 14.3.1: Solve the problem in Example 1 if f(8) = { 50, 0, 0 < () < 7T/2 7T/...
 14.3.2: The solution u(r, 8) in Example 1 could also be interpreted as the ...
 14.3.3: Find the solution of the problem in Example 1 if f ( 8) = cos (), 0...
 14.3.4: Find the solution of the problem in Example 1 if f(8) = 1  cos 28,...
 14.3.5: Find the steadystate temperature u(r, 8) within a hollow sphere a<...
 14.3.6: The steadystate temperature in a hemisphere of radius c is determi...
 14.3.7: Solve when the base of the hemisphere is insulat.ed.; that is, au I...
 14.3.8: Solve for r > c.
 14.3.9: The dependent temperature within a sphere of radius 1 is detennined...
 14.3.10: A uniform solid sphere of radius 1 at an initial constant temperatu...
 14.3.11: Solve vibrations: the boundaryvalue problem involving spherical <1...
 14.3.12: A conducting sphere of radius c is grounded and placed in a uniform...
 14.3.13: (a) Proceed as in Example 1 but using u(r, 8, ) = R(r)8(6)4>( + m2c...
 14.3.14: (a) Assume that m and n are nonnegative integers. Then find a produ...
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
Get Full SolutionsThis 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 stepbystep 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 stepbystep solutions.

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

Adjusted R 2
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.

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

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.

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 tradeoff 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.

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

Fisherâ€™s least signiicant difference (LSD) method
A series of pairwise 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.