**SYLLABUS**

**PHYSICS (PH)**

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*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'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.

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*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, Maxwelll'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, 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, Schrodinger equation and its solution for
one, two and three dimensional boxes. Solution of Schrodinger 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.