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Unit - 1 Linear Differential Equations

Unit1Linear differential equations

1.1 LDE of nth order with constant coefficient

1.2 The general method and Short methods

1.3 Methods of variation of parameters

1.4 Cauchy’s and Legendre’s Different1ial Equation

1.5 Simultaneous and symmetric simultaneous differential equations

Unit - 2 Transforms

Unit2Transforms

2.1 Complex Exponential form of Fourier series

2.2 Fourier integral theorem

2.3 Fourier sine and cosine integrals

2.4 Fourier transform

2.5 Fourier sine and cosine transforms and their inverses

2.6 Discrete Fourier transform

2.7 Z transform Introduction Definition standard properties

2.8 ZT of standard sequences and their inverses

2.9 Solution of difference equations

Unit - 3 Statistics

Unit3Statistics

3.1 Measure of central tendency

3.2 Measures of dispersion and Standard Deviation

3.3 Coefficient of variation

3.4 Moments Skewness and Kurtosis

3.5 Curve fitting of a straight line

3.6 Fitting Parabola and related curves

3.7 Correlation and regression

3.8 Reliability of regression estimates

Unit - 4 Probability and Probability Distributions

Unit4Probability and Probability Distribution

4.1 Theorems on Probability

4.2 Bayes theorem

4.3 Random variables

4.4 Mathematical expectation

4.5 Probability density function

4.6 Probability distributions Binomial Poisson and Normal distributions hypergeometric distribution

4.7 Test of Hypothesis ChiSquare test tdistribution.

4.8 ChiSquare test

4.9 tdistribution Test

Unit - 5 Numerical Methods

Unit5Numerical Methods

5.1 Bisection

5.2 Secant

5.3 RegulaFalsi

5.4 Newton Raphson and successive approximation method convergence and stability

5.5 Numerical Solutions of System of linear equations Gauss elimination method

5.6 LU Decomposition Cholesky

5.7 Jacobi and GaussSiedel methods

Unit - 6 Numerical Methods

Unit6Numerical Methods

6.1 Interpolation Finite differences

6.2 Newton’s and Lagrange interpolation formulae

6.3 Numerical differentiation

6.4 Numerical integration Trapezoidal and Simpson’s Rules Bound of truncation error

6.5 Solution of ordinary differential equations Euler’s method

6.6 Modified Euler’s method

6.7 RungeKutta 4th order method Predicator and corrector

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