MATLAB by rudra pratap

236 Computer Algebra and The Symbolic Math Toolbox
Macsyma, later imitated by Mathematica and others. In the recent past, computer
algebra packages have added the ability to give numeric solutions and make nice
plots. Even though these programs run slower, are harder to learn, and are harder
to use than MATLAB for these purposes, Mathworks has felt the competition and
responded by providing this toolbox.
To master the Symbolic Math Toolbox, you have to master MuPAD, which is at
least as much work as learning MATLAB. You also have to learn how to run MuPAD
from inside MATLAB and keep your head straight at the same time. Basically, you
type a command that makes sense to either plain MATLAB or MuPAD, and if
plain MATLAB can't make sense of what you are requesting, it checks to see if you
have typed a legitimate MuPAD command (i.e., MATLAB's version of the MuPAD
command) .
8.1.1 Should you buy it?
Although some people swear by them, symbolic calculations seem to be less useful
than numeric computation to many people for two reasons. First, many problems
are too hard to do symbolically. An infinitely fast computer doing symbolic computation
will never tell you a formula for the integral of sin(log(x?), but MATLAB
will tell you the area under the curve as accurately as you would like (see Section
5.4, page 152) . Second, the symbolic formulas one obtains are often unwieldy.
How does, say, a 50-term symbolic formula give one more insight than a numeric
calculation?
With the Symbolic Math Toolbox, MATLAB can do essentially all that Mathematica,
Maple, or MuPAD can do. Because the Symbolic Math Toolbox comes
with the student edition of MATLAB, you might as well use MuPAD there for free.
If you don't have the Symbolic Math Toolbox and you don't know of any symbolic
calculations that you need to do, wait. Most engineers can do fine without it.
If you want to do a lot of back and forth between symbolic and numeric computation,
then MATLAB's Symbolic Math Toolbox is just the thing for you.
8.1.2 Two useful tools in the Symbolic Math Toolbox
Before getting more involved, you should note two cute and useful tools that come
with the Symbolic Math Toolbox.
1. A quick way to make plots: ezplot. Here is the simplest way to make
simple plots. This function (along with its cousins) is also available in basic
MATLAB (see Section 3.8 on 92 for examples) .
• The command ezplot sin(t), or more elaborately, ezplot (' sin(t) ') ,
makes a plot of the sin function on the default interval ( -27f, 21r).
• The command ezplot ( 't-2/exp (t) ' , [- 1 5] ) plots the function t2 jet
over the interval ( -1, 5).