Curriculum and Syllabi - Indian Institute of Technology Bhubaneswar

(xxii) Theory of groups and its application to physical problems (MA6013):3-1-0: 4 Credits Prerequisite: AlgebraElements of Group theory, Operators in Hilbert Space, Representation theory – finite groups,Continuous groups, Group theory and Quantum mechanics, Crystallographic and MolecularSymmetries.Texts:1. C. J. Bradley and A. P. Cracknell, Mathematical Theory of Symmetry in Solids, OUP, 1972.2. A. P. Cracknell, Applied Group Theory, Elsevier Science & Technology, 1968.References:3. N. Hammermesh, Group Theory and Its Application to Physical Problems, Courier Dover Publications,1962.4. S. Bhagavantam and T. Venkatarayudu, Theory of groups and its application to physical problems,Academic Press, 1969.5. W Joshi, Elements Of Group Theory For Physicists, New Age International, 1997.(xxiii) Computational Fluid Dynamics (MA6014):3-1-0: 4 Credits Prerequisite: Fluid Dynamics, Numerical methodsClassification of Partial Differential Equations; Classification of system of first order PDE’s;Classification of system of second order PDE’s; Boundary conditions; consistency, stability andconvergence of FDE; Lax’s equivalence theorem. Finite difference approximations to partialderivatives for equally spaced grid points and unequally spaced grid points. Methods to solveParabolic partial differential equations, Elliptic and Hyperbolic partial differential equations andstability analysis; Vorticity Stream function formulation of the Navier-Stokes equations, Finitedifference methods for steady, viscous incompressible N-S equations: Flow in a lid driven cavity,Viscous flow past a circular cylinder, flow past a sphere. Line Gauss-Seidal, Point Gauss Seidal , SORschemes, Finite difference applications in Heat conduction and convection; Discussion on first, secondand higher order accurate methods. Higher order compact schemes to Navier Stokes equations.Texts:1. Computational Fluid Dynamics, Volume 1 by K. A. Hoffmann and S. T. Chiang .2. Computational Fluid Flow and Heat transfer by K. Muralidhar and T. Sundararajan.(Narosa)References:1. Computational Methods for Fluid Dynamics by J. H. Ferziger and M. Peric (Springer)2. Computational Fluid Dynamics by J. F. Wendt (Springer)3. Computational Fluid Dynamics by T. J. Chung (Cambridge University Press).4. Fundamentals of Computational Fluid Dynamics by T. K. Sengupta (Universities Press).(xxiv) Algebraic Graph Theory (MA6015):3-1-0: 4 Credits Prerequisite: Linear Algebra, Elements of Graph TheoryFundamental Concepts: independent sets, matchings, spanning trees, Hamiltonian cycles, Eulerianorientations, cycle covers, etc.; Operations on Graphs and the Resulting Spectra: the polynomial of agraph, eigenvalues and eigenvectors, line graphs and total graphs. etc.; The Divisor of Graphs: Thedivisor and cover, symmetry properties, some generalizations; Spectral Characterizations: Eigenvaluesof L-, Q-, and adjacency matrix, co-spectral graphs, graphs characterized by their spectra; Spectral