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ODEs of first order: Method of separation of variables, homogeneous and nonhomogeneous equations, exactness and integrating factors, linear equations and Bernoulli equations, General linear ODEs of nth order: solutions of homogeneous and nonhomogenous equations, operator method, method of undermined coefficients and variation of parameters, Solutions of simple simultaneous ODEs.Power series method of solution of DE, Legendres Equation, Legendres Polynomials, Bessels equation, Bessels function.
Probability and Statistics: Random Variables, Discrete and Continuous Distribution, Mean and Variance of a Distribution, Moments, Moment Generating Functions, Skewness, Kurtosis, Binomial, Poisson, Normal Distributions, Testing of Statistical Hypothesis, F-Test, T-test, Wave particle duality, de Broglie waves, evidences for the wave nature of matter the experiment of Davisson and Germer, electron diffraction, physical interpretation of the wave function and its properties, the wave packet, the uncertainty principle. The Schrodinger wave equation (1-dimensional), Eigen values and Eigen functions, expectation values, simple Eigen value problems solutions of the Schrodingers equations for the free particle, the infinite well, the finite well, tunneling effect, simple harmonic oscillator (qualitative), zero point energy. The statistical distributors: Maxwell Boltzmann, Bose-Einstein and Fermi-Dirac statistics, their comparisons, Fermions and Bosons Applications: Molecular speed and energies in an ideal gas, The Black body spectrum, the failure of classical to give the correct explanations the applications of Bose-Einstein statistics to the Black body radiation spectrum, Fermi-Dirac distribution, free electron theory, electronic specific heats, Fermi energy and average energy its significance. Origin of energy bands in solids, motion of electrons in a periodic potential the Kronig Penny model, Brillouin zones, effective mass, metals, semi-conductors and insulators and their energy band structures, Extrinsic and Intrinsic semiconductors, doping-fermi energy for doped and undoped semiconductors, the p-n junction (energy band diagrams with fermi energy), the unbiased diode, forward and reverse biased diodes tunnel diodes, zener diode, photo diode its characteristics, LED, Introduction to transistors. Elementary Probability theory, Random Variables: discrete and continuous, distribution and density functions, Expectation, Moments, Moment Generating function, Skewness, Kurtosis, Binomial, Poisson and Normal distribution, Method of least square for linear and parabolic curves, Correlation of a bivariate distribution, Linear regression, properties of regression coefficient, Sampling distribution of mean and variance, Testing of Statistical hypothesis, F-test, T-test and chi square test.17 hrs.Mathematical Preliminaries, Formulation of the Problem and Solution by Graphical method, The simplex Method, Dual problem formulation and Solution, Application to Transportation and Assignment Problems. Switching technologies, multiplexing, circuit switching, packet switching X.25, frame relax, SMDs ATM, B-ISDN, traffic matrix, traffic pattern calculations, performance issues of packet networks, delay, availability and reliability Campus network design, leased line and radio modems, DDR & ISDN Access Network design, X.25 remote access network design, Frame-relay interfaces & traffic shaping VSAT & WLAN network design. Telecommunications transmission : Basic Switching System, Simple Tele-phone Communication, evolution of switching systems -Stroger swithching systems, cross bar switching , Electronic Switching Space Division Switching, Time Division Switching Time Division space switching, Time Division Time Switching, Time multiplexed space switching, Time multiplexed Time Switching, Combination Switching.Reuse processes: Object oriented business engineering, applying business engineering to define processes & organization, application family engineering, component system engineering, application system engineering Online Transaction Processing and Online Analytical Processing, OLAP Systems Vs Other Systems, Evolution of OLAP, OLAP characteristics, OLAP architecture, Different types of OLAP multidimensional OLAP, Hybrid OLAP and relational OLAP; Codds OLAP product evalution rules, Decision Making in the OLAP environment, Dataware-housing and OLAP software, Implementation Issues, Strategic planning.Data Storage: Primary and Secondary storage, Introduction to various computer devices such as keyboard, mouse, printers, disk files, floppies etc.Concept of computing, contemporary, Operating Systems such as DOS, Windows95, UNIX etc. Introduction to organization and architecture of mainframe, mini and micro systems.Fuels: Definition and classification, combustion and chemical principles involved in it.
Calorific value: Gross and Net Calorific values and their determination by Boys Gas Calorimeter and Bomb Calorimeter.Partial derivatives, Chain rule, Differentiation of Implicit functions, Exact differentials, Tangents and Normals, Maxima, Minima and Saddle Points, Method of Lagrange multipliers, Errors and Approximations, Differentiation under integral sign, Jacobians and transformations of coordinates, Multiple Integrals-Double and Triple integrals, Applications to areas, Volumes etc.Scalar and vector fields, Curves, Arc length, Tangent, Directional Derivative, Gradient of scalar field, divergence and curl of a vector field, Line integrals (independent of path), Greens theorem, Divergence theorem and Stokes theorem (without proofs), Surface Integrals.The student will submit a synopsis at the beginning of the semester for approval from the departmental committee in a specified format.The student will have to present the progress of the work through seminars and progress reports.Functional requirements of OLAP Systems, Limitations of Spreadsheet and SQL, n-dimensional modeling and analysis, internal structure of a dimension, Hypercube or semantic spaces, Multi-dimensional formula, Analytical visualization, Practical steps for design and implementation of OLAP models.