## JEST SYLLABUS

##### **JEST 2017**

** 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

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

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.

Last modified: Saturday, 5 August 2017, 11:32 PM