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 matrices-Given’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. (Text.Book:2)
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 functions-illustrations. Poisson, Gaussian and Erlang distributionsexamples. (Text Book: 3)
Engineering Applications on Random processes:
Classification. Stationary, WSS and ergodic random process. Auto-correlation functionproperties, Gaussian random process. (Text Book: 3)