ENGINEERING MATHEMATICS - III

Linear Differential Equations (LDE) Solution of nth order LDE with constant coefficients, Method of variation of parameters, Cauchy's and Legendre's DE, Solution of simultaneous and symmetric simultaneous DE, Modeling of electrical circuits. Complex Variables Functions of complex variables, Analytic functions, C-R equations, Conformal mapping, Bilinear transformation, Cauchy's theorem, Cauchy's integral formula, Laurent's series, Residue theorem. Transforms Fourier Transform (FT) : Complex exponential form of Fourier series, Fourier integral theorem, Sine and cosine integrals, Fourier transform, Fourier sine and cosine transform and their inverses, Application to wave equation. Introductory Z-Transform (ZT) : Definition, Standard properties, ZT of standard sequences and their inverses. Solution of simple difference equations. 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 order methods. 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. Vector Integral Calculus Line, Surface and volume integrals, Work-done, Green's lemma, Gauss's divergence theorem, Stoke's theorem, Applications to problems in electro-magnetic fields.