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 and linear second order
differential equations. 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, Centre 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. Principal
moments and axes. Elasticity, Hooke's law and elastic constants of
isotropic solid, stress energy. Kinematics of moving fluids, equation
of continuity, Euler's equation, Bernoulli's theorem, viscous fluids,
surface tension and surface energy, capillarity.
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. Zeroeth 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.
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,
Schrödinger equation and its solution for one, two and three
dimensional boxes. Reflection and transmission at a step potential,
tunneling through a barrier. Pauli exclusion principle.
Distinguishable and indistinguishable particles. Max-well-Boltzmann,
Fermi-Dirac and Bose-Einstein statistics. Structure of atomic nucleus,
mass and binding energy. Radioactivity and its applications. Laws of
radioactive decay. Fission and fusion.
Solid State Physics, Devices and Electronics: Crystal
structure, Bravais lattices and basis. Miller indices. X-ray
diffraction and Bragg's law, Einstein and Debye theory of specific
heat. Free electron theory of metals. Fermi energy and density of
states. Origin of energy bands. Concept of holes and effective mass.
Elementary ideas about dia-, para- and ferromagnetism, Langevin's
theory of paramagnetism, Curie's law. Intrinsic and extrinsic
semiconductors. Fermi level. p-n junctions, transistors. Transistor
circuits in CB, CE, CC modes. Amplifier circuits with transistors.
Operational amplifiers. OR, AND, NOR and NAND gates.
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