(for MBA 1st Quarter)
Short presentation (Social and Business contexts), Presentations in Group Discussions, Presentation in interviews and meetings, Technical seminar presentations – format, organization of matter. The use of power point, pronunciation, body language, analysis of presentations, corporate etiquette, Polite/Elitist use of language.
Text Book :
STATISTICS FOR MANAGEMENT
(for MBA 1st Quarter)
L-P-T: 4-0-0 Credits : 2
Introduction to Statistics, Grouping and displaying data to convey meaning, tables and graphs, descriptive statistics, Measures of central tendency and dispersion, frequency distribution.
Introduction to probability theory, probability distribution : Binomial, Poisson, Exponential. Sampling and sampling distribution; Estimation : point and interval estimates.
Hypothesis testing : Type I and Type II errors, one-sample tests, two-samples tests, Chi-square and ANOVA.
DECISION METHODS FOR MANAGEMENT
(for MBA 2nd Quarter)
L-P-T: 4-0-0 Credits : 2
Linear Programming : Graphical and simplex methods, Duality, Dual simplex method, sensitivity analysis, Transportation and Assignment models, Integer Programming, Dynamic Porgramming, Game Theory : Zero sum and non-zero sum games.
Complex Variables and Integral Transforms
M.Sc.(Tech.) Engg. Physics I Semester
COMPLEX VARIABLES :
Functions of a complex variable, limits, continuity, derivative, Cauchy-Riemann conditions, Analytic functions, elementary functions, line integrals in complex plane, Cauchy’s theorem (Simple proof only), Cauchy’s integral formula, Taylor’s and Laurent’s series expansions, poles, residue theorem, evaluation of real integrals using residue theorem.
Laplace Transformation :
Laplace Transform, transforms of elementary functions, properties of Laplace transforms, inverse Laplace transforms, Laplace transforms of unit step functions, impulse function and periodic functions. Solution of linear differential differential equations with constant coefficients using Laplace Transforms.
Fourier Transforms :
Fourier sine and cosine transforms, complex form of fourier transform, inverse fourier transforms, convolution theorem, transforms of derivatives.
Fast Fourier Transforms :
Introduction to fast fourier transforms and its applications to signal processing.
1. Complex Variables and Applications by R.V.Churchill
2. Operational Mathematics by R.V.Churchill
1. Laplace transforms by M.R.Spiegel (Schaum Series)
2. Complex Variables by M.R.Spiegel (Schaum Series)
Numerical Methods and Optimization Techniques
M.Sc.(Tech.) Engg. Physics II Semester
Finite differences, Newton’s forward and backward interpolation formulae, Lagrange’s interpolation formula for unevenly spaced ordinates.
Numerical Integration :
Trapezoidal rule, Simpson’s 1/3 rule and 3/8 rule.
Numerical solution of first order Ordinary Differential Equations:
Euler’s method, Modified Euler method, Taylor series method, Fourth order Runge-Kutta method.
OPTIMIZATION TECHNIQUES :
One dimensional minimization methods:
Elimination method, unrestricted search, exhaustive search, dichotomous search.
Unconstrained Optimization methods:
Direct search methods, random search methods, univariate method, patter search methods, Hookes and Jeeves method, Powell’s methods, descent methods, method of steepest descent, Fletcher Reeve’s method, Quasi Newton methods.
Recommended Text Books:
1. Introductory methods of Numerical Analysis : S.S.Sastry
2. Optimization – Theory and Applications : S.S.Rao
Numerical Methods for Scientific and Engineering Computation :
M.K.Jain, S.R.K.Iyengar and R.K.Jain.
MCA I Semester
Sets, relations and functions, fundamentals of logic, logical inferences, first order logic, quantified propositions, mathematical induction.
Combinations and permutations, Enumeration - with repetitions, with constrained repetitions.
Generating functions, coefficients of generating functions, recurrence relations, inhomogeneous recurrence relations.
Relations and digraphs:
Relations and digraphs, binary relations, equivalence relations, ordering relations, lattices, paths and closures, directed graphs, adjacency matrices.
Graphs, Isomorphism, trees, spanning trees, binary trees, planar graphs, Euler circuits, Hamiltonian graphs, Chromatic numbers, Four-colour problem.
J.L.Mott, A.Kandel and T.P.Baker : Discrete Mathematics for Computer Scientists,
Second Edition, Reston, 1986.
PROBABILITY, STATISTICS AND QUEUEING THEORY
M.C.A. I Semester
Probability as a Mathematical system:
Sample spaces, events as subsets, probability axioms, simple theorems, addition theorem, conditional probability, multiplication theorem, independent events, Baye’s formula.
Random variables and their distributions:
Random variables (discrete and continuous), probability functions, desity and distribution functions, special distributions (Binomial, Hypergeometric, Poisson, Uniform, exponential and normal). Mean and variance. Chebyshev’s inequality, joint probability mass function, marginal distribution function, joint density function.
Theory of estimates:
Estimation, point and interval estimates, unbiased and efficient estimators, estimation of parameters by the method of moments and maximum likelihood method.
Testing of Hypothesis:
Testing of Hypothesis, Null and alternative hypothesis, level of significance, one-tailed and two-tailed tests, tests for large samples (tests for single mean, difference of means, single proportion, difference of proportions), tests for small samples (t,F and Chi-square tests), goodness of fit, contingency tables, analysis of variance (one way and two way classification), Non-parametric tests, regression, correlation.
Concepts, applicability, classification, birth and death process, poisson queues, single server, multiple server, queueing models, infinite (including waiting times) and finite capacities, erlangian distribution, erlangian service time queueing models.
1. Miller and Freund : Probability and Statistics for Engineers, PHI
2. Freund : Modern elementary statistics, PHI
3. S.C.Gupta and V.K.Kapoor : Fundamentals of Mathematical Statistics.
4. Kantiswarup, P.K.Gupta and Manmohan Singh : Operations Research, S.Chand & Co.
5. H.A.Taha : Operations Research – An introduction, 4th Edition, McMillan.
M.Tech. (Transportation & R.S.G.I.S)
Probability Distributions :
Summarising and Presentation of Data, Mathematics of Probability : Bayesian approach; Case Studies, Discrete Distributions : Binomial, Poisson, Negative Binomial, Generalised Poisson and Geometric Distributions, Case Studies, Continuous Distributions : Rectangular, Normal, Log Normal, Negative Exponential, Shifted exponential, Erlong, Pearson Type I, II and III, Gamma, Beta and Weibull Distributions; Case Studies.
Sampling Theory :
Inferences and significances, Random sampling; Stratified random sampling; Sequential sampling, Central limit theorem
Hypothesis Testing :
Student t-Distribution – Confidence limits; Z, F and Chi-square distributions
Regression and Correlation :
Two variables, scatter diagrams, Bivariate Distribution, Linear Regression and Correlation coefficient, Polynomial regression – Least squares, Multinomial regression – Multiple correlation – Partial Correlation; Multiple linear and non-linear regression, Two stage regression; Stepwise regression; R2 value.
Time Series models :
Properties of Stochastic Time Series, Linear time series models – moving average models – Autoregressive models, Introduction to ARMA and ARIMA models.
Parameter Estimation methods :
Least square estimation, Generalised least squares estimation, Method of moments, Maximum likelihood estimation.
1. Ang AHS and WH Tang : Probability Concepts in Engg., Planning and Design, Vol. I & II, John Wiley & Sons.
M.Tech. (Power Systems, EMID and Industrial Metallurgy) I Semester
Linear Programming :
Introduction and formulation of models, Convexity, simplex method, Big-M method, two-phase method, degeneracy, non-existent and unbounded solutions, duality in LPP, dual simplex method, sensitivity analysis, revised simplex method, transportation and assignment problems, traveling salesman problem.
Nonlinear Programming :
Classical optimization methods, equality and inequality constraints, Lagrange multipliers and Kuhn-Tucker conditions, quadratic forms, quadratic programming problem and Beale’s method.
Search Methods :
One dimensional optimization, sequential search, fibonacci search, multidimensional search methods, univariate search, gradient methods, steepest descent/ascent methods, conjugate gradient method, Fletcher-Reeves method, penalty function approach.
Dynamic Programming :
Principle of optimality, recursive relations, solution of LPP, simple examples.
Integer Linear Programming :
Gomory’s cutting plane method, Branch and bound algorithm, Knapsack problem, linear 0-1 problem.
Reference Books :
1. J.C. Pant : Introduction to Optimization, Jain Brothers
2. S.S. Rao :Optimization Theory and applications, Wiley Eastern Ltd.
3. K.V.Mittal : Optimization Methods, Wiley Eastern Ltd.