Math 313 Syllabus

### M ATH 313 - COMPLEX ANALYSISFall 2013

Instructor: Cristina Pereyra
E-mail: crisp @ math . unm . edu
Office: SMLC 320, 277-4613 (best communication by e-mail)
Schedule:TTh 2:00-3:15pm, SMLC 356
Office Hours: Mon 2:30-4pm, Tue 3:30-5pm, or by appointment

Review 1, Study Guide for midterm 1, Solutions to Review 1, Midterm 1 .

Study Guide and Review Problems for midterm 2. Midterm 2 .

Study Guide and Review Problems for midterm 3.

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, 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.
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 not yet approved by the Undergraduate Committee.

Prerequisites: Grade of C (not C-) or better in 264.

Required Textbook:
Fundamentals of complex analysis with applications to Engineering and Science by E. B. Saff and A. D. Snider; Prentice Hall, 3rd ed., 2003, ISBN 0139078746
We will cover most of Chapter 1-7 in the book as outlined in the syllabus. The syllabus may change since some topics may take longer or shorter than planned. Check periodically the webpage for the most current syllabus.

Recommended books:
Visual Complex Analysis by Tristan Needhan; Oxford University Press, USA, 1999, ISBN 978-0198534464. See also the website mantained by the author.
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 . It never hurts to read from several sources to broaden your understanding.

Exams: There will be two midterms during weeks 6 and 12. There will be a third optional exam during review week (you can take it if you missed or want to replace one of the other exams). The final exam is during finals week as scheduled by UNM.

Homework and Quizes: Homework problems will be assigned weekly, most likely on Thursdays to be returned the next Tuesday. 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.

Americans with Disabilities Act: Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.

Last updated: 19 August 2013