Syllabus: Joint Admission Test For
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..
Kinematics of moving fluids, equation of continuity, Euler’s equation,
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
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, Pauli exclusion principle. Structure of atomic nucleus,
mass and binding energy. Radioactivity and its applications. Laws of
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 gates.