Curriculum and Syllabi - Indian Institute of Technology Bhubaneswar

14. Seminar II (MA4402):0-0-3: 2 CreditsLiterature survey on assigned topic and presentation.15. Functional Analysis (MA5001):Semester IIITotal Credits = 293-1-0: 4 Credits Prerequisite: LinearAlgebraFundamentals of normed linear spaces: Normed linear spaces, Riesz lemma, characterization of finitedimensional spaces, Banach spaces. Bounded linear maps on a normed linear spaces: Examples, linearmap on finite dimensional spaces, finite dimensional spaces are isomorphic, operator norm. Hahn-Banach theorems: Geometric and extension forms and their applications. Three main theorems onBanach spaces: Uniform boundedness principle, divergence of Fourier series, closed graph theorem,projection, open mapping theorem, comparable norms. Dual spaces and adjoint of an operator: Dualsof classical spaces, weak and weak* convergence, Banach Alaoglu theorem, adjoint of an operator.Hilbert spaces : Inner product spaces, orthonormal set, Gram-Schmidt ortho-normalization, Bessel’sinequality, Orthonormal basis, Separable Hilbert spaces. Projection and Riesz representation theorem:Orthonormal complements, orthogonal projections, projection theorem, Riesz representation theorem.Bounded operators on Hilbert spaces: Adjoint, normal, unitary, self adjoint operators, compactoperators, eigen values, eigen vectors, Banach algebras. Spectral theorem: Spectral theorem forcompact self adjoint operators, statement of spectral theorem for bounded self adjoint operators.Texts:1. E. Kreyzig, Introduction to Functional Analysis with Applications, John Wiley &Sons, New York,1978.2. J. B. Conway, A Course in Functional Analysis, 2nd ed., Springer, Berlin, 1990.References:3. B.V. Limaye, Functional Analysis, 2nd ed., New Age International, New Delhi, 1996.4. A. Taylor and D. Lay, Introduction to Functional Analysis, Wiley, New York,1980.5. W. Rudin, Functional analysis, McGraw-Hill (1991).6. C. Goffman and G. Pedrick, A First Course in Functional Analysis, Prentice-Hall, 1974.16. Continuum Mechanics (MA5002):3-0-0: 3 Credits Prerequisite: NilBodies, Deformation, Strain, Characterization of rigid deformations, Small Deformations,Characterization of infinitesimal rigid displacements, Motions, Smoothness Lemma, Types ofmotions, Rate of Stretching, Characterization of rigid motions, Transport Theorems, Volume,Isochoric motions, Spin, Circulation, Vorticity; Conservation of mass, linear and angular momentum,Centre of mass; Force, Theorem of Virtual Work, Stress, Cauchy's Theorem for Existence of stress,