Defining Functions and Procedures

1. You can define the real valued function f whose rule is f(x)=x^2:
> f := x-> x^2;

                                        2
                             f := x -> x

> f(2);

                                  4

> f(a+b);

                                      2
                               (a + b)

> expand(");

                            2            2
                           a  + 2 a b + b

> (f(x+h)-f(x))/h;

                                   2    2
                            (x + h)  - x
                            -------------
                                  h

> simplify(");

                               2 x + h

2. Create a procedure using proc to define more complicated real-valued functions:
> f := proc(x)
> if x > 3 then x^2
> else x-5 fi
> end;

           f := proc(x) if 3 < x then x^2 else x - 5 fi end

> f(2);

                                  -3

> f(5);

                                  25

> plot(f);

> plot(f, style=POINT);

Unassign the definition of f:
> f := 'f';

                                f := f

Functions of Several Variables

> f := (x,y) -> x^2 + y^2 -3;

                                      2    2
                      f := (x, y) -> x  + y  - 3

> f(2,5);

                                  26

Such functions can be ploted in three-dimensions:
> plot3d(f, -2..2, -2..2);

Automating Commands

Frequently, you will want to repeat some command or set of commands
several times with slightly different values. You do this with a looping structure
using for and do commands.

1. Print a table of values:
> for k from 1 to 3
> do
>   print(k, k^2);
> od;

                                 1, 1


                                 2, 4


                                 3, 9

> for k from 1 by .5 to 3
> do
>   print(k,k^2);
> od;

                                 1, 1


                              1.5, 2.25


                              2.0, 4.00


                              2.5, 6.25


                              3.0, 9.00

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