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.