Curriculum and Syllabi - Indian Institute of Technology Bhubaneswar

equivalence of fractals; Multifractal Analysis; Applications of fractals: Iterated function systems (IFS)and Recurrent IFS, Applications to image compression, Julia sets and the Mandelbrot set, Randomfractals, Brownian motion and Random walks, Percolation, Fractal interpolation,Texts:1. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons2. K. Falconer, Techniques in Fractal Geometry, John Wiley & Sons, 1997References:1. B. Mandelbrot, Fractal Geometry of Nature, W.H. Freeman and Company.2. M. F. Barnsley, Fractals Everywhere , 2nd edition, Academic Press, 1995.3. Mattila , Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, CambridgeUniversity Press, 19994. Peitgen, Jurgens and Saupe, Chaos and Fractals: New Frontiers(xiv) Computational Topology (MA6005):3-1-0: 4 Credits Prerequisite: NilTopological space, subspace, base, subbase, continuous function, connectedness, paths, homotopy,homotopy of paths and homotopy of maps, simplicial complex, polyhedral, graphs, homology theory,computation of beti numbers.Texts:1. James R., Munkres, Topology, 2 nd Edition, Pearson Education.2. J Dugundji – Topology, PHI.3. J L Kelley –General Topology (Von Nostrand).References:1. G F Simmons – Introduction to Topology and Modern Analysis (McGraw Hill).2. Steen & Seebach – Counterexamples in Topology (Holden Day).3. S Willard –General Topology (Addison Wesley).(xv) Integral Equations and Variational Methods (MA6006):3-1-0: 4 Credits Prerequisite: Differential EquationsIntegral Equations: Basic concepts, Volterra integral equations, relationship between linear differentialequations and Volterra equations, resolvent kernel, method of successive approximations, convolutiontype equations, Volterra equations of first kind, Abels integral equation, Fredholm integral equations,Fredholm equations of the second kind, the method of Fredholm determinants, iterated kernels,integral equations with degenereted kernels, eigen values and eigen functions of a Fredholmalternative, construction of Green's function for BVP, singular integral equations.Calculus of variations: Euler-Lagrange equations, degenerate euler equations, Natural boundaryconditions, transversality conditions, simple applications of variational formulation of BVP, minimumof quadratic functional. Approximation methods-Galerkin's method, weighted-residual methods,Colloation methods.Variational methods for time dependent problems.Texts:1. A Jerri, Introduction to Integral Equations with Applications, Wiley.2. L. Elsgoltz, Differential Equations and Variational Calculus, Rubinos 1860; 4 Tra edition, 1996.3. F. G. Tricomi, Integral Equations, Dover Pub, 1985.