- 13.1.1: au au ax ay
- 13.1.2: au + 3 au = ax ay
- 13.1.3: ux+uy=u
- 13.1.4: ux=uy+u
- 13.1.5: au au x ax ay
- 13.1.6: au au y ax ay
- 13.1.7: a2u a2u a2u -+--+-=O ax2 axay ay2
- 13.1.8: y--+u=O axa
- 13.1.9: k--u = - k>O ax2 at'
- 13.1.10: k i!!_ = au k > O ax2 at'
- 13.1.11: a2_ ax2 at2
- 13.1.12: a2 -= -+ 2k- k > 0 ax2 at2 at'
- 13.1.13: a2u a2u au -+-+2k- k>O ax2 ay2 at'
- 13.1.14: x2-+-=0
- 13.1.15: U:xx + Uyy = U
- 13.1.16: a2uxx -g = Utt, g a constant
- 13.1.17: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.18: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.19: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.20: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.21: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.22: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.23: In 17 -2 6, classify the given partial differential equation as hyp...
- 13.1.24: In 17 -2 6, classify the given partial differential equation as hyp...
- 13.1.25: In 17 -2 6, classify the given partial differential equation as hyp...
- 13.1.26: In 17 -2 6, classify the given partial differentialequation as hype...
- 13.1.27: k ( a2u + _!_au ) = au ; ar2 r ar at u = e-ka2t(c110(ar) + c2Y0(ar))
- 13.1.28: a2u 1 au 1 a2u ar + 2 -;. ar + r2 afP = O;
- 13.1.29: Verify that each of the products u = X(x)Y(y) in (6), (7), and (8) ...
- 13.1.30: Definition 13.1.1 generalizes to linear PDEs with coefficients that...
- 13.1.31: a2 -u =
- 13.1.32: a 1 u + au = o ax axay ax
Solutions for Chapter 13.1: Separable Partial Differential Equations
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 statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
The probability of an event given that the random experiment produces an outcome in another event.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
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 parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
The response variable in regression or a designed experiment.
A matrix that provides the tests that are to be conducted in an experiment.
A property of a collection of events that indicates that their union equals the sample space.
A series of tests in which changes are made to the system under study
A signal from a control chart when no assignable causes are present
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.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.