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Faculty of Engineering and Computer Science ENGR 391 Numerical Methods in Engineering Assignment 1 Due February 2nd, 2011 Introduction to error analysis Objective: Review some basic mathematical concepts Be aware of round-off errors Apply the Taylor series to estimate truncation errors 1. Problem 1.14 in the textbook 2. Given the following function: f (x) = x 3 – 6.1 x 2 + 3.2 x + 1.5 a) Use a calculator to obtain the exact solution with value determined to be at least six digits for x = 4.71 b) Evaluate the same function using three-digit arithmetic with 1) chopping and 2) rounding. Compute the relative errors for the three-digit methods. c) Redo the calculation in part b) by first rewriting the above equation in a nested manner. 3. Given x x x x x x f sin sin cos ) ( a) Find x f Limit x 0 b) Use four digit rounding arithmetic to evaluate f (0.1) c) Replace each trigonometric function with its third Maclaurin polynomial and repeat part b)
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