Complex Analysis with *Mathematica*

**News: "Complex Analysis
with Mathematica" honoured by American Library Association**

Every year The American Library Association gives a
number of books the award of "Outstanding Academic Title" status in their
review publication Choice. "Complex
Analysis with Mathematica" has been given this accolade in the January
2008 edition of Choice. The book was also reviewed in their September 2007
edition, where it was described as a "truly next-generation book" and
"Essential" (see below for full review).

** **

**September
2007: Review in American Library Association “Choice” magazine**

Reprinted
with permission from CHOICE, © American Library Association. Contact permissions@ala-choice.org
for permission to reproduce or redistribute. CHOICE reviews are available
on-line at http://www.cro2.org

Traditionally,
teaching complex analysis requires overcoming steep pedagogical hurdles.
Complex analytic functions, the objects of study, have graphs that form
two-dimensional subsets of four-dimensional space, so their visualization (if
it happens at all) requires indirect approaches--the more the better. Also,
many important results in complex analysis (conformal mapping) express
themselves in only very limited examples such as one may work out by hand. So
computers should transform the teaching of the subject, as Tristan Needham
pointed out in his breakthrough 1997 *Visual Complex Analysis* (CH, Jan'98,
35-2767). But Needham avoided integrating computer technology into his
exposition, presumably because of limited distribution of powerful hardware and
awkwardness of then-available software. Shaw, taking advantage of considerable
technological progress, offers a truly next-generation book: Mathematica's
graphics make old ideas leap off the page, and Mathematica's computational
powers permit students to interact effectively with complicated and typical
examples. Technology aside, Shaw expands typical undergraduate complex analysis
itinerary with excursions through dynamics and fractals, solution of cubic and
quartic equations, hyperbolic tessellations, and even an introduction to
spinors and twistors, important tools in contemporary approaches to relativity.
A vital library resource. **Summing Up:** Essential. General readers;
lower- and upper-division undergraduates; professionals; two-year technical
program students. -- *D. V. Feldman, University of New Hampshire*

**July 2007: New
notebooks with enhanced Version 6 information**

Having played
with Mathematica 6.0.1 for a few days, I have now produced updates to the
material on the CD with improved features. These can now be downloaded as
rather large files with all the output, or smaller files with no output
included (recommended)

Smaller files are
here;
larger files are here.
Coming soon… Demonstrations…

**May 2007 :
Mathematica 6 released!**

Tips and hints
for making the most of version 6 will be posted here during the course of
summer 2007. To get you going here are the passwords for accessing the files in
the “Goodies” directory. Note that these were produced with an early test
version of Mathematica 6 so there will probably be a few issues. Check back at
the end of May for an update and any revised notebooks. The book is essentially
Mathematica 6 compatible and only a few changes are needed in a very small
number of places, and most of this is covered in the Goodies zone.

The first
password is:

kdlZDQ9S_qWhtzrmFCov2ywJeuOAT7n1

The second
password is:

rwlgCO1TLnR6VsDY7vQacj4yitIxoES5

I recommend you copy and paste
where possible, otherwise type carefully and note there are 1s and Is.

E-mail me with
any issues!

June 2006

The ISBN is
0521836263

This was
published by Cambridge University Press in the UK in mid-April of 2006 - in the
US it was published at the end of May. You can see the CUP catalogue
information and buy direct from the publisher - click on the right geographical
area in the CUP global site
to get pricing and ordering information.

Tips on using the
CD – if you have problems.

The table
of contents is available.

Here are the
editorial reviews:

"William
Shaw's *Complex Analysis with Mathematica* is a remarkable achievement. It
masterfully combines excellent expositions of the beauties and subtlety of
complex analysis, and several of its applications to physical theory, with
clear explanations of the flexibility and the power of Mathematica for
computing and for generating marvellous graphical displays."
*Roger
Penrose, University of Oxford*

"This
is an innovative text in which the basic ideas of complex analysis are
skillfully interwoven with geometry, chaos and physics through the learning and
repeated application of Mathematica. This text moves from complex numbers,
quadratic and cubic equations through to the Schwarz-Christoffel transformation
and four-dimensional physics, and at each stage promotes understanding through
geometric intuition and reader participation. It should appeal to anyone with
an interest in the geometric side of complex analysis."
*Alan F.
Beardon, University of Cambridge*

"This
book provides an inspiring way to learn complex analysis thanks to the
inclusion of many topics of current interest in the field as well as the
integration of highly visual Mathematica routines throughout. The book is sure
to excite students about the field."
*Bob Devaney, Boston University*

The preface contains
a summary of the book and some suggestions for its use in courses, and is
available here.
The index is available here.
A picture of the front and back of the book is available here. You can also see some short excerpts
from sample chapters as follows – these illustrate some of the ways the book
can enhance a traditional complex variable course (note that these are PDFs
produced by the author to a downloadable size and do not have as good quality
graphics as the published work):

The first few
pages of Chapter 4 are available here.
They show how the classical theory of polynomial equation-solving can be
extended via Newton-Raphson iteration, and give a brief explanation of Cayley’s
solution for a quadratic and the reason for his difficulty with the cubic
(fractals!).

In Chapter
21 I look at using Mathematica to illuminate the theory of
Schwarz-Christoffel transformations.

Chapter
22 contains some hyperbolic tilings – this excerpt shows the “Ghosts and
Birdies” tiling in one representation of the hyperbolic plane and the full
version of the cover image in another (see below as well).

You can also
order the book on-line from

Blackwell.com,
Blackwell.co.uk

Amazon.co.uk,
Amazon.com
, Amazon.de,
Amazon.fr,
Amazon.co.jp.
Be warned that there are some fake listings of “used” books from booksellers
selling new books in the Amazon marketplace! Some booksellers are even trying
to charge above list price for brand new books passed off as used (do not ask
me why someone would do it this way round). The UK list price is £40.00 and the
US list is $75.00. Do NOT pay more than this, shipping aside.

Check back for
information on:

Solutions manual
for “Complex Analysis with
Mathematica”;

“Complex Analysis with Mathematica” and
Mathematica technologies beyond version 5.2.

**Another view
of a hyperbolic tiling, from "Complex Analysis with Mathematica: **