Complex Variables MATH313 Fall 2026

Please note the following information. The communication of all course information, including the homework, will rely on MS Teams and the associated OneNote. You need to be registered for the course with a @unm.edu email. Any other email will disable features of Microsoft Teams. I will send you by email a link to join the MATH 313 team. Alternatively, you can use the link in the course page on Canvas to request access.

Instructor: Dimiter Vassilev Office: SMLC 326 Email: vassilev@unm.edu

Class Time: 9:30 - 10:45 TR in SMLC 120.

Office Hours: TTh 2:30 pm – 3:30 pm. You can also stop by my office if you have a quick question or you can send me an email to arrange a meeting.

Description: Theory of functions of a complex variable with applications to physical and engineering problems. Although not required, skill in vector analysis will be helpful in taking this course.

Course Materials Access, https://coursematerialsaccess.unm.edu/: Your required digital course materials are available through My Shelf in Canvas. To access them, log in to Canvas on a browser, click Account in the left navigation menu, and select My Shelf. If your course requires physical materials, such as textbooks or lab/studio kits, they can be picked up at the UNM Bookstore on central campus. To simplify access to your course materials, you are automatically enrolled in the Complete option of the UNM Course Materials Access program at a flat rate of $279 per semester, which will appear on your Bursar account. The Complete option includes all required course materials for your Albuquerque campus courses, including any graduate-level courses you may be taking. (Course materials for branch campuses are billed and provided separately.) If you prefer to purchase only selected digital or print course materials, or if you wish to opt out of the program entirely, you may change your enrollment through My Shelf in Canvas. Changes must be made by the Registrar’s Last Day to Drop Without a “W” Grade to receive a 100% tuition refund.

Final Exam: TBD, https://schedule.unm.edu/final-exams/. It is the student's responsibility to inform their instructors before TBD, if they have conflicts with this exam schedule. The Scheduling Office must be notified before TBD. Exams will take place in the rooms in which the individual classes have been meeting.

Attendance and Conduct : Attendance at UNM is mandatory, see policy. Disruptive behavior will result in a student being asked to leave a class meeting, which will be recorded as an unexcused absence and the student will be dropped after 5 unexcused absences. In order to avoid any FERPA violations and privacy issues you are not allowed to record or take photos while in the classroom.

Grades: The final grade will be determined by homework (10%), quizzes (10%), two midterms (50%) and a final exam (30%). Bonus Points: Each submitted lecture is worth .5 of a point. Note that each lecture has to be submitted in a separate page in your "Class Notes" section and the page has to be labeled in the format "Lecture # Date", for example the first lecture in the course should be labeled "Lecture 1 08/18/26". The total of your bonus points will be added to your total (as a bonus!). Although a small curve might be used, 90% , 80% or 70% of the possible maximum points guarantees at least a grade in the ranges of A(A-, A, A+), B (B-, B, B+) or C (C-,C, C+), respectively. Missed Exams: Make-up exams can be arranged for exams missed with a VALID excuse (illness, family emergency, active participation in scholarly or athletic activities), and ONLY if prior notice is given unless there was an emergency.

Accommodations: UNM is committed to providing equitable access to learning opportunities for students with documented disabilities. As your instructor, it is my objective to facilitate an inclusive classroom setting, in which students have full access and opportunity to participate. To engage in a confidential conversation about the process for requesting reasonable accommodations for this class and/or program, please contact Accessibility Resource Center at arcsrvs@unm.edu or 505-277-3506.

UAP 2720 and 2740. Our classroom and university should foster mutual respect, kindness, and support. If you have concerns about discrimination, harassment, or violence, please seek support and report incidents. Find confidential services at LoboRESPECT Advocacy Center, the Women’s Resource Center, and the LGBTQ Resource Center. UNM prohibits discrimination on the basis of sex (including gender, sex stereotyping, gender expression, and gender identity). All instructors are “responsible employees” who must communicate reports of sexual harassment, sexual misconduct and sexual violence to Compliance, Ethics and Equal Opportunity. For more information, please see UAP 2720 and UAP 2740.

Credit-hour statement: This is a three-credit-hour course. Class meets for two 75-minute sessions of direct instruction for fifteen weeks during the Fall 2025 semester. Please plan for a minimum of six hours of out-of-class work (or homework, study, assignment completion, and class preparation) each week.

Homework: Homework is due every Thursday by the beginning of the class. It will be posted in Homework (Web view) and in MS Teams and has to be submitted on-line - see Inserting a printout in the homework starting from Teams for help. I encourage you to work on the homework with your classmates; while not forbidden, using generative AI to complete submitted coursework in this course might interfere with the advantages in learning and understanding that this course offers you. In all cases you are required to write up your own solutions in your own words. To help the grader, please write your solutions neatly using correct grammar and mathematical notation (no points will be given for work that the reader cannot follow). The ten best homework grades will be used in computing the homework score. Please do not turn-in late homework! You should see me as early and as often as necessary if you are having difficulties with the homework problems .

1. The complex plane
2. Functions and limits - the exponential, logarithm, and trigonometric functions
3. Line integrals and Green's theorem.
4. Basic properties of analytic functions - Analytic and harmonic functions; the Cauchy-Riemann equations; Flows, fields, and analytic functions.
5. Power series.
6. Cauchy's theorem and Cauchy's formula - The Cauchy-Goursat theorem; Consequences of Cauchy's formula.
7. Isolated singularities - The residue theorem and its application to the evaluation of definite integrals
8. Analytic functions as mappings
9. The zeros of an analytic function
10. Maximum modulus and mean value
11. Conformal mapping - Linear fractional transformations; Conformal mapping and flows; The Riemann mapping theorem and Schwarz-Christoffel transformations
12. Analytic and harmonic functions in applications - Harmonic functions as solutions to physical problems; Integral representations of harmonic functions; Boundary-value problems; Impulse functions and the Green's function of a domain.