Volume 11, Issue 2
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Visualizing Complex Functions with the Presentations Application
Visualization is an invaluable companion to symbolic computation in understanding the complex plane and complex-valued
functions of a complex variable. The Presentations application, an add-on to Mathematica, provides a rich set of tools for assisting such visualization. This article
demonstrates some capabilities of the application, especially those relevant in an introduction to complex analysis, and it
indicates some teaching and learning issues that arise. Included are examples of how complex functions map objects in the
complex plane and on the Riemann sphere, and of how complex functions behave near singularities and at branch points.
| About the Authors
Murray Eisenberg is a professor of mathematics and statistics at the University of Massachusetts Amherst and received his A.B. and A.M. from the University of Pennsylvania and his Ph.D. from Wesleyan University. Eisenberg’s principal mathematical interest is the topology of dynamical systems. He has published articles on topological dynamics, the APL and J programming languages, and the use of computers in teaching undergraduate mathematics, and is the author of three undergraduate textbooks. David J. M. Park, Jr. received a B.S. and M.S. in electrical engineering from M.I.T. Park worked on microwave and beam design elements of early cesium beam tubes for atomic clocks and on masers. While working as a computer consultant he became involved in biochemistry and developmental biology, published a number of articles in the field, and worked for a period of time at the Laboratory for Theoretical Biology at N.I.H. In his retirement he has used Mathematica to renew an interest in mathematical physics and in the process has developed packages used by many Mathematica users. Most recently he has been collaborating with Renan Cabrera and Jean-François Gouyet to design Tensorial, a Mathematica package for tensor calculus. Murray Eisenberg Department of Mathematics and Statistics University of Massachusetts F-25000 Besan¨on, France 710 North Pleasant Street Amherst, MA 01003-9305 USA murray@math.umass.edu www.math.umass.edu/~murray David J. M. Park, Jr. 1429 Searchlight Way Mount Airy, MD 21771 USA djmpark@comcast.net home.comcast.net/~djmpark |
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