Unit I Linear Differential Equations (LDE) and Applications 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. Modelling of Electrical circuits. (Chapters - 1, 2) Unit II Transforms Fourier Transform (FT) : Complex exponential form of Fourier series, Fourier integral theorem, Fourier Sine & Cosine integrals, Fourier transform, Fourier Sine and Cosine transforms and their inverses. Z - Transform (ZT) : Introduction, Definition, Standard properties, ZT of standard sequences and their inverses. Solution of difference equations. (Chapters - 3, 4) Unit III 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 : Euler’s, Modified Euler’s, Runge-Kutta 4th order methods and Predictor-Corrector methods. (Chapters - 5, 6) Unit IV Vector Differential Calculus Physical interpretation of Vector differentiation, Vector differential operator, Gradient, Divergence and Curl, Directional derivative, Solenoidal, Irrotational and Conservative fields, Scalar potential, Vector identities. (Chapter - 7) Unit V Vector Integral Calculus & Applications Line, Surface and Volume integrals, Work-done, Green’s Lemma, Gauss’s Divergence theorem, Stoke’s theorem. Applications to problems in Electro-magnetic fields. (Chapter - 8) Unit VI Complex Variables Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal mapping, Bilinear transformation, Cauchy’s integral theorem, Cauchy’s integral formula and Residue theorem. (Chapters - 9, 10)
