Fall 2013

** Homework**,
Supplementary **reading**,
** Quizes**,

** 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.

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

Last updated: 19 August 2013