**PLOTTING IN MAPLE**

MAPLE is available in the PSII (William Small
Centre), GAUSS and JUPITER labs.

Here is a sample MAPLE session to
plot the function ( p - x)/2 if 0 < x < 2 p and the first three partial sums of its
Fourier series. The function has Fourier
coefficients a_{n} = 0, b_{n} = 1/n.

1. Start the
computer (if it is off) and click OK on the notice. Enter your ACADLAB username and
password. Wait for the programs to
Load. BE
PATIENT – it takes a while.

2. Click on the START button in the lower left-hand
corner of the screen and choose Program – Maple 8 – Maple 8.

(Maple 9 is also
available but it didn’t seem to open properly in PSII. In any case, there is not much difference
between them for the purpose of this course).

3. You will get a MAPLE window in which you can
enter the commands as listed below. Note
that > is the MAPLE prompt.

> f:=(Pi-x)/2;

> s1:=sin(x);

> s2:=s1+sin(2*x)/2;

> s3:=s2+sin(3*x)/3;

> plot([f,s1,s2,s3],x=0..2*Pi,colour=black);

You can add text to your worksheet by using
the command ctrl-t. You should do this
to explain what you are doing and to answer questions on the MAPLE part of the
assignment. Using the colour=black
option produces clearer output when printing the file. You can find out more about using the
plotting command by using the help file.

> help(plot);

Try using MAPLE to plot the function f(x) =
|x| if -1 < x < 1 and the first few partial sums of its Fourier
series. Here the coefficients are a_{0}
= ˝, a_{2n} = 0, a_{2n+1} = 4/(p(2n+1))^{2}, b_{n} = 0. This function has period 2 so the series
contains the terms cos(npx).

You can save your work by using the
SAVE AS command on the FILE menu. Since
you have limited space to store files and the plots can take a lot of memory,
go to the EDIT menu and click on REMOVE OUTPUT -> WORKSHEET. When you open the file next time you can
regenerate the plots by going to the EDIT menu and clicking EXECUTE ->
WORKSHEET.

In order to print
your work click on the PRINT command on the FILE menu. If you are in the Jupiter lab choose PARKING-LAB
as your printer. You will then have to
go to the parking Garage lab to retrieve your output (and pay for it). The Gauss and PSII labs have printers on
site.

In order to quit the MAPLE program
go to the file menu and click on EXIT.

There are lots of other features of
MAPLE which you can explore using the help command.

There will be a MAPLE tutorial in
the Jupiter lab (226 Petrie) on Wednesday, Sept 24 at