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 19.13: Find a Maclaurin expansion off(z) = e' cos z. [Hint: Use the identi...
 19.14: Show that the functionf(z) = 1/sin( 7T/z) has an infinite number of...
 19.15: In 1518, use known results as an aid in expanding the given functi...
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 19.19: Expand f (z) = 2 2 in an appropriate series valid for z  4z + 3 (a...
 19.20: Expandf(z) = 2 in an appropriate series valid for (z  5) (a) lzl <...
 19.21: In 2130, use Cauchy's residue theorem to evaluate the given integr...
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 19.31: In 31 and 32, evaluate the Cauchy principal value of the given impr...
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 19.33: In 33 and 34, evaluate the given trigonometric integral. J0 2 + sin8
 19.34: In 33 and 34, evaluate the given trigonometric integral.
 19.35: Use an indented contour to show that ioo 1 COS X dx _ 7T P.V. 2  ...
 19.36: Show that f0ea2x2 cos bx dx = eb2/4a2Vii/2a by considering the co...
 19.37: The Laurent expansion off (z) = e<"12)<zllz) valid for 0 < lzl can...
Solutions for Chapter 19: Series and Residues
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 19: Series and Residues
Get Full SolutionsAdvanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Chapter 19: Series and Residues includes 37 full stepbystep solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Since 37 problems in chapter 19: Series and Residues have been answered, more than 37400 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Acceptance region
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

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Bivariate distribution
The joint probability distribution of two random variables.

Central tendency
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

Coeficient of determination
See R 2 .

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Contrast
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.

Cook’s distance
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.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Dispersion
The amount of variability exhibited by data

Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a modelitting process and not on replication.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications