The venerable math programs Maple and Mathematica long ago outgrew pure math to include numerical and symbolic math, graphics, document preparation, and more. Maplesoft and Wolfram have each recently released a major update—Maple 12 and Mathematica 7—and Maple has a new simulation package as well. The company is increasingly pitching to engineers—an approach that has long been successful for another big math program, MathWorks’ Matlab.

For example, Maple’s new Dynamical Systems package helps users study the behavior of discrete and continuous time systems, central to many signal-processing and control applications. Maple can now communicate with the two leading computer-aided design packages, Autodesk Inventor and SolidWorks, allowing an engineer to optimize a design in Maple and then send data back to the CAD program.

The new Exploration Assistant lets a user vary a parameter in an equation or graph and see the results. And inexperienced Maple users now have new templates that take common commands. Mathematica has had many of these features for some time. It’s great to see that competition between the two companies is easing the learning curve users faced on earlier releases.

The new MapleSim is an elegant product that runs in parallel with Maple 12. With a few mouse clicks, you can create, say, a model of a circuit, or a thermal or mechanical system, and the program will transparently call on Maple 12 to show how it performs. Models can even handle several domains, including motors, for example, as well as mechanical elements and the attendant friction and backlash.

MapleSim has a lot in common with MathWorks’ Simulink, but, interestingly, it works by finding the differential equations for a system, which Maple simplifies analytically before solving. This process is potentially faster and more accurate than Simulink’s purely numerical approach.

I found MapleSim easy and even fun to use. But automating it has some limits. Many of the things an engineer would want to do—for example, fitting data to a model to obtain a best set of parameters or tweaking a model’s parameters to meet design constraints—are likely to force you to delve deeply into Maple and possibly require extra-cost software as well. There is also a key restriction to lumped parameter models (electrical circuits perhaps, but no electromagnetics).

#### Wolfram

Mathematica 7

Mathematica tries even harder than Maple to be all things mathematical to all people. Its latest version can locate information about subatomic particles, the human genome, historical weather data, the geometry of polyhedrons, and on and on. The program also includes many new graphical and mathematical functions and supports parallel computing on computers with multicore processors.

Users fortunate enough to work in institutions with maintenance contracts will probably have received these latest versions by now. The rest of us should carefully examine the vendor literature to decide whether the additional features of either program are worth a pricey upgrade.

Other programs for the mathematically inclined continue to evolve as well. Design Science has a new version of its stand-alone equation editor, MathType 6.5. Engineers acquainted only with the stripped-down MathType that’s embedded in Microsoft Word will be pleasantly surprised to find a product that supports various mathematics markup languages and a wide variety of application software.

Do you want to copy an equation from Wikipedia, Mathematica, or Maple and produce a nicely formatted and editable equation in Microsoft Word? Or copy an equation from a Word document and paste it as an executable equation into Maple? Developers have tried for years to build this kind of capability into applications using the language MathML [see ”MathType 5 With MathML for the WWW,” IEEE Spectrum, December 2001] only to be stymied by the way different applications use different flavors of MathML. But now built into it for many different math packages, which should make copy-and-paste operations simple for the user. Neat.

Finally, there’s QuickField, which I first reviewed back in 1993 as a program that numerically solved problems in a variety of physical domains—thermal, mechanical, electrical, mixed—using the finite element method. It featured a nice graphical interface and blazingly fast calculations. Now, numerous versions later, QuickField has acquired many advanced features, including optimization, publication-quality graphics, and so on. There’s even a useful textbook, James Claycomb’s *Applied Electromagnetics Using QuickField & Matlab* (Infinity Science Press, 2008), to go with a free student version that you can download from QuickField’s Web site.

**Maple 12:**http://maplesoft.com

**Mathematica 7:**http://wolfram.com

**MathType 6.5:**http://dessci.com

**QuickField 5.6:**http://quickfield.com

## About the Author

KENNETH R. FOSTER, an IEEE Fellow and professor of bioengineering at the University of Pennsylvania is a regular reviewer of books and software for IEEE Spectrum.

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