Unit 01: MATHEMATICAL PHYSICS I
Matrices and determinants, Fourier series. Algebra of complex numbers.
Unit 02: MATHEMATICAL PHYSICS II
Transformation of Coordinates – Jacobian – Taylor expansion – Differential equations . Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems.
Unit 03: MATHEMATICAL PHYSICS III
Vector algebra and vector calculus, multiple integrals.
Unit 04: KINETIC THEORY & THERMODYNAMICS I 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.
Unit 05: THERMODYNAMICS II
Maxwell’s thermodynamic relations and simple applications. Thermodynamic potentials and their applications. Phase transitions and Clausius-Clapeyron equation.
Unit 06: MECHANICS I
Newton’s laws of motion and applications. System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy. Elastic and inelastic collisions. Conservative and non-conservative forces.
Unit 07: MECHANICS II
Angular velocity, Angular momentum, 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.
Unit 08: MECHANICS III
Gravitational Law and field, Motion under a central force, Kepler’s laws. Variable mass systems. Uniformly rotating frame, centrifugal and Coriolis forces.
Unit 09: SHM, SOUND & BERNOULLI’S THEOREM
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. Sound waves in media. Doppler effect. Equation of scontinuity, Euler’s equation, Bernoulli’s theorem.
Unit 10: OPTICS
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.
Unit 11: ELECTROSTATICS
Coulomb’s law, Electric field and potential, Gauss’s law. Electrostatic boundary conditions, Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy.
Unit 12: E M I & A.C CIRCUITS
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. Lorentz force and motion of charged particles in electric and magnetic fields.
Unit 13: ELECTROMAGNETISM
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).
Unit 14: BOOLEAN ALGEBRA, GATES AND NUMBER SYSTEM
Binary number systems; conversion from one system to another system; binary addition and subtraction. Boolean algebra. Logic Gates AND, OR, NOT, NAND, NOR, Exclusive OR; Truth tables; combination of gates; de Morgan’s theorem.
Unit 15: SEMICONDUCTORS, P.N DIODE AND ZENER DIODE
Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. p-n junction diode, I-V characteristics, Zener diode and its applications.
Unit 16: TRANSISTORS, OP-AMP and 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.
Unit 17: ATOMIC & NUCLEAR PHYSICS
Photoelectric effect, Compton effect, Bohr’s atomic model, X-rays, Pauli exclusion principle. Structure of atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay.
Unit 18: STATISTICAL MECHANICS & SOLID STATE PHYSICS:
Ideas of ensembles, Maxwell-Boltzmann, Fermi Dirac and Bose Einstein distributions. Blackbody radiation. Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg's law.
Unit 19: QUANTUM MECHANICS
Group velocity and phase velocity, 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.
Unit 20: RELATIVITY
Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy equivalence.