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 24, Problem 37P
Compute work as described in Sec. 24.4, but use the following equations for
The force is in newtons and the angle is in radians. Perform the
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1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where v₁,..., Un are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1,2,-2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show…
1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E+) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where vi,..., are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1, 2, -2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show that P - Q is its own inverse.
4. Show that the Frobenius product on n x n-matrices,
(A, B) =
= Tr(B*A),
is an inner product, where B* denotes the Hermitian adjoint of B.
5. Show that if A and B are two n x n-matrices for which {1,..., n} is a basis of eigen-
vectors (for both A and B), then AB = BA.
Remark: It is also true that if AB = BA, then there exists a common…
Chapter 24 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 24 - Perform the same computation as Sec. 24.1, but...Ch. 24 - 24.2 Repeat Prob. 24.1, but use Romberg...Ch. 24 - 24.3 Repeat Prob. 24.1, but use a two- and a...Ch. 24 - 24.4 Integration provides a means to compute how...Ch. 24 - Use numerical integration to compute how much mass...Ch. 24 - 24.6 Fick’s first diffusion law states...Ch. 24 - The following data were collected when a large oil...Ch. 24 - 24.8 You are interested in measuring the fluid...Ch. 24 - Prob. 10PCh. 24 - 24.11 Glaucoma is the second leading cause of...
Ch. 24 - One of your colleagues has designed a new...Ch. 24 - Video an giography is used to measure blood flow...Ch. 24 - 24.14 Perform the same computation as in Sec....Ch. 24 - Perform the same computation as in Sec. 24.2, but...Ch. 24 - 24.16 As in Sec. 24.2, compute F using the...Ch. 24 - Stream cross-sectional areas (A) are required for...Ch. 24 - 24.18 As described in Prob. 24.17, the...Ch. 24 - 24.21 A transportation engineering study requires...Ch. 24 - 24.22 A wind force distributed against the side of...Ch. 24 - 24.23 Water exerts pressure on the upstream ...Ch. 24 - 24.24 To estimate the size of a new dam, you have...Ch. 24 - The data listed in the following table gives...Ch. 24 - The heat flux q is the quantity of heat flowing...Ch. 24 - 24.27 The horizontal surface area of a lake at a...Ch. 24 - 24.28 Perform the same computation as in Sec....Ch. 24 - 24.29 Repeat Prob. 24.28, but use five...Ch. 24 - Repeat Prob. 24.28, but use Romberg integration to...Ch. 24 - Faradays law characterizes the voltage drop across...Ch. 24 - 24.32 Based on Faraday’s law (Prob. 24.31), use...Ch. 24 - Suppose that the current through a resistor is...Ch. 24 - If a capacitor initially holds no charge, the...Ch. 24 - 24.35 Perform the same computation as in Sec....Ch. 24 - 24.36 Repeat Prob. 24.35, but use (a) Simpson’s ...Ch. 24 - 24.37 Compute work as described in Sec. 24.4, but...Ch. 24 - As was done in Sec. 24.4, determine the work...Ch. 24 - 24.39 The work done on an object is equal to the...Ch. 24 - The rate of cooling of a body (Fig. P24.40) can be...Ch. 24 - 24.41 A rod subject to an axial load (Fig....Ch. 24 - If the velocity distribution of a fluid flowing...Ch. 24 - 24.43 Using the following data, calculate the work...Ch. 24 - 24.44 A jet fighter’s position on an aircraft...Ch. 24 - 24.45 Employ the multiple-application Simpson’s...Ch. 24 - The upward velocity of a rocket can be computed by...Ch. 24 - Referring to the data from Problem 20.61, find the...Ch. 24 - Fully developed flow moving through a 40-cm...Ch. 24 - Fully developed flow of a Bingham plasticfluid...Ch. 24 - 24.50 The enthalpy of a real gas is a ...Ch. 24 - Given the data below, find the isothermal work...Ch. 24 - 24.52 The Rosin-Rammler-Bennet (RRB) equation is...Ch. 24 - For fluid flow over a surface, the heat flux to...Ch. 24 - The pressure gradient for laminar flow through a...Ch. 24 - 24.55 Velocity data for air are collected at...
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