Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 3.1, Problem 17ES
To determine
The choice of step size would make to ensure that
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(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define
E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}.
(a) (2 points) Calculate the divergence V. F.
(b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that
the triple integral
√ (V · F) dV = √ 2²(1.
= x²(1 − x² - y²) dA.
E
Business Discuss
(2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy).
(a) (2 points) Calculate V. F.
(b) (6 points) Given a vector field
is everywhere defined with V
G₁(x, y, z) = *
G2(x, y, z) = −
G3(x, y, z) = 0.
0
0
F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that
F = 0, let G = (G1, G2, G3) where
F₂(x,
y,
y, t) dt
- √ F³(x, t, 0) dt,
*
F1(x,
y, t) dt,
t) dt - √ F
Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).
Chapter 3 Solutions
Numerical Analysis
Ch. 3.1 - For the given functions f(x), let x0 = 0, x1 =...Ch. 3.1 - Use Theorem 3.3 to find an error bound for the...Ch. 3.1 - Prob. 4ESCh. 3.1 - The data for Exercise 6 were generated using the...Ch. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ESCh. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 17ES
Ch. 3.1 - It is suspected that the high amounts of tannin in...Ch. 3.1 - Prob. 21ESCh. 3.1 - Prove Taylors Theorem 1.14 by following the...Ch. 3.1 - Prob. 1DQCh. 3.1 - If we decide to increase the degree of the...Ch. 3.2 - Let P3(x) be the interpolating polynomial for the...Ch. 3.2 - Nevilles method is used to approximate f(0.4),...Ch. 3.2 - Nevilles method is used to approximate f(0.5),...Ch. 3.2 - Suppose xj = j, for j = 0, 1, 2, 3, and it is...Ch. 3.2 - Nevilles Algorithm is used to approximate f(0)...Ch. 3.2 - Prob. 11ESCh. 3.2 - Prob. 13ESCh. 3.2 - Can Nevilles method be used to obtain the...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Approximate f(0.05) using the following data...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The Newton forward-difference formula is used to...Ch. 3.3 - Prob. 14ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Show that the polynomial interpolating the...Ch. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Compare and contrast the various...Ch. 3.3 - Is it easier to add a new data pair using...Ch. 3.3 - Prob. 3DQCh. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - The data in Exercise 1 were generated using the...Ch. 3.4 - The data in Exercise 2 were generated using the...Ch. 3.4 - Let f (x) = 3xex e2x. a. Approximate f (1.03) by...Ch. 3.4 - The following table lists data for the function...Ch. 3.4 - a. Show that H2n + 1 (x) is the unique polynomial...Ch. 3.4 - Prob. 1DQCh. 3.4 - Prob. 2DQCh. 3.4 - Prob. 3DQCh. 3.5 - Determine the natural cubic spline S that...Ch. 3.5 - Determine the clamped cubic spline s that...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - The data in Exercise 3 were generated using the...Ch. 3.5 - Prob. 6ESCh. 3.5 - Prob. 8ESCh. 3.5 - Prob. 11ESCh. 3.5 - Prob. 12ESCh. 3.5 - Prob. 13ESCh. 3.5 - Prob. 14ESCh. 3.5 - Given the partition x0 = 0, x1 = 0.05, and x2 =...Ch. 3.5 - Prob. 16ESCh. 3.5 - Prob. 21ESCh. 3.5 - Prob. 22ESCh. 3.5 - Prob. 23ESCh. 3.5 - It is suspected that the high amounts of tannin in...Ch. 3.5 - Prob. 29ESCh. 3.5 - Prob. 30ESCh. 3.5 - Prob. 31ESCh. 3.5 - Prob. 32ESCh. 3.5 - Let f C2[a, b] and let the nodes a = x0 x1 xn...Ch. 3.5 - Prob. 34ESCh. 3.5 - Prob. 35ESCh. 3.6 - Let (x0, y0) = (0,0) and (x1, y1) = (5, 2) be the...Ch. 3.6 - Prob. 2ESCh. 3.6 - Prob. 5ESCh. 3.6 - Prob. 1DQ
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