This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: University of Durham EXAMINATION PAPER date May/June 2006 exam code MATH2051/01 description NUMERICAL ANALYSIS II Time allowed: 3 hours Examination material provided: None Instructions: Credit will be given for the best FOUR answers from Section A and the best THREE answers from Section B. Questions in Section B carry TWICE as many marks as those in Section A. Approved electronic calculators may be used. ED01/2006 Durham University Copyright continued 2 MATH2051/01 SECTION A 1. Let f ( x ) = e x sin x . Prove that the equation f ( x ) = 0 has a unique solution, p , in the interval (0 , . 8). Carry out two stages of the bisection method to estimate p , and give a bound on the magnitude of the error in your estimate. How many stages of the bisection method would be necessary to guarantee an error of no more than 10 6 ? 2. The roots x 1 and x 2 of the quadratic equation x 2 + 2 bx + c = 0 are given by x 1 = b + b 2 c and x 2 = b b 2 c. Let b = 1 and c = 5 10 4 . Using threedigit arithmetic with rounding after every arithmetic operation, calculate x 1 and x 2 using the formulae above. How do these two values compare with that of your calculator to three significant figures? If there is a difference, suggest an alternative, mathematically equivalent formula which overcomes this difference....
View
Full
Document
 Fall '11
 Dr.A.Wacher
 Math, Numerical Analysis

Click to edit the document details