ADVANCED ENGINEERING MATHEMATICS
10th Edition
ISBN: 9781119664697
Author: Kreyszig
Publisher: WILEY
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1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to
this behavior?
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).
Define sinc(x) = sin(x)/x, except with the singularity removed. Differentiate sinc(x) once and twice.
Chapter 18 Solutions
ADVANCED ENGINEERING MATHEMATICS
Ch. 18.1 - Prob. 1PCh. 18.1 - Prob. 2PCh. 18.1 - Prob. 3PCh. 18.1 - Prob. 4PCh. 18.1 - Prob. 5PCh. 18.1 - Prob. 6PCh. 18.1 - Prob. 7PCh. 18.1 - Prob. 9PCh. 18.1 - Prob. 10PCh. 18.1 - Prob. 11P
Ch. 18.1 - Prob. 12PCh. 18.1 - Prob. 13PCh. 18.1 - Prob. 14PCh. 18.1 - Prob. 15PCh. 18.2 - Prob. 1PCh. 18.2 - Prob. 3PCh. 18.2 - Prob. 4PCh. 18.2 - Prob. 6PCh. 18.2 - Prob. 7PCh. 18.2 - Prob. 8PCh. 18.2 - Prob. 9PCh. 18.2 - Prob. 11PCh. 18.2 - Prob. 12PCh. 18.2 - Prob. 13PCh. 18.2 - Prob. 14PCh. 18.2 - Prob. 15PCh. 18.2 - Prob. 16PCh. 18.2 - Prob. 17PCh. 18.2 - Prob. 18PCh. 18.2 - Prob. 19PCh. 18.2 - Prob. 20PCh. 18.3 - Prob. 1PCh. 18.3 - Prob. 2PCh. 18.3 - Prob. 4PCh. 18.3 - Prob. 5PCh. 18.3 - Prob. 6PCh. 18.3 - Prob. 7PCh. 18.3 - Prob. 8PCh. 18.3 - Prob. 9PCh. 18.3 - Prob. 10PCh. 18.3 - Prob. 11PCh. 18.3 - Prob. 12PCh. 18.3 - Prob. 13PCh. 18.3 - Prob. 14PCh. 18.3 - Prob. 15PCh. 18.3 - Prob. 16PCh. 18.3 - Prob. 17PCh. 18.3 - Prob. 18PCh. 18.3 - Prob. 19PCh. 18.3 - Prob. 20PCh. 18.4 - Prob. 1PCh. 18.4 - Prob. 2PCh. 18.4 - Prob. 3PCh. 18.4 - Prob. 4PCh. 18.4 - Prob. 5PCh. 18.4 - Prob. 6PCh. 18.4 - Prob. 7PCh. 18.4 - Prob. 8PCh. 18.4 - Prob. 9PCh. 18.4 - Prob. 10PCh. 18.4 - Prob. 11PCh. 18.4 - Prob. 12PCh. 18.4 - Prob. 13PCh. 18.4 - Prob. 14PCh. 18.4 - Prob. 15PCh. 18.4 - Prob. 16PCh. 18.4 - Prob. 17PCh. 18.4 - Prob. 18PCh. 18.4 - Prob. 19PCh. 18.5 - Prob. 1PCh. 18.5 - Prob. 2PCh. 18.5 - Prob. 3PCh. 18.5 - Prob. 4PCh. 18.5 - Prob. 5PCh. 18.5 - Prob. 6PCh. 18.5 - Prob. 7PCh. 18.5 - Prob. 8PCh. 18.5 - Prob. 9PCh. 18.5 - Prob. 10PCh. 18.5 - Prob. 11PCh. 18.5 - Prob. 12PCh. 18.5 - Prob. 13PCh. 18.5 - Prob. 14PCh. 18.5 - Prob. 15PCh. 18.5 - Prob. 16PCh. 18.5 - Prob. 17PCh. 18.5 - Prob. 18PCh. 18.6 - Prob. 1PCh. 18.6 - Prob. 2PCh. 18.6 - Prob. 3PCh. 18.6 - Prob. 4PCh. 18.6 - Prob. 5PCh. 18.6 - Prob. 6PCh. 18.6 - Prob. 7PCh. 18.6 - Prob. 8PCh. 18.6 - Prob. 9PCh. 18.6 - Prob. 10PCh. 18.6 - Prob. 13PCh. 18.6 - Prob. 14PCh. 18.6 - Prob. 15PCh. 18.6 - Prob. 16PCh. 18.6 - Prob. 17PCh. 18.6 - Prob. 18PCh. 18.6 - Prob. 19PCh. 18.6 - Prob. 20PCh. 18 - Prob. 1RQCh. 18 - Prob. 2RQCh. 18 - Prob. 3RQCh. 18 - Prob. 4RQCh. 18 - Prob. 6RQCh. 18 - Prob. 7RQCh. 18 - Prob. 9RQCh. 18 - Prob. 10RQCh. 18 - Prob. 11RQCh. 18 - Prob. 12RQCh. 18 - Prob. 14RQCh. 18 - Prob. 15RQCh. 18 - Prob. 16RQCh. 18 - Prob. 17RQCh. 18 - Prob. 18RQCh. 18 - Prob. 21RQCh. 18 - Prob. 22RQCh. 18 - Prob. 23RQCh. 18 - Prob. 25RQ
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Similar questions
- 1.4. 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_forwardShow that the function f(x) = sin(x)/x has a removable singularity. What are the left and right handed limits?arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21, 2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). 之一 dz, (b). dz, (b). COS 2 coz dz, dz (z+1) (d). z 2 +2 dz, (e). (c). (2z+1)zdz, z+ 1 (f). £, · [e² sin = + (2² + 3)²] dz. (2+3)2arrow_forward
- 18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0<|z|< 1, f(E) f(E) 2πif(z) = --- d.arrow_forward18.4. Let f be analytic within and on a positively oriented closed contoury, and the point zo is not on y. Show that L f(z) (-20)2 dz = '(2) dz. 2-20arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21,2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). rdz, (b). dz (b). COS 2 coz dz, (z+1) (d). 之一 z 2 +2 dz, (e). dz (c). (2z + 1)2dz, (2z+1) 1 (f). £, · [e² sin = + (2² + 3)²] dz. z (22+3)2arrow_forward
- 18.8. (a). Let be the contour z = e-≤0≤ traversed in the า -dz = 2xi. positive direction. Show that, for any real constant a, Lex dzarrow_forwardf(z) 18.7. Let f(z) = (e² + e³)/2. Evaluate dz, where y is any simple closed curve enclosing 0.arrow_forward18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1 and show that A„|(Am - 2) if m > n.]arrow_forward
- For each real-valued nonprincipal character x mod k, let A(n) = x(d) and F(x) = Σ : dn * Prove that F(x) = L(1,x) log x + O(1). narrow_forwardBy considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).arrow_forwardBy considering appropriate series expansions, ex · ex²/2 . ¸²³/³ . . .. = = 1 + x + x² +…… when |x| < 1. By expanding each individual exponential term on the left-hand side and multiplying out, show that the coefficient of x 19 has the form 1/19!+1/19+r/s, where 19 does not divide s.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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