In the previous sections we have been defining expressions instead of functions/procedures. Below f is an expression and g is a procedure. Compare the definitions and their use.
f := x^3 + x + 5; defining an expression f g := proc(x) x^3 + x + 5 end; defining a procedure g subs( x=1, f ); g(1); evaluating f and g at x=1. diff(f, x); diff(g(x), x); differentiationOccasionally, one must deal with procedures instead of expressions. Consider the definition below.
h := proc(x) Hit Line Feed
if ( type(x,numeric) ) Line Feed
then if (x<0) then 1 else -1 fi Line Feed
else 'h'(x) Line Feed
fi Line Feed
end: Return
It defines a procedure named h, of one variable x, for which
Note that every if statement is ended by fi and the
proc definition is ended by an end. In the definition
of 
the part about ``x is not a number'' is included to handle
those situations - there is more to it but we skip the details for the moment.
Now try the following and examine whether the results are what you
expected.
h(3); h(-5); h(0); plot( h(x), x=-5..5 ); plot( x^2, x=-5..5 ); plot( h(x)*x^2, x=-5..5 );It is imperative to keep in mind that whenever an expression containing a procedure is evaluated the arguments of the procedure are evaluated before the procedure is invoked. This leads to the most frequently occurring errors in the use of procedures. Be sure you understand why the the Maple output of the following statements is what it is.
a := 2; b :=3;
f := proc(x,y) x+2*y end;
f(c,d); f(a,x);
f(a,d^2); f(a^2,d);
f(a,b); f('a','b'); f('a^2',b^2);
The last executed line is particularly important - if an argument
of a function is an expression enclosed in right quotes
then the result of evaluating that argument is the expression
inside the quotes - we saw this in Subsection 1.9.
For more about defining procedures, using ``if then else'' etc.
see the book on Maple on reserve in the library.
