UNIT I: 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

UNIT II: 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
• Parallel And perpendicular axes theorem
• Principal moments and axes
• Kinematics of moving fluids
• Equation of continuity
• Euler’s equation
• Bernoulli’s theorem

UNIT III: 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 travelling and standing waves in one-dimension.
• Energy density 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
• Polarisation: linear, circular and elliptic
• Double refraction and optical rotation

UNIT IV: 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
• Polarisation 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.

UNIT V: Electricity and Magnetism

• 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-Waalsgas 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

UNIT VI: 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
• 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
• Pauli Exclusion Principle
• Structure of atomic nucleus, mass and binding energy
• Radioactivity and its applications
• Laws of radioactive decay

UNIT VII: 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
• OP AMP 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.