Linear Algebra-I
Introduction to vector spaces and sub-spaces, definitions, illustrative example. Linearly independent and dependent vectors- Basis-definition and problems. Linear transformations-definitions. Matrix form of linear transformations-Illustrative examples (Text Book:1).
Linear Algebra-II
Computation of eigen values and eigen vectors of real symmetric matricesGiven’s method. Orthogonal vectors and orthogonal bases. Gram-Schmidt orthogonalization process (Text. Book:1).
Calculus of Variations :
Concept of functional-Eulers equation. Functional dependent on first and higher order derivatives, Functional on several dependent variables. Isoperimetric problems-variation problems with moving boundaries.
Probability Theory:
Review of basic probability theory. Definitions of random variables and probability distributions, probability mass and density functions, expectation, moments, central moments, characteristic functions, probability generating and moment generating functionsillustrations. Poisson, Gaussian and Erlang distributions-examples. (Text Book: 3)
Engineering Applications on Random processes:
Classification. Stationary, WSS and ergodic random process. Auto-correlation functionproperties, Gaussian random process. (Text Book: 3)