I remember the day I got my first
slide rule: a small
cheap plastic thing bought from a junk shop. It was more
than a bit beyond my mathematical prowess at the time – I
was only ten, and hadn’t a clue what a logarithm
was, let alone a trigonometric function. But, hey, it
was fun to play with!
Unlike my little slide rule, Mathcad is a serious mathematical
calculation tool aimed at engineers. With it, you can
do in a few seconds what it would have taken a week to
do with a PC a few years back. Or a year with a slide-rule.
But I got the same feeling in using Mathcad as I did
with the slide rule: fun to fool around with and capable
of doing a lot more than I was.
Mathcad is often mentioned in same context as the other
two symbolic mathematical systems, Maple and Mathematica.
While it does a lot of the same things as Maple and Mathematica,
it’s really quite a different beast. First, it’s
aimed at engineers and those who need to document and
annotate technical and engineering solutions. It runs
on a Windows PC – there’s no pretence of
running on a Mac or Linux – and it closely integrates
into Office. Further, there’s a good implementation
of OLE (Microsoft’s Object Linking and Embedding
technology), particularly for Excel. When you embed or
create an Excel spreadsheet in a Mathcad document, you’ll
see the full Excel menu appear, overwriting the Mathcad
main menu as you activate the Excel object.
The Mathcad environment
However, in the initial release of Mathcad 13, this
didn’t extend to other Office objects like Word
and Access. While you could successfully embed Office
objects (and type text into a Word object, say) you didn’t
get Word or Access menus displayed. But with the recently
released Service Pack, I’m happy to report that
you can now type ‘War and Peace’ into a Word
object embedded into a Mathcad worksheet. And format
Easy Does It
Mathcad is very easy to start working with. First off,
there are some excellent Flash tutorials on the Mathcad
website. These take you through the basics of entering
a formula, doing a calculation, importing data and generally
moving around. A picture is worth a thousand words: in
this case, it’s true. I was up and running without
having to open the help system once. It really is that
The second reason why it’s easy to use is Mathcad’s ‘whiteboard’ concept.
The best way of thinking about a Mathcad worksheet is
like being in front of a whiteboard where you scribble
out your equations. The whiteboard is mostly free format
and you can position your equations more or less where
you like. This differs from other techniques, particularly
Mathematica’s rather clunky, to my mind, cell based
approach. However, Maple 10 does have a similar whiteboard-style
Equally, the input format is mostly quite intuitive
and quick to enter with the aid of simple floating palettes.
I did, however, find it a bit tricky to enter the square
root of minus 1. Every time I tried to enter i in
a formula, Mathcad assumed it was a variable. It seems
that you have to enter 1i (a
number before the symbol) to get it to work. Confusingly,
if the number is one, it disappears and you are left
back with a plain i.
One other minor quibble: you are limited to a single
style of round parenthesis - no curlies or squares.
minor niggle is having to enter a number before the i.
Otherwise, Mathcad thinks it’s a variable.
The other thing I really liked was the graphing tool:
it’s excellent - and intuitive, to boot. To plot
a graph you click on the graph palette and plonk a graph
object roughly where you want it; you can drag it around
to where you really want it afterwards. When
created the basic graph (2D in this case), you fill in
two placeholders, say x on
the x-axis and f(x) on the y-axis – and
got your graph of f(x) against x. Now that is exactly
what I want to do 99 times out of 100. It’s the
way I think about graphs and, I suspect, the way most
people (apart from professors of mathematics) do. To
customise the graph further, you can adjust the axis
limits (which are placeholders) or double click on the
graph to get a complete customisation dialog box. Neat.
a graph is very easy and really works the way that most
people think about drawing graphs.
But how did Mathcad cope with the real business of actually
doing the math? There are three hundred built in functions
to choose from, so these should cover most engineering
requirements. In fact, the functions are mainly geared
towards engineering and the more ‘practical’ aspects
of mathematics. It doesn't have spherical harmonics
for example (though, to be fair, Mathcad tells us that
there are several ways around this limitation).
But for a truly difficult test, I threw my favourite ‘nasty’ integral
at Mathcad. This is actually from a real life problem
I came across in an argument about the performance of
a telescope. The integral is a highly oscillatory Fresnel
integral, and to be honest, I didn’t expect Mathcad
to cope. Well, it didn’t. But it was in good company – neither
did the considerably more expensive Maple. Mathematica
was the only product of the three that actually came
up with the goods (see The Bitwise review of Mathematica
This type of integral is very difficult to
deal with. Out of the three, Mathcad, Maple and Mathematica,
only Mathematica did the business.
But apart from trick questions like the Fresnel integral,
Mathcad generally performs absolutely solidly. It inverts
matrices, solves differential equations and does symbolic
mathematics – all the stuff you normally want to
Mathcad has a simple programming language. It’s
so simple that it only has eight keywords or so, but
that is quite sufficient to write scripts of reasonable
complexity. However, I found it quite slow to use, mainly
because I had to use the Programming Toolbar to do anything.
Typically, you don’t type the keyword while,
you select it from the Toolbar which creates placeholders
for the keywords. I wouldn’t like to enter anything
very complicated in it, such as adding spherical harmonics,
for example. You could do it, but it might take some
Programming Mathcad is very simple, but for
anything complicated, it could take a long time to enter.
However, there’s also a ‘programmable interface’.
With this, you can code the complicated stuff in C or
C++ using algorithms from, say, ‘Numerical
Recipes in C, Second Edition’. Just look up the relevant
page (page 254 for spherical harmonics, if you are interested)
and type it in.
Initially, this struck me as being slightly odd. There
is a vast gulf between C/C++ and the ‘baby-talk’ programming
of Mathcad. But on reflection, I decided that it wasn’t
so dumb after all. Few people will code something like
a spherical harmonic in script. It’s far quicker
to copy it from a textbook like Numerical
it independently and then package it as a DLL to be used
But there’s another scripting tool available.
In line with Mathcad’s Windows/Office approach,
you can also use VBScript to hook up other ActiveX controls.
If you wished, you could write a custom ActiveX control
to perform mathematical or, particularly, database oriented
applications. In conjunction with the Data Acquisition
Control (DAC) – an ActiveX control that can connect
to a hardware data logger (or similar) – you can
write a pretty sophisticated data logger and processor
for an engineering test bed. Write it quickly, too.
Most engineers and scientists must have had the experience
of staring at a number on a piece of paper and wondering “where
on earth did I get that value from?” Usually six
months after the event while you’re trying to explain
some unfortunate mishap to your boss. It’s certainly
happened to me. More than once.
To help with potentially embarrassing situations like
this, Mathsoft has built an ‘audit trail’ system
into Mathcad. You can ‘annotate’ a worksheet,
showing where the numbers came from. Further, you can
create a ‘provenance’ audit-trail back through
several worksheets for complex systems. I’m not
sure it’s lawyer-proof, but it should help with
figuring out how you got to a particular answer.
So how does Mathcad stack up against Mathematica and
Maple? Well, in my view it isn’t in the same league.
But then it isn’t intended to be. It costs a
good bit less than Mathematica or Maple
and is clearly aimed at the engineering community – not
research scientists. Moreover, it’s embedded firmly
in the Windows/Office automation environment with no
pretence of portability. Consequently, for someone coming
from a Microsoft Office background – word-processing
and spreadsheets - it is much easier to use than Mathematica
or Maple and is amazingly simple to integrate into Office
A better comparison would be with Mathematica CalcCenter
(see The Bitwise review). CalcCenter is a bit cheaper
($595 / £515
ex VAT at the time of writing); but if you are interested
in Office integration, Mathcad is the better option.
While it doesn’t have the same symbolic mathematical
representation that CalcCenter has, its ease of use and
flexibility make up for that. Underneath the covers,
CalcCenter is a cut down Mathematica and works like its
big brother; if you don’t like Mathematica, there’s
a good chance you won’t get on with CalcCenter.
On the other hand, Mathcad isn’t a cut down version
of anything and its integration into the everyday Microsoft
world is superb. If you need to get a practical solution
to a real world problem, you might want to consider Mathcad.
Mathcad 13 :: System Requirements
- Pentium/Celeron processor, 400 MHz or higher; 700+
- 256 MB of RAM; 512 MB or more recommended
- 550 MB of hard disk space (250MB for Mathcad, 100MB
for prerequisites, 200MB temporary space during installation)
- Windows 2000 SP4, Windows XP SP2 or later
- CD-ROM or DVD drive (for CD installation only)
- SVGA or higher graphics card and monitor
- Mouse or compatible pointing device