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# Solutions for Chapter 14.3: Problems in Spherical Coordinates

## Full solutions for Advanced Engineering Mathematics | 5th Edition

ISBN: 9781449691721

Solutions for Chapter 14.3: Problems in Spherical Coordinates

Solutions for Chapter 14.3
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##### ISBN: 9781449691721

This expansive textbook survival guide covers the following chapters and their solutions. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Since 14 problems in chapter 14.3: Problems in Spherical Coordinates have been answered, more than 34930 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Chapter 14.3: Problems in Spherical Coordinates includes 14 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Backward elimination

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

• Biased estimator

Unbiased estimator.

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• Chi-square (or chi-squared) 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.

• Components of variance

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Dispersion

The amount of variability exhibited by data

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Error of estimation

The difference between an estimated value and the true value.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• First-order model

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

• Fisherâ€™s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Generator

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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