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Unit - 1 Partial Differential Equations

1.1 Definition of Partial Differential Equations1.2 First order partial differential equations

1.3 Solutions of first order linear PDEs

1.4 Solution to homogenous and nonhomogenous linear partial differential equations of second order by complimentary function and particular integral method.

1.5 Secondorder linear equations and their classification

1.6 Initial and boundary conditions

1.7 D Alembert’s solution of the wave equation

1.8 Duhamels principle for one dimensional wave equation

1.9 Heat diffusion and vibration problems

1.10 Separation of variables method to simple problems in Cartesian coordinates

1.11 The Laplacian in plane

1.12 Cylindrical and spherical polar coordinates

1.13 Solutions with Bessel functions and Legendre functions

1.14 One dimensional diffusion equation and its solution by separation of variables

Unit - 2 Probability Spaces

2.1 Probability spaces2.2 Conditional probability

2.3 Independence Discrete random variables

2.4 The Multinomial distribution

2.5 Poisson approximation to the binomial distribution

2.6 Infinite sequences of Bernoulli trials

2.7 Sums of independent random variables

2.8 Expectation of Discrete Random Variables Moments

2.9 Variance of a sum

2.10 Correlation coefficient

2.11 Chebyshevs Inequality

2.12 Continuous random variables and their properties

2.13 Distribution functions and densities

2.14 Normal exponential and gamma densities

2.15 Bivariate distributions and their properties

2.16 Distribution of sums and quotients

2.17 Conditional densities

2.18 Bayes rule

Unit - 3 Statistics

3.1 Basic Statistics3.2 Measures of Central tendency Moments skewness and Kurtosis

3.3 Probability distributions Binomial Poisson and Normal Evaluation of statistical parameters for these three distributions

3.4 Correlation and regression – Rank correlation

3.5 Curve fitting by the method of least squares fitting of straight lines

3.6 Second degree parabolas and more general curves

3.7 Difference of proportions

3.8 Tests for Sample mean

3.9 Difference of means and difference of standard deviations

3.10 Test for ratio of variances Chi square test for goodness of fit and independence of attributes

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