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Complex Variables
MAT 3730

Welcome to the course pages for Brian Gill's Spring 2008 Complex Variables Course!

Course Handouts

• Syllabus

• History of complex numbers (notes from first day of class)

• Homework #1

• For additional homework assignments, see the homework page.

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

• Mobius transformations revealed: video
• 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 a couple of 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.
• Complex variables toolbox for MATLAB
• 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