Here are some resources that you can use to help you succeed in the course (and may help youy with course project ideas).

There are some great webpages on applying complex variables to explain the Mandelbrot and Julia sets.

The first is Mathworld's explanation of  the Mandelbrot Set and of the Julia Set

The second is Professor David Joyce's wonderful Mandelbrot Explorer, complete with a wonderful explanation section.

The third is John Hoggard's incredibly well-written site which explains Fractal Geometry with a link to some beautiful pictures of the Mandelbrot and Julia sets.

Here is another very clear description of the Mandelbrot set.

Other Websites Devoted to Complex Analysis

1. John Mathews & Russ Howell's Complex Variables/ Complex Analysis site at CSU Fullerton
   

2. Tristan Needham's Visual Complex Analysis website list of links

3. Hans Lundmark's "Visualizing complex analytic functions using domain coloring"

4. Terence Tao's Interactive Mapping of the Complex Plane Using f(z)

5. Bert Wachsmuth's Interactive Complex Analysis

6. John Baez Essay on The Beauty of  Roots
   

7. Mathematica Demonstrations (requires download of Mathematica CDF Player)

   1. A Catalog of Conformal Mappings

   2. Complex Mapping of Contours and Regions

   3. Roots of Unity in the Complex Plane

   4. Mapping Lines and Circles onto the Riemann Sphere

8. Geogebra Demonstration of Roots of Unity
   
   
9. Visualizing the Point at Infinity
10. Definitions of Contours (Bernd Schroder)
    

     

Last Updated December 28 2015