Preliminary concepts, probability theory, introduction to central limit theorem, random walk problem, quasi-static process,thermal and mechanical interactions, laws of thermodynamics, thermodynamic potentials. Statistical description of a system of particles,microstates, concept of ensembles, basic postulates, phase space, Liouville's theorem, microcanonical, canonical and grand canonical ensembles. Partition functions. Chemical potential,free energy and connection with thermodynamic variables. Equivalence of ensembles. Ideal gas,Gibbs paradox, M-B gas velocity distribution.

Probability Theory: Elementary concepts on probability – axiomatic definition of probability – conditional probability – Bayes’ theorem – random variables – standard discrete and continuous distributions – moments of random variables – moment generating functions – multivariate random variables – joint distributions of random variables – conditional and marginal distributions – conditional expectation – distributions of functions of random variables – t and χ2 distributions – Schwartz and Chebyshev inequalities – weak law of large numbers for finite variance case – central limit theorem for

Discrete time signals and systems, Properties of LTI Systems, DTFT, Z-T/F; Minimum phase-All pass decomposition, Generalized linear phase; DFS, Frequency sampling and Time aliasing, DFT, Periodic & Circular convolutions; FFT computations using DIT and DIF algorithms; Infinite Impulse Response Digital Filter design: Impulse invariant and Bilinear transformation approaches, Finite Impulse Response Digital filter design: Windowing and Optimal Equiv.-ripple filter design; Filter structures and realization: Signal flow graph representation, Direct form I & II, Cascade and Parallel forms,

Probability Theory: Elementary concepts on probability – axiomatic definition of probability –conditional probability – Bayes’ theorem – random variables – standard discrete and continuous distributions – moments of random variables – moment generating functions – multivariate randomvariables – joint distributions of random variables – conditional and marginal distributions – conditional expectation – distributions of functions of random variables – t and χ2 distributions – Schwartz and Chebyshev inequalities – weak law of large numbers for finite variance case – central limit theorem for i