Program Overview

Course Information

Course Description

The course explores the rich and beautiful theory of functions of complex variables. Students will learn the foundational concepts of complex analysis, including analytic functions, contour integration, Cauchy's Integral formula, maximum principle, and open mapping principle. This course will equip students with tools that are both powerful and widely applicable in various fields such as pure mathematics, physics, engineering, and others.

Course Details

• Lectures: Monday-Wednesday-Friday (11:30-12:35)
• X-hours: Tuesdays (12:15-1:05)
• Classroom: Kemeny 108
• Office Hours: Tuesdays (12:15-1:05) and Wednesdays (2:00-3:00) Kemeny 310
• Instructor: Ahmad Reza Haj Saeedi Sadegh
• Prerequisites: Calculus of vector-valued functions (MATH 13) or equivalent
• Textbook: Fundamentals of Complex Analysis with Applications to Engineering and Science, 3 rd Edition, by Saff and Snider

Grading

• Homework: 15
• Discussion: 5
• Midterm Exam 1: 20
• Midterm Exam 2: 20
• Final Exam: 40

Homework

There will be weekly written assignments due on Wednesdays. The lowest homework score will be dropped at the end of the class. Homework must be written neatly and submitted on time.

Discussion

Each week, students will submit a post on the Discussions page prompted by a specific topic. The goal is to foster a weekly conversation inspired by mathematical ideas. Students must write one original post and one reply to another student each week.

Exams

• Midterm 1: Thursday, April 24, 5-7 PM, Kemeny Hall 108
• Midterm 2: Thursday, May 22, 5-7 PM, Kemeny Hall 108
• Final Exam: Sunday, June 8, 3:00 PM, TBA

Timetable

The course timetable includes the following topics:

• M 3/31: Intro. to Complex Numbers (1.1)
• W 4/2: Complex Plane and Polar Coordinate (1.2 & 1.3)
• F 4/4: Polar Coordinates (1.4 & 1.5)
• M 4/7: Domains (1.6 & 1.7)
• W 4/9: Functions of Complex Variables (2.1 & 2.2)
• F 4/11: Analytic Functions and Cauchy-Riemann Equation (2.3 & 2.4)
• M 4/14: Cauchy-Riemann Equations and Harmonic Functions (2.4 & 2.5)
• W 4/16: Julia and Mandelbrot Sets & Elementary Functions (2.7 & 3.1)
• F 4/18: Rational and Exponential Functions (3.1 & 3.2)
• M 4/21: Hyperbolic, and Logarithmic Functions (3.2 & 3.3)
• W 4/23: Complex Powers and Inverse of Trigonometric Functions (3.2 & 3.5)
• F 4/25: Contours (4.1)
• M 4/28: Contour Integral (4.2)
• W 4/30: Path Independence and Cauchy Integral Theorem (4.3 & 4.4)
• F 5/2: Path Independence and Cauchy Integral Theorem (4.3 & 4.4)
• M 5/5: Computations & Cauchy Integral Formula (4.5)
• W 5/7: Bounds for Analytic Functions (4.6)
• F 5/9: Hyperbolic and Logarithmic Functions (3.2 & 3.3)