ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE
10th Edition
ISBN: 9781119809210
Author: Kreyszig
Publisher: WILEY
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1.5. Run Programs 1 and 2 with esin(x) replaced by (a) esin² (x) and (b) esin(x)| sin(x)||
and with uprime adjusted appropriately. What rates of convergence do you observe?
Comment.
Use Taylor Series to derive the entries to the pentadiagonal and heptadiagonal (septadiagonal?) circulant matrices
1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to
this behavior?
Chapter 17 Solutions
ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE
Ch. 17.1 - Prob. 1PCh. 17.1 - Prob. 2PCh. 17.1 - Prob. 3PCh. 17.1 - Prob. 4PCh. 17.1 - Prob. 5PCh. 17.1 - Prob. 6PCh. 17.1 - Prob. 7PCh. 17.1 - Prob. 8PCh. 17.1 - Prob. 9PCh. 17.1 - Prob. 11P
Ch. 17.1 - Prob. 12PCh. 17.1 - Prob. 13PCh. 17.1 - Prob. 14PCh. 17.1 - Prob. 15PCh. 17.1 - Prob. 16PCh. 17.1 - Prob. 17PCh. 17.1 - Prob. 18PCh. 17.1 - Prob. 19PCh. 17.1 - Prob. 20PCh. 17.1 - Prob. 21PCh. 17.1 - Prob. 22PCh. 17.1 - Prob. 23PCh. 17.1 - Prob. 24PCh. 17.1 - Prob. 25PCh. 17.1 - Prob. 26PCh. 17.1 - Prob. 27PCh. 17.1 - Prob. 29PCh. 17.1 - Prob. 30PCh. 17.1 - Prob. 31PCh. 17.1 - Prob. 32PCh. 17.1 - Prob. 33PCh. 17.1 - Prob. 34PCh. 17.1 - Prob. 35PCh. 17.2 - Prob. 1PCh. 17.2 - Prob. 2PCh. 17.2 - Prob. 3PCh. 17.2 - Prob. 4PCh. 17.2 - Prob. 5PCh. 17.2 - Prob. 6PCh. 17.2 - Prob. 7PCh. 17.2 - Prob. 8PCh. 17.2 - Prob. 9PCh. 17.2 - Prob. 10PCh. 17.2 - Prob. 11PCh. 17.2 - Prob. 12PCh. 17.2 - Prob. 13PCh. 17.2 - Prob. 14PCh. 17.2 - Prob. 15PCh. 17.2 - Prob. 16PCh. 17.2 - Prob. 17PCh. 17.2 - Prob. 18PCh. 17.2 - Prob. 19PCh. 17.2 - Prob. 20PCh. 17.3 - Prob. 8PCh. 17.3 - Prob. 9PCh. 17.3 - Prob. 10PCh. 17.3 - Prob. 11PCh. 17.3 - Prob. 12PCh. 17.3 - Prob. 13PCh. 17.3 - Prob. 14PCh. 17.3 - Prob. 15PCh. 17.3 - Prob. 16PCh. 17.3 - Prob. 17PCh. 17.4 - Prob. 1PCh. 17.4 - Prob. 2PCh. 17.4 - Prob. 3PCh. 17.4 - Prob. 4PCh. 17.4 - Prob. 5PCh. 17.4 - Prob. 6PCh. 17.4 - Prob. 7PCh. 17.4 - Prob. 9PCh. 17.4 - Prob. 10PCh. 17.4 - Prob. 11PCh. 17.4 - Prob. 15PCh. 17.4 - Prob. 16PCh. 17.4 - Prob. 17PCh. 17.4 - Prob. 18PCh. 17.4 - Prob. 19PCh. 17.4 - Prob. 20PCh. 17.4 - Prob. 21PCh. 17.4 - Prob. 22PCh. 17.4 - Prob. 25PCh. 17.5 - Prob. 1PCh. 17.5 - Prob. 2PCh. 17.5 - Prob. 5PCh. 17.5 - Prob. 7PCh. 17.5 - Prob. 10PCh. 17 - Prob. 1RQCh. 17 - Prob. 2RQCh. 17 - Prob. 3RQCh. 17 - Prob. 4RQCh. 17 - Prob. 5RQCh. 17 - Prob. 6RQCh. 17 - Prob. 7RQCh. 17 - Prob. 8RQCh. 17 - Prob. 9RQCh. 17 - Prob. 10RQCh. 17 - Prob. 11RQCh. 17 - Prob. 12RQCh. 17 - Prob. 13RQCh. 17 - Prob. 14RQCh. 17 - Prob. 15RQCh. 17 - Prob. 16RQCh. 17 - Prob. 17RQCh. 17 - Prob. 18RQCh. 17 - Prob. 19RQCh. 17 - Prob. 20RQCh. 17 - Prob. 21RQCh. 17 - Prob. 23RQCh. 17 - Prob. 24RQCh. 17 - Prob. 25RQCh. 17 - Prob. 26RQCh. 17 - Prob. 27RQCh. 17 - Prob. 28RQCh. 17 - Prob. 39RQ
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- 1.6. By manipulating Taylor series, determine the constant C for an error expansion of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative. Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the dashed line corresponding to this leading term rather than just N-4. This adjusted dashed line should fit the data almost perfectly. Plot the difference between the two on a log-log scale and verify that it shrinks at the rate O(h6).arrow_forwardDefine sinc(x) = sin(x)/x, except with the singularity removed. Differentiate sinc(x) once and twice.arrow_forward1.4. Run Program 1 to N = 216 instead of 212. What happens to the plot of error vs. N? Why? Use the MATLAB commands tic and toc to generate a plot of approximately how the computation time depends on N. Is the dependence linear, quadratic, or cubic?arrow_forward
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