Random Thoughts

Paper 2: Mechanics Syllabus ( Rigid body dynamics, Radius of Gyration, Moment of Inertia,Non-Inertial Systems, Elasticity, Fluid motion and Types of Vibration, Newtonian theory through Gravitation, Central force motion, Keplar’s laws, GPS, Special theory of Relativity, Michelson- Morley experiment, Lorentz transformation, Relativistic Doppler effect. ) Unit I Rotational Dynamics : Centre of Mass, Motion of CoM, Centre of Mass and Laboratory frames, Angular momentum of a particle and system of particles, Principle of conservation of angular momentum, Rotation about a fixed axis, Moment of Inertia, Perpendicular and Parallel Axis Theorems, Routh Rule, Calculation of moment of inertia for cylindrical and spherical bodies, Kinetic energy of rotation, Euler’s Equations of Rigid Body motion, Motion involving both translation and rotation. Moment of Inertia of a Flywheel. Non-Inertial Systems : Non-inertial frames and fictitious forces, uniformly rotating frame, Laws of Physics in rota...

Paper 1: Mathematical Physics I Syllabus Differential equations and their solutions, calculus, Vector calculus and its differentiation, vector integration, Dirac delta function, Orthogonal curvilinear coordinates, functional algebra and error analysis. Unit I Calculus -I : Plotting of functions, Intuitive ideas of continuous, differentiable functions and plotting of curves, Approximation: Taylor and binomial series (statements only), First Order Differential Equations and Integrating Factor, Second Order Differential equations: Homogeneous Equations with constant coefficients, Wronskian and general solution, Statement of existence and Uniqueness Theorem for Initial Value Problems, Particular Integral. Calculus-II : Calculus of functions of more than one variable: Partial derivatives, exact and inexact differentials. Integrating factor with simple illustration, Constrained Maximization using Lagrange Multipliers. Unit II Vector algebra : Recapitulation of vectors: Properties ...