 11.3.1: Show that (0, 0) is an asymptotically stable critical point of the ...
 11.3.2: When expressed in polar coordinates, a plane autonomous system take...
 11.3.3: dx dt = kx(n + 1 x)
 11.3.4: dx x = kxln x>O dt k'
 11.3.5: dT dt = k(T T0)
 11.3.6: dv m dt = mg  kv
 11.3.7: dx dt = k(a x)(/3 x), a> {
 11.3.8: dx dt = k(a x)(/3 x)('Y x), a> {3 > 'Y
 11.3.9: dP = P(a  bP)(l  cP1), P > 0, a < be
 11.3.10: dA = kVA(K  VA), A > 0 dt
 11.3.11: x' = 1  2xy y' = 2xy y
 11.3.12: x' = x2  y2  1 y' = 2y
 11.3.13: x' = y  x2 + 2 y' = x2 xy
 11.3.14: x' = 2x  y2 y' = y + x
 11.3.15: x' = 3x + y2 + 2 y' = x2 y2
 11.3.16: x' = xy  3y  4 y' = y2 x2
 11.3.17: x' = 2xy y' = y  x + xy  y3
 11.3.18: x' = x(l  x2  3y2) y' = y(3 x2  3y2)
 11.3.19: x' = x(lO  x  !J) y' = y(16  y  x)
 11.3.20: x' = 2x + y + 10 y'= 2x y 15 y y+ 5
 11.3.21: ()" = (cos()  0.5) sin(), 181 < 7T
 11.3.22: ()" = (cos()  0.5) sin(), 181 < 7T
 11.3.23: x' + x'(l x3)  x2 = 0
 11.3.24: x' + 4+ 2x' = o
 11.3.25: x'+x=ex3 fore>O
 11.3.26: x' + x exlxl = 0 for E > 0 [Hint: dx xi.xi = 21xl .]
 11.3.27: Show that the nonlinear secondorder differential equation (1 + a2x...
 11.3.28: Show that the dynamical system x' =ax+ xy y' = 1  {3y x2 has a u...
 11.3.29: (a) Show that the plane autonomous system x' = x + yx3 y' = x y...
 11.3.30: (a) Show that (0, 0) is the only critical point of the Raleigh diff...
 11.3.31: Use the phaseplane method to show that (0, 0) is a center of the n...
 11.3.32: Use the phaseplane method to show that the solution to the nonline...
 11.3.33: (a) Find the critical points of the plane autonomous system x' = 2x...
 11.3.34: The origin is the only critical point of the nonlinear secondorder...
 11.3.35: A solution of the nonlinear secondorder differential equation x' +...
 11.3.36: The nonlinear differential equation x' + x = 1 + e:x2 arises in the...
 11.3.37: When a nonlinearcapacitoris present in anLRCseries circuit, the vo...
 11.3.38: The nonlinear secondorder differential equation m:X' + kx + kix3 =...
 11.3.39: The nonlinear differential equation d2() 1  + sin()=  dt2 2 can b...
 11.3.40: (a) Show that (0, 0) is an isolated critical point of the plane aut...
Solutions for Chapter 11.3: Linearization and Local Stability
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 11.3: Linearization and Local Stability
Get Full SolutionsAdvanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Since 40 problems in chapter 11.3: Linearization and Local Stability have been answered, more than 33373 students have viewed full stepbystep solutions from this chapter. Chapter 11.3: Linearization and Local Stability includes 40 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5.

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

Bivariate distribution
The joint probability distribution of two random variables.

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Coeficient of determination
See R 2 .

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Density function
Another name for a probability density function

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

Error variance
The variance of an error term or component in a model.

Estimate (or point estimate)
The numerical value of a point estimator.

Experiment
A series of tests in which changes are made to the system under study

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Fraction defective control chart
See P chart

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials