## Weekly outline

• • ### MATHEMATICAL METHODS

Vector algebra and vector calculus, tensors, curvilinear coordinate systems, linear algebra;Linear differential equations, elements of Sturm–Liouville theory;Special functions; Complex analysis; Fourier series and Fourier transforms, Laplace transforms;Elementary properties of discrete groups; Elements of probability theory, error analysis.

• ### CLASSICAL MECHANICS

Newton’s laws, conservation of energy and momentum, collisions;generalized coordinates, principle of least action,Lagrangian and Hamiltonian formulations of mechanics;symmetry and conservation laws; central force problem, Kepler problem;small oscillations and normal modes; special relativity in classical mechanics.

• ### ELECTROMAGNETISM AND OPTICS

Electrostatics and magnetostatics, boundary value problems, multipole expansion;fields in conducting, dielectric, diamagnetic and paramagnetic media;Faraday’s law and time varying fields; displacement current;
Maxwell’s equations; energy and momentum of electromagnetic fields;propagation of plane electromagnetic waves, reflection, refraction;electromagnetic waves in dispersive and conducting media;diffraction, interference, polarization.

• ### QUANTUM MECHANICS

Uncertainty principle; Schrodinger equation; central potentials, hydrogen atom;orbital and spin angular momenta, addition of angular momenta;matrix formulation of quantum theory, unitary transformations, Hermitian operators;variational principle, time independent perturbation theory, time dependent perturbation theory

• ### THERMODYNAMICS AND STATISTICAL PHYSICS

Laws of thermodynamics, work and heat, thermodynamic potentials;Elements of kinetic theory; Maxwell’s relations;statistical ensembles; partition function; classical ideal gas, harmonic oscillators;
classical and quantum statistics; Fermi and Bose gases;black body radiation; statistics of paramagnetism

• ### ELECTRONICS

Basics of semiconductor; p-n junctions, diodes, transistors;LCR circuits, rectifiers, amplifiers, active filters and oscillators;basics of OPAMPs and their applications; basics of digital electronics.