 12.2.1: f(x) = {O, 7T < x < 0 1, 0:5x<7
 12.2.2: {1 7T < x < 0 f(x) = 2, ' 0:5x<7T
 12.2.3: f(x) = {1 1 < x < 0 x, 0:5x
 12.2.4: f(x) = {0 1 < x < 0 x, 0:5x
 12.2.5: f(x) = 2 7T < x < 0 X, 0:5x<7
 12.2.6: f(x) = 7T 2  2 x' 7T < x < 0 0:5x<7T
 12.2.7: f(x) = x + 7T, 7T < x < 7T
 12.2.8: f(x) = 3  2x, 7T < x < 7T
 12.2.9: f(x) = {O, sinx, 7T < x < 0 0:5x<7T
 12.2.10: f(x) = {O, 7T/2 < x < 0 cosx, 0 :5 x < 7r/2
 12.2.11: f(x) = r 2<x< 1 l:5x<O 0 :5x < 1 l:5x<2
 12.2.12: r f 2 < x < 0 0 :5x < 1 l:5x<2
 12.2.13: f(x) = 1 + x 5 < x < 0 0:5x<5
 12.2.14: 2 + x, f 2 < x < 0 0:5x<2
 12.2.15: f(x) = ex , 7T < x < 7T
 12.2.16: f(x) = ex _ l, 0:5x<7
 12.2.17: Use the result of to show and 7T2  1 1 1 = l++++ 6 22 3 2 42 7T...
 12.2.18: Use to find a series that gives the numerical value of 7T2/8.
 12.2.19: Use the result of to show 7T 1 1 1 = 1 + + . 4 3 5 7
 12.2.20: Use the result of to show 7T 1 1 1 1 1 =+++ . 4 2 13 35 57 79
 12.2.21: The rootmeansquare value of a function! (x) defined over an inter...
Solutions for Chapter 12.2: Fourier Series
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 12.2: Fourier Series
Get Full SolutionsAdvanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Since 21 problems in chapter 12.2: Fourier Series have been answered, more than 36933 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Chapter 12.2: Fourier Series includes 21 full stepbystep solutions.

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

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.

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

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

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.

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

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

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

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

Conditional variance.
The variance of the conditional probability distribution of a random variable.

Continuous distribution
A probability distribution for a continuous random variable.

Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

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.

Event
A subset of a sample space.

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

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.