Unit-1 (Classical Mechanics):
Lagrangian and Hamiltonian formulation, Poisson bracket, concepts of Geodesics and Curved Space Geometry
Unit-II (Quantum Mechanics):
Time independent, Time dependent, degenerate, non-degenerate perturbation theory, WKB approximation, Variational principle, Scattering, Interaction of matter with radiation
Unit-III (Statistical Mechanics):
Microcanonical, canonical, Grandcanonical ensembles, Density matrix formulation, Phase transitions
Unit-IV (Electrodynamics):
Electromagnetic theory, Special theory of relativity, charged systems, Magnetostatics.
References
H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics, Third Edition.
S. T. Thornton and J. B. Marion, Classical Dynamics of Particles and Systems.
J. J. Sakurai, Modern Quantum Mechanics, Second Edition.
R. Shankar, Principles of Quantum Mechanics, Second Edition.
M. Kardar, Statistical Mechanics of Particles.
R. K. Pathria, Statistical Mechanics, Third Edition.
J. D. Jackson, Classical Electrodynamics, Third Edition.
E. M. Purcell and D. J. Morin, Electricity and Magnetism, Third Edition.