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 18, Problem 28P
The following data define the sea-level concentration of dissolved oxygen for fresh water as a function of temperature:
| T°,C | 0 | 8 | 16 | 24 | 32 | 40 |
| o, mg/L | 14.621 | 11.843 | 9.870 | 8.418 | 7.305 | 6.413 |
Estimate
(a) Linear Interpolation,
(b) Newton's interpolating polynomial, and
(c) Cubic splines
Note that the exact result is 7.986 mg/L.
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2
3
4
5
6
7
8
9
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12
pH above 7 (X)
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A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States.
They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained
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DATA:
Observation
1
2
3
4
5
6
7
8
9
10
11
12
pH above 7 (X)
0.65
0.75
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0.94
1.12
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18.9
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21.1
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24.9
26.1
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19.3
30.7
33.7
29.4
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In thermodynamics,
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to its molar volume v at some temperature T as follows:
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temperature is held fixed, and R is a constant. What is the value of
when p = 3.5 and v = 9.7?
a. 10769.096062
5.9
(p+ 52 ) (v − 1.7)
- = RT
O b. -0.432409
O c. -0.299589
d. -0.507066
e. 0.011601
O f. -0.444243
dp
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Chapter 18 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 18 - 18.1 Estimate the common logarithm of 10 using...Ch. 18 - 18.2 Fit a second-order Newton’s interpolating...Ch. 18 - 18.3 Fit a third-order Newton’s interpolating...Ch. 18 - Repeat Probs. 18.1 through 18.3 using the Lagrange...Ch. 18 - 18.5 Given these...Ch. 18 - 18.6 Given these data
x 1 2 3 5 7 8
...Ch. 18 - Repeat Prob. 18.6 using Lagrange polynomials of...Ch. 18 - 18.8 The following data come from a table that was...Ch. 18 - 18.9 Use Newton’s interpolating polynomial to...Ch. 18 - Use Newtons interpolating polynomial to determine...
Ch. 18 - 18.11 Employ inverse interpolation using a cubic...Ch. 18 - 18.12 Employ inverse interpolation to determine...Ch. 18 - 18.13 Develop quadratic splines for the first five...Ch. 18 - 18.14 Develop cubic splines for the data in Prob....Ch. 18 - Determine the coefficients of the parabola that...Ch. 18 - Determine the coefficients of the cubic equation...Ch. 18 - 18.17 Develop, debug, and test a program in either...Ch. 18 - 18.18 Test the program you developed in Prob....Ch. 18 - 18.19 Use the program you developed in Prob. 18.17...Ch. 18 - Use the program you developed in Prob. 18.17 to...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - 18.22 A useful application of Lagrange...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - Use the software developed in Prob. 18.23 to fit...Ch. 18 - Use the portion of the given steam table for...Ch. 18 - The following is the built-in humps function that...Ch. 18 - 18.28 The following data define the sea-level...Ch. 18 - 18.29 Generate eight equally-spaced points from...Ch. 18 - 18.30 Temperatures are measured at various points...
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