MA 405 George Ashline SMC
Complex Analysis Resource List
f(z) – The Complex Variables Program is a commercial graphics program written by Lascaux Graphics for Windows and Win95 for visualizing complex mappings. There is a free, downloadable demo version available at http://www.primenet.com/~lascaux/fzwindem.html. Also, a Special Edition of f(z) is included with our text Complex Variables and Applications, 6th edition, by Churchill and Brown. You will be asked to occasionally use this resource during the course of the semester.
Graphics for Complex Analysis contains a nice collection of graphical demonstrations written by Douglas Arnold (Penn State University) of some of the concepts and mappings in complex analysis. The demonstrations can be viewed in animated GIF format or controllable Java applet format. The latter can be found at http://www.math.psu.edu/dna/complex-j.html.
Java Complex Function Viewer is an applet written by Keith Orpen and Djun Kim (University of British Columbia) to help you visualize certain complex mappings (in particular, sin(z), cos(z), and exp(z)). The applet allows you to vary the location of a square grid in the domain and to view the accompanying image of that grid by the complex function selected. You can access this applet at http://sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/ComplexViewer/complex.html
Resources for the Teaching Complex Variables contains links to several files that can be downloaded for use with the graphics program f(z) and listings of pertinent reading and internet sources. This site is maintained by Paul Fishback (Grand Valley State University) and can be accessed at http://www2.gvsu.edu/~fishbacp/complex/complex.htm.
Visualizing Complex-Valued Functions in the Plane offers multi-color representations of a few complex mappings. Created by Frank Farris (Santa Clara University), these illustrations can be found at http://www-acc.scu.edu/~ffarris/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.umn.edu/~dpvc/CVM/1997/01/ucfg/welcome.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 the geometry of an inversioni (reflection through a circle). The mechanism can transform linear motion (such as that of a piston) to circular motion (such as that of a wheel). Three simulations of this linkage (the first two in Java and the last in JavaSketchpad) can be found at http://www.cut-the-knot.com/pythagoras/invert.html, http://www.saltire.com/applets/peaucellier/paucellier.html, and http://kunden.swhamm.de/Geometriepage/jsp/JSP_DEMO_PEAUCELLIER.HTM. Background information on this linkage and its construction can be accessed at http://www.geom.umn.edu/education/math5337/linkage/.