Vector spaces and matrices, transformations, eigenvalues and eigenvectors, norms; geometrical concepts ‐ hyperplanes, convex sets, polytopes and polyhedra; unconstrained optimization ‐ condition for local minima; one dimensional search methods ‐ golden section, fibonacci, newtons, secant search methods; gradient methods ‐ steepest descent; newton's method, conjugate direction methods, conjugate gradient method; constrained optimization ‐ equality conditions, lagrange condition, second order conditions; inequality constraints ‐ karush‐kuhntucker condition; convex optimization; introduction t

Elements of probability theory - random variables - Gaussian distribution - stochastic processes characterizations and properties - Gauss-Markov processes - Brownian motion process - Gauss-Markov models - Optimal estimation for discrete-time systems - fundamental theorem of estimation - optimal prediction.

Optimal filtering - Weiner approach - continuous-time Kalman Filter - properties and implementation - steady-state Kalman Filter - discrete-time Kalman Filter - implementation – sub optimal steady-state Kalman Filter - Extended Kalman Filter - practical applications.

Signals and systems, Vector space, Norms, Matrix theory: Inversion formula, Schur’s complement, Singular Value Decomposition, Positive definiteness; Linear Matrix Inequality: Affine function, Convexity, Elimination lemma, S‐procedure; Calculus of variation, Euler’s Theorem, Lagrange multiplier. Linear fractional transformation (LFT), Different uncertainty structures: Additive, Multiplicative, Uncertainty in Coprime factors; Concept of loop shaping, Bode’s Gain and phase relationship, Small Gain theorem.

Discrete Random Process: Expectation, Variance and Co‐variance, Uniform, Gaussian and Exponentially distributed noise, Hillbert space and inner product for discrete signals, Energy of discrete signals, Parseval’s theorem, Wiener Khintchine relation, power spectral density, Sum decomposition theorem, Spectral factorization theorem.

Introduction of Soft-computing tools - Neural Networks, Fuzzy Logic, Genetic Algorithm, and Probabilistic Reasoning; Neural network approaches in engineering analysis, design, and diagnostics problems; Applications of Fuzzy Logic concepts in Engineering Problems; Engineering optimization problem-solving using genetic algorithm; applications of probabilistic reasoning approaches.