## Krishna University Syllabus

Krishna University Syllabus 2018-19: Revised CBCS Krishna University Exam Syllabus is available now! The updated Krishna University Syllabus of MBA/MCA/BBM/B.Tech and other courses is available at this page!

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### Krishna University Syllabus

Krishna University MSC Physics Syllabus:

 SEMESTER – I MATHEMATICAL PHYSICS 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. Krishna University Syllabus for CLASSICAL MECHANICS 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. QUANTUM MECHANICS-I 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 Krishna University Syllabus For ELECTRONICS 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.

Krishna University B.Tech Syllabus

I Year - I Semester
ENGLISH AND PROFESSIONAL COMMUNICATION SKILLS
Subject Code: HS10117

UNIT -I Topics: Paragraph writing, writing letters, role play, reading graphs, prepositions, designing posters, tenses, making recommendations.
Text: ENVIRONMENTAL CONSCIOUSNESS Climate Change - Green Cover ­ Pollution
UNIT -II Topics: Compound nouns, imperatives, writing instructions, interpreting charts and pictures, note making, role play, prefixes, subject-verb agreement.
Text: EMERGING TECHNOLOGIES Solar Thermal Power - Cloud Computing ­ Nanotechnology
UNIT -III Topics: Making conversations, homonyms and homophones, SMS and use of emoticons, past participle for irregular verbs, group discussion, E-mail communication, antonyms, preparing projects
Text: GLOBAL ISSUES Child Labour - Food Crisis - Genetic Modification - E-Waste - Assistive Technology
UNIT -IV Topics: Group discussion, affixes, double consonants, debates, writing a book / film review, predicting and problem-solving-future tense, adverbs
Text: SPACE TREK from MINDSCAPES Hubble Telescope - Chandrayan-2 - Anusat - Living Quarters - Space Tourism
UNIT -V Topics: Compare and contrast, effective writing, group discussion, writing reports, writing advertisements, tweeting and blogging, types of interviews, framing questions.
Text: MEDIA MATTERS History of Media - Language and Media - Milestone in Media - Manipulation by Media - Entertainment Media - Interviews Text Book: MINDSCAPES: English for Technologists and Engineers, Orient Blackswan, 2016.

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References:

1. A Practical Course in Effective English Speaking Skills by J.K.Gangal, PHI Publishers, New Delhi.2012
2.Technical Communication, Meenakshi Raman, Oxford University Press,2011.
3.Spoken English, R.K. Bansal & JB Harrison, Orient Longman,20B, 4Th edition.
4. Murphy's English Grammar with CD, Murphy, Cambridge University Press,3 Rd edition.
5. An Interactive Grammar of l'v1odern English, Shivendra K. Verma and Hemlatha Nagarajan , Frank Bros & CO,2008.

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I Year - I Semester
ENGINEERING MATHEMATICS - I
Subject Code: MA10117

UNIT 1: Matrix Theory: Elementary row and column operations on a matrix, Rank of matrix
- Normal form - Inverse of a matrix using elementary operations -Consistency and solutions of systems of linear equations using elementary operations, linear dependence and independence of vectors - Characteristic roots and vectors of a matrix - Caley-Hamillton theorem and its applications, Complex matrices, Hermitian and Unitary Matrices - Reduction to diagonal form - Reduction of a quadratic form to canonical form - orthogonal transformation and congruent transformation.
UNIT 2: Differential Calculus: Rolle's theorem; Mean value theorem; Taylor's and Maclaurin's theorems with remainders, Expansions; Indeterminate forms; Asymptotes and curvature; Curve tracing; Functions of several variables
UNIT 3 : Partial Differentiation, Total Differentiation, Euler's theorem and generalization, maxima and minima of functions of several variables (two and three variables) - Lagrange's method of Multipliers; Change of variables ­ Jacobians.
UNIT 4 : Ordinary differential equations of first order: Formation of differential equations; Separable equations; equations reducible to separable form; exact equations; integrating factors; linear first order equations; Bernoulli's equation; Orthogonal trajectories and Newton's law of cooling.
UNIT 5: Ordinary linear differential equations of higher order : Homogeneous linear equations of arbitrary order with constant coefficients - Non-homogeneous linear equations with constant coefficients; Euler and Cauchy's equations; Method of variation of parameters; System of linear differential equations, Vibrations of a beam.

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Books:

1. R.K.Jain and SoR oK.lyengar, Advanced Engineering Mathematics, Narosa Pub. House, 2008.
2. Erwyn Kreyszig , Advanced Engineering Mathematics, John Wiley and Sons, 8th Edition, 2008.
3. BoS.Grewal, Higher Engineering Mathematics, Khanna Publications, 20090

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