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 12, Problem 14P
Civil/Environmental Engineering
Perform the same computation as in Sec. 12.2, but for the truss depicted in Fig. P12.14.
FIGURE P12.14
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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 12 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 12 - Chemical/Bio Engineering
12.1 Perform the same...Ch. 12 - Chemical/Bio Engineering If the input to reactor 3...Ch. 12 - Chemical/Bio Engineering Because the system shown...Ch. 12 - Chemical/Bio Engineering
12.4 Recompute the...Ch. 12 - Chemical/Bio Engineering Solve the same system as...Ch. 12 - Chemical/Bio Engineering
12.6 Figure P12.6 shows...Ch. 12 - Chemical/Bio Engineering
12.7 Employing the same...Ch. 12 - Chemical/Bio Engineering The Lower Colorado River...Ch. 12 - Chemical/Bio Engineering A stage extraction...Ch. 12 - Chemical/Bio Engineering
12.10 An irreversible,...
Ch. 12 - Chemical/Bio Engineering
12.11 A peristaltic pump...Ch. 12 - Chemical/Bio Engineering
12.12 Figure P12.12...Ch. 12 - Civil/Environmental Engineering A civil engineer...Ch. 12 - Civil/Environmental Engineering Perform the same...Ch. 12 - Civil/Environmental Engineering
12.15 Perform the...Ch. 12 - Civil/Environmental Engineering Calculate the...Ch. 12 - Civil/Environmental Engineering In the example for...Ch. 12 - Civil/Environmental Engineering Employing the same...Ch. 12 - Civil/Environmental Engineering Solve for the...Ch. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Civil/Environmental Engineering
12.22 A truss is...Ch. 12 - Electrical Engineering
12.23 Perform the same...Ch. 12 - Electrical Engineering Perform the same...Ch. 12 - Electrical Engineering
12.25 Solve the circuit in...Ch. 12 - Electrical Engineering
12.26 An electrical...Ch. 12 - Electrical Engineering
12.27 Determine the...Ch. 12 - Electrical Engineering Determine the currents for...Ch. 12 - Electrical Engineering The following system of...Ch. 12 - Electrical Engineering
12.30 The following system...Ch. 12 - Mechanical/Aerospace Engineering Perform the same...Ch. 12 - Mechanical/Aerospace Engineering
12.32 Perform the...Ch. 12 - Mechanical/Aerospace Engineering
12.33 Idealized...Ch. 12 - Mechanical/Aerospace Engineering Three blocks are...Ch. 12 - Mechanical/Aerospace Engineering Perform a...Ch. 12 - Mechanical/Aerospace Engineering Perform the same...Ch. 12 - Mechanical/Aerospace Engineering
12.37 Consider...Ch. 12 - Mechanical/Aerospace Engineering The steady-state...Ch. 12 - Mechanical/Aerospace Engineering
12.40 A rod on a...
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