Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 12.2, Problem 2E
To determine
To Identify:
The classification of the critical point of a given system of linear equation at the origin.
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Answer questions 8.2.11 and 8.2.12 respectively
8.4.2 An article in Knee Surgery, Sports Traumatology, Arthroscopy [“Arthroscopic Meniscal Repair with an
Absorbable Screw: Results and Surgical Technique” (2005, Vol.
13, pp. 273–279)] showed that only 25 out of 37 tears (67.6%)
located between 3 and 6 mm from the meniscus rim were healed.
a. Calculate a two-sided 95% confidence interval on the proportion of such tears that will heal.
b. Calculate a 95% lower confidence bound on the proportion of such tears that will heal.
8.4.3 An article in the Journal of the American Statistical Association [“Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling” (1990, Vol. 85, pp.
972–985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats.
a. Calculate a 95% two-sided confidence interval on the true
proportion of rats that would show underweight from the
experiment.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95%…
8.4.8 Use the data from Exercise 8.4.2 to compute the two-sided
Agresti-Coull CI on the proportion of tears that heal. Compare
and discuss the relationship of this interval to the one computed
in Exercise 8.4.2.
Chapter 12 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 12.2 - In Problem 16, classify the critical point at the...Ch. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - In Problem 712, find and classify the critical...
Ch. 12.2 - In Problem 712, find and classify the critical...Ch. 12.2 - In Problem 712, find and classify the critical...Ch. 12.2 - Prob. 13ECh. 12.2 - In Problems 13-20, classify the critical point at...Ch. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - In Problems 13-20, classify the critical point at...Ch. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Show that when the system x(t)=ax+by+p,...Ch. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Show when the roots of the characteristic equation...Ch. 12.2 - Prob. 27ECh. 12.3 - In Problems 1 -8, show that the given system is...Ch. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - In Problems 9 -12, find all the critical points...Ch. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - In Problems 9 -12, find all the critical points...Ch. 12.3 - In Problems 13-16, convert the second-order...Ch. 12.3 - In Problems 13-16, convert the second-order...Ch. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - van der Pols Equation. a. Show that van der Pols...Ch. 12.3 - Consider the system dxdt=(+)x+y, dydt=x+(+)y,...Ch. 12.3 - Prob. 23ECh. 12.3 - Show that coexistence occurs in the competing...Ch. 12.3 - When one of the populations in a competing species...Ch. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - Prob. 4ECh. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - In problem 9-14, use Lyapunovs direct method to...Ch. 12.5 - In problem 9-14, use Lyapunovs direct method to...Ch. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prove that the zero solution for a conservative...Ch. 12.6 - Semistable Limit cycle. For the system...Ch. 12.6 - Prob. 2ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - In Problems 512, either by hand or using a...Ch. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - In Problems 5-12, either by hand or using computer...Ch. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - In Problems 5-12, either by hand or using computer...Ch. 12.6 - In Problems 13-18, show that the given system or...Ch. 12.6 - In Problems 13-18, show that the given system or...Ch. 12.6 - Prob. 15ECh. 12.6 - In Problems 13-18, show that the given system or...Ch. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Prob. 25ECh. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Prob. 28ECh. 12.7 - Prob. 1ECh. 12.7 - Prob. 2ECh. 12.7 - Prob. 3ECh. 12.7 - Prob. 4ECh. 12.7 - Prob. 5ECh. 12.7 - Prob. 6ECh. 12.7 - Prob. 9ECh. 12.7 - Prob. 10ECh. 12.7 - Prob. 11ECh. 12.7 - Prob. 12ECh. 12.7 - Prob. 13ECh. 12.7 - Prob. 14ECh. 12.7 - Prob. 15ECh. 12.7 - Prob. 16ECh. 12.7 - Prob. 17ECh. 12.7 - Prob. 18ECh. 12.8 - Calculate the Jacobian eigenvalues at the critical...Ch. 12.8 - Prob. 2ECh. 12.8 - Prob. 3ECh. 12.8 - Prob. 4ECh. 12.RP - In Problems 1-6, find all the critical points for...Ch. 12.RP - Prob. 2RPCh. 12.RP - Prob. 3RPCh. 12.RP - Prob. 4RPCh. 12.RP - In Problems 1-6, find all the critical points for...Ch. 12.RP - In Problems 1-6, find all the critical points for...Ch. 12.RP - Prob. 7RPCh. 12.RP - In Problems 7 and 8, use the potential plane to...Ch. 12.RP - In Problems 9-12, use Lyapunovs direct method to...Ch. 12.RP - Prob. 10RPCh. 12.RP - In Problems 9-12, use Lyapunovs direct method to...Ch. 12.RP - Prob. 12RPCh. 12.RP - Prob. 13RPCh. 12.RP - In Problem 13 and 14, sketch the phase plane...Ch. 12.RP - In Problems 15 and 16, determine whether the given...Ch. 12.RP - Prob. 16RPCh. 12.RP - In Problems 17 and 18, determine the stability of...Ch. 12.RP - In Problems 17 and 18, determine the stability of...
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