ADVANCED ENGINEERING MATH W/ACCESS
10th Edition
ISBN: 9781119096023
Author: Kreyszig
Publisher: WILEY
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Chapter 22.1, Problem 10P
CAS EXPERIMENT. Steepest Descent. (a) Write a program for the method.
(b) Apply your program to
c) Apply your program to
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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
ADVANCED ENGINEERING MATH W/ACCESS
Ch. 22.1 - Prob. 1PCh. 22.1 - Prob. 2PCh. 22.1 - Prob. 3PCh. 22.1 - Prob. 4PCh. 22.1 - Prob. 5PCh. 22.1 - Prob. 6PCh. 22.1 - Prob. 7PCh. 22.1 - Prob. 8PCh. 22.1 - Prob. 9PCh. 22.1 - CAS EXPERIMENT. Steepest Descent. (a) Write a...
Ch. 22.2 - Prob. 1PCh. 22.2 - Prob. 2PCh. 22.2 - Prob. 3PCh. 22.2 - Prob. 4PCh. 22.2 - Prob. 5PCh. 22.2 - Prob. 6PCh. 22.2 - Prob. 8PCh. 22.2 - Prob. 9PCh. 22.2 - Prob. 10PCh. 22.2 - Prob. 11PCh. 22.2 - Prob. 12PCh. 22.2 - Prob. 13PCh. 22.2 - Prob. 14PCh. 22.2 - Prob. 15PCh. 22.2 - Prob. 16PCh. 22.2 - Prob. 17PCh. 22.2 - Prob. 18PCh. 22.2 - Prob. 19PCh. 22.2 - Prob. 20PCh. 22.2 - Prob. 21PCh. 22.2 - Prob. 22PCh. 22.3 - Prob. 1PCh. 22.3 - Prob. 2PCh. 22.3 - Prob. 3PCh. 22.3 - Prob. 4PCh. 22.3 - Prob. 5PCh. 22.3 - Prob. 6PCh. 22.3 - Prob. 7PCh. 22.3 - Prob. 8PCh. 22.3 - Prob. 9PCh. 22.3 - Prob. 10PCh. 22.3 - Prob. 11PCh. 22.3 - Prob. 12PCh. 22.3 - Prob. 13PCh. 22.3 - Prob. 14PCh. 22.4 - Prob. 1PCh. 22.4 - Prob. 2PCh. 22.4 - Prob. 3PCh. 22.4 - Prob. 4PCh. 22.4 - Prob. 6PCh. 22.4 - Prob. 7PCh. 22.4 - Prob. 8PCh. 22.4 - Prob. 9PCh. 22 - Prob. 1RQCh. 22 - Prob. 2RQCh. 22 - Prob. 3RQCh. 22 - Prob. 4RQCh. 22 - Prob. 5RQCh. 22 - Prob. 7RQCh. 22 - Prob. 8RQCh. 22 - Prob. 9RQCh. 22 - Prob. 10RQCh. 22 - Prob. 11RQCh. 22 - Prob. 13RQCh. 22 - Prob. 14RQCh. 22 - Prob. 15RQCh. 22 - Prob. 16RQCh. 22 - Prob. 17RQCh. 22 - Prob. 18RQCh. 22 - Prob. 19RQCh. 22 - Prob. 20RQ
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