Code	Course
BT402	Introduction to Molecular Biology
CH101	Chemistry I
CH102	Chemistry II
CH115	Chemistry Lab I
CH116	Chemistry Lab II
CS101	Computer Programming & Utilization
CS201	Advanced Programming
CS212	Electronic Design I
CS214	Data Structures & Algorithms
CS431	Introduction to Computer Systems
CS446	Computational Learning Theory
CS462	Analytical Models of Computing Systems
CS470	Modelling and Simulation
CS472	Introduction to VLSI Design Automation
CS476	Reliable Computing
CS478	Advanced Microprocessors
EN402	Introduction to Energy Engineering
EP208	Statistical Physics
EP302	Computational Methods
EP409	Applied Solid State Physics
EP410	Advanced Photonics
EP413	Advanced Statistical Mechanics
HS101	Economics
HS202	Introduction to Philosophy
HS203	Introduction to Psychology
HS204	Introduction to English
HS205	Introduction to Sociology
MA103	Mathematics I
MA104	Mathematics II
MA203	Mathematics III
MA204	Complex Analysis & PDE
MA403	Real Analysis I
MA406	General Topology
MA410	Differential Equations II
MA416	Mathematical Methods I
MA420	Principles of Optimization
MA422	Probability Theory
MA520	Spline Theory & Variational Methods
MA543	Finite Element Methods and Applications
ME111	Workshop Practice I
ME112	Workshop Practice II
ME118	Engineering Graphics & Drawing
ME305	Energy Conversion
ME604	Robotics
MG630	Product Planning and Management
MG662	Financial Management I
MG666	Information Technology for Management Decision
MG670	Leadership, Vision and Entrepreneurship
MM271	Introduction to Materials Science (DO-2)
MM434	Science and Technology of Thin Films
MM440	Non Destructive Evaluation
MM484	Electronics Ceramics
PH101	Physics I
PH102	Physics II
PH104	Physics IIIS (DO-1)
PH115	Physics Lab I
PH116	Physics Lab II
PH201	Physics IV
PH400	Lasers
PH426	Astrophysics
PH504	Quantum Electronics
PH528	Modern Optics
SC403	System Modelling and Simulation
SI406	Applied Stochastic Process
SI501	Discrete Algorithms
SI512	Combinatorial Optimization
SI525	Finite Difference Methods for Partial Differential Equation

BT402 Introduction to Molecular Biology 6.00 ñ

Structure of Eucaryortic chromosomes, heterochromatin, euchromatin, molecular components,packing and organization nucleosome phasing, DNase I hypersensitive regions. Organization of bacterial genome. DNA structure and replication, proteins and enzymes in DNA replication, Okazaki fragments, replication of double strand circle and single strand circle DNA, RNA transcription, operon, amino acid synthetic operons, transcription control in lambda phage,regulation of eucaryotic transcription, structure of proka ryotic genes.Expression and processing of heterogeneous nuclear RNA, ribosomal RNA, tRNA.Universal Genetic code, degeneracy of codons, termination codons, wobble hypothesis, isoaccepting tRNA, genetic code in mitochondria, protein synthesis. Mutations, no nsense, missense, point mutation, intragenic and intergenic suppression, frameshift mutations, overlapping genes. DNA repair, photoreactivation, excision repair, mismatch correction, SOS repair Recombination, Rec A gene, Holliday structure, chi sequences, Site specific recombination. Transduction, transformation, conjugation, gene mapping, Insertion sequences, Transposons, natural plasmids.

Text/References:

Benjamin Lewin, GENES, John Wiley and Sons, 1987. J.D.Watson N.H.Hopkins, J.W.Roberts, J.A.Seitz and A.M.Weiner, Molecular Biology of the Gene, Fourth edition, Benjamin Cummings Publishing company Inc. 1987.

CH101 Chemistry-I 2 1 0 6 ñ

The wave equation, particle in a box; quantum numbers; electron energy levels in atoms; chemical bonding-ionic and covalent bonds; molecular orbitals r and n bonds; intermolecular forces; types of solids, crystals structure; close packed structure; point defects; metallic bonding; electrical and magnetic properties of solids. Physical and chemical equilibria; free energy and entropy; equilibrium constant; Nernst equation; colligative, properties; rate of chemical reactions; collision theory; catalysis.

Texts/References

B.H. Mahan, University Chemistry India Book Co. 1988

S.H. Maron and 0 F. Prutton, Principles of Physical Chemistry, The MacMillan Co., New York, 1969.

CH102 Chemistry-II 2 1 0 6 ñ

Prerequisite: CH 101

Principles involved in the general methods of extraction of metals from their ores. oxidation state, spectral and magnetic properties and important applications of transition and innertransition elements and their compounds. Hydrides of boron silicons. Important applications of non-transition elements and their com- pounds.

Structural features of organic compounds and correlation with their properties and applications. In this context, the chemistry of petroleum and petrochemicals. Chemical from coal, industrial solvents, oils, fats and waxes, detergents, natural and synthetic polymers, will be briefly discussed.

Texts/References

M.J. Sienko and B.A. Plane Chemical

Principles and Applications, McGraw Hill, 1980

L.O. Srr@th, Jr. and S.J. Cristol, Organic Chemistry, Aff iliated East-West Press Pvt. Ltd., New Delhi, 1981.

R.T. Morrison and R.N .Boyd, Organic Chemistry, 3rd Ed ., Prentice Hall of India Pvt. Ltd., New IDelhi. 1978 (5th edition (1990).

CH115 Chemistry Lab.-I 0 0 1.5 1.5 ñ

Experiments illustrating the concepts of 1) galvanic cells, (2)thermochemistry, (3) chemical kinetics, (4) equilibrium constant, (5) analysis by oxidation reduction titration.

CH116 Chemistry Lab.-II 0 0 1.6 1.5 ñ

Experiments pertaining to (1) volumetric analysis by complexometry, (2) analysis by ion exchange resins, (3) analysis of a drug, (4)equilibrium constant, (5) analysis by oxidation reduction titrationn.

CS101 Computer Programming and Utilization 6.00 ñ

Functional organisation of computers, algorithms, basic progamming concepts, FOR-TRAN language programming. Program testing and debugging. Modular programming subroutines: Selected examples from Numerical Analysis, Game playing, sorting/searching methods, etc.

Text/References:

N.N. Biswas, FORTRAN IV Computer Programming, Radiant Books, 1979. K.D> Sharma, Programming in Fortran IV, Affiliated EAST WEST, 1976.

CS212 Electronic Design I 3 0 0 6 ñ

Prerequisite: EE201 (Exposure)

Steady State and transient switching characteristics of diodes and transistors, digital integrated circuit technologies, analysis of basic circuits in these families, PLAs, PALs and PLDs, flip - flops, memory elements, line drivers, multiplexers, demultiplexers, counters, encoders, decoders, registers, ALUs, interfacing techniques, transmission line effects, design examples.

Texts/References:

H.Taub & D. Schilling, Digital integrated Electronics, McGraw Hill, 1977.

D.A.Hodges & H.G. Jackson, Analysis & Design of Digital Integrated Circuits, International Student Ed., McGraw Hill 1983.

Richard S.Sandige, Modern Digital Design, McGraw Hill, 1990.

CS214 Data Structures and Algorithms 3 1 0 8 ñ

Prerequisite: CS 203 (Exposure)

Introduction to data structures. Introduction to complexity of algorithms.

Creation and manipulation of linear data structures viz. arrays, lists, stacks, queues and nonlinear data structures viz. trees, graphs, heaps. Comparison of different data structures.

File organization methods, Internal and external sorting. Abstract data types.

Texts/References

A. V. Aho, J.D. Ullman, Data Structures, Addision Wesley, 1984.

E. Horowitz, S. Sahni, Fundamentals of Data Structures, Gaigotia Publishers 1983.

D. E. Knuth, The art of Computer Programming, Vol.1, Narosa Publishers, 1985.

N. Wirth, Algorithms + Data Structures

Programs-Prentice Hall, 1976

CS292 Electronic Design Lab.-I 0 1 1.5 3.5 ñ

Study of device characteristics of diodes and transistors. Familiarity with the instruments for measuring various parameters of diodes and ,transistors- curve tracers, betatesters, etc. 9 of logic probes, pursers, logic analysers, etc. for trouble shooting. Digital Circuits using LIMOS lCs. Design, bread boarding and ting. Designing with PLAs, PALs, PLDs. Software support, PCB software.

CS462 Analytical Models of Computing Systems 3 0 0 6 ñ

Queueing models of scheduling, in batch and time sharing systems. Priority scheduling. Queueing models of a disc system. Queueing models for multiprogrammed systems.

Texts/References

E.G.Coffman, P.J.Denn'ing, Operating Systems Theory, Prentice Hall, 1973.

P.B.Hansen, Operating System Principles, Prentice Hall, 1973.

L.Kleinrock, Queueing Systems, Vol.1 and 11, Wiley,1976.

CS470 Modelling and Simulation 3 0 0 6 ñ

Selected illustrative examples of simulation applications. Models: Structural, Process, Continuous, Discrete, Deterministic, Random, in- put/output, static, dynamic, multilevel. Simulation: Analog/Digital/Hybrid, verification, validation. Data Modelling and Analysis: Population parameters, hypotheses testing, confidence- intervals, goodness of fit, estimating transient/ steady-state characteristics, variance reduction. simulation Process: Problem formulating, model building, data acquisition, model translation, verification, validation, strategic and tactical planning, experimentation, analysis of results, implementation and documentation. Simulation Languages: Examples from SIMSCRIPT, GPSS, GASP, SIMULA, etc.

Texts/References

G.Gordon, 'System Simulation', 2nd ed., Prentice Hall, 1978.

Narsing Deo, 'System Simulation with Digital Computers', Prentice Hall, 1976.

R. Leigh, 'Modelling and Simulation', Peter Peregrims Ltd.,. 1983.

M.Law, W.D.Kelton, 'Simulation Modellin and Analysis, Mcgraw Hill, 1982.

CS472 Introduction to VLSI Design Automation 3 0 0 6 ñ

Introduction to VLSI technology. Complexity of design and need for automation. Placement and routing. PLA's : folding and partitioning. Physical layout design. Design rule checking. Simulation, testing and design for testability. Reliability and yield analysis.

Texts/References

C.A.Mead, L.A.Conway, Introduction to VLSI, Addison Wesley, 1980.

J.D.Ullman, Computational Aspects of VLSI, Computer Science Press, 1984.

T-0-Hu, E.S.Kuh, VLSI Circuit Layout: Theory and Design, IEEE Press, 1985.

M.A.Breuer,ed., Design automation of Digital Systems, Prentice Hall, 1972.

T. Ohtsuki, series ed., Advanced in CAD for - VLSI, Vols 2-7, North-Holland, 1986.

CS476 Reliable Computing: Basic Concepts 3 0 0 6 ñ

Errors and failures in computing

Basic reliability models, structure function, system reliability, bounds, redundancy aspects, common distributions in quality and reliability, fault tree analysis.

Fault tolerant computing, fault diagnosis, hardware redundancy. Software failures and debugging, software reliability models, redundancy in software, effect on hardware.

Integrated perspective on reliable computing. Applications from reliability critical areas.

Texts/References

G.F.Myers, Software Reliability Principles and Practices, Wiley lnterscience, 1976.

R.S.Barlow, F.Proschan, Statistical Theory of Reliability: Probability Models and Life Testing, Holt, Rinehart and Whinston'1975.

Haken, H. : Light Vol. I and 2, North Holland, 1984

Shimoda, A.:Introduction to Laser Physics, Springer, 1984

Maftland, A. and M.H.Dunn Laser Physics, North Holland, 1969

EN402 Introduction to Energy Engineering 2 1 0 6 ñ

Prerequisite: Nil

Energy resources of India, availability and utilisation of modern resources, viz. coal, petroleum, gaseous fuels, hydel and nuclear fuel, traditional resources, viz. firewood, cattledung, animal power and solar sources. Principles of energy conversion, heat engines, thermal power plants using coal, petroleum nuclear power plants using coal, petroleum nuclear fuels and hydel energy, fundamentals of energy conversion using solar thermal, photovolatic, fuel cell, biogas, firewood, wind mini-hydel and tidal resources. lnvestments for resource development cost and effeciences of motive and thermal power generation and consumption, etc., environmental effects of energy use. Strategy for energy development in India, prob- lems and prospects of centralised and decentralised patterns, potential for biomass and biogas system.

Texts/References

M. Khovakh Ed., Motor Vehiclu@, Engines Mir Publishers, Moscow, 1979

D.M. Simmons, Wind Power Noyes Data Corporation, New Jersey, 1975.

S.P. Sukhatme, Solar Energy, Principles of Thermal Collection and Storage, Tata Mcgraw-Hill, New Delhi, 1984

J.J. Duderstadt, Nuclear Power, Marcel Dekker, New Jersey, 1979.

P.J. Meynel, Methane PlanningaDigesterPrism Press, United Kingdom, 1976 E.Mosinye, Water Power Plants, Akademiai Kiado, Budapest, 1963

EP409 Applied Solid State Physics 2 1 0 6 ñ

Boltzman transport equation, scattering and relaxation time. Optical properties of solids, excitations, concept of plasmons, polarons and polaritons. Dielectric function, dielectric and ferroelectric materials. Band structure of semiconductros, density of states and conductivity effective masses, carrier diffusion processes, excess carrier life time, recombination and trap centres, photo conductivity, electronic properties of surfaces. Dia, para and ferro magnetism, magnetic domains, magnetic materials and application. Magnetic resonance techniques, spin-spin and spin-lattice relaxation. Superconductivity, Meissner effect, tunneling in superconductors, Josephson junctions, squids, superconducting magnets.

Texts/References:

C. Kittel, Introduction to Solid State Physics, 6th Edition, John Wiley, 1991.

N.W. Ashcroft and N.D. Mermin, Solid State Physics, Holt Rinehart and Winston, 1976.

S. Wang, Solid State Electronics, McGraw Hill, 1966.

F. Wooten, Optical Properties of Solids, Academic Press, 1972.

K. Seeger, Semiconductor Physics - An Introduction, 4th ed. II, 1989.

R. Dalven, Introduction to Applied Solid State Physics, 2nd ed.1990.

HS101 Economics ñ

Basic economic problems. Resource Constraints and Welfare maximization. Nature of Economics: Positive and normative economics; Micro and macroeconomics, Basic concepts in economics. The role of the State in economic activity; market and government failures; New Economic Policy in India.

Theory of utility and consumer's choice. Theories of demand, supply and market equilibrium. Theories of firm, production and costs. Market structures. Perfect and imperfect competition, oligopoly, monopoly.

An overview of macroeconomics, measurement and determination of national income. Consumption, saving, and investment. Commercial and central banking. Relationship between money, output and prices. Inflation - causes, consequences and remedies. International trade, foreign exchange and balance payments, stabilization policies: Monetary, Fiscal and Exchange rate policies.

Text/References:

P.A. Samuelson & W.D. Nordhaus, Economics, McGraw Hill, New York, 1995.

A. Koutsoyiannis, Modern Microeconomics, Macmillan, 1975.

R. Pindyck and D.L. Rubinfeld, Microeconomics, Macmillan Publishing Company, New York, 1989.

R.J. Gordon, Macroeconomics 4th Edition, Little Brown & Co., Boston, 1987.

William F. Shughart II, The Organization of Industry, Richard D. Irwin, Illinois, 1990. (Chapter 3).

HS104 Perspectives in Social Sciences 3 0 0 6 ñ

Definition of psychology, work of psychologist, modern perspectives of psychology, methods of psychology.

Learning and memory.

Motivation, frustration and conflict.

Intelligence.

Social Behavior.

Distinction between sociological and psych, logical approaches.

The nature of human society. Some Sociological concepts: status and role, norms and viruses.

Socialization. Primary and secondary groups, social stratification, social control a system of regulation.

Population and Society.

Major Institutions. Processes of Social chan Text/References

Text/References:

C.T.Morgan, R.A.King, J.A. Weisz and J. Schopler, Introduction to Psychology 7th Edition, McGraw Hill, 1986.

G.A.Kimble, N.Garmezy, E.Zigler, Principles of Psychology, 6th Edition, Wiley Eastern,1985.

T.B.BottOmore,SociolOgy,George Unwin, 1975.

M.Harlambos and R.Heald, Sociology:Themes and Perspectives, Oxford University Press, 1980.

L.Broorn,P.Selznickand D.Darrock, SociOI09YI Harper International Edition, 7th Edition,1981.

HS202 Introduction to Philosophy ñ

The course will acquaint the students of science and engineering with the some issues on the nature and methods of science and mathematics, and the ethical issues arising out of the application of science and technology. The objective is to develop a critical, reflective and historical awareness on the issues relating to the following topics:

Philosophy and History of Science: Growth of scientific knowledge: factors leading to the emergence of modern science. Conceptual evolution: internal and external history. Methodology of science: induction, falsificationism, confirmation and probability. Nature of scientific laws and theories: realism, instrumentalism and under determination. Relationship between scientific observation, experient and scientific theory. Nature of scientific explanation: teleological explanations and the covering law model. Selected case studies on scientific theories.

Logic and the nature of mathematical reasoning: Inductive and deductive forms of reasoning. Nature of axioms: formal axiomatic systems. Concept of consistency, independence and completeness. Nature of rules of inference and proof. Selected examples of axiomatic systems and proof procedures.

Cognition: Current approaches to the understanding of mind and mental processes: empiricist, rationalist, behaviourist and cognitivist.

Ethics: Impact of science and technology on man and society: elements of environmental and professional ethics.

Texts/References:

A.C. Grayling (ed.) Philosophy: A Guide through the subject, Oxford Univ. Press, London, 1995.

Marx W. Wartofsky, Conceptual Foundations of Scientific Thought: An Introduction to the Philosophy of Science, Macmillan, London, 1968.

I.B. Cohen, The Birth of a New Physics, Vakils, Feffer and Simons Pvt. Ltd., Bombay, 1968.

H. Eves and C.V. Newsom, Foundations and Fundamental Concepts of Mathematics, Boston, PWS-Kart Pub. Co., 1990.

K.E. Goodpaster and K.M. Sayre (eds.) Ethics and Problems of 21st Century, Univ. of Notre Dame Press, London, 1979.

S.D. Agashe, A. Gupta & K. Valicha (eds.) Scientific Method, Science, Technology and Society: A Book of Readings, Univ. of Bombay Press, 1963.

HS203 Introduction to Psychology ñ

Understanding human experience and behaviour: Definition, schools, methods, branches and application of psychology for engineers; Measuring human abilities: Intelligence, Personnel testing; The individual working life: Personality - definition, approaches and theories; Psychological problems of everyday life: Stress and coping; Psychological disorders, work and mental health; Human learning; Motivation : the concept and theoretical framework, motivating people at work; Attitude and work behaviour; Group dynamics Intergroup relations, conflict resolutions; Leadership and management.

Texts/References:

McConnell, J.V. (1986) Psychology, New York: Holt., Rinehart & Wiaton.

Morgan, C.T., King, R.A., Weiss, J.R., & Schopler, J. (1986). Introduction to Psychology (VIIth Ed.), New York: McGraw-Hill.

Myers, D.G. (1995). Psychology (IVth Ed.), New York: Worth.

Asch, S.E. (1987). Social Psychology, OUP Oxford.

HS204 Introduction to Literature ñ

1. NATURE OF LITERATURE :

Literature as a Humanistic Experience.

Definitions:

(i) Humanities : concern with culture, values, ideologies;

(ii) Literature : concepts of imitation, expression, intuition & imagination.

2. MAJOR THEMES OF LITERATURE :

Nature, Science, Selfhood, Love, Rebellion.

3. THE LANGUAGE OF LITERATURE :

Modes of literary and non-literary expression.

The concepts of Figurative language, Imagery, Symbolism, Style.

4. THE FORMS OF LITERATURE :

Prose Narratives (short stories & novels)

Poetry

Drama

Essays.

[NOTE: 1. Suitable texts are to be chosen by the instructor from the Texts and References listed below as well as from other sources. 2. Use of a Learner Dictionary (e.g.Oxford Advanced Learner's Dictionary is prescribed for language work.]

Texts/References:

David Murdoch (Ed.). The Siren's Song: An Anthology of British and American Verse, Orient Longman, 1988.

S. Alter & W. Dissanayake (eds.) The Penguin Book of Modern Indian Short Stories. Penguin Books (India), 1989.

Bertrand Russell, Impact of Science on Society. Allen & Unwin, 1952.

Henrik Ibsen, A Doll's House, Macmillan India, 1982.

George Orwell, Animal Farm, Penguin, 1951.

J. Bronowski. The Ascent of Man, BBC, 1973.

HS205 Introduction to Sociology ñ

1. What is sociology, some sociological concepts: social structure, status, role, norms, values etc. Socialization, and culture and change.

2. Social stratification - various approaches and concept of social mobility.

3. Population and society - Trends of demographic change in India and the world, Human Ecology, Trends of Urbanization in the developing countries and the world.

4. Major social institutions - Family and marriage, caste and tribe and organizations: (i) formal organization (bureaucracy) (ii) informal organization.

5. Processes of social change - Modernization (including Sanskritization), industrialization, environmental/ecological changes and Development.

6. Social movements - protest movements, reformist movement and radical movements in India.

Texts/References:

L. Broom, P. Selznick and D. Dorrock, Sociology, 11th Edn. 1990 (Harper International).

M. Haralambos Sociology: Themes and Perspectives, Oxford University Press, 1980.

M.S.A. Rao (ed) Social movements in India, vols. 1-2, 1984, Manohar.

David Mandelbaum, Society in India, 1990, Popular.

M.N. Srinivas, Social change in modern India, 1991, Orient Longman.

Guy Rocher, A. General Introduction to Sociology, MacMillan, 1982.

HS699 Communication and Presentation Skills 4.00 ñ

The aim of this course is to equip the post-graduate students with basic communication and presentation skills for academic and professional purposes. Remedial work will be conducted wherever necessary. The course will focus on the following topics: The process of communication; barriers to communication and how they can be overcome. Types of communication: verbal and non-verbal. Non-verbal communication: body language Verbal communication: Oral and Written Oral: elements of pronunciation, oral presentation, group discussion Written: technical reports, business letters Reception skills: reading and listening skills Vocabulary and Grammar Style and Usage: Punctuation, Readability and Culture-sensitivity Use of computerized audio-visual aids for academic and professional presentations. Psychological and Sociological Aspects of communication

Text/References:

Bell, Arthur H. Tools for Technical and Professional Communication. NTC Publishing Group, Lincolnwood, 1995. Eisenberg, Anne A Beginner’s Guide to Technical Communication. WBC McGraw-Hill, Boston, 1998.

Hicks, T.G. & C. M. Valorie Handbook of Effective Technical Communication. McGraw-Hill, NY, 1989.

Huckin, T N. and L. A. Olson Technical Writing and Professional Communication for Nonnative Speakers of English. McGraw-Hill, NY, 1991.

Little, Peter Oral and Written Communication. Longman, London. 1979.

Murphy, R. Intermediate English Grammar: Reference and Practice for South Asian Students. Cambridge University Press, New Delhi, 2001.

Singh, R. K. Using English in Science and Technology. Prakash Book Depot, Bareilly, 2000.

MA103 Mathematics I 2 0 2 6 ñ

Review of the prerequisites such as limits of sequences and functions, continuity, uniform continuity and differentiability. Rolle's theorem, mean value theorem and Taylor's theorem. Newtons method for approximate solution. Riemann integral and the fundamental theorem of integral calculus. Approximate integration. Applications to length, area, volume, surface area of revolution. Moments, centres of mass and gravity.

Review of vectors. Cylinders and quadric surfaces. vector functions of one variable and their derivaties.

Partial derivatives. Chain rule. Gradient, directional derivative. Tangent planes and normals. Maxima, minima, saddle points. Lagrange multipliers. Exact differentials.

Repeated and multiple integrals with applications to volume, surface area, moments of inertia etc.

Texts/Reference:

G.B.Thomas, and R.L.Finney, Calculus and Analytic Geometry, 6th ed., Addison-Wesley Narosa, 1985.

T.M.Apostol, Calculus, Vol. I, 2nd ed., Wiley Eastern, 1980.

MA104 Mathematics II 3 0 2 8 ñ

Vector fields, surface integrals, line integrals, independence of path, conservative fields, divergence, curl. Green's theorem. Divergence theorem of Gauss, Stokes' theorem and applications of these theorems.

Transformations of coordinate systems and vector components. lnvariance of divergence and curl. Curvilinear coordinates.

Vector spaces. Inner products. Matrices and determinants, linear transformations. Systems of linear equations. Gauss elimination, rank of a matrix. Inverse of a matrix. Bilinear and quadratic forms. Eigenvalues and eigenvectors. -Similarity transformations. ldiagonalization of Hermitian matrices.

Numerical methods for solving systems of linear equations. III conditioning. Methods of Gauss and least squares. Inclusion of matrix eigenvalues. Finding eigenvalues by iteration.

Texts/References

E. Kreyszig, Advanced Engineering Mathematics, 5th ed., Wiley Eastern, 1985.

V. Krishnamurthy, V. P. Mainra and J.L. Arora, An Introduction to Linear Algebra, Affiliated East-West, 1976.

T.M. Apostol, Calculus, Vol. 11, 2nd ed., Wiley Eastern, 1980.

MA203 Mathematics III 3 0 2 8 ñ

Ordinary differential equations of the 1st order, exactness and integrating factors, variation of parameters, Picard's iteration method.

Ordinary linear differential equations of nth order, solution of homogeneous and nonhomogeneous equations. Operator method. Methods of undetermined coefficients and variation of parameters.

Systems of differential equations. Phase plane. Critical points. Stability.

Infinite sequences and series of real and complex numbers. Improper integrals. Cauchycriterion, tests of convergence, absolute and conditional convergence. Series of functions. Improper integrals depending on a parameter. Uniform convergence. Power series, radius of convergence.

Power series methods for solutions of ordinary differential equations. Legendre equation and Legendre polynomials, Bessel equations and Bessel functions of first and second kind. Orthogonal sets of functions. Sturm-Liouville problems. Orthogonality of Sessel functions and Legendre polynomials.

Laplace transform. Inverse transform. Shifting on the s and t axes, convolutions, partial fractions.

Fourier series, half-range expansions. Approximation by trigonometric polynomials. Fourier integrals.

Transform techniques in differential equations.

Texts/References:

E. Kreyszig, Advanced Engineering Mathematics, 5th ed., Wiley Eastern, 1985.

W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 3rd ed., Wiley, 1977.

G.F. Simmons, Differential Equations with Applications and Historical Notes, Tata McGraw-Hill, 1972.

MA204 Mathematics IV 2 1 0 6 ñ

Analytic functions. Cauchy-Riemann equations, Laplace equation. Elementary functions. Cauchy's integal theorem (proof by using Green's theorem), Cauchy's integral formula. Taylor series and Laurent series.

Residues and applications to evaluating real improper integrals and inverse Laplace transforms. Conformal mapping. Linear fractional transformations.

Boundary value problems involving partial differential equations such as the wave equation, the heat equation, the Laplace equation. Solutions by the method of separation of variables and by Fourier and Laplace transforms.

Texts / References:

P.E. Danko, A.G. Popov, T.YA. Koznevnikova, Higher Mathematics in Problems and Exercises, Part 2, Mir Publishers, 1983.

E. Kreyszig, Advanced Engineering Mathematics, 9th ed., John Wiley & Sons 1999.

MA403 Real Analysis I 8.00 ñ

Metric spaces, compactness, connectedness, completeness. Continuity. Monotonic functions. Differentiation of vector-valued functions. Functions of bounded variation and absolutely continuous functions. Riemann-Stieltjes integral and its properties. Fundamental theorem of integral calculus. Sequences and series of functions, uniform convergence and its relation to continuity, differentiation and integration. Equicontinuous families of functions, Ascoli-Arzela theorem. Weierstrass approximation theorem. Fourier series, Fejer"s theorem, pointwise convergence.

Text/References:

T. Apostol, Mathematical Analysis, 2nd ed., Addison-Wesley, 1974.

Ganapati Iyer, Mathematical Analysis, Tata McGraw-Hill, 1977.

W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, 1983.

MA406 General Topology 8.00 ñ

Topologies through open sets, bases, sub-bases, closure, interior, boundary, subspaces. Continuity, open functions, homeomorphisms, embeddings, strong and weak topologies generated by families of functions. Quotient spaces. First and Second countable, separable, Lindeloff, compact spaces. Separation axioms, Urysohn"s lemma. Products, embeddings into products, Urysohn metrisation theorem, Convergence of nets and filters. Filters and compactness, ultrafilters, Tychonoff compactness theorem. Local compactness, Alexandroff compactification. Function spaces, compact-open topology. Connectedness, components, local connectedness, paths, loops. Homotopy, fundamental group. Computation of the fundamental group of the circle.

Pre-requisites : MA 403

Text/References:

K.D. Joshi, Introduction to General Topology, Wiley Eastern, 1983.

J.L. Kelly, General Topology, Van Nostrand, 1955.

MA410 Differential Equations II 8.00 ñ

Classification of partial differential equations in general: second order equations in several variables, first order systems. Stability theory, energy conservation and dispersion. Wave equation: Uniqueness, D"Alembert"s method, method of spherical means, method of descent and method of successive approximation. Fourier transforms and applications to initial value problems for heat and wave equations. Review of method of separation of variables, construction of Green"s function and properties. Uniqueness of solution by energy method, maximum principle for elliptic and parabolic equations. Symmetric Hyberbolic Systems: Basic energy inequality, existence and uniqueness of solution.

Pre-requisites : MA 409

Text/References:

F. John, Partial Differential Equations, 3rd ed., Narosa, 1979.

I.N. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, 1957.

I.N. Tychonov and A.S. Samarski, Partial Differential Equations of Mathematical Physics, Vol. I, Holden-Day, 1970. H.F. Weinberger, A First Course in Partial Differential Equations, Blaisdell, 1965.

Erich Zanderer, Partial Differential Equations of Applied Mathematics, 2nd ed., Wiley, 1989.

MA416 Mathematical Methods I 8.00 ñ

Introduction to perturbation theory : Asymptotic expansions. Method of steepest descent. Regular and singular perturbation methods. Methods of strained coordinates, multiple scales, matched asymptotic expansions. Singular perturbation methods. Variational techniques : Ritz method, Galerkin method, Least square method.

Pre-requisites: MA 409

Text/References:

S.G. Mikhlin, Variational Methods in Mathematical Physics, Macmillan, 1964.

Ali Nayfeh, Perturbation Methods, Wiley, 1973.

C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineer, McGraw-Hill, 1978.

J. Kevorkian and J.D. Cole, Perturbation Methods in Applied Mathematics, Springer Verlag, 1985.

MA420 Principles of Optimization 8.00 ñ

Mathematical foundations. Linear Optimization. Simplex method. Revised simplex method. Duality and sensitivity. Unconstrained optimization of functions of several variables. Classical techniques. Numerical methods for unconstrained optimization. Constrained optimization of functions of several variables. Lagrange multipliers. Kuhn-Tucker theory. Numerical methods for constrained optimization. Convex optimization. Quadratic optimization. Dynamic programming.

Text/References:

G. Hadley, Linear Programming, Addison Wesley, 1962.

G. Hadley, Non-linear and Dynamic Programming, Addison Wesley, 1964.

M. Panik, Classical Optimization : Foundations and Extensions, North Holland/American Elsevier, 1976.

S.S. Rao, Optimization Theory and Applications, Wiley Eastern, 1978.

J.K. Sharma, Mathematical Models in Operations Research, Tata McGraw-Hill, 1989.

D.M. Himmelblau, Applied Nonlinear Programming, McGraw-Hill

MA422 Probability Theory 8.00 ñ

Probability space, conditional probability, independence of events, Borel-Cantelli lemmas, zero-one laws. Random variables, distribution functions, sequences of random variables, expected value, convergence theorems, various modes of convergence. Fubini"s theorem (statement only). Joint distributions, independence of random variables. Moment generating function, characteristic function, central limit theorems, laws of large numbers. Radon-Nikodym Theorem (statement only), conditional expectation, conditional distribution.

Text/References :

H. Bauer, Probability Theory and Elements of Measure Theory, Academic Press, 1981.

P. Billingsley, Probability and Measure, Wiley, 1985.

MA520 Spline Theory and Variational Methods 6.00 ñ

Piecewise linear approximation. Piecewise cubic interpolation. Cubic spline interpolation and its errors. Representation of piecewise polynomial diminishing splines. Interpolating and smoothing splines. Approximate representation of linear functions. Optimal quadratures. Variational formulation of generalized splines. Surface approximation by tensor product splines. The Rayleigh-Ritz-Galerkin procedures of elliptic problems, Semi-discrete Galerkin procedure for parabolic problems.

Pre-requisites : MA 403

Text/References :

C. de Boor, A Practical Guide to Splines, Springer-Verlag, 1978.

M.H. Schultz, Spline Analysis, Prentice-Hall, 1973.

P.J. Laurent, Approximation et Optimization, Hermann, 1972.

MA543 Finite Element Methods and Applications 6.00 ñ

The fundamentals of finite element method. The shape functions, Ritz and Galerkin finite element formulations. Finite element formulation for Laplace, wave and diffusion equations.

Text/References:

J.N. Reddy, Finite Element Method, 2nd ed., McGraw-Hill, 1993.

D.H. Norrie and G. DeVries, Introduction to Finite Element Method Analysis, Academic Press, 1957.

ME111 Workshop Practice I 0 1 3 5 ñ

Introduction to wood working, kinds of woods, hand tools and machines, pattern making, types of patterns, contraction allowance, draft and machining allowances. Principles of moulding methods, cores and core boxes. Introduction to fitting shop tools, equipment and operations. Sheet metal practice. Exercises: Simple exercises in patternmaking, moulding, fitting and sheet metal work.

Text/References:

S.K. Hajrachoudhury, Elements of Workshop Technology, Vol.1 Asia Publishing House, 1986.

ME112 Workshop Practice II 0 1 3 5 ñ

Introduction to safety measures, introduction to the principles of working, construction, operation, types of cutting tools, selection of cutting speeds and feeds etc. regarding basic machine tools e.g. lathe, shaping, slotting, milling and grinding machines, etc. Introduction to gas and arc welding Processes, soldering and brazing.

Exercise: Simple jobs on centre lathe and shaping machines and welding.

Demonstrations; Slotting, milling and grinding machines.

Text/References

S.K. Hajrachoudhury, Elements of Workshop Technology, Vol. 11 Asia Publishing House, Si 1986

ME6O4 Robotics 3 0 0 6 ñ

Introduction. Construction of manipulators, advantages and disadvantages of various kinematic structures. Applications, Actuators, pneumatic, hydraulic and electric. Characteristics and control. Nonservo robots, motion planning. Feed back systems, encoders, servocontrol PTP and CP. Kinematics, homogenous coordinates, solution of the inverse kinematic problem, multiple solutions, jacobian, work envelopes.Trajectory planning.Manipulator dynamics and force control. Sensors: Vision, ranging, laser, acoustic, tactile.

Developments in sensor technology, sensory control. Programming Language: VAL, RAIL, AML. Mobile robots, walking devices. Robot reasoning.

Texts/references:

K.S.Fu, R.C.Gonzalez, C.S.G.Lee, Robotics, McGraw Hill, 1987.

Y.Koren, Robotics for Engineers, McGraw Hill, 1985.

J.J.Craig, Robotics, Addison-Wesley, 1986.

MM271Introduction to Material Science 6.00 ñ

Atomic Structure & Bonding, Crystal Structure & Defects, Diffusion, Non Crystalline Materials, Phase Equilibria and Phase Diagrams,

Phase Transformation, Microstructural Development.Conductivity, Electron Mobility, Energy levels, Electrical Resistivity of Metals & Alloys,

Semiconductors, Hall Effect, Carrier Concentration.Dielectric Properties, Capacitance, Types of polarisations, Piezoelectricity &

Ferroelectricity.Optical properties, Interaction of solids with radiation, Luminescence, Photoconductivity, Lasers. Mechanical properties, Fracture,

Fatigue, Creep, Structure and properties of polymers, Composite Materials and their application, Corrosion, Oxidation, Friction and Wear. Material

Selection and Design Considerations.

Text/References :

L.H. Van Vlack, Elements of Materials Science and Engineering, Addison-Wesley, New York, 1989.

W.D. Callister, Jr., Materials Science and Engineering An Introduction, John Wiley, New York, 1997.

Z.D.Jastrzebski, the Nature and Properties of Engineering Materials, John Wiley, New York, 1987.

MM434 Science and Technology of Thin Films ñ

Historical development. Fundamentals of vacuum technology, rotary, diffusion, roots blower, turbomolecular, titanium sublimation and cryopumps, low and high vacuum gauges. Thermodynamics and kinetics of thin film growth, nucleation and modes of growth, surface and interface phenomena. Techniques of film deposition; physical vapor deposition, sputtering, various chemical vapor deposition methods, molecular beam epitaxy and liquid phase epitaxy, Langmuir-Blodgett films. Characterization of thin films; structural, electrical and optical properties, low angle XRD, LEED and RHEED, ellipsometry, XPS. Applications; semiconductor thin films, hard coatings, barrier layers, optical and infrared windows.

Text/References:

Handbook of Thin Film Technology. Ed. L.I. Maissel and R. Glang (McGraw Hill Now York, 1970.

Thin Film Processes, J.L. Vossen and W. Kern, Academic Press, New York, 1978.

Thin Film Phenomena, K.L. Chopra, McGraw- Hill, New York, 1969.

Scientific Foundations of Vacuum Techniques, 9nri Pri q Dushman and J.M. Lafferty,

MG630 Product Planning and Marketing 4.00 ñ

Corporate strategy for product planning,Management thinking on new products,Seeing products as part of the image of the company,Moving into future; Defining companies business. Technology transfer problems,SWOT analysis, Analysis of strength,Weakness, Opportunities and threat brief in production to assessing of companies financial performance. Study of Product life cycle,Monitoring of sale and competition,When to introduce new products. Assessing market potentials for new products,Market research,Consumer research and its demographic aspects,Setting up a questionnaire for these aspects. Establishing market segments and their dimensions. Assessing competitors,Marketing approach and developing a strategy to introduce new products,Using market gaps as competitive edge,Cost considerations and profitability of new products,Developing a product plan and product mix,Price policy,Positioning the company,product positioning, Planning for future position. Evolving a design brief by interlinking with market/product plan. Seeing product design as a part of a scheme to develop broad image,Bouse style,Marketing strategy and corporate image. Discriminating product range from each other and from competitor"s range. Developing product specifications for different products within the range. Market communication,Launching the product, Monitoring the market performance.

Text/References:

Wind J. and Mahajan V. and Cardogo,New Product Forecast,Lexington Book,(1981).

Holt K.,Geschka H. and Peterlongo G.,Need Assessment - A key to user oriented Product Innovation, John Wiley,London,(1984).

Churchill G.A., Marketing Research, Drydin Press, Chicago, (1993).

PH101 Physics I 6.00 ñ

Physical quantities, dimensional analysis, velocity and acceleration in plane polar coordinates. Dynamics in non- inertial frame: linearly acelerating frames, rotating frame, centrifucal and Coriolis forces. Conservation of momentum: many particle system, collison in two dimensions, system with variable mass, principle of rocket motion. Motion of rigid bodies: kinematics of rigid body motion, Euler angles, fixed axis rotation, inertia tensor, motion of a symmetrical top. Special theory of relativity: Galilean relativity, Michelson Morley experiment, Fitzgerald contraction and time dilation, Lorentz transformation, Einsteins s formulation of special relativity, space time view -points, four vectors.

Text/References :

G.Basavaraju and Dipan Ghosh, Mechanics and Thermodynamics, Tata McGraw Hill, 1989.

D.Kleppner and R.J.Kolendow, An introduction to Mechanics, McGraw Hill, 1973.

M.Alonso and E.J.Finn, Fundamental University Physics, Addison- Wesley, 1980.

PH102 Physics II 2 1 0 6 ñ

Coulomb's Law. Electrostatic field and Gauss'Law, Conservative fields and potential Poission's equation. Conductors, simple image problems and Electric fields in dielectrics, polarization and for displacement.

Capacitance, Electrostatic energy, Steady currents, Kirchhoff's Laws. Biot-savart Law. Magnetic field. Lorentz force and charged particle motion. Araday's Law of electromagnetic induction, frames of reference. Displacement current and Maxwell's equations. Electromagnetic waves.

Texts/References

A.S Mahajan and A Rangwala, Electricity and Magnetism, Tata Mcgraw.

PH104 Physics - III (Quantum Physics and Applications) 2 1 0 6 ñ

Review of quantum concepts : particle nature of light, photoelectric effect, Compton effect, matter waves, wave packets, phase and group velocity, Davisson Germer experiment, Heisenberg uncertainty principle. Schrödinger equation : probabilistic interpretation of wave function, one dimensional problems – particle in a box, harmonic oscillator, potential barrier and tunneling. Hydrogen atom, electrons in a magnetic field, Landau levels.

Elements of statistical physics : density of states, Fermi energy, Bose condensation. Solid state physics : Free electron model of metals, classical and quantum Hall effect, superconductivity, London equation, coherence and penetration depth, flux quantization, applications of superconductivity, SQUIDS.

Nuclear physics : binding energy, nuclear reactions, elements of nuclear reactors, fission and fusion, fundamental forces, elementary particles, quarks and leptons.

Texts/References

S. H. Patil, Elements of Modern Physics, Tata McGraw Hill, 1989.

H. S. Mani and G. K. Mehta, Introduction to Modern Physics, Affiliated East West, 1988.

A. Beiser, Perspectives in Modern Physics, McGraw Hill, 1969.

PH201 Physics IV ( Optics ) 2 1 0 6 ñ

Wave nature of light, Fresnel's equations and their consequences. Spatial and temporal coherence, spectral resolution of a finite wave train, Fourier transform spectroscopy. Interference, Fraunhofer and Fresnel diffraction, interferometers, Polarization. Propagation of light through matter, dispersion and absorption. Introduction to lasers.

Texts/References :

G. B. Fowles, Introduction to Modern Optics, Holt Reinhart and Winston, 1975.

M. Born and E. Wolf, Principles of Optics, McMillan,1974.

S. C. Lipson and H. Lipson, Optical Physics, Cambridge University Press, 1969.

PH203 Physics V (Thermodynamics ) 3 1 0 8 ñ

Thermal equilibrium, zeroth law and concepts of temperature. First law and its consequences, reversible, irreversible and quasi-static processes.

Second law : heat engines, concept of entropy and its statistical interpretation, thermodynamic potentials, Maxwell's relations.

Chemical equilibrium, stability, elements of chemical

thermodynamics.

Phase transition: Joule Kelvin effect, first order and continuous transitions, critical exponents, applications to magnetism, superfluidity and superconductivity.

Texts/References :

M.W. Zemansky and R. H. Dittman, Heat and Thermodynamics (7th ed.), McGraw Hill (1997).

H. B. Callen, Thermodynamics and an Introduction to Thermostatistics (2nd ed.), John Wiley (1985).

D. ter Haar and H. Wergeland, Elements of Thermodynamics, Addison- Wesley (1966).

H. E. Stanley, Phase Transition and Critical Phenomenon, Cambridge University Press (1988).

PH115 Physics Lab. I 0 0 1.5 1.5 ñ

Error analysis and accuracy of measurement, linear regression. Selected experiments from the following : current and voltage sensitivities of a moving coil galvanometer, measurement of self inductance using Anderson s bridge, resistivity of a thermistor, Helmholtz coil. Fresnel biprism, dispersive power of a prism, Newton s rings. Young s modulus using Koenig s method, moment of inertia of a fly wheel, physical pendulum.

Text/References :

B. L. Worsnop and H. T. Flint, Advanced PRactical Physics for students, Asia Publishing House, 1971.

PH116 Physics Lab II 0 0 1.5 1.5 ñ

same as PH115

PH400 Lasers 2 1 0 6 ñ

Electric and magnetic dipole transtions. Einsteein's transition probabilities. Lifetime and collision broadening of atomic transitions. Doppler broadening. Master amplification. Rate equation for atomic transtitions. Microwave solid state measers. Optical resonators and lens waveguides. Lasers and their general characteristics. Resonant cavities and laser modes. Different types to lasers. Sample applications (scientific and technological).

Texts/References:

B.A.Lengyel, Introduction to Laser Physics, Wiley lnterscience 1971.

A.P. Siegman, An Introduction to Laser and Masers, McGraw'Hill 1971.

W.V. Smith and P P Sorokin, The Laser McGraw Hill.

PH426 Astrophysics 2 1 0 6 ñ

Spectral Classification of stars, electro-magnetic spectrum, Doppler shift, flux and intensity, Plank's radiation formula, thermal equilibrium and Boltzmann factor, Saha-Boltzmann ionization equation. Astronomical scale, units of stellar brightness, radius of star, effective temperature. Equation of state for stellar atmosphere, sources of continuous spectrum, opacity, equation of radiative transfer, abundance of elements, variation of abundances and isotope ratios. Structure equations, mode of energy transport, nuclear reactions, formation and evolution of stars, white dwarfs, neutrons stars and Black holes. Interstellar matter, 21 cm and molecular lines. Galaxies and Quasars.

Cosmology : The Universe at largest possible scales, observational constructs, onset of isotropy and homogeneity, the notion of a metric from General Relativity, Friedmann-Robertson-Walker models, cosmic microwave background, Standard Model of hot big bang cosmology, alternative models.

Texts/References:

E. V. P. Smith and K. C. Jacobs, Introductory Astronomy and Astrophysics, W.B. Saunder, 1973.

T. L. Swihart, Astrophysics and Stellar Astronomy, John Wiley, 1968.

J. V. Narlikar, Structure of the Universe, Oxford University Press, 1977.

J. V. Narlikar, Introduction to Cosmology, 2nd ed., Cambridge University Press/Foundation Books, 1993

T. Padmanabhan, Cosmology and Astrophysics through problems, Cambridge University Press, 1996.

PH504 Quantum Electronics ñ

Nature of light, wave propagation in dielectric media, wave guides and optical fibers, interaction of light with matter, semiclassical theory of radiation, laser resonators and Gaussian beams, solid state lasers, molecular and atomic gas lasers, semiconductor lasers and free electron laser. Non-linear optical frequency conversion, phase conjugation and optical bistability, applications of lasers.

Text/References :

O. Svalto , Principles of Laser Physics, Plenum, 1982. A.Yariv , Quantum Electronics, II Edition, 1975.

M. Sargent , M.O. Scully and W.E. Laurh Laser Physics, McGraw Hill, 1974.

Haken, H. : Light Vol. 1 and 2, North Holland, 1984.

Shimoda, A. : Introduction to Laser Physics, Springer, 1984.

Maitland, A. and M.H. Dunn Laser Physics, North Holland, 1969.

PH528 Modern Optics 2 1 0 6 ñ

Theory of partial coherence; the auto-correlation function, interference spectroscopy, Michelson Steller Interferometer, Intensity Interferometer. Diffraction theory of image formation; Fresnel and Fraunhofer Diffraction, Fourier transforming and Imaging properties of lenses. Frequency ananlysis of optical imaging systems; spatial filtering; optical data processing. Speckle; speckle photography; speckle interferometry and applications of speckle.

Texts/References :

J. W. Goodman, An Introduction of Fourier Optics, McGraw Hill,N.Y., 1968.

M. Born and E. Wolf, Principles of Optics Pergamon, N.Y., 1975.

W. T. Cathey, Optical information processing and holography, Wiley interscience, N.Y., 1974.

S. H. Lee, Optical Information Processing Fundamentals,Springer, N.Y., 1974.

S. R. J. Collier, C.D. Burkhardt and L.H. Lin, Optical Holography, Academic Press, 1971.

A. R. Shulman, Optical Data Processing, John Wiley, 1970.

SI501 Discrete Algorithms 6.00 ñ

Mathematical preliminaries : Asymptotic notation. Advanced Data structures : Hash tables, Binomial Heaps, Disjoint sets. Greedy Algorithms : Huffman coding, Minimum spanning Tree construction, Dijkstra"s shortest path construction. Dynamic programming Algorithms : Matrix - chain multiplication, All pairs shortest path problems, Minimum weight triangulation of convex polygons. Divide and conquer : Linear time selection, Educlidean closest pair problem, Strassen"s matrix multiplication algorithm. Backtracking and Branch and Bound methods : Graph colouring, Integer programming, Approximation algorithms : Vertex cover, Euclidean travelling salesman problem, Set cover problem.

Text/References:

T. Cormen, C. Leiserson, and R. Rivest, Introduction to Algorithms, MIT Press and McGraw Hill Book Company, 1991. U. Manber, Introduction to Algorithms : A Creative Approach, Addison-Wealey, 1989.

SI533 Finite Difference Methods for Partial Differential Equations 8.00 ñ

Review of 2nd order PDEs : Classification, separation of variaqbles and fourier transform techniques. Automatic mesh generation techniques : Structure mesh ( transfinite interpolation), unstructured grids ( triangulation for polygonal and non - polygonal domains). Finite difference Methods : Elliptic equations ( SOR and conjugate gradient methods, ADI schemes), parabolic equations ( explicit, back - ward Euler and Crank - Nicolson method, LOD), hyperbolic equations ( Law - Wendroff scheme, Leapfrod method, CFL conditions), Stability, consistency and convergence results. Lab Component : Implementation of Algorithms developed in this course and exposure to software packages : ODEPACK and MATLAB.

Pre-requisites: SI525

Text/References:

Gene H. Golub and James M. Ortega, Scientific Computing and Differential Equations : An Introduction to Numerical Methods, Academic Press, 1992.

P. Knupp and S. Steinberg, Fundamentals of Grid Generation, CRC Press Inc., Boca Raton, 1994.

A. R. Mitchell and D. F. Griffiths, The finite Difference Methods in Partial Differential Equations, Wiley, 1980.

G. D. Smith, Numerical Solutions of Partial Differential Equations, Oxford Press, 1985.

J. C. Stickwards, Finite Difference Schemes and PDEs, Chapman and Hall, 1989.

J. F. Thompson, Z. U., A. Waarsi and C. W. MAstin, Numerical Grid Generations - Foundations and Applications, North Holland, 1985.

Erich Zauderer, Partial Differential Equations of Applied Mathematics, 2nd ed., Wiley, 1989.

SI406 Applied Stochastic Processes 8.00 ñ

Stochastic processes : description and definition. Markov chains with finite and countably infinite state spaces. Classification of states, irreducibility, ergodicity. Basic limit theorems. Statistical Inference. Applications to queueing models. Markov processes with discrete and continuous state spaces. Poisson process, pure birth process, birth and death process. Brownian motion. Applications to queueing models and reliability theory. Basic theory and applications of renewal processes, stationary processes. Branching processes. Markov Renewal and semi-Markov processes, regenerative processes.

Text/References:

U. N. Bhat, Elements of Applied Stochastic Processes, Wiley, 1972.

P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Stochastic Processes, Houghton Mifflin, 1972.

A. O. Allen, Probability, Statistics and Queueing Theory with Computer Science Applications, 2nd ed., Academic Press, 1990.

J. Medhi, Stochastic Models in Queueing Theory, Academic Press, 1991.

SI512 Combinatorial Optimization 6.00 ñ

Networks and Matroids : Maximum flow, minimum cost flow, bipartite and nonbipartite matchings. Matroids : Greedy algorithm, matroid intersection and union. Integer Programming : Model formulations, properties of integral polyhedra and computational complexity, relaxation and valid inequalities, duality, cutting plane algorithms, branch and bound. Heuristics.

Text/References:

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows : Theory, Applications and Algorithms, Prentice Hall, 1993. G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley, 1988.

A. Schrijver, Theory of Linear and Integer Programming, Wiley, 1986.