Defining Functions and Constants

Maple allows us to use symbols, like f, g, and so on to represent functions. The syntax for defining functions in Maple uses the assignment operator := and the symbol -> which is built up from - and >. For example to define , enter

      f:= x->x^2*(sin(x)+1)^2;

After a function has been defined, it can be evaluated at a point or used in a subsequent Maple command. To plot this function, we can use

      plot(f(x), x=0..2*Pi);

To evaluate a function at a point to find a numerical value use the evalf command. For example,

      evalf(f(2));

We can also use this construction to define a constant. For example,

      a:=Pi/2;

defines a to be . This is useful if we're using the same constant repeatedly.

We can also use this construction to define a function that depends on a parameter. For example,

     f:=(x,a)->sin(a*x);

Then we can plot the function for a particular value of a by using:

      plot(f(x,3), x=0..2*Pi);

We can also use this to plot several functions in a family of functions:

      plot({f(x,1),f(x,2),f(x,3)}, x=0..2*Pi);