Monday, August 25, 2008

Computational Mathematics - Examples on Difference Operators

Ex 1. For the function f(x) = x3 - x2 + 5, create the forward difference table. Range of values of x is -2 ≤ x ≤ 3

Ex 2. If y = x3 + x2 - 2x + 1, calculate values of y for x = 0, 1, 2, 3, 4, 5 and form the difference table. Find the value of y at x = 6 by extending the table and verify that the same value is obtained by substitution.

Ex 3. Form the forward difference table for the function f(x) = x3 + 5x - 7 for x = -1, 0, 1, 2, 3, 4, 5. Continue the table to obtain f(6) and f(7).

Ex 4. Construct the table of differences for the data given below:
f(0) = 1.0, f(1) = 1.5, f(2) = 2.2, f(3) = 3.1, f(4) = 4.
Evaluate Δ3f(2).
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