# Vidyasagar University Syllabus

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## Vidyasagar University Syllabus

Vidyasagar University MSC Syllabus (Semester – I):

Mathematical Computation

 Propositional logic Syntax, semantics, valid, satisfiable and unsatisfiable formulas, encoding and examining the validity of some logical arguments. Proof techniques- forward proof, proof by contradiction, contra positive proofs, proof of necessity and sufficiency. Sets, relations and functions Operations on sets, relations and functions, binary relations, partial ordering relations, equivalence relations, principles of mathematical induction Size of a set Finite and infinite sets, countable and uncountable sets, Cantor’s diagonal argument and the power set theorem, Schroeder-Bernstein theorem. Introduction to counting Basic counting techniques – inclusion and exclusion, pigeon-hole principle, permutation, combination, summations. Introduction to recurrence relation and generating function. Algebraic structures and morphisms Algebraic structures with one binary operation – semigroups, monoids and groups, congruence relation and quotient structures. Free and cyclic monoids and groups, permutation groups, substructures, normal subgroups. Algebraic structures with two binary operations – rings, integral domains and fields. Boolean algebra and Boolean ring Introduction to graphs Graphs and their basic properties – degree, path, cycle, subgraphs, isomorphism, Eulerian and Hamiltonian walks, graph coloring, planar graphs, trees.

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 Overview of von Neumann architecture Instruction set architecture; The Arithmetic and Logic Unit, The Control Unit, Memory and I/O devices and their interfacing to the CPU; Measuring and reporting performance; CISC and RISC processors Pipelining Basic concepts of pipelining, data hazards, control hazards, and structural hazards; Techniques for overcoming or reducing the effects of various hazards. Hierarchical Memory Technology Inclusion, Coherence and locality properties; Cache memory organizations, Techniques for reducing cache misses; Virtual memory organization, mapping and management techniques, memory replacement policies. Instruction-level parallelism Concepts of instruction-level parallelism (ILP), Techniques for increasing ILP; Superscalar, super-pipelined and VLIW processor architectures; Vector and symbolic processors; Case studies of contemporary microprocessors Multiprocessor Architecture Taxonomy of parallel architectures; Centralized shared-memory architecture, synchronization, memory consistency, interconnection networks; Distributed shared memory architecture, Cluster computers Non von Neumann Architectures Data flow Computers, Reduction computer architectures, Systolic Architectures.

Computer Networks:

 Introduction to networks and layered architecture. Data communication concepts, transmission media and topology, multiplexing Circuit switching and packet switching, data link layer, layer 2 switches and ATM switches, SONET/SDH. Medium access control. CSMA CD, TDMA, FDMA, CDMA. Network layer and addressing, IP version 4 and 6. Routing algorithms. Transmission layer, TCP and UDP. Congestion control techniques. WAN, ATM. Internetworking. Wireless communications. Network management and security

Computer Graphics:

 Graphics hardware and display devices; graphics primitives drawing lines and curves; 2d and 3d transformations; segments and their applications; generating curves, surfaces and volumes in 3d, wire-frame models, Bezier and spline curves and surfaces Geometric modeling elementary geometric algorithms for polygons, boundary representations, constructive solid geometry, spatial data structures; hidden surface and line elimination Rendering shading, light models, realistic image synthesis techniques, textures and image-based rendering; video games and computer animation. Laboratory Programming for generating lines, curves and rendered surfaces Interactive graphics programming modeling and updating objects in an object hierarchy, video games, computer animation and realistic image synthesis. Programming environments OpenGL (or equivalent), Java graphics environments, X windows (or equivalents).

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Multimedia:

 Introduction to Multimedia System Architecture and components, Multimedia distributed processing model, Synchronization, Orchestration and Quality of Service (QOS) architecture. Audio and Speech Data acquisition, Sampling and Quantization, Human Speech production mechanism, Digital model of speech production, Analysis and synthesis, Psycho-acoustics, low bit rate speech compression, MPEG audio compression. Images and Video Image acquisition and representation, Composite video signal NTSC, PAL and SECAM video standards, Bilevel image compression standards- ITU (formerly CCITT) Group III and IV standards, JPEG image compression standards, MPEG video compression standards Multimedia Communication Fundamentals of data communication and networking, Bandwidth requirements of different media, Real time constraints- Audio latency, Video data rate, multimedia over LAN and WAN, Multimedia conferencing. Hypermedia presentation Authoring and Publishing, Linear and non-linear presentation, Structuring Information, Different approaches of authoring hypermedia documents, Hyper-media data models and standards. Multimedia Information Systems Operating system support for continuous media applications- limitations is usual OS, New OS support, Media stream protocol, file system support for continuous media, data models for multimedia and hypermedia information, content based retrieval of unstructured data.

B.Sc Electronics (Honours) Part I (Theory)

Group -A: Mathematical Methods

 Vector Analysis Vector algebra, products, polar and axial vector, differentiation, Gradient, Divergence and curl of vector and applications to simple problems, Vector Integration- Line, Surface and Volume integral, Gauss’ divergence theorem, Stokes’ theorem, Green’s theorem and related integral theorems, Curvilinear coordinates. Matrix Inverse of a matrix, Matrix algebra, Hermitian and Unitary matrices. Similarity transformation, Diagonalisation of matrices with non degenerate Eigen values, Eigen values and Eigen vectors. Differential equations First order, second order differential equations with constant coefficient, partial differential equations and its solutions for simple problems with separation of variable methods, Bessel, Legendre, Hermite polynomial differential equation, generator recursion relation, Rodrigue formula, orthogonal properties, Nonlinear Differential equation – Preliminary. Laplace Transform and inverse Laplace Transform Definitions, Conditions for existence of Laplace transforms, Lerch’s theorem, important properties, Methods of finding transforms. Fourier Analysis Fourier theorem, Fourier series, evaluation of coefficient, Analysis of simple waveform using Fourier series, Fourier integrals, Relationship of Fourier and Laplace transforms. Complex Variable f(z) its limit and continuity, Derivative of f(z), Cauchy- Riemann equations, Analytic function, Harmonic functions, Orthogonal systems, Applications to flow problem, Geometrical representation of f(z),Conformal transformation, Integration of complex functions, Cauchy’s theorem.

Group-B: Classical Mechanics

 Conservation Principals (laws), constrained motion, degrees of freedom, Generalized Co-ordinate, Generalized motion. Variational Principle and Lagrangian formulation, Calculus of variation, delta variation, Euler- Lagrange differential equation, Conservative and non conservative systems, Hamiltonian variational principal, Concept of Lagrange and equation of motion, D- Alembert’s principle Rayleigh’s dissipation function, Conservation of momentums, Conservation of Energy (Jacobi’s Integral), Concept of Symmetry, Homogeneity and Isotropy, Hamiltonian formulation of Mechanics.

Group -C: Optics

 Physical Optics Fermat’s principle and its applications – Matrix method of Paraxial optics. Magnification, Helmholtz -Lagrange Laws, Cardinal points of an optical system-thick lens and lens combinations, telephoto lenses, paraxial approxin1ation. Aberration in images, Seidal aberration, Aplenetic points of sphere, Ach- romantic combination of lenses, oil immersion objectives, eye pieces Ramsdan & Huygen. Interference Interference of light waves, spatial and temporal coherence, Young’s experiment, intensity distribution, Fresnel biprism, interference in thin film, Fringes of equal thickness and equal inclination, Newton’s ring. Diffraction Diffraction of light waves, Fresnel and Fraunhofer class, Fresnel’s half period zones, explanation of rectilinear propagation of light, zone plate, Fraunhofer diffraction due to single slit, double slit, grating.

Group-D: Electrostatics and Magneto statics:

Electrostatics:

 Introduction Fundamental relations of the electrostatics field, Gauss law, The potential function, Field due to a continuous distribution of charge, Equipotential Surface, Divergence theorem, Possion’s equation and Laplace equation, Capacitance, Electrostatics Energy Magneto statics Theories of the Magnetic Field, Magnetic Induction and Faradays law, Magnetic flux density, Magnetic field strength and Magneto motive force, Ampere’s work law, Permeability, Energy stored in Magnetic Field, Ampere’s law for a current element, Volume distribution of current element and the Dirac delta, Ampere’s law, Magnetic vector potential, Analogies between Electric and Magnetic field.

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