## SYLLABUS

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**Mathematical Methods:-** Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and per¬fect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. First and lin¬ear second order differential equations. Matrices and de¬terminants, 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, uni¬formly rotating frame, centrifugal and Coriolis forces, Mo¬tion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces. Sys¬tem of particles, Centre of mass, equation of motion of the CM, conservation of linear and angular momentum, con¬servation 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..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. Super-position of two or more simple harmonic oscillators.Lissajous figures. Damped and forced oscillators, reso¬nance. 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 combina¬tions. 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 condi¬tions, 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 electromag¬netic induction, Self and mutual inductance. Alternating currents.Simple DC and AC circuits with R, L and C com¬ponents. Displacement current, Maxwell’s equations and plane electromagnetic waves, Poynting’s theorem, reflec¬tion 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.Zeroeth law and concept of thermal equilibrium.First law and its consequences.Iso-thermal 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 addi¬tion theorem, mass energy equivalence. Blackbody radia-tion, 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, Pauli exclusion prin¬ciple.Structure of atomic nucleus, mass and binding energy.Ra¬dioactivity and its applications. Laws of radioactive decay.Solid State Physics, Devices and Electronics: Crystal structure, Braves lattices and basis. Miller indices.X-ray diffraction and Bragg'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 ga