In today's engineering
environment, it's often difficult to anticipate what problems you
may need to solve. Most of us work under significant competitive
pressure, and sooner or later we're likely to find that the mathematical
functionality and syntax of Excel (which, lest we forget, is designed
primarily for business and financial applications, not engineering
calculations) aren't up to the job. When you need solutions involving
differential equations, geometry, calculus, linear algebra, number
theory, advanced statistics, group theory or mathematical modelling,
you're moving way beyond spreadsheets.
That's why we need to
look at the "higher end" mathematical tools, where the
market is dominated by MATLAB, Maple and Mathematica. These programs
all require a bit of getting used to – they're heavyweight
applications – but they offer a huge range of tools to help
you tackle the most demanding engineering problems.
MATLAB (www.mathworks.com)
is widely used by engineers who need a lot of sheer number-crunching
power. Essentially a third-generation programming language, it provides
core mathematical tools for data analysis, visualisation, and algorithm
and application development; and a broad collection of add-on toolboxes
for specific applications.
Maple (maple.adeptscience.co.uk)
and Mathematica (www.wolfram.com)
have friendlier, customisable interfaces, and do a very different
job from MATLAB. They're basically symbolic maths engines, and are
vital for many engineering calculations because they maintain levels
of precision beyond the ability of number-crunching routines.
The use of algebraic symbols
avoids the almost inevitable loss of accuracy that occurs when you
put actual numbers through a series of computations. Rounding errors
are the most obvious source of this, something that Excel users
are very familiar with. Where tolerances are critical, to many places
to the right of the decimal point, you need a symbolic maths application
to keep your variables intact and ensure accurate results.
Maple is pretty much ubiquitous
in academia, and academic research labs continue to contribute to
its development. This has helped it deliver a broad and comprehensive
library of routines which are finding increasing favour among engineers
in industry. Its open source code means that you can easily program
your own procedures; and there's a huge selection of ready-made
applications freely available for download.
Mathematica has long been
a favourite with engineers, and it too offers a powerful computational
engine and a large library of functions. Like Maple, it's a mature
product that has stood the test of time, and which one you choose
is often simply a matter of personal preference.
One thing Excel can’t
do is generate code. The ability to produce error-free, optimised
code is especially valuable to engineering designers. It allows
you, for example, to develop complex models and generate exact equations
of motion, then automatically produce optimised code in a wide range
of popular programming languages, including C, FORTRAN, Java and
BASIC. You can do this with both Maple and Mathematica: code generation
is included in Maple, and is available as an add-on module for Mathematica.
Both Maple and Mathematica
also provide numeric solvers, integrated within their symbolic environments.
Maple incorporates some of the numeric libraries developed by the
British company NAG (www.nag.co.uk),
which specialises in developing software to manipulate, analyse
and visualise large amounts of numeric data accurately.
Many engineers will choose
to have both MATLAB and a symbolic program available on their desktops.
You can access MATLAB functions from both Maple and Mathematica,
although you'll need to create a toolbox for the latter; Maple's
MATLAB connectivity is built in.
Whichever combination
of mathematical software you use, you're still likely to make extensive
use of spreadsheets. MATLAB interfaces directly with Excel, so it's
easy to transfer your spreadsheet data. Maple's built-in Excel link
lets you access Maple commands and plotting capabilities from within
Excel (there's a Wizard to help you do this), and a Maple toolbar
makes it easy to copy and paste data between the programs. Mathematica
offers similar capabilities, though you need to purchase a separate
Excel link package.
Next month we’ll
return to the Excel theme, and look at ways in which you can feed
your measurement data straight into a spreadsheet.
Dr
Know's recommended download is the 'Top 10 reasons to invest in
Maple' brochure - download yours today.