Homework

Supplementary material Chapter 1 from Visual Complex Analysis

Course aim: This is a first course in complex analysis. The aim is to introduce the student to the classical theory of functions of a single complex variable. The course develops the theory of differential and integral calculus of complex functions, with emphasis on applications.

Course content: In this course we will discuss complex numbers, functions of a single complex variable, elementary functions and their transformations, limits, continuity and derivatives, differentiability and the Cauchy-Riemann equations, analytic functions. contour integration, integral theorems, representation of analytic functions by power series, Taylor and Laurent expansions, zeros and poles, the theory of residues, applications to the evaluation of definite integrals, and, time permitting, conformal mappings. The topics will be interspaced with applications as appropriate.
There is a lot you already know from calculus in one and two variables, some of those tools we will use as we develop calculus in the complex plane. One of the surprising results in this setting is that the notion of differentiability in the complex plane (analyticity) is very strong, if a complex function is analytic in its domain then it is infinitely differentiable and all its derivatives are analytic. Complex analysis is ubiquitous in electrical engineering, in physics, and certainly in mathematics. Complex analysis has been described as "one of the most beautiful as well as useful branches of Mathematics". I hope by the end of the semester you can appreciate its beauty and usefulness! Here is a list of Student Learning Outcomes.

Prerequisites: Math 2531: Calculus III and one course 300-level or above.

Required Textbook:
Complex Variables and Applications by J. W. Brown and R. V. Churchill; McGraw-Hill, 8th edition 2009. ISBN# 978-0-07-305194-2.
We will cover material from Chapters 1-10 in the book as outlined in the syllabus. The syllabus may change since some topics may take longer or shorter than planned, and it will be updated throughout the semester.

Recommended books:
Visual Complex Analysis by Tristan Needhan; Oxford University Press, USA, 1999, ISBN 978-0198534464. Complex analysis is a mature subject and there are many books around including several Dover books at very good prices and the Schaum's Outlines - Complex Analysis which is recommended. It never hurts to read from several sources to broaden your understanding.

Exams: There will be two midterms during weeks 6 and 12. The final exam will be during finals week (May 12-17) as scheduled by UNM.

Homework and Quizes: Homework problems will be assigned weekly, most likely on Thursdays to be uploaded the next Tuesday by 11:59pm in Canvas. Please no late homework! There will be some quizes spread through the semester, to hone your test taking skills, and practice the basics.

Grades: The final grade will be determined by your performance on homeworks and quizes, the two midterm exams and the final. The grading policies will be discussed in class.

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 ( https://arc.unm.edu/) at arcsrvs@unm.edu or by phone at 505-277-3506.

Title IX: UAP 2720 and 2740. Our classroom and university should always be spaces of mutual respect, kindness, and support, without fear of discrimination, harassment, or violence. If you ever need assistance or have concerns about incidents that violate this principle, please access campus support resources. These include confidential services at LoboRESPECT Advocacy Center, the Women's Resource Center, and the LGBTQ Resource Center. The University of New Mexico prohibits discrimination on the basis of sex (including gender, sex stereotyping, gender expression, and gender identity). UNM faculty and graduate teaching assistants are considered "responsible employees." "Responsible employees" must communicate reports of sexual harassment, sexual misconduct and sexual violence to Compliance, Ethics and Equal Opportunity. For more information on the campus policy regarding sexual misconduct, reporting, and reporting for "responsible employees," 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 Spring 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.

Land Acknowledgement Founded in 1889, the University of New Mexico sits on the traditional homelands of the Pueblo of Sandia. The original peoples of New Mexico Pueblo, Navajo, and Apache since time immemorial, have deep connections to the land and have made significant contributions to the broader community statewide. We honor the land itself and those who remain stewards of this land throughout the generations and also acknowledge our committed relationship to Indigenous peoples. We gratefully recognize our history.

Citizenship and/or Immigration Status: All students are welcomed in this class regardless of citizenship, residency, or immigration status. Your professor will respect your privacy if you choose to disclose your status. UNM as an institution has made a core commitment to the success of all our students, including members of our undocumented community. The Administration's welcome is found on our website: http://undocumented.unm.edu/.

Responsible Learning and Academic Honesty: Cheating and plagiarism (academic dishonesty) are often driven by lack of time, desperation, or lack of knowledge about how to identify a source. Communicate with me and ask for help, even at the last minute, rather than risking your academic career by committing academic dishonesty. Academic dishonesty involves claiming that work created by another source is your own original work. It is a Student Code of Conduct violation that can lead to a disciplinary procedure. When you use a resource in work submitted for this class, document how you used it and distinguish clearly between your original work and the material taken from the resource.

Wellness: If you do need to stay home due to illness or are experiencing a wellness challenge, please take advantage of the resources below. You can communicate with me at [crisp @ math . unm . edu] and I can work with you to provide alternatives for course participation and completion. Let me, an advisor, or another UNM staff member know that you need support so that we can connect you to the right resources. UNM is a mask friendly, but not a mask required, community. If you are experiencing COVID-19 symptoms, please do not come to class.
Student Support: Student Health and Counseling (SHAC) at (505) 277-3136. TimelyCare: Free 24/7 virtual care services (medical, emotional support, health coaching, self- care, basic needs support). LoboRESPECT Advocacy Center (505) 277-2911: help with contacting faculty and managing challenges that impact your UNM experience.

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated: 18 January 2025