EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 42, Problem 70A
To determine
To solve:
The equation by using addition principle of equality.
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12.42 The steady-state distribution of temperature on a heated
plate can be modeled by the Laplace equation,
0=
FT T
+
200°C
25°C
25°C
T22
0°C
T₁
T21
200°C
FIGURE P12.42
75°C
75°C
00°C
If the plate is represented by a series of nodes (Fig. P12.42), cen-
tered finite-divided differences can be substituted for the second
derivatives, which results in a system of linear algebraic equations.
Use the Gauss-Seidel method to solve for the temperatures of the
nodes in Fig. P12.42.
9.22 Develop, debug, and test a program in either a high-level language or a macro
language of your choice to solve a system of equations with Gauss-Jordan elimination
without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the
program using the same system as in Prob. 9.18. Compute the total number of flops in
your algorithm to verify Eq. 9.37.
FIGURE 9.10
Pseudocode to implement the
Gauss-Jordan algorithm with-
out partial pivoting.
SUB GaussJordan(aug, m, n, x)
DOFOR k = 1, m
d = aug(k, k)
DOFOR j = 1, n
aug(k, j) = aug(k, j)/d
END DO
DOFOR 1 = 1, m
IF 1 % K THEN
d = aug(i, k)
DOFOR j = k, n
aug(1, j)
END DO
aug(1, j) - d*aug(k, j)
END IF
END DO
END DO
DOFOR k = 1, m
x(k) = aug(k, n)
END DO
END GaussJordan
11.9 Recall from Prob. 10.8, that the following system of equations
is designed to determine concentrations (the e's in g/m³) in a series
of coupled reactors as a function of amount of mass input to each
reactor (the right-hand sides are in g/day):
15c3cc33300
-3c18c26c3 = 1200
-4c₁₂+12c3 = 2400
Solve this problem with the Gauss-Seidel method to & = 5%.
Chapter 42 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
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Ch. 42 - Prob. 11ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 13ACh. 42 - Prob. 14ACh. 42 - Prob. 15ACh. 42 - Prob. 16ACh. 42 - Prob. 17ACh. 42 - Prob. 18ACh. 42 - Prob. 19ACh. 42 - Prob. 20ACh. 42 - Prob. 21ACh. 42 - Prob. 22ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 26ACh. 42 - Prob. 27ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Prob. 33ACh. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Prob. 37ACh. 42 - Prob. 38ACh. 42 - Prob. 39ACh. 42 - A Shaft rotates in a bearing that is 0.3968 inch...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - Prob. 43ACh. 42 - For each of the following problems, substitute the...Ch. 42 - Prob. 45ACh. 42 - Prob. 46ACh. 42 - Prob. 47ACh. 42 - Prob. 48ACh. 42 - Prob. 49ACh. 42 - Prob. 50ACh. 42 - Prob. 51ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 53ACh. 42 - Prob. 54ACh. 42 - Prob. 55ACh. 42 - Prob. 56ACh. 42 - Prob. 57ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 60ACh. 42 - Prob. 61ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 63ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 66ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 68ACh. 42 - Prob. 69ACh. 42 - Prob. 70ACh. 42 - Prob. 71ACh. 42 - Prob. 72ACh. 42 - Prob. 73ACh. 42 - Prob. 74ACh. 42 - Prob. 75ACh. 42 - For each of the following problems, substitute the...Ch. 42 - Prob. 77ACh. 42 - Prob. 78ACh. 42 - Prob. 79ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - The feed of a drill is the depth of material that...Ch. 42 - Prob. 109ACh. 42 - For each of the following problems, substitute the...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Prob. 118ACh. 42 - Prob. 119ACh. 42 - Prob. 120ACh. 42 - Prob. 121ACh. 42 - Prob. 122ACh. 42 - Prob. 123ACh. 42 - Prob. 124ACh. 42 - Solve each of the following equations using either...Ch. 42 - Prob. 126ACh. 42 - Solve each of the following equations using either...Ch. 42 - Prob. 128ACh. 42 - Prob. 129ACh. 42 - Prob. 130A
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