MA332 Maple notes, Fall 1998

The assignment statement in Maple is :=

I don't know what, if anything, = means.

x := 6;

Creates a variable named x, assigns it the value 6.
All statements in Maple end with ;  (if you want output)
or : (if you want the statement executed silently).

Some variable names are protected (like names of math functions,
for example).

Digits is a protected variable that controls the number of
digits of precision when Maple does SOFTWARE floating point.

Digits := 40;      // sets the precision to 40 digits

By default, Maple does symbolic evaluation of expressions.

x := (x + 6/x) / 2;

yields  7/2, and

abs_error := x - sqrt(6);

yields 7/2 - sqrt(6)    (although Maple formats that nicely).

In order to evaluate these expressions in floating point, you
have to use the evalf command:

x := evalf((x + 6/x) / 2);
abs_error := evalf(x - sqrt(6));

These lines do what you expect, printing the result in all
its 40-digit splendor.

You might also want to try:

rel_error := evalf (abs_error / sqrt(6));
digits := -log (rel_error);

For the last command, it turns out that we don't need the evalf,
although it is not clear why (perhaps log and the other math functions
automatically use FP arithmetic if the argument is a FP value).

To execute a statement again, you can move the cursor to the line
you want to execute and press enter.  Thus, once you have typed in
the lines I suggested, you can execute the repeatedly to get
successive estimates.

Plotting:

To get the help page for the plot command, type

?plot

Then try the following:

plot (tan(x)-x, x=3.2..4.6);

You can define functions as follows:

f:=x->tan(x)-x;

And then plot them:

plot (f(x), x=3.2..4.6);

You can also plot more than one function on the same axes by
providing a list of functions:

plot ({tan(x), x}, x=3.2..4.6);