Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.1, Problem 9E
a.
To determine
To find: The two different solutions
b.
To determine
To find: The condition on
c.
To determine
To find: The condition on
d.
To determine
To find: The condition on
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4. Consider a square service region of unit area in which travel is right angle and directions of travel are parallel
to the sides of the square. Let (X, Y₁) be the location of a mobile unit and (X₂, Y₂) the location of a demand
for service. The travel distance is
D =Dx + Dy
where
Dx = |X₁ - X₂ and Dy = |Y₁ — Y2\.
Assume that the two locations are independent and uniformly distributed over the square.
a. Show that the joint pdf for Dx and Dy is
(4(1-x)(1-y),
fpx.D¸y (x, y) = {4(1 –
b. Define Ryx = D/Dr. Show that the pdf of Ryx is
2
3
fryx (r) = .
2
3r²
1
r,
3
1
3r3'
0,
0≤x≤ 1,0 ≤ y ≤ 1
otherwise
0 ≤r≤1
1 ≤r <∞0
Evaluate
Ic1²
(2x - y) dx + (x + 7y) dy.
C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7)
4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line
%(x-4) = ½ (y) = z+ 2.
Chapter 7 Solutions
Numerical Analysis
Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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- If y, and y2 are linearly independent solutions of ty" +4y' + tey = 0 and if W(y1, y2)(1) = 4, find W(y1, y2)(4). %3D Round your answer to two decimal places. W(y1, y2)(4) =Larrow_forwardIf y, and y₂ are linearly independent solutions of ty" + 3y' + te²y = 0 and if W(y₁, y₂)(1) = 3, find W(y₁, y2)(2). Round your answer to two decimal places. W(y₁, y₂)(2) = i I'arrow_forward4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.arrow_forward
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