Unit I Linear Differential Equations (LDE) LDE of nth order with constant coefficients, Complementary Function, Particular Integral, General method, Short methods, Method of variation of parameters, Cauchy’s and Legendre’s DE, Simultaneous and Symmetric simultaneous DE. (Chapters - 1, 2) Unit II Transforms Fourier Transform (FT) : Complex exponential form of Fourier series, Fourier integral theorem, Fourier Sine and Cosine integrals, Fourier transform, Fourier Sine and Cosine transforms and their inverses, Discrete Fourier Transform. Z-Transform (ZT) : Introduction, Definition, Standard properties, ZT of standard sequences and their inverses. Solution of difference equations. (Chapters - 3, 4) Unit III Statistics Measures of central tendency, Measures of dispersion, Coefficient of variation, Moments, Skewness and Kurtosis, Curve fitting : fitting of straight line, parabola and related curves, Correlation and Regression, Reliability of Regression Estimates. (Chapter - 5) Unit IV Probability and Probability Distributions Probability, Theorems on Probability, Bayes theorem, Random variables, Mathematical Expectation, Probability density function, Probability distributions : Binomial, Poisson, Normal and Hypergeometric, Sampling distributions, Test of Hypothesis : Chi-Square test, t-test. (Chapter - 6) Unit V Numerical Methods Numerical Solution of Algebraic and Transcendental equations : Bisection, Secant, Regula-Falsi, Newton-Raphson and Successive Approximation Methods, Convergence and Stability. Numerical Solutions of System of linear equations : Gauss elimination, LU Decomposition, Cholesky, Jacobi and Gauss-Seidel Methods. (Chapter - 7) Unit VI Numerical Methods Interpolation : Finite Differences, Newton’s and Lagrange’s Interpolation formulae, Numerical Differentiation. Numerical Integration : Trapezoidal and Simpson’s rules, Bound of truncation error. Solution of Ordinary differential equations .
