Math 313 - Complex Variables, Fall 2021

Time and Location:	Tue 2:00 - 3:15 pm, Zoom Discussions & Lectures Thur 2:00 - 3:15 pm, typically in DSH 227
Office Hours:	Wed 4:10 - 5:00 pm in Zoom; also by email; also ask questions in class; also request other Zoom time in case of conflicts
Professor Info:	Anna Skripka, skripka [at] math [dot] unm [dot] edu

Description: Math 313 is the first course in complex analysis. The aim of this course is to introduce students to the classical theory of functions of a single complex variable, differential and integral calculus of complex functions. In this course we will discuss complex numbers, functions of a single complex variable, elementary functions and their transformations, limits, continuity, differentiability and the Cauchy-Riemann equations, 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 mapping. The topics will be interspaced with applications as appropriate.
Course goals and basic study guide are posted on Learn
Prerequisite: Calculus III and one 300-level or 400-level Math course

Course Resources: zoom link, lecture notes, handouts, goals, assignments, zoom recordings are to be posted on Learn. The completed assignments are to be submitted on Learn; the grades and feedback are to be posted on Learn.
Tutoring: CAPS
Textbook: Fundamentals of complex analysis with applications, by E.B. Saff and A.D. Snider, Prentice Hall, 3rd ed., 2003, ISBN-10: 0139078746 or 0134689488
Extra examples and exercises: Schaum's outlines. Complex variables, by M. Spiegel, S. Lipschutz, J. Schiller, D. Spellman, McGraw-Hill, 2nd ed., 2009, ISBN 0071615695
Supplementary textbooks:
Visual Complex Analysis, by T. Needham, Oxford University Press, 1999, ISBN 0198534469
A First Course in Complex Analysis, by M.Beck, G.Marchesi, D.Pixton, L.Sabalka
Some video lectures on complex analysis: Snider, Glesser, Schroder, Viacci, Ali, Vieira
Some video courses on related topics: Proof Writing, MIT Calculus: 18.005, 18.006, 18.007, 18.008
Online calculators: Sage/Octave, Octave, Matlab
Free PDF scanners: CamScanner, TinyScanner

Grades: 5% for polls (answers to questions asked during zoom meetings), 35% for homework+quiz, 60% for three exams (two midterm and one final).
Policies: You are expected to attend every classroom meeting and come prepared by reading the book on new material ahead of lectures as well as reading lectures and doing exercises on old material.
The homework is to be submitted on UNMLearn as a single PDF file. Please make sure that the files you submit are legible. Your work will be graded on the clarity, completeness, correctness of your reasoning and presentation. On the homework assignments you are allowed to work in groups, but you must write up your own solutions in your own words. Submitting solutions obtained from third parties, including the internet, is strictly prohibited.
NO LATE ASSIGNMENT WILL BE ACCEPTED, but two lowest scores on homework/quizzes will be dropped to accommodate for unavoidable circumstances such as emergencies, illnesses, official UNM function. (You can start working on the assignment as soon as it is posted without waiting for the day it is due.) A replacement by a final exam score or make-up exam will be given for a missed midterm exam only in case of a documented absence prescribed by the university (family emergency, serious medical problem, official UNM function). All objections to grades should be made within one week since the assignments are graded.

Tentative Schedule (to be updated at the end of each week)

Week	Class dates	Book sections	Topics
1	Aug 24, 26	1.1, 1.2, 1.3; Schaum p. 9-32	Complex numbers. Polar form.
2	Aug 31, Sep 2	1.4, 1.5; home reading: 1.6	Complex exponential. Roots. Planar sets.
3	Sep 7, 9 Drop with no grade: Sep 10	2.1, 2.2; Schaum p. 62-67	Functions of complex variables. Limits and continuity.
4	Sep 14, 16	2.3, 2.4, 2.5; Schaum p. 85-96	Analytic functions. Cauchy-Riemann equations. Harmonic functions.
5	Sep 21, 23	3.1, 3.2, 3.3	Polynomials and rational functions. Exponential, trigonometric, and logarithmic functions.
6	Sep 28, 30	3.4, 3.5	Application: boundary value problems. Complex powers & inverse trigonometric functions.
7	Oct 5, 7 (Exam 1)	covered material of 1.1-3.3	Review.
8	Oct 12	4.1, 4.2, 4.3	Complex integration.
9	Oct 19, 21	4.4, 4.5, 4.6; home reading: 5.1; Schaum p. 184-186	Cauchy's integral theorem. Cauchy's integral formula. Bounds for analytic functions.
10	Oct 26, 28	5.2, 5.3, 5.5; Schaum p. 188-190	Review of series. Power, Taylor, and Laurent Series.
11	Nov 2, 4	5.6, 5.7, 6.7	Laurent Series. Classification of singularities. Argument principle and Rouche's theorem.
12	Nov 9, 11 Withdrawal deadline: Nov 12	6.1, 6.2, 6.3, 6.4; Schaum p. 214-226	Residue theorem and its applications. Trigonometric integrals. Improper integrals.
13	Nov 16, 18 (Exam 2)	3.4,3.5,4.1-4.6,5.1-5.7,6.7	Review.
14	Nov 23	6.5, 6.6	Indented contours. Integrals involving multiple-valued functions.
15	Nov 30, Dec 2	7.1, 7.2, 7.3	Conformal mappings and their applications. Möbius transformations and boundary value problems.
16	Dec 7, 9	7.4, 7.6	Boundary value problems. Review.
17	Dec 14 (Tuesday), 10:00 am - noon Final Exam

Academic Integrity: Each student is expected to maintain the highest standards of honesty and integrity in academic and professional matters. The University reserves the right to take disciplinary action, including dismissal, against any student who is found responsible for academic dishonesty. Any student who has been judged to have engaged in academic dishonesty in course work may receive a reduced or failing grade for the work in question and/or for the course. Academic dishonesty includes, but is not limited to, dishonesty on quizzes, tests or assignments; claiming credit for work not done or done by others (plagiarism); and hindering the academic work of other students.
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American Disabilities Act: In accordance with University Policy 2310 and the American Disabilities Act (ADA), reasonable academic accommodations may be made for any qualified student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor's attention, as the instructor is not legally permitted to inquire. The student is responsible for demonstrating the need for an academic adjustment by providing Student Services with complete and appropriate current documentation that establishes the disability, and the need for and appropriateness of the requested adjustment(s). However, students with disabilities are still required to adhere to all University policies, including policies concerning conduct and performance. Contact Accessibility Resource Center at 505-277-3506 or arcsrvs@unm.edu for additional information.
UNM Requirement on Masking in Indoor Spaces: All students, staff, and instructors are required to wear face masks in indoor classes, labs, studios and meetings on UNM campuses, see masking requirement. Students who do not wear a mask indoors on UNM campuses can expect to be asked to leave the classroom and to be dropped from a class if failure to wear a mask occurs more than once in that class.
UNM Administrative Mandate on Required Vaccinations: All students, staff, and instructors are required by UNM Administrative Mandate on Required Vaccinations to be fully vaccinated for COVID-19 as soon as possible, but no later than September 30, 2021, and must provide proof of vaccination or of a UNM validated limited exemption or exemption no later than September 30, 2021 to the UNM vaccination verification site. Students seeking medical exemption from the vaccination policy must submit a request to the UNM verification site for review by the UNM Accessibility Resource Center. Students seeking religious exemption from the vaccination policy must submit a request for reasonable accommodation to the UNM verification site for review by the Compliance, Ethics, and Equal Opportunity Office. For further information on the requirement and on limited exemptions and exemptions, see the UNM Administrative Mandate on Required Vaccinations.
Disclaimer: It is your responsibility to know and understand the course policies. The professor reserves the right to change this syllabus. This might become necessary in the current circumstances, when rules that are beyond professor's control change frequently. An up-to-date syllabus is posted on this webpage and on UNMLearn.

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