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SYLLABUS-
CORE PAPER-1
MATHEMATICAL PHYSICS-I


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.
UNIT-II
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,
Vector algebra: Recapitulation of vectors: Properties of vectors under rotations.
Scalar product and its invariance under rotations, Vector product, Scalar triple
product and their interpretation in terms of area and volume respectively, Scalar
and Vector fields.
UNIT-III
Orthogonal Curvilinear Coordinates: Orthogonal Curvilinear Coordinates,
Derivation of Gradient, Divergence, Curl and Laplacian in Cartesian, Spherical and
Cylindrical Coordinate Systems, Comparison of velocity and acceleration in
cylindrical and spherical coordinate system
Dirac Delta function and its properties: Definition of Dirac delta function.
Representation as limit of a Gaussian function and rectangular Function,
Properties of Dirac delta function.
UNIT-IV
Vector Differentiation: Directional derivatives and normal derivative, Gradient
of a scalar field and its geometrical interpretation, Divergence and curl of a vector
field, Del and Laplacian operators, Vector identities
Vector Integration: Ordinary Integrals of Vectors, Multiple integrals, Jacobian,
Notion of infinitesimal line, surface and volume elements, Line, surface and volume
integrals of Vector fields, Flux of a vector field, Gauss’ divergence theorem, Green’s
and Stokes Theorems and their applications (no rigorous proofs)

CORE PAPER-II
MECHANICS

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, Eulers Equations of Rigid Body motion, Motion involving
both translation and rotation. Moment of Inertia of a Fly wheel.
Non-Inertial Systems: Non-inertial frames and fictitious forces, Uniformly rotating
frame, Laws of Physics in rotating coordinate systems, Centrifugal force, Coriolis
force and its applications.
UNIT-II Elasticity: Relation between Elastic constants, Twisting torque on a Cylinder
or Wire, Bending of beams, External bending moment, Flexural rigidity, Single and
double cantilever
Surface Tension: Excess pressure across a curved membrane, Quink’s drop
Fluid Motion: Kinematics of Moving Fluids: Poiseuilles Equation for Flow of a
Liquid through a Capillary Tube, Surface tension, Gravity waves and ripple
Viscocity: Poiseuilles Equation for Flow of a Liquid with corrections.
UNIT-III Gravitation and Central Force Motion: Law of gravitation, Gravitational
potential energy, Inertial and gravitational mass, Potential and field due to spherical shell
and solid sphere, Motion of a particle under a central force field, Two-body problem and its
reduction to one-body problem and its solution, Differential Equation of motion with central
force and its solution, The first Integrals (two), Concept of power Law Potentials, Keplers
Laws of Planetary motion, Satellites:. Geosynchronous orbits, Weightlessness, Basic idea of
global positioning system (GPS), Physiological effects on astronauts.
UNIT-IV
Oscillations: Simple Harmonic Oscillations. Kinetic energy, potential energy, total energy
and their time-average values. Damped oscillation. Equation of motion and solution (cases
ofEtc.................