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IISC Syllabus of Integrated Ph.D course (Physics) |

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Re: IISC Syllabus of Integrated Ph.D course (Physics)
Here I am providing you the syllabus. SYLLABUSMechanics Newtonian mechanics of a system of particles. Conservation of energy and momentum, collisions, simple harmonic motion, static equilibrium of a rigid body, rotational dynamics, angular momentum, gravitation, Kepler’s laws. Properties of Matter Stress and strain, elastic properties of solids, elastic modulii; Hydrostatics, elements of fluid mechanics, surface, tension and viscosity. Wave MotionWave propagation, phase and group velocities, standing waves, Fourier analysis, sound as elastic waves, interference and diffraction of sound waves, Doppler effect. Thermal PhysicsKinetic theory of gases, the Maxwell-Boltzmann distribution, thermal properties of ideal and real gases, liquids and solids, laws of thermodynamics, entropy, reversible and irreversible processes, Carnot cycle, heat engines, changes of phase, blackbody radiation, the Stefan-Boltzmann law. Planck’s law. Electromagnetism, Electronics and OpticsElectric field and potential, Gauss law, Laplace and Poisson equations, electrostatic equilibrium, capacitance, dielectrics, electrostatic energy: The magnetic field, magnetic forces on moving changes and current carrying wires, the Biot-Savart law, electromagnetic induction and Faraday’s law, magnetic susceptibility and permeability, direct and alternating current circuits, Maxwell’s equations, electromagnetic waves; Semiconductors junctions, principles of rectification and amplification. Reflection, refraction and polarisation of light, ray optics, thin lenses, aberrations, interference and diffraction of light, optical instruments. Modern Physics Frames of reference, time dilation and length contraction, simultaneity, the Lorentz transformation, relativistic energy and momentum, mass-energy relation; The photoelectric effect, the Compton effect, atomic spectra, wave-particle dualism, the wave function and its interpretation, the uncertainty principle, the Schrodingor equation. Atomic structure, the Pauli exclusion principle, periodic classification of elements, spin of electrons, the Zeeman effect; generation and diffraction of x-rays, radioactivity, nucleus-constituents, binding, nuclear reactions, fission and fusion, nuclear reactors, particle accelerators, cosmic rays. Experiments and Measurements Errors in measurement, accuracy, measurements of length, mass and charge of small and large objects, fundamental constants. Basic knowledge of scientific instruments and their working. Mathematical PhysicsTheory of Systems of linear Equation. Linear algebra and matrices. Series and their convergence. Limits and continuity, differentiation and integration, Taylor’s expansion, L’Hospital rule, maxima, minima. Analytical geometry of curves and surfaces. Ordinary (first and second order) differential equations. Complex numbers, roots of complex numbers, trigonometric identities, Argand’s diagram. Vector addition and products, gradient, divergence and curl, Gauss and Stokes theorems. Probability, basic laws of probability, mean, standard deviation. MATHEMATICAL SCIENCESSYLLABUS1. Algebra Theory of Equations Relations between roots and Coefficients. Newton’s identities. Rolle’s theorem, Reciprocal Equations, Des Cartes, Rule of Signs, Cubic and quark equations, Complex numbers and De Moivre’s Theorem. Determinants Cofactors, Properties of determinants, Solution of a Linear System, Cramer’s Rule. Inequalities AM-GM inequality, Cauchy-Schwarz inequality. Set Theory : Relations, Functions, Cardinality. Algebraic Structures Binary Operations, Groups, Rings: Definitions, Examples and Elementary Theorems. Vector Spaces Subspaces, Linear Independence, Bases, Dimension Linear Transformations, Matrices, Rank Nullity, Eigen values and Eigen vectors. 2. Geometry :Two-dimensional Coordinate Geometry Conics and their equations in Cartesian and Polar Coordinates, Ellipse, Parabola and Hyperbola. Three-dimensional Co-ordinate Geometry Planes, Lines, Spheres and Cones. 3. Vector Algebra and Vector Calculus : Vectors, addition, Scalar multiplication. Dot Product, Cross Product, Triple Product, Equations to the Line and the Plane. Grad, Divergence and Curl, Vector Integration, Green’s Gauss’ and Stokes’ Theorems. 4. Calculus and Analysis Real Number System, Sequence and Series. Continuity, Differentiability. Mean Value Theorems, Indeterminate Value Theorem, L’Hospital Rule, Tangents and Normals, Maxima and Minima. Riemann Integration, Multiple Integrals, Partial differentiations, Lengths, areas and volumes by integration. 5. Differential Equations First Order ODE Method of Separation of Variables: Exact equations: Euler’s equation: Orthogonal Family of curves, Second Order Linear ODE : Variation of Parameters.
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