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
• Conservation of linear and angular momentum
• Conservation of energy, variable mass systems
• Elastic and inelastic collisions
• Rigid body motion, fixed axis rotations
• 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
• Superposition of simple harmonic oscillators
• Lissajous figures
• Damped and forced oscillators, resonance
• Wave equation, traveling and standing waves
• Energy density and 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
• 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
• 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
• DC and AC circuits with R, L and C components
• Maxwell’s equations and plane electromagnetic waves
• Poynting’s theorem
• Reflection and refraction at dielectric interface
• Transmission and reflection coefficients
• Lorentz Force and motion of charged particles

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
• Laws of thermodynamics
• Zeroth law and thermal equilibrium
• First law and its consequences
• Isothermal and adiabatic processes
• Second law and entropy
• Carnot cycle
• Maxwell’s thermodynamic relations
• Thermodynamic potentials
• Phase transitions and Clausius-Clapeyron equation
• 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
• Schrödinger equation and solutions
• Pauli Exclusion Principle
• Structure of atomic nucleus
• 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
• Fermi level
• p-n junction diode
• Zener diode and applications
• BJT characteristics
• Single stage and two stage R-C coupled amplifiers
• Simple Oscillators
• OPAMP applications
• Boolean algebra
• Binary number systems
• Logic Gates
• Truth tables and de Morgan’s theorem