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# Solutions for Chapter 2: First-Order Differential Equations

## Full solutions for Advanced Engineering Mathematics | 5th Edition

ISBN: 9781449691721

Solutions for Chapter 2: First-Order Differential Equations

Solutions for Chapter 2
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##### ISBN: 9781449691721

Since 42 problems in chapter 2: First-Order Differential Equations have been answered, more than 37651 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Chapter 2: First-Order Differential Equations includes 42 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• 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

• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• 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

• Bivariate distribution

The joint probability distribution of two random variables.

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square 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 .

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• 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 .

• 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.

• Cumulative sum control chart (CUSUM)

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

• Distribution function

Another name for a cumulative distribution function.

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Event

A subset of a sample space.

• Experiment

A series of tests in which changes are made to the system under study

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• 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.

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