 13.5.1: u(O, y) = 0, u(a, y) = 0 u(x, 0) = 0, u(x, b) = f(x)
 13.5.2: u(O, y) = 0, u(a, y) = 0  = 0, u(x, b) = f(x)
 13.5.3: u(O, y) = 0, u(a, y) = 0 u(x, 0) = f(x), u(x, b) = 0
 13.5.4: au I au I ax x=O ' ax x=a u(x, 0) = x, u(x, b) = 0
 13.5.5: u(O, y) = 0, u(l, y) = 1  y :; ly=O = O, :; ly=l = O
 13.5.6: u(O, y) = g(y), au I = 0 ax x=l au I = O au I = O ay y=o ' ay y=7T
 13.5.7: au I = u(O, y), u(7r, y) = 1 ax x=O u(x, 0) = 0, u(x, 7T') = 0
 13.5.8: u(O, y) = 0, u(l, y) = 0  = u(x, 0), u(x, 1) = f(x) au I ay y=O
 13.5.9: u(O, y) = 0, u(l, y) = 0 u(x, 0) = 100, u(x, 1) = 200
 13.5.10: u(O, y) = lOy, au I = 1 ax x=l u(x, 0) = 0, u(x, 1) = 0
 13.5.11: In 11 and 12, solve Laplace's equation (1) for the semiinfinite pl...
 13.5.12: In 11 and 12, solve Laplace's equation (1) for the semiinfinite pl...
 13.5.13: u(O, y) = 0, u(a, y) = 0 u(x, 0) = f(x), u(x, b) = g(x)
 13.5.14: u(O, y) = F(y), u(a, y) = G(y) u(x, 0) = 0, u(x, b) = 0
 13.5.15: u(O, y) = 1, u(7T, y) = 1 u(x, 0) = 0, u(x, 7T) = 1
 13.5.16: u(O, y) = 0, u(2, y) = y(2  y) u(x, 0) = 0, u(x, 2) = { x, 2  x, O
 13.5.17: In 16, what is the maximum value of the temperature u for 0 ::5 x :...
 13.5.18: (a) In suppose a = b = 7T andf(x) = l OOx ( 7T  x). Without using ...
 13.5.19: (a) Use the contourplot application of yourCAS to graph the isothe...
 13.5.20: Use the contourplot application of your CAS to graph the isotherms...
 13.5.21: Solve the Neumann problem for a rectangle: a2u a2u a x2 + ay2 = o, ...
 13.5.22: Consider the boundaryvalue problem a2u a2u a x2 + a y2 = o, o < x ...
Solutions for Chapter 13.5: Laplace's Equation
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 13.5: Laplace's Equation
Get Full SolutionsSince 22 problems in chapter 13.5: Laplace's Equation have been answered, more than 37559 students have viewed full stepbystep solutions from this chapter. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.5: Laplace's Equation includes 22 full stepbystep solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

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.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Coeficient of determination
See R 2 .

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Correlation
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

Design matrix
A matrix that provides the tests that are to be conducted in an experiment.

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

Error propagation
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.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Fisher’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.

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

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .