Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 4, Problem 5P
Use zero- through third-order Taylor series expansions to predict
using a base point at
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Theorem:- if A 2×2 prove i-
At = 2 Re(Q)
where
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if 21 = 2
Theorem: show that XCH) = M(E) M" (6) E +
t
Mcfic
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Solution of ODE
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x = ACE) x + g (t) + X (E) - E
5. (a) State the Residue Theorem. Your answer should include all the conditions required
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(4 marks)
(b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the
anti-clockwise direction. Evaluate
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You must check all of the conditions of any results that you use.
(5 marks)
(c) Evaluate
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You must check all of the conditions of any results that you use.
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x sin(Tx)
x²+2x+5
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Chapter 4 Solutions
Numerical Methods for Engineers
Ch. 4 - The following series can be used to approximate...Ch. 4 - 4.2 The Maclaurin series expansion for cos x...Ch. 4 - 4.3 Perform the same computation as in Prob. 4.2,...Ch. 4 - 4.4 The Maclaurin series expansion for the...Ch. 4 - 4.5 Use zero- through third-order Taylor series...Ch. 4 - 4.6 Use zero- through fourth-order Taylor series...Ch. 4 - Use forward and backward difference approximations...Ch. 4 - 4.8 Use a centered difference approximation of to...Ch. 4 - 4.9 The Stefan-Boltzmann law can be employed to...Ch. 4 - Repeat Prob. 4.9 but for a copper sphere with...
Ch. 4 - Recall that the velocity of the falling...Ch. 4 - 4.12 Repeat Prob. 4.11 with.
Ch. 4 - 4.13 Evaluate and interpret the condition numbers...Ch. 4 - Employing ideas from Sec. 4.2, derive the...Ch. 4 - Prove that Eq. (4.4) is exact for all values of x...Ch. 4 - Mannings formula for a rectangular channel can be...Ch. 4 - If |x|1, it is known that 11x=1+x+x2+x3+ Repeat...Ch. 4 - A missile leaves the ground with an initial...Ch. 4 - To calculate a planets space coordinates, we have...Ch. 4 - 4.20 Consider the function on the interval . Use...Ch. 4 - Derive Eq. (4.31).Ch. 4 - 4.22 Repeat Example 4.8, but for .
Ch. 4 - 4.23 Repeat Example 4.8, but for the forward...Ch. 4 - 4.24 Develop a well-structured program to compute...
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