Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 5, Problem 14P
Use bisection to determine the drag coefficient needed so that an 82-kg parachutist has a velocity of 36 m/s after 4 s of free fall. Note: The acceleration of gravity is
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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
Chapter 5 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 5 - 5.1 Determine the real roots...Ch. 5 - 5.2 Determine the real root of:
(a) Graphically....Ch. 5 - 5.3 Determine the real root of:
(a)...Ch. 5 - Determine the roots of f(x)=1221x+18x22.75x3...Ch. 5 - Locate the first nontrivial root of sin x=x2wherex...Ch. 5 - 5.6 Determine the positive real root of (a)...Ch. 5 - 5.7 Determine the real root of:...Ch. 5 - 5.8 Find the positive square root of 18 using the...Ch. 5 - 5.9 Find the smallest positive root of the...Ch. 5 - 5.10 Find the positive real root of using the...
Ch. 5 - 5.11 Determine the real root of: (a) analytically...Ch. 5 - 5.12 Given
Use bisection to determine the...Ch. 5 - 5.13 The velocity v of a falling parachutist is...Ch. 5 - 5.14 Use bisection to determine the drag...Ch. 5 - As depicted in Fig. P5.15, the velocity of water,...Ch. 5 - 5.16 Water is flowing in a trapezoidal channel at...Ch. 5 - 5.17 You are designing a spherical tank (Fig....Ch. 5 - The saturation concentration of dissolved oxygen...Ch. 5 - 5.19 According to Archimedes principle, the...Ch. 5 - 5.20 Perform the same computation as in Prob....Ch. 5 - 5.21 Integrate the algorithm outlined in Fig. 5.10...Ch. 5 - Develop a subprogram for the bisection method that...Ch. 5 - 5.23 Develop a user-friendly program for the...Ch. 5 - Develop a subprogram for the false-position method...Ch. 5 - 5.25 Develop a user-friendly subprogram for the...Ch. 5 - 5.26 Develop a function for bisection in a similar...
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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?arrow_forward1.6. 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_forward
- 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
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