Topic

Subtopic

Mathematical Methods

This topic covers Calculus of single and multiple variables, partial derivatives along with Jacobian, imperfect and perfect differentials, Fourier series, etc. It also includes Vector algebra and Calculus, Divergence theorem, Green’s theorem, Stokes’ theorem. Apart from that, there are details on First order equations as well as linear second order differential equations along with constant coefficients. Matrices and determinants, different sections of Algebra for complex numbers, etc.

Mechanics and General Properties of Matter

All the topics that fall under this section are Newton’s laws of motion along with its applications, Velocity and acceleration in Cartesian, uniformly rotating frame, and Coriolis forces, polar as well as cylindrical coordinate systems. Besides, Motion under a central force, details on Kepler’s laws, concepts of Gravitational Law and field, and also Conservative and non-conservative forces. There are also some others like the System of particles, motion’s equation of the CM, details on conservation of linear and angular momentum, facts on conservation of energy and variable mass systems, etc. Concept and analysis of Elastic and inelastic collisions. Rigid body motion, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem, and the most important moments and axes. There are also some theories like Kinematics of moving fluids, equation of continuity, Euler’s equation, and Bernoulli’s theorem, etc.

Oscillations, Waves and Optics

Under this unit, all the subtopics are a distinctive equation for the common harmonic oscillator along with the outcome of it. The top position of two or more than that simple harmonic oscillators. Also, there are Lissajous figures; details on Damped and forced oscillations and resonance. Aside from that, Wave equation and standing waves in one-dimension. Detail analysis of Energy density and energy transmission in waves. The concept of Group and phase velocity. And also, Sound waves in the media. There are a lot of theories in this unit such as the Doppler Effect. Principle of Fermat. The common theory of image formation. All the forms of the lens, Interference of light, and optical path retardation. Rayleigh criterion as well as resolving power. Diffraction gratings. The polarization includes not only linear and circular but also elliptic polarization. Details about Double refraction along with optical rotation.

Electricity and Magnetism

This section comprises some of the main areas that are the law of Coulomb and the law of Gauss. Basic concept on Electric field and potential. It also covers Electrostatic boundary conditions and the Outcome of Laplace’s equation that are made for common cases. There is also dielectric polarization, volume along with surface charges, details on electrostatic energy. Some other theory portions are there such as the law of Biot-Savart, the law of Ampere, details on Faraday’s law of electromagnetic induction along with Self and mutual inductance. Al the process and forms of Alternating currents. Displacement current, Maxwell’s equations, and plane electromagnetic waves. Also, there are Poynting’s theorem, detailed analysis on transmission and reflection coefficients used for only normal incidence.

Kinetic theory and

Thermodynamics

In this unit, all the areas are all the Elements of Kinetic theory of gases, details on Velocity distribution as well as Equipartition of energy. There is also the concept of Specific heat of Mono-, di- and tri-atomic gases. All kinds of equations of state. Details on Thermodynamics law. Zeroth law and the overall idea of thermal equilibrium. All about First law and the consequences of the same. What’s more, Isothermal along with adiabatic processes. The process regarding Reversible and irreversible and also quasi-static. Concept of Carnot cycle. Maxwell’s thermodynamic relations and some applications that are not difficult. Everything on Thermodynamic potentials along with its applications. Detail Idea of ensembles. And also, 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, the superposition principle, calculation of expectation values, Schrödinger equation and its solution for one, two and three-dimensional boxes. A solution of Schrödinger equation for the one-dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle. Structure of the atomic nucleus, mass, and binding energy. 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, a 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. OPAMP 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; a combination of gates; de Morgan’s theorem.