- 18.1.1: f c(z + 3 )dz, where Cisx = 2t,y = 4t - 1, 1::5t::53
- 18.1.2: f c(2z - z)dz, where Cisx = -t,y = t2 + 2, 0 ::5 t ::5 2
- 18.1.3: f c z2 dz, where C is z(t) = 3t + 2it, -2 ::5 t ::5 2
- 18.1.4: f c(3z2 - 2z)dz, where C is z(t) = t + it2, 0 ::5 t ::5 1
- 18.1.5: f c 1 + z dz, where C is the right half of the circle lzl = 1 z fro...
- 18.1.6: f clzl2 dz, where C is x = t 2 , y = lit, 1 ::5 t ::5
- 18.1.7: .PcRe(z) dz, where C is the circle lzl = 1
- 18.1.8: .Pc( 1 . 3 - 5-. + 8 dz, whereCisthe circlelz + i i= 1, (z + z) z +...
- 18.1.9: f c(x2 + iy) dz, where C is the straight line from z = 1 to z = i
- 18.1.10: f c(x3 - iy) dz, where C is the lower half of the circle lzl = 1 fr...
- 18.1.11: f c e' dz, where C is the polygonal path consisting of the line seg...
- 18.1.12: f c sin z dz, where C is the polygonal path consisting of the line ...
- 18.1.13: f c Im(z - i) dz, where C is the polygonal path consisting of the c...
- 18.1.14: fcdz, whereCis the left half ofthe ellipsex2/36 + y2 /4 = 1 fromz =...
- 18.1.15: .Pcze' dz, where C is the square with vertices z = 0, z = 1, z = 1 ...
- 18.1.16: f cf(z)dz, wheref(z) = 6 ' and C is the parabola x, x > 0 y = x2 fr...
- 18.1.17: In 17-20, evaluate the given integral along thecontour C given in F...
- 18.1.18: In 17-20, evaluate the given integral along thecontour C given in F...
- 18.1.19: In 17-20, evaluate the given integral along the contour C given in ...
- 18.1.20: In 17-20, evaluate the given integral along thecontour C given in F...
- 18.1.21: In 21-24, evaluate f c(z2 - z + 2)dz from i to 1 along the indicate...
- 18.1.22: In 21-24, evaluate f c(z2 - z + 2)dz from i to 1 along the indicate...
- 18.1.23: In 21-24, evaluate f c(z2 - z + 2)dz from i to 1 along the indicate...
- 18.1.24: In 21-24, evaluate f c(z2 - z + 2)dz from i to 1 along the indicate...
- 18.1.25: 1 dz , where C is the circle lzl = 5
- 18.1.26: ( 2 1 . dz, where C is the right half of the circle lzl = 6
- 18.1.27: Jc (z2 + 4) dz, where C is the line segment from z = 0 to z = 1 + i
- 18.1.28: L dz, where C is one quarter of the circle lzl = 4 from z = 4ito z = 4
- 18.1.29: (a) Use Definition 18.1.1 to show for any smooth curve C between z0...
- 18.1.30: Use Definition 18.1.1 to show for any smooth curve C between Zo and...
- 18.1.31: Use the results of 29 and 30 to evaluate pc( 6z + 4) dz where Cis (...
- 18.1.32: f(z) = 1/z, where C is the circle lzl = 2
- 18.1.33: f(z) = 2z, where C is the circle lzl = 1
- 18.1.34: f(z) = 1/(z - 1), where C is the circle lz - 11 = 2
- 18.1.35: f(z) = z, where C is the square with vertices z = 0, z = 1, z = 1 +...
Solutions for Chapter 18.1: Contour Integrals
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
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
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.
The probability of an event given that the random experiment produces an outcome in another event.
See Control chart.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
A subset of effects in a fractional factorial design that deine the aliases in the design.
The response variable in regression or a designed experiment.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Another name for a cumulative distribution function.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
A study in which a sample from a population is used to make inference to the population. See Analytic study
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
In statistical quality control, that portion of a number of units or the output of a process that is defective.