Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 6, Problem 14P
Use (a) the Newton-Raphson method and (b) the modified secant method
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4. In each case, sketch the closure of the set:
(a) -л 0.
1. For each of the functions below, describe the domain of definition that is understood:
1
(a) f(z)
=
(b) f(z) = Arg
z²+1
Z
1
(c) f(z) =
(d) f(z) =
1 - | z | 2°
Ans. (a) z±i;
(b) Rez 0.
Chapter 6 Solutions
Numerical Methods for Engineers
Ch. 6 - 6.1 Use simple fixed-point iteration to locate the...Ch. 6 - 6.2 Determine the highest real root of...Ch. 6 - Use (a) fixed-point iteration and (b) the...Ch. 6 - Determine the real roots of f(x)=1+5.5x4x2+0.5x3:...Ch. 6 - 6.5 Employ the Newton-Raphson method to determine...Ch. 6 - Determine the lowest real root of...Ch. 6 - 6.7 Locate the first positive root of
Where x...Ch. 6 - 6.8 Determine the real root of, with the modified...Ch. 6 - 6.9 Determine the highest real root of:...Ch. 6 - 6.10 Determine the lowest positive root...
Ch. 6 - 6.11 Use the Newton-Raphson method to find the...Ch. 6 - 6.12 Given
Use a root location technique to...Ch. 6 - You must determine the root of the following...Ch. 6 - Use (a) the Newton-Raphson method and (b) the...Ch. 6 - 6.15 The “divide and average” method, an old-time...Ch. 6 - (a) Apply the Newton-Raphson method to the...Ch. 6 - 6.17 The polynomial has a real root between 15...Ch. 6 - Use the secant method on the circle function...Ch. 6 - You are designing a spherical tank (Fig. P6.19) to...Ch. 6 - 6.20 The Manning equation can be written for a...Ch. 6 - 6.21 The function has a double root at. Use (a)...Ch. 6 - 6.22 Determine the roots of the following...Ch. 6 - 6.23 Determine the roots of the simultaneous...Ch. 6 - Repeat Prob. 6.23 except determine the positive...Ch. 6 - A mass balance for a pollutant in a well-mixed...Ch. 6 - Fir Prob. 6.25, the root can be located with...Ch. 6 - 6.27 Develop a user-friendly program for the...Ch. 6 - Develop a user-friendly program for the secant...Ch. 6 - 6.29 Develop a user-friendly program for the...Ch. 6 - 6.30 Develop a user-friendly program for Brent’s...Ch. 6 - 6.31 Develop a user-friendly program for the...Ch. 6 - 6.32 Use the program you developed in Prob. 6.31...
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- 44 4. Write the function f(x)=2+ ANALYTIC FUNCTIONS 1 (z = 0) Z. in the form f(z) = u(r, 0) + iv(r, 0). Ans. f(z) = = (1 + ² ) cos+ir i ( r — 1 ) sin 0. r CHAP. 2arrow_forwardGiven the (3-2-1) Euler angle set (10,20,30) degrees, find the equivalent (3-1-3) Euler angles. All the following Euler angle sets are 3-2-1 Euler angles. The B frame relative to N is given through the 3-2-1 EAs (10,20,30) degrees, while R relative to N is given by the EAs (-5,5,5) degrees. What is the attitude of B relative to R in terms of the 3-2-1 EAsarrow_forward3. Suppose that f(z) = x² − y² −2y+i (2x-2xy), where z = x+iy. Use the expressions (see Sec. 6) x = z┼え 2 Z - Z and y = 2i to write f(z) in terms of z, and simplify the result. Ans. f(z)²+2iz.arrow_forward
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