ADVANCED ENGINEERING MATH.>CUSTOM<
ADVANCED ENGINEERING MATH.>CUSTOM<
10th Edition
ISBN: 9781119480150
Author: Kreyszig
Publisher: WILEY C
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4. Consider Chebychev's equation (1 - x²)y" - xy + λy = 0 with boundary conditions y(-1) = 0 and y(1) = 0, where X is a constant. (a) Show that Chebychev's equation can be expressed in Sturm-Liouville form d · (py') + qy + Ary = 0, dx y(1) = 0, y(-1) = 0, where p(x) = (1 = x²) 1/2, q(x) = 0 and r(x) = (1 − x²)-1/2 (b) Show that the eigenfunctions of the Sturm-Liouville equation are extremals of the functional A[y], where A[y] = I[y] J[y]' and I[y] and [y] are defined by - I [y] = √, (my² — qy²) dx and J[y] = [[", ry² dx. Explain briefly how to use this to obtain estimates of the smallest eigenvalue >1. 1 (c) Let k > be a parameter. Explain why the functions y(x) = (1-x²) are suitable 4 trial functions for estimating the smallest eigenvalue. Show that the value of A[y] for these trial functions is 4k2 A[y] = = 4k - 1' and use this to estimate the smallest eigenvalue \1. Hint: L₁ x²(1 − ²)³¹ dr = 1 (1 - x²)³ dx (ẞ > 0). 2ẞ
You recieve a case of fresh Michigan cherries that weighs 8.2 kg. You will be making cherry pies. Each pie will require 1 3/4 pounds of pitted cherries. How many pies can be made from the case if the yield percent for cherries is 87
Q/ show that the system: x = Y + x(x² + y²) y° = =x+y (x² + y²) 9 X=-x(x²+ y²) 9 X Y° = x - y (x² + y²) have the same lin car part at (0,0) but they are topologically different. Give the reason.

Chapter 14 Solutions

ADVANCED ENGINEERING MATH.>CUSTOM<

Ch. 14.1 - Prob. 11PCh. 14.1 - Prob. 12PCh. 14.1 - Prob. 13PCh. 14.1 - Prob. 14PCh. 14.1 - Prob. 15PCh. 14.1 - Prob. 16PCh. 14.1 - Prob. 17PCh. 14.1 - Prob. 18PCh. 14.1 - Prob. 19PCh. 14.1 - Prob. 20PCh. 14.1 - Prob. 21PCh. 14.1 - Prob. 22PCh. 14.1 - Prob. 23PCh. 14.1 - Prob. 24PCh. 14.1 - Prob. 25PCh. 14.1 - Prob. 26PCh. 14.1 - Prob. 27PCh. 14.1 - Prob. 28PCh. 14.1 - Prob. 29PCh. 14.1 - Prob. 30PCh. 14.1 - Prob. 32PCh. 14.1 - Prob. 33PCh. 14.1 - Prob. 35PCh. 14.2 - Prob. 1PCh. 14.2 - Prob. 2PCh. 14.2 - Prob. 3PCh. 14.2 - Prob. 4PCh. 14.2 - Prob. 5PCh. 14.2 - Prob. 6PCh. 14.2 - Prob. 7PCh. 14.2 - Prob. 9PCh. 14.2 - Prob. 10PCh. 14.2 - Prob. 11PCh. 14.2 - Prob. 12PCh. 14.2 - Prob. 13PCh. 14.2 - Prob. 14PCh. 14.2 - Prob. 15PCh. 14.2 - Prob. 16PCh. 14.2 - Prob. 17PCh. 14.2 - Prob. 18PCh. 14.2 - Prob. 19PCh. 14.2 - Prob. 20PCh. 14.2 - Prob. 21PCh. 14.2 - Prob. 22PCh. 14.2 - Prob. 23PCh. 14.2 - Prob. 24PCh. 14.2 - Prob. 25PCh. 14.2 - Prob. 26PCh. 14.2 - Prob. 27PCh. 14.2 - Prob. 28PCh. 14.2 - Prob. 29PCh. 14.2 - Prob. 30PCh. 14.3 - Prob. 1PCh. 14.3 - Prob. 2PCh. 14.3 - Prob. 3PCh. 14.3 - Prob. 4PCh. 14.3 - Prob. 5PCh. 14.3 - Prob. 6PCh. 14.3 - Prob. 7PCh. 14.3 - Prob. 8PCh. 14.3 - Prob. 11PCh. 14.3 - Prob. 12PCh. 14.3 - Prob. 13PCh. 14.3 - Prob. 14PCh. 14.3 - Prob. 15PCh. 14.3 - Prob. 16PCh. 14.3 - Prob. 17PCh. 14.3 - Prob. 18PCh. 14.3 - Prob. 19PCh. 14.3 - Prob. 20PCh. 14.4 - Prob. 1PCh. 14.4 - Prob. 2PCh. 14.4 - Prob. 3PCh. 14.4 - Prob. 4PCh. 14.4 - Prob. 5PCh. 14.4 - Prob. 6PCh. 14.4 - Prob. 7PCh. 14.4 - Prob. 8PCh. 14.4 - Prob. 9PCh. 14.4 - Prob. 10PCh. 14.4 - Prob. 11PCh. 14.4 - Prob. 12PCh. 14.4 - Prob. 13PCh. 14.4 - Prob. 14PCh. 14.4 - Prob. 15PCh. 14.4 - Prob. 16PCh. 14.4 - Prob. 17PCh. 14.4 - Prob. 18PCh. 14.4 - Prob. 19PCh. 14 - Prob. 1RQCh. 14 - Prob. 2RQCh. 14 - Prob. 3RQCh. 14 - Prob. 4RQCh. 14 - Prob. 5RQCh. 14 - Prob. 6RQCh. 14 - Prob. 7RQCh. 14 - Prob. 8RQCh. 14 - Prob. 9RQCh. 14 - Prob. 10RQCh. 14 - Prob. 11RQCh. 14 - Prob. 12RQCh. 14 - Prob. 13RQCh. 14 - Prob. 14RQCh. 14 - Prob. 15RQCh. 14 - Prob. 16RQCh. 14 - Prob. 17RQCh. 14 - Prob. 18RQCh. 14 - Prob. 19RQCh. 14 - Prob. 20RQCh. 14 - Prob. 21RQCh. 14 - Prob. 22RQCh. 14 - Prob. 23RQCh. 14 - Prob. 24RQCh. 14 - Prob. 25RQCh. 14 - Prob. 26RQCh. 14 - Prob. 27RQCh. 14 - Prob. 28RQCh. 14 - Prob. 29RQCh. 14 - Prob. 30RQ
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