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, Stokes’
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’slaws 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 magnetic 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, FermiDirac 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 boxes. 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.