Introduction to Matlab - to be used in conjunction with some book or
article of more substance, e.g. the student edition of Matlab, or the
Matlab Primer 

         How to plot data in MATLAB (for your information; work
           through this, but do not hand it in.)

  To display 2-dimensional data in MATLAB, use the function plot(),
  whose argument needs to be a vector.  MATLAB does not do symbolic
  math, so a command like plot(sin(t)) makes no sense unless MATLAB
  knows what "t" is (It does have its own algorithms for sine, cosine,
  etc. ).  Proceed thusly to graph the sine function on the interval
  [0,4*pi] using 125 equally spaced points (enter the commands as
  written to the right of the MATLAB prompt >>):

      >>t = 0:4*pi/125:4*pi       This creates a vector named t with entries
                                  [0,4*pi/125,8*pi/125,...,4*pi]

      Notice that this entire list of numbers was displayed on the
      screen, which is not generally what you want.  To SUPPRESS the
      display, end the line with a semi-colon(;)!

      >> x = sin(t);              This creates a vector named x with entries
                                  [sin(0),sin(4*pi/125),...,sin(4*pi)]

      >>plot(x)                   Notice the units...
      >>plot(t,x)                 What's the difference?

      >>y = sin(t+.25);           Phase shift
      >>z = sin(t+.5);            Another
    
      >>hold on                   The next graph drawn will not erase
                                  the present one.

      >>plot(t,y,'--')
      >>plot(t,z,'.')

      >>title('sine function with phase shift')
      >>xlabel('t')
      >>ylabel('sin(t+)')         Self-explanatory

      >>hold off

      >>plot(x,z)                 What is this?

      >>subplot(3,1,1), plot(x)
      >>subplot(3,1,2), plot(y)
      >>subplot(3,1,3), plot(z)   Subplot(m,n,p) creates an m by n array
                                  of plots on a single screen, and refers
                                  to the pth one, counting from the upper
                                  left.  Experiment with this a bit,
				  till you're sure how it works.  

      To get a printout from MATLAB:

      >>print -dps2               Sends whatever's displayed to the
                                  printer; once something's gone from
				  the screen, it can't be printed. The
				  -dps2 makes it print faster; just
				  plain "print" will also work.

      >>print -dps2 filename.ps   Command to save the current image as a
                                  text file with the name "filename.ps".
				  At some later time, this can be sent
				  to the printer by using the command
				  %lp filename.ps (this command is
				  issued from outside MATLAB, in a
				  cmdtool window.)

VERY IMPORTANT!!  MATLAB has an extremely useful "help" facility.  If
you don't know how the print command works, do

      >>help print

and similarly for everything else.  In the next section, you may want to
type help eul at some point....

Before beginning the next section, do

      >>subplot(1,1,1)

to get back to a single figure.  There are other ways to do this,
including

      >>clf

To save your favorite variable(s) so that they'll be available to you the
next time:

     >>save myfile x y z

saves x, y, and z in a file named myfile.mat

To leave Matlab, 

     >>quit

To LOAD the file myfile.mat,

     %matlab               
     >>load myfile

Last but not least, YOU CAN RECALL AND EDIT THE PREVIOUS COMMANDS.  This
means you do not have to type in a complicated expression more than once.
The commands are (try them out).

    ctrl-p  (hold down the control key and then press p) displays the
            previous command.  Doing it twice displays the "next" previous
	    command. 

    ctrl-n  the next command in case you went back too far.
   
Once you've got the line you want on the screen, you can edit it by doing

    ctrl-b     non-destructive backspace
    ctrl-f     forward one character
    ctrl-d     delete the character under the cursor
    backspace  delete the character to the left of the cursor
    ctrl-a     beginning of the line
    ctrl-e     end of the line
    ctrl-k     erase everything to the right of the cursor

That should be enough to get you going.......You'll learn more as you
proceed through the labs.  Be aware that Matlab is a professional research
tool, used daily by thousands of working scientists.  It will be a useful
addition to your collection of skills to become proficient in its use.

NOTE:  As a last resort, there's a user's guide and a reference manual on
the table near the door to the lab.  Please refrain from stealing them.

As a next-to-the-last resort, you can purchase the Student Edition of
Matlab at one of the bookstores.  You can either get a DOS version (that
requires Windows) or a Macintosh version.  Retail price (as of this
writing) is about $65-70.  Be sure to get the 4.x (instead of 3.5x)
version.  This has a rather useful manual, and the Matlab software
(slightly limited in that it will only handle 90x90 matrices, but for most
people, that's plenty) which includes the Maple symbolic toolbox.  It's a
pretty good deal, in my opinion, particularly compared to the comparable
deals for Mathematica.