WEST BENGAL STATE UNIVERSITY (WBSU) B.SC (PHYSICS) HONOURS SEMESTER-I SYLLABUS(THEORY)

PAPER-1

TOPIC-Mathematical Physics-I

1.Calculus- Recapitulation: Limits, continuity, average and instantaneous quantities, differentiation. Plotting functions.Intuitive ideas of continuous, differentiable, etc. functions and plotting of curves. Approximation: Taylor and binomial series (statements only). Convergence condition of Taylor series and corresponding tests.First Order and Second Order Differential equations: First Order Differential Equations and Integrating Factor. Homogeneous and Inhomogeneous second order differential equations with constant coefficients,particular integral. Wronskian and general solution. Statement of existence and Uniqueness Theorem forInitial Value Problems.Calculus of functions of more than one variable: Partial derivatives, exact and inexact differentials.Integrating factor, with simple illustration. Constrained Maximization using Lagrange Multipliers.

2.Vector Calculus- 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.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 using Kronecker delta and Levi-civita symbols.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).Orthogonal Curvilinear Coordinates. Derivation of Gradient, Divergence, Curl and Laplacian in Cartesian,Spherical and Cylindrical Coordinate Systems.

3.Introduction to probability- Independent random variables: Probability distribution functions; binomial, Gaussian, and Poisson, with examples. Mean and variance.Dependent events: Conditional Probability. Bayes' Theorem.

PAPER-2

TOPIC-MECHANICS.

1.Fundamentals of Dynamics - Reference frames. Inertial frames; Review of Newton’s Laws of Motion. Galilean transformations; Galilean invariance. Momentum of variable- mass system: motion of rocket. Dynamics of a system of particles.Centre of Mass. Principle of conservation of momentum. Impulse.

2.Work and Energy - Work and Kinetic Energy Theorem. Conservative and non- conservative forces. Potential Energy. Qualitative study of one dimensional motion from potential energy curves. Stable and unstable equilibrium. Elastic potential energy. Force as gradient of potential energy. Work & Potential energy. Work done by nonconservative forces. Law of conservation of Energy.

3.Collisions- Elastic and inelastic collisions between particles. Centre of Mass and Laboratory frames.

4.Rotational Dynamics- Angular momentum of a particle and system of particles. Torque. Principle of conservation of angular momentum. Rotation about a fixed axis. Moment of Inertia. Perpedicular axes theorem and parallel axes theorem and their applications in calculations of moment of inertia for rectangular, cylindrical and spherical bodies. Kinetic energy of rotation. Motion involving both translation and rotation.

5.Elasticity Relation between Elastic constants. Twisting torque on a Cylinder or Wire. Bending of a beam – internal bending moment.

6.Fluid Motion Kinematics of Moving Fluids: Equation of continuity. Idea of streamiline and turbulent flow, Reynold’s number. Poiseuille’s Equation for Flow of a viscous Liquid through a Capillary Tube.

7.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. The energy equation and energy diagram. Kepler’s Laws. Satellite in circular orbit and applications. Geosynchronous orbits. Weightlessness. Basic idea of global positioning system (GPS).

8.Oscillations- SHM: Simple Harmonic Oscillations. Differential equation of SHM and its solution. Kinetic energy, potential energy, total energy and their time-average values. Damped oscillation. Forced oscillations: Transient and steady states; Resonances, sharpness of resonance; power dissipation and Quality Factor.

9.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.

10.Special Theory of Relativity- Michelson-Morley Experiment and its outcome. Postulates of Special Theory of Relativity. Lorentz Transformations. Simultaneity and order of events. Lorentz contraction. Time dilation. Relativistic transformation of velocity, frequency and wave number. Relativistic addition of velocities. Relativistic Doppler effect.