Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 22, Problem 18P
To determine
To prove: The equation 22.15 mentioned in the textbook is equivalent to Boole’s rule.
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Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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Chapter 22 Solutions
Numerical Methods for Engineers
Ch. 22 - 22.1 Use order of Romberg integration to...Ch. 22 - Use Romberg integration to evaluate I=12(x+1x)2dx...Ch. 22 - Use Romberg integration to evaluate 02exsinx1+x2dx...Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - 22.6 Obtain an estimate of the integral from Prob....Ch. 22 - 22.7 Perform the computation in Examples 21.3 and...Ch. 22 - Employ two- through six-point Gauss-Legendre...Ch. 22 - Prob. 9PCh. 22 - 22.10 Develop a user-friendly computer program for...
Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - 22.13 Develop a user-friendly computer program for...Ch. 22 - There is no closed form solution for the error...Ch. 22 - 22.15 The amount of mass transported via a pipe...Ch. 22 - The depths of a river H are measured at equally...Ch. 22 - 22.17 Recall that the velocity of the freefalling...Ch. 22 - 22.18 Prove that Eq. (22.15) is equivalent to...
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