EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 11, Problem 20P
Repeat Prob. 11.19. but for the case of a six-dimensional Vandermonde matrix (see Prob. 10.17) where
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The natural exponential function can be expressed by . Determine e2by calculating the sum of the series for:(a) n = 5, (b) n = 15, (c) n = 25For each part create a vector n in which the first element is 0, the incrementis 1, and the last term is 5, 15, or 25. Then use element-by-element calculations to create a vector in which the elements are . Finally, use the MATLAB built-in function sum to add the terms of the series. Compare thevalues obtained in parts (a), (b), and (c) with the value of e2calculated byMATLAB.
2- Derive the rule-of-mixtures expression for the composite extensional modulus E₁ assuming the existence
of an interphase region. The starting point for the derivation would be the model shown below. For
simplicity, assume the interphase, like the matrix, is isotropic with modulus E¹. With an interphase region
there is a volume fraction associated with the interphase (i.e.,V;). For this situation:
vf + vm + vi = 1
H
|w²||wm|
1. Consider the following square matrix
A =
9 6
(a) Determine the eigenvalues and eigenvector(s) of A.
(b) Find the modal matrix M and diagonalize A through similarity transformation M 'AM.
do we get a Jordan form or not? Explain why?
Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 11 - 11.1 Perform the same calculations as in (a)...Ch. 11 - Determine the matrix inverse for Example 11.1...Ch. 11 - 11.3 The following tridiagonal system must be...Ch. 11 - 11.4 Confirm the validity of the Cholesky...Ch. 11 - Perform the same calculations as in Example 11.2,...Ch. 11 - Perform a Cholesky decomposition of the following...Ch. 11 - Compute the Cholesky decomposition of...Ch. 11 - Use the Gauss-Seidel method to solve the...Ch. 11 - Recall from Prob. 10.8, that the following system...Ch. 11 - 11.10 Repeat Prob. 11.9, but use Jacobi...
Ch. 11 - 11.11 Use the Gauss-Seidel method to solve the...Ch. 11 - Use the Gauss-Seidel method (a) without relaxation...Ch. 11 - 11.13 Use the Gauss-Seidel method (a) without...Ch. 11 - Redraw Fig. 11.5 for the case where the slopes of...Ch. 11 - 11.15 Of the following three sets of linear...Ch. 11 - Use the software package of your choice to obtain...Ch. 11 - Given the pair of nonlinear simultaneous...Ch. 11 - An electronics company produces transistors,...Ch. 11 - Use MATLAB or Mathcad software to determine the...Ch. 11 - Repeat Prob. 11.19. but for the case of a...Ch. 11 - 11.21 Given a square matrix , write a single line...Ch. 11 - Write the following set of equations in matrix...Ch. 11 - In Sec. 9.2.1, we determined the number of...Ch. 11 - 11.24 Develop a user-friendly program in either a...Ch. 11 - 11.25 Develop a user-friendly program in either a...Ch. 11 - Develop a user-friendly program in either a...Ch. 11 - As described in Sec. PT3.1.2, linear algebraic...Ch. 11 - A pentadiagonal system with a bandwidth of five...
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