 9.9.1: In 110, show that the given line integral is independent of the pa...
 9.9.2: In 110, show that the given line integral is independent of the pa...
 9.9.3: In 110, show that the given line integral is independent of the pa...
 9.9.4: In 110, show that the given line integral is independent of the pa...
 9.9.5: In 110, show that the given line integral is independent of the pa...
 9.9.6: In 110, show that the given line integral is independent of the pa...
 9.9.7: In 110, show that the given line integral is independent of the pa...
 9.9.8: In 110, show that the given line integral is independent of the pa...
 9.9.9: In 110, show that the given line integral is independent of the pa...
 9.9.10: In 110, show that the given line integral is independent of the pa...
 9.9.11: In 1116 , determine whether the given vector field is a conservati...
 9.9.12: In 1116 , determine whether the given vector field is a conservati...
 9.9.13: In 1116 , determine whether the given vector field is a conservati...
 9.9.14: In 1116 , determine whether the given vector field is a conservati...
 9.9.15: In 1116 , determine whether the given vector field is a conservati...
 9.9.16: In 1116 , determine whether the given vector field is a conservati...
 9.9.17: In 17 and 18, find the work done by the force F( x ,y) = (2x + eY)...
 9.9.18: In 17 and 18, find the work done by the force F( x ,y) = (2x + eY)...
 9.9.19: In 1924, show that the given integral is independent of the path ....
 9.9.20: In 1924, show that the given integral is independent of the path ....
 9.9.21: In 1924, show that the given integral is independent of the path ....
 9.9.22: In 1924, show that the given integral is independent of the path ....
 9.9.23: In 1924, show that the given integral is independent of the path ....
 9.9.24: In 1924, show that the given integral is independent of the path ....
 9.9.25: In 25 and 26, evaluate f c F dr. F(x,y,z) = (y yzsnix)i + (x + zcs...
 9.9.26: In 25 and 26, evaluate f c F dr. F(x, y, z) = (2 el)i + (2y  l)j ...
 9.9.27: The inverse square law of gravitational attraction between twomasse...
 9.9.28: Find the work done by the force F(x, y, z) = 8xy3zi + 12x2y2zj + 4x...
 9.9.29: If F is a conservative force field, show that the work done along a...
 9.9.30: A particle in the plane is attracted to the origin with a force F =...
 9.9.31: Suppose Fis a conservative force field with potential function </J....
 9.9.32: Suppose that C is a smooth curve between points A (at t = a) and B ...
Solutions for Chapter 9.9: Independence of the Path
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 9.9: Independence of the Path
Get Full SolutionsChapter 9.9: Independence of the Path includes 32 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 32 problems in chapter 9.9: Independence of the Path have been answered, more than 33356 students have viewed full stepbystep solutions from this chapter. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

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

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

Bivariate normal distribution
The joint distribution of two normal random variables

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

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.

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Distribution function
Another name for a cumulative distribution function.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

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.

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

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

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 .