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Unit - 1 Partial Differential Equations

1.1 Origin of Partial Differential Equations1.2 Lagrange’s Equations linear and NonLinear Partial Equations of the first order

1.3 Charpit’s method

1.4 Cauchy’s method of Characteristics

1.5 Solution of Linear Partial Differential Equation of Higherorder with constant coefficients

1.6 Equations reducible to linear partial differential equations with constant coefficients

Unit - 2 Applications of Partial Differential Equations

2.1 Classification of the linear partial differential equation of second order2.2 Method of separation of variables

2.3 Solution of wave and heat conduction equation up to two dimensions Laplace equation in two dimensions

2.4 Equations of Transmission lines

Unit - 3 Statistical Techniques I

3.1 Introduction Measures of central tendency3.2 Moments Moment generating function MGF

3.3 Skewness Kurtosis

3.4 Curve Fitting Method of least squares fitting of straight lines fitting of a seconddegree parabola Exponential curves

3.6 Correlation and Rank correlation

3.7 Regression Analysis Regression lines of y on x and x on y regression coefficients properties of regressions coefficients and nonlinear regression

Unit - 4 Statistical Techniques II

4.1 Probability and Distribution Introduction Addition and multiplication law of probability4.2 Conditional probability

4.4 Random variables Discrete and Continuous Random variable Probability mass function and Probability density function

4.5 Expectation and variance

4.6 Discrete and Continuous Probability distribution Binomial Poisson and Normal distributions

Unit - 5 Statistical Techniques III

5.1 Introduction Sampling Theory Small and Large5.2 Hypothesis Null hypothesis Alternative hypothesis

5.3 Testing a Hypothesis Level of significance Confidence limits

5.4 Test of significance of the difference of means

5.5 Ttest Ftest and Chisquare test

5.6 Oneway Analysis of Variance ANOVA

5.7 Statistical Quality Control SQC Control Charts Control Charts for variables X and R Charts Control Charts for Variables p np and C charts.

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