Maple Worksheet Math 356 February 1, 2007 Problem 1. A Prime Example. Make a list of the prime numbers between 1 and 100. Find their sum. Problem 2. A Graphic Example. Replicate Figures 1.27, 1.28a, 1.28b, and 1.28c. Problem 3. A Loopy Example. Write a program that inputs a list L and uses iterated first differences to output a polynomial f(x) such that f(i)=L[i] for all i. (To make Problem 3 easier, you may assume that the polynomial is of degree 4 or less. You will get a bonus point if your program works for a polynomial of any degree on a list of finite length.) Background for Problem 3: Given a list of numbers, you can determine if the list comes from a polynomial of degree n or less by seeing if the list of nth differences is constant. As an example: If f(x)=5x+3, then [seq(f(i),i=1..5)]=[8,13,18,23,28]. The first differences are [5,5,5,5]. This tells us that f(x) is of degree 1 (linear). [Be careful to investigate first what the second differences of L[i]:=i^2 are, the third differences of L[i]:=i^3 are, and the fourth differences of L[i]:=i^4 are.] Back to the Maple Page. Back to the Math 356 Home Page.