KAZI NAZRUL UNIVERSITY OLD PAPER -B.Sc(PHYSICS HONS.) 1ST SEMESTER (C1)-2017

KAZI NAZRUL UNIVERSITY

OLD PAPERS

BSC PHYSICS HONOURS

1ST SEMESTER

PAPER-C1 (MATHEMATICAL METHODS OF PHYSICS-I)

YEAR-2017

KAZI NAZRUL UNIVERSITY(KNU) B.Sc PHYSICS HONOURS 1ST SEMESTER SYLLABUS

KAZI NAZRUL UNIVERSITY, ASANSOL

PHYSICS HONOURS SYLLABUS

1ST SEMESTER

Core Course-I :

MATHEMATICAL METHODS OF PHYSICS –I

[Credit: 6, Lecture : 60 hours, Marks : 50]

1. Calculus :

Infinite sequences and series; Conditional and Absolute Convergence; Tests for Convergence (proofs not required, only applications), Functions of several real variables – partial differentiation, Taylor's series, multiple integrals (5)

2. Vector Analysis :

Definition, Transformation properties, Differentiation and integration of vectors; Line integral, volume integral and surface integral involving vector fields; Gradient, divergence and curl of a vector field; Gauss' divergence theorem, Stokes' theorem, Green's theorem - application to simple problems; Orthogonal curvilinear co-ordinate systems, unit vectors in such systems, illustration by plane, spherical and cylindrical co-ordinate systems only. (15)

3. Determinant and Matrices :

Algebra of matrices – Equality, Addition, Multiplication; Transpose and conjugate transpose of a matrix, Singular and non-singular matrices; Adjoint and Inverse of a Matrix; rank of a matrix; Normal Forms; Solution of simultaneous equation of matrices by Cramer’s rule; Solution of systems of linear homogenous and inhomogeneous equations by matrix method; Cayley- Hamilton theorem; Characteristics equation of a square matrix and diagonalization; Properties of Eigenvalues and eigenvectors of matrices; Types of matrices - Symmetric, Skew- symmetric, Hermitian, Orthogonal and unitary matrices and their properties. (15)

4. Fourier Series:

Periodic functions. Orthogonality of sine and cosine functions, Dirichlet Conditions (Statement only). Expansion of periodic functions in a series of sine and cosine functions and determination of Fourier coefficients. Complex representation of Fourier series. Expansion of functions with arbitrary period. Expansion of non-periodic functions over an interval. Even and odd functions and their Fourier expansions. Application. Summing of Infinite Series. Term-by-Term differentiation and integration of Fourier Series. Parseval Identity. (15)

5. Partial Differential Equations

Functions of several variables; Partial Derivatives; Partial Differential Equations; Partial Differential Equations in Physics; Solutions by the method of separation of variables; Simple examples, Laplace's equation and its solution in Cartesian, spherical polar (axially symmetric problems), and cylindrical polar (`infinite cylinder' problems) coordinate systems; Diffusion equation. (10)

Core Course-II: MECHANICS (NEW)

[Credit:4, Theory Lecture: 45 hours, Marks:50]

1.Mechanics of a Single Particle

Velocity and acceleration of a particle in (i) plane polar coordinates - radial and cross-radial components (ii) spherical polar and (iii) cylindrical polar coordinate system; Time and path integral of force; work and energy; Conservative force and concept of potential; Conservation of energy; Dissipative forces; resistive motion and friction. Conservation of linear and angular momentum. (12 L)

2.Mechanics of a System of Particles

Linear momentum, angular momentum and energy - centre of mass decomposition; Equations of motion, conservation of linear and angular momenta. (8L)

3.Surface Tension:

Surface energy and surface tension, angle of contact, excess pressure on curved surface, capillary rise, equilibrium vapour pressure over curved surface. (6L)

4.Mechanics of Ideal Fluids and Viscosity

Definition of Newtonian and non-Newtonian fluids, Streamlines and turbulent flow. Stokes’ law-terminal velocity. Equation of continuity; Euler's equation of motion; Streamline motion -Bernoulli's equation and its applications. (7L)

5.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; Resonance, sharpness of resonance; power dissipation and Quality Factor. Concept of different types of waves (plane, spherical, cylindrical), Group and phase velocity, Growth and decay of sound waves in hall, Sabine’s formula reverberation. (12)

MECHANICS LAB [Credit:2, Marks: 50]

1. Measurements of length (or diameter) using vernier calliper, screw gauge and travelling microscope.

2. To study the random error in observations.

3. To study the Motion of Spring and calculate (a) Spring constant, (b) g and (c) Modulus of rigidity.

4. To determine the Moment of Inertia of a Flywheel.

5. To determine the Coefficient of Viscosity of water by Capillary Flow Method (Poiseuille’s method).

6. To determine the Young's Modulus of a Wire by Optical Lever Method.

7. To determine the elastic Constants of a wire by Searle’s method.

8. To determine the value of g using Bar Pendulum.

9. Determination of surface tension of a liquid by Jaeger’s method.

10. Determination of Young’s modulus by flexure method.

Kazi Nazrul University Bsc Physics (Honours) 1st semester Paper-C2(Year-2016)

Kazi Nazrul University Previous Year's Questions

B. Sc Physics Honours 1st Semester - 2016

1st Semester (Paper-C2)

KAZI NAZRUL UNIVERSITY OLD PAPER -B.Sc(PHYSICS HONS.) 2ND SEMESTER (C3)-2018

KAZI NAZRUL UNIVERSITY

OLD PAPERS

BSC PHYSICS HONOURS

2ND SEMESTER

PAPER-C3 (MATHEMATICAL METHODS IN PHYSICS-II)

YEAR-2018

IIT-JAM PHYSICS SYLLABUS

IIT-JAM PHYSICS SYLLABUS

Mathematical Methods: Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green's theorem, Stokes' theorem. First order equations and linear second order differential equations with constant coefficients. Matrices and determinants, Algebra of complex numbers.

Mechanics and General Properties of Matter: Newton's laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal and Coriolis forces, Motion under a central force, Kepler's laws, Gravitational Law and field, Conservative and non-conservative forces. System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems. Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem. Principal moments and axes. Kinematics of moving fluids, equation of continuity, Euler's equation, Bernoulli's theorem.

Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general solution. Superposition of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, resonance. Wave equation, traveling and standing waves in one-dimension. Energy density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media. Doppler Effect. Fermat's Principle. General theory of image formation. Thick lens, thin lens and lens combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double refraction and optical rotation.

Electricity and Magnetism: Coulomb's law, Gauss's law. Electric field and potential. Electrostatic boundary conditions, Solution of Laplace's equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Biot-Savart law, Ampere's law, Faraday's law of electromagnetic induction, Self and mutual inductance. Alternating currents. Simple DC and AC circuits with R, L and C components. Displacement current, Maxwelll's equations and plane electromagnetic waves, Poynting's theorem, reflection and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only). Lorentz Force and motion of charged particles in electric and magnetic fields.

Kinetic theory, Thermodynamics: Elements of Kinetic theory of gases. Velocity distribution and Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas and equation of state. Mean free path. Laws of thermodynamics. Zeroth law and concept of thermal equilibrium. First law and its consequences. Isothermal and adiabatic processes. Reversible, irreversible and quasi-static processes. Second law and entropy. Carnot cycle. Maxwell's thermodynamic relations and simple applications. Thermodynamic potentials and their applications. Phase transitions and Clausius-Clapeyron equation. Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions.

Modern Physics: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy equivalence. Blackbody radiation, photoelectric effect, Compton effect, Bohr's atomic model, X-rays. Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation values, Schrodinger equation and its solution for one, two and three dimensional boxes. Solution of Schrodinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle. Structure of atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay.

Solid State Physics, Devices and Electronics: Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg's law; Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. p-n junction diode, I-V characteristics, Zener diode and its applications, BJT: characteristics in CB, CE, CC modes. Single stage amplifier, two stage R-C coupled amplifiers. Simple Oscillators: Barkhausen condition, sinusoidal oscillators. OPAMP and applications: Inverting and non-inverting amplifier. Boolean algebra: Binary number systems; conversion from one system to another system; binary addition and subtraction. Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth tables; combination of gates; de Morgan's theorem.

GATE PHYSICS SYLLABUS

GATE Physics Syllabus

Section 1: Mathematical Physics- Linear vector space: basis, orthogonality and completeness; matrices; vector calculus; linear differential equations; elements of complex analysis: CauchyRiemann conditions, Cauchy’s theorems, singularities, residue theorem and applications; Laplace transforms, Fourier analysis; elementary ideas about tensors: covariant and contravariant tensor, Levi-Civita and Christoffel symbols.

 
Section 2: Classical Mechanics- D’Alembert’s principle, cyclic coordinates, variational principle, Lagrange’s equation of motion, central force and scattering problems, rigid body motion; small oscillations, Hamilton’s formalisms; Poisson bracket; special theory of relativity: Lorentz transformations, relativistic kinematics, mass‐energy equivalence.

Section 3: Electromagnetic Theory- Solutions of electrostatic and magnetostatic problems including boundary value problems; dielectrics and conductors; Maxwell’s equations; scalar and vector potentials; Coulomb and Lorentz gauges; Electromagnetic waves and their reflection, refraction, interference, diffraction and polarization; Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation from a moving charge.

Section 4: Quantum Mechanics- Postulates of quantum mechanics; uncertainty principle; Schrodinger equation; one-, two- and three-dimensional potential problems; particle in a box, transmission through one dimensional potential barriers, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and spin; addition of angular momenta; time independent perturbation theory; elementary scattering theory.

Section 5: Thermodynamics and Statistical Physics- Laws of thermodynamics; macrostates and microstates; phase space; ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body radiation and Planck’s distribution law; Bose‐Einstein condensation; first and second order phase transitions, phase equilibria, critical point.

Section 6: Atomic and Molecular Physics- Spectra of one‐ and many‐electron atoms; LS and jj coupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; rotational and vibrational spectra of diatomic molecules; electronic transition in diatomic molecules, Franck‐Condon principle; Raman effect; NMR, ESR, X-ray spectra; lasers: Einstein coefficients, population inversion, two and three level systems.

Section 7: Solid State Physics & Electronics- Elements of crystallography; diffraction methods for structure determination; bonding in solids; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids: nearly free electron and tight binding models; metals, semiconductors and insulators; conductivity, mobility and effective mass; optical, dielectric and magnetic properties of solids; elements of superconductivity: Type-I and Type II superconductors, Meissner effect, London equation. Semiconductor devices: diodes, Bipolar Junction Transistors, Field Effect Transistors; operational amplifiers: negative feedback circuits, active filters and oscillators; regulated power supplies; basic digital logic circuits, sequential circuits, flip‐flops, counters, registers, A/D and D/A conversion.

Section 8: Nuclear and Particle Physics- Nuclear radii and charge distributions, nuclear binding energy, Electric and magnetic moments; nuclear models, liquid drop model: semi‐empirical mass formula, Fermi gas model of nucleus, nuclear shell model; nuclear force and two nucleon problem; alpha decay, beta‐decay, electromagnetic transitions in nuclei; Rutherford scattering, nuclear reactions, conservation laws; fission and fusion; particle accelerators and detectors; elementary particles, photons, baryons, mesons and leptons; quark model.

Joint Entrance Screening Test Syllabus (JEST-PHYSICS)

Joint Entrance Screening Test(JEST) Syllabus

1.Mathematical Methods- Vector algebra and vector calculus, tensors, curvilinear coordinate systems, linear algebra; Linear differential equations, elements of Sturm–Liouville theory; Special functions; Complex analysis; Fourier series and Fourier transforms, Laplace transforms; Elementary properties of discrete groups; Elements of probability theory, error analysis.

2.Classical Mechanics- Newton’s laws, conservation of energy and momentum, collisions; generalized coordinates, principle of least action, Lagrangian and Hamiltonian formulations of mechanics; Symmetry and conservation laws; central force problem, Kepler problem; Small oscillations and normal modes; special relativity in classical mechanics.

3.Electromagnetism & Optics- Electrostatics and magnetostatics, boundary value problems, multipole expansion; Fields in conducting, dielectric, diamagnetic and paramagnetic media; Faraday’s law and time varying fields; displacement current; Maxwell’s equations; energy and momentum of electromagnetic fields; Propagation of plane electromagnetic waves, reflection, refraction; Electromagnetic waves in dispersive and conducting media; diffraction, interference, polarization.

4.Quantum Mechanics- Uncertainty principle; Schrodinger equation; central potentials, hydrogen atom; Orbital and spin angular momenta, addition of angular momenta; Matrix formulation of quantum theory, unitary transformations, Hermitian operators; Variational principle, time independent perturbation theory, time dependent perturbation theory.

5.Thermodynamics & Statistical Physics- Laws of thermodynamics, work and heat, thermodynamic potentials; Elements of kinetic theory; Maxwell’s relations; Statistical ensembles; partition function; classical ideal gas, harmonic oscillators; Classical and quantum statistics; Fermi and Bose gases; black body radiation; statistics of paramagnetism

6.Electronics- Basics of semiconductor; p-n junctions, diodes, transistors; LCR circuits, rectifiers, amplifiers, active filters and oscillators; basics of OPAMPs and their applications; basics of digital electronics. _________________________________________________________