## JEST SYLLABUS

##### Syllabus
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 & 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 & 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.