Complex Variables

Instructor: Dr. Francis J. Narcowich

Office: 611D Blocker

E-mail: f-narcowich@tamu.edu

Phone: 979-845-7554 (Messages only.)

URL: http://www.math.tamu.edu/~francis.narcowich/

Office Hours: MF 11:30-12:30, W 2:40-3:40, and by appointment, and by appointment.

Catalogue Description: MATH 407. Complex Variables. Fundamental theory of analytic functions, including residues and their applications. Prerequisite: MATH 221 or MATH 251 or MATH 253

Goals: This is a mathematics course. One of the goals is for you to learn to be able to prove theorems concerning complex variables. This will give you a solid foundation is the following topics: the algebra and geometry of complex numbers; various important functions that arise; apply the notion of analyticity, the Cauchy-Riemann equations (note: Riemann is pronounced REEMANN) to solving important applied problems; the theory of residues and its application in evaluating contour integrals and definite integrals; and, if time, conformal mapping.

To achieve these goals, you must diligently do the homework assignments and read the assigned material and notes, and come to class regularly.

Required Texts: Introductory Complex Analysis, by Richard A. Silverman and Shaum's Outline of Complex Variables, by Murray R. Spiegel et al.

Suggested Texts:

• Complex Variables and Applications, Eighth Ed., by James Ward Brown and Ruel V. Churchill, McGraw-Hill Inc., 2009.
• Complex Variables, 2nd ed., by Sthephen D. Fisher. Dover Publications, 1999. (pdf download.)
• Complex Analysis, Theodore W. Gamelin, Spring-Verlag, 2001. A free pdf or free eBook can be downloaded. (You may need your TAMU NetID and password to download the book.) Hard copy is available for about $30.00.

Time & Place: MWF 1:50-2:40 pm, BLOC 160

Grading System & Tests: Your grade will be based on two in-class tests (Monday, 9/25/23 & Friday, 11/17/23), a final exam (Monday, 12/11/23, 3:30-5:30) and homework. Each in-class test will count for 25% of your grade, the homework for 20%, and the final examination will count for the remaining 30%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Class Attendance: Attending class is very important. Roll will be taken most class days. It will be used to decide your grade in borderline cases.

Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, contact me as soon as possible.

Homework: You may consult with each other on homework problem sets, BUT only submit work which is in your own words AND be sure to cite any sources of help (either texts or people). Be aware that usually only some of the problems from an assignment will be graded. Late homework will not be accepted.

Academic Integrity

Copying Course Materials:   "All printed hand-outs and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor."

Aggie Honor Code:   "An Aggie does not lie, cheat, or steal or tolerate those who do."

Authentication of work: "Texas A&M University students are responsible for authenticating all work submitted to an instructor. If asked, students must be able to produce proof that the item submitted is indeed the work of that student. Students must keep appropriate records at all times. The inability to authenticate one’s work, should the instructor request it, may be sufficient grounds to initiate an academic misconduct case (Section 20.1.2.3, Student Rule 20)." AI text generators such as ChatGPT may not be used for any work for this class without explicit permission of the instructor and appropriate attribution.

Americans with Disabilities Act Policy Statement: "The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact the Department of Disability Services.

Title IX and Statement on Limits to Confidentiality

Texas A&M University is committed to fostering a learning environment that is safe and productive for all. University policies and federal and state laws prohibit gender-based discrimination and sexual harassment, including sexual assault, sexual exploitation, domestic violence, dating violence, and stalking.

With the exception of some medical and mental health providers, all university employees (including full and part-time faculty, staff, paid graduate assistants, student workers, etc.) are Mandatory Reporters and must report to the Title IX Office if the employee experiences, observes, or becomes aware of an incident that meets the following conditions (see University Rule 08.01.01.M1):

• The incident is reasonably believed to be discrimination or harassment.
• The incident is alleged to have been committed by or against a person who, at the time of the incident, was (1) a student enrolled at the University or (2) an employee of the University.

Mandatory Reporters must file a report regardless of how the information comes to their attention – including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Although Mandatory Reporters must file a report, in most instances, a person who is subjected to the alleged conduct will be able to control how the report is handled, including whether or not to pursue a formal investigation. The University’s goal is to make sure you are aware of the range of options available to you and to ensure access to the resources you need. Students wishing to discuss concerns in a confidential setting are encouraged to make an appointment with Counseling and Psychological Services (CAPS).

Students wishing to learn more about filing a report, accessing supportive resources, and navigating the Title IX investigation and resolution process should visit the University's Title IX webpage

Texas A&M University recognizes that mental health and wellness are critical factors that influence a student’s academic success and overall wellbeing. Students are encouraged to engage in healthy self-care by utilizing available resources and services on your campus.

Statement on the Family Educational Rights and Privacy Act (FERPA)

FERPA is a federal law designed to protect the privacy of educational records by limiting access to these records, to establish the right of students to inspect and review their educational records and to provide guidelines for the correction of inaccurate and misleading data through informal and formal hearings. Currently enrolled students wishing to withhold any or all directory information items may do so by going to howdy.tamu.edu and clicking on the "Directory Hold Information" link in the Student Records channel on the MyRecord tab. The complete FERPA Notice to Students and the student records policy is available on the Office of the Registrar webpage.

Items that can never be identified as public information are a student’s social security number, citizenship, gender, grades, GPR or class schedule. All efforts will be made in this class to protect your privacy and to ensure confidential treatment of information associated with or generated by your participation in the class.

Directory items include name, UIN, local address, permanent address, email address, local telephone number, permanent telephone number, dates of attendance, program of study (college, major, campus), classification, previous institutions attended, degrees honors and awards received, participation in officially recognized activities and sports, medical residence location and medical residence specialization.

Schedule

Updated 8/20/2023.