Here are two versions of the iterlin() program described in Chapter 1.

• A Maple procedure

  iterlin := proc(a, b, x0, n)
  local i,x;
  x := x0:
  for i from 1 to n do
  x := a*x + b:
  print(evalf(x)):
  end do:
  end proc:
  

  As you enter the code, you need to press [SHIFT-ENTER] at the end of each line, except for the last, where you press [ENTER]. The code defines a procedure that takes four arguments, a, b, x₀, and n. So, for example, to generate the first ten iterates of the function f(x) = -0.5x+4 starting with x₀ = 5, we enter

  > iterlin(-0.5, 4, 5, 10);
  

• A Mathematica function

  iterlin[a_, b_, x0_, n_] := 
     NestList[(a #1 + b)&, x0, n]
  

  Type this in as a single line, followed by [SHIFT-ENTER]. Now iterlin is defined as a function of the four variables a, b, x₀, and n. To get a list of the first ten iterates of the function f(x) = -0.5x+4 starting with x₀ = 5, we type in

  > iterlin[-0.5, 4, 5, 10]
  

  followed by [SHIFT-ENTER].