Mathematical Methods

Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion, Fourier series

Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green's theorem, Stoke's theorem

First order equations and linear second order differential equations with constant coefficients

Matrices and determinants, Algebra of complex numbers

Mechanics and General Properties of Matter:

Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces

System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems

Elastic and inelastic collisions

Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem

Principal moments and axes. Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem

Oscillations, Waves and Optics:

Differential equation for simple harmonic oscillator and its general solution

Superposition of two or more simple harmonic oscillators

Lissajous figures. Damped and forced oscillators, resonance

Wave equation, traveling and standing waves in one-dimension

Energy density and energy transmission in waves

Group velocity and phase velocity

Sound waves in media

Doppler Effect

Fermat’s Principle

General theory of image formation

Thick lens, thin lens and lens combinations

Interference of light, optical path retardation

Fraunhofer diffraction

Rayleigh criterion and resolving power

Diffraction gratings

Polarization: linear, circular and elliptic polarization

Double refraction and optical rotation.

Electricity and Magnetism:

Coulomb’s law, Gauss’s law

Electric field and potential

Electrostatic boundary conditions, Solution of Laplace’s equation for simple cases

Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy

Biot-Savart law, Ampere’s law, Faraday’s law of electromagnetic induction, Self and mutual inductance

Alternating currents

Simple DC and AC circuits with R, L and C components

Displacement current, Maxwell’s equations and plane electromagnetic waves, Poynting’s theorem, reflection and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only)

Lorentz Force and motion of charged particles in electric and mag-netic fields.

Kinetic theory, Thermodynamics:

Elements of Kinetic theory of gases

Velocity distribution and Equipartition of energy

Specific heat of Mono-, di- and tri-atomic gases

Ideal gas, van-der-Waals gas and equation of state

Mean free path. Laws of thermodynamics

Zeroth law and concept of thermal equilibrium

First law and its consequences

Isothermal and adiabatic processes

Reversible, irreversible and quasi-static processes

Second law and entropy

Carnot cycle

Maxwell’s thermodynamic relations and simple applications

Thermodynamic potentials and their applications

Phase transitions and Clausius-Clapeyron equation

Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions

Modern Physics:

Inertial frames and Galilean invariance

Postulates of special relativity

Lorentz transformations

Length contraction, time dilation

Relativistic velocity addition theorem, mass energy equivalence

Blackbody radiation, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays

Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation values, Schrödinger equation and its solution for one, two and three dimensional boxesv

Solution of Schrödinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle

Structure of atomic nucleus, mass and binding energy

Radioactivity and its applications

Laws of radioactive decay

Solid State Physics, Devices and Electronics:

Crystal structure, Bravais lattices and basis

Miller indices

X-ray diffraction and Bragg's law; Intrinsic and extrinsic semiconductors, variation of resistivity with temperature

Fermi level

p-n junction diode, I-V characteristics, Zener diode and its applications, BJT: characteristics in CB, CE, CC modes

Single stage amplifier, two stage R-C coupled amplifiers

Simple Oscillators: Barkhausen condition, sinusoidal oscillators

OPAMP and applications: Inverting and non-inverting amplifier

Boolean algebra: Binary number systems; conversion from one system to another system; binary addition and subtraction

Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth tables; combination of gates; de Morgan’s theorem