Complex Analysis
Autumn 2014
Class notes: part I,
part II,
part III.
These notes will serve
as the text for this course. It is a draft. It will be updated during the
quarter. Please send me any typos or suggestions for improvement that
you might observe.
Books on reserve at the Math Library:
1. Ahlfors, Complex Analysis (If you are going to buy a book, buy this one)
2. Gamelin, Complex Analysis
3. Conway, Functions of One Complex Variable
Other books you might consult:
4. Sarason, Notes on Complex Function Theory.
5. Greene and Krantz, Functions of One Complex Variable
6. Needham, Visual Complex Analysis (a bit too elementary, but
good geometry)
7. Rudin, Real and Complex Analysis
8. Hille, Analytic Function Theory, Vol. 1 and 2
9. Knopp, Theory of Functions (has lots of problems)
FINAL EXAM MONDAY DECEMBER 8, 8:30-10:20 in C-36
Here are two matlab programs to draw "pictures" of analytic functions:
fcn.m
This program has lots of functions which
are commented out using %. To change the function, remove the % in
front of the one you want and put a new % in front of the old
function.
complexfcn.m
This one requires that
you type the function in a box. It displays the domain and range as
well as a 3D version which can be rotated.
If you don't have matlab on your machine and if you have an account on
the math machines, you can use the department
mathapp server. See:
Dept
Wiki page for MathApps RDP
Contact help@math.washington.edu (or 616-9310) if you have trouble. Or use the PC program
below.
Here is a PC program that doesn't require matlab.
complexfcn_pkg.exe.
Download it (by clicking on it).
Then install it (e.g. click on the file on your computer or type the name
of the file including the .exe at a command prompt).
You might need administrator privileges on your computer to do this.
It might take a long time before anything happens
when you first run it. After you have run it once, the next time you
need only run complexfcn.exe, it will be much faster. You can rotate the 3D picture (lower
left) by holding down mb1 and moving it around. You can change the
function in the lower right window (hit Enter after making a change).
You can also iterate the function by clicking on the number at the
bottom (which can be changed). Suggestions for improvement are wanted
(and needed!)
Important results Fall 2014