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Unit - 1 Partial Differential Equations

Unit 1Partial differential equation

1.1 Origin of Partial Differential Equations

1.2 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

Unit 2Applications of partial differential equation

2.1 Classification of the linear partial differential equation of second order

2.2 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 2

Applications of partial differential equation

Unit 2

Applications of partial differential equation

2.1 Classification of the linear partial differential equation of second order

2.2 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

Unit 3Statistical techniques1

3.1 Introduction Measures of central tendency

3.2 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

4.6 Discrete and Continuous Probability distribution Binomial Poisson and Normal distributions

Unit 3

Statistical techniques1

3.1 Introduction Measures of central tendency

3.2 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

4.5 Expectation and variance

Unit 3

Statistical techniques1

3.1 Introduction Measures of central tendency

3.2 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

Unit 4Statistical techniques2

4.1 Probability and Distribution Introduction Addition and multiplication law of probability

4.2 Conditional probability

4.3 Bayes’ theorem

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 4

Statistical techniques2

5.3 Testing a Hypothesis Level of significance Confidence limits

Unit 4

Statistical techniques2

4.1 Probability and Distribution Introduction Addition and multiplication law of probability

4.2 Conditional probability

4.3 Bayes’ theorem

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 4

Statistical techniques2

4.1 Probability and Distribution Introduction Addition and multiplication law of probability

4.2 Conditional probability

4.3 Bayes’ theorem

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

Unit 5Statistical techniques3

5.1 Introduction Sampling Theory Small and Large

5.2 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.

Unit 5

Statistical techniques3

5.1 Introduction Sampling Theory Small and Large

5.2 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

Unit 5

Statistical techniques3

5.1 Introduction Sampling Theory Small and Large

5.2 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.

Unit 5

Statistical techniques3

5.1 Introduction Sampling Theory Small and Large

5.2 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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