**Krishna University Syllabus**

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Name of the University | Krishna University |

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Category | Krishna University Syllabus 2019-2020 |

Krishna University Exam held in | May, June & November & December 2019-2020 |

Krishna University Syllabus Of | BA, BSc, B.com, MA, MSc & others |

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**Krishna University Syllabus 2019-20**

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**Krishna University Syllabus**

**Krishna University Syllabus of M.Sc. Physics (Semester-I)**

Paper-I: MATHEMATICAL PHYSICS (PHY 1.1) |

Unit-I (Special Functions) |

Solution by series expansion – Legendre, associated Legendre, Bessel, Hermite and Laguerre equations, physical applications – Generating functions, orthogonality properties and recursion relations. |

Unit-II (Integral Transforms) |

Laplace transform; first and second shifting theorems – Inverse Laplace transforms by partial fractions – Laplace transform of derivative and integral of a function |

Unit-III (Fourier Series) |

Fourier series of arbitrary period – Half-wave expansions – Partial sums – Fourier integral and transformations; Fourier transform of delta function |

Unit-IV (Complex Variables) |

Complex, Algebra, Cauchy – Riemann conditions – Analytic functions – Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s Series – Laurent’s expansion – Singularities – Calculus of residues – Cauchy’s residue theorem – Evaluation of residues – Evaluation of contour integrals. |

Unit-V (Tensor Analysis) |

Introduction – Transformation of coordinates – Contravariant, Covariant and Mixed tensors – Addition and multiplication of tensors – contraction and Quotient Law – The line element – fundamental tensors. |

Paper-II: CLASSICAL MECHANICS (PHY 1.2) |

Unit-I |

1. Mechanics of a particle: Conservation laws, Mechanics of a system of particles: Conservation laws. |

2. Constraints, D’Alembert’s principle and Lagrange’s equations, Velocity Dependent potentials and the Dissipation function Simple applications of the Lagrangian Formulation, Generalized potential. |

Unit-II |

3. Generalized momentum and Cyclic Coordinates, Hamilton function H and conservation of energy, Derivation of Hamilton‘s equations, Simple applications of the Hamilton Formulation. |

4. Reduction to the equivalent one body problem. The equation of motion and first Integrals, The equivalent One – Dimensional problem and classification of orbits, The differential equation for the orbit, and Integrable power –law potentials, Conditions for closed orbits (Bertrand‘s theorem), The Kepler problem inverse square law of force, The motion in time in the Kepler problem, Scattering in a central force field. |

Unit-III |

5. Hamilton’s principle, Deduction of Hamilton’s equations form modified Hamilton principle, Derivation of Lagrange’s equations from variational Hamilton‘s principle, Simple applications of the Hamilton principle Formulation, Principle of Least Action. |

6. Legendre transformations, Equations of canonical transformation, Examples of Canonical transformations, The harmonic Oscillator, Poisson brackets and other Canonical invariants, Equations of motion, Infinitesimal canonical transformations, and conservation theorems in the Poisson bracket formulation, the angular momentum Poisson bracket relations. |

Unit-IV |

7. Hamilton – Jacobi equation of Hamilton‘s principal function, The Harmonic oscillator problem as an example of the Hamilton – Jacobi Method, Hamilton –Jacobi equation for Hamilton‘s characteristic function. Action – angle variables in systems of one degree of freedom. |

8. One dimensional oscillator, Two coupled oscillations, solutions, normal coordinates and normal modes, kinetic and potential energies in normal coordinates, vibrations of linear triatomic molecule. |

Unit-V |

9. Independent coordinates of rigid body, The Euler angles, infinitesimal rotations as vectors (angular velocity), components of angular velocity, angular momentum and inertia tensor, principal moments of inertia, rotational kinetic energy of a rigid body. |

10. Symmetric bodies, Euler’s equations of motion for a rigid body, Torque-free motion of a rigid body,Gyroscope, Coriolis Effect. |

Paper-III: QUANTUM MECHANICS-I (PHY 1.3) |

Unit-I (Schrodinger wave equation and potential problems in one dimension) |

Necessity of quantum mechanics, Inadequacy of classical mechanics; Schrodinger equation; continuity equation; Ehrenfest theorem; admissible wave functions; Stationary states. Onedimensional problems, wells and barriers. Harmonic oscillator by Schrodinger equation. |

Unit-II (Vector spaces) |

Linear Vector Spaces in Quantum Mechanics: Vectors and operators, change of basis, Dirac’s bra and ket notations. Eigen value problem for operators. The continuous spectrum. Application to wave mechanics in one dimension. Hermitian, unitary, projection operators. Positive operators. Change of orthonormal basis. Orthogonalization procedure. |

Unit-III (Angular momentum and three dimensional problems) |

Angular momentum: commutation relations for angular momentum operator. Angular Momentum in spherical polar coordinates, Eigen value problem for L2 and Lz , L+ and Loperators, Eigen values and eigen functions of rigid rotator and Hydrogen atom. |

Unit-IV (Time-independent perturbation) |

Time-independent perturbation theory: Non-degenerate and degenerate cases; applications to a) normal helium atom b) Stark effect in Hydrogen atom. Variation method. Application to ground state of Helium atom. WKB method. |

Unit-V (Time dependent perturbation) |

Time dependent perturbation: General perturbations, variation of constants, transition into closely spaced levels –Fermi’s Golden rule. Einstein transition probabilities, Interaction of an atom with the electromagnetic radiation, Sudden and adiabatic approximation |

Paper-IV: ELECTRONICS (PHY 1.4) |

Unit-I (Operational Amplifiers) |

Differential Amplifier –circuit configurations – dual input, balanced output differential amplifier – DC analysis – Ac analysis, inverting and non-inverting inputs CMRR – constant current bias level translator. Block diagram of a typical Op-Amp-analysis. Open loop configuration inverting and noninverting amplifiers. Op-amp with negative feedback- voltage series feedback – effect of feedback on closed loop gain input resistance output resistance bandwidth and output offset voltage- voltage follower. |

Unit-II (Practical Op-amps) |

Input offset voltage- input bias current-input offset current, total output offset voltage, CMRR frequency response. Summing amplifier- scaling and averaging amplifiers, instrumentation amplifier, integrator and differentiator. Oscillators principles – oscillator types – frequency stability – response – The phase shift oscillator, Wein bridge oscillator – Multivibrators- Monostable and astable –comparators – square wave and triangular wave generators. |

Unit-III (Communication Electronics) |

Amplitude modulation – Generation of AM waves – Demodulation of AM waves – DSBSC modulation. Generation of DSBSC wages. Coherent detection of DSBSC waves, SSB modulation, Generation and detection of SSB waves. Vestigial side band modulation, Frequency division multiplexing (FDM). |

Unit-IV (Digital Electronics) |

Combinational Logic- Decoder- encoders- Multiplexer (data selectors)-application of multiplexer – De multiplexer (data distributors) Sequential Logic- Flip-Flops: A 1 bit memory – the R-S Flip – Flop, JK Flip-Flop – JK master slave Flip-Flops – T- Flip – Flop – D Flip – Flop – Shift registers – synchronous and asynchronous counters – cascade counters. |

Unit V-(Microprocessors) |

Introduction to microcomputers – memory – input/output –interfacing devices 8085 CPU – Architecture – BUS timings – Demultiplexing the address bus – generating control signals – instruction set – addressing modes – illustrative programmes – writing assembly language programmes –looping, counting and indexing – counters and timing delays – stack and subroutine. |

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**Krishna University Syllabus of M.Sc. Physics (Semester-II)**

Paper-I: COMPUTATIONAL METHODS AND PROGRAMMING (PHY 2.1) |

Unit-I (Fundamentals and Operators) |

(a) Fundamentals of C Language: C character set-Identifiers and Keywords-ConstantsVariables-Data types-Declarations of variables – Declaration of storage class – Defining symbolic constants –Assignment statement. |

(b) Operators: Arithmetic operators-Relational Operators-Logic Operators-Assignment operators- Increment and decrement operators –Conditional operators. |

Unit –II (Expressions, I/O and Control Statements) |

(a) Expressions and I/O Statements: Arithmetic expressions –Precedence of arithmetic operators-Type converters in expressions –Mathematical (Library ) functions –Data input and output-The getchar and putchar functions –Scanf – Printf-Simple programs. |

(b) Control statements: If-Else statements –Switch statements-The operators –GO TO – While, Do-While, FOR statements-BREAK and CONTINUE statements. |

Unit –III (Arrays and User Defined Functions) |

(a) Arrays: One dimensional and two dimensional arrays –Initialization –Type declaration – Inputting and outputting of data for arrays –Programs of matrices addition, subtraction and multiplication |

(b) User Defined Functions: The form of C functions –Return values and their types – Calling a function – Category of functions. Nesting of functions. Recursion. ANSI C functions-Function declaration |

Unit-IV (Linear, Nonlinear and Simultaneous Equations) |

(a) Linear and Nonlinear Equations: Solution of Algebra and transcendental equationsBisection, False position and Newton-Raphson methods-Basic principles-Formulaealgorithms |

(b) Simultaneous Equations: Solutions of simultaneous linear equations – Gauss elimination and Gauss Seidel iterative methods-Basic principles- Formulae-Algorithms |

Unit-V (Interpolations, Numerical Differentiation and Integration) |

(a) Interpolations: Concept of linear interpolation-Finite differences-Newton‘s and Lagrange‘s interpolation formulae-principles and Algorithms |

(b) Numerical Differentiation and Integration: Numerical differentiation-algorithm for evaluation of first order derivatives using formulae based on Taylor‘s series-Numerical integration-Trapezoidal and Simpson‘s 1/3 rule-Formulae-Algorithms |

Paper-II: QUANTUM MECHANICS -II (PHY 2.2) |

UNIT-I (Total angular momentum) |

Total angular momentum J, Commutation relations of total angular momentum with components. Eigen values of J2 and JZ, Eigen values of J+ and J_ .Explicit matrices for J2 , J x, Jy & Jz . Addition of angular momenta. Clebsch-Gordon coefficients for J1 = ½, J2 = ½ and j1 = 1, j2 = ½. Wigner-Eckart theorem. |

UNIT-II (Spin Angular Momentum) |

Pauli’s exclusion principle and connection with statistical mechanics, spin angular momentum, Stern-Gerlach experiment and limitations, Pauli spin matrices, commutation relations, operators, Eigen values and Eigen functions, Electron spin functions |

UNIT-III (Quantum Dynamics and Identical Particles) |

Equation of motion in Schrodinger’s picture and Heisenberg’s picture, correspondencebetween the two. Correspondence with classical mechanics. Application of Heisenberg’s picture to Harmonic oscillator. The indistinguishability of identical particles – The state vector space for a system of identical particles – Creation and annihilation operators. Dynamical variables – the Quantum dynamics of identical particle systems. |

UNIT-IV (Scattering Theory) |

Introduction to scattering – notion of cross section – scattering of a wave packet – Green’s function in scattering theory – Born’s approximation – first order approximation – criteria for the validity of Born’s approximation. Form factor – scattering from a square well potential – partial wave analysis – Expansion of plane wave – optical theorem – calculation of phase shifts – low energy limit – energy dependence of βe – Scattering from a square well potential. |

UNIT-V (Molecular Quantum Mechanics) |

Thee Born-Oppenheimer Approximation – The hydrogen molecule-ion – The valance bond method – The molecular orbital method – Comparison of the methods – Heitler – London method |

Paper-III: STATISTICAL MECHANICS (PHY 2.3) |

Classical Statistical Mechanics |

Unit-I |

Foundations of statistical mechanics; specification of states of a system. Contact between statistics and thermodynamics, Postulate of classical statistical mechanics, phase space, trajectories – Ensembles – micro canonical, canonical and grand canonical. |

Unit-II |

Density of states – Liouville’s theorem – equipartition theorem – Classical ideal gas; entropy of ideal gas in micro canonical ensemble – Gibb’s paradox. |

Unit-III |

Canonical ensemble – ensemble density – partition function – Energy fluctuations in canonical ensemble – Grand canonical ensemble – Density fluctuations in the Grand canonical ensemble – Equivalence between the canonical ensemble and Grand canonical ensemble. Quantum Statistical Mechanics |

Unit-IV |

Postulates of quantum statistical mechanics – Density matrix – Ensembles in quantum statistics – statistics of indistinguishable particles, Maxwell – Boltzmann, Bose- Einstein and Fermi – Dirac statistics, Thermodynamic properties of ideal gases on the basis of micro canonical and grand canonical ensemble. The partition function: Derivation of canonical ensemble using Darwin and Fowler method. |

Unit-V |

Ideal Fermi Gas: Equation of state of an ideal Fermi gas, theory of w hite dwarf stars, Landau diamagnetism. Ideal Bose Gas: Photons – Phonons – Bose Einstein condensation – Random walk – Brownian motion. |

Paper-IV: SOLID STATE PHYSICS (PHY 2.4) |

Unit-I (Crystal Structure) |

Periodic array of atoms-Lattice translation vectors and lattices, symmetry operations, Basis and the Crystal Structure, Primitive Lattice cell, Fundamental types of lattices-Two Dimensional lattice types, three Dimensional lattice types, Index system for crystal planes, simple crystal structures- sodium chloride, cesium chloride and diamond structures. |

Unit-II (Crystal Diffraction and Reciprocal Lattice) |

Bragg’s law, Experimental diffraction methods – Laue method and powder method, derivation of scattered wave amplitude, indexing pattern of cubic crystals and non-cubic crystals (analytical methods). Geometrical structure Factor, Determination of number of atoms in a cell position of atoms. Reciprocal lattice, Brillouin Zone, Reciprocal lattice to bcc and fcc lattices. |

Unit-III (Free Electron Fermi Gas) |

Energy levels and density of orbitals in one dimension, Free electron gas in 3 dimensions, Heat capacity of the electron gas, Experimental heat capacity of metals, Motion in Magnetic Fields – Hall effect, Ratio of thermal to electrical conductivity. |

Unit-IV (Fermi Surfaces of Metals) |

Reduced zone scheme, periodic Zone schemes, Construction of Fermi surfaces, Electron orbits, hole orbits and open orbits, Experimental methods in Fermi surface studies – Quantization of orbits in a magnetic field, De-Hass-van Alphen Effect, external orbits, Fermi surface of Copper. |

Unit-V (Band Theory of Solids) |

Nearly free electron model, Origin of the energy gap, The Block theorem, Kronig-Penney Model, wave equation of electron in a periodic potential, Crystal momentum of an electron Approximate solution near a zone boundary, Number of orbitals in a band – metals and isolators. The distinction between metals, insulators and semiconductors. |

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**Krishna University Syllabus of B.A. POLITICAL SCIENCE**

PAPER-I(CORE): BASIC CONCEPTS OF POLITICAL SCIENCE |

Unit-1: Explanatory Frameworks of Politics |

1. What is Politics: Nature and Scope of Political Science |

2. Approaches to the Study of Politics: Normative, Historical, Empirical Traditions |

Unit-2: What is the State |

1. Origin and Evolution of the Modern State |

2. Different Conceptions on the role of the Modern State: Social Democratic and Neo Liberal conceptions |

Unit-3: Nations and Nationalism |

1. Conceptual Distinction between Nationality and Nation |

2. Varieties of Nationalism: Culture and Civic Nationalism |

Unit-4: Rights and Citizenship |

1. Evolution of Rights: Civil and Social rights |

2. Citizenship: Universal and Differential Citizenship |

Unit-5: Freedom, Equality and Justice |

1. Freedom: Negative and Positive Freedom |

2. Equality: Formal Equality, Equality of Opportunity, Equality of Outcome |

3. Justice: Justice based on Needs, Deserts and Rights |

PAPER-II (CORE): POLITICAL INSTITUTIONS (CONCEPTS, THEORIES AND INSTITUTIONS) |

Unit-1: Constitutionalism |

1. The Purpose of Constitutional law, Theory of Separation of Powers |

2. Structural Forms of the Modern State: Basic features of Parliamentary and |

Presidential forms of Government |

Unit-2: Territorial Division of Authority of the Modern State |

1. Basic features of Federal form of Government |

2. Basic features of Unitary form of Government |

Unit-3: Institutional forms of the Modern State |

1. Democracy: Basic features of Classical and Modern Representative Democracy |

2. Models of Democracy: Procedural Democracy and Substantive Democracy |

Unit-4: Judiciary and Democratic State |

1.The nature, role and functions of the Judiciary |

2.Judicial Review: Debates on the Supremacy of legislature or Judiciary in the protection of Constitutional law |

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**Krishna University Syllabus of BA/BSC I YEAR : STATISTICS **

Paper – I Descriptive Statistics and Probability |

Unit-I |

Introduction to Statistics: Concepts of Primary and Secondary data. Methods of collection and editing of primary data, Secondary data. Designing a questionnaire and a schedule. Measures of Central Tendency – Mean, Median, Mode,Geometric Mean and Harmonic Mean. |

Unit-II |

Measures of dispersion: Range, Quartile Deviation, Mean Deviation and Standard Deviation. Descriptive Statistics -Central and Non-Central moments and their interrelationship. Sheppard’s correction for moments. Skewness and kurtosis. |

Unit-III |

Introduction to Probability: Basic Concepts of Probability, random experiments, trial, outcome, sample space, event, mutually exclusive and exhaustive events, equally likely and favourable outcomes. Mathematical, Statistical, axiomatic definitions of probability. Conditional Probability and independence of events, |

Unit-IV |

Probability theorems:Addition and multiplication theorems of probability for 2 and for n events. Boole’s inequality and Baye’s theorems and problems based on Baye’s theorem. |

Unit-V |

Random variable: Definition of random variable, discrete and continuous random variables, functions of random variable. Probability mass function. Probability density function, Distribution function and its properties. Bivariate random variable – meaning, joint, marginal and conditional Distributions, independence of random variables. |

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**Krishna University Syllabus 2019-2020**

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