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Math 5030/6030: Complex Variables with Applications I

2021 Fall, Auburn University

Contacts

Lecture Instructor Dr. Le Chen lzc0090@auburn.edu
Class Time and Room TR, 11:00 AM -- 12:15 PM TBA
Office hours TR, 14:00 PM -- 14:50 AM, PARKR 203, or via appointment/Zoom upon request

Course description

Complex analysis is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, probability. It has also widely used in engineering and physical sciences. In addition to being mathematically elegant, complex analysis provides a powerful tool for solving problems that are either very difficult or virtually impossible to solve in other ways.

This course is the first course of the two-semester sequential courses -- Math 5030/6030 and Math 5040/6040. In Math 5030/6030 -- Complex Variables with Applications I, we will cover basics on complex numbers, analytic functions, Laurent series, residue calculus, contour integration, etc. In Math 5040/6040 -- Complex Variables with Applications II, we will cover comformal mappings, asymptotics evaluations of the integrals and Riemann-Hilbert problems.

Textbook

Coverage

This course will cover topics such as complex numbers, analytic functions, Caucy integral, Laurent series, residue calculus, contour integrations, etc. We will follow mostly most parts of the first four chapters of the text book:

Prerequisite

Students obligations and tips

This is a demanding course and it requires a great deal of work from your side. In order to successfully master the material and complete the course, you are expected to


Note: The syllabus was created in April 2022, and it is subject to changes during the semester.


Homework

Test and exam

Attendance

Assessment


Tentative schedule


Gradescope


Honor code

Accessibility

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility to determine how you could improve your learning as well. You can register and make a request for services from the Office of Accessibility. In this case, please do inform me of such requests. See the following link for more information:

Harassment and Discrimination


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discrimination and harassment and to fostering a nurturing and vibrant community founded upon the
fundamental dignity and worth of all its members. Auburn University prohibits harassment of its
students and employees based on protected classes and works to eliminate prohibited behavior from
its academics and employment through corrective measures and education.

The Office of AA/EEO oversees compliance with the Policy Prohibiting Harassment of Students, the
Policy Prohibiting Harassment of Employees, and the Policy on Sexual and Gender-Based Harassment and
Other Forms of Interpersonal Violence.

Protected classes are race, color, sex (which includes sexual orientation, gender identity, and
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Auburn University also prohibits retaliation against any individual for opposing a practice he/she
reasonably believed to be discriminatory; for filing an internal or external complaint, grievance,
or charge; or for participating in any investigation or proceeding, in accordance with Auburn
University's policies.

Acknowledgement


© Le Chen, Math 5030/6030 -- Fall 2022, Auburn.