course contents - ug - National Institute of Technology Karnataka

NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA, SURATHAKAL
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MA308 STATISTICAL ANALYSIS AND APPLICATIONS (3–0–0) 3 PREREQ: MA208
Sampling theory: random samples, statistic, sampling distribution, 2 , t and F distributions, central
χ
limit theorem, statistical inference, point estimation, unbiasedness, MLEs, interval estimation of mean
and variances, hypothesis testing, types of errors, one � sided, two � sided tests, tests concerning means
and variances, goodness of fit tests, data analysis: correlation and regression of data, simple linear
regression.
P.L. Meyer, Introductory Probability and Statistical Applications, Oxford & IBH Publishing Co.
S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, John Wiley.
MA401 COMPUTATIONL FLUID DYNAMICS (3–0–0) 3 PREREQ: MA207
CFD applications in Engineering, Overview of CFD, Governing equations of fluid dynamics, Introduction
to finite differences, Explicit and implicit approaches, Advances in CFD, Upwind schemes, High �
resolution schemes.
Hanif Chaudhry, Open – channel Flow.
J.D. Anderson, Computational Fluid Dynamics.
MA402 FINITE ELEMENT METHODS (3–0–0) 3 PREREQ: MA207
Introduction to calculus of variations, Approximate methods, Finite Elements, nodes classifications,
approximate functions, Solution of Boundary value problems of second order differential equations,
Finite element equations for the heat conduction equation, vibration equation, elliptic problems using
Galerkine and Ritz methods.
M.K. Jain, Numerical Solution of Differential Equations, PHI Ltd.
A.R. Mitchell and R. Wait, Finite Element methods in partial Differential Equations, Edn. John Wiley,
1977.
MA403 MATHEMATICAL MODELING (3–0–0) 3 PREREQ: MA101/ MA151
Introduction: Mathematical modeling through ordinary differential equations and systems of ordinary
differential equations of first order, Mathematical modeling through difference equations, Modeling using
partial differential equations, Mathematical modeling through graphs
J.N. Kapoor Mathematical Modeling, 1988, Wiley Eastern.
R. Aris, Mathematical Modeling Techniques 1978, Pitman.
MA404 NON – LINEAR OPTIMIZATION (3–0–0) 3 PREREQ: MA304
Classical optimization techniques: Unconstrained optimization �constrained optimization, Quadratic
Programming, Construction of Kuhn- Tucker conditions, Wolfe�s method and Beale�s method; separable
programming, Geometric Programming: unconstrained and constrained geometric programming problems
Dynamic Programming: Deterministic dynamic programming, probabilistic dynamic programming
Hamdy A.Taha, Operations Research, fifth edition, 1992, Mc Millan.
Fedrick S. Hillier, Gerald J. Libermann, Operations Research, 1974, Holden Day Inc.
Kanti Swarup, Gupta and Manmohan, Operations Research, 1995, Sultan Chand Publications.
MA405 RELIABILITY THEORY AND APPLICATIONS (3-0-0) 3 PREREQ: MA208
Reliability, concepts and definitions, causes of failure, concept of hazard, failure models, bath tub curve,
MTTF, MTBF, system reliability for various configurations, reliability improvement, redundancy,
reliability-cost trade � off, maintainability and availability concepts, system safety analysis, FTA,
FMEA.
E.E. Lewis, Introduction to Reliability Engineering, John Wiley.
K S. Trivedi, Probability and Statistics with Reliability, Queuing and Computer Science Applications,
PHI.
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