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🔴LiveClass10Complementary FunctionSecond Order Differential Equation3 1st Semester PhysicsHon
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How to Buy course 👇👇👇 • • How to Buy course from Study And Stud... • WhatsApp Group Link👇👇👇 • https://chat.whatsapp.com/HuTQfMBfvn0... • Download Study And Study App 👇👇👇 • https://play.google.com/store/apps/de... • Telegram link👇👇👇 • https://t.me/studyandstudyofficials • 🔴Live/Class-7/Mathematical Physics/Linear Differential Equation /I.F/+3 1st Semester Physics(Hon.) • #physics • #bscphysics • #cbcspatternexamodisha • #odishagovt • #odishaeducation • #govtschool • #teacherjob • #syllabus • 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 • of oscillatory, critically damped and over damped) Forced oscillations: Transient and steady • states; Resonance, sharpness of resonance; power dissipation and Quality Factor, Bar • Pendulum, Katers Pendulum • Special Theory of Relativity: Michelson-Morley Experiment and Etc.................
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