ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE
10th Edition
ISBN: 9781119809210
Author: Kreyszig
Publisher: WILEY
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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 13 Solutions
ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE
Ch. 13.1 - Prob. 1PCh. 13.1 - Prob. 2PCh. 13.1 - Prob. 3PCh. 13.1 - Prob. 4PCh. 13.1 - Prob. 5PCh. 13.1 - Prob. 6PCh. 13.1 - Prob. 8PCh. 13.1 - Prob. 9PCh. 13.1 - Prob. 10PCh. 13.1 - Prob. 11P
Ch. 13.1 - Prob. 12PCh. 13.1 - Prob. 13PCh. 13.1 - Prob. 14PCh. 13.1 - Prob. 15PCh. 13.1 - Prob. 16PCh. 13.1 - Prob. 17PCh. 13.1 - Prob. 18PCh. 13.1 - Prob. 19PCh. 13.1 - Prob. 20PCh. 13.2 - Prob. 1PCh. 13.2 - Prob. 2PCh. 13.2 - Prob. 3PCh. 13.2 - Prob. 4PCh. 13.2 - Prob. 5PCh. 13.2 - Prob. 6PCh. 13.2 - Prob. 7PCh. 13.2 - Prob. 8PCh. 13.2 - Prob. 9PCh. 13.2 - Prob. 10PCh. 13.2 - Prob. 11PCh. 13.2 - Prob. 12PCh. 13.2 - Prob. 13PCh. 13.2 - Prob. 14PCh. 13.2 - Prob. 15PCh. 13.2 - Prob. 16PCh. 13.2 - Prob. 17PCh. 13.2 - Prob. 18PCh. 13.2 - Prob. 21PCh. 13.2 - Prob. 22PCh. 13.2 - Prob. 23PCh. 13.2 - Prob. 24PCh. 13.2 - Prob. 25PCh. 13.2 - Prob. 26PCh. 13.2 - Prob. 27PCh. 13.2 - Prob. 28PCh. 13.2 - Prob. 29PCh. 13.2 - Prob. 30PCh. 13.2 - Prob. 31PCh. 13.2 - Prob. 32PCh. 13.2 - Prob. 33PCh. 13.2 - Prob. 34PCh. 13.2 - Prob. 35PCh. 13.3 - Prob. 1PCh. 13.3 - Prob. 2PCh. 13.3 - Prob. 3PCh. 13.3 - Prob. 4PCh. 13.3 - Prob. 5PCh. 13.3 - Prob. 6PCh. 13.3 - Prob. 7PCh. 13.3 - Prob. 8PCh. 13.3 - Prob. 10PCh. 13.3 - Prob. 11PCh. 13.3 - Prob. 12PCh. 13.3 - Prob. 14PCh. 13.3 - Prob. 15PCh. 13.3 - Prob. 16PCh. 13.3 - Prob. 17PCh. 13.3 - Prob. 18PCh. 13.3 - Prob. 19PCh. 13.3 - Prob. 20PCh. 13.3 - Prob. 21PCh. 13.3 - Prob. 22PCh. 13.3 - Prob. 23PCh. 13.4 - Prob. 1PCh. 13.4 - Prob. 2PCh. 13.4 - Prob. 3PCh. 13.4 - Prob. 4PCh. 13.4 - Prob. 5PCh. 13.4 - Prob. 6PCh. 13.4 - Prob. 7PCh. 13.4 - Prob. 8PCh. 13.4 - Prob. 9PCh. 13.4 - Prob. 10PCh. 13.4 - Prob. 11PCh. 13.4 - Prob. 12PCh. 13.4 - Prob. 13PCh. 13.4 - Prob. 14PCh. 13.4 - Prob. 15PCh. 13.4 - Prob. 16PCh. 13.4 - Prob. 17PCh. 13.4 - Prob. 18PCh. 13.4 - Prob. 19PCh. 13.4 - Prob. 20PCh. 13.4 - Prob. 21PCh. 13.4 - Prob. 22PCh. 13.4 - Prob. 23PCh. 13.4 - Prob. 24PCh. 13.4 - Prob. 27PCh. 13.4 - Prob. 28PCh. 13.4 - Prob. 29PCh. 13.5 - Prob. 1PCh. 13.5 - Prob. 2PCh. 13.5 - Prob. 3PCh. 13.5 - Prob. 4PCh. 13.5 - Prob. 5PCh. 13.5 - Prob. 6PCh. 13.5 - Prob. 7PCh. 13.5 - Prob. 8PCh. 13.5 - Prob. 9PCh. 13.5 - Prob. 10PCh. 13.5 - Prob. 11PCh. 13.5 - Prob. 12PCh. 13.5 - Prob. 13PCh. 13.5 - Prob. 14PCh. 13.5 - Prob. 15PCh. 13.5 - Prob. 16PCh. 13.5 - Prob. 17PCh. 13.5 - Prob. 19PCh. 13.5 - Prob. 20PCh. 13.5 - Prob. 21PCh. 13.5 - Prob. 22PCh. 13.6 - Prob. 1PCh. 13.6 - Prob. 2PCh. 13.6 - Prob. 3PCh. 13.6 - Prob. 4PCh. 13.6 - Prob. 5PCh. 13.6 - Prob. 6PCh. 13.6 - Prob. 7PCh. 13.6 - Prob. 8PCh. 13.6 - Prob. 9PCh. 13.6 - Prob. 10PCh. 13.6 - Prob. 11PCh. 13.6 - Prob. 12PCh. 13.6 - Prob. 13PCh. 13.6 - Prob. 14PCh. 13.6 - Prob. 15PCh. 13.6 - Equations. Find all solutions 16. sin z =100Ch. 13.6 - Prob. 17PCh. 13.6 - Prob. 18PCh. 13.6 - Prob. 19PCh. 13.6 - Prob. 20PCh. 13.7 - Prob. 1PCh. 13.7 - Prob. 2PCh. 13.7 - Prob. 3PCh. 13.7 - Prob. 4PCh. 13.7 - Prob. 5PCh. 13.7 - Prob. 6PCh. 13.7 - Prob. 7PCh. 13.7 - Prob. 8PCh. 13.7 - Prob. 9PCh. 13.7 - Prob. 10PCh. 13.7 - Prob. 11PCh. 13.7 - Prob. 12PCh. 13.7 - Prob. 13PCh. 13.7 - Prob. 14PCh. 13.7 - Prob. 15PCh. 13.7 - Prob. 16PCh. 13.7 - Prob. 17PCh. 13.7 - Prob. 18PCh. 13.7 - Prob. 19PCh. 13.7 - Prob. 20PCh. 13.7 - Prob. 21PCh. 13.7 - Prob. 22PCh. 13.7 - Prob. 23PCh. 13.7 - Prob. 24PCh. 13.7 - Prob. 25PCh. 13.7 - Prob. 26PCh. 13.7 - Prob. 27PCh. 13.7 - Prob. 28PCh. 13.7 - Prob. 29PCh. 13 - Prob. 1RQCh. 13 - Prob. 2RQCh. 13 - Prob. 3RQCh. 13 - Prob. 4RQCh. 13 - Prob. 6RQCh. 13 - Prob. 7RQCh. 13 - Prob. 8RQCh. 13 - Prob. 9RQCh. 13 - Prob. 10RQCh. 13 - Prob. 11RQCh. 13 - Prob. 12RQCh. 13 - Prob. 13RQCh. 13 - Prob. 14RQCh. 13 - Prob. 15RQCh. 13 - Prob. 16RQCh. 13 - Prob. 17RQCh. 13 - Prob. 18RQCh. 13 - Prob. 19RQCh. 13 - Prob. 20RQCh. 13 - Prob. 21RQCh. 13 - Prob. 22RQCh. 13 - Prob. 23RQCh. 13 - Prob. 24RQCh. 13 - Prob. 25RQCh. 13 - Prob. 26RQCh. 13 - Prob. 27RQCh. 13 - Analytic Functions. Find fz=ux,y+ivx,y with u or v...Ch. 13 - Prob. 29RQCh. 13 - Prob. 30RQCh. 13 - Prob. 31RQCh. 13 - Prob. 32RQCh. 13 - Prob. 33RQCh. 13 - Prob. 34RQCh. 13 - Prob. 35RQ
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