Contents

• Mathematica Applications Library

• How to Get the X Front End

• Electronic Publishing with MathSource

• Feature Focus: Customizing Mathematica with init.m

Mathematica Days: More to Come

Over a thousand people attended the five Mathematica Days held earlier this fall in the United States and Europe. The Mathematica Days were intended for new Mathematica users and other people interested in Mathematica. The Days focused on elementary and intermediate tutorials, covering introductory Mathematica programming, graphics, notebooks, and MathLink. Attendees also received practical information from fellow Mathematica users in the areas of engineering, finance, and education. A special highlight was that each day opened with a talk by Stephen Wolfram, entitled "Mathematica and the Future of Technical Computing."

Attendees said that they now feel better equipped to apply Mathematica to daily projects to enhance their productivity. Laurie Iten, a professor of biological sciences at Purdue University, said, "I wanted to see how other people are using the program and I did. I'm looking forward to incorporating Mathematica into my research."

Mathematica Days attendees told us that their colleagues are also interested in learning more about Mathematica. When asked what is the best way for their colleagues to learn about Mathematica, they responded, "Attend a Mathematica Day."

Positive feedback from those who attended, and requests from others who weren't able to make it, have encouraged us to hold future Mathematica Days in more locations throughout the world. If you or someone you know would like to receive information about future Mathematica Days near you, call Wolfram Research or send us an email message to mdays@wri.com to add your name to our mailing list. As soon as dates and locations for future Days are scheduled, we will mail a brochure and registration form to you.

*Lecture Tour In Japan
Because of the success of the Mathematica Days, we have scheduled a series of "mini" Mathematica Days for late January 1994 throughout Japan. Keep an eye out--more information will be sent to local Mathematica users soon.

*Selected Tutorial Notes
Mathematica Days attendees also had the opportunity to buy the new Wolfram Research publication, Selected Tutorial Notes, a collection of tutorial notes from previous conferences. If you are a new user, the Selected Tutorial Notes are a great way to get started with Mathematica. To order a copy of the Selected Tutorial Notes, call 217-398-0700. (In Europe call +44-(0)993-883400).

New Applications Library Set for Release

Professionals use Mathematica's numerical, symbolic, graphics, and programming capabilities to solve problems in their fields every day. To make it even easier for professionals to incorporate Mathematica in different areas, Wolfram Research has introduced the Mathematica Applications Library. The Applications Library supplements tools that Mathematica already contains with profession-specific notebooks and packages. The notebooks contain examples that show and describe specific techniques for using Mathematica. The packages predefine common algorithms and formulas used in various fields.

The first two available volumes of the Applications Library are the Electrical Engineering Pack and the Finance Pack. These volumes can be used in many ways and provide users with

• ready-to-use Mathematica functions

• introductory tutorials on a given topic

• examples of Mathematica programming

• a core for user algorithms
• ideas for project documentation in notebook format

*Electrical Engineering Pack
The Electrical Engineering Pack is a collection of notebooks and packages that cover electrical engineering problems, ranging from elementary to advanced topics. Examples, drawn from circuit analysis, transmission line theory, and antenna analysis, show how to use Mathematica in electrical engineering.

*Finance Pack
The Mathematica Finance Pack is designed for traders, investment analysts, portfolio managers, and others in the financial community who want to use Mathematica to analyze financial data and design strategies. Individual investors, as well as research staff from small brokerage houses to large financial institutions, will find this toolkit valuable.

Topics covered in the Finance Pack include interest rates, bonds, general cash flow, options, and finance calendar computations. The specialized tools cover term structure of interest rates and all commonly used sensitivity functions needed for risk management.

*How to Order a Library Volume
Order a volume and start increasing your productivity today. For a limited time, Wolfram Research is offering the Electrical Engineering Pack at an introductory price of $99 (regularly $195). This offer ends January 31, 1994. The Finance Pack is available for $395. Both volumes run on Microsoft Windows, Macintosh, and Unix. To order, contact us at 217-398-0700. (In Europe, call +44-(0)993-883400.)

The Electrical Engineering Pack includes examples from:

• Mesh Circuit Analysis

• Nodal Circuit Analysis

• Bode Plots

• Laplace Transforms

• Circuit Sensitivity Analysis

• Ideal Diode and Bipolar Transistor Models

• Chaotic Behavior in a Nonlinear Circuit

• Passive Component Noise

• Amplifier Noise Figure

• Harmonic Distortion

• Crossover Distortion

• Clipping Distortion

• Resistor Selection

• Y to S Parameter Conversion

• Project Documentation

• Symbolic Derivation of Transmission Line Parameters

• Analysis of Reflections Using Animations

• Suppression of Line Ringing by Lossy Lines

• Matrix Techniques for Microwave Transmission Line Analysis

• Dispersion in Uniform Microstrip Lines

• Smith Chart Design Tools

Topics of the Finance Pack include the following:

• Flat Constant Rates

• Term Structure of Interest Rates

• Spot Rates

• Forward Rates

• Discount Factors

• Interest Rates Conversion

• Simple Representation of Interest Rates

• Bonds

• Simple Representation of Cash Flows

• Options

• Finance Calendar Computations

• Random Number Generation

• Markowitz Efficient Portfolio

• Betas and Security-Market Line

• Moving Averages

How to Get the X Front End

Shipments of the Mathematica X front end recently began for Sun SPARC-based systems (under Sun OS 4.1), Silicon Graphics, Hewlett-Packard 700 Series, DEC MIPS, Sun Solaris (2.0 or higher), and IBM RISC System/6000 computers, providing notebooks, a function browser, and on-line help to Unix users. Mathematica notebooks are interactive documents in which a user can combine text, calculations, and graphics. Notebooks are also transferable between platforms--a notebook created on a Unix machine, for example, can be used on a Macintosh, or vice versa.

How can you get the notebook front end on your workstation as soon as possible? The answer is Mathematica Plus, the automatic customer update program for Mathematica. If you have bought a subscription to Mathematica Plus for one of the six platforms listed above, you will automatically receive a complimentary X Front End Update Kit. This kit is not considered one of the two updates regularly provided under the Mathematica Plus program, so you can expect to receive two other updates in addition to this kit. (Please note that you are only eligible to receive the update kit if you bought a full Mathematica Plus subscription.)

If you haven't yet purchased a subscription to Mathematica Plus for one of the platforms mentioned above, you can still subscribe by December 31, 1993 to receive your complimentary X Front End Update Kit and two additional Mathematica updates as soon as they are released.

To subscribe to Mathematica Plus, contact Wolfram Research at 217-398-0700 or send email to info@wri.com. In Europe, call +44-(0)993-883400 or send email to info-euro@wri.com.

New Versions

NEXTSTEP for Intel
Mathematica 2.2 is now available for NEXTSTEP, NeXT's object-oriented software for Intel-486 and Pentium-based computers, including COMPAQ Deskpro L, Dell ME, Gateway V, IBM ValuePoint 466DX2/D, and Zenith Z-Station XEn computers. The NEXTSTEP version is identical to Mathematica for the NeXT and compatible with all other notebook front end versions.

X Window System
The X notebook front end is currently shipping for Sun SPARC-based systems (under Sun OS 4.1), Silicon Graphics, Hewlett-Packard 700 Series, DEC RISC, Sun Solaris (under 2.0 or higher), and IBM RISC System/6000 computers. The X front end is compatible with other notebook versions and runs under Motif.

OS/2
A native OS/2 port of the Mathematica kernel is in testing. It will be available soon and will feature full 32-bit addressing. (Currently, Mathematica for Microsoft Windows runs under OS/2v2.1. Mathematica Version 2.2 for MS-DOS runs under OS/2v2.0.)

Windows NT
A Mathematica version for Windows NT is also in testing and will feature both a 32-bit kernel and a 32-bit front end. Mathematica for Windows NT will also be compatible with Windows 3.1.

MathLink Developer Kit for Microsoft Windows

MathLink for Windows is currently in testing. It is expected to ship after the first of the new year, enabling Microsoft Windows users to link Mathematica to external programs, such as Microsoft Excel or a remote kernel or front end from other Mathematica platforms.

MathLink for Microsoft Windows is a DLL (dynamic link library) that can be used from any Windows development environment that supports DLLs. With the MathLink Developer Kit, many kinds of programs can be adapted to exchange data and commands with Mathematica. The kit includes MathLink documentation and sample MathLink applications: a small Mathematica front end and programs written in C and Visual Basic.

Registered users of Mathematica 2.2 can get the MathLink Developer Kit for Microsoft Windows by calling Wolfram Research. You can also request the kit by email at orders@wri.com. (In Europe, send mail to info-euro@wri.com.) Be sure to include your postal address and Mathematica license number.

Special Functions with Mathematica

Of the infinite number of mathematical functions that exist, only several hundred have been given names. Everyone knows about the "elementary" functions: circular and hyperbolic trigonometric functions, the exponential function, their inverses, and polynomial functions. All other functions are considered "special" functions.

There are several broad classes of special functions, including the special functions of mathematical physics, elliptic integrals, and integrals of elementary functions. Mathematica contains the most important special functions in these and other classes. For example, Mathematica has groups of Bessel and elliptic functions, as well as the Gamma and Zeta functions.

Mathematica has several principles that apply to the evaluation of mathematical functions:

• Mathematica algorithms evaluate each function throughout the complex plane to any precision.

• When given a machine number as an argument, Mathematica attempts to return the machine number closest to the value of the function at that argument.

• Mathematica's interface is designed to make it easy to use special functions as building blocks of other functions.

• Mathematica's algorithms are designed to be efficient and well-conditioned (i.e., insensitive to errors either in the arguments to the function or in values intermediate in the calculation).

In addition, Mathematica uses meta-algorithms to select the best of several algorithms for any particular set of parameters. For example, if the best algorithm for evaluating e^x were the series expansion, Mathematica would distinguish between the cases x<0 and x>0. The series expansion at x = -12.0 suffers from catastrophic cancellation of digits: 1 - 12. + 72. - 288. + ... + 17062.8 - 18613.9 + 18613.9 - 17182.1..., but e^(-x )= 1/(e^x) and 1/(1 + 12. + 72. + 288. + ...) involves no cancellation.

Occasionally all algorithms are more ill-conditioned than the function itself, and digits will be lost in cancellation. Mathematica's arbitrary-precision arithmetic monitors the precision of the calculation to know how many extra digits are needed when reevaluating the function with higher precision. Mathematica automatically reevaluates the function with higher precision to compensate for any ill-conditioning of the algorithm in excess of the ill-conditioning of the function. However, when the function itself is ill-conditioned, the algorithm does not give more digits than justified by the function.

For more information about special functions in Mathematica, see Section 3.2.10 of Stephen Wolfram's book, Mathematica: A System for Doing Mathematics by Computer, Second Edition.

Examples The closest machine number to erf(10) is 1.

In[1] := Erf[ N[10] ]
Out[1] = 1.

Considerably more than 20 digits are justified by a 20-digit approximation to erf(10).

In[2] := Erf[ N[10, 20] ]
Out[21] =0.999999999999999999999999999999999999999999998

Log[Gamma[z]] restricts the imaginary part to be between -Pi and Pi and results in the complex plane being cut by infinitely many curved branch cuts. By analytic continuation, LogGamma[z] just has a branch cut along the negative real axis.

In[3] := LogGamma[ 2.3 + 8.9I ]
Out[3] = -9.11504 + 13.207 I

The Airy Ai function is related to Bessel functions of order 1/3. The Airy Ai function can be used to describe the probability of finding a quantum particle, such as an electron, at various distances from a linear potential barrier.

In[4] := Plot[ AiryAi[x], {x, -10, 5} ]
[graphic deleted]

Riemann's Zeta function can be evaluated anywhere in the complex plane. This is near the first zero on the critical line with an imaginary part greater than 1000. The precision of the result is only as high as justified by the input.

In[5] := Zeta[ 1/2 + 1001.3494826377827371221033 I]
-23 -23 Out[5] = -2. 10 - 3. 10 I

JacobiSN[ ] is an elliptic function related to the motion of a simple pendulum. When x is near 1, the function corresponds to a pendulum that swings almost from vertical to vertical, nearly balancing at each end of the swing.

In[6] := Plot[ JacobiSN[x, .99], {x, 0, 15} ]
[ graphic deleted ]

Updating Registered User Information

Keeping your registration information up to date helps us manage license information more efficiently, issue passwords faster, and send update and new product information. Please take a moment to check the name and address on the mailing label of this issue of MathUser. (Note that we send MathUser, update information, and all other Mathematica mailings to the same address.) An R after your name indicates that you are a registered user. An N after your name indicates that you are a MathUser subscriber, but not a registered user.

Please contact User Services if

• the address information is incorrect

• you are a registered user, but do not have an R code

• the person on the label is no longer with your organization, or

• you receive more than one copy of MathUser

You can reach User Services by fax at 217-398-0747 or by email at register@wri.com. As always, we welcome your comments and suggestions.

Starting a Mathematica User Group? Wolfram Research Can Help

User groups help spread Mathematica news and knowledge. Wolfram Research supports Mathematica user groups with materials, information, and promotion. If you would like to join or start a Mathematica user group, we can put you in contact with other interested users. For information about Mathematica user groups, contact the User Group Administrator at mug@wri.com. (In Europe, send email to mug-euro@wri.com.)

Electronic Publishing with MathSource

As more books are supplemented with Mathematica packages and notebooks, authors and publishers need a convenient, effective way to publish electronically. The best way to publish electronic supplements, periodicals, and documentation is with MathSource, the electronic resource for Mathematica-related materials.

Here are some of the important advantages of publishing with MathSource.

• MathSource reaches Mathematica users around the world, averaging 2000 sessions weekly from over 50 countries.

• MathSource is accessible by email, direct dialup, anonymous ftp, and Gopher.

• MathSource sends materials in formats appropriate for different computer systems, making it unnecessary for publishers to make different versions of supplements. MathSource can send files formatted for Macintosh, DOS, and Unix computers, and also send NeXTmail.

• Users can search MathSource by keyword to easily find all Mathematica materials on a topic.

• Authors and publishers save the production cost of packaging disks with books.

• To distribute a new version or bug fix, an author has only to submit updated materials to MathSource, instead of mailing disks to each person who bought the book. MathSource can automatically notify users when an author updates materials, ensuring that everyone has the most current version.

*How to Publish with MathSource
Do you have materials that you would like to publish with MathSource? You can send us the materials via email, on disk, or give the address of an anonymous ftp site. When submitting materials to MathSource, be sure to include the title of the material, an abstract, suggested keywords, and who to contact for more information about the materials.

If you would like more information about publishing Mathematica-related materials with MathSource, send email to the MathSource administrator at ms-admin@wri.com, or call 217-398-0700.

A Sample Email Session with MathSource

In addition to Find and Send, MathSource has commands that you can use to indicate your file format preference, tell MathSource whether or not it should compress files before sending, and modify search parameters. Here is a sample email session that shows how you can search for and download MathSource materials.

Find Request to MathSource	To: mathsource@wri.com
If you indicate your computer type, MathSource can pick an appropriate compression scheme and put correct end-of-line characters in files.	System Macintosh
This tells MathSource to return the results of the Find command in a Mathematica notebook.	Format Notebook
This sets 100K to be the maximum mail message size that MathSource sends to you.	MaxKBytes 100
This returns a list of the items whose titles and summaries contain the string "Programming in Mathematica".	Find "Programming in Mathematica"
MathSource Reply
In response to the Find request, MathSource sends this notebook. In addition to notebooks, you can instruct MathSource to send Find results in PostScript, TeX, or ASCII files.	[ picture not shown ]
Send Request to MathSource	To: mathsource@wri.com
This requests item 0205-186.	Send 0205-186
This searches for all submissions from Wolfram Research.	Find Organization: Wolfram Research
This indicates that the remainder of your message should be read by a human operator.	Operator Please send more information about submitting materials to MathSource.

For more detailed descriptions of these and other features, download the MathSource Technical Report, item 0202-554.

Two Ways to Get a Faster Reply from MathSource

1. Send each Find command in a separate message. Because MathSource processes your entire message before returning a response, a single message containing several Find commands can take longer than several messages with one Find command each.

2. Send MathSource as few keywords as possible for each item. For example, to find information on modified Bessel functions, send the command Find Bessel instead of Find Modified Bessel Function. Because MathSource does a full search for each keyword in your message, sending one keyword for an item will get results faster than several keywords.

A Few Electronic Supplements Now on MathSource

• The Mathematica Journal

• Mathematica in Action

• Programming in Mathematica

• Economic and Financial Modeling with Mathematica

• Partial Differential Equations with Mathematica

• Simulating Neural Nets with Mathematica

• Mathematica in Education

• Applied Mathematica: Getting Started, Getting It Done

• Introduction to Programming with Mathematica"

WRILaTeX

Authors writing books or technical reports based on Mathematica can get the WRILaTeX document system from Wolfram Research. The WRILaTeX document system was used to produce Stephen Wolfram's Mathematica: A System for Doing Mathematics by Computer, and other Mathematica documentation. WRILaTeX consists of LaTeX style files, macro definitions files, and other utilities that make it easy for authors to incorporate Mathematica input and output into a TeX-based document. For information about WRILaTeX, send email to wrilatex@wri.com.

New Books

These new Mathematica books range from introductory tutorials in programming, mathematics, and Mathematica, to specialized professional reference books. For information, contact the publishers or any technical bookstore.

*English Titles

Applied Mathematica: Getting Started, Getting It Done
William T. Shaw and Jason Tigg (Addison-Wesley, ISBN 0-201-54217-X)
Shows how to solve complex, practical problems in engineering, finance, environmental engineering, and image processing. Provides a quick start for scientists and engineers. Electronic accompanying materials are available on MathSource.

Calculus Using Mathematica
K.D. Stroyan (Academic Press)
ISBN 0-12-672971-9 (with Macintosh disks)
ISBN 0-12-672972-7 (with IBM/DOS disks)
ISBN 0-12-672973-5 (with NeXT disks)
Textbook for three-semester undergraduate calculus. Fully integrates Mathematica into the primary text and comes with Mathematica notebooks on disk.

Scientific Projects and Mathematical Background for Calculus Using Mathematica
K.D. Stroyan (Academic Press, ISBN 0-12-672975-1)
A companion workbook to Calculus Using Mathematica.

Introduction to Computer Performance Analysis with Mathematica
Arnold Allen (Academic Press, ISBN 0-12-051070-7)
Beginner's guide to computer performance analysis. Topics include benchmarking, measurement requirements, simulation, and forecasting. Comes with Mathematica files on disk.

Introduction to Programming with Mathematica
Richard J. Gaylord, Sam N. Kamin, and Paul R. Wellin
(TELOS/Springer-Verlag, ISBN 0-387-94048-0)
A textbook introducing programming in the Mathematica language. Emphasizes the functional and rule-based styles unique to the Mathematica programming language. Does not assume prior programming or Mathematica experience. Comes with electronic supplement.

Simulating Neural Networks with Mathematica
James A. Freeman (Addison-Wesley, ISBN 0-201-56629-X)
Introduces the operations and application of neural networks in the context of Mathematica's programming language. Shows professionals and students how to use Mathematica to simulate neural network operations to assess neural network behavior and importance. Electronic materials available on MathSource.

*Non-English Titles

Erste Schritte mit Mathematica [First Steps in Mathematica]
W. Burkhardt (Springer-Verlag, ISBN 3-540-56650-3)
An introduction to Mathematica designed for independent study or introductory courses. Emphasizes the most important areas of application through the use of problems in high school and university mathematics.(in German)

Informatik fur Mathematiker und Naturwissenschaftler: Eine Einfuhrung mit Mathematica [Computer Science for Mathematicians and Scientists: An Introduction with Mathematica]
Roman Maeder (Addison-Wesley, ISBN 3-89319-519-X)
A textbook for introductory computer science, especially for mathematicians, scientists, and engineers. Treats traditional computer science topics and shows how modern computer-based tools can be used to do scientific computation. (in German)

Mathematica: Ein systematisches Lehrbuch mit Anwendungsbeispielen [Mathematica: A Comprehensive Guidebook with Practical Examples]
Ernst H.K. Stelzer (Addison-Wesley Deutschland, ISBN 3-89319-495-9)
Introduction to Mathematica with applications based on problems taken from physics, chemistry, and biology. Special emphasis on analysis, linear algebra, and numerical mathematics. (in German)

*Translations

Mathematica griffbereit, Version 2 [Mathematica: Quick Reference, Version 2]
Nancy Blachman (Verlag Vieweg, ISBN 3-528-06524-9) (in German)

Mathematica in Aktion [Mathematica in Action]
Stan Wagon (Spektrum Akademischer Verlag, ISBN 3-86025-041-8) (in German)

*Forthcoming Books

These books will be available in early 1994.

Animating Calculus
Ed Packel and Stan Wagon (W.H. Freeman, ISBN 0-7167-2428-6)
A supplement for first-year calculus. Contains a series of 22 Mathematica notebooks exploring topics in calculus of a single variable.

Grafik mit Mathematica [Graphics with Mathematica]
Ralf Schaper (Addison-Wesley Deustchland, ISBN 3-89319-612-9)

Mastering Mathematica: Programming Methods and Applications
John Gray (Academic Press Professional, ISBN 0-12-296040-8)
Discusses functional, rule-based, procedural, and object-oriented programming with Mathematica. Also covers graphics programming and writing Mathematica packages. Comes with electronic supplement.

The Mathematica Programmer
Roman Maeder (Academic Press Professional, ISBN 0-12-464990-4)
Covers the use of Mathematica as a programming language. Topics include object-oriented programming, abstract data type design, relational databases, minimal surfaces, and fractal curves. Comes with electronic supplement.

Revised Edition of Mathematica by Example
Martha Abell and Jim Braselton (Academic Press Professional, ISBN 0-12-041530-5)
Compatible with Mathematica Version 2.2 and shows fundamental Mathematica techniques for the beginning user. Topics covered include calculus, linear algebra, differential equations, and discrete mathematics.

Quantum Methods with Mathematica
James M. Feagin (TELOS/Springer-Verlag, ISBN 0-201-58221-X)
For students and experienced professionals who would like to explore quantum physics using Mathematica. Divided into two parts: Systems in One Dimension, and Quantum Dynamics. Comes with an electronic supplement.

In addition to these books, which feature special topics with Mathematica, there are many books that come with Mathematica supplements. In the next issue of MathUser, we will list books that use Mathematica. If you have written a book that comes with a Mathematica supplement, please tell us about it by sending email to mathuser@wri.com, or fax to 217-398-0747.

Opportunities at Wolfram Research

Wolfram Research is expanding and we are looking for outstanding people to join our team. Positions are open in research and development, technical writing, and technical marketing. Send applications for all positions to Personnel department, Wolfram Research (resumes@wri.com).

Wolfram Research is an affirmative action/equal opportunity employer.

Feature Focus

Customizing Mathematica with init.m

You can customize your version of Mathematica by changing init.m, an initialization file loaded when Mathematica starts up. By writing a new init.m file, or changing the default init.m, you can set Mathematica to

• prompt users for different option settings while the kernel is launching

• automatically load packages and launch MathLink applications you use every day instead of manually loading them

• print a message as Mathematica starts up; for example, a network administrator might add a Print statement to init.m that users will see when starting the network copy of Mathematica

surface = Plot3D[Log[Cos[y]/Cos[x]], {x,-1,1}, {y,-1,1},
            BoxRatios->{1,1,.5}, DefaultFont->{"Times-Italic", 10},
            AxesLabel->{"x","y","z"}, Mesh->False]
[ plot not shown ]

Show[ {surface, Graphics3D[Text["saddle point", {0,0,.1}]]} ]
[ plot not shown ]