EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 23, Problem 11P
Develop a user-friendly program to obtain first-derivative estimates for unequally spaced data. Test it with the following data:
| x | 1 | 1.5 | 1.6 | 2.5 | 3.5 |
| f(x) | 0.6767 | 0.3734 | 0.3261 | 0.08422 | 0.01596 |
where
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Consider the function p(x) = x² - 4x³+3x²+x-1. If bisection is used with the function with a starting interval [2 3], which of the following is the absolute value of
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0.0213
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Number
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Evaluate the following variables and use them as given in the following problems.
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Strain, in/in.
FIGURE P1.17
1.18 Use Problem 1.17 to graphically determine the following:
a. Modulus of resilience
b. Toughness
Hint: The toughness (u) can be determined by calculating the area under
the stress-strain curve
u =
de
where & is the strain at fracture. The preceding integral can be approxi-
mated numerically by using a trapezoidal integration technique:
u, = Eu, = o, + o e, - 6)
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c. If the specimen is loaded to 40 ksi only and the lateral strain was found to
be -0.00057 in./in., what is Poisson's ratio of this metal?
d. If the specimen is loaded to 70 ksi only and then unloaded, what is the
permanent strain?
Stress, ksi
Chapter 23 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 23 - 23.1 Compute forward and backward difference...Ch. 23 - 23.2 Repeat Prob. 23.1, but for evaluated at...Ch. 23 - 23.3 Use centered difference approximations to...Ch. 23 - Use Richardson extrapolation to estimate the first...Ch. 23 - Repeat Prob. 23.4, but for the first derivative of...Ch. 23 - 23.6 Employ Eq. (23.9) to determine the first...Ch. 23 - 23.7 Prove that for equispaced data points, Eq....Ch. 23 - Compute the first-order central difference...Ch. 23 - Prob. 9PCh. 23 - Develop a user-friendly program to apply a Romberg...
Ch. 23 - 23.11 Develop a user-friendly program to obtain...Ch. 23 - 23.12 The following data are provided for the...Ch. 23 - 23.13 Recall that for the falling parachutist...Ch. 23 - The normal distribution is defined as f(x)=12ex2/2...Ch. 23 - 23.15 The following data were generated from the...Ch. 23 - Evaluate f/x,f/y, and f/(xy) for the following...Ch. 23 - 23.17 Evaluate the following integral with...Ch. 23 - 23.18 Use the diff command in MATLAB and compute...Ch. 23 - The objective of this problem is to compare...Ch. 23 - Use a Taylor series expansion to derive a centered...Ch. 23 - Use the following data to find the velocity and...Ch. 23 - 23.22 A plane is being tracked by radar, and data...Ch. 23 - 23.23 Develop an Excel VBA macro program to read...Ch. 23 - Use regression to estimate the acceleration at...Ch. 23 - You have to measure the flow rate of water through...Ch. 23 - The velocity y (m/s) of air fl owing past a flat...Ch. 23 - Chemical reactions often follow the model:...Ch. 23 - 23.28 The velocity profile of a fluid in a...Ch. 23 - 23.29 The amount of mass transported via a pipe...
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