Complex Analysis Project
Complementary Materials for Math 412
Modules for Complex Variables & Complex Analysis
Research Experience for Undergraduates
Computer Software Supplements
Complex Analysis Textbook
History of the Complex Analysis Project
The motivation for this project started with the software program
F(z) which was designed by
Martin Lapidus and is available from Lascaux Software. In 1988 we distributed an F(Z) supplement
for our textbook and the web page Complex Analysis - Complex Variables, Explorations with F(Z).
In 2000 a web project titled Complex Analysis: Mathematica 4.0 Notebooks was made, and then
the web project titled Complex Analysis: Maple 7 Worksheets was made. For the 2001 edition of our
book, a CD-ROM titled "Complex Analysis for Mathematics and Engineering," ISBN: 0-7637-1530-1,
was packaged free with each copy and contained color plate pictures of the Julia and Mandelbrot sets
and all the computer software supplemnts: the F(Z) files, Maple worksheets and Mathematica notebooks.
This version of our complex analysis web project was started in 2003,
and since that early beginning
it has been updated several times and it is under continuous upgrading and improving. If you are one to notice
all the details then you probably will find some remnants dated 2003 and the most current version of modules
are dated 2012. But you need not worry about the time line because the core material in complex analysis has
not changed much in the past sixty years and some currently available textbooks have actually made their 60th
year milestone. We cannot brag to have such longevity and are just thankful that our textbook has just achieved
it's 30th year milestone. There have been significant improvements in the textbook since 1982. Noteworthy is
the new Chapter 9: The Z-transform and it's applications to Difference Equations and Digital Signal Filters.
We try to keep things up to date and this complex analysis web site
is one way to do it. You will find
several instances where the content of the web site goes significantly beyond the material in the textbook:
e. g. Harmonic Functions and their Riemann Sheets in Section 3.3; 3-D graphical visualizations for the residue
calculus involving Trigonometric Integrals, Rational Functions, Improper Trig. Integrals, Indented Contours, and
Branch Points; the argument principle and winding number is associated with Riemann surfaces; new 3-D graphs
for the Dirichlet problem, and conformal mapping. This is intentional since it allows us to present more details for
the solutions to the examples and exercises. Also you will notice that we have illustrated how to use Mathematica
and Maple as a pedagogical tool for teaching and exploring concepts the in complex analysis. Although these
details are much too extensive to print in any textbook, they are easy to squeeze in on the web pages.
For certain we can say that our book is the first to have included MapleTM and MathematicaTM supplements.
We started encouraging the use of computer algebra software since we made our first complementary
Computer Software Supplements, the Maple Version 4 worksheets in 1997, and Mathematica Version 3
notebooks in 1998. They have been improved for the past 15 years and can serve as a tutorial on how to
learn to use Maple and Mathematica to study Complex Analysis. You may want to get the new copies of the
Version 8 and Maple Version 15 supplements, which are available as
student supplement to our textbook from the Jones and Bartlett web page.
We find that there is a tendency to teach complex analysis with pencil and paper, and it is the hope of this
web site to overcome this inertia. Perhaps you will find useful computer illustrations that will encourage students
to explore complex analysis using Mathematica and Maple. Since we are a bellwether in this movement we hope
that you will follow us through the pages in this web site and see the beautiful explorations that can be made.
Hopefully you will gain some insight as to how this can help you teach complex analysis and the benefits your
students can gain by making their own computer explorations.
Finally, we would like to emphasize that this web site is a complementary supplement that is coordinated
with the current version of our textbook Complex Analysis for Mathematics and Engineering, Sixth Ed., 2012.
You are welcome to correspond with us on matters regarding the content and any suggestions you have or typos
you may find. You are welcome to correspond with us by mail or e-mail.
John H. Mathews
Department of Mathematics
California State University Fullerton
Fullerton, CA 92634
Prof. Russell W. Howell
Mathematics & Computer Science Department
Santa Barbara, CA 93108
This material is coordinated with our book Complex Analysis for Mathematics and Engineering.
(c) 2012 John H. Mathews, Russell W. Howell