MAT 3730
Complex Variables
Spring 2010
 

Spring 2010 Office Hours:
     MWF 10:30-11:30
     or any time my door is open
     or by appointment

I will NOT be at SPU at all on Tuesday or Thursday due
to my research work at the University of Washington.

Course Information:

• Dr. Gill's Schedule

• Syllabus
• Homework Assignments
• Handouts from class
• Some useful links on the Internet

Classic Newton fractal from teamfresh on Vimeo.

Handouts from Class

• Syllabus
• History of Complex Numbers (notes from 1st day of class)
• Homework assignment #1
• A Definition for the Complex Numbers

Some useful links on the internet

Software for graphing and visualizing complex functions as mappings:

In order to help to visualize complex functions as mappings of the plane, we will frequently make use of computers.  Feel free to experiment with different programs listed in the links below

• Möebius transformations revealed: video by Douglas Arnold & Jonathan Rogness
• Bombelli: a java complex function viewer:  a simple java applet that you can use on any computer (but it has a few problems -- I've managed to crash it several times...).
• Table of conformal mappings using continuous coloring: very nice static graphs for a selected list of functions, but you can't change anything.
• Graphics for complex analysis (animated GIFs illustrating many mappings)  Also available in a java version.  Nice animations.  Flash animations also
• Complex variables toolbox for MATLAB BROKEN
• Holo: a complex mapping program in MATLAB.  Holo is a Matlab m-file, so you will need to work on a campus computer that has Matlab installed.  Go to the Holo webpage and download the file.  I suggest saving the file to your Netstore drive.  Then run Matlab.  Assuming that you have the file on Netstore, when Matlab starts up, type

  addpath N:\

  and then hit enter.  This tells Matlab to look in Netstore for files.  Then type Holo and the program will start.  From there it is very self-explanatory how to use the program.

Articles about complex function visualization:

• Frank Farris: Visualizing complex-valued functions in the plane
• Hans Lundmark: Visualizing complex analytic functions using domain coloring
• Tom Banchoff and David Cervone: Understanding Complex Function Graphs

Other Useful Links

• Textbook website for Complex Analysis for Mathematics and Engineering
• The Visual Complex Analysis textbook web site
• Resources for teaching complex analysis
• Julia and Mandelbrot Set Explorer