- 18.2.1: f(z) = i3 - 1 + 3i
- 18.2.2: f(z) = z2 + z --4
- 18.2.3: f(z) = 2z + 3
- 18.2.4: f(z) = z2 + 2z + 2
- 18.2.5: f(z) = (z2 - 25) (z2 + 9)
- 18.2.6: f(z) = 2z2 + 1 lz + 15
- 18.2.7: f(z) = tan z
- 18.2.8: f(z) = cos hz
- 18.2.9: Evaluate i ! dz , where C is the contour shown in FIGURE 18.2.9.y
- 18.2.10: Evaluate i 5 dz , where C is the contour shown in FIGURE c z - z 18...
- 18.2.11: i ( z + ) dz; lzl = 2
- 18.2.12: i ( z + z 1 2) dz; lzl = 2
- 18.2.13: i 2 z 2 dz; lzl = 3
- 18.2.14: i 10 . 4 dz; lz + ii = 1
- 18.2.15: i 2z + 1 --dz (a) lzl = !, (b) lzl = 2, (c) lz - 3il = 1 c z2 + z
- 18.2.16: i z 2 2 : 3 dz; (a) lzl = 1, (b) lz - 2il = 1, (c) lzl = 4
- 18.2.17: i -3z + 2 2 dz; (a) lz - 51 = 2, (b) lzl = 9 c z - 8z + 12
- 18.2.18: i ( z ! 2 - z 2J dz; (a) lzl = 5, (b) lz - 2il = !
- 18.2.19: i ( z - 1 3 0 dz; lz - ii = !
- 18.2.20: i 3 + 1 2 . 2 dz; lzl = 1
- 18.2.21: Evaluate i 8 - 3 dz , where C is the closed contour shown in FIGURE...
- 18.2.22: Suppose Zo is any constant complex number interior to any simple cl...
- 18.2.23: i ( - 3z) dz , C is the unit circle lzl = 1
- 18.2.24: Pc(z3 + z2 + Re(z) ) dz, C is the triangle with vertices z = 0, z =...
Solutions for Chapter 18.2: Cauchy-Goursat Theorem
Full solutions for Advanced Engineering Mathematics | 5th Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
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
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
Another term for the conidence coeficient.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
A subset of effects in a fractional factorial design that deine the aliases in the design.
A property of a collection of events that indicates that their union equals the sample space.
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.
A signal from a control chart when no assignable causes are present
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.