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They discuss what types of variables can exist within a procedure and the evaluation rules applied to each. Parameters Chapter 1 introduced you to local and global variables, but procedures have a more fundamental type of variable: parameters. Parameters are variables whose name appears between the parentheses of a proc()expression. They have a special role within procedures, as Maple replaces them with arguments when you execute the procedure. 48 • Chapter 2: Fundamentals Examine the following procedure which squares its first argument and assigns the answer to the second argument, which must be a name.

Write a Maple procedure called sigma which, given n > 1 data values, x1 , x2 , . . , xn , computes their standard deviation. The following equation gives the standard deviation of n > 1 numbers, σ= 1 n n (xi − µ)2 i=1 where µ is the average of the data values. You create lists and many other objects in Maple out of more primitive data structures called sequences . The list X defined previously contains the following sequence. 1 You can select elements from a sequence in the same way you select elements from a list.

P := randpoly(x, degree=50) * randpoly(x, degree=99); p := (77 x48 + 66 x44 + 54 x37 − 5 x20 + 99 x5 − 61 x3 ) (−47 x57 − 91 x33 − 47 x26 − 61 x25 + 41 x18 − 58 x8 ) > max( coeffs( map(abs, expand(p)) ) ); 9214 Exercise 1. Write a procedure that computes the Euclidean norm of a polynomial; n 2 that is, i=0 |ai | . The Chebyshev Polynomials, Tn (x) The Chebyshev polynomials, Tn (x), satisfy the following linear recurrence. Tn (x) = 2xTn−1 (x) − Tn−2 (x), for n ≥ 2. The first two Chebyshev polynomials are T0 (x) = 1 and T1 (x) = x.