 15.1: a2u a2u 1. 2 + 2 = 0, x > 0, 0 < y < 7T ax ay au I = 0, O < Y < 7...
 15.2: a2u au 2 = , 0 < x < 1, t > 0 ax at u(O, t) = 0, u(l, t) = 0, t >...
 15.3: a2u au 2  hu = , h > 0, x > 0, t > 0 ax at 1. au u(O, t) = 0, rm...
 15.4: u a2u   = elxl oo < x < oo t > 0 at ax 2 ' ' u(x,O) = u0,  oo
 15.5: 2u au 2 = , x > 1, t > 0 ax at u(O, t) = t, limu(x, t) = 0 xoo u(...
 15.6: a2u a2u 2 2 , 0 < x < 1, t > 0 ax at u(O, t) = 0, u(l, t) = 0, t >...
 15.7: k 2 = , oo < x < oo, t > 0 ax at {o, x < o u(x, 0) = u0, 0 < x <...
 15.8: a2u a2u 2 + 2 = 0, 0 < x < 7T, y > 0 ax ay { O, 0 < y < 1 u(O,y) ...
 15.9: a2u a2u 2 + 2 = 0, x > 0, y > 0 ax ay {50, 0 < y < 1 u(O, y) = 0,...
 15.10: a2u au O 1 2 + r = , 0 < x < 1, t > 0 ax at au I = 0, u(l, t) = 0...
 15.11: a2u a2u 11. 2 + 2 = 0, x > 0, 0 < y < 7T ax ay u(O, y) = A, 0 < y...
 15.12: a2u au 2 = , 0 < x < 1, t > 0 ax at u(O, t) = u0, u(l, t) = u0, t...
 15.13: k =  oo < x < 00 t > 0 ax2 at' ' {o, u(x, 0) = x e ' a2u au xO
 15.14: a2u au xO 2 = , x > 0, t > 0 ax at  = 50, limu(x, t) = 100, t >...
 15.15: Show that a solution of the BVP a2u a2u +  = 0 oo < x < oo, 0 < ...
 15.16: 0 5 a2u = au . 2 ' x > 0, t > 0 ax at aul = 0, t > O ax =O u(x, 0) ...
 15.17: a2u ax 2 au 0 < x < 7T, at' t > 0 u(O, t) = 1, u(7T, t) = 1, t > 0 ...
 15.18: a2u au 2 = , x > 0, t > 0 ax at u(O, t) = lOO[oU(t 5)  oU(t  1...
 15.19: Consider the boundaryvalue problem a2u au 2 = , x > 0, t > 0 ax ...
 15.20: (a) Solve the BVP in using a Fourier transform. (b) Show that the a...
Solutions for Chapter 15: Integral Transform Method
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 15: Integral Transform Method
Get Full SolutionsThis textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Since 20 problems in chapter 15: Integral Transform Method 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. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Chapter 15: Integral Transform Method includes 20 full stepbystep solutions.

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.

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

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

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

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

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Chance cause
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Convolution
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.

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.

Discrete random variable
A random variable with a inite (or countably ininite) range.

Dispersion
The amount of variability exhibited by data

Distribution function
Another name for a cumulative distribution function.

Estimate (or point estimate)
The numerical value of a point estimator.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

Fraction defective control chart
See P chart

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.