Course Archives Theoretical Statistics and Mathematics Unit

Course: Function Spaces Instructor: Soumyshant Nayak Room: G26 Level: Undergraduate Time: Currently offered

Syllabus Past Exams Syllabus: Review of compact metric spaces. C([a; b]) as a complete metric space, the contraction mapping principle. Banachs contraction principle and its use in the proofs of Picards theorem. Uniform convergence. The Stone-Weierstrass theorem and Arzela-Ascoli theorem for C(X). Periodic functions, Elements of Fourier series - uniform convergence of Fourier series for well behaved functions and mean square convergence for square integrable functions. Reference Texts: (a) T. M. Apostol: Mathematical Analysis. (b) T. M. Apostol: Calculus. (c) S. Dineen: Multivariate Calculus and Geometry. (d) R. R. Goldberg: Methods of Real Analysis. (e) T. Tao: Analysis I & II. (f) Bartle and Sherbert: Introduction to Real Analysis. (g) H. Royden: Real Analysis. Evaluation: Mid-term 25 marks Assignment 25 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 24.pdf 25.pdf 26.pdf Semestral 24.pdf 25.pdf 26.pdf Supplementary and Back Paper 25.pdf 25.pdf 26.pdf Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]