Course Details

Review of graphs:
Connectivity and Mengers theorem. Structure of 2-connected and 3-connected graphs, Maders theorem.
Basic counting:
Corradi's Lemma. Turan's theorem, Dirichlet's theorem, Erdos-Szekeres theorem. Hall's theorem. Sunflower Lemma and applications, Erdos-Ko-Rado theorem.
Vertex and Edge colouring:
Planar graphs, Kuratowski's theorem, Four color theorem, Discharging Method and applications, Tait's theorem. Intersection edge colourings, List colouring conjecture: Galvin's result.
Extremal graphs:
Ramsey theory, Ramsey number R(p,q). Intersection number, Erdos-Goodman-Posa theorem. Interval graphs, boxicity. Partition using paths and cycles, Erdos-Gallai theorem, Bondy's theorem.
Probabilisitc Method and Random graphs:
Lovasz Local Lemma, Second Moment method, Concentration results. Caros theorem, Erdos theorem (girth and chromatic number), Szele theorem. Random graph models, properties for almost all graphs, evolution and threshold functions, connectivity of random graphs.

Course References:

Text Books:
1. Extremal Combinatorics: Stasys Jukna, Springer. 2001.
2. The Probabilistic Method: Noga Alon, Joel Spencer, Wiley. 2000.
3. Random graphs: Bela Bollobas, Cambridge. 2004.
References:
1. Extremal Graph Theory: Bela Bollobas, Dover. 1978.
2. Introduction to Graph Theory: D B West, Prentice Hall India. 2001.
3. Graph Theory: Reinhard Diestel, Springer. 2006.

Course Details

Unit I: Simple linear regression, multiple linear regression, model adequacy checking, transformations and weighting to correct model inadequacies.
Unit II: Polynomial regression models, orthogonal polynomials. dummy variables, variable selection and model building, multicollinearity.
Unit III: Nonlinear regression. Generalized linear models, autocorrelation, measurement errors, calibration problem, bootstrapping.

Course References:

Text Books:
1. 1. Montgomery, D. C., Peck, E. A., and Vining, G. (2012), Introduction to Linear Regression Analysis (5th ed.), Hoboken, NJ: Wiley.
References:
1. Draper, N. R., and Smith, H. (2003), Applied Regression Analysis, New York: Wiley.
2. Sen, A. A. and Srivastava, M. (1990). Regression Analysis ? Theory, Methods & Applications, Springer-Verlag, Berlin.
3. Bowerman, B. L. and O'Connell, R. T. (1990). Linear Statistical Models: An Applied Approach, PWS-KENT Pub., Boston.

Course Details

Discrete-Time Markov Models:
Discrete-Time Markov Chains, Transient Distributions, Occupancy Times, Limiting Behavior, First-Passage Times.
Poisson Processes:
Poisson Processes, Superposition of Poisson Processes, Thinning of a Poisson Process, Compound Poisson Processes.
Continuous-Time Markov Models:
Continuous-Time Markov Chains, Transient Analysis: Uniformization, Occupancy Times, Limiting Behavior, First-Passage Times.
Generalized Markov Models:
Renewal Processes, Cumulative Processes, Semi-Markov Processes.
Queueing Models:
Queueing Systems, Single-Station Queues, Birth and Death Queues.
Brownian Motion:
Standard Brownian Motion, Brownian Motion, First-Passage Times, Martingales and Semimartingales, BlackScholes Formula.

Course References:

Text Books:
1. V. G. Kulkarni, Introduction to modeling and analysis of stochastic systems, second edition, Springer, 2011.
References:
1. S. M. Ross, Stochastic processes, second edition, Wiley, 1996.
2. S. Karlin and H. M. Taylor, A first course in stochastic processes, second edition, Academic Press, 1975.
3. S. M. Ross, Introduction to Probability Models, tenth edition, Academic Press, 2009.

Course Details

To introduce the concepts of stochastic calculus and demonstrate their use in finance
Course contents:
Infinite Probability Spaces, Random Variables and Distributions, Expectations, Computation of Expectations, Change of Measure, General Conditional Expectations.
Martingale Property for the Symmetric Random Walk, Quadratic Variation of the Symmetric Random Walk, Scaled Symmetric Random Walk, Limiting Distribution of the Scaled Random Walk, Definition of Brownian Motion, Distribution of Brownian Motion, Filtration for Brownian Motion, Martingale Property for Brownian Motion, Distribution of Brownian Motion and Its Maximum.
Ito's Integral for Simple Integrands, Construction of the Integral, Properties of the Integral, Ito's Integral for General Integrands, Ito-Doeblin Formula, Formula for Brownian Motion, Formula for Ito Processes.
Evolution of Portfolio Value, Evolution of Option Value, Equating the Evolutions, Solution to the Black-Scholes-Merton Equation, The Greeks, Put-Call Parity. Multiple Brownian Motions, Ito-Doeblin Formula for Multiple Processes, Recognizing a Brownian Motion, Brownian Bridge, Gaussian Processes, Brownian Bridge as a Gaussian Process, Brownian Bridge as a Scaled Stochastic Integral, Multidimensional Distribution of the Brownian Bridge, Brownian Bridge as a Conditioned Brownian Motion.
Multidimensional Market Model, Existence of the Risk-Neutral Measure, Uniqueness of the Risk-Neutral Measure. Continuously Paying Dividend, Continuously Paying Dividend with Constant Coefficients, Lump Payments of Dividends Lump Payments of Dividends with Constant Coefficients, Forward Contracts, Futures Contracts, Forward-Futures Spread.

Course References:

Text Books:
1. Shreve, S. E. (2004). Stochastic calculus for finance II: Continuous-time models (Vol. 11). New York: springer.
References:
1. Karatzas, I., & Shreve, S. (2012). Brownian motion and stochastic calculus (Vol. 113). Springer Science & Business Media.
2. Shreve, S. (2005). Stochastic calculus for finance I: the binomial asset pricing model. Springer Science & Business Media.

Course Details

Course Content:
General solution of wave equation in R, energy methods, waves with a source, Duhamel’s Principle, reflections of waves, wave equation on an interval: separation of variables, wave equation in higher dimensions, Shock wave: weak solution, entropy condition and Riemann’s problem, shock structure.Sound waves: acoustic energy, simple source, acoustic dipole, and source regions in different fields, ripple, scattering, and radiation from various bodies. One-dimensional waves in fluids: theory of longitudinal waves, transmission of waves, and propagation through branching systems. Water waves: surface gravity waves, internal waves, sinusoidal waves on deep water, ripples, group velocity, wave patterns, Fourier analysis of dispersive systems.

Course References:

Text Books:
1. Evans, Partial differential equations, AMS, 1997,
2. Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, SIAM, 1973,
3. Waves in fluids, James Lighthill, Cambridge, 2001,
4. Linear and nonlinear waves, Whitham, Wiley-Interscience, 1999,

Reference Books:
1. Geophysical Fluid Dynamic, Joseph Pedlosky, Springer, 1987,
2. Internal Gravity waves, B. R. Sutherland, Cambridge University Press, 2010,
Prerequisite:Nil

Course Details

Algebra of Cartesian Tensors, Index notation, Isotropic tensors, Invariants of a tensor, Polar decomposition theorem.
Course contents:
Continuum Hypothesis, Kinematics of deformation, Compatibility conditions, Balance principles, Euler's laws of motion, Stress-Laws of Thermodynamics, Energy Balance, Constitutive equations of fluids and elastic materials, principles of material objectivity, Applications (simple problems of fluid dynamics and elasticity)

Course References:

D.S. Chandrasekhraiah and Loknath Debnath, Contiuum Mechanics, Academic Press (1995)

Course Details

Curvilinear coordinates:
Transformation of coordinates, Orthogonal curvilinear coordinates, unit vectors in curvilinear systems, arc length and volume elements, Gradient, divergence and curl, special orthogonal coordinate systems, general curvilinear coordinates. ( 8 L)
Tensor Algebra:
The concept of tensor and law of transformation of it's components, the summation convention, invariants, covariant and contravariant vectors, covariant, contravariant and mixed tensors, symmetric and skew- symmetric tensors, outer and inner multiplications of tensors, quotient law of tensors, metric tensors, associated tensors, reciprocal tensor of a tensor. (16 L)
Tensor Calculus:
Christoffel Symbols of first and second kind, properties of Christoffel symbols, Covariant differentiation of tensors, the intrinsic or absolute derivative, gradient, divergence and curl in tensor form, Ricci's theorem, Riemann-Christoffel curvature tensor, Ricci's tensor, Einstein tensor, Geodesics, Riemannian and Geodesic coordinates, Geodesic curves in space, Serret-Frenet formulae, Geodesic curvature, First and second fundamental forms of a surface.

Course References:

Text Books:
1. Introduction to Tensor Analysis and the calculus of moving surfaces by Pavel Grinfeld, Springer, New York, 2010
2. Tensor Analysis by I. S. Sokolnikoff, John-Wiley, 2000.
References:
1. A brief on Tensor Analysis by James G. Simmonds, Springer-Verlag, New York, 1994
2. Tensor Analysis by Leonid P. Lebedev and Michael J. Cloud, World Scientific Publishing Co., London, 2003
3. Tensor Algebra and Tensor Analysis for Engineers with Applications to Continuum Mechanics by Mikhail Itskov, Springer, 2013.

Course Details

Introduction: Stochastic analogs of classical differential equations.
Mathematica;
Preliminaries: Probability space, random variable, stochastic process, Brownian motion.
Ito Integral: Definition, Properties, extensions.
Ito formula and Martingale representation Theorem: One-dimensional Ito formula, Multi-dimensional Ito formula, Martingle representation Theorem.
Stochastic differential equations: Examples and some solution methods, Existence an Uniqueness result, weak and strong solutions.
Applications: Boundary valur problems, filtering, optimal stopping, stochastic control, mathematical finance.

Course References:

Text Books:
1. B. K. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 6th edition, Apringer, 2010.
Reference:
1. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calxulus, SPringer, 1991.
2. P. Protter, Stochastic Integration and Diferential Equations, Springer, 2nd edition. 2010.
3. I. Karatzas and S.E. Shreve, Methods of Mathematical Finance, Springer, 2010.
4. S. Watanabe and N. Ikeda, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981.

Course Details

Linear Programming: Basic feasible solutions and extreme points of a linear polytope, Change of basic feasible solutions and simplex algorithm, time complexity of simplex algorithm. Duality theory, Complementary slackness conditions, Farka's Lemma, LP Based ALgorithms: Min-Max relations and LP-duality, Maximum flow Minimum Cut Theorem Primal-dual algorithms for Minimum Ste cover, Minimum Vertex cover (half-integrality), Minimum Feedback Vertex Set, Algorithms for Maximum Satisfiability

Course References:

Text Books:
1. Combinatorial Optimization: Algorithms and Complexity, C. H. Papadimitrou, K. Steiglitz, Dover Publications, Inc, New York, 1998.
2. Approximation Algorithms, V. V, Vazirani, Springer 2003.
Reference Books:
1. Linear Programming, K. G. Murthy, Springer, 1983.
2. The Design of Approximation Algorithms, D.P. Williamson, D. B. Shmoys, Cambridge University Press, 2010.

Course Details

Riemann - Lebesgue Lemma, localization lemma, Fourier integral theorem, Fourier Transform, Inversion, Convolution and Parseval's Theorem, Applications to Partial Differential Equations. Laplace transform :Definition, properties, Complex inversion, Applications to initial and boundary value problems. Z - Transform and Difference equations

Course References:

Text Books:
1. I.N. Sneddon, The Use of Integral Transforms, Tata Mc-Graw Hill (1974)
2. J.L. Schiff, The Laplace Transform, Springer (1999)
3. Michael Frazier, An Introduction to wavelets through Linear Algebra, Springer, 1999 (Chapter 2)
4. A.V. Oppenheim & R.W. Schafer, Digital Signal Processing, Prentice-Hall, 1975.
References:
1.M.R. Spiegel, Laplace Transforms (Schaum's Series), McGraw-Hill, 1965.
2.M.R. Spiegel, Advanced Mathematics for Engineers and Scientists, (Schaum's Series), McGraw Hill, 1983.
3.Jeffery M. Cooper, Introduction to PDE with MATLAB (Chapter 6) Birkhauser, 1997.

Course Details

Kinematics of Fluid flow, Laws of fluid motion, Inviscid incompressible flows, two and three-dimensional motions, Airfoil theory, inviscid compressible flows;
Viscous incompressible flows, Navier-Stokes equations of motion and some exact solutions; Flows at small Reynolds numbers; Boundary layer theory.

Course References:

Text Books:
1. M.E.O Neill and F. Chorlton, Ideal and Incompressible Fluid Dynamics, John Wiley and Sons, New York, 1986.
2. M.E.O Neioll and FD. Chorlton, Viscous and compressible Fluid Dynamics, John Wiley and Sons, New York, 1989.
References:
1. F. Chorlton, Textbook of Fluid Dynamics, CBS Publishers, 1998.
2. A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid mechanics,Springer-Verlag, 1999.
3. G-Emanuel, Analytical Fluid Dynamics, CRC Press, 2001.
4. P.K. Kundu and I.M. Cohen, Fluid Mechanics (3rd edition) Elsevier Science & Technology, 2002.

Course Details

1. FEM Simulations: 1d/2d/3d Poisson Equation Solver, Convection-Diffusion Solver, Heat Equation Solver, Efficient solutions of the Wave Equation, Non-Linear Finite Element Problems.
2. Grid free Simulations: Simulating 2d/3d Boundary Value Problems, 2d incompressible/compressible Navier-Stokes equations, Free surface flow problems, Moving interface problems and moving boundary problems.
3. FVM Simulations: Fluid-Structure interaction problems, Flow through Porous media problems

Course References:

1. "Computational Partial Differential Equations", Hans Petter Langtangen, Lecture Notes in Computational Science and Engineering 2, Springer, 1999.
2. "The Finite Element Method Using MATLAB", Young W.Kwon, Hyochoong Bang, CRC Press, 2000.
3. "Partial Differential Equations and the Finite Element Method", Pavel Solin, Wiley-Interscience, 2006.
4. "Numerical Approximation of Partial Differential Equations", Alfio Quarteroni and Alberto Valli, Springer Series in Computational Mathematics 23, 1994.
5. "Numerical Schemes for Conservation Laws", Dietmar Kroener, Wiley Teubner, 1997.
6. "Methods of Computer Modeling in Engineering & the Sciences: Volume I", Satya N. Atluri, Tech Science Press, 2005.

Course Details

Linear Optimization: Formulation and Geometrical Ideas of Linear Programming Problems, Simplex Method, Revised Simplex Method, Duality, Sensitivity Analysis, Transportation and Assignment Problems, Introduction to Interior-Point Methods. (Ellipsoid Method, Karmarkar's Method).
Unconstrained optimization of functions of several variables, Basic theory, Classical techniques and numerical methods for unconstrained optimization (Gradient methods, Newton's method, Conjugate Direction methods, and Quasi-Newton methods).
Constrained nonlinear optimization of functions of several variables, Method of Lagrange multipliers, Kuhn-Tucker theory, Convex optimization, Quadratic optimization, Numerical methods for constrained optimization, Dynamic programming.

Course References:

1. E.K.P. Chong, and S.H. Zak: An Introduction to Optimization, 4th Edn., Wiley Interscience, 2013.
2. D. G. Luenberger and Yinyu Ye, Linear and Nonlinear Programming, 2nd Edn., Kluwer, 2003.
3. N. S. Kambo, Mathematical Programming Techniques, East West Press, 1997.
4. M. S. Bazarra, H.D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, 3rd Edn., Wiley, 2006.
5. D.P. Bertsekas, Nonlinear Programming, 2nd Edn., Athena Scientific, 1999.

Course Details

Description:
The course will focus on designing algorithms for matrix computations, analysing these algorithms (in terms of complexity, communication costs, stability, performance in finite precision and exact arithmetic), implementation on different computer architectures.
Course Content:
Floating point arithmetic (1 lecture)
Stability of algorithms (2 lectures)
conditioning of a problem (2 lectures)
perturbation analysis (2 lectures)
algorithmic complexity (1 lecture)
Matrix decomposition including LU, Cholesky, QR, SVD, etc. (12 lectures)
Iterative techniques mainly focussing on Krylov subspace methods including Lanczos, Arnoldi, Conjugate Gradient, GMRES, etc. (12 lectures)
Preconditioning (2 lectures)
structured matrix computations (4 lectures)
designing matrix algorithms on modern computer architectures (3 lectures)

Course References:

Text Books:
1. James W. Demmel, Applied Numerical Linear Algebra, Publisher : Society for Industrial and Applied Mathematics, Year : 1997
2. N. Trefethen & David Bau III, Numerical Linear Algebra, Publisher : Society for Industrial and Applied Mathematics, Year : 1997
Reference Books:
1. Biswa Nath Datta, Numerical Linear Algebra and applications, 2nd Edition, Publisher : Society for Industrial and Applied Mathematics, Year : 2010

Prerequisite:
Linear Algebra at undergraduate level

Course Details

Introduction and basic concepts, Finite element spaces, Mathematical fundamentals and computer algorithms, Variations and weighted residual techniques, Abstract formulation of FEM for elliptic equations, Applications to Elastic stress analysis using linear elements, FEM for parabolic and hyperbolic equations, Unsteady heat flow analysis, Mixed-FEM, Nonlinear, Curved, Isoparametric plate and shell elements, Fluid flow, Material nonlinearity including plasticity, Creeping viscous flow and Boundary element formulation for elastostatic problem, Adaptive mesh refinement and large problem solvers.

Course References:

Course Details

Introduction to Stochastic Processes, Poisson Process, Browian Motion, Martingales.
Present Value Analysis, Interest rate analysis, Marlet model Specification problems.
Arbitage theorem, Multi-Period binomial Model, Block- Scholes formula.
Valuing investments by expected utility, Portfolio selection problem, Capital Assets Pricing model, Rates of return, Single period and geometric Browian motion, Mean-Variance analysis of risk- neutral-priced call options, Autoregressive models and mean regression, Other pricing options and applications.

Course References:

Course Details

Introduction to linear codes and error correcting codes. Encoding and decoding of a linear code, dual codes. Hamming codes and perfect codes. Cyclic codes. Codes with Latin Squares, Introduction to BCH codes. Weight ennumerators and MDS codes. The main linear coding theory problems and conclusions.

Course References:

Books:
1. Raymond Hill, A first course in Coding Theory, Clarandon Press, Oxford (1986).
2. J. H. Van Lint, Introduction to Coding Theory, Springer (1998).

Course Details

Review of Schur’s unitary triangularization theorem, its consequences: Denseness of diagonalizable matrices, simultaneous triangularization, continuity of eigenvalues, eigenvalues of rank one perturbation, Various characterizations of normal matrices.
Singular value decomposition and its applications including Moore-Penrose inverse, Polar decomposition.
Hermitian matrices and congruences: Characterizations, Variational principles of eigenvalues, Courant Fischer minimax theorem, Weyl’s inequality and Cauchy’s interlacing theorem.
Algebraic, Analytic and geometric properties of vector norms, various matrix norms, Gershgorin’s theorem, spectral radius and Gelfand’s formula.
Positive definite matrices: Various characterizations, Schur product, Hadamard and Fischer inequalities.
Non-negative matrices: Perron-Frobenius theory, Birkhoff theorem for doubly stochastic matrices.

Course References:

Text Book:
1. R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge university press, 2013.
References:
1. F. Zhang, Matrix Theory: Basic Results and Techniques, 2nd Ed., Springer, 2011.
2. M. Fiedler, Special Matrices and Their Applications in Numerical Mathematics, Dover Publications, 2008.

Course Details

Classification of Integral Equations, various examples, Abel's problem, 2nd order ordinary differential equations and Integral Equations, Initial and boundary value problems, singular boundary value problems.
Integral Equations of second kind: degenerate kernels, Neumann series.
Compact self-adjoint operators: Structure theorem, spectrum, Applications to integral equations, positive operators and Integral equations arising from Sturm-Liouville theory.
Approximate methods for eigenvalues and eigenvectors of self-adjoint operators, Approximation of integral equations based on variational principles.
Singular integral equations: introduction, solution methods, applications.

Course References:

Books:
David Porter & David S.G. Stirling, Integral Equations: A Practical Treatment, from Spectral Theory to Applications, Cambridge texts in Applied Mathematics, 1990.

Course Details

Why DNA computing, Overview of Turing machines, NP-completeness, Universal computers, Structure of DNA, Operations on DNA, Adleman's experiment: Solving TSP and 3-SAT using DNA molecules, overview of basics of Formal language theory, DNA memory: Advantages over a computer chip, organic DNA memory, Design of DNA sequences : Algorithmic, experimental, software and theoretical approach.

Course References:

Books:
1. G.Paun, G.Rozenberg and A.Salomaa, DNA Computing, Springer 1998.
2. Martyn Amos, Theoretical and Experimental DNA Computing, Springer 2005.
3. R.Rama and K.Krithivasan, Introduction to Formal Languages, Automata and Languages, Pearson 2009.

Course Details

One-dimensional flows: fixed points and stability, linear stability analysis, Saddle- node bifurcation, Transcritical bifurcation, Pitchfork bifurcation, Flows on the circle
Two-dimensional flows: Linear systems, nonlinear autonomous systems, phase portraits, Fixed points and linearization, conservative systems, index theory, limit cycles, Poincare Bendixson theorem, Lienard systems, Saddle-node, Transcritical and Pitchfork bifurcations, Hopf bifurcation
Chaos
Discrete dynamical systems

Course References:

Books:
(1) Steven H Strogatz, Nonlinear dynamics and Chaos, Perseus books publishing, 1994
(2) James T Sandefur, Discrete dynamical systems Theory and applications, Clarendon press, 1990

Course Details

Integral and differential forms of conservation laws, Burgers equation, Shock formation, Weak solutions, Entropy conditions, Riemann problem, scalar and non-linear vector examples, Euler equations of an ideal gas, Courant Fredrick Levy conditions, Upwind methods, Conservative schemes, Godunov methods, Riemann solvers.

Course References:

R.J. Leveque, Numerical methods for conservation Laws, Bikhauser Verlag, 1992.

Course Details

Grammars and Languages: Language basics, Regular expressions, Regular grammars, Contextfree grammars, context-sensitive grammars, unrestricted grammars, Chomsky hierarchy. Automata: Finite automata, pushdown automata, Pumping Lemmas and Closure properties, Turing machines and recursively enumerable languages. Computability: Computable functions, non-recursively enumerable languages, Undecidability, Rice's theorem, Post's correspondence problem, Undecidability of validity problem of First Order Logic. Complexity: Asymptotic order symbol, Space and Time complexity, Classes P and NP, NP-completeness, Cook-Levin tehorem, Other NP-complete problems.

Course References:

Text Books:
1. K.Krithivasan and R.Rama, Introduction to Formal Languages, Automata and Computation, Pearson Education, 2009.
2. A.Singh, Elements of Computation Theory, Springer (In: Texts in Computer Science Series),2009.

Course Details

Complexity of optimization problems: Complexity classes P and NP; Karp reduction; decision, solution and evaluation vertions of an optimization problem.
Design techniques for approximation algorithms: Greedy methods for knapsac, independent set and TSP; sequential algorithms for scheduling, bin packing and graph coloring; local search algorithms for max-cut and TSP.
Approximation classes: Approximate solutions with guaranteed absolute error and relative error; approximability and non-approximability of TSP; limits to approximability (gap technique); complexity classes PTAS and FPTAS; strong NP-completeness and pseudo-polynomiality.
Approximation algorithms for various problems: Set-cover, graph coloring, minimum multi-cut, edge coloring, bin packing.

Course References:

Texts books:
1. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. M. Protasi, Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer, 1999.
References:
1. V. Vazirani, Approximation Algorithms, Springer 2005.
2. C. H. Papadimitriou, K. Steiglitz, Combinatorial optimization: Algorithms and Complexity, PHI 2001.
3. J. Kleinberg, E. Tardos, Algorithm Design, Pearson India, 2007.

Course Details

PART I: STATIC GAMES
1. Two-person zero-sum finite games: MAtrix games, Pure and mixed strategies, saddle point equilibrium strategies, extensive form games.
2. N-person finite games: Nash equilibrium, Refinements of Nash equilibirum, N-person games in extensive form.
3. Infinite games: Equilibrium strategies, continuous-kernel games, stackelberg equilibirum.
PART II: DYNAMIC GAMES
3. Formulation of dynamic games: Discrete-time dynamic games, continuous-time dynamic games, mixed and behaviour strategies in dynamic games, representations of strategies along trajectories, time-consistency of optimal policies.
5. Equilibria of dynamic games: Open-loop and feedback equilibria for dynamic games in discrete-time, informational properties of Nash equilibrium in discrete-time dynamic games, Open-loop and Feedback equilibria for differential games.
6. Pursuit-evasion games: Necessary and sufficient conditions for equilibrium, captuability, singular surfaces.

Course References:

TEXT BOOKS:
T.Basar and G.J.Olsder, Dynamic Noncooperative Game Theory, SIAM, 2nd edn, 1999.
REFERENCES:
1. R. B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1999
2. M. J. Osborne and A.Rubinstein, A course in Game Theory, MIT Press, 1994
3. D. Fudenberg and J. Tirole, Game Theory, MIT Press, 1991

Course Details

Hillbert spaces: The Projection theorem- Approximation- minimum norm problems.
Calculus of variations: Extrema of Functionals- Gateax variation- Euler- Langrange equations- Problem with variable end points- Isoperimetric problem- Direct methods for solving variational problems.
Optimal Control Theory: Pontryagin's maximum principle- Time optimal problems.

Course References:

Course Details

Inventory and Stock Control: Practical stock systems, Various associated costs, Lead time- Type of Systems- Inventory Policies, Objective functions- Mathematical Methods of Inventory and applications.
Reliability Theory: Replacement and maintenance, discounting, Group replacements- System Reliability and availability- Simple Reliability models.
Quality Control: Acceptance sampling for attributes and for variables, operating Characteristic and average runlength; Single-Double and sequential plans, Control Charts- their construction and use.
Simulation: Simulation Concepts- Generation of uniform variates, generation of Variates fro Standard distributions; Monte Carlo Calculus and variance reduction techniques, Analogue simulation of systems.

Course References:

Course Details

Review of the governing equations of Incompressible viscous flows, Stream function -vorticity approach, upwind schemes, Primitive variables, Staggered grid, Artificial compressibility, pressure correction and vortex methods; Compressible inviscid flows, central schemes with combined and independent space time discretisation, Compressible viscous flows, Explicit, implicit and PISO methods; Grid generation: Structured and unstructured grid generation methods; Finite volume method: Finite volume method to convection-diffusion equations.

Course References:

Books:
1. P Wessling, Principles of Computational Fluid Dynamics, Springer, 1991.
2. John D Anderson, Jr., Computational Fluid Dynamics, The Basics with Applications, McGraw-Hill, 1995.