive questions and you are encouraged to work on these problems together. You may be asked to prove a general statement, compute a certain integral or derivative, or provide an example of a function that satisfies or fails a theorem. You will be given each midterm one week prior to its due date. The final exam will be closed book and held during the scheduled final exam period for our class (listed below). The final will incorporate questions from both the quizzes and the three midterms.

  4. (Tentative) Exam Due Dates:

Exam 1: Thursday, 02/16

Exam 2: Thursday, 03/23

Exam 3: Thursday, 04/20

Final: Thursday, 05/05 8:00 am - 10:00 am (Comprehensive)

  1. Exam Policies: The final exam has been scheduled to be written in GP 151.

Collaboration

Grading

The University of Alabama
Brandon Sweeting
Brandon Sweeting
NSF MPS-Ascend Postdoctoral Research Fellow, Mathematics

My current research interests are in harmonic analysis, specifically weighted norm inequalities for singular integral operators and Riesz potentials in both the scalar and matrix setting.