Mathematical Physics & Newtonian Mechanics (Physics) Book B.Sc 1st Sem U.P. State Universities

Units

Topics

Part-A: Basic Mathematical Physics

I

Introduction to Indian ancient Physics and contribution of Indian Physicists, in context with the holistic development of modern science and technology, should be included under Continuous Internal Evaluation (CIE).

Vector Algebra: Coordinate rotation, reflection and inversion as the basis for defining scalars, vectors, pseudo scalars and pseudo-vectors (include physical examples). Component form in 2D and 3D. Geometrical and physical interpretation of addition, subtraction, dot product, wedge product, cross product and triple product of vectors. Position, separation and displacement vectors.          (07)

II

Vector Calculus: Geometrical and physical interpretation of vector differentiation, Gradient, Divergence and Curl and their significance. Vector integration, Line, Surface (flux) and Volume integrals of vector fields. Gradient theorem, Gauss-divergence theorem, Stoke-curl theorem, Greens theorem and Helmholtz theorem (statement only). Introduction to Dirac delta function.              (08)

III

Coordinate Systems: 2D & 3D Cartesian, Spherical and Cylindrical coordinate systems, basis vectors, transformation equations. Expressions for displacement vector, arc length, area element, volume element, gradient, divergence and curl in different coordinate systems. Components of velocity and acceleration in different coordinate systems. Examples of non-inertial coordinate system and pseudo-acceleration.                                                                                                                     (08)

IV

Introduction to Tensors: Principle of invariance of physical laws w.r.t. different coordinate systems as the basis for defining tensors. Coordinate transformations for general spaces of nD, contravariant, covariant & mixed tensors and their ranks, 4-vectors. Index notation and summation convention. Symmetric and skew symmetric tensors. Invariant tensors, Kronecker delta and Epsilon (Levi Civita) tensors. Examples of tensors in physics.                                                                                      (07)

Part-B: Newtonian Mechanics and Wave Motion

V

Dynamics of a System of Particles: Review of historical development of mechanics up to Newton. Background, statement and critical analysis of Newton's axioms of motion. Dynamics of a system of particles, centre of mass motion, and conservation laws and their deductions. Rotating frames of reference, general derivation of origin of pseudo forces (Euler, Coriolis and centrifugal) in rotating frame, and effects of Coriolis force.                                                                                           (08)

VI

Dynamics of a Rigid Body: Angular momentum, Torque, Rotational energy and the inertia tensor. Rotational inertia for simple bodies (ring, disk, rod, solid and hollow sphere, solid and hollow cylinder, rectangular lamina). The combined translational and rotational motion of a rigid body on horizontal and inclined planes. Elasticity, relations between elastic constants, bending of beam and torsion of cylinder.                                                                                                                                         (08)

VII

Motion of Planets and Satellites: Two particle central force problem, reduced mass, relative and centre of mass motion. Newton's [aw of gravitation, gravitational field and gravitational potential. Kepler’s laws of planetary motion and their deductions. Motions of geosynchronous and geostationary satellites and basic idea oi Global Positioning System (GPS).        (07)

VIII

Wave Motion: Differential equation of simple harmonic motion and its solution, use of complex notation, damped and forced oscillations, quality factor. Composition of simple harmonic motion, Lissajous figures. Differential equation of wave motion. Plane progressive waves in fluid media, reflection of waves and phase change, pressure and energy distribution. Principle of superposition of waves, stationary waves, phase and group velocity.                                                                                                (07)