Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Chapter 9.5, Problem 26P

r(t) = [cos t, sin t, 9t], P: (1, 0, 18π)

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9.7 Given the equations 0.5x₁-x2=-9.5 1.02x₁ - 2x2 = -18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a modified slightly to 0.52. Interpret your results.
12.42 The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 0= FT T + 200°C 25°C 25°C T22 0°C T₁ T21 200°C FIGURE P12.42 75°C 75°C 00°C If the plate is represented by a series of nodes (Fig. P12.42), cen- tered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Fig. P12.42.
9.22 Develop, debug, and test a program in either a high-level language or a macro language of your choice to solve a system of equations with Gauss-Jordan elimination without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the program using the same system as in Prob. 9.18. Compute the total number of flops in your algorithm to verify Eq. 9.37. FIGURE 9.10 Pseudocode to implement the Gauss-Jordan algorithm with- out partial pivoting. SUB GaussJordan(aug, m, n, x) DOFOR k = 1, m d = aug(k, k) DOFOR j = 1, n aug(k, j) = aug(k, j)/d END DO DOFOR 1 = 1, m IF 1 % K THEN d = aug(i, k) DOFOR j = k, n aug(1, j) END DO aug(1, j) - d*aug(k, j) END IF END DO END DO DOFOR k = 1, m x(k) = aug(k, n) END DO END GaussJordan

Chapter 9 Solutions

Advanced Engineering Mathematics

Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 13PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 17PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - What laws do Probs. 12–16 illustrate? 12. (a + b)...Ch. 9.1 - Prob. 20PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Prob. 22PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Equilibrium. Find v such that p, q, u in Prob. 21...Ch. 9.1 - Find p such that u, v, w in Prob. 23 and p are in...Ch. 9.1 - Unit vector. Find the unit vector in the direction...Ch. 9.1 - Restricted resultant. Find all v such that the...Ch. 9.1 - Prob. 30PCh. 9.1 - For what k is the resultant of [2, 0, −7], [1, 2,...Ch. 9.1 - If |p| = 6 and |q| = 4, what can you say about the...Ch. 9.1 - Same question as in Prob. 32 if |p| = 9, |q| = 6,...Ch. 9.1 - Relative velocity. If airplanes A and B are moving...Ch. 9.1 - Same question as in Prob. 34 for two ships moving...Ch. 9.1 - Prob. 36PCh. 9.1 - Prob. 37PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 8PCh. 9.2 - Prob. 9PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 11PCh. 9.2 - What does u • v = u • w imply if u = 0? If u ≠...Ch. 9.2 - Prove the Cauchy–Schwarz inequality. Ch. 9.2 - Verify the Cauchy–Schwarz and triangle...Ch. 9.2 - Prob. 15PCh. 9.2 - Triangle inequality. Prove Eq. (7). Hint. Use Eq....Ch. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Prob. 20PCh. 9.2 - Prob. 21PCh. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - What will happen to the angle in Prob. 24 if we...Ch. 9.2 - Prob. 26PCh. 9.2 - Addition law. cos (α − β) = cos α cos β + sin α...Ch. 9.2 - Prob. 28PCh. 9.2 - Prob. 29PCh. 9.2 - Prob. 30PCh. 9.2 - Prob. 31PCh. 9.2 - Prob. 32PCh. 9.2 - Prob. 33PCh. 9.2 - Prob. 34PCh. 9.2 - Prob. 35PCh. 9.2 - Prob. 36PCh. 9.2 - Prob. 37PCh. 9.2 - Prob. 38PCh. 9.2 - Prob. 39PCh. 9.2 - Prob. 40PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 11PCh. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Prob. 16PCh. 9.3 - Prob. 17PCh. 9.3 - Prob. 18PCh. 9.3 - Prob. 19PCh. 9.3 - Prob. 20PCh. 9.3 - Prob. 21PCh. 9.3 - Prob. 22PCh. 9.3 - Prob. 23PCh. 9.3 - Prob. 25PCh. 9.3 - Prob. 26PCh. 9.3 - Prob. 27PCh. 9.3 - Prob. 28PCh. 9.3 - Prob. 29PCh. 9.3 - Prob. 30PCh. 9.3 - Prob. 31PCh. 9.3 - Prob. 32PCh. 9.3 - Prob. 33PCh. 9.3 - Prob. 34PCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9.4 - Prob. 7PCh. 9.4 - Prob. 9PCh. 9.4 - Prob. 10PCh. 9.4 - Prob. 11PCh. 9.4 - Prob. 12PCh. 9.4 - Prob. 13PCh. 9.4 - Prob. 14PCh. 9.4 - Prob. 15PCh. 9.4 - Prob. 16PCh. 9.4 - Prob. 17PCh. 9.4 - Prob. 18PCh. 9.4 - Prob. 19PCh. 9.4 - Prob. 20PCh. 9.4 - Prob. 22PCh. 9.4 - Prob. 23PCh. 9.4 - Prob. 24PCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.5 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.5 - Prob. 9PCh. 9.5 - Prob. 10PCh. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 14PCh. 9.5 - Prob. 15PCh. 9.5 - Prob. 16PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.5 - Prob. 21PCh. 9.5 - r(t) = [10 cos t, 1, 10 sin t], P: (6, 1, 8)Ch. 9.5 - r(t) = [cos t, sin t, 9t], P: (1, 0, 18)Ch. 9.5 - Prob. 27PCh. 9.5 - Prob. 29PCh. 9.5 - Prob. 30PCh. 9.5 - Prob. 31PCh. 9.5 - Prob. 32PCh. 9.5 - Prob. 33PCh. 9.5 - Prob. 34PCh. 9.5 - Prob. 35PCh. 9.5 - Prob. 36PCh. 9.5 - Prob. 37PCh. 9.5 - Prob. 38PCh. 9.5 - Prob. 43PCh. 9.5 - Prob. 44PCh. 9.5 - Prob. 45PCh. 9.5 - Prob. 46PCh. 9.5 - CURVATURE AND TORSION 47. Circle. Show that a...Ch. 9.5 - Prob. 48PCh. 9.5 - Prob. 49PCh. 9.5 - Prob. 50PCh. 9.5 - Prob. 51PCh. 9.5 - Prob. 52PCh. 9.5 - Prob. 53PCh. 9.5 - Prob. 54PCh. 9.5 - Prob. 55PCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 4PCh. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 10PCh. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9.7 - Prob. 13PCh. 9.7 - Prob. 14PCh. 9.7 - Prob. 15PCh. 9.7 - Prob. 16PCh. 9.7 - Prob. 17PCh. 9.7 - Prob. 18PCh. 9.7 - Prob. 19PCh. 9.7 - Prob. 20PCh. 9.7 - Prob. 21PCh. 9.7 - Prob. 22PCh. 9.7 - Prob. 23PCh. 9.7 - Prob. 24PCh. 9.7 - Prob. 25PCh. 9.7 - Prob. 26PCh. 9.7 - Prob. 28PCh. 9.7 - Prob. 29PCh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 6PCh. 9.8 - Prob. 7PCh. 9.8 - Prob. 8PCh. 9.8 - CAS EXPERIMENT. Visualizing the Divergence. Graph...Ch. 9.8 - Prob. 11PCh. 9.8 - Prob. 12PCh. 9.8 - Prob. 13PCh. 9.8 - Prob. 14PCh. 9.8 - Prob. 15PCh. 9.8 - Prob. 16PCh. 9.8 - Prob. 17PCh. 9.8 - Prob. 18PCh. 9.8 - Prob. 19PCh. 9.8 - Prob. 20PCh. 9.9 - Prob. 1PCh. 9.9 - Prob. 2PCh. 9.9 - Prob. 3PCh. 9.9 - Prob. 4PCh. 9.9 - Prob. 5PCh. 9.9 - Prob. 6PCh. 9.9 - Prob. 7PCh. 9.9 - Prob. 8PCh. 9.9 - Prob. 9PCh. 9.9 - Prob. 10PCh. 9.9 - Prob. 11PCh. 9.9 - Prob. 12PCh. 9.9 - Prob. 13PCh. 9.9 - Prob. 15PCh. 9.9 - Prob. 16PCh. 9.9 - Prob. 17PCh. 9.9 - Prob. 18PCh. 9.9 - Prob. 19PCh. 9.9 - Prob. 20PCh. 9 - Prob. 1RQCh. 9 - Prob. 2RQCh. 9 - Prob. 3RQCh. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Prob. 6RQCh. 9 - Prob. 7RQCh. 9 - Prob. 8RQCh. 9 - Prob. 9RQCh. 9 - Prob. 11RQCh. 9 - Prob. 12RQCh. 9 - Prob. 13RQCh. 9 - Prob. 14RQCh. 9 - Prob. 15RQCh. 9 - Prob. 16RQCh. 9 - Prob. 17RQCh. 9 - Prob. 18RQCh. 9 - Prob. 19RQCh. 9 - Prob. 20RQCh. 9 - Prob. 21RQCh. 9 - Prob. 22RQCh. 9 - Prob. 23RQCh. 9 - Prob. 24RQCh. 9 - Prob. 25RQCh. 9 - Prob. 26RQCh. 9 - Prob. 27RQCh. 9 - Prob. 28RQCh. 9 - Prob. 29RQCh. 9 - Prob. 30RQCh. 9 - Prob. 31RQCh. 9 - Prob. 32RQCh. 9 - Prob. 33RQCh. 9 - Prob. 34RQCh. 9 - Prob. 35RQCh. 9 - Prob. 36RQCh. 9 - Prob. 37RQCh. 9 - Prob. 38RQCh. 9 - Prob. 39RQCh. 9 - Prob. 40RQ
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