- 3.11.1: In 1 -4, the given differential equation is a model of an undamped ...
- 3.11.2: In 1 -4, the given differential equation is a model of an undamped ...
- 3.11.3: In 1 -4, the given differential equation is a model of an undamped ...
- 3.11.4: In 1 -4, the given differential equation is a model of an undamped ...
- 3.11.5: In 3, suppose the mass is released from the initial position x(O) =...
- 3.11.6: In 3, suppose the mass is released from an initial position x(O) = ...
- 3.11.7: Find a linearization of the differential equation in 4.
- 3.11.8: Consider the model of an undamped nonlinear spring/mass system give...
- 3.11.9: In 9 and 10, the given differential equation is a model of a damped...
- 3.11.10: In 9 and 10, the given differential equation is a model of a damped...
- 3.11.11: The model mx" + kx + k1x3 = F0 cos wt of an undamped periodically d...
- 3.11.12: (a) Find values of k1 < 0 for which the system in is oscillatory. (...
- 3.11.13: Consider the model of the free damped nonlinear pendulum given by d...
- 3.11.14: (a) Use the substitution v = dyldt to solve (13) for v in terms of ...
- 3.11.15: (a) In Example 4, show that equation (16) possesses a constant solu...
- 3.11.16: a) In Example 4, what docs (21) predict to be the maximum amount of...
- 3.11.17: The Caught Pendulum. Suppose the massless rod in the discussion len...
- 3.11.18: The Caught Pendulum-Continued (a) Use a graphing utility to obtain ...
- 3.11.19: Pursuit Curve In a naval exercise, a ship S 1 is pursued by a subma...
- 3.11.20: Pursuit Curve In another naval exercise , a destroyer S1 pursues a ...
- 3.11.21: Discuss why the damping term in equation (3) is written as 1:1: ins...
- 3.11.22: (a) Experiment with a calculator to find an interval 0 ::5 8 < 81, ...
- 3.11.23: (a) Consider the nonlinear pendulum whose oscillations are defined ...
- 3.11.24: Consider the initial-value problem d28 7T dt2 + sin8 = 0, 8(0) = 12...
- 3.11.25: Consider a pendulum that is released from rest from an initial disp...
Solutions for Chapter 3.11: Nonlinear Models
Full solutions for Advanced Engineering Mathematics | 5th Edition
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.
The joint probability distribution of two random variables.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Another name for a cumulative distribution function.
Error of estimation
The difference between an estimated value and the true value.
Estimate (or point estimate)
The numerical value of a point estimator.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
Exponential random variable
A series of tests in which changes are made to the system under study
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Fraction defective control chart
See P chart