Theory of complex Variable:
Analytic functions, Cauchy-Riemann equation, Line integral, Cauchy’s theorem and Cauchy’s integral. Simple form of conformal transformation with application of the solution of two-dimensional problems.
Finite Differences And Difference Equations:
Finite differences interpolation. Newton’s and LaGrange’s formula. Difference equation with constants co-efficient. Solution of ordinary and partial differential equations with boundary conditions by finite difference method.
Roots of algebraic equations. Solution of linear simultaneous equations. Solution of linear simultaneous equations. Numerical differentiation and integration. Numerical methods to solve first order, first degree ordinary differential equations.
Definition, Laplace transform of elementary functions. Properties of Laplace transform, Inverse Laplace transforms. Transform derivatives, Transform of integration. Multiplication by tn, Division by t, Convolution theorem. Unit step and Heaviside’s unit function, Dirac-delta function. Periodic functions Solution of ordinary linear differential equations Simultaneous equations with constant coefficient applied to electrical circuits.
Definition of periodic function. Euler’s formula. Functions having points of discontinuity. Change of intervals. Odd and even functions. Expansion of odd or even periodic functions. Half range cosine and sine series. Elements of harmonic analysis.
first order, second order and nth order, with integer argument and their solutions; First order, second order, nth order, with continuous variables and their solutions; The state space form &Kalman-Bucy filter, Riccati Matrices (Equations) and applications