MA 315      Complex Analysis Resource List 

Explorations in Complex Analysis is a book “…written for undergraduates who have studied some complex analysis and want to explore additional topics in the field.” This may be a valuable resource for your final paper/presentation topic consideration. The book’s website is http://www.maa.org/ebooks/crm/EXCA.html and the ComplexTool java applet link is http://www.maa.org/ebooks/EXCA/ComplexTool.html.

 

Graphics for Complex Analysis contains a nice collection of graphical demonstrations written by Douglas Arnold (Penn State University) of some concepts and mappings in complex analysis.  The demos can be viewed in animated GIF or controllable Java applet format.  See http://www.math.psu.edu/dna/complex-j.html for more details.

 

Java Complex Function Viewer is an applet written by Keith Orpen and Djun Kim (University of British Columbia) to visualize complex mappings [in particular, sin(z), cos(z), and exp(z)].  In the applet you can vary the location of a domain square grid and view its image by the complex function selected.  See http://sunsite. ubc.ca/LivingMathematics/V001N01/UBCExamples/ComplexViewer/complex.html.

 

Resources for the Teaching Complex Variables is maintained by Paul Fishback (Grand Valley State University) and has links to several files for f(z) and reading and internet resource lists.  See http://faculty.gvsu.edu/fishbacp/complex/complex.htm.

 

Visualizing Complex-Valued Functions in the Plane offers for a few complex mappings multi-color representations created by Frank Farris (Santa Clara University).  See http://www.maa.org/pubs/amm_complements/complex.html.

 

Understanding Complex Function Graphs is a paper written by Tom Banchoff (Brown University) and Davide Cervone (Union College) and published in Communications in Visual Mathematics.  It offers animations to enhance the understanding of the structure of complex graphs as four-dimensional surfaces.  See http://www.geom.uiuc.edu/~banchoff/script/CFGInd.html.

 

Julia and Mandelbrot Set Explorer contains a program that constructs Mandelbrot and Julia sets based on specified parameters and links to more information concerning these sets.  Available at http://aleph0.clarku.edu/~djoyce/julia/explorer.html,

this explorer was created by David Joyce (Clark University).

 

A Peaucellier’s linkage is a simple mechanism based on geometry of an inversion (reflection through a circle). It transforms linear motion (e.g. a piston) to circular motion (e.g. a wheel). For simulations, visit http://www.saltire.com/applets/peaucellier/paucellier.html and http://www.cut-the-knot.org/pythagoras/invert.shtml. For background information, see  http://www.geom.umn.edu/education/math5337/linkage/.