- 13.7.1: In Example 1 find the temperature u(x, t) when the left end of the ...
- 13.7.2: Solve the boundary-value problem a 2 u au k-2 = -, 0 < x < 1, t > 0...
- 13.7.3: Find the steady-state temperature for a rectangular plate for which...
- 13.7.4: Solve the boundary-value problem a 2 u a 2 u + -2 = 0, x > 0, 0 < y...
- 13.7.5: Find the temperature u(x, t) in a rod of length L if the initial te...
- 13.7.6: Solve the boundary-value problem a 2 u a 2 u a 2 -2 = -2, 0 < x < L...
- 13.7.7: Solve the boundary-value problem a2u a2u -2 + ---:2 = 0, 0 < x < 1,...
- 13.7.8: The initial temperature in a rod of unit length isf(x) throughout. ...
- 13.7.9: Use the method that starts with (15) of Section 13.6 to solve the n...
- 13.7.10: A vibrating cantilever beam is embedded at its left end (x = 0) and...
- 13.7.11: (a) Find an equation that defines the eigenvalues when the ends of ...
Solutions for Chapter 13.7: Orthogonal Series Expansions
Full solutions for Advanced Engineering Mathematics | 5th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
The probability of an event given that the random experiment produces an outcome in another event.
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 .
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
Another name for factors that are arranged in a factorial experiment.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
A probability distribution for a discrete random variable
A series of tests in which changes are made to the system under study
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.