Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 22, Problem 7P
Perform the computation in Examples 21.3 and 22.5 for the falling parachutist, but use Romberg
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πT
| cos x |³ dx
59
2
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
True or False and why
Chapter 22 Solutions
Numerical Methods for Engineers
Ch. 22 - 22.1 Use order of Romberg integration to...Ch. 22 - Use Romberg integration to evaluate I=12(x+1x)2dx...Ch. 22 - Use Romberg integration to evaluate 02exsinx1+x2dx...Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - 22.6 Obtain an estimate of the integral from Prob....Ch. 22 - 22.7 Perform the computation in Examples 21.3 and...Ch. 22 - Employ two- through six-point Gauss-Legendre...Ch. 22 - Prob. 9PCh. 22 - 22.10 Develop a user-friendly computer program for...
Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - 22.13 Develop a user-friendly computer program for...Ch. 22 - There is no closed form solution for the error...Ch. 22 - 22.15 The amount of mass transported via a pipe...Ch. 22 - The depths of a river H are measured at equally...Ch. 22 - 22.17 Recall that the velocity of the freefalling...Ch. 22 - 22.18 Prove that Eq. (22.15) is equivalent to...
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- 10 5 Obtain by multiplying matrices the composite coordinate transformation of two transformations, first x' = (x + y√√2+2)/2 y' = z' (x√√2-2√2)/2 z = (-x+y√√2-2)/2 followed by x" = (x'√√2+z'√√2)/2 y" = (-x'y'√√2+2')/2 z" = (x'y'√√2-2')/2.arrow_forwardNot use ai pleasearrow_forward4 The plane 2x+3y+ 6z = 6 intersects the coordinate axes at P, Q, and R, forming a triangle. Draw a figure and identify the three points on it. Also find vectors PQ and PR. Write a vector formula for the area of the triangle PQR and find its value.arrow_forward
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- 5 Obtain by multiplying matrices the composite coordinate transformation of two transformations, first x' = (x + y√2+ z)/2 followed by y' = (x√√2-2√2)/2 z' = (-x+y√2-2)/2 x" = y" 2" = (x'√√2+2'√√2)/2 (-x'y'√√2+)/2 (x'y' √√2-z)/2.arrow_forwardWhat is the answer in 10.3arrow_forward4 The plane 2x + 3y+ 6z = 6 intersects the coordinate axes at P, Q, and R, forming a triangle. Draw a figure and identify the three points on it. Also find vectors PQ and PR. Write a vector formula for the area of the triangle PQR and find its value.arrow_forward
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