By Richard L. Burden, J. Douglas Faires, Annette M. Burden
This well-respected booklet introduces readers to the speculation and alertness of recent numerical approximation innovations. offering an available remedy that in basic terms calls for a calculus prerequisite, the authors clarify how, why, and while approximation thoughts might be anticipated to work-and why, in a few occasions, they fail. A wealth of examples and routines increase readers' instinct, and show the subject's functional functions to special daily difficulties in math, computing, engineering, and actual technology disciplines. 3 many years after it was once first released, Burden, Faires, and Burden's NUMERICAL research continues to be the definitive advent to an important and sensible topic.
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Additional info for Numerical Analysis
5. 15242 x x x x x x x x x 10' 10° 10° lO"1 10"' lO"2 lO-2 lO"3 10"3 Relative error 9 I 9 8 8 7 6 x x x x x x x ur5 lO"3 10~3 lO"2 lO"1 10° 10' Now consider this recursive equation: pn = 2pn_, - Pn—i, forn = 2,3,... „_i - Pu—2 = 2(C| + c'2(n - 1)) - (c, + C2(n - 2)) = C| (2 - 1) + C2 (2n - 2- n + 2)=C|+ C2n = pn. If we are given pa = 1 and p, = f, then constants in this equation are uniquely determined to be C| = 1 and C2 = — |. This implies that pn = \ — |n. 33333. 66667. 6. 43333 x x x x x x x x x 10' 10° 100 10' 10' 10' 10' 10' 10' Relative error 9 x ur5 0 0 4 x lO"5 0 0 2 x lO"5 Copvright 2016 ("engage Learning.
28 CHAPTER 1 ■ Mathematical Preliminaries and Error Analysis APPLIED EXERCISES 26. The opening example to this chapter described a physical experiment involving the temperature of a gas underpressure. 100 m3. 08206. 15 K = 17 C. 08206) In the laboratory, it was found that T was 150C under these conditions, and when the pressure was doubled and the volume halved, T was 190C. Assume that the data are rounded values accurate to the places given, and show that both laboratory figures are within the bounds of accuracy for the ideal gas law.
Compute the absolute error and relative error in the following approximations of e\ in a. b EE! /i=0n" rt=0n" Let fix) = 14. x cos x — sin x : ■ x — sin x a. Find limA^o/(x). b. 1). c. Replace each trigonometric function with its third Maclaurin polynomial and repeat part (b). d. 99899998. Find the relative error for the values obtained in parts (b) and (c). Let fix) = 15. a. Find linv^oCe* — e~x)/x. b. 1). c. Replace each exponential function with its third Maclaurin polynomial and repeat part (b).