Machine Design

Math Matters

"Math matters" is a phrase our company recently adopted in an effort to raise awareness of key deficiencies in commonly used engineering software tools and methods.

Tom Lee
Executive Product Director Maplesoft
Waterloo, Ontario, Canada

Edited by Lawrence Kren

Our recent survey of over 2,000 engineers asked how they approach the task of design. On a daily basis, 52% of respondents said they use hand calculators and paper; 47% use electronic references and tables (CD-ROM, Web); 35% use print reference books and tables; and 39% use spreadsheets, which incidentally, remains the most common software tool for analysis and design.

The net of all of this: Engineers still do an awful lot of technical work on antiquated tools or, at best, spreadsheets, which are notoriously prone to formula error. Math is the common dimension of all the above methods, from basic number crunching, to more sophisticated equation-based modeling.

CAE systems generally bury the math in exchange for a more-intuitive, graphical, and realistic representation of information. The approach works well as evidenced by what engineers have accomplished to date with these tools. But the survey results reveal that engineering is more than solid modeling and PCB layout. Reams of supporting mathematical work are behind designs done on CAE systems. In fact, CAE and traditional math are symbiotic. Engineers able to work effectively through the background math of designs have a better command of parameters, which reduces the number of CAE iterations.

That said it remains a running joke among engineers that, once you leave college, you never again see an integral or differential equation. The fact is, while engineers typically leave the rigorous mathematical techniques to design software, many continue to scribble and wrestle with math. Fortunately, attitudes seem to be changing and mainstream engineering is starting to come to grips with effective techniques for managing math.

The Modelica Association, for example, enjoyed its most successful conference ever. Large companies including DaimlerChrysler, ABB, and Dassault attended the show. Modelica is an emerging open standard for describing models of physical systems. It captures and manages all of the necessary relational, physics, and mathematical information needed to model complex systems and develop high-fidelity models.

On a similar note, our Japanese distributor recently held its annual TechnoForum conference in Tokyo. The theme: The role of general-purpose mathematical computation in engineering design. The event as planned targeted the "R" side of R&D. Surprisingly, hundreds of mainstream "D"-side engineers from major automotive, electronics, and other industries attended as well. Apparently, product developers have a keen interest in how math can boost the effectiveness and performance of simulations.

Keynote for the event was Toyota executive Akira Ohata, who heads software strategies for all the company's design groups. In essence, Ohata's message was that pure numerical simulation has reached its limits. Future design innovation must draw on the flexibility and power of mathematics.

We agree. In our view, math, with the right tools, can be a catalyst for better design and not simply a necessary evil.

Maplesoft ( is a developer of mathematical software.

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