Introduction
On one hand, complex numbers afford a coherent explanation for diverse
observations from areas such as geometry and calculus.
On the other hand, there are new phenomena, both beautiful and important, which arise
only in studying functions of a complex variable.
This course is a foundation in complex analysis. We will roughly
cover the first seven chapters of the textbook. Broadly, the topics are:
- Complex numbers and the complex plane
- The complex derivative and analytic functions
- Complex integrals
- Series representations of functions
- Residues and poles
- Geometry of the complex plane
Prerequisites
I assume you have taken and understood M261, multivariable calculus, and the courses
leading up to it.
Logistics
- Textbook: J. Brown and R. Churchill, Complex Variables and
Applications, seventh edition, McGraw-Hill, 2004.
- MWF 8:00am - 8:50 am, ENGRG E206.
Requirements and other expectations
As in any other 400-level class, you will need to work both diligently
and creatively.
- Homework and class participation -- 35% The work you do in
class and for homework is by far the most important
component of the course. Homework will be assigned weekly,
and is due at the beginning of class on Fridays.
No late homework will ever be accepted. Your work must be
neat, and pages stapled, in order to be graded.
- Midterm -- 30% There will be a midterm on Friday, October
6, in class.
- Final -- 35% The final is on Tuesday, December 12, from
7:00AM to 9:00AM.
If you miss an exam without a note from a doctor or dean you will receive
a zero for that exam. You must take the exam during the scheduled
time; no make-ups will be given. You must pass the final in
order to pass the course.
Help
This is challenging material; it's fully expected
that sometimes you'll need a little help. Unless specifically
noted, you're encouraged to work with other students in the class.
(Please observe that the work you actually turn in must be your own.)
Questions directed to j.achter@colostate.edu
will be answered swiftly.
However, some questions are best answered in person. You
can come by office hours or schedule an appointment.
This page is available at http://www.math.colostate.edu/~achter/419